NMR, Water and Plants
CENTRALE LANDBOUWCATALOGUS
0000 0004 9920
Promotor : dr. T. J. Schaafsma,
hoogleraar in de molcculaire fysica
Co-referent: dr. M. A. Hemminga,
wetenschappelijk hoofdmedewerker
Y\\n 6**10\
<s&(?
d
H. Van As
NMR, Water and Plants
Proefschrift
ter verkrijging van de graad van
doctor in de Landbouwwetenschappen,
op gezag van de rector magnificus,
dr. C. C. Oosterlee,
hoogleraar in de veeteeltwetenschap,
in het openbaar te verdedigen
op woensdag 3 1 maart 1982
des namiddags te vier uur in de aula
van de Landbouwhogeschool te Wageningen.
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NMR, Water and Plants
Proefschrift vanH.VanAs
Wageningen, februari 1982.
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STELLINGEN
1.Depuis proton NMR-methode zoals beschreven doorHemminga en DeJager,
is geschikt omdoormiddel vanhet meten vanbloedstroraing eventueel
bloedvatvernauwende en/of -verruimende effecten van geneesmiddelente
bepalen.
M.A. Hemminga enP.A.deJager,J. Magn. Reson. 37(1980),1
Ditproefschrift,hoofdstuk 4
2. Het ontledenvan eenniet-exponentieel verval bij spin-echo NMR
spin-spin relaxatietijd metingen aanwater inbiologische systemen
ineen somvan e-machten vertoont een grotemate vanwillekeur;voor
de rechtvaardigingvan een dergelijke ontleding is onafhankelijke
experimentele informatienodig.
B.M. Fung,Biochim. Biophys. Acta 497(1977),317
B.M. Fung enP.S.Puon,Biophys.J. 33(1981),27
3.Het verdient aanbeveling pas van dubbele fluorescentie te sprekenals
uit excitatiespectra eenduidig blijkt dat dewaargenomen fluorescenties
van eenen dezelfde verbinding afkomstig zijn.
D.L.Philen en R.M. Hedges,Chem. Phys. Letters 43(1976),358
4. Het isdehoogste tijd dat indeevolutie van debeschrijving vande
fysische toestand vanwater inbiologische systemen een scheppende
daad wordt gesteld.
M.J. Tait enF. Franks,Nature 230(1971),91
P.T. Beall,The Sciences 2J_(1981),6
5. De theorie ontwikkeld terverklaring van CIDNPverschijnselen, zoals
waargenomen met behulp vanNMR aanverbindingen inverdunde oplossing,
mag niet zondermeer toegepast worden op reactiecentra van fotosynthetiserende bacterien.
R. Kaptein,J. Am. Chem. Soc. 94(1972),6251
6. Het is tebetwijfelen of de resulaten verkregen met demethode beshreven
door Radda et al., ommet behulp van NMRbloedstroomsnelheden temeten,
onafhankelijk zijnvan de spin-rooster relaxatietijd.
G.K. Radda,P. Styles,K.R. Thulborn enJ.C.Waterton,
J. Magn. Reson. 42(1980,488
7.Het iswaarschijnlijk dat er een eenvoudig verband bestaat tussen de
waterpotentiaal ende spin-spin relaxatiesnelheid.
Dit proefschrift,hoofdstukken 5en7
8.Het "Voorontwerp van eenwet gelijke behandeling" bevat onvoldoende
garanties om tevoorkomen datnieuwe vormen van discriminatie ontstaan.
Voorontwerp van eenwet gelijke behandeling
VOORWOORD
Voor 1977waswatertransport inplantenvoormijeenstukjemiddelbare schoolstof dat allang inhet moerasvan devergetelheidwas
weggezonken enwater eenzoalgemeenaanwezigmolecuul,datikhet
hooguitalsoplosmiddelofdorstlesser gebruikte.Dankzijvelenaan
deLandbouwhogeschool,zowelbinnenalsbuitendevakgroepMoleculaire
Fysica, ishierin eenwendingtengoedegekomen,waarvoormijnoprechtedank.MarcusHemmingaenAdriedeJagerdankikvoordevele
stimulerende discussies, de uitwisselingvaninformatieenhetbeschikbaarstellen van het computerprogramma,waarmeedesimulaties
werden berekend. Ikhoop Adrie, dat ikjetroetel-engeesteskind
(hetNMR apparaat)nietalteveelmisbruiktheb.
MargaHerweijer, RietHilhorst, IdyvanLeeuwen-Pannekoek en
JohanReinders dank ikvoorhunbijdragentotditproefschrift.Ze
zijn onontbeerlijk geweest voordeafrondingvanhetonderzoek.De
nagedachtenis aanWimvanVlietisereenvanvriendschap.
Mijnpromotor,Tjeerd Schaafsma,wilikinhetbijzonderbedanken.
Tjeerd,jeoptimismeenkritischezinhebbenmijsteedsgestimuleerd.
Steedswasjeookbereidommijmetraadendaadterzijdetestaan.
Ditproefschriftbewijstdatjeoorspronkelijke ideeengoedwaren.
Ikwil mijn waardering uitspreken voor dewijzewaaropdeheer
A.Hogeveen en EllyGeurtsen van de afdeling Tekstverwerkingvorm
hebben gegeven aan dit proefschrift. GeoffSearle corrigeerdevan
enkelehoofdstukkendeEngelsetekst,waarvoorookdank.
Tenslottewil ikjouw,Janneke,bedankendatjealdezetijd als
eenhulptegenovermijhebtwillenzijn,enzelfsmeerdandat.
Ik spreek de wensuitdatookditproefschriftmag strekkentot
de eer van de Schepper van hemel en aarde,Die mij de krachten
wijsheid gaf om ditwerk te doen,inWiensvrezehetbeginselvan
dewetenschap isenDieook indewetenschapsbeoefening toekomtalle
lof,eer,aanbidding endankzegging.
CONTENTS
page
LIST
OF ABBREVIATIONS
AND FREQUENTLY USED SYMBOLS
xi
1
GENERAL INTRODUCTION
1
2
WATER AND PLANTS
6
2.1 Stateofwater inthecell
2.2 Waterpotential
2.3 Watertransport intheplantstem
References
3
PULSED NUCLEAR MAGNETIC RESONANCE IN
6
8
9
11
BIOLOGICAL
SYSTEMS
3.1 Basic theoryofpulsedNMR
3.2 Mechanisms forthespin-spinrelaxation
3.2.1
Dipolar interaction
3.2.2
Paramagnetic ions
3.2.3
Sampleheterogeneity
3.2.4
Exchangeanddiffusion
3.2.5
Summary
3.3 MeasurementofT 2 ,diffusionand flow
3.3.1
MethodofT 2 measurement
3.3.2
Effectofdiffusionand flow
3.4 NMRdiffusionmeasurements inbiological
samples
3.5 NMR flowmeasurements inbiological samples
3.5.1
History of in vivo blood flow
measurements
3.5.2
PulsedNMR flowmeasurements
3.5.3
NMR flowmeasurements inplants
3.6 T 2 andwatercontent
References
12
15
16
18
20
22
25
25
25
27
29
33
33
34
36
39
42
FLOW MEASUREMENTS IN MODEL SYSTEMS
4.1 Introduction
4.2 Theory
4.2.1
System description
4.2.2
Motionofthemagnetizationin
therotating frame
4.2.3
7tpulses
4.2.4
Asemi-empirical approach
4.2.5
Laminar flow
4.2.6
Determinationoftheflowvelocity
4.2.7
DeterminationofT 2 andvolume
flowrate
4.3 Somecommentsonthesemi-empirical
approach
4.3.1
Approximations
4.3.1.1 Distributionofther.f.field
4.3.1.2 Off-resonanceeffectsontheeffective
r.f. field
4.3.1.3 Samplingtime
4.3.1.4 EffectofT x relaxationanddiffusion
4.3.2
Comparisonbetween theoretical
approaches
45
45
46
49
50
51
55
57
58
59
59
60
60
61
63
63
4.4 Experimental
68
4.5 Results andDiscussion
70
4.5.1
Calibration
70
4.5.1.1 Theneedofalinear fieldgradient
70
4.5.1.2 EffectofTx andT 2 relaxation
72
4.5.1.3 Effectofflowprofile
75
4.5.2
DeterminationofT 2 andvolume flowrate
75
4.5.2.1 Effectof 11
75
4.5.2.2 Off-resonance signalofstationarywater
80
4.5.3
Optimum experimental conditions
82
4.6 Conclusions
4.7 Acknowledgement
References
83
84
85
FLOW MEASUREMENTS IN PLANTS
5.1 Introduction
5.2 Experimental
86
87
5.2.1
5.2.2
5.2.3
NMR flowmeasurements
NMRT 2 measurements
Plantmaterial
5.3 Results anddiscussion
5.3.1
Stemsegments
5.3.2
Intactplants
89
89
96
5.4 Conclusions
5.5 Acknowledgement
References
6
87
88
89
103
103
104
COMPARISON OF FLOW MEASUREMENTS WITH NMR, HEAT PULSE
AND BALANCE METHOD
6.1 Introduction
6.2 Experimental
6.2.1
NMR flowmeasurement
6.2.2
Heatpulse flowmeasurement
6.2.3
Balancevolume flowratemeasurement
6.2.4
Cross-sectional area
6.2.5
Plantmaterial
6.3 Results
6.4 Discussion
6.5 Acknowledgement
References
7
105
106
106
107
107
108
108
108
112
114
114
1
H SPIN-ECHO NUCLEAR MAGNETIC RESONANCE IN PLANT
TISSUE.
I.
EFFECT OF Mn(II)
AND WATER CONTENT IN
WHEAT LEAVES
7.1
7.2
7.3
7.4
8
Introduction
Materials andmethods
Results anddiscussion
Conclusions
References
APPLICATION
OF NMR FLOW MEASUREMENTS
115
116
117
120
121
122
SUMMARY
126
SAMENVATTING
128
CURRICULUM VITAE
131
LIST
OF ABBREVIATIONS
AND FREQUENTLY USED SYMBOLS
A
-
cross-sectional area
B
-
static magnetic field
Bi
-
radio frequency field
C
-
calibration constant relating v and t *
CPMG
-
Carr-Purcell-Meiboom-Gill
D
-
(self-)diffusion coefficient
Dx
-
theoretical value of S(t
IUclX
)at t_, =0
max
EPR
-
electron paramagnetic resonance
FETS
-
fast-exchange two-state
FID
-
free induction decay
g
-
electron g factor
G
-
magnetic field gradient
G(x)
-
autocorrelation time
max
H
-
height of signal of stationary water at t=0
•n
-
h/2n,
I
-
angular momentum vector
I
-
nuclear spin quantum number
J(u>)
-
spectral density function
k
L £f, 1
M ,M
-
Boltzmann's constant
(effective) length of the r.f. coil
-
magnetization
NMR
P f , Pfa
where h is Planck's constant
-
nuclear magnetic resonance
free, bound water fraction
Q
-
volume flowrate
R
-
vessel radius
R j , R2
-
spin-lattice, spin-spin relaxation rate
Re
-
Reijnold's number
S(t)
-
signal amplitude as function of time
t
-
duration of a r.f. pulse
S
-
electron spin quantum number
T], T2
-
spin-lattice, spin-spin relaxation time
v
V
a
V
i
Ta
tn
te
-
mean linear flowvelocity
amount (volume)of flowingwater inr.f. coil
rotation angle due to ar.f. pulse
gyromagnetic ratio
timebetween two r.f. pulses
mean residence time insitea
diffusional correlation time
correlation time for scalar interactions
T
T.
T
V
M
w
-
rotational correlation time
translational correlation time
electron spin relaxation time
water potential
magnetic moment
precession frequency inamagnetic field
GENERAL INTRODUCTION
Plantsrequirewater;deprivedofit,theywillwiltanddie.In
fact,thetypical landplantconsumesprodigious quantities ofwater,
much more than any of the other substances thatenterit.Mostof
thiswaterdoesnotremainwithintheplant,butpassesthroughthe
planttotheatmosphere.Thisprocess iscalled transpiration.
Water
transport over long distancesprimarily occursthroughasystemof
capillariescalled xylem. Thexylem forms anextra-protoplasmicpathway for solute flow, consisting inparticular ofwater, ionsand
certain organic solutes upwards from the roottotranspiringsurfacesofshootsystem. Incontrast,there isasecondpathway through
the sieve elements of the phloem. Withinthissystem concentrated
solutes such as carbohydrateproducedbyphotosynthetically active
structures flow to sink regions ofvarious kinds inwhich these
solutes areconsumed forgrowthorstored infruitsorotherreservoirs.
Theseeminglywasteful consumption ofwaterthrough transpiration
isessential tothegrowthofplants.Innature andeveninagriculture, itisarareand fortunateplantthatenjoysanoptimum supply
ofwaterthroughoutitslifecycle.Withoutirrigation,mostcropsare
inhibited, oftenseriously, fromachieving fullgrowth anddevelopment.
Out of all process controlling the growth ofwild orcultured
plants there isperhaps no single factorthatismorecrucialand
nonemore amenable toourintervention (atleastinprinciple)than
that of control overtranspiration inplants.Also inhorticulture
(greenhouses)thisbecomes increasingly important as energycosts
arerisingandtranspiration aswell asuptakeofwater intheroots
require large amountsofenergy.
The transpirational process is one of the factors contributing
to the water balance of the plant,beside uptake, transport and
storageofwater;theseprocesses arestronglymutually coupled[1].
The rate ofwatertransport inthexylem incombinationwithwater
contentofthe surrounding stemtissue areusefulparameters tostudy
andcontrol thewaterbalance,especially inrelationtotheeffects
ofenvironmental factors suchaslightintensity,airhumidity, C0 2
concentration, soil- and air temperature on crop production. In
addition,theseparametersmaybeused forselectionofbreedswhich
combine favourable parameters forthewaterbalance and lowenergy
use.
Several methods have been used to study water transport and
-content[2].
Concerningwatertransport,eitherthemeanlinear flowvelocity
v orthevolume flowrateQofthemovementofwater inthevascular
system inplantstemshasbeenmeasured.Themajorexistingmethods
are:
injection and monitoring of dyes or radio-active tracers (e.g.
[3]).Thesemethods arehighly sensitivebutcannotmeasure flow
afterequilibrium hasbeenreached.Also,itisuncertain ifthe
transport rate of tracers represents the actual rate of water
flow, since dyes orradio isotopes areabsorbed atthevessel's
surface[3].
heatpulsemethods,measuring theunbalance createdbynetwater
transportthroughplantstemsby aunitcontaining aheatinjecting
resistor andtwotemperature sensors symmetricallyplaced around
the injector [4,5]. Thismethod cannotmeasureabsoluteflowrates,
but only changes. Itdoes not provide reliable figures onthe
volume of waterflow per unit of time.The time-resolution is
relatively long (5-10 min.).
themagnetohydrodynamictechnique,where amagnetic fieldperpendicular to the flow generates a small induction voltage ina
directionatrightanglesbothtothe flowandthe field,dueto
themovementofchargedparticles [6,7]. Thevoltagemeasuredby
meansofanelectronic detectionsystem isdirectly proportional
to magnetic flux density,totheinternal radiusofthevessels
and to the instantaneousvelocityofthestream.Themethodcan
be used for instantaneous (repetitive) aswell as continuous
(steady state)measurements.A disadvantage of this method is
theneedofarelativelyhigh flowvelocity.
the weight balance method, by which the loss ofweightofthe
plant per unit of time is determined by a sensitive balance
(e.g. [8]).The methodrequires isolationoftheplantandsurrounding soil and isvulnerable to air-currents.Ithasatimeresolutionofafewminutes.Incontrasttothepreviousmentioned
methodsthismethodyieldsvolume flowrates.Thisisalsoobtained
by a related method based on lysimeters [2].Increase inplant
weightby C0 2 and/orwateruptake introduces errors indetermining
theactualvolume flowratethroughtheplantstem.
Noneofthesemethodsdetectsthemovementofwateritself,however,
andmany are invasive.Nuclear magnetic resonance (NMR)does not
havethesedisadvantages,andhasbeenshowntebe asuitabletechnique to study liquid flow [9].Tomeasure flowinplantstemsthe
techniquemustbe abletomeasure linear flowvelocities intherange
of 1-30 mm/s [2],andmustbeabletodiscriminatebetweenasmall
fraction of flowing water (2-10%)andalargeamountofstationary
water in the plant stem tissue. Two different pulsed NMRmethods
have been developed satisfying theseconditions [10,11],the first
ofwhich is a difference method and requires that theamountand
physicalproperties ofstationary waterdonotchange inthecourse
of the measurements. In Chapter 5we show that this situationin
plantsclearly cannotbeobtained.
Thesecondmethod [11]doesnothavethisdisadvantage andallows
determination of flow in a single experiment.ThisNMRmethodhas
the followingadvantages:
itisnon-destructive andnon-invasive.Whereasthe firstadvantage is obvious,the importance of thesecond isnotgenerally
realized.Someplantsreactexcessively tomechanical orelectrical
contact, and itmustbe suspected thatmost ifnotallplants
exhibit some change in one or more rate-processes upon such
contact.
itallowsinstantaneous aswell ascontinuousmeasurements,
it selectively measures flowing water only anddoesnotrecord
stationary water. In addition itmeasures the movement of the
watermolecules itselfby "labelling"andmonitoring theprotons
ofthewatermolecules.
themethod isinsensitive toair-currents afterthesampleremains
inafixedposition inthemagnet.
aswillbeshowninChapter4,themethodpermitsmeasurementof
linear aswell asvolume flowrates afternon-destructive calibrationusingaglasscapillary system.
the method, when used to perform instantaneous measurements,
allowsahightime-resolution (3-10s ) .
Thedisadvantages ofthisNMRmethodare:
intrinsic lowsensitivity ofNMR.
theNMR apparatus isrelatively expensive incomparisontoalternativemethods,describedbefore.
Themethodcanequallywellbeappliedtoliquid flowinotherbiologicalobjects thanplants,e.g. forthemeasurementofblood flow
(see Chapter8) and the circulation ofbody fluids inhuman and
animals. Finally, there appearstobenotechnicalbarrier forthe
measurementofspatially resolved flowpatterns invariousobjects,
using acombinationof flowmeasurementsbypulsedNMR andzeugmatography.
Forthedeterminationofthewater content,severalmethodshave
been used and are still inuse [2],butthey areeitherinvasive,
indirect, or destructive. Already in 1961 ithas been shownthat
NMR can be usedtodeterminethewatercontentofgrain [12].From
basic theory ofNMR (seeChapter 3), itfollowsthattheNMR signals
areproportional to the amount ofprotons in the detector ofthe
NMR apparatus. In Chapter 7 it is demonstrated thatthesesignals
canindeedberelated tothewatercontent. Inadditionthedynamical
information in these NMR signals (see Chapter 3), canbe usedto
distinguish various water fractions in the tissue with different
physical properties, e.g. surface-bound, exchanging or bulkwater
fractions.
Thus NMR flow measurements canbe used to selectively measure
flowing water only,without interference of thestationary tissue
water, whereas by choosing a different pulse-sequence stationary
water content can bemonitored inthesameexperiment,withoutreplacing theplant.Thisisagreatadvantage ofthe non-destructive
NMRmethod overtheexisting othermethods.
The goal of thisThesis istodescribe theapplication (andits
limits)ofthepulsedNMRmethod toplantstems.Chapter2summarizes
the process ofwatertransport inplants andthephysical stateof
water in the cell.BasicNMRtheory aswell asNMRpulse sequences
todetermine flow,diffusionandwatercontentinbiological systems
arepresented and reviewed in Chapter 3.Chapter4presents adetailed description and discussion of the NMR method to determine
flow inplant stems, showing that linear flowvelocity aswellas
volume flowratecanbedetermined simultaneously,yielding inaddition
an estimate of theeffectivecross-sectional areaofthetransport
vessels.NMR flowmeasurements instemsegments andinintactplants
arereported inChapters 5and6.Chapter 5explains thereasonfor
somenegative results anddiscusses theresults ofsimultaneous flow
measurements andwatercontentmonitoring.Acomparisonbetweenthe
results of flow measurements obtainedwithNMR,theheatpulseand
weightbalancemethod ispresented inChapter 6.
Throughout this Thesis weareconcernedwithtransportofwater
in the xylem. Thephloem transport isdownwards,which shouldgive
rise to an opposite signoftheNMR signalwithrespecttothatof
theupwardsxylemtransport.Phloemtransporthasnotbeenobserved,
duetoitsmuch lowervelocity.
REFERENCES
1. R.O.Slatyer,"Plant-WaterRelationships"(AcademicPress,NewYork,1967).
2. B.Slavik,"MethodsofStudyingPlantWaterRelations",EcologicalStudies,
Vol. 9(Springer-Verlag,Berlin,1974).
3. S.C.vandeGeijn,Thesis,Utrecht,TheNetherlands (1976).
4. B.Huber,Ber.Deut.Bot.Ges.50 (1932),89.
5. K.Schurer,H.Griffioen,J.G.Kornet,G.J.W.Visscher,Neth.J.Agric.
Sci.27 (1979),136.
6. D.W.Sheriff,J.Exp.Bot.23 (1972),1086.
7. D.W.Sheriff,J.Exp.Bot.25 (1974),675.
8. P.Tegelaar,A.F.vanderWal,Neth.J.PI.Path.80(1974),77.
9. D.W.Jones,T.F.Child,in"AdvancesinMagneticResonance"(J.S.Waugh,
ed.),Vol.8,p.p.123-148(AcademicPress,NewYork,1976).
10. M.A.Hemminga,P.A.deJager,A.Sonneveld,J.Magn.Reson.27 (1977),359.
11. M.A.Hemminga,P.A.deJager,J.Magn.Reson.37 (1980),1.
12. S.V.Kuznetsov,VestnikSelskokhoz.Nauki6(1961),117(fromref. 2).
2
WATER IN PLANTS
This Chapter summarizes somecharacteristics ofwater transport
intheplantstem andthephysical stateofwater intheplantcell,
in order to define somebasicconceptsunderlying themainresults
ofthisThesis.
Water transport and -balances inplants anditspartshavebeen
treated in several reviews [1-6], onwhichthelastpartsofthis
Chapter arebased. The state ofwater in the cell isreviewed in
ref. 5-9.
2.1 STATEOFWATER INTHECELL
Biological tissuescontain60-90percentwaterand living organisms
areabsolutely dependentonwaterinavariety ofways.Nevertheless,
basicknowledge aboutthephysical stateofcellularwater israther
limited.There aretwoclassicalviewpoints aboutcellularwater:
cellulose cell wall
intercellular
space
modesmnta
plasmalemma
cytoplasm
onoplast
central vacuole
nucleolus
Fig. 1 Structure of avacuolated plant cell (adapted from [10]).
(i)mostwater in the cell isconsidered tobe inthe freeliquid
state (bulk water); then, a living cellisequivalenttoadilute
aqueous solution surrounded by a semipermeable membrane.
In avacuolated plantcell (Fig.1)thecytoplasm isconsidered as
such a semipermeable membrane. Following this model, ithas been
thought that the totalcellbehaves asanosmometer,anideawhich
isstillinuse [1],(ii)ontheotherhandthereisalsoexperimental
evidence that the cellular water partially ortotally existsina
physical state significantly different from normal liquidwater.
Water, ions and biopolymers inside the cell formahighly ordered
phase.
Hechter [11],discussing theseclassical concepts,concluded that
both ideasarepartlycorrectandpartlywrong.
For water near interfaces there is considerable evidence that
thereexistsindeed astructurally changedboundary layerofwater,
called hydration water. Thewatermolecules inthehydration layer
of biological macromolecules exhibit restricted motion due to a
significantdecrease intranslational androtational degrees ofmotion
by interactionwiththemacromolecules.Clifford [7]hasdescribed
Simpleinterface
SURFACE ORIENTED
ZONE
B
narrow pore
no bulk water
second phase
biological
interface
Fig. 2 Possible surface environments: (A) surface in contactwithbulkwater,
(B) thin films and narrow pores, (C)particular surface in biological
material, (adapted from[7]).
the effect of surface environments on the behaviour of water, as
illustrated in Fig. 2. In A there is simply an interface between
bulk water and a second phase, which may be solid, liquid, or vapour.
In B there is a thin layer of water between two interfaces, not
allowing sufficient space for the development of bulk water structure.
In biological material surfaces are usually more like C: the surface
available for adsorption is many times the superficial surface area
and water molecules exist in spaces comparable with molecular dimensions.
2.2 WATER POTENTIAL [4]
In plant physiology, it is customary to express the free energy
content of water by the water potential
t|i.Derivations of water
potential from strict thermodynamic principles can be found in [1]
and [ 4 ] .For our purposes, it is sufficient to define water potential
as the free energy per unit volume of water, assuming the potential
of pure water to be zero under standard conditions.
Because water potential increases with temperature, it is important
to maintain constant temperature during a series of measurements.
In contrast, water potential is lowered below that of pure water by
dissolved solutes and also by the binding of water to surfaces by
matrix forces. Since these effects are considered to be mutually
independent, the water potential of a solution (t|i)can be expressed
as
t|i = t|i + t|<
(2.1)
where tb,the solute
potential,
is the reduction in water potential
due to dissolved solutes (negative), tb, the matrix
potential,
is
the reduction in water potential due to matrix forces (negative)
and thus tbwill be negative. Consequently, in the soil-plant-atmosphere system, water potentials are usually negative, and water flows
towards regions with more negative values.
In plant tissue, water potentials may be increased by hydrostatic
pressure and, therefore, eqn. 2.1 must be modified to give
tli=41 +tb +tb
T
T
s Y m ^p
(2.2)
whereijj,the pressure
potential,
istheincrease inwaterpotential
due to hydrostatic pressure (positive). Since I|J ispositive,the
resulting water potential is less negative thanwouldbeexpected
ifonlysoluteandmatrix effectswereconsidered.
2.3 WATERTRANSPORT INTHEPLANTSTEM
Longitudinal water transport in the plant stem is primarily
located in the vascular system,where itmoves fromthexylemterminals in the root to those in the leaf. Inprinciple,thewhole
cross-sectional areaoftherootorthestem isavailable fortransport.However,the flowthroughcellwalls inthestempathwaycan,
atleastundernormalconditions,beneglected.Thepermeability of
theprotoplast isassumedtobe 50times lessthanthatofthecell
wall [2,3]andconsequently thispathwaycanalsobeneglectedwith
respect tovascular transport. This does notmeanthattransverse
water transport is absentinthestem.Thishasbeendemonstrated,
by adding isotopically labelledwatertotherootmedium [12],causing
thewater inthexylemtoberapidly replacedbythelabelledwater,
concomitant with a slow progressive replacement ofwater inthe
remainder oftheouter stemtissue.
In a freely-transpiring plant,water evaporates fromthemoist
wallsofepidermal andmesophyllcellsinthe interior oftheleaves
and is lost to the atmosphere through the stomata. Aswater loss
proceeds, thewaterpotential inthe leafapoplast fallsbelowthat
of the leaf cells and also belowthewaterpotential inthexylem
and the soil. (The apoplast is defined asthenon-livingpartsof
theplant,e.g.xylem,cellwalls,etc.). Thisresults intherapid
withdrawal ofwater from leaf cells and a lowering ofcellwater
potential.Although there iscontinuity ofliquidwaterbetweenleaf
and soil via thexylem,equalization ofwaterpotential throughout
theplantbyupwardwatermovementcannotoccurveryrapidlybecause
there is a resistance to hydraulic flowintheplant/soil system.
Consequently, transpiration establishes awaterpotential gradient
causing flowofwater fromthesoiltotheleaf.
The flow of water to a transpiring leafinresponse toawater
potential gradienthasbeendescribedby anexpression analogousto
Ohm's Law [13].Inasymplified formthisresultsin
10
Q="'" I"'leaf
(2.3)
whereQisthevolume flowrateofthewatermoving from soiltoleaf,
i|irs is thewater potential of thesoilattherootsurface, i|)-,_~
xeax
isthewaterpotential ofthetranspiring leaf,andRistheresistance to hydraulic flow between the root surface and thesiteof
evaporation.Forasimpleplant (e.g.aseedling),Rcanbedivided
intoaseriesofcomponentresistanceswithintheplant:
R=r
+r„
root
+r- ,
stem
(2.4)
leaf
wherer root
.istheresistance to flowbetweentherootandthe lumen
of the xylem, r . istheresistance inthexylem (root,stemand
leaf), and r-, leaf
~is the resistance to flowacrossthe leaftothe
evaporation site.Of those quantities, r, f and r r o o t have been
considered as the most important resistances.Experimentally, it
has been found thattheresistance inthexylemvesselsdependson
thelumenwall surface sculptures[14].
When aplantistranspiring rapidly (>l>soil-4>rs)and (t|»rg-<l>leaf'
cannot exceed values of 10-30 bar (1bar= 10 s Pa) whereas
(I]>T
t-<|<.:T,air
.)varies between 100 and 2000 bar [4].Therefore,as
VT
leaf
long as steady state flowismaintained, leafdiffusive resistance
controls the rate of water throughout the soil-plant-atmosphere
system aswell astranspirationrate.
Great care must be exercised in applying this model to the
behaviour of plants.Most plants do notconsistofasingleroot,
stemandleafinseries;theyshould ratherbeconsidered asanumber
of root axes, branches andleaves attached inparallel toasingle
(ormultiple)stem.Another difficulty isthatwatercanbewithdrawn
into,orreleased from,storage reservoirs (e.g.stemorleaftissue,
fruits, etc.)at differentpoints alongthepathway,thus altering
the flowrate. InChapter 5weshow,thatcellsbordering thexylem
inthestem androotsystem losewaterduringperiods ofwaterstress
(e.g.duringtheday)andadsorbwaterduringthenight.Thisproblem
can be overcome by extending the electrical analogy to include
capacitance, aswell as resistance in the soil, stem andleaves;
11
t h e e x c h a n g e of w a t e r w i t h s t o r a g e r e s e r v o i r s i s t h e n a n a l o g o u s t o
c h a r g i n g and d i s c h a r g i n g an e l e c t r i c a l c a p a c i t a n c e .
Such a model
has been proposed i n [ 5 ] .
An i n d i c a t i o n of t h e v a l u e o f t h e a v e r a g e maximum v e l o c i t i e s of
w a t e r t r a n s p o r t i n xylem i s g i v e n i n [ 1 5 ] . I n mm/s v i s 0 . 3 - 0 . 6
i n f e r n s , 0.33 i n e v e r g r e e n c o n i f e r s ,
0 . 2 7 - 1.7 i n l e a f y t r e e s w i t h
s c a t t e r e d p o r o u s wood ( e . g . b i r c h , b e e c h , l i m e ) , 3 . 9 - 1 2 . 2 i n r i n g
p o r o u s wood ( o a k , a s k t r e e s ) , 2 . 8 - 1 6 . 7 i n h e r b s and 42 i n l i a n e s .
REFERENCES
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
R.O. S l a t y e r , "Plant-Water R e l a t i o n s h i p s " (Academic P r e s s , New York, 1967).
M.B. R u s s e l l , J . T . Woodley, i n "Growth i n Living Systems" (M.X. Zarrow, e d . )
p . p . 695 - 722 (Basic Books, New York, 1961).
P.E. Weatherley, in "The Water R e l a t i o n s of P l a n t s " ( A . J . R u t t e n ,
F.H. Whitehead, e d s . ) p . p . 85 - 100 (Blackwell, London, 1963).
A.H. F i t t e r , R.K.M. Hay, "Environmental Physiology of P l a n t s " (Academic P r e s s ,
London, 1981).
H.Meidner,D.W.Sheriff,"WaterandPlants" (Blackie,Glasgow, 1976).
G.Peschel,in"WaterandPlant Life:ProblemsandModernApproaches"(O.L.
Lange,L.Kappen,E.D.Schulze, eds.),Ecological Studies,Vol.19, p.p.
6 - 1 8 (Springer-Verlag, Berlin, 1976).
J. Clifford, in"Water-A Comprehensive Treatise" (F.Franks, ed.), Vol.
5,p.p.75-132(Plenum Press,New York, 1975).
H.J.C. Berendsen, idem,p.p.293
- 330.
F.Franks,Phil.Trans.R.Soc.LondonB278(1977),
89.
J.Sutcliffe,"PlantsandWater" (Edward Arnold,London, 1968).
0.Hechter,Annal.NewYork Acad.Sci.125(1965), 625.
0.Biddulph,F.S.Nakayama,R.Cory,Plant Physiol.Lancaster36(1961), 429.
T.H.van
der Honert,Disc.Faraday Soc.3(1948),
146.
A.A.Jeje,M.H. Zimmermann,J.Exp.Bot.30(1979), 817.
B.Slavik, "MethodsofStudying PlantWater Relations",Ecological Studies,
Vol. 9,p.223(Springer-Verlag, Berlin, 1974).
12
3
PULSED NUCLEAR MAGNETIC RESONANCE SPECTROSCOPY IN BIOLOGICAL
SYSTEM
ReviewsontheNMRpulsemethod andthetheoryofrelaxationhave
beenpublished [1-6,13].Hence,thisChapterdoesnotcontainadetailed treatment ofmethods,theory and interpretation ofpulsed
NMR. Only the necessary background for theChapters4-8ofthis
thesis isprovided, aswell asshortreviewsonsomespecialapplicationsofNMR,i.e. self-diffusion and flowmeasurements.Inaddition, the relationship betweentherelaxationparameters andwater
content,emphasizingbiological systems,isshortlydiscussed.
3.1 BASICTHEORYOFPULSEDNMR
Most nuclei posses theproperty of spin, characterized by an
angularmomemtumvectortandamagneticmomentjjrelatedby
M=Y *I,
(3.1)
where y is thegyromagneticratio,aconstant foragivennucleus;
ftish/2nwhereh isPlanck'sconstant.Whenanucleusofspin Iis
placed in a staticmagnetic fieldB ,themagnetic interactionbetween the nuclear magnetic moment |jandB givesriseto (21+1)
equidistantenergy levels,with aseparation
AE=yfiB
(3.2)
Forprotons ( X H),theonlynuclei considered inthisthesis,I= \ .
At thermal equilibrium, nuclei aredistributed among theenergy
levels according to aBoltzmann distribution. This results ina
macroscopic magnetization
M alongthedirectionofB .Forasample
containing N nuclei, the equilibrium magnitude ofM is givenby
[2]
|M | = Ny2fi2 1(1 + 1)B /3kT
(3.3)
13
We shall find it adequate in our treatment ofpulsephenomenato
deal almost entirely withthemacroscopicmagnetizationbyaclassical description [1].A complete theoretical description, ina
quantummechanical formalism, isgiveninseveraltextbooks [2-4].
Blochet al. [5]foundthatthemotionofmacroscopicmagnetizationinthepresenceofanappliedmagnetic field§couldbeexplained
in terms ofphenomenologicaldifferential equations.The classical
equationofmotion forthemagnetization isgivenby
(3.4)
dM/dt= yMxB
describing aprecession of the magnetization around the magnetic
fieldvector§atanangular frequencyit) =-yB.Theprecession frequency ofM inB is called the Larmor frequencyu>.Inorderto
stimulate spin transitions, the frequency of the electromagnetic
radiation must be equal to the frequency oftheLarmorprecession
according to UJ=-yB .This isthe resonance
condition.
In NMR experiments, commonly a rotating frame of reference
{x.' ,y' ,z'} is defined forwhichthez 1 axishasthesamedirection
as the z axisinalaboratory frame,coincidingwiththedirection
ofB .The frame {x',y',z'}rotates atanangular frequency \u(iu =w )
aroundI (Fig.1]
(b)
(a)
\
X
V
X'
Fig. 1 Magnetization M ina laboratory frame (a)and a rotating frame (b),when
UJ=U)
14
Theequationofmotion (Eqn.3.4) intherotating framebecomes
dM'/dt=M'x-y(B'+w/y)=M'xyB'
eff
(3.5)
On resonance w=-y§ •When§'=B ,M',themagnetization inthe
rotating frame,isconstant.Whenweapply inadditiontoB aradio
frequency field B x , with angular frequency w, perpendicular toB
(i.e. in the x,y plane), theeffective field intherotating frame
becomes S x , and the magnetization rotates aroundB\ atanangular
frequency yBi.During atimet theangleoverwhichMrotatesis
yBit
(radians)
Strictly speaking,thisrelation onlyholds fortheexactresonance
frequency. Itcan be shownhowever,thatthecondition (3.6)holds
relatively well even when the resonance condition is not exactly
fulfilled,provided the B% pulse issufficiently strong anditsrise
time short (afew M S ) .
If theB1-field isswitchedoffatthemomentwhen a =90°,the
pulse in question is a 90° (VO pulse. Correspondingly, if the
lengthofthepulse ischoseninsuchawaythat a =180°,thepulse
iscalled a180° (n)pulse (Fig.2 ) .
i
Fig.2 The90°and180°pulses.
(3.6)
15
After thepulse, Ba is absent andB_ ff = o.BecauseMisnolonger
initsequilibrium state,nuclearmagnetic relaxationprocessesensure itsreturntotheequilibrium valueM .Bloch [5]hasdescribed
the motion of the components of magnetization by the following
equations:
dMx,/dt=-Mx,(t)/T2 or Mx,(t)=Mx,(o)exp(-t/T2)
dMy,/dt=-M ,(t)/T2 or My,(t)=My,(o)exp(-t/T2)
(3.7a)
(3.7b)
d(Mz,-MQ)/dt=-(Mz,(t)-Mo)/Tx or Mz,(t)=(Mz,(o)-M^exp^t/Ti)
(3.7c)
Theterms-M , ,/T2 and- (M ,(t)-M r .)/T l representthetendency
ofthemagnetizationtoreturntoitsequilibriumvalue,i.e.nuclear
magnetic relaxation. The time constant 11 referstothereturnof
M to its equilibrium value M ;Tx is called the spin-lattice
or
the longitudinal
relaxation
time.
Thetransverse componentofMdecaysexponentiallywiththetime
constant T 2 , the spin-spin
orthe transverse
relaxation
time (also
calledthephase coherence time). Infact,thespin-latticerelaxation time T t characterizes theexchangeofenergybetweenthespin
system and the degrees offreedom ofthelatticewhereas thespinspinrelaxationtimeT 2 characterizes theexchangeofmagnetic energy
insidethespinsystem, i.e.,withoutaglobal changeoftheequilibrium magnetization. The lattercharacterizes themeanlifetimeof
the spins in agivenenergy state,duetotheexchange ofmagnetic
energybetweenthespins.
Asshownin eqns.3.7a-cMapproachesequilibrium exponentially.
However, because of the heterogeneity of biological systems,the
nuclear relaxation is ingeneralnotcharacterized by asingleexponentialdecay,butby asumofexponentials,eachwithitscharacteristic relaxationtime.Thissituation applies alsototheresults
forplantsamples asdescribed inthisthesis (Chapter7 ) .
3.2 MECHANISMS FORTHESPIN-SPIN RELAXATION
The NMR relaxation times ofwater inbiological samples,which
have been widely used to measure the physical properties ofthis
water, areaffectedbymany factorsandingeneral astraightforward
16
theoretical interpretation of theobserved relaxationbehaviouris
therefore impractical. Inthissectionwewillgivethemechanisms
anddynamicprocesseswhichcausenuclearrelaxation,especially in
biological tissue. In favourable cases one ofthesemechanismsor
dynamic processes dominates therelaxationbehaviour andinterpretationofthedataisquitesimple.Unfortunately, inmostbiological
tissuesthis isnotthecaseandapproximationsmustbemadetoexplaintherelaxationmeasurements.
3. 2.1
Dipolar
interaction
Oneofthemostimportantmechanisms fornuclearmagneticrelaxationinvolvesmagnetic dipole-dipole interaction.Duetothisinteractionamagneticnucleusexperiences asmall local field B-, ,producedbytheneighbouring nuclearmagnets[1]:
B.
=1.-3
(3cos26.-l)
loc
ir?
i
(3.8)
I
where r. is the internuclear distance, and6.theanglebetweenr
and the magnetic field. This interaction may be intra- orintermolecular.
Secondly, molecules are inthermal translational and rotational
motion, andatoms,orevengroupsofatoms,maychangeplaceswithin
orbetweenmolecules.Duetothesemotions,thelocalmagnetic field
&-, experiencedbyaparticularnucleus continuouslyvaries intime.
IfB-, fluctuates atasuitable frequency itmay induce transitions
betweenspinstatessimilar tothosecausedbytheexternal resonance
frequency field. Thermal motions inaliquidcover awide spectrum
characterized by the 'spectral
density'
function J(w) [6], which
represents the power atfrequencyw.J(w)istheFourier transform
of the so-called autocorrelation
function G(x), measuring the
persistence ofthe fluctuations ofthemotion.Frequently G ( T ) drops
off exponentially with a decay time T ,which is called the correlation
time. It is the time taken for a typical fluctuationto
die away. Inmanycases, T uniquelydefinestheJ(u>)ofthelocal
field. For translational motion x canbe considered as thetime
c
17
needed foramolecule tomake adisplacement correspondingtoits
diameter; similarly, forrotational motion, t canbeviewedas the
time needed tomakearotation throughanangleofoneradian;for
collisions x istheaverage timebetweenmolecular collisions.
Ifweassume that a single correlation time characterizesthe
molecular rotation,thedipole-dipole interaction fortwoidentical
nuclei with I= \ gives rise to nuclear spin relaxation, with
relaxation times:
(
T->intra = ^ ^
Ti intra
+
* "
6
1 + ^2 2
~
o 4* 2
T 2 intra
2 Q r6
oc
^"^
(i-).. =^ — 2 - {3x +
c
"
x+ 4u)2 X2
o c
i
(3 9a)
J
l + ^2 T 2
^"^
+
x + ^ 2 T2
o c
^
}
(3.9b)
oc
whereristheinternuclear distanceandx istherotational correlation time.Forthetranslational motions involvedinintermolecular
interactions,thegeneral expressions for(f-)in+-era n d ^T^inter a r e
similar toeqns. 3.9a-b, where therotational correlation timex
mustbereplacedbythetranslational correlation time xfc[2].
For fast rotational motion (1/t >>w ),Tj equals T 2 andboth
are inversely proportional tox.This conditioniscommonlymetin
aqueous solution atroom temperature,where x forwater molecules
is oftheorder of10 _ 1 1 s.Asthecorrelation time x increases,
the component ofthelocal fluctuating fieldattheresonance frequency u) decreases, tending tozero whenwx>>1.T t nowbecomes
proportional tox andincreases once moreasthemagnitudeoft
increases. T 2 , however, continues todecrease linearly with x,
because T 2 isalso sensitive tolowfrequency fluctuations, until
the molecular motion slows down somuch thatitreachestherigid
lattice condition. Whenwater molecules interactwithmacromolecules
in solutionorwithmembranes therotational andtranslational motion
slows down considerably, causing T x andT 2 tobecome different,and
resulting inavalueofT 2 much less thanforfreewater.
In analyzing relaxation measurements itisastandard procedure
to include only intramolecular dipolar interactions.However, evidence hasbeen presented that intermolecular dipolar interactions
18
between water molecules, especially in the hydration layer, and
protons of themacromolecules may have a significant or dominant
contribution in the relaxation mechanism [e.g. 7-9].There is an
additional effect thatmay influencetheobservednuclearmagnetic
relaxation:diffusionthroughlocalgradients inthemagnetic field,
due to local differences in the magnetic susceptibility, asfound
forheterogeneous systems [10].However,ithasbeenconcluded that
inbiological tissues thiseffectissmall andoftencanbeneglected
[9].
3. 2. 2 Paramagnetic
ions
A significant effect on nuclear relaxation times inbiological
tissuescanbeattributed toparamagnetic ions insolution,resulting
fromthedipolar interactionbetweenelectron andnuclear spinsand
the scalar interaction depending on the unpaired electrondensity
atthepositionofthenucleus.Therelaxationtimesofnucleibound
near aparamagnetic sitearegivenbytheequations ofSolomon (11)
andBloembergen (12),
Y 2 g 2 S(S + l){5 2
3x
^ 7 = JF ( ) {
— +
TlM
15
r6
l+u>2x2
71
— } + |S(S+1) Q) {
3
l+tu2X2
*
Ic
V2g2S(S+l)p2
f=
-JF15
(TzM
r6
){4T+—C - +
3x
Sc
131
t
2
}
l+w 2 x 2
Se
2
- } +is(S+l)
(£) { — ^ - +t}2
2 2
3
l+u)2T2 l+iu
T
1c
bc
(3.10a)
*
l+w T2
I
e
be
(3.10b)
where u)T andw arethenuclear andelectronLarmorprecession frequencies respectively, S is the electron spin, g the electron g
factor (adimensionless constant), 0theelectronBohrmagneton,r
the distance between thenucleus andtheparamagnetic ion,A/ftthe
electron-nuclear hyperfinecouplingconstant,andx andx thecorrelation times characterizing the modulation of the dipolar and
scalar interactions,respectively.These aregivenby
^-=— +— +—
Xc Ts TMM Tr
(3.11)
19
and
e
s
M
where T M is the life-time of anucleus atthebinding site,t is
the rotational correlation timeoftheboundparamagnetic ion,and
x istheelectron-spin relaxationtime.
When fastchemicalexchange occursofwatermolecules inthebulk
water and those near aparamagnetic site,theobserved relaxation
timescanbeshowntobe
j
l,obs
I
-m—+ j —
lw
1M
=ir^+ J2,obs
2w
(3.13a.)
(3.13b)
2M
where fisthe fractionoftimethateachproton spends inthecoordination shell of the paramagnetic ion. Ifn is the coordination
number, N is the concentration ofparamagnetic species,andN„is
the molar concentration ofprotons we have f=n/N„.NeglectingT,
andT» ,therelaxation times inpurewater,eqn.3.13 becomes
h
=(s->f 5l,obs
k
H
-
1M
=(J")f2"
2,obs
(3 14a)
H 2M
showing a linear dependence of both 1/T, , and 1/T2 , on N
(Chapter 7). Fromeqn.3.10 itcanbeseenthat1/T, . and1/T2 ,
are also roughly proportional to Miff/ the mean square magnetic
momentoftheparamagnetic species,which isaboutathousand times
larger for electrons than forprotons, causing avery effective
relaxationmechanism.
Inbiological tissues oneismainlyconcernedwiththeionsCl~,
Na ,and K .At physiological concentrations, theeffectofthese
ions on the relaxation times ofpure water is usuallyverysmall
and can in general be neglected [14,15]. However, in biological
tissue these ions can influence the relaxation time of water by
osmosis, affecting the water content of thetissue,and -athigh
(3.14b)
20
ionic concentrations
structure [16,17].
3.2.3
Sample
by adirecteffectoftheseionsonthewater
heterogeneity
Themeasurement andinterpretationofnuclear relaxation inbiological tissue isalsocomplicatedbytissueheterogeneity,bothon
a macroscopic and onamicroscopic scale [18].Inthisrespect,we
can distinguish regions with e.g. different cell size, different
water content, different chemical composition. Furthermore, these
regionsarespatiallyorganized inanon-randommanner,theycontain
molecules of different sizes, and -finally -,water andionsmay
bedistributed throughoutthesystem inanon-uniform way,asindicated inFig.3.Watermoleculesmay exchangebetweenregionsAand
B ataratethatisafunctionoftheself-diffusioncoefficientof
water in each region and of the potential barrier constitutedby
theinterface separating thetworegions.
Onamicroscopic scaletheheterogeneity influencesthetimeconstantsofthedifferentdynamicprocesses thatcharacterizethe
t
Fig. 3 Schematic illustration of large scale heterogeneity. Distinct regions
(e.g. A and B) of the material may have differing compositions (e.g.
water contents), geometries and dimensions (e.g.X,Y, etc.)and may also
differ ine.g. degrees of order and anisotropy in internal structure (from
Packer [18]).
21
motionofthewatermoleculesandprotonexchangeinsuchsystems.
Fig.4gives aschematic illustrationoftwointeracting regionsa
andponamicroscopic scale [18].Theshaded regions a andprepresent
two macromolecular structures characterizedbydimensionsd,x,y,
orientations Ba and6 definedwithrespecttoanexternal reference
axis,andcorrelationtimesfortumbling t.Thedistancedisoften
much largerthanthesizeofawatermolecule,andinsystemswhere
themacromolecules concerned arestructural components suchasin
collagen,t mcanbevery longoreveninfinite.Inprotein solutions
T w i l 1 re
m
flect thetumblingoftheproteinmoleculeinpartoras
awhole.Thewatermoleculescanundergoavarietyofmotionsinsuch
asystemasillustrated inFig.4.
REGIONa
9
1*
REGIONft
vrri 111i111)i II I)) i) u)) m 111))n
\
Tm
H TD
I
H-0
/VA ex
H H
,H H>
W//////////777777778&77777771
F i g . 4 A schematic i l l u s t r a t i o n of small s c a l e h e t e r o g e n e i t y and various dynamic
processes which may he experienced by water in a b i o l o g i c a l system (from
Packer [ 1 8 ] ) .
Water molecules outside the region of influence of t h e macromolecules
d i f f u s e , r o t a t e and exchange protons with c h a r a c t e r i s t i c times t n ,
22
t andi respectively.Watermolecules interactingwiththemacromolecules tumble anisotropically, thisprocessbeingrepresentedby
a collective correlation time T' andhavealifetime inthisstate
designated by t' .Water molecules may diffuse fromoneregionto
another,theirlifetime inagivenregionbeing t„ (~ d2/2D ),with
D the self-diffusion coefficient, while the exchange of protons
with the macromolecules corresponds to a lifetime of t" .Water
molecules near the macromolecular surface move in an anisotropic
potential which remains almost unchanged during the reorientation
ofawatermolecule,resulting inananisotropicmagnetic interaction,
mainly of dipolar nature which is notaveragedouttozeroduring
the reorientation time of such awater molecule.Water molecules
outside the region of influence of the macromolecules, the bulk
liquidwater,alsoexperience atanyinstantananisotropicpotential,
but the axes definingthisanisotropy changesdirection asfastas
individual molecules reorient, consequently the effects duetoan
anisotropicpotential aregenerally averagedoutontheNMRtimescale.
As isevident fromFig.4thedynamicsofwater inbiological tissue
containsmanydifferentprocesses andafulldescription isvirtualy
impossiblewithoutmakingsuitable approximations.
3. 2. 4 Exchange and
diffusion
Inbiological tissues each region (i.e.a and 0, fig.4)will
probablycontain anumber ofdifferenttypesofbinding siteswhich
giverisetodifferentvaluesofe.g. correlationtimesand relaxation
times. If t' for each such sitewere sufficiently largethenthe
observednuclear relaxationwouldcontain asuperposition ofrelaxationratesof freeandthetotalofbound sites.Byexchangeprocesses
however,thenuclearrelaxationofthedifferentsitesiscompletely
or partially averaged, depending on the rateofexchange.Forthe
fastexchangecondition (x'<<T2fa,whereb isthebound site)ina
single region assuming only asingletypeofbinding site,theobserved relaxationtimebecomes [19]
2 f -' + P b T 2 b -i
(3.15)
23
where frefers tothefree (bulk)water andP f , P, arethemole
fractions ofthefree andbound water, respectively.Forasystem
with exchange betweentwositesaandb,therelaxation times depend
ontheexchange rates (T —X andt.-1)andtherelaxation timesof
the sitesintheabsenceofexchange (T=2andT2,)asgivenby[20-22]
cl
T
^II
=\ IV +V +C + tfi
with S = i (T2- 1
±
[ < * + ^ +rij h
JJ
(3.16)
alb
- Tz^ 1 )
(3.17)
and a = | ( t " 1 - i " 1 )
2 a
b
(3.18)
The fractionsaregivenbyP =T/(r +t,).
In this description thechemical shift difference betweenthe
two states (thedifference intheLarmorprecession frequency)has
been neglected. However,inconsideringtherelaxation rateswemust
also take into account that theexchange process itself causesan
additional relaxation mechanism becausethenuclei experience timedependentmagnetic fieldsbyexchange between differentenvironments.
This resultsinadependenceofthenuclear relaxation timesonthe
chemical shift differences and,inthecase ofaT 2 measuredvia
the Carr-Purcell-Meiboom-Gill method [23,24 andSection 3.3],on
thepulse separation 2xofthen-pulses [21,22andreferences cited
therein]. For2x6 <<1,where26isthechemical shiftdifference,
the effectofthechemical shift disappears, resulting inegn.3.16.
Ontheother hand, for2x6>>1,T2-1 isgivenby [21,22]
T
2l,II= \ (T2~a+ T2"b+ X a _1+^
*P
(3 19)
"
wherepcanbecalculated from
2
2
(p+iq)=
(i6+s+a) +
(t a I b ) -1
(3.20)
andSandaaredefined ineqns.3.17and3.18.Thephysical reason
for thedependence ofT 2 onthepulse spacing2tmaybeexplained
as follows. During thetimetafteranecho,themagnetizationsMand M R rotate intherotating frame with anangular frequency-6
and +6,respectively. M, and1VLhaveaphase difference 2 T 6after
24
timei,intheabsence ofexchange.Asaresult,theobservedrelaxationtimesvarywith increasing 2x betweenthelimitingvaluesgiven
byeqn.3.16 andeqn.3.19.Therefore,acomparisonofT 2 relaxation
timesshouldtake intoaccounttheexperimentalpulse spacing 2T.
The dependence of T 2 on 2t inplanttissue suchasbeanleaves
and apple pulp has been demonstrated byFedotovetal. [25].From
these measurements these authors concluded that (intermsofFig.
4) x' is of the order of 10~ 8 s,t" varies from3.5 x 10- 3 sfor
maize leaves to 9.5 x 10" 3 s for onionbulb,andt' ^ 10 - 4 s.In
all measured plant tissues these authors observed only a single
relaxation time forT x andT 2,incontrasttothemeasurementsreported inthisThesis (Chapter7 ) .
So far, exchange betweentwositeshasbeenconsidered assuming
that any water molecule atanyinstanthasequalprobability tobe
found ineitheroneofthetwo sites.This situationisclearlynot
metinheterogeneous systems.Thediscrete jumpsofawatermolecule
or aproton betweentwowell-defined sitescanthenbegeneralized
to random, quasicontinuous displacements,asinfreediffusion.It
depends on the distance over which thetissue ishomogeneous,the
presence of diffusion barriers andthediffusioncoefficent,which
kind of relaxation behaviour isobserved:asingle relaxation time
formorehomogeneous tissueswithunrestricted diffusionoradistributionofrelaxationtimes formorecomplex systems.A fulltheoretical description, in whichmanyexchange siteswithdifferentrelaxationtimes areincorporated,hasnotyetbeendeveloped.
Recently,Brownstein [26]andBrownstein andTarr [27]applieda
simpletheorybased onadiffusionequationusingthebulkdiffusivity ofwater [28,29] to explain themulti-exponential decay seen
innuclear relaxation measurements ofwater inbiologicaltissues.
They showedthatsuchmulti-exponential behaviour arises asaconsequence of an eigenvalueproblem associatedwiththesizeandshape
ofthecell andthatthismulti-exponential decaycanonlybeobserved
forsampleswith asizecomparable tothatofabiological cell.
25
3.2.5
Summary
In summary we conclude thatnuclear relaxationtimesTx andT 2
containthe following information:
concentration anddynamicsoftheobservedmagneticnuclei
nature oftheenvironmentofthenuclei,inparticular themicroscopic geometryoftheirenvironment.
influenceoftheboundaries (e.g.walls)surrounding thehomogeneous
regionsofthesample.
3.3 MEASUREMENTOFT 2 ,DIFFUSIONANDFLOW
3. 3.1
Method of T2
measurement
AfterthemagnetizationM isrotatedbya \ n pulse applied along
the x' axis as shown in Fig.2,M isparallel tothey1 axis,and
immediately begins to decay. The nuclear induction signal canbe
detectedwith acoilthatispartofacircuittuned attheresonance
frequency u>.The apparatus isarranged insuchawaythatsignals
are detected when M has a componentperpendicular toB ,i.e.the
receiver coil isparallel tothexory axis.Accordingly,thetransverse magnetization rotating in the laboratory frame induces an
alternatingvoltage inthecoil, attheLarmor frequency.Thisoscillating signal canbephase-sensitive detected anddecays exponentially
if the resonance condition issatisfied.Thissignal iscalledthe
free induction
decay (FID).
AsdefinedbytheBlochequations (eqns.3.7a-c),T 2 isthedecay
time of the transverse magnetization. However, only in favourable
caseswilltheFIDdecaywiththerelaxationtimeT 2 • Inparticular,
theinhomogeneityofthemagnetic fieldB accelerates thedecayof
the transverse magnetization, because the nuclei inthedifferent
partsofthe fieldprecess atdifferent frequencies andhence rapidly
become outofphasewithrespecttoeachother.TheFIDhasaneffectivetransverse relaxationtimeT 2 *,givenby[2].
(T2*)-i=T 2 _1+yABQ/2
(3.21)
26
whereAB istheinhomogeneityofB.
The effect of themagnetic field inhomogeneity ofB canberepresentedby adistribution oftheLarmor frequencies g(Auj).Dueto
this inhomogeneity, the average Larmor frequency w inthesample
is associated with arangeofprecession frequencies UJ ±Aw.Ata
given w-, anumber of nuclei precess,andtheseareassignedtoa
spin isochromatic
group [30].After a%n pulse at t=o (Fig. 5a)
each isochromatic group precesses at a slightly differentratein
the x',y'plane and fans out (Fig.5b).When,afteratimet,an
pulse along the y' axis is applied (Fig. 5c),a180°reversalto
theisochromatic spingroups isgivenwithrespecttothey',z'plane,
theslower andfastermovinggroups againapproacheachother.Thus,
attime2xphasecoherence isrestored forashortperiod oftime,
(b)
(d)
TCt£2T
t=2T
Fig. 5 The production of a spin echo (a) t=o : \n pulse along x',(b) free
induction decay at 0<t<l, (c) at t=T a71pulse along they' axis results
in a 180° reversal of the isochromatic spin groups, (d)restoration of
phase at x<t<2t yields, (e) a spin-echo at t=2T, (f) phase coherence
is again lost.
27
giving rise to a spin-echo
(Fig. 5e).Thereafter the spin-groups
fan out again (Fig.5f).Theheightoftheecho attime2x depends
on the initial magnetization |M| andonthetransverse relaxation
timeT 2 ,whichcanbeobtained fromtheecho amplitude asafunction
ofT.
However, molecular diffusion also affects the echo height. If
between pulses the observed nuclei (attached to themolecules of
interest)move fromonepartoftheinhomogeneous fieldB toanother
by diffusion, then thecompensation forthe field inhomogeneityis
incomplete and the echo does not reach its full height.Carrand
Purcell have shown [23] that for the multiple pulse sequence
Vt„i _(t -n -- T ) the effect ofdiffusioncanbeneglectedwhen
t ismade small enough. The envelope of the heights of the spin
echoes,whichoccurinbetweenthepulses attimes2nt,hastheform
exp(-2nt/T2)and thus yields T 2 . Meiboom andGill [24]introduced
a modification to compensate for off-resonance effects andimperfections in the length of the pulses by the sequence:
Vt x , -(x - ny, - x ) n
Thispulse sequenceisknownastheCarr-Purcell-Meiboom-Gill (CPMG)
sequence which is used fortheT 2 measurements asreported inthis
Thesis.
3. 3. 2 Effect
of diffusion
and flow
Ashasbeenstated above,NMR isoneofthemostversatiletechniques for the studyofmolecularmotionthrough itseffectonthe
Larmor precession frequency. When amolecule moves a distance Az
during a time At along afieldgradientG ,thephase shiftdueto
thatmotionis
A*=yG (AZ)(AT)
(3.22)
Thesemotionscanbeviewed aseither incoherentorcoherent.Examples
of the former are thermal motions ofthemolecules,e.g.translational androtational diffusion,andchemical exchange,whereas flow
represents coherent motion. Turbulent flow mightbeconsidered as
havingboththeproperties ofcoherence (onashorttimescale)and
randomness (onalongertime scale).
28
Theeffectsofmoleculardiffusion andflowinspin-echoexperimentshasalreadybeenrecognizedbyHahn [30]andCarrandPurcell
[23]. Infacttheechoamplitude inaCPMGpulse sequence isattenuatedbymolecular diffusion according to [23]
S(t) « exp[-(t/T2)-iY2G2Dl2t]
(3.23)
G isaspatialmagnetic fieldgradient,Dthe self-diffusioncoefficient. As stated before, S(t)ispurely exponential for smallT,
i.e. if v 2 G 2 Dx 2 <<T 2 - 1 . Stejskal [31] and Stejskal andTanner [32]
noted that the effectofdiffusion istoattenuate theechoheight
whereastheeffectofflowistoshiftthephaseoftheechosignal.
When the signal isphase sensitive detected,thisalso attenuates
the echo height. Packer [33] showed thatinaCPMGpulse sequence
only the odd-numbered echoes are affected by flow by a factor
cos(vGvt2), where v isaconstantvelocity (inm/s)andthelinear
gradientGisinthedirectionofflow.
Severalmodifications ofthisbasicpulse sequence combinedwith
a linearmagnetic field gradient have beenproposed and employed
for the measurement ofself-diffusionorflow.Ofthesetheuseof
time-dependent field gradients has the advantage ofextendingthe
rangeofD-valuesaccessibletomeasurementtosmallervalues[32],
because itpermits theuseofhigh fieldgradientswithoutaffecting
the effective r.f. pulse length and the shape of the echo.This
concepthas alsobeenappliedto flowmeasurements[73].
Flowcanalso affecttheecho amplitude inaCPMGpulsesequence
without the use of amagnetic fieldgradient [34,35].Thiseffect
is simply explained by noting thatwhen the liquid isflowing,a
fraction of the molecules labelled by a \n pulse is replaced by
unlabelledmolecules.Theeffectofflowpatternandr.f. fieldinhomogeneityonthedecrease oftheechoamplitudehasbeeninvestigatedbyHemmingaetal[36].
ThenextSectionsrepresent ashortreviewofdiffusion andflow
measurements by NMR, with emphasis on the applicability of this
method tobiological systems,especiallyplants.
29
3.4 NMRDIFFUSIONMEASUREMENTS INBIOLOGICAL SAMPLES
Most of the reported self-diffusion coefficients ofwater in
biological sampleshavebeenmeasuredusingthetime-dependentmagnetic field gradient method (see Section 3.3) [32].Inplantand
animal tissues itwasobserved thatthemeasuredvalues ofDdepend
onthepulse spacing xwhich isindicative ofrestricted diffusion.
This can be explained if the diffusing molecules are notableto
travel for an appreciable distance inthetime-interval*Twithout
either meeting apartially reflecting barrier orventuring intoa
region of decreased mobility.Thisresults inabehaviour thatapproaches that of apure liquid forshortpulse spacing,while for
longer times the measuredvalue ofDdecreases [31,37]. Restricted
diffusion theory has been developed for a number of differently
shaped restrictions. Expressions have been derived for planar
[38,39,42], spherical [31,38], andcylindrical [38]impermeablewalls
and one-,two-,or three dimensional diffusion [40].Formulae for
geometrieswith anarbitrary diffusionbarrierpermeability aregiven
byTanner [41]andAnisimovet al. [43,44].Tanner'sequations contain
thedistancebetweenthebarriers asaparameter,whichcanbederived
from the NMR relaxation data. Inplant tissue the tonoplast, in
addition to the plasmalemma,were suggested aspossible barriers
causingrestricted diffusion.Thusmeasurements ofDmayyieldinformation about the cell size or thedistribution ofthesizeofthe
cells [41-45].
Intissuescontainingmanycomponents,theobservedNMRrelaxationbehaviour intime-dependent fieldgradientspin-echoexperimentsis
dependent on the fractionofeachtypeofspincontributing tothe
echo. Karger [46] has presented a theoretical investigation of a
twophase system.Hederived complicated expressions similar inform
toeqns. 3.15 and3.16,giveninSection3.2 formultisiterelaxation
including exchange.By aproper choice ofther.f. pulse-sequence
andmagnetic fieldgradientpulses [45]togetherwithotherexperimentalvariables suchasthepulse spacingtime x,themagnitude of
In reality, the use of the parameter T is not completely correct; further
details arebeyond the scope of this Section,and canbe found in ref.[41].
30
the magnetic f i e l d g r a d i e n t , the duration of t h i s g r a d i e n t and the
time between the g r a d i e n t pulses [45,47,48] the time-window of the
diffusion measurement can be s e l e c t e d , defining the phase or compartment which i s under o b s e r v a t i o n .
Data for the s e l f - d i f f u s i o n c o e f f i c i e n t measurements for several
p l a n t t i s s u e s and c e l l s are l i s t e d in Table 3 . 1 . Abetsedarskaya e t
a l . [52] have made c o r r e c t i o n s for the presence of vacuoles which
were suggested to occupy 30-50% of the i n t e r n a l c e l l volume and to
contain bulk water, t o obtain the value of D in protoplasm.
Table 3 . 1 . Values of T i , T 2 , D and c e l l s i z e for v a r i o u s p l a n t t i s s u e s and c e l l s
a t d i f f e r e n t resonance frequencies and t e m p e r a t u r e s .
Sample
MHz Temp
°C
Water
Maize leaves
Bean leaves
Bean leaves
Pea leaves
Maize roots
Apple fruit
Tobacco pith
Onion scales
Wheat caryopsis
embryo
Endosperm tissue
ofwheat grains
cells of lyophilically dried
yeasts cryptococci
wheat weevil
buds
yeast
yeast
Chlorella pyrenoidosa
a.
b.
c.
d.
20
20
20
20
20
20
20
20
25
25
25
25
25
26
26
-10
20
60
-10
22
20
20
20
20
20
25
25
26
20
25
Weight
% dry
matter
T2
ms
Ti
ms
2500
2500
9.5
96
110
250
300
9.1
133
885
10.5
2 .4-2.5
2.0
1.81
1.59
1.82
1.76
1.84
2.37.
0.15b
Dxl0 9 m 2 S - ! Cell,
d
inp roto- size
plasma
|Jm
Ref
49,50
1 82--1 60
1 56--1 20
1 49--1 12
43
111
0.17b
0.18
83
73
52
52
53
53
52
42
42
54
54
40
1.2
40
35
Dxl0 9 m 2 s" 1
in cell
0.25
0.84C
0.60c
0.68
1.03°
Corrected for presence of vacuoles
Nonfreezing water: 0.27 - 0.45 g/g dry matter
For the higher m o b i l i t y f r a c t i o n (85-90%). Less mobile f r a c t i o n
D: 0.2 - 1.0xl0~ 6 cm 2 /s (Hydration water: 0.2 - 0.6 g/g dry m a t t e r ) .
Inner diameter as measured by NMR d i f f u s i o n measurements.
0.6
44
5.3
53
52
42
52
31
The values ofD, as shown inTable3.1.,canbeuptoafactorof
16lessthanthevalue forpurewater,butthey aremostly comparable
to the values obtained in protein solutions and gels (D~ 1a
2x10~ 9m 2 . s - 1 ) . ThesmallerDvaluesofwater inprotein solutions
compared to that inpure water has been proposed [57] to be the
result of (a)an obstruction effect, causedbythelargeandless
mobile proteins, impeding the translational motion of the water
molecules, (b)the hydration effect,which mayeither increaseor
decreasethemotionofthehydrationwateroftheproteins,depending
ontheeffectoftheproteinonthewaterstructure inthevicinity
oftheprotein.Abetsedarskaya etal. [52]considered theobstruction
effect tobe thepredominantcauseofthedecreasedvaluesofDin
leavesofmaizeandbeanand inmaizeroots.
Inthe endosperm tissue ofwheat grains Callaghan et al.[40]
measured thevalueofD forwater asafunctionofthetissuewater
content. Assuming one-dimensional diffusioninarandomly oriented
arrayofcapillarieswithtransverse dimensions <100nmtheseauthors
find a single diffusioncoefficientateachwatercontent,varying
from 0.18 x 10~ 9 atthelowestto 1.2 x 10" 9 n^.s-1 atthehighest
water content, corresponding toanincrease ofthehydrationwater
filmthickness from~0.5 to~2.5 nm.ThesevaluesofD agree fairly
wellwiththoseofthenonfreezingwater fraction inonionscales
Table 3.2 Values of Tj, T 2 ,D,X and P, forvarious plantsamples.
Sample
Chlorella
vulgaris
Elodea leaves
Ivy bark
Mean
cell
size
(|Jm)
MHz Temp
°C
3.2 a
11
20
96x27 b
11
20
20
36a
18.5
T2
ms
54(intra)
14(extra),
^230(intra)
84(intra)
9(extra)
Ti
ms
205
45
182
28
DxlO 9 m 2 s- -1 T
a
ms
incell
< 1.7
0.76
1.43
a diameter
b length xdiameter,both in^m
c P,= diffvisionalwater permeability ofplasmalemma. P, isdefined by
P,= T ,(cm/s ,whereD isthe diffusion constant ofwater intheplasmalemma, and 8 is the thickness of theplasmalemma-membrane.
d T2 of extracellular water not quoted in reference55.
P
cm.sd !
Ref.
19-28
2.1xl0"3
48
18.2
3xl0"2
~3xl0-2
55
56
-40
32
and wheat caryopsis embryo [54],and with water in lyophilically
dried yeast cryptococci [44],but are a factor of 10higherthan
thevalueofDofthelessmobile (hydration)water fractionmeasured
byMiftakhutdinovaet al. [53]inwheatweevilbuds andyeast.
Theself-diffusion ofwater inthecell andthediffusionalwater
permeability (P^, see Table3.2.) oftheplasmalemmahasbeenmeasuredbyStoutetal.inanattempttoevaluatetheeffectofdifferen
freezing stresses aswell as drought andcoldhardinessofplants
[48,55,56,58].These authorshavecombined thetime-dependentmagnetic
field gradient method with atechniquetomeasureP,asappliedby
Conlon and Outhred [59]andFabry andEisenstadt [60]toredblood
cells. Inthis latterNMRtechnique,intracellularwater isdistinguished fromextracellularwaterbythedifference inT 2 whenT 2 of
the extracellular water is controlled by addedMnCl2 (seeSection
3.2, eqns. 3.14a-b). From suchmeasurements themeanresidence time
(T ) for water molecules within the cell has been determined
[48,55,56]sincemovementthroughthemembrane intothe extracellular
medium (which has a shorter T 2), influencesthemeasuredvalueof
T 2 (eqns.3.15 and 3.16 Section 3.2).Using x andtheknownmean
cell radius, the mean value ofP,canbecalculatedprovided that
x islimitedbyP,andnotby intracellular unstirred layers[61].
The results for three different plant samples arepresented in
Table3.2.
IntheabsenceofextracellularMn ,T 2 in2+
these samples reveals
thepresence ofatleasttwopopulations ofwater,eachwithdifferent
T 2 values.The fast relaxing population wasbelieved tobeextracellular water [48,56], whereas the longer T 2 was associatedwith
intracellularwater. Intracellular structurewas ignored. InElodea
leaves, however, diffusion measurements yielded ameandistanceof
13.5 pm over which thewater molecules could freelydiffuse.This
distance ismuch shorter than the average geometrical cell size.
This indicates internal cell structure,which canexplainthelow
value of D observed in cells of these leaves: these structures
restrict diffusion of the water molecules.Themagnitudes ofDin
Ivy bark and in Chlorella
vulgaris are of comparable size with
respecttothose inotherplantcells (Table3.1).
33
3.5 NMRFLOWMEASUREMENTS INBIOLOGICALSAMPLES.
NMR flow measurements include both steady state and pulse NMR
methods.Despite theearlyobservationsofNMR signals arising from
flowing water in aU-tube by Suryan [62],very little additional
informationwaspublisheduntil 1960.Theearlierworkwas reviewed
byZhernovoi andLatyshev [63],who alsoderivedtheoreticalexpressions relating signal amplitude and width toexperimental factors
involved inNMR experiments in flowing fluids, and who developed
several devicesofpractical interest. InamorerecentreviewJones
andChild [64]havediscussed theapplication ofNMR flowmeasurements
inindustrial,chemical,andphysiologicalsituations.
3. 5. 1 History
of in vivo blood flow
measurements
For biological samples,therecognition ofthepotential ofNMR
in biological and physiological flow measurements has stimulated
the study ofblood flow in vitro and in vivo. The earliest work
directed towardtheapplicationoftheNMRprinciples tononinvasive
in vivo measurementofblood flowwascarried outin1956byBowman
[65] (usingthemethod reportedby Suryan [62]),whoobserved alinear
relationduetosaturationeffectsbetween signal amplitude and flow
rate, inacontinuous B1 field.
Absolute flow rates havebeenmeasured usingmagnetic labelling
of nuclei by determining the "time-of-flight" of tagged nuclei
travelling thedistancebetweentwocoils,placed inastaticmagnetic
field [66].Many improvements andvariations onthistechniquehave
beenreported [63,65], yieldingvarioustagging techniques fornoninvasivemeasurementofblood flowinhumans[65].
The firstmeasurementofblood flow in vivo wasreportedby Singer
in1959 [67].Hemeasured theNMR signal amplitudesA f andA inthe
presence and absenceofflow,respectively, using Suryan'sexpression
[62]toobtaintheaverage linearvelocity offlow [68]
v=(Lo/T!)[(Af-A)/A]
(3.24)
34
where L is theeffective lengthoftube inther.f. field.Dueto
thecontribution oftissue signal tothetotalNMRsignal,however,
the method only yields relative blood flowrates.Recently,Radda
etal [99]described apulsedversionofSuryan'soriginal experiment
which satisfies the requirement that the flowmeasurementmustbe
independent on T 2•This requirement is duetothe factthatT 2 of
blood is determined by the oxygenation oftheblood [100]. Singer
also presented the theory ofthe "time-of-flight"method.Measurements ofblood flowvelocity inthemedianveinsofhuman subjects
by this tagging technique have been reported in1970byMorseand
Singer [69].NMRblood flowmeasurements arereviewedbyBattocletti
et al. [65,70]. Ithas been observed that the measurementofNMR
signal amplitude in time-of-flightmeasurements leadstoknowledge
ofvolume flowrate[65].
3. 5. 2 Pulsed
NMR flow
measurements
As stated in Section 3.3, pulsed NMR methods with andwithout
steady stateortime-dependentmagnetic fieldgradients,canbeused
to measure flow velocities.Hahn [71]was the first toemploy a
spin-echo technique in combination with amagnetic field gradient
tomeasurethemotionofseawater andderived theimportantresult
A*=yGvt2
where A* is the average phase shiftofthe fluid signalduetoan
average linear velocity v, G is themagnetic fieldgradientandx
is the time between the r.f. pulses.Grover and Singer [72]have
used a similar two-pulse method to determine thevelocitydistribution function, defined as the density of flowing protons per
velocity interval, characterizing the blood flow in a finger.
Following \n and n pulses separated intimebyx,theecho amplitude
A(2t)wasmeasured asafunctionof2x.Untilnow,noother spin-echo
NMR blood flow measurements have been reported intheliterature.
This may be due to the pulse sequencesused intheseexperiments,
all consisting of one ormore \ n pulses,creating acontribution
ofstationary tissuewater totheNMR signal (seealsoSection 3.5.3).
(3.25)
35
SeveralCPMGtypemultiple spin-echo sequenceshavebeenrecommended
forexamining theinfluenceofflowpatterns onthespin-echodecays.
Packer andhisgrouphavemadeaseriesofcareful experimental and
theoretical studies inthis area,usingboth static and time-dependent
magnetic fieldgradients [33,73,74].TheCPMGpulse sequence (Section
3.3)hasbeenreplacedbythesequenceVt -x-n(- x'-n) ,witht1
slightly larger than x, or by %7i (- x - n) ,bothofthesepulse
sequences minimize the effect of diffusion on the time dependent
NMR signal,whereas the effect of flowonthis signal canbemore
easily determined, as compared tothatintheCPMGmethod [33].In
the latter pulse sequence,plug flow forexampleproduces acosine
modulationofthespin-echo amplitude,whereastheeffectofdiffusion
isthesameasintheCPMGsequence (Section3.3).Ithasbeenshown
thatlaminar flowresults ina (sinx)/xmodulation [73,74].Garroway
[75]has used a %n-x- \n sequence incombinationwith alinear
magnetic field gradient to determine the spatial profile of the
velocity distribution forthelaminar flowofwater incircularand
rectangular pipes,fromtheshapeoftheFID (Section3.3) following
thesecondVtpulse.Animprovedmethod,usingtheVi [- x-Vi]
pulse sequence [75]allowed directmeasurementofthevelocity distribution.Thisauthorhas alsosuggested theuseofmultiple-pulse
line-narrowing techniques [76,77] (yielding an effective T 2 of
10-40ms)inordertomeasure flowofsolidse.g. inslurries.
Using a %n - x- n pulse sequence,Lucaset al. [78]havemeasured
flowprofiles ofpressure-driven flowinarectangular flowchannel,
and of convective flow, driven by thetransverse density gradient
due to a temperature gradientbetween two flatplates.Becauseof
the large value of T 2 of the fluid which these authors studied
- superfluid 3 He/ 4 Hemixtures -theywere abletodetect flowvelocities as small as 10 pm/s. Using aCPMG sequence in combination
with a linear magnetic field gradient, FukudaandHirai [79]were
abletoobtainthevelocityprofiles anddistributions ofPoiseuille
(laminar) and turbulant flow.These authors measured themagnetic
field gradient dependence of the first and the second spin-echo
amplitude, demonstrating that information on the velocity profile
can be obtained from the first spin-echo amplitude,whereas the
amplitude of the second echo depends onthevelocity fluctuations
[79]. A more detailed discussion on flow profiles is given in
Chapter4and5.
36
Hemminga et al. [36,80,96,98] have described twoNMR spin-echo
methods to detect flow velocities and profiles of flowing fluids
in the presence of stationary fluid. These methods are described
inthe following Section (3.5.3)
3.5.3 NMRflow measurements
in
plants
Inorder to measurewater flowrates inbiological objects such
asplant stems,the method must be sensitive to small flowrates
(1-30mm/s), andtobe abletodiscriminatebetweenasmall fraction
of flowing water (about2-10%)ofthetotalamountofwater inthe
samplevolume andalargeamountofstationarywater.BothNMRmethods
describedbyHemmingaetal.[36,80,96,98] candiscriminate between
flowingandstationarywater.The firstisadifferencemethodbased
on the CPMG pulse sequence and does not require amagnetic field
gradient [36].In the case of stationarywater,theechodecayin
theCPMGsequence isgivenby
S(t)=S Qexp(-t/T2)
(3.26)
where S is theamplitude ofthesignal attime t=o,which isproportional to the equilibrium magnitude of themagnetization (eqn.
3.3). Whenthe liquidmoveswithauniformvelocityv=v (plug flow),
eqn. 3.26 ismultipliedbyafactor1-fvt/l [35],giving
S(t)=S (l-fvt/1)exp(-t/T2) fortSl/v
(3.27a)
and
S(t)=S (l-f)exp(-t/T2) fort>1/v
(3.27b)
for a rectangularly shaped Bx r.f. field, where frepresents the
fraction of flowing waterw.r.t.thetotal and1the lengthofthe
r.f. coil. After t > 1/v, thevolumeofflowingwater inther.f.
coil has been completely replaced andtheechodecay isdetermined
only by the stationary water fraction. The contribution of the
stationarywater totheechodecay S(t)ineqn.3.27aand3.27bcan
beremovedby subtracting twoechodecays,onewithv f o,theother
withv =o;thedifference signal isgivenby
37
AS(t) = fSQ (vt/1) exp(-t/T 2 )
for t g 1/v
(3.28a)
and
AS(t) = fSQ exp(-t/T 2 )
for t > 1/v
(3.28b)
Difference decaycurveshavealsobeenderived forlaminar flowand
foraGaussianB!r.f. field.
Theapplicationofthisspin-echo differencemethod formeasurements of flow rates in the plantstem isofcourse limitedbythe
fact that an echo-decay atv=0mustbeavailable asareference.
Theauthors [36]have suggested thatinthedarkthesapstreamhas
almost stopped and thusthedecaycurveatv=0canbedetermined
andstored insome form.However,inChapter 5itisshownthatthe
Z
/
l"/2 i - i fl\
X
B,(x)
.B„
X
*
j
1 |
JUT± X _ ^ _ ^ '
I
'
|
I v >»-si-*.-»* f-T It x- pulse
l
l
X(direction of flow)
Fig. 6 Basic principles of the n-(-T-n) pulse method for flowmeasurements:
n
water molecules receive r.f. pulses with a pulse angle gradually increasing from 0 to 71,as the distance from the center of the r.f. coil
increases from infinity to zero, and simultaneously move along the
magnetic field gradient G.
38
situation v = ocannotbeeasily realized -eveninthedark-and
inChapter 7thatT 2 ofstationarywater changeswithwatercontent
andwith flowvelocity.Thisrenders thedifferencemethod impractical
forflowmeasurements instemsofintactplants.
The second method reported by Hemminga et al. [80]isapulsed
NMR method, based on a sequence ofequidistantnpulses incombination with a linear magnetic field gradient.As showninChapter
4, the NMR signalsof flowingwater aretheresultofthemovement
ofwaterintother.f. coil fromaregionoutside it.Thusthewater
molecules receive r.f.pulseswith apulse anglegradually increasing
from 0 to n, as the distance fromthecenterofther.f. coilincreases from infinity tozero.Thisoccurs inreverse attheother
side of the coil (Fig. 6 ) .Simultaneously, movement of thewater
molecules alongthemagnetic fieldgradientGproduces aphase shift
A* of the echoes with respect to the rotating frame ofreference
[31,33,seealsoSection 3.3].Usingeqn.3.25 andnotingthatvi=
Ax, where Ax isthedistancetravelled duringtime tinthedirectionof5 (Fig.6 ) ,weobtain forthephase shiftA*:
A*=vGAxT
(3.29)
For flowingwaterbotheffectsyield asignal S(t)thatisincreasing
intime,andismodulatedbyaperiodical functionwith afrequency
directly proportional to the mean flow velocity v. At resonance,
stationarywateryields zerosignal (base-line), andthemethodthereforediscriminates flowingwater from stationarywater (seeChapter
4).
Inaddition,themethod allowsdetermination of flow inasingle
experiment. These features makethemethod attractive forstudyof
biological samples,asshown forplantstems (Chapter 5and 6). Linear
flowvelocity aswell asvolume flowratecanbedetermined simultaneously by this method (Chapter 4), yielding an estimate of the
effective areaofthetransportvessels andofthespin-spinrelaxation time T 2 ofwater contained by these vessels (Chapters4,5
and 6). The limitations ofthismethod asapplied tomeasurementof
water flowinplantstemsarediscussed inChapter5.
39
3.6 T 2 ANDWATER CONTENT
Although there is no straightforward theoretical model forthe
interpretation oftheobservedNMR relaxationbehaviour (Section3.2),
many authorshavedemonstrated arelationship betweenT x ,T 2 andwater
contentinbiological objects.Daszkiewiczetal. [81]werethefirst
toshowthattheNMRrelaxationratesdependonprotein concentration
inproteinsolutions,andderived therelation
Tj-1=Ti~1 +kxC
(3.30)
forprotein concentrations less than 100mg/ml, where Tx isthe
spin-lattice relaxation time of pure water, kx an experimental
constant and C the concentration ofproteining/g H 2 0.A similar
relationship has been shown for T 2 [81].Cooke andWien [82]have
shownthatthesameresultisobtained formuscle tissueandsolutions
ofmuscle proteins. They interpreted their results in terms ofa
fast-exchange-two-state
(FETS)model,including fastexchangebetween
abulkwater fractionanda-minor -water fractionboundtomacromolecules. This results in a single experimental relaxation time
which is theweighted average of thetwoseparatetimesT l f (free
>/ater)andTx, (boundwater)asgiveninegn.3.15.The relationship
DetweenT t , T 2 and water content hasbeendemonstrated inseveral
Diologicalobjects,e.g.,muscle andbraintissue [83-85], mammalian
tissue and cells [86,87], normal and cryolesion rat liver tissue
[88], andinnormal andmalignanttissues [e.g.89,90].These authors
lavealsoexplained thisrelationship intermsoftheFETS-model.
A more general expression for the weighted average relaxation
rate should include theresidence time x, ofaprotonofthewater
nolecule,ortheresidence timeofthewholewater-molecule,whicheverisshorter,inthehydration layerofthemacromolecule,resultingintheexpression (seealsoeqn. 3.16):
T r 1 -Pf Tif1 +Pb(Tlb+T b )~ 1
(3.31)
jherethesymbolshavethesamemeaning asineqn.3.15, andt b >T l b .
40
Underphysiological conditions,themeantimebetweenprotonjumps
is shorter than ~2xl0-3s [91].Thisvalueoft b islessthanthat
found forTlfc)inalbinomousemuscle andliver [83]andinsolutions
of hen egg albumin [83],inwhichTi. ~7xl0 -2 s, illustrating that
x b may be neglected in eqn.3.31. InskeletalmuscleHazlewood et
al. [19]estimated thevalue ofT l h tobe~0.42 ms, comparableto
orlessthanthatof T,.
Inthosecaseswheretheroleofintermolecular dipolar relaxation
cannot be neglected in the proton relaxation of the bound water
molecules, the total proton relaxation rate oftheboundwateris
the sum of the intra- and intermolecular dipolar relaxationrates
[8].
Beall et al. [92],studying 71 andwatercontentasafunction
of the growth cycle ofHela cells,demonstrated that during the
mitosis andsynthesisperiodofDNATi isrelated tothewaterconteni
ofthecell.Duringthetransition fromtheDNA synthesisperiodto
the post-DNA synthesis period, however, significant changes inTx
wereobserved,whichwere independentofchanges inthewater content
Samuilovetal [93]observedthatingerminatingRussianbeanseeds
Tx increases with increasingwatercontentinthecourseofwateruptakebytheseeds.Fromthedependence of Tx ontheratioofweight
drymatterperweightwatertheseauthors demonstrated theexistence
ofthreesuddenchanges intherelationshipbetweenT x andthisratio
enablingthem todiscriminate notlessthanfourwater fractions in
theseeds,differingwithrespecttotheirphysicalproperties (e.g.
relaxation rates) and, accordingly, with respect tothenatureof
theirinteractionwithdifferentsurfaces andcomponents ofthecellstructure [93].
InthecrownofwinterwheatcerealsGustaetal.[94,95]demonstrated a linear relationship between the long component of the
transverse relaxation rate T 2 - 1 and the water content. From this
relationship theseauthors calculatedT l f values forthebulkwater,
whichwere lower forcoldacclimatisedwheatgenotypesthanforless
hardygenotypes.
Therelationship betweenT t - 1 andwatercontent (eqn.3.15), and
the effect of Li ,K and Cl~ionsonthisrelationship, inroots
of Zea mays hasbeenstudiedbyBacicetal [16].Itwas foundthat
aminimum inthemagnitudeof^ versusexternal saltconcentration
existsat~ 10~ 3 M,whichcorrespondswith aminimum inwatercontent
41
The changes inTi reflecta)theosmoticeffectofionsonP f ,the
freewater fraction,andb)thedirecteffectofionsonmacromolecular
hydration shells and the disordering of the freewater structure
([16], seealso [17]).
Hsi et al. [97] studied T 2 inmilledNorthernwhite-cedarwood
chips (Thuja occidentalis
L). Atwatercontentsbelow 0.38 gofwater
pergramofdrywood,no freezingeffectonT 2 isdetected.Atlarger
watercontentsthespin-spinrelaxation isfoundtobenon-exponential.
This was explained by assumingthatatwatercontents above0.38 g
ofwater per gram of dry wood, additional water only increasesa
second slowlyrelaxingwatermoleculepopulation,whichwas associated
withbulkwater,theprotonsofwhichexhibitrapidexchangewitha
few surface-sites with very efficient relaxation [97].Using a
different approachbyemploying adiffusionmodel,includingmagnetic
sinks, Brownstein [26]wasabletoexplainthemeasurementsofHsi
et al. [97].Thismodelessentially involvestworegions ofwater,
a surface layer ofmacromolecules i 0.26 pmthick,withaseverely
reduced diffusion constant forwater (D< 2.7*10 -12 m 2 . s - 1 ) , and
theadditionalwateroutsidethislayer.
InChapter 7ofthisThesistheresultsofthestudyoftheeffect
ofMn
Mn2+(a(a
paramagnetic
paramagneticion)
ion)
on
on
the
the
relationship
relatic
betweenT 2 _ 1 and
watercontentinwheatleavesarepresented.
42
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45
4
FLOW MEASUREMENTS IN MODEL SYSTEMS
4.1 INTRODUCTION
Several indirectmethodshavebeenusedtostudywater transport
inplants by measuring themeanlinear flowvelocity orthevolume
flowrate ofwater in the vascular systemofplantstems [1].None
ofthesemethodsdetects themovementofwater itself,however,and
many areinvasive.
Nuclear magnetic resonance (NMR) is a suitable technique to
study liquid flow [2-7]. Inmost oftheseNMRmethods,stationary
liquid -suchasnon-flowingwater inthetissueoftheplantstemgives rise to a large NMR signal inadditiontothesignaldueto
flowing liquid. A recent paper [8] describes a spin-echo NMR
method, based on apulse sequence of equidistant n pulses and a
linearmagnetic fieldgradientinthedirectionofflow.Thismethod
permits the detection of flowvelocities of flowing fluid inthe
presence of stationary fluid, and NMR signals are generated, the
shapeofwhichiscorrelated tothe flowvelocity and flowprofile.
This Chapter presents a semi-empirical formalism ofthispulse
NMR method, resulting inananalytical expression fortheshapeof
thetimedependence oftheNMR signal-amplitude, allowing astraightforward simulation of the experimental signals ofplug flow and
laminar flow. In this way insight is gained in theeffectofthe
experimentalparameters onthesignal shape.Thishasnotbeenpossible using the formalism given by Hemminga and de Jager [8].In
addition,we present adetaileddiscussionofthispulsemethodas
applied toflowinplantstemsandbased onmeasurements incapillary
model systems, simulating the plant stem. It is shown that from
these flowmeasurements themeanlinear flowvelocityv,thevolume
flowrateQ,theeffectivecross-sectionofthecapillaryA,andthe
spin-spinrelaxationtimeT 2 ofthe flowingwatercanbedetermined.
4.2 THEORY
The response of a spin system, flowing in a r.f.Bj-fieldand
along alinearmagnetic fieldgradient,toasequenceofequidistant,
46
identical pulses has been treated by Hemminga and de Jager[8].
Because ofthecomplexity ofthetheory theshapeoftheNMR signals
couldnotbeexpressed inaclosed analytical form andthishasbeen
obtained by these authors using computer simulations.With this
approachdetermination oftheeffectoftheparameters ofthemethod
on the size andshapeofthesignal andthepresenceof additional
informationhidden inthesignals isatediousmatter.
After abrief outline oftheir results,wepresenthereasemiempirical approach, resulting in an analytical expression, which
can be straightforwardly applied to experimental NMR signals of
flowingfluids.
4.2.1
System
description
Consider a system of nuclei (I - h) in a magnetic field B
directed along thezaxisofalaboratory coordinate system {x,y,z};
\
t
/
N
/
B, \
Fig. 1 A schematic representation of acapillary system and sample coil within
the magnetic field. The fluid in the inner tube is flowing with flow
velocity v.The r.f. coil is indicated by C,x,y and zare the axes ofa
right-handed laboratory coordinate system.
47
a linear magnetic gradient G (gauss/m)is imposed on B ,along
y, so that B (y)=B +yG (Fig.1 ) .Letthenucleimove inthe+y
direction with auniformvelocityv (mm/s),whichisthe situation
forplugflow.
The sample is contained inatubethatextends alongtheyaxis
through the transmitter/receiver coilofapulsedNMR spectrometer
(Fig.1 ) .Theaxisofthiscoilcoincideswiththeyaxis.
Themotion of the spinmagnetization is considered in aframe
{x',y',z'} rotating about theB (z)directionwiththeLarmor frequency UD.Itisassumed thatoff-resonance effects ontheeffective
r.f. field can be ignored, so thatitisequaltoBi anddirected
alongthex' axis (seeSection4.3.1). LetthemeanLarmor frequency
ofallnucleibew =-vBo,where
8 B =B (y=0).
o
o
zw '
A sequence of equidistantr.f.pulses (timedurationt ,period
x, t>>t )is applied to the sample.Duringthepulse sequencethe
nucleimovethroughtheBx field andalongthelinear field gradient
G.
To describe the effect of flow, thenuclei inthe fluidsample
are considered tobe divided into small equal groups alongthey
axis. The position of such a groupofnuclei atthenthpulse (at
timet=nx)isthengivenby
y =y +vnx
n
(4.1)
J
o
where y is theposition of the group at the start of thepulse
sequence at t-0. Intherotating frame,theprecession frequency
ofthemagnetizationvectorMofsuchagroup isthengivenby
u)n=YGyn
(4-2)
Y is the gyromagnetic ratio.The precession angle in a time dt
betweenthepulses isd*=wdt.This isillustrated inFig.2.
Between the (n-l)th and nth pulse the precession angle A* n
becomes
A*
nt
= J
w(t)dt=YGyT+!j(2n-l)YGvT2
nX
(n-l)t
°
(4.3)
48
F i g . 2 Schematic r e p r e s e n t a t i o n of the magnetization Mof a group of n u c l e i a t
time dt a f t e r a (^7l) , p u l s e , as viewed along the y a x i s . Each group has a
p r e c e s s i o n frequency, which i s a function of the p o s i t i o n on the y a x i s ,
due t o t h e magnetic f i e l d g r a d i e n t G = dB / d y . The r o t a t i n g frame { x ' , y ' , z ' }
r o t a t e s with Larmor frequency w = -yB .
(Note t h a t to reach eqn. 4.3 we have replaced nt by t in eqn. 4 . 1
and made use of eqn. 4 . 2 , whereas in eqn. 4 . 1 we have used the
model of spin isochromatic groups with f i n i t e thickness ( V T ) , assuming
t h a t the f i e l d g r a d i e n t can be considered to vary stepwise, r e s u l t i n g
i n AA = w x . However, the difference between these two approaches
i s VyGvi 2 , W hich i s n e g l i g i b l e with r e s p e c t t o nyGvt2 for n>>l.
Throughout t h i s Chapter we w i l l use eqn. 4 . 3 . In view of t h i s
approximation, we may a l s o use the model of spin isochromatic groups).
Before we can apply these concepts to the case in hand, we have
t o make an a d d i t i o n a l assumption. I t i s assumed t h a t the nuclei of
the flowing f l u i d have experienced the s t a t i c f i e l d B long enough
49
to have attained Boltzmann equilibrium before entering the transmitter/
receiver coil, so that at the beginning of the pulse sequence the
total magnetization vector of all groups of nuclei is M , directed
along the z' axis.
4.2.2
Motion of the magnetization
in the rotating
frame.
Hemminga and de Jager [8] noted that the nth pulse of the
sequence rotates the magnetization of an isochromatic group (M) about
the x' axis by an angle a , defined as
% = VBi(yn)tp
(4.4)
where B1(y ) is the spatial distribution of the B x field in the y
n
-»+.
direction. The magnetization immediately after the nth pulse M is
related to the magnetization before the pulse M~ by the rotation
matrix R .(a
):
x 1v n'
M +=R ,(a)M"
n
x n n
(4.5)
Between pulses, the magnetization freely precesses about the z axis
and the magnetization at the beginning of the (n+ l)th pulse is
given by
M~+J={1-exp(-x/T1)}Mo+Rz,(A*n)S(x,T1,T2)Mn,
(4.6)
R ,represents a rotation about the z' axis and S ( T , T 1 , T 2 ) is a diagonal
matrix with elements
Sx,x,=S,,=exp(-T/T2)andSz,z,=exp(-x/T1),
where T t and T 2 are the spin-lattice and spin-spin relaxation times
respectively.
50
When t<<T2, only the integral A , ofthex1 componentofthe
magnetization between the nth and (n+l)th pulses is relevant and
thisisgivenby
A , = sinA<|> M+, /A<|> + (1-cosAd) ) M+, /Ad)
T
T
x ,n
n x ' , n Yn
n y' ,n Yn
A,
isnegligible with respect to A ,
jf zII
(t«T2)
v
2
when x<<T2. Theactual
X f11
NMRsignalS isderivedbymultiplying eqn.4.7 bythe sensitivity
of the r.f. coil, which is givenbyBx(y ),andthensummingover
allgroupsofnuclei alongtheyaxis:
+00
-00
'
wherey isafunctionoft=nx asdefined ineqn.4.1.
It is notpossible to obtain eqns.4.1 to4.8 inaclosed form
andthusS hasbeencalculated numerically fordifferentr.f. field
distributions and flow profiles [8].These calculations are very
timeconsuming,however.
4.2.3
n pulses
Untilnowtherotationangleofthepulses inthepulse sequence
was ofminor importance for the theoretical description.Fromnow
onwe restrict our treatment to the case of apulse sequence of
equidistant n pulses, alsoassuming t<<T2.Thisassumptionisvery
reasonable, since for our measurements x=1.6ms andcurve fitting
hasbeencarriedoutforT2S200ms.
Assuming thatwe have aGaussian shaped distribution oftheBa
field, B x (y)is then given by B t (y)=BjCO)exp(-2y 2 /L 2 ),whereL
is the distance between the inflection pointsofthe distribution
andBi(0)=7i/yt.
At t=0 the firstpulse rotates the magnetization M ofanisochromaticgroup atpositiony by anangle a - 7i-exp(-2y?/L2). This
results in a component A in the x',y'-plane given by
A=M sin{n'exp(-2y2/L2)}, directed alongthey' axis.
(4.7)
v
'
51
During the period t=0-»t=x this group ofnuclei gainsaphase
angleA<|> withrespecttothey'axisasgivenbyeqn.4.3 withn=l:
A<t>T = YGyoT + i^Gvx 2
(4.9)
At t=t the component of the magnetization ofthisgroupofnuclei
alongthex'axisA t(x)is
A , ( T ) = M sin{n-exp(-2y2/L2)} sin(A(|))
(4.10)
Thetotalx'componentofthemagnetization is foundby summingthe
A ,of two isochromatic groups which arepositioned att=0symmetrically around y=0,andintegrating overy from 0to»,yielding
S ,(x)oc J" sin{n-exp(-2y2/L2)}sin(^YGvt2)cos(^Gy x)dy
o
(4.11)
Attimet=t theisochromatic group ofspinsreceives asecondpulse,
which now equals a =n•exp[-2(y +vx) 2 /L 2 ]. This pulse rotatesthe
magnetization of the isochromatic group by a around the x'axis,
leaving A ,unaffected butchanging thetotalmagnetization inthe
x',y'-planebyrotating thez'andy' components.Attempts toevaluate
thisprocess completely inordertoobtainaclosed expressionhave
beenunsuccessful.Bymaking someplausible assumptions ontheshape
ofther.f. field B ^ y ) , wemayobtainanapproximate closedexpression forS,'
4.2.4
A semi-empirical
approach
Ithas been stated by Hemminga and de Jager [8] that theNMR
signal of flowing fluidwillmainly arise fromtheregionofyvalues
whereBi(y)corresponds to \n to \n pulses.Letustherefore assume
thatwe can represent the distribution B ^ y ) as a rectanglewith
length 1, corresponding to n pulses for|y|<Hl;atthe fallingand
rising edges of this r.f. field at|y|=41 a = %n(Bx = H B ^ O ) ) ;
outside thecoilB,vanishes.This isshowninFig.3.
52
TT -
TT .
0'
«1
'/2l
1
T~ 1 —
fcl
Fig. 3 Distribution of the r.f. field of the transmitter/receiver coil along
axi
the y axis:
for -^l<y<^l a(= VBit )=n, for |y|=Sjl a=^n and for
M>hl a=o.
We define the magnetization of an isochromatic group by
M = M -vx/1
o
(4.12)
assuming that after n=1/vx pulses the flowing fluid inthecoil
(magnetizationM )hasbeencompletely refreshed.Thisalso implies
thattherearen=1/vtdifferent isochromatic groups inthecoil.
Now we can follow the signal that is generated by the pulse
sequence while fluid moves intotheinsideofther.f. coil, along
themagnetic fieldgradient.Atthe firstpulse (t=0)theVipulses
at the edges of the Bx fieldrotatethemagnetizationoftheisochromatic groupsMat|y|= \1.
The isochromatic group aty=%1movesoutofther.f. coiland
itsmagnetization isnotobserved.The isochromatic group aty=-^1
moves intothecoilandduringtheperiod t=0-»t=t itgainsaphase
angle A<|> with respect to the y' axis as givenbyegn.4.10 with
y = -HI, resulting inanx'component attimet=x:A ,(t)=MsinAt(>
O
Attimet=t this isochromatic group ofspinsreceives asecondpulse,
whichnowequals a n pulse,rotatingthemagnetizationofthisgroup
bynaroundthex' axis, i.e.
X
T
53
<|>T+= n-A$x
(4.13)
where ty. isthetotal phase angle atagiven time tand x thetime
immediately following the second pulse. (Allpulses areassumed to
be ofnegligible duration). During theperiod T->2T the isochromatic
group ofnuclei gains aphase angle A(j)_ which isgiven by egn. 4.3
with n=2:A<|>?= yGy x+jyGvx2
. This results in anetgain ofphase
at t=2i of <|>„= &$7 +<)) = n+yGvt 2.The third pulse at t=2t also
rotates themagnetization ofthespin isochromatic group by n around
the x 1 axis, resulting in
<t>2T+ = n-<|>2t = -VGVT 2
(4.14)
In general itcanbe shown that
(()
= 71+^vGvT2
(n even)
(4.15a)
and
*(n+l)t = ^
YGVT2+
^GV
(4
-15b)
Now, ifphase sensitive detection isused andthedetector isadjusted formaximum signal along the x 1 axis the x'-component ofthe
magnetization of this isochromatic group of nuclei at t=nx is
proportional to
A ,(nx)=M sind)
x
(neven orodd)
(4.16)
nT
Alas, attime t=t a second isochromatic group arrives aty=-ijl
and receives theVt part ofthepulse. Inaddition, the magnetization
inthex',y'plane is attenuated bythespin-spin relaxation characterized byT 2 • Sothetotal signal detected att=2t, S ( 2 T ) , is given
by
S ( 2 l ) = M [sin<|> e " T / T 2 + sin<|>
e"2l/T2]
(4.17)
54
Continuing this process, at time t=2x a third isochromatic group
arrives aty= -%1, receives the Vt part of the pulse andstarts
relaxationinthex',y'plane,andsoon,resultingin
nX/T2
S(nx)= I A,(nx),forn l-r
e"
,
x
m=l
(4.18)
vt
A f t e r n > 1/VT t h e s i g n a l r e a c h e s a s t e a d y s t a t e . The sum i n
e g n . 4 . 1 8 can be g i v e n by a c l o s e d e x p r e s s i o n u s i n g e q n s . 4 . 1 5 and
4 . 1 6 , by r e p l a c i n g nt by t ' , i n t e g r a t i n g o v e r t ' from 0 t o t f o r
t h e even and uneven p h a s e a n g l e s and d i v i d i n g by x, r e s u l t i n g f o r
t % 1/v i n
S(t) = j ^ -
[{cos(|> o -l}{e" t/T2 0 | sin<(>(t) - ^Gvx cos<t>(t)) + ^yGvx}
- sin<|> { e " t / T 2 ( - i cos(|)(t) + VtfGvT sin(|»(t)) + | }]
0
*
2
(4.19a)
*2
'
where S is the signal detected from the magnetization M,
C=2{(l/T2)+2(1-5yGvt)2},<t>o=HvGvi2+HvGxl and <|)(t)=V*Gvxt.Att> 1/v
the flowing fluid has been refreshed in the coil and the signal
reaches asteady state,which isgivenby
S
E
=
S
V
1/ T
1
r r [{co8«|» o -l}{e" 1/vl2 ( - i sin<l>E - ^yGvx c o s ^ ) + ^Gvt}
- sincj) { e " 1 / v T 2 ( - i cos«t>r + VyGvx sirntO + | }]
O
12
£>
t
(4.19b)
12
w i t h <t>F = HvGlx . For T2=°° e q n s . 4 . 1 9 r e d u c e t o
S(t) = S (vGxl) -1 [cos<|> + cos(|)(t) - cos{(|> - <)>(t)} - 1] , t i S£
= S Q (YGX1)- 1 [cos(t)o + cos0E - cos{<t>o - ^} - 1] , t > i
(4.20a)
(4.20b)
Sofarwehaveconsidered thesignal generatedby apulse sequence
of equidistant n pulses from fluid thatmoves into arectangular
r.f. field along alinearmagnetic field.Bydoing sono signalis
observed formthe fluid already inthecoil att=0.
55
However, as canbe shown from eqn.4.11,thisdoesnotcorrespond totheexperimental situation,where the Bx-field distribution
isnon-rectangular.Then fluidpresentinthecoil att=0givesrise
toasignal.This isequivalenttoassuming thatthesamplecontains
a magnetization P(//y1)at t=0 of the isochromatic groups at
-Hl<y<isl,inthepresenceofarectangular Bt-field, asusedbefore.
Following the above description for the fluidthatmoves intothe
B!-field it canbe easily shown that the signal generatedbythe
isochromatic groups situated inthecoil att=0justbeforeanodd
numberedpulse,isgivenby
E{(2n+l)x)=-Eo(l- ~^)
o T
sin(nyGvT2)e
-2nx/T2
,for(2n+l) i ±
,
(4.21a)
and
E{(2n+l)x}= 0
,for(2n+l)>i
(4.21b)
whereE isthesignalduetoP .Notingthatthesignal duetothe
even numbered pulses (E(2nx))has a similar shape to the signal
E{(2n+l)t}, we can replace (2n+l)tbytineqn.4.21 andobtainan
approximate expression forthetotal signal generated byplugflow:
Splug(t)=S(t)+E(t)
(4.22)
where S(t)isgivenbyeqn.4.19 andE(t)byeqn.4.21.Theamplituderatio of E(t) and S(t), E/S isanadjustableparameterbetween0
and 1.Wewillusethisparameter forcurve-fitting.
Fig.4A and4Bshowscalculated S(t)andE(t)signals,resp.,fora
particular setofG, T,T 2 and1andvariousvalues ofv,using4.22.
4. 2.5 Laminar
flow
Forlaminar flow,theliquidvelocityvvarieswiththedistance
r fromthetubeaxisasgivenby
v(r)=2v(l-r 2 /R 2 ),
where v is the mean liquid velocity andRisthetuberadius.The
amountoffluidwithvelocityv(r)lyingbetweenrandr+dris27trdr.
(4.23)
56
S(l) <arb.units)
I ECt) (
F i g . 4 Calculated NMR s i g n a l s S ( t ) (A) andE ( t ) (B) of plug flow in a r e c t a n g u l a r
Bi-field distribution,
c a l c u l a t e d with eqns. 4.19a,b and 4 . 2 1 a , b ,
r e s p . 1 = 15 mm,G= 20 G/m,T2 = 2.4 s and t = 1.6 ms. The values of v
( i n mm/s) a r e : 30 ( a ) , 10 ( b ) , 5 (c) and 2( d ) .
The s i g n a l for laminar flow can now be c a l c u l a t e d from eqn. 4.22
using
lam(t)
R
= 2(R)-2 J S p l u g { t , v ( r ) } rdr = (2v)-* J
2v
plug
( t , v ) dv , for t g
2v
(4.24a)
57
At t i l/2v the flowing fluid with higher velocity components
hasbeenrefreshed inthecoilandthesignal fromthis fluidreaches
the steady state asgivenby eqns.4.19b and4.21b. Attimetthis
holds for v between 2v and 1/t.Therefore at t>l/2v thesignal
forlaminar flowmustbecalculated using
S
lam(t)
= (2
^rl
[
1/t
•<" S p l u g ( t ' v )
2v
dv +
J"
S
(v) dv]
E
f0r t >
k
(A 24b)
-
For T 2 =a> and P =0 e q n . 4 . 2 4 a becomes
S
lam(t)
=
S (vGTl)- 1 [(cos* - 1)(1 - s i n $ ( t ) / $ ( t ) ) - sin* sin 2 *j>(t)A0(t)],
for t g | v
(4.25)
where (ji(t)=yGvTt.A comparison between eqns. 4.19a and4.25 shows
that for plug flow we have sineandcosineterms,whereas laminar
flow gives 1-sinx/x and sin2x/x terms.Thesameconclusionholds
for12=°°andP-^O.Thus, ingeneral,weexpectS, u a (t)andS-, (t)
tohavedifferentshapes.
4.2.6
Determination
of the flow
velocity
To obtain the flow velocity from thesignalsofflowing liquid
using a sequence of n pulses two methods have been suggested by
HemmingaanddeJager [8]:(i)fromananalysis oftheinitial slope
ofthe (spp)0# whichhasbeenshownexperimentally tobeproportional
tov (orv inthecaseoflaminar flow); (ii)ifthesignalreaches
amaximum orminimum, thepositiont
ofthatextremumhasempiricr
max
_
allybeen showntobe inverselyproportional tov (or v ) .
For
plug flowtherelationship betweenv and (<rr)0andbetweenv
1
andt - max
canbeeasily obtained forthecasewhere the contribution
of E(t) to the total signal is small (as fora n pulse sequence)
usingeqn.4.19a, yielding
(|f)o= -hSo sin4ov/1
(4.26)
58
fortheinitialslope,
and,via^r=o fort=.
31
max
v= (yGt)- 1 (<(> ± n) t" 1
1
T
o
max
(4.27)
To obtain eqn. 4.26 ithas been assumed that T 2 hasnoeffecton
(g+r)0- Eqn. 4.27 shows that thepositionoftheextremumdoesnot
depend on T 2 . The small contribution of E(t) to thetotalsignal
however introduces aT 2 dependence onthepositionoftheextremum
ofthesignal (seeSection4.2.7).Whether thisextremum isamaximum
oraminimum dependsonthedirectionof5 andv.Ascanbeverified
fromeqns.4.19 and4.21 thesignal alterssignwhenvorGreverses
direction. (Note that 0 isG dependent and sin* becomes-sini))
when G alters sign). This illustrates thatthemethod canalsobe
usedtoreveal the direction
offlow.
For laminar flow (gr) Q l a m can be found using eqns. 4.24aand
4.19, resultingin
(Mr) n
= ~\ S sin(t) v/1
9t o,lam
o
o
(4.28)
whereas the relationship between v and t _ 1 can only beobtained
r
J
max
numerically. Comparison of eqns. 4.26 and 4.28 shows that for a
system undergoing laminar flow with an average velocity equal to
thatofplug flow,theinitial slopeofthesignal isequaltothat
observedwithplugflow.
4. 2. 7 Determination
of T2 and volume
flowrate
The effect of spin-spin relaxation on the signal from flowing
liquid canbeexplainedbyconsideringthetwoseparate contributions
tothesignal,i.e. S(t)and E(t). Ashasbeenpointed outinSection
4.2.4 themagnetization oftheisochromaticgroups flowing intothe
r.f. coil starts relaxation in the x',y'plane atthemomentthat
suchaspingroup reachesy= -%1. Owingtothismechanism S(t)decays
not as a simple exponential in time,butasasumofexponentials
(see eqn. 4.18) which start at different times,resulting in an
59
effectivedecaytimethatislongerthanT 2 .Thesecond contribution
tothe signal,fromtheliquid thatwasalready situated inthecoil
at t=0,has been assumed to be generated at t=0andtodecayexponentiallywithT 2 .
Assuming againthatthecontributionofEft)tothetotalsignal
issmall forplug flowitcanbe shown fromeqns.4.19 and4.27 that
thespin-spin relaxationtimeT 2 canbe found from
ln[3(S(t )t )/3t ]=lnDi-t /T2,
max max
max
(4.29)
max z '
whereD1=So(vGxl)1 D Q {(cos<)>0-l)sinDQ -sin<t>0cosDo},DQ=H(<|>0±7i)and
S(t )is the height of the signal att m ,„.This isthebasisof
the determination of thespin-spinrelaxationtimeT 2 fromtheNMR
signals offlowingwater.
The signal S detected from the total magnetization M inthe
r.f. coil is directly proportional to theamountofflowingwater
in the coil V. This amount canbedeterminedbyextrapolating the
ln[3(S(t
)t )/3t ]vs.t
curvetot
= 0 (eqn.
4.29).V
Lxv
v
max'max" maxJ
max
max
^
mustbecalibrated forgivenvaluesofGandx (seeDx ineqn.4.29).
Thevolume flowrateQcannowbecalculated from
Q=W / L e f £ ,
where L
is theeffective r.f.coil length.L cc doesnotneceseff
^
eff
sarily equal 1, owing to the difference in the shapeofther.f.
field distribution in theory and practice. It isnoticeable that
V/L f f equalsthecross-sectional areaAofthecapillary.
For laminar flow itisimpossible toobtain fromeqns.4.24expressions similar to eqns.4.29 and4.30.However,empirically,T 2
canbeobtained usingthesameprocedure asforplugflow.
cc:
4.3 SOMECOMMENTSONTHE SEMI-EMPIRICALAPPROACH
4. 3.1
Approximations
In the semi-empirical formalism developed in Section 4.2.4 we
have made the following approximations: (i)ther.f. fielddistri-
(4.30)
60
butionisassumedtoberectangular (seeFig.3 ) ;(ii)off-resonance
effectsontheeffective r.f. fieldBf f havebeenneglected; (iii)
thevariationofthemagnetization duringthepulse sequencehasbeen
followed by sampling thesignal attimet=nt, justbefore apulse;
(iiii) the effects of spin-lattice relaxation and diffusion have
beenneglected.
4.3.1.1 Distributionofther.f. field
The actual r.f. field distribution depends on the geometry of
thetransmitter/receiver coil inuse:asolenoidtypecoildoesnot
produce the same distribution as aHelmholtztype.TheirBx-field
distributions will differ, inparticular with respecttothefull
width athalfmaximum (L).Inour model this isaccounted forby
the lengthoftherectangular r.f. fielddistribution 1 (tobedistinguished from Lgff, used inSection4.2.7).Varying 1resultsin
twoeffects (eqns.4.19): (i)thetimeatwhichthesteadystateis
reached is affected: t=l/v, (ii) the value of <}> changes.The
effective length of ther.f.coil asexperimentally found fromthe
time atwhichthesignal reaches itssteadystate,isused insimulations ofthesignal,taking (i)intoaccount.
However,wehavestated above (Section4.2.4)thattheNMRsignal
offlowingwaterwillmainly arise fromtheregionofyvalueswhere
B x (y)corresponds to %nto4npulses.Ingeneral,thisregionwill
notcoincidewith |yj=*gl,asinthemodel fortherectangularBx-field
distribution. Actually, by taking 1equal totheeffective length
of the r.f. coil, the off-resonance frequency oftheregionwhere
thesignal isgenerated, i.e. ^$0> istoohigh.Therefore infitting
procedures we have used<|) <(VyGil+VyGvx 2 ). Thus,$ istheonly
adjustable parameter which does not follow from experiment, and
which isused forcurve-fitting.
4.3.1.2 Off-resonance effects ontheeffectiver.f. field
Theoff-resonance effects ontheeffective r.f. field aredependentonthedurationofthe n pulse (thequality factorofther.f.
coil)andthemagnitude ofthemagnetic fieldgradient.Experimentally
we have used asolenoid aswell asaHelmholtz typer.f. coil (see
61
Section 4.4),with n pulses of 15usand30 us, respectively.The
valuesofG are intheorder of10G/m.
For the solenoid thewidthofB 1 (y)athalfmaximum is~10mm.
Assumewehave aGaussian shapedBj-field distribution. IfB1(y)=10°,
B ff =10.5° andBf ,istilted towardsthez'axisby 15°withrespect
to the x' axis. ForBx(y)=45°B „ becomes45° andhas onlya 2.5°
deviation from thex' axis.
The Bj distribution of the Helmholtz coil has a fullwidth at
half maximum of about7mm.Then, forBt(y)=10°,B ff =10.8° andis
tipped away from the x' axis by 21°,whereas for B1(y)=45° B~becomes45°and thedeviation from thex' axisis3.4°.
Thesecalculationsdemonstrate thattheoff-resonance effectson
theeffective r.f. field atthevaluesofGused areofminorimportance, but they becomemore serious forhighervaluesofG and for
less sensitive r.f. coils.
CalculationsperformedbyHemminga anddeJagerontheeffectof
B ff on the NMR signal shape of flowing fluid have shown little
variations forvaluesofGbelow about25G/m forthe solenoid r.f.
coil [8].Extrapolating this findingwiththe aidofthe above calculations, thesignal shapemeasuredwiththeHelmholtzcoil isnot
expected to be affectedby off-resonance effects forG<18G/m.Experimentally wehaveusedGS15 G/m.
4.3.1.3 Samplingtime
Experimentally the signal of flowing fluidhasbeenobtainedby
integrating thex' componentofthemagnetizationbetweenthepulses
(see Section 4.4.). To derive eqns. 4.19 and4.20 wehave followed
the variation of the magnetization by sampling the signal attime
t=nt, justbefore ar.f.pulse. Intheseequations integrationhas
beenomitted.
Sampling on t=(n+lj)T, just between two pulses, for the phase
angle0we obtaintheresult:
^(n+^T~8 Y G v l 2"4^GlT
(neven)
(4.31a)
and
4>(n+!i.)T=71+| Y G V T 2 +J^Glt
(nodd)
(4.31b)
62
Comparing eqns.4.31 and4.15 showsthatinthe latter<j> isdependen'
on n, whereas in the former <t>,_,.i> doesnotdepentonn. Inview
of4.31a,bM ,{(n+H)x}becomes stationary intime fornevenaswell
as odd. Clearly this is due to (i)the useofarectangular r.f.
field distribution with the property thatwe have effectively n
pulses for |y|<ijl(Fig. 3), and (ii)samplingont=(n+H)T.Forevery
othersamplingtimet=(n+x)x,o<x<l,thevalueofM ,{(n+x)x}depends
onn.Thus, simplifyingtheactualr.f. fieldbyarectangular distribution,results inapredicted dependence ofthesignal shapeon
samplingtime.
tS(t)(arb.units)
125-
'S(t)(arb.units)
300200
1000
•100
•200
•300
•Us)
Fig. 5 Experimental NMR signals S(t)of flowing water vs.time,generated bya
sequence of equidistant npulses. (A)Signal obtained by sampling at time
t=(n+\)x,
justbetween the two pulses, (B)signal obtained by integrating
the magnetization between the pulses. Further experimental conditions
are identical for (A)and(B).
63
Experimentally we have sampled themagnetization ofthe flowing
fluid at times t=(n+H)x (Fig. 5A).Under identical experimental
conditions,butnowintegrating thesignalbetweenthepulses,signals
were obtained with identical shape,butwith amuchhighersignalto-noise ratio (seeFig.5B).Noothersampling timeshavebeenused,
so we have no further information onthedependence ofthesignal
shapeonsamplingtime.
By sampling at t=nt, the off-resonance contribution $ of the
regionwherethe signal isgeneratedbecomes too large (Comparethe
VtfGlx part in eqns. 4.31 and VyGlt in eqns. 4.15). This is an
additional argument to use<|><VyGlt +VyGvi2 infittingprocedures
(seealsoSection4.3.1.1).
4.3.1.4 Effectof 11 relaxationanddiffusion.
Theneglectofspin-lattice relaxationinourmodel isjustified
since the fluid in the r.f. coil only experiences n pulses.Any
change inmagnetization alongthez'axis,therefore,isnotrotated
tothex',y'plane.Inreality,thespin-lattice relaxationmechanism
causesthemagnetizationtoreturntotheequilibrium positionalong
the z' axis. Besides,we have apulse angledistribution overthe
r.f. coil (eqn.4.4),so thatpartofthez'magnetization canbe
rotated to the x',y' plane.However, aslongasT 2 <<T 1 thesignal
shape ismostly influenced by the spin-spinrelaxationmechanism.
Thiscondition iscommonlymetinbiological systems.
The effect of diffusion canbe incorporated intothetheoryby
replacing nx/T2 in eqns. 4.18 and 4.21a bynT/T2+g-y2G2DT2nT [3],
where D is the translational diffusion constant. However, if
T2<<(|-Y2G2Dt2) _ 1 thediffusiontermcanbeneglected.UsingG^15G/m,
Y=2.7xio4 rad/G-s (forprotons), i=1.6ms, andassumingD~2xl0-9 m2/s
forwaterthiscondition iseasilymet.
4. 3. 2 Comparison between theoretical
approaches.
In Figures 6, 7and8acomparisonispresentedbetweenexperimental NMR signals of flowing fluid as obtained with the n pulse
sequencewithcomputersimulationsbasedontheformalism developed
by Hemminga and de Jager [8] (eqns.4.1 through4.8) andcomputer
64
simulations based on ourtreatment (eqns.4.19a,band4.21a,b)for
laminar flow. Inthese Figures A and B are respectively theexperimental NMR signals and the computer simulations as givenby
HemmingaanddeJager [8],whereasCshowsourcomputersimulations.
Fig.6showstheeffectofthe fieldgradientGontheNMRsignals.
Fig. 7 and 8 represent NMR signals s, (t)obtained withvarious
lam
values of the mean liquid velocity v. InFig.7Ghasbeenchosen
in such away that the signals do not have amaximum,whereas in
Fig.8ahighervalueofGisemployed.
Withinthe limitations ofthetheoreticalmodel theagreementis
verygoodbetweenoursimulations andtheexperimental NMRsignals,
aswell asthecurves calculatedbyHemminga anddeJager. Inorder
to obtain our simulations we have usedtheexperimentalvaluesof
i,T 2,G andv asgivenin [8].Thevalue of1hasbeen determined
from plug flow curves ascalculatedwiththecomputerprogramused
byHemminga anddeJager [8].The timeatwhichtheplug flowsignal
reaches itssteady statehasbeentakenast=l/v.Forallvelocities
1 has been calculated to be 27mm for thedimensions ofther.f.
coil used by Hemminga and de Jager [8].Thevalueof<b (seeeqn.
4.19 and Section4.3.1.1)has been adjusted to give thebestfit
for the shape of the signals. Itisrathersurprisingthatinall
simulationsftwas found toequal 0.5,whereas intheoryftisproportional to G. The amplitude-ratio E/S in eqn. 4.22 has been
choosen to yield the best agreement between the experimental and
calculated S(t„„)
vst
curve. This ratio was found to be
max
max
0.03SEQ/SSO.05. The vertical scaling factor is the same for all
simulations inFigs. 6C,7Cand8C.
Thesimulations given inFigs.6C,7Cand8Chavebeencalculated
onaMINC-11/03microcomputer,using aBASICprogram.The calculation
time of a theoretical NMR signal is about 5min.The calculation
time (CPU-time)of the curves in Figs. 6B, 7B and8B,whichhave
been performed on aDEC SYSTEM-1090, using a FORTRAN program,is
about30min.So,ourtreatmentyields anenormous gainincomputingtime.
Fig. 6 (A)Effect of the field gradient G on the experimental NMR signals S(t)
of flowing water in a capillary, generated by a sequence of equidistant
71pulses, asgivenbyHemminga and deJager [8].The mean flow velocity
v is 4.7 mm/s. The values of G (inG/m) are: 3.3(a), 7.6(b), 12.3(c),
(tobe continued at next page)
65
ior
5
6
•Its.c)
10 •
S(t) (arb. units)
t 10-
©
t(s)
17.0(d), and 0.0(e). Thepulse period I is 1.6 ms. The spin-spin relaxation time T 2 of thewater sample is2.4 s. (B).Computer simulations of
the effect of G as calculated in [8].All parameters and conditions used
in the calculations are identical to those inthe experiment (seeA ) .
(C) Computer simulations of the effect of G onS(t)based on eqns. 4.19
through 4.22. For T,T2, Gand v the experimental values have been used
as inA.The value of the length of the rectangular I^-field distribution
1 was determined tobe 27mm (see text). The value of<|) (eqn.4.19) for
all four curves equals 0.5 rad.The amplitude-ratio E 7S was taken to
be 0.05.
In (B) and (C) laminar flow is simulated using 20 calculated plug flow
NMR signals.The vertical scales are given in arbitrary units.Thevertical scaling factor of the simulations are for (B)the same as inFigs.
7B and 8B, and for (C)as inFigs. 7C and 8C.Figs. A and B reproduced
from [8]by permission of the authors and Academic Press.
66
®
0
1
0
1
2
3
2
3
4
4
5
5
6
»t(s»c)
6
— • t[s«cl
Fig. 7 Effect of flow velocity v on experimental (A) and calculated (B)NMR
signals both from [8].The field gradient G is3.3 G/m. The values ofv
(inmm/s)are: 25.4(a), 7.0(b), 3.0(c), 1.0(d), and 0.0(e). (C)Computer
simulations based on eqns. 4.19 through 4.22. See caption of Fig. 6
for other conditions.
67
10
*
®
i
Sltl
5
V
d
0
•
•
5
6
—*.t(s«c)
10h
5•
0
I
Fig. 8
1
2
S ( t ) (arb.uni ts)
,0-1
3
4
5
6
M(s«c)
©
Effect of flow velocity v on experimental (A) and calculated (B)NMR
signals as given in [8].G=6.7 G/m. The values of v (inmm/s)are:
15.5(a), 8.8(b), 4.3(c), 2.0(d), and 0.0(e). (C) Computer simulations
based on eqns. 4.19 through 4.22. See caption of Fig. 6 for other
conditions.
68
Packer [3]has also devised multipulse sequenceswhichallowa
"one-shot" determination ofv and T 2•Hehasdiscussed theeffect
of flow along amagnetic field gradientusingtwodifferentpulse
sequences: (i)l ^ , - x - ( - n ,-T) n and (ii)Vt x , -x-(-n
-t'
, ) n , with
x'>x. Inthe theoretical analysis Packer has only considered the
liquid alreadypresentinther.f. coilatthebeginning ofthepulse
sequence.Theeffectof n pulsesonthemagnetization offluidmoving
into the r.f. coil and the loss ofmagnetization offluidmoving
out of the coilvolumehavebeenneglected.Thetimedependenceof
the amplitude of the echoes,occurring attime2nx, andresulting
fromthe firstpulse sequence isgivenby[3]:
E(2nx)=E(0)cos(nYGvx2)e-2nX/T2
(4.32)
This result is similar to our eqns. 4.21a,b taking into account
liquid already situated inthecoilatt=0,where the sine-function
is replaced by acosineduetophase sensitivedetectionalongthe
y' axis instead of the x' axis in ourmethod. InPacker's pulse
sequences (i)and (ii)there is alsoacontributiontothesignal
dueto fluidmoving intother.f. coil,where itreceives npulses.
This results in a contribution S(t)to the signal equal to that
givenineqns.4.19.However,duetothe firstVcpulse inthepulse
sequences used by Packer, the aforementioned contribution due to
liquid already present inthecoil,att=0,ismuchlargerthanin
the 7ipulse sequence used in ourexperiments. Inotherwords,the
value of P usingPacker'spulse sequences ishigher thaninour n
pulse sequence (see also the E/S ratio in eqn. 4.22). These
arguments justify theuseofeqn.4.32 inPacker'scase.
Inbiological tissues Packer'smethodsarenotattractive since
stationary fluid also gives rise to a signal due tothe first \n
pulse.
4.4 EXPERIMENTAL
Theexperimentshavebeenperformed ona15MHz singlecoilpulsed
NMR spectrometerwith a7-in. electromagnet.Detailsofthespectrometer have been described elsewhere [9].Severalhome-made sample
probeshavebeenusedwithtransmitter/receiver coilsoftheHelmholtZ'
69
orthesolenoidtype.TheHelmholtztypecoilhasalength anddiameterof10mm,whereas thesolenoid typecoilshavevariousdimensions. The field homogeneity is optimized using a shim unit.A
gradient in the y direction (direction offlow)isproducedusing
the y-shim control.Thecenterofthetransmitter/receiver coilis
positioned exactly in the middle of theshimcoils.Priortoeach
experimentthemagnetic fieldB isseton-resonance (i.e.nobeats
inthe freeinduction decay).
To measure flow, a pulse sequence of 4096 n pulses is given
directed alongthex'axisoftherotating frame.Thereferencephase
ofthephase-sensitive detector isadjusted todetectthex'component
of the magnetization. The receiver was used incombinationwitha
circuit,which integrates thesignalbetweenpulses.Onedatapoint
of the NMR signalcontains theintegrated signal resulting from16
pulses, so that experimental signals are built up from 256 data
points.Further experimental details aregivenin[8].
Two types of simulationsystems foraplantstemhavebeenconstructed. Both contain stationary water in a glass tube with an
inner diameter of 7mm. Inthesinglecapillary system acapillary
containing flowing water with a diameter of 1.25 mm is fittedin
the center of the glass tube. This results in a flowing water
fraction of 5%, as calculated from the dimensions of thesystem.
A four-capillary system hasalsobeenused,containing fourcapillaries with inner diameter of 1mm, which arepositioned inthe
glasstube atthefouredgesofasquareatequaldistances (1.7mm)
from the center of the glass tube.The flowing water fractionin
this system is 8%. The capillaries are connected to areservoir,
from which water flowsthroughthecapillaries under anadjustable
hydrostatic pressure.The mean flow velocity viscalculated from
the flowquantity andthe areaoftheinnercapillaries.Thelength
ofthecapillary systems isabout6mm.Thesystem issymmetrically
positionedwithintheNMR sampleprobe.
The flowvelocity v can be obtained from the positiont
of
theextremum intheNMR signalsofflowing fluid.Previously ithas
beenshown (Fig.8andref. [8])thatt .„isinversely proportional
max
tov :v=C/t
(seeeqn.4.27). ThecalibrationconstantCdepends
max
^
on the value of G. At aparticular value ofG,Ccanbe foundby
plotting v versus t _ 1 , where v can be calculated from the
rriciX
70
measured flow quantity and the known internal diameter of the
capillaries of a capillary calibration system [8,10]. To perform
thiscalibrationmethod itisnotnecessary toknowtheexactvalue
ofthe fieldgradientG.Thereforewehaveonlyestimated theactual
value of G. Ifnecessary,calibrationofGcanbecarriedoutmore
accuratelyusingthe freeinductiondecayF(t)bymeasuring thetime
tx atwhich F(tj.)=HF(o)[8].tx isrelatedtoGby
(Y/27I)Gt,=Cj
(A.33)
where G is expressed ingausspermeter, X.xinseconds andy/2nin
hertz per gauss. C1isaconstant (inm _ 1 ) foraparticulartransmitter/receiver coil, and reflects the spatial distributionB x (y)
of the r.f. field.Forthevarioustransmitter/receiver coilsused
wehaveassumedthatBi(y)maybeapproximatedby aGaussian function
(see Section 4.2.3). Inthis way C : canbecalculated foragiven
transmitter/receiver coil. The value of G calculated in this way
hasamaximum deviationof25%fromtheactualvalue.
4.5 RESULTSANDDISCUSSION
In this Section we presents the results of a series ofNMRexperiments onwater flow in glass capillary systems designed to
model the use of the n pulse sequence for themeasurementofthe
flowvelocityofwater inplantstems.
4. 5.1
Calibration
4.5.1.1 Necessity ofalinear field gradient
Flowvelocities caninprinciplebeobtained fromtheNMR signals
of flowing water from either the initial slope (rr) (eqns.4.26
and 4.28), which has been shown experimentally tobeproportional
to v [8],or,ifthesignal reaches amaximum orminimum, fromthe
position t__„
of that extremum via v=C/t
[8,10].
The initial
iucix
in3.x
slopedependsonthegainoftheaplifiersofthepulsedNMRspectrometer andontheamountofflowingwater (eqns.4.26 and4.28). The
second method is independent of these experimental variables
71
andisthereforeprefarableforpractical applications.Unknownflow
velocities cannowbedetermined aftercalibrationofthespectrometer,
yieldingCforaparticularvalueofG.
When G=0 the NMR signal is expected tobezero (eqns.4.19 and
4.21). Experimentally, NMR signals have been obtained, however,
without applying an external field gradient, because the natural
gradientinthemagnetic fieldproducedbyourelectromagnet inthe
directionofflowisalready sufficienttoproducethesignals.So,
ifthesystem containing flowingwater isalwaysplaced atthesame
positioninthemagnetic field,then flowvelocities canbemeasured
without applying an external field gradient, aftercalibrationat
this particular position, yielding C for this local natural y
gradient.Thissituation appliestoallmeasurementswhichwecarried
outonasinglecapillary system,wherethecapillarywas concentric
with a larger glasstube,placed inthecenterofthetransmitter/
receiver coil. The outer tube may contain water, thus simulating
plant-tissue surroundingxylemtransportvessel inaplantstem.
Ingeneralwater flowinplantstemscannotbeconsidered asbeing
concentrated in a singlecapillary.Thereforewehave investigated
the shape of thenatural gradientinthex,z-plane (seecoordinate
system in Fig.1)by measuring the NMR signal ofaconstantwater
flow through one of the capillaries ofthe four-capillary system.
By rotating the capillary system around the y axis (Fig. 1)NMR
signals of flowing water atdifferent x,z-coordinates have been
measured. Not surprisingly these measurements revealed that the
magnitude anddirectionofthenatural gradientstrongly dependson
thex,z-coordinates.Whenwater flowsthroughtwoneighbouringcapillaries ithasevenbeenobserved thatatcertainx,z-coordinates of
the capillaries virtually no net signal isobserved (seeFig.9 ) .
This canbe explainedby assumingthatthesignalsproducedbythe
water flowineachcapillary arenearly equally shaped,butreversed
insign,indicating thatthelocalnaturalygradients atthepositionofthesecapillaries haveaboutthesamemagnitude,butareof
opposite sign. Similar results have been obtainedwithwater flow
through all fourcapillaries.Optimizingthehomogenityofthestatic
magnetic field by using the shim unit and applying anexternaly
gradient results inNMR signals of flowingwaterwhicharealmost
orcompletely independentofthex,z-coordinates ofthecapillaries.
72
's(t)
D
v^,^^
1
6
t(s)
Fig. 9 Experimental NMR signals S(t) of flowing water vs.time as obtained by
the n pulse method as a function of theposition in the local natural
gradient inthemagnetic field.N and Sdenote thepoles of the electromagnet, x are the flowing water containing capillaries,whereas oare
capillaries with stationary water. No external field gradient has been
used.
Differences observed in this situationprobably areduetoinhomogeneitiesintheBx-fielddistribution.
4.5.1.2 EffectofTx andT 2 relaxation.
Up to now calibration curves ofvvs.t - 1 havebeenshownfor
max
water with T x ^ i 2.4.s [8,10]. In Section 4.2.6 wehavestated
thatthecontributionE(t) (seeeqns.4.21)tothetotalNMR signal
of flowing water introduces aT 2 dependence onthepositionofthe
73
In general, T x andT 2 ofwaterinbiological
extremum att=t
max
tissueareshortened with respecttothevaluesfordistilledwater,
and, inaddition, Tt i T 2 • InChapter 5wedemonstrate thatT xas
wellasT 2 strongly dependonthediameterofthecapillary containing
flowing water.Forthis reasonwehave investigatedtheeffectof
T\andT 2 relaxationontherelationship v=C/t
'
max
6-^ 1 QX (s- 1 )
Fie. 10Plotofvvs.t - 1 forexperimental NMR signals,obtained with thesingle
max
c a p i l l a r y system. G = 7.6 ± 1.5 G/m, x = 1.6 ms. The t r a n s m i t t e r / r e c e i v e r
c o i l was of the Helmholtz type with length and diameter 10 mm. (0)
Ti = T2 = 2.4 s ,
(x) T t = 2.2 s , T 2 = 1.6 s, and (A) Tj = 1.5 s ,
T 2 = 0.5 s .
Fig. 10 p r e s e n t s the r e s u l t s of calibration-measurements using
2+
the s i n g l e c a p i l l a r y system containing pure water, and two Mn
s o l u t i o n s with d i f f e r e n t T1 and T2 v a l u e s , r e s p e c t i v e l y . For both
the samples with Tt = T2 = 2.4 s, and t h a t with Tx = 2.2 s, T2 = 1.6 s,
we find t h a t t ~ 'rricixindeed has a r e c i p r o c a l r e l a t i o n s h i p with v as
long as v < ~ 25 mm/s, with C = 6.7 ± 0.3 mm. At higher v e l o c i t i e s
Forthesample
d e v i a t i o n s are found leading t o higher values of t
max
74
withTi =1.5 s,T 2 =0.5 stherelationvvs.t"1 clearly deviates
max
fromastraightline.
WiththeaidofcalculatedNMR signalswewereableto investigate
theeffectsof Tt andT 2 relaxationontherelationship v= C / t ,
separately. Due to theassumed rectangular r.f. field distribution
our theoretical treatment isinsensitive forvariations inTj (see
Section 4.3.1.4). Therefore, the calculations have beenperformed
withthecomputerprogrambased onthe formalism ofHemmingaandde
Jager [8].Theresults ofthesecalculations (seeFig.11)showthat
aslongasv<20mm/stherelationshipv=C/t
holds.Forhigher
r
max
valuesofv,t i n c r e a s e s withrespecttoitsvaluederived from
Fig.11Plotofvvs.t* for calculated NMRsignals.Calculations
havebeen
e
"
max
performed based on the formalism as given in [8].G=7.6G/m,
T=1.6ms.TheshapeofBjCy)waschoosenasin [8],basedontheBjCy)
distribution ofasolenoid with length3.5mmanddiameter 13.2mm(o)
Ti=T 2 , (x)Tj=2.4s,T 2=1.2s, (A)T x=2.4s,T 2=0.5 s, (•)
T!=2.4s, T 2=0.2s, (+) Tx=1.0, T 2=0.5 s, (o)Tj=1.0s,
T 2 =0.2s.
75
this relationship. IfTi =T 2 thereisnoshiftinthepositionof
the maximum. The effectofdecreasingT 2 istoshiftt
tolower
values, whereas a decrease ofT t hastheopposite effect.Forthe
optimum conditions to obtain a linear relationship v= C / t i n
therange0 i v<30mm/s,werefertoSection4.5.3.
4.5.1.3 Effectofflowprofile
In Section 4.2.5 we have argued that in general s D n u a (t) anc*
S, (t)have adifferent shape.Consequently, thevalueofCinthe
relationship v=C/t
for aparticularvalueofGdependsonthe
actual flowprofile.Theoretically thishasbeenconfirmedbycomparing
theresultsofthecalculations forlaminar flowasgiveninFig.11
with analogous plug flowcalculations. Inthecaseoflaminar flow
C was found tobe7.8 ±0.1 mm,whereasunder identicalexperimentalconditions C=12.0±0.1 mm forplug flow.So,calibrationmust
be performed with acalibration system inwhich the behaviourof
the flowingwater isidentical tothatinplantstems.InChapter5
we will argue that flow ofwater in thevascular system inplant
stemsmaybeexpected tobe laminar,implying thattheReynoldsnumber
(Re)inthatsystem is<2000 [11].For flowvelocitiesupto40mm/s
(the range of flowvelocities thatmaybeexpected forwater flow
in plant stems [1])Re ispredicted to be <2000 in cylindrical
systemswith adiameter $0.05 m.Thus, forthecalibration systems
used in our experimentsRe isalways<< 2000, andthereforewemay
safely assume, that fluid flow in these calibration systems is
laminar.Flowprofiles inplantvessels arediscussed inChapter5.
4.5.2
Determination
of T2 and volume
flowrate
4.5.2.1 EffectofTi
InSection4.2.7 wehaveshownthatthespin-spinrelaxationtime
T 2 of the flowing fluid canbe found from theslopeofaplotof
VS
(seeeqn 4 29)
^ ^ W ' W ^ W
-Snax
-- -
in Figure 12we show plots of S ± a m ( t m a x )•t m a x vs.t m a x derived
from the experimental NMR curves of flowingwaterwhichhavebeen
used to obtain Fig.10, with a) Tj.=T 2 =2.4 s,b)T t =2.2 s,
76
T 2 =1.6 sandc)Tx =1.5 s,T 2 0.5 s,respectively. Fromtheslope
ofcurve a)plottedvs.t
wehavecalculated -via egn.4.29 -a
value of T 2 of 2.6 ± 0.3 s,whereas from the slope of curve b)
T 2 =1.2 ±0.2 swasderived.Theslopeofcurvec)ispartlynegative
andtherefore itwasnotpossibletocalculate aT 2 valueviaegn.4.2'
It seems that thedeviationoftheT 2 value foundwiththismethod
from the actual value of T 2 increasesbothwithdecreasing T 2 and
with increasing Ti/T2 ratio.To investigate theeffectofTi onthe
determination of T 2 according to this method, we have used the
calculated flowcurves fromwhichFig.11wasobtained.
t
s
< t m a x > ' m a x < a r b -u^ts)
8-
4-
Fig.12PlotofS(t
).t
vs.t fromexperimental
NMRsignals.Experimental
r
6
r
max max
max
conditions as given inFig.10.(0)Tj=T 2=2.4s, (x)Tt=2.2s,
T 2 =1.6s,and (A)Ti=1.5s,T 2=0.5s.
77
t
SKmax^max (arb.units)
S(tmax)tmax<arbuni,s>
2
1-
1-
0.5
— i —
0.5
1.0
1.0
—»-tma«(s)
1.5
—*t m a x (s)
Fig.13PlotofS(t
).t
vs.t fromcalculatedNMRsignals.Experimental
max max
max
conditions asgiven inFig. 11.A).T 2=0.5 s, 11 (ins)is2.4(0),
1.0 (x),0.5 (A), B). T 2=0.2s, Tx(ins)is2.4 (0),1.0 (x),0.5 (A)
and0.2 (•).
Table4.1CalculatedvaluesofT 2and B1 fromcalculated flowcurves
withdifferentT^andT 2values.T 2andDihavebeencalculatedviaeqn.4.29.
Actualvalueof
T^s)
T2(s)
2.4
2.4
2.4
1.0
0.5
2.4
1.0
0.5
0.2
2.4
1.2
0.5
0.5
0.5
0.2
0.2
0.2
0.2
Calculatedvalueof
T2(s)
Di(arb.units)
2.3 ±0.1
1.1 ±0.1
0.36±0.04
0.40±0.06
0.55±0.06
a
a
a
78
72
73
75
76
0.27±0.07
65+10
Duetothepartlynegativeslope3(S, (t ).t )/3t
r
°
lam max max
(seeFig.13)T 2andDjcannotbedetermined.
+4
±4
±4
±5
±4
a
a
a
max
1.5
78
Fig.
a 13 demonstrates that the slope 9(S, (t
^ v lamv).t
max')/9t
max" max
obtained fromthesetheoretical curves strongly dependsonthevalue
ofT t , inagreementwiththeexperimental results showninFig.12.
InTable4.1 T 2 values arepresentedwhichwerecalculatedviaeqn.
4.29 from these theoretical curves.This Table also contains Dt ,
obtainedbyextrapolating theIn [3(Sn (t ).t )/3t ]vs.t
2
l x
*
*
lanr max' max" maxJ
max
curve to t„ =
0.
Apart
from
a
calibration
constantthisvalueof
max
Di isequaltoV,the amountof flowingwater,whichwasheldconstant
forallcalculatedcurves.
The results of Table 4.1 clearly show that the calculated T 2
values stronglydependonTj. IfTj=T 2 thecalculatedvalue ofT 2
corresponds with the actual T 2 value. IncreasingT t results inan
increased deviation of T 2 (calc)from the actual T 2 value.These
results alsoshowthat D1 ismuch lesssensitivetovariations inT t
andT 2 andindeedcanbeusedtocalibrate anddeterminethe amount
offlowingwaterV,which inturncanbeusedtocalculate thevolume
flowrate (seeeqn.4.30).
The deviations of the calculated values of T 2 from theactual
values canbeexplainedbyconsidering thecontributionE(t)ofthe
fluid already in the coil att-0 to the total signal:S•, or
S, (seeSection4.2.4,eqns. 4.21). Inderiving eqn.4.29 wehave
assumed thatthecontribution ofE(t)issmall andcanbeneglected.
However, if E(t) cannotbeneglected itintroduces adistortionof
the relationship as given in eqn.4.29. One can rationalize that
v =C/t max
holds for S(t)aswell asforE(t). Ifthis issothen
itcanbe found fromeqn.4.21a that
3(E(t ).t )/3t )=(1-t /T2)sin(^GTC)e
max max max
max z
'
maX
-t
,t
/T 2
i 1/v (4.34)
max
Thus, E(t) introduces a t_.„ dependence in the slope
9
r
(Sni.mltm,.)
^ v ) / 3max
^ , . - A similar dependence
is expected for
plugv max'•^max
laminar flow.TheeffectofTx inour formalism cannowbe accounted
for by the relativecontribution ofE(t)withrespecttoS(t),the
signal generated by the Vi pulse region of our rectangular r.f.
fielddistribution. InFig.12BwepresentthecasewhereT 2 =0.2 s
isheldconstantandTjisvaried from0.2 to2.4 s. Itcanbe seen
thatthepositionatwhichtheslopeofthecurvebecomes zero shifts
79
towards t__„=T 2 asTi increases.For highervalues oftm_,„this
slopebecomes increasingly negative.Fromeqn.4.34 itfollowsthat
v the slope3(E(t
forE(t)
)/3t
becomeszeroatt „ =Tmax
2,
'
t> \ \ m a).t
*'
x ' max'' max
whereas forhighervaluesoft
thisslope isindeedpredictedto
benegative.Fromtheseobservationsweconcludethatby increasing
the T x /T 2 ratio, the relative contribution of E(t) increases. If
this contribution ismuch larger than that of S(t) (Tx >>T 2 )we
expect that T 2 canbedetermined fromaplotofl n [ s D i u a (t x )]or
ln[si--m(t„,v)]vs. t_,„ (eqn. 4.21). Indeed, from the theoretical
J.etui
fflclX
IUGIX
curves with Tt =2.4 s and T 2 =0.2 s the slopeof ln[ s i a m ( t m a x )]
vs. t
yields T2(calc.)=0.28 ± 0.03 s andDx =88±4.Onthe
other hand, such aplot forthecurveswithT x =T 2 =0.2 syields
T 2 (calc)=0.72 ±0.03 s and Dt =66±4 and thus ismuch less
satisfactory. These observations support our conclusion mentioned
above.
In determining T 2 and V via S(t )we have takenforgranted
that the nuclei of the flowing fluid have experienced thestatic
magnetic fieldB longenoughtohave attainedBoltzmannequilibrium
beforeentering thetransmitter/receiver coil.However, experimentally
thisconditionisnotalwaysmet.Supposewehaveafluidwithspinlattice relaxation time T1.The time inwhich themagentization
attaines equilibrium is about5xT x .Letdbethediameter ofthe
pole face of the electromagnet, and let the transmitter/receiver
coilbepositioned inthecenterofthemagnet.Nowthemagnetization
of the flowing fluid reaches equilibrium before entering thecoil
ifvg (Hd/5T!). Experimentally we have d=17.5cm, meaning that
when Tx =2.4 s for v?7mm/s the observed NMR signal does not
reache itsmaximum possible height,but isattenuatedbyT x .This
is clearly observed in Figs. 7 and8,where thecalculated curves
(B)and (C)arehigherthantheexperimental curves,duetothisTi
effect. Inthe calculated curves of Figs.7and8thiseffecthas
beenneglected.
IfTj isaknownparameter,corrections canbemadetotheexperimental signalheightS(t)using [12]
S(t)=S(t){1-exp(-d/2vT1)}-1
where S (t)isthesignal atequilibriummagnetization.
(4.35)
80
4.5.2.2 Off-resonance signal ofstationarywater.
InSection4.4 ithasbeenstated thatall flowmeasurements have
been performed on-resonance.Underthisconditionno signal isobserved fromwaterwithv=0 (seeFigs.7and 8). Indeed,usingour
model systems filledwithtapwaternosignalhasbeenobserved from
stationary water surrounding the capillaries.However,by making
the stationary water fraction inhomogeneous, forinstancebyusing
papertissueorglassbeads,ithasbeenobserved thatthis fraction
may sometimes give rise to an additional signal, even when the
system ison-resonance.Thisadditional signal decays exponentially
with adecaytimeapproximately equaltoT 2 ofthestationarywater.
Obviously,this signalwill introduce errors inS(t
)andthusin
max
thedetermination ofT 2 andVofnon-stationarywater. Inplantstems
the stationary water fractioncanalsobeconsidered asaninhomogeneous system andthesameadditional signalsmaybeexpected.
InFig. 14 theheightH ofthesignal observed from stationary
water att=0ispresented asafunctionoftheoff-resonance frequency u),G, and x, for thesinglecapillary systemwith apaper
tissue-water system asstationary fraction,wherew =w -•yB.To
obtainthestationary fraction,theoutertubeofthesinglecapillary
system was filled with anundefined amountofpapertissue andwith
water.
From this Figure it can be seenthatH =0atw =0.Thisis
valid when the Bx field and theinhomogeneitiesinthesampleare
symmetricwithrespecttothemiddle ofther.f. coil. Ifthissymmetry isnotpresent,H =0canshifttohigherorlowervaluesof
ui.For paper tissue-water systems H may shift up to60Hzfrom
w
c=°-
Theoretically thedependence ofH onw ,GandTcanbeexplained
by the signal generatedby the firstpulse,asgivenineqn.4.11.
For calculations of H (w ,x,G) we have incorporated the offresonance frequency w in this equation, followed by integrating
the signal over t, as in the experimental situation. Underthese
conditions eqn. 4.12 for stationary water (v=0) is transformed
into
i °°
H (w ,I,G) = J J 2 s i n { 7 t . e x p ( - 2 y 2 / L 2 ) } . sin(ui x) cos(yGy x) dy .dx (4.36)
oo
81
|H0(arb.uni
Fig. 14Height H of the stationary water signal at t - 0as a function of the
off-resonance frequency w .Experimental conditions: t (inms )is 0.8
(A), 1.6 (B);G (calculated via eqn. 4.33) is (in G/m): 0.7 (x),8.7 (o)
and 15.6 (A).The continuous curves have been calculated using eqn. 4.36,
with L= 7.2 mm.Thevertical scale isgiven inarbitrary units,but the
scale factor is the same in (A)and(B).
82
By replacing the integral over y by an integral overy/Lit
can be shown thatthecosine-term depends ontheproductofGxL.
Thus,G andLarestronglycoupled andcannotbedetermined separately
from these calculations.Therefore, the continuous curves inFig.
14have been calculated by using L=7.2 mm, taken asbeingthat
lengthofasample forwhichtheheightoftheFIDbecomes insensitive
for increasing sample length.ThevaluesofGhavebeencalculated
fromegn.4.33,againusingL=7.2 mm.Theshapeofthecalculated
curves isinreasonable agreementwiththeexperimental data. Itis
clearthatexperimental datasuchasgiveninFig.14canbeutilized
todetermineG foraparticularvalue ofL.
Thedependence ofH onw canbeusedtolockthemagnetic field
B on the frequencyoftherotating frame,particularly atx= 0.8
ms,wheretheshapeofH becomesmuchlesssensitive forvariations
inG.
4.5.3 Optimum experimental
conditions
Theoptimum conditionstodeterminevarethosewherethelinear
relationship v= c / t m a x isvalid. This is true whenever T 2 S h^i
(see Section 4.5.1.2). Under this condition v can be determined
without the need to know the valueofT 2•Ontheotherhand,when
T!/T2 >2andT 2 <~ 1s,thecalibrationcurvevvs.t~i strongly
dependsonthevalueoftheratioT x /T 2 andonthevalueofT 2 (see
Fig. 11).Then,v starts to deviate appreciably fromC/t
andv
canonly reliablybedetermined ifTx andT 2 areknown. Inaddition,
T 2 and V can be reliably determined from the NMR flow curves if
T 2 = Tl or T 2 <<Tx (seeSection4.5.2.1). Fromthese observations
we conclude that T 2 =Tx represents theoptimum conditiontocarry
outourexperiments.
Unfortunately, inmostbiological tissuesTj>T 2 .However,the
pulse sequence used to measure flow canbe considered asaCarrPurcell-Meiboom-Gill (CPMG)pulse sequence (Section 3.3.1)minus
the firstHnpulse.Thus, itcanbeexpected thatthe flowingwater
curves containthesamevalueofT 2 asmeasured usingtheCPMGpulse
sequence. Inbiological tissueanumber ofmechanismsmay contribute
to the spin-spin relaxation (Chapter 3 ) .FortheCPMG sequenceit
is known that themeasured T 2 dependson T, thetimebetween the n
83
pulse, if (i)exchange occursbetweendifferentsites (seeSection
3.2.4 and [13-16]), or (ii)thematerial isnonhomogeneous,byexhibiting either adistributionofslowdiffusioncorrelationtimes
[17], orinhomogeneity inmagnetic susceptibility [18,19], orboth.
IneverycasetheobservedT 2 increases astdecreases,and forvery
small xT 2 approaches the corresponding 11 value.Due totheinhomogeneous character of the plant xylem vessel system, itmaybe
expected thatthesameholds forwaterinthatvessels.
Experimentally wehaveused apulse spacing t=1.6 ms. Reducing
i in order toincrease theeffectiveT 2 hastwoeffectsontheNMR
signal of flowing water: (i)t
shiftstohighervalues andthe
maximum broadens,resulting inanincrease inthelower limitofv
that canbe measured, and (ii)thesignal-to-noise ratio decreases
due to the fact that the signal ismeasuredby integratingthex'
component of the magnetization over the time t. The firsteffect
(i)canbe compensated by increasing G. As long asGxtisheld
constanttheshapeoftheNMR signal ishardly affected atotherwise
constantexperimental conditions.The lattereffect (ii)isremoved
by summing over morepulses (seeSection4.4) sothatthetimebetweenthedatapoints remainsunchanged. Ifwe assumethatareduction
of Tby afactor 10 (160ps)isrequiredtoobtainT 2 > h^i> Ghas
to be increased byafactor10 (50-150G/m)inordertomaintain
the same shape of the signal ascomparedwith x=1.6 ms.Then,a
total of 40960 pulsesmustbegiven forthesametime-interval and
each data point thencontainsthe integrated signal resulting from
160npulses.These conditions arewithin experimental reach.The
net gain is an effective longer T 2 , resulting in an increase of
S(t ).Inaddition,reductionofxhastheadvantage thatthesign
ofthesignal ofstationarywaterbecomes insensitive tothemagnitudeofG (seeFig.14),meaning thatthis signalbecomesmore suitable asalocksignal tostabilizethemagnetic field.
4.6 CONCLUSIONS
The results reported here, demonstrate that the n pulsemethod
can be used to measure the meanlineair flowvelocityofwaterin
plant stems. Although v can inprinciple be determined from the
initial slope of S(t),this slopedependsontheamountof flowing
84
water andaplifiergain;itisalsopossiblethatanadditionaloffresonance signalofthestationarywater affectsthis slope.Therefore, determination of v from t _ 1 ispreferable for practical
max
applications. IfT 2 i ^ \ , vcanbedeterminedwithoutaprioriknowledgeofthevalue ofTj andT 2 •
In addition, T 2 , V, andconsequently thevolume flowrate canbe
determined fromtheNMR signals.WhenT t >> T 2 ,T 2 maybe determined
from the slope ofaplotofS(t_.„„)vs.t_,__inasemilog fashion.
For T x >T 2 or T t =T 2 the slope of a semilog plot of
3 S(t
I
t a a x > - W / 8 t m a xVS* W
* i e l d s T *'F o r T * >T * onl* t h a t P a r t
oftheplotwitht
?T 2 isused,whereas forTj=T 2 theplotis
valid fort
?3T 2 .ThedeterminationofV ismuchlesssensitive
to the value ofT t and T 2,andcanbe found fromthe interceptat
t =0 from semilog plots
) vs.
t
as well
3 r of S(t
max
maxas
3[S(t
).t
]/3t
vs.
t
1 v
max7 max J/ max _ max
The lower limit ofv that can be measured strongly dependson
the absolute value ofTx andT 2 andontheamountofflowingwater
V. A typical combination of values fortapwater flowingthrougha
singlecapillary, surroundedby a100-fold excessofstationarywater,
isv i 0.5 mm/s,V i 5 pi. Forplants,wehavemeasuredvaluesas
lowas3mm/s forvandV~ 5pi.
4.7 ACKNOWLEDGEMENT
We are indebted to Mr. J. Reinders,who has performedpartof
the experiments and calculations, and to Dr.M.A. Hemminga and
Mr.P.A.deJager for many helpful andstimulating discussionsand
for making available theircomputerprogram forsimulatingtheNMR
flowcurves.
This work was inpartsupportedbytheNetherlands Organization
fortheAdvancementofPureResearch (ZWO).
85
REFERENCES
1. B.Slavik,"MethodsofStudyingPlantWaterRelations",Chapter4(SpringerVerlag,Berlin,1974).
2. D.W. JonesandT.F.Child,in"Advances inMagneticResonance" (J.S.Waugh,
ed.),Vol.8(AcademicPress,NewYork,1976).
3. K.J.Packer,Mol.Phys.17(1969),355.
4. K.J. Packer,C.ReesandD.J.Tomlinson,Advan.Mol.RelaxationProcesses3
(1972),119.
5. J.R. Singer,J.Phys.E:Sci.Instrum.11.(1978),281.
6. A.N.Garroway,J.Phys.D:Appl.Phys.7(1974),L159.
7. K.FukudaandA.Hirai,J.Phys.Soc.Japan47 (1979),1999.
8. M.A.HemmingaandP.A.deJager,J.Magn.Reson.37 (1980),1.
9. M.A.Hemminga,P.A.deJager,A.Sonneveld,J.Magn.Reson.27.(1977),359.
10. P.A.deJager,M.A.Hemminga,A.Sonneveld,Rev.Sci.Instr.49 (1978),1217.
11. A.T.J.Hayward,"Flowmeters,aBasicGuideandSourcebook forUsers",Chapter
1(TheMacMillanPress,London,1979).
12. L.R.Hirschel,L.F.Libelo,J.Appl.Phys.32(1961),1404.
13. J.Jen,J.Magn.Reson.30 (1978),111.
14. V.D.Fedotov,F.G. Miftakhutdinova,Sh.F.Murtazin,Biofizika 14 (1969),
873(Biophysics (USSR)14(1969),918).
15. H.S.Gutowsky,R.L.Void,E.J.Wells,J.Chem.Phys.43 (1965),4107.
16. A.Allerhand,E.Thiele,J.Chem.Phys.45 (1966),902.
17. J.G.Diegel,M.M.Pintar,Biophys.J. 15 (1975),855.
18. R.Cooke,R.Wien,Biophys.J. 11(1971),1002.
19. B.M.Fung,T.W.McGaughy,J.Magn.Reson.43 (1981),316.
86
FLOW MEASUREMENTS IN PLANTS
5.1 INTRODUCTION
In biology and agriculture knowledge of the water balance of
plants isofcrucial interest.Uptake,transport,storage andtranspirationofwatercontribute tothisbalance andarestronglymutually
coupled: transport in thexylemvessels isdeterminedby soil-and
leafwater potential [1,2,3]. Thelatteriscontrolledbystomatal
transpiration,which initsturnisgovernedbyplantwaterstatus,
C0 2 concentration, light intensity and air humidity [1,2]. Thus,
sapstreamvelocitycanbeused asanindicator ofthe transpirational
process [4].Several indirectmethodshavebeenusedto studywater
transportbymeasuring themeanlinear flowvelocityvorthevolume
flowrateQofthesapstream [5].None ofthesemethodsdetectsthe
movementofwater itself,however,andmany areinvasive.
InChapter4wehavediscussed apulsednuclearmagnetic resonance
(NMR)method,basedonapulse sequence ofequidistantnpulsesand
a linearmagnetic fieldgradient [6],based onmeasurements inglass
capillarymodel systems,asapplied tomeasure flowinplantstems.
Inthat Chapter we have shown that these flow measurementsyield
themean linear flowvelocityv,thevolume flowrateQ,theeffective
cross-sectionA,andthespin-spinrelaxation timeT 2 ofthe flowing
water, without observing the stationary fluid, such as thenonflowingwater inthetissueoftheplantstem.
Inthis Chapter we report the useofthispulsedNMRmethodto
measure linear flowvelocity ofwater inthevascular system ofstem
segments. These measurements havebeensuccessful instem segments
of Cucurbitaceae (e.g. cucumber, gherkin, pumpkin) andtomato.On
the other hand, forseveralotherplantstemsegmentsnosignalof
flowingwater could bedetectedunderourexperimental conditions.
Theseobservations canbeexplained onthebasisofthe relationship
between the radius R of the transportvessels andT 2 ofthewater
inthesevessels.
87
NMR flowmeasurements inintactcucumber andgherkinplantshave
been published recently in apreliminary note [7].In anearlier
communication [8] (seeChapter 7)theeffectofplantwater content
onthe 1HT 2 ofthetissuewaterhasbeendiscussed.Herewereport
simultaneousNMR flowandT 2 measurements inanintactgherkinplant
in response to light intensity and soil water potential, showing
thatthecombination ofthesetwopulsedNMRmeasurementsprovidea
new approach instudying importantpartsoftheplantwaterbalance.
5.2 EXPERIMENTAL
5. 2. 1 NMRflow
measurements
Fortheexperimentswehaveused a15MHz : HpulsedNMRspectrometer asdescribed inChapter 4.The linear flowvelocityvwasobtained from theposition t
oftheextremum intheNMR signal (see
Chapter 4), viatherelationship v = c / t m a x - Calibration ofChasbeen
carried outwith asinglecapillary system, consisting ofacapillary
containing the flowing water, with a diameter of 1.25 mm, fitted
into a glass tubewith aninner diameter of7mm, filledwithstationarywater (T2=2.4 s). Attheparticularvalueofthelinear field
gradientG (inthedirectionofthe flow)used intheexperiments,C
was foundtobe6.3 ±0.3 mm.The flowingwaterused forcalibration
wastapwaterwithrelaxationtimesTi=T2=2.4s.
A totalof4096npulseshasbeengiven,withpulseperiod x=1.6ms.
Each datapoint represents the integrated signal over25.6ms (16
pulses). The results reported in this Chapter have been obtained
from single trace experiments.The magnetic fieldB was adjusted
to such avalue thatnosignalwasobserved fromstationarywater.
Thiswasobtained on-resonance (nobeats inthe freeinduction deceay)
or slightly off-resonance, depending on the sample measured (see
Section4.5.2.2). Forintactplants itisdifficulttocontrolthis
condition, because the conditionv=0cannoteasilyberealized,in
contrasttothesituation incutstem-segments. InpracticetheNMR
signal of flowing wateratt=0ismadecoincidentwithzerosignal
level for model systems. Further experimental conditions are as
giveninSection4.4.
AHelmholtz-typer.f. coilhasbeenusedwithL=l.landR=0.5cm.
Inordertoperformmeasurements onintactplants,ther.f. coilwas
88
constructed i n such a way t h a t i t can be opened and folded around
the p l a n t stem (see Fig. 1 ) . The q u a l i t y factor of t h i s c o i l was
-50.
F i g . 1 Helmholtz-type r . f .
c o i l used for measurements in i n t a c t p l a n t stems.
L = l . l cm, R=0.5 cm. The c o i l has been c o n s t r u c t e d in such a way t h a t i t
can be opened and folded around the p l a n t stem.
5 . 2 . 2 NMRT2
measurements
The s p i n - s p i n r e l a x a t i o n time T2 was measured by the C a r r - P u r c e l l Meiboom-Gill (CPMG) method [ 9 ] , c a r r i e d out with the same 15 MHz 1H
pulsed spectrometer and r . f . c o i l as used for the flow measurements.
Because of the i n t e r n a l inhomogeneity and the s i z e of the samples a
time-dependent b a s e l i n e ("baseline d r i f t " ) must be expected [ 1 0 , 1 1 ] .
A f i r s t order c o r r e c t i o n for t h i s phenomenon was made by the following
pulse sequence:
V t x - t - ( - n y - 2 i ) n - W(=5T 1 )-H7T_ x -t-(-7t y -2x) n ,
where Wi s the waiting time between the two CPMG sequences. By subt r a c t i n g the two CPMG-decays, the e f f e c t of missetings in the n pulses
was diminished. The CPMG T2 decay was measured by sampling the height
of the echoes. The time 2t was chosen to be 1.6 ms. The echo decays
have been analysed by use of a n o n - l i n e a r l e a s t squares f i t [12] on a
t o t a l of 1960 d a t a p o i n t s . Due t o a considerable s c a t t e r in echo heights
89
the firstdatapointsofthedecayhavebeen rejected before analysing.
Invariably, anon-exponential T 2 decaywasobserved. Least squares
fitting hasbeen performed toamaximumoffour exponentials.The
best solution contains thesumofthree exponentials.Wedefinea
mean effective relaxation rate R 2,
3
**=& P±Tji
(5.1)
where P• denotes thefractionofcomponent i. T 2 measurementsas
wellasflowmeasurements weremadeatprobe temperature (29°C).
5.2.3
Plant
material
Freshly excised stem segments havebeen used with length10 cm.
Flow velocity hasbeen varied byhydrostatic pressure.Plant stem
segment andtube have been connected usinganuniversalvariablebore connector (Omnifit Inc.,Cedarhurst,NewYork).
5.3 RESULTSANDDISCUSSION
5.3.1 Stem segments
Fig.2representsNMRsignalsofwater flowing throughanexcised
segment ofcucumber stem (Cucumis sativus L.)Themean linear flow
velocity vwasvariedbyhydrostatic pressure.InChapter4wehave
shown forglass capillary systems that v canbedetermined from
the time t max
atwhich theNMRsignal S(t)
3 reachesamaximum,by
the relationship
v=C/t
(5.2)
max
This relationship isvalid whenever T 2 ^ T ! (seeSection 4.5.1.2).
In Fig.3thesignalsofFig.2havebeen represented asaplotof
thevolume flowrate Q (asvolumetrically determined)vs- t~l . Assuming
thattheeffective cross-sectionisindependentofvolume flowrate
(orhydrostatic pressure)weconclude from Fig.3thateqn.5.2. is
equally valid forthis stem segment.
90
^ S ( t ) (arb.units)
-T-
0
6
Fig. 2 Single scan 15MHzNMR signal height S(t) vs.time for water flowing
through an excised stem segment of a cucumber plant.Water flowwas variedby
hydrostatic pressure. A total of 4096 71pulses hasbeen applied,with
pulse period 1=1.6ms. Each point of the curve represents the integrated
signal over 25.6ms (16pulses). G=13 ± 3 G/m.
Thevalidityofeqn.5.2.forthisstemsegmentsuggeststhat
T2=HT1.AsstatedinChapter4whenthisconditionholds,T2canbe
determinedfromtheNMRsignalsasgiveninFig.2byplotting
^ S ^ m a x J - W / ^ m a x vs " Snaxi n a semilo< 3fashion.ForTl >T 2 only
thatpartoftheplotwitht X ?T 2 isused,whereasforT1sT2the
plotisvalidfort ?3T2
Theslopeofsuchaplotforthecurves
r
c max
ofFig.31yields
T
=250
±
20
ms
for
t
<400ms.
^
2
-*
max
91
fa(ml
/mln)
/
/
/ +
/
t
1
1 *
• fmax Is"1)
F i g . 3 P l o t of volume flowrate Q (ml/min) v s . t " 1
x
for the measurements shown in
max
Fig.1
IfT t =T 2 the decay timeobtained fromasemilogplotofS(t
)
From the resultsof
vs. t
must be >3T2 (see Section4.5.2.1)
Fig.
S(tvmax'
)vs.t max'•
yielded adecaytimethatequals610±40ms,
y 2max
only slightly lessthanthreetimesthepreviously calculated T 2 of
250±20ms.WhenT 1 =2T 2 thedecaytimeobtained from asemilogplot
ofS(t_,„)vs.t
isabout2T 2 . Here,wehavetheintermediatecase,
in agreement with the validity of eqn. 5.2. (Asnoted inSection
4.5.2.1, theshapeoftheplotS(t „„)'t„„vs.t^..,,strongly depends
max max
max
onthevalue oftheratio T1/T2 , andthusthepositionatwhichthe
slope of this plot becomes zero. For T!>>T2 this positionequals
thetimeT 2 ,whereas fordecreasing Ti/T2 ratio thispositionshifts
to higher
values oft .For
at r
3
3
maxthecurvesofFig.2theposition
which the sloperofS(t )-t
vs.
t
^
becomes
zero
was
found
to
max max
max
be~1.0s,equalto4T2(calculated).This isanadditional argument
thatT2>HTi forthis stem segment (seeFig.13,Chapter4.)).
92
Similar signalsofflowingwaterhavebeenobserved instemsegments
ofgherkin (Cucumis sativus),
pumpkin (Cucurbita
ficifolia)
andtomato
(Lycopersicon
esculentum).
Ontheotherhand,forseveralotherplant
stemsegments,suchaspapyrus (Cyperus alternifolius),
sweetpepper
(Capsicum annuum L.)and seedlings of tomato,cucumber and bean
(Phaseolus
vulgaris),
wehavetriedtoobtainNMR signals offlowing
water without success,although for some of these the amount of
flowingwater (volumetricallydetermined)shouldhavebeen sufficient
forobservationwithourNMRapparatus.
These negative results may be explained by (i)aflowvelocity
whichistoolow,and/or (ii)thevalueofT 2 (andTi)ofthe flowing
water. Concerning (i):the lower limit ofv that canbemeasured
stronglydependsontheabsolutevalueofTx andT 2 andonthe amount
offlowingwater (Chapter 4 ) . Calculations ofthelinear flowvelocity
from the measured volume flowratebasedonestimatesofthe amount
ofxylemvessels andtheirdiameters revealedthatine.g. thepapyrus
stem segments the flowvelocitywasintherange2-10 mm/s.Atthe
value of the linear field gradient usedthese flowvelocities can
be measured if T 2 >~175ms.AtlowervaluesofT 2 theNMR signal
broadens and the maximum disappears.Theresulting signal thencan
be easily misintepreted asbeing an off-resonance signal of the
stationary water (see Section 4.5.2.2.), which has aboutthesame
shape.KnowledgeofthevaluesofT 2 andTjofwater inthesexylem
vessels isthereforeofprimeimportance.
As stated above, in the cucumber segment of Fig.2we found
T2=250±20ms. The flowing water fraction used was tap water
(T2 =2.4 s). Thus,theT 2 ofwater flowingthroughthexylemvessels
isconsiderably shortened.Thisbehaviourcanbeexplained inafirst
approach in terms of a two-state fast-exchange model [13,14]. In
the framework of thismodel we may assignonestatetowaterina
xylem vessel ("free"water)with T 2 f =2.4 s and water, bound on
thevesselwall,withT2, ?1mstothesecond state.There isfast
exchange ofwaterbetweenboth states.Theobserved single relaxation
rateR2 istheweighted averageoftheseparate relaxationratesof
thetwoexchangingfractions:
R-JCET;,-1)-Tg"1+Pb(T2"1-Tg"1)
(5.3)
93
where P. is the mole fraction ofthe "bound"water.Letusassume
thatwehave athinlayerofboundwaterwiththickness dranddr<<R,
the radius of the vessel.Now egn.5.3 canbewritten intermsof
drandR,resultingin
2dr
«*-**f •l
+ =fr (Tz^1"Tz"1)
(5.4)
showing thatR2 is expected tobe inversely proportional withR.
This approachcanbeextended forintermediate andslowexchangeby
use of the equations as given by [15] (see alsoChapter3,eqns.
3.16 -3.20). Comparable results have been obtained byBrownstein
andTarr [16,17].Using asimpletheorybased onadiffusionequation
usingthebulkdiffusivity ofwater,theseauthorshavederivedexpressions for the relaxation times Tj aswell asT 2 inbiological
cells in terms of the diffusion constant D and thedimensionsof
thecell [17].These authorshaveshownthatmultiexponentialdecay
of the spin relaxationcanariseasaconsequence ofaneigenvalue
problem associated with thesizeandshapeofthecell. Brownstein
en Tarr have alsoconsidered relaxation inacellwithcylindrical
geometry [17].We will use their resultstoexplainrelaxation in
an xylem vessel. In deriving their equations for relaxation
Brownstein and Tarr have neglected relaxation offreewater(i.e.
T 2 £ 1 = 0 ) . The surface of the cylinder is considered as an active
surface,with surfacelike sinks forthemagnetization.Attheactive
surface the sink strength density M (incm/s) is assumed to be
constant. (NotethatMhasthesamedimensionasflow. Indeed, flow
can also be incorporated intheir integraltheorem [16],resulting
intheequations asderivedbyHemmingaetal [18]forthedifference
decaycurveofstationary and flowingwater).Now,thelongestdecay
timeT ofthespinrelaxation isgivenby
T=R2/Dn2
o
(5.5a)
'o
where n 'o
isthepositive
rootof
r
n
o J l ( n o ) / J o ( n o )=
m/B
(5
-5b)
94
andJ ,Jx arecylindrical Bessel functions.
Brownstein en Tarr discerne three qualitatively differentregions
ofbehaviour according tothevalueofMR/D:
(i)MR/D<<1. This canbeconsidered astheregionthatcorresponds
tothe fast-exchange limitofdiscretemultiphase analysis [13-15].
Thecorresponding decaytime isgivenbyT=V/MswhereV isthesample
volume andsistheactive surface area.Foracylinder thisresults
in
TQ=W M
(5.6)
ForT 2 ,here againwe findthatR2(=T_ 1 ) isinversely proportional
toR, inagreementwitheqn.5.4.
(ii)1<MR/D<10.This iscalled the "intermediate-diffusion" region,
(iii) 10<<MR/D. This canbecalled the "slowdiffusion"region.In
thisregionthedecaytime foracylinder isgivenby
T Q =R2/D(0.75
rt)2
(5.7)
showing aquadratic relationship betweenRandT.
In Fig.4 we have plotted T vs.RasafunctionofM.Wehave
assumedD=2.5xl0"5 cm 2 /s.WhenMR/D>>10thantherelationship between
T andRbecomes independentonM (eqn.5.7).
Values ofM inbiological tissuehavenotyetbeenpublished in
literature.However,thediffusional formalism developedbyBrownstein
enTarrcanbeused toexplainthespinrelaxationbehaviour ofwater
protons in rat gastrectonemiusmuscle [17] andofwater inmilled
Northernwhite-cedarwood chips [19].Inthe firstcasetherelaxation
behaviourhasbeenexplainedwith anannularcylinder geometry.The
outer surface atR=a has a sink strength density Mthatsatifies
Ma/D=4.9.With thedatagivenin [17]wewereabletocalculate a,
resulting in a=14.7p . With D=2.5xl0"5cm2/s this yields
M=8xl0 -2 cm/s. In the study ofwood chips [19] Brownstein useda
surface layer of macromolecules containing water of thickness
dr Z0.26 pmandT 2 = 1mstoexplaintherelaxationbehaviour ofwatei
adsorbedonwood [19].Sinks inthebulkvolumehavebeenneglected.
95
*ToM2(x103)(cm2/s)
icr
10'
10'
10J
c
—»-MR(x106)(cm/s)
Fig. 4 Calculated plot ofTM vs.MR,based on eqns. 5.5.The diffusion constant
D=2.5xi0" 5 cm 2 /s.
The initial slopeoftheobserved relaxationdecaycurve isgoverned
by 1/T2 of this surface layer. In [17]ithasbeenexplained that
this initial decay isrelatedbyMviaT2=V/Ms,whereV isthesample
volume andsistheactive surface area.Foraplanargeometrywith
thickness drthisresults inT2=dr/M.Forthesurface layerofwood
[19]thisresults inM?2.6xl0-2 cm/s,only afactorthree lowerthan
thevalue ofMinratmuscle.Takingthelowestvalue ofM calculated
above (2.6xl0~2 cm/s inwood) as a representative ofxylemvessel
walls, we can makeanestimationofthexylemvesselradiusofthe
cucumber stem segment of Fig.2.Using our experimental value of
T2=250±20ms for such a segment we find R=60pm from Fig.4.
Incucumber stemsxylemvesselshavebeen foundwithR5300nm.
With the results ofFig.4wecanalsoexplainwhynosignalof
flowingwaterhasbeenobserved instem segmentsofanumber ofother
plants. In these plant stems the maximum vessel radius Risless
thanthatfound incucumber,and,according toFig.4,T 2 isexpected
96
to be <250ms. Thus, observation of flowing water NMR signals
strongly dependsonthemaximum vesselradius.
In the diffusional formalism presented by Brownstein and Tarr
[16,17] the expected dependence of T 2 on the pulse period x(see
Section4.5.3)is not incorporated. As stated inSection4.5.3 we
expect anincreaseofthemeasuredT 2 uponadecreaseoftallowing
themeasurementof flowinsmallerxylemvessels.
5.3. 2 Intact
plants
Fig. 5Al and A2 represent flowing water signals inanintact
cucumber stembefore and after addingwatertothe soil, respectively,
resulting inanincrease ofv=9.9±0.8 mm/sto 14.3±1.1mm/s.
1
5
6
*•t(sec)
Fig. 5 15MHzNMR signal (single trace)amplitude S(t)vs.time forwater flowing
in the stem of an intact cucumber. (A) Signal of flowing water under
illumination with two Na-lamps at 1mmean distance from the leaves,zero
airvelocity, ambient temp.23°C.
1. v=9.9 mm/s
2. v=14.3mm/s
before and after adding water to the soil, respectively.
(B) Signal 15min. after cut-off of flow closely below stem section in
the r.f. coil; all other conditions identical to those inA.
97
The performance ofthemethod canbejudged inFig. 5B,where, after
interrupting thesupply ofwater tothe measuring region ofthestem,
no signal isobserved, notevenofthestationary tissue-water(90%
ofthetotal water content).
The effectofsoil water potential andillumination intensityon
v andtheaverage spin-spin relaxation rate R 2 have been measured
inthestem ofanintact gherkin plant. (Figs.6and8 ) .Fig.6 shows
that thesoil containing plant iswell watered atthemomentof
measurement: afurther addition ofwater doesnotalter the mean linear
flow velocity, incontrast towhat isobserved inFig.5.
R,(s-i)
K
wateradded
t V(mm/s)
lamps off
i
X
X
-
15
*
4
\x
X
"xv-xX--x**
|_.H_
-x
X-X*
K
*>
10
V
5-
4
-*•t(hours)
Fig. 6
5
1
H pulsed NMRmeasurements of mean l i n e a r flow v e l o c i t y v (o) and s p i n - s p i n
r e l a x a t i o n r a t e R2 (x) in an i n t a c t gherkin p l a n t , measured i n the stem
a t ~ 0.5 m above s o i l s u r f a c e . The response of the NMRs i g n a l s t o the
a d d i t i o n of water and t o v a r i a t i o n in l i g h t i n t e n s i t y i s shown.
Under t h i s c o n d i t i o n i t i s expected t h a t the flow v e l o c i t y i s cont r o l l e d by the t r a n s p i r a t i o n process in the l e a v e s . Under the a c t u a l
environmental c o n d i t i o n s ( r e l a t i v e a i r humidity: 44 %, t e m p e r a t u r e :
98
24.5 °C, illumination with two 400W Na-lamps at about 2m above
the soil surface, zero air velocity) amaximum flow velocity of
13mm/s was found. After turning off the lamps,v decreases from
13mm/sto~7mm/sover aperiod of~30min.Atlongertimesafter
turningoffthelampsthedecrease invismuchslower.Thedecrease
inv when thelightisturned offisduetoclosure ofstomata.As
suggestedby Slatyer [1]atthatmomenttheupwardmovementofwater
to the leaves, due to amildwater stress intheleavesandstem,
begins to exceed the rate of loss due to transpiration, and the
differences inwaterpotentialbetween soil,rootand leafdecreases
(seealso [22]). Consequently, theleafapoplastandcellsandstem
cells are rehydrated. This is reflected inthedecreaseofR2.As
shownin [8]R 2 (=l/T 2 )isinverselyproportionalwithwatercontent.
The slight change inR2 atturning offillumination indicatesthat
thecellsinthestemwereonlymildly dehydrated duringthe light-on
period due to the well watered soil (low resistance betweensoil
and root). After turning on illumination, vandR2 increase again
and approach about the same value as at the beginningoftheexperiment. (v=13.0-13.5mm/s,R2=3.4 s - 1 ) - TheresponseofT 2 ondark/
lightperiods has been measured in the stem of anintactpapyrus
plant (Fig.7 ) .ThisisinfairagreementwiththedataofFig.6.
T2(msec)
285>
225-
*•»«
„„»«>•»
255-
«•« •
•».»•»
. "- .",V
"
.«•
.„*•....*.„••
195165lamps off
wmmmtmii
1
1
10
20
lamps off
mmnmmmm.
1
30
t(hours)
1
40
Fig. 7 Change in J H spin-spin relaxation time T 2 (taken as the time atwhich
the value of the decay curve reaches 1/eof its initial value)measured
in the stem of an intact papyrus plant in response to light/dark periods.
r-
50
99
The effectofadecreaseinsoilwaterpotentialonvandR2in
the stem ofthesame gherkin plant isrepresented inFig.8.At
t=0wehavemeasuredtheflowvelocity,twodaysafteraddingwater
to thesoil.Themeasuredvalue,v=17.5±1.2mm/s,ishigherthan
thatmeasured inFig.6.Thismaybeduetoanincreaseinrelative
airhumidityandtemperature (65%and26°C,resp.)withrespectto
theconditionsforFig.6(44%and24.5°C,resp.).Thefollowingday
the flowvelocitywasfoundtobedecreased considerably,inagreement
withthedrysoilandthewiltingofthelowestleafonthestem.
"T--
lamps off
V////////////A
l a m p s Off
iwater added
•water added
c *1L
/\
R2(S-')
|water
•
{added . g |
15| V(mm/s)
10
\
\
J1
5-
'
x
K-X-' 1 -
10
20
30
40
•t(hours)
50
F i g . 8. 1H pulsed NMR measurements of v (o) and R2 (x) i n the stem of an i n t a c t
gherkin, demonstrating the e f f e c t of dehydration and r e h y d r a t i o n of the
s o i l . For f u r t h e r experimental c o n d i t i o n s : see t e x t .
Under these conditions the s o i l r e s i s t a n c e increases and root water
p o t e n t i a l decreases, r e s u l t i n g i n dehydration of c e l l s i n r o o t , stem
and leaves [ 1 ] . This i s r e f l e c t e d by the i n c r e a s i n g value of R 2 . At
the beginning of the t h i r d day R 2 =8.5 s _ 1 , twice the value measured
a t t h e beginning of the second day, i n d i c a t i n g a strong decrease i n
hydration of t h e stem t i s s u e . The flow v e l o c i t y i s also decreased
100
with respecttothatonthesecondday.Now,addingasmall amount
ofwatertothesoilresultsinanincreaseinv (measured aftera
few seconds afterthewater gift)andadecreaseinR2.Addinga
secondandthird larger amountofwatertothesoil,v increases
shortly,andnext reachesasteady stateatv=8.9±0.6mm/s.This
valueislower thanthemaximum valuev=17.5±1.2mm/s(att=0),
reachedunderthesameenvironmental conditions.Thesupplyofwater
resultsinadecreaseofR2,which after aboutthreehoursreaches
approximately thesamevalue (R2=3.2s _ 1 )asmeasured under well
watered conditionswith lampsoff(seeFig. 6 ) .
Ashas beenstatedinChapter4,theamountofflowingwater(in
mm3)isfoundbyeitherplotting 3[ S l ^ j.t m a x ]/3t m a x vs.t m a xor
S(tmax
_„)vs.t _ „max
andextrapolatingtot„_=0.
InFig.9thedataof
max
Fig.6areshownintheformofasemilogplotofS(t_„)vs.t „.
100
(arb. units)
t
10
•3fc"**i
'--<}.
-
^
•
0.5
1.0
tmax(s)
Fie. 9 Semilog plot of S(t ) vs. t
of the data of Fig. 6. (x) data obtained
°
°r
max
max
i n t h e dark period following t h e t u r n i n g off of lamps, (o) data obtained
i n t h e l i g h t p e r i o d , a f t e r t u r n i n g lamps on.
Fig. 9 c l e a r l y shows t h a t t h e r e i s a s y s t e m a t i c d e v i a t i o n between
t h e v a l u e s of S ( t
) during a dark p e r i o d following t h e t u r n i n g
off of lamps and those during a l i g h t p e r i o d , a f t e r t u r n i n g lamps
101
on. Though t „ _nicix
. andthusv,iswithinthesametimeintervalfor
thesetwoprocesses,S ( t ) measuredwith lampsoffissystematically
higher thanwith lampson.Extrapolationofthetwocurvestot =0
max
reveals thattheslopeofthecurvesareapproximately thesame,
but S(0), andthusthevolume flowrate,issignificantly largerfor
the "lamps off"plotthanforthe"lampson"plot.(Fig.9 ) .These
findings indicateahysteresis effectinthevolume flowratebetween
lightanddarkperiodsandviceversa.
A plotofS(t )vs.
t__„forthe
processesofdehydrationand
nicix
iucix
rehydrationofthesoil, obtainedbyusingthedataofFig.8, is
presented inFig.10.ThisFiguredemonstrates thatnowsystematic
deviations between thedata points obtained byrehydrationand
dehydrationareabsent,incontrasttothephenomenoninFig.9.
100
S ( t m a x ) (arb.units)
t
10-
"Hi. -*U
- i —
0.5
1.0
•*max(s)
Fie. 10 Semilog plot
of S(t
) vs. t
of the data of Fie. 8. (x)
data obtained
6
°
°r
max
max
by dehydration of the soil, (o) data obtained after rehydration of the
soil.
I t i s n o t i c e a b l e t h a t S(0) obtained by e x t r a p o l a t i n g t h e curve of
Fig. 10 t o t x =0 i s s i g n i f i c a n t l y higher than S(0) obtained from
the "lamps off" curve i n F i g . 9. I t i s noteworthy, t h a t t h e data of
Fig. 9 and 10 have been obtained using t h e same gherkin p l a n t ,
whereas the time elapsed between measuring t h e data of F i g . 6 and 9
102
on one hand andthedataofFig.8and10ontheotherhandisone
week. This may be the reason forthedifference inS(0)inFig.9
and 10.Nevertheless, theslopesoftheplotsofFig.9and10are
equal within experimental error: Fig.9 yields a decay time of
480±55ms, whereas the deceay timeobtained fromFig.10results
in520±50ms.
Concerning the reliability of the values ofvinFig.6and8,
we note first that calibration has been performed with aglass
capillary model system (Section 5.2.1)inwhich the flow may be
considered aslaminar (Section4.5.1.3).Frommeasurements inisolated
strandsofxylemvessels of Plantago major Lithasbeen demonstrated
that the flow inthesevessels isessentially laminar,eventhough
flowresistance inthesevessels strongly dependsonthewall surface
sculptures [20].The Reynolds numbers (ResiO6 Q/R,whereQisthe
volume flowrate and Rthevesselradius)foundinxylemvesselsof
Plantago major Lareintherange~0.1 [20].Fromourmeasurements
in cucumber and gherkin the maximum value of Re calculated from
volume flowrate and estimatedvessel radius is~1.Also theeffect
ofsurface sculptures andcurvature ofthevesselsmaynotbeexpected to introduce turbulence [21].Ashasbeenstatedelsewherethe
shapeoftheNMRsignals of flowingwater aresensitive fortheflow
profile (Chapter 4 and [6]).Indeed, theshapeoftheNMR signals
supporttheexpected laminar flowpattern.
Secondly, flowvelocityhasbeenobtainedviaeqn.5.2,whichis
valid if T^^h^i (Section 4.5.1.2). In Section 5.3.1 wehave shown
that this conditions holds foraparticular cucumber stemsegment,
which is not necessarily true for every type ofplant stem. In
Chapter 6we show bycomparing flowmeasurementswiththeNMR-and
balancemethodthatinaparticular cucumberplanteqn.5.2 results
in systematic deviations, indicating that for water in the xylem
vessels of thatplant stem T 2 <^T 1 (seeSection4.5.1.2).Thishas
been verified by theNMRresults alone.Wecannotexclude thatfor
the measurement of the flowing water in the xylem vessel of the
gherkin plant presented inFigs. 5-10 alsoT2<HT!.WhenT2<HTjthe
values ofv must be corrected according to the datapresented in
Fig.11ofChapter4.Thishasnoeffectontheshapeoftheresponse
ofvonvariations inlightintensity andsoilwaterpotential,however (seealso Figs.6and8ofthis Section).
103
5.4 CONCLUSIONS
ThevalueofT 2 ofthewater inthexylemvessels inplantstems
hasbeenshowntobe strongly related tothevessel radiusR.Dependingonthisvalue,linear flowvelocities (v)andvolume flowrates
(Q)havebeenobtainedbyuseoftheNMRnpulsemethod.
Combination of these flowmeasurementswithNMRT 2 measurements
ofthestationarywater (tissuewater surrounding thevascular system)
in intact plants turnouttobeusefultostudytheeffectsofenvironmental factors,suchaslightintensity,temperature,relative
airhumidity, soilwaterpotential,etc.,onv,Qand,viaT 2,water
content ofxylem water andtissuewater,respectively.Theeffects
of changes in theseenvironmental conditions onv,QandT 2 canbe
measuredwith atimeresolutionofafewseconds.Thisstudydemonstrates that these pulsed NMR measurements provide anew approach
tothestudyofparts oftheplantwaterbalance.
5.5 ACKNOWLEDGEMENT
Weareindebted toDr.A.P.M.denNijsofthe InstituteofPlant
Breeding (IVT)forhiskindly giftoftheplantmaterial.
104
REFERENCES
1. R.O.Slatyer,"Plant-WaterRelationships"(AcademicPress,NewYork,1967).
2. A.H.Fitter,R.K.M.Hay,"Environmental Physiology ofPlants"(AcademicPress,
London,1981).
3. C.R.Black,J.Exp.Bot.30 (1979),235.
4. J.Balek,0.Pavlik,J.Hydrol.34(1977),193.
5. B. Slavik,"MethodsofStudyingPlantWaterRelations",EcologicalStudies,
Vol.9,p.p.223-235 (Springer-Verlag,Berlin,1974).
6. M.A.Hemminga,P.A.deJager,J.Magn.Reson.37 (1980),1.
7. H.VanAs,T.J.Schaafsma,Bull.Magn.Reson.2 (1981),359.
8. H.VanAs,W.P.A.vanVliet,T.J. Schaafsma,Biophys.J.32(1980),1043
(Chapter7thisThesis).
9. S.Meiboom,D.Gill,Rev.Sci.Instrum.29 (1958),688.
10. R.L.Void,R.R.Void,H.E.Simon,J.Magn.Reson.11(1973),283.
11. D.G.Hughes,G.Lindblom,J.Magn.Reson.26 (1977),469.
12. S.W.Provencher,J.Chem.Phys.64(1976),2772.
13. R.Cooke,R.Wien,Biophys.J. 11 (1971),1002.
14. J.R. Zimmerman,W.E.Brittin,J.Phys.Chem.61 (1957),1328.
15. J.Jen,J.Magn.Reson.30(1978),111.
16. K.R.Brownstein,C.E.Tarr,J.Magn.Reson.26(1977),17.
17. K.R.Brownstein,C.E.Tarr,Phys.Rev.A.19 (1979),2446.
18. M.A.Hemminga,P.A.deJager,A.Sonneveld,J.Magn.Reson.27 (1977),359.
19. K.R.Brownstein,J.Magn.Reson.40 (1980),505.
20. A.A.Jeje,M.H.Zimmermann,J.Exp.Bot.30 (1979),817.
21. T.R.F.Nonweiler,in"TransportinPlants.I:PhloemTransport",Encyclopedia
ofPlantPhysiology,NewSeries,VolumeI(M.H.Zimmermann,J.A.Milburn,
eds.),p.p.474-477 (Springer-Verlag,Berlin,1974).
22. M.H.Behboudian,Thesis,Wageningen,TheNetherlands,1977.
105
6
COMPARISON OF FLOW MEASUREMENTS WITH NMR, HEAT PULSE AND BALANCE
METHOD
6.1 INTRODUCTION
InChapters4and 5ofthisThesiswehavepresented theuseofa
non-destructive pulsedNMRmethod tomeasure flowingwaterinplant
stem xylem. In Chapter4wehave shownthatthisNMRmethod,based
on apulse sequence of equidistant n pulses incombinationwitha
linearmagnetic fieldgradientinthedirectionof flow [1],isvery
suitable to determine the mean linear flowvelocityv,aswellas
thevolume flowrateQ,theeffective cross-sectional areaA available
for flow,andthespin-spinrelaxationtimeT 2 ofthe flowingwater.
InChapter 5wereported theresults ofthismethodwhenappliedto
plant stem segments and intactplants. Ithasbeenobservedthat,
using the experimental parameters, this method issuccessfulwhen
applied toplant stems with large diameter xylem vessels,dueto
therelationshipbetweenthevessel radius andT 2 ofwaterinthese
vessels (Chapter 5).InChapter4,however,wehavepointed outthat
theobservedvalue ofT 2 depends onthepulseperiod T.Infact,the
effectiveT 2 increaseswithdecreasing T, thusallowingmeasurements
insmaller diameterxylemvessels.
The combination of T 2 measurements of stationary tissue water
and flow measurements in aparticular sectionofaplantstemhas
beenshowntoprovide anew approach forthenon-destructive analysis
ofimportantparts oftheplantwaterbalance,with atime resolution
ofafew (4-12)seconds (Chapter5 ) .
UptoheretheNMR flowmeasurements inplantshavebeencompared
and calibrated with theresultsofmeasurements inglass capillary
model systems.Toavoid in-breeding, inthisChapterwecomparethe
results ofNMR flowmeasurements inthestemofanintactcucumber
with those obtained by the weight balance method and themicroscopically determined cross-sectional areaofthexylemelements.A
linear relationship between v asmeasured withNMR andQobtained
by thebalancemethod isshown.Fromtheslopeofv(Q)theeffective
cross-sectional area A available for flowhasbeendetermined.The
106
cross-sectional area can also be determined formNMRmeasurements
alone,andisshowntobe ingood agreementwiththepreviousvalue
oftheslopeofv(Q). Inaddition,theresults of flowmeasurements
with aheatpulse method [2] arecomparedwiththeresults ofthe
balance- andNMRmethod.
6.2 EXPERIMENTAL
6.2.1 NMRflow
measurements
NMR flowmeasurements havebeencarried outbythepulse technique
asdescribed inChapter4and [1].Fortheexperimentswehaveused
a 15MHz *HpulsedNMR spectrometer asdescribed inChapter 4.The
linear flowvelocityvwasobtainedviathe relationship
v=c/t
(6.1)
max
where C is acalibration constantandt
thepositionoftheextremumintheNMR signal (seeChapte 4). Calibrationhasbeencarried
out as described in Chapter 5, using flowing andstationarywater
with T1=T2=2.4s. Calibration of C at theparticularvalueofthe
linear fieldgradientGused intheexperiments yields C=7.5±0.2 mm.
With the same capillary systemused tocalibrate C (seeChapter 5)
at the particular value ofGusedherewehave alsocalibrated the
amount of flowing water V (inmm 3 ) via S(0),the height of the
maximum att =0,obtainedbyplotting S(t )vs.t
andextraiUclX
IflelX
IRclX
polating tot =0 (Chapter 4). Forthecapillary systemVhasbeen
calculated fromthecross-sectional areaAofthecapillary andthe
effective lengthofther.f. coilLf f (defined asthatlengthofa
sample forwhichtheheightofthe freeinductiondecaybecomes insensitive for increasing sample length)via V=A/L f f . The volume
flowrate in aplant is obtained fromvandV (asmeasured inthat
plant)via
Q=vV/Lef£
whereas the cross-sectional area of the xylem vessels in aplant
hasbeen foundby
(6.2)
107
A=V/Leff
(6.3)
Topreventradio frequency interference fromsurrounding equipment
(e.g. microcomputer, etc.) reaching thereceiverthroughtheplant
(working as an aerial), the soil has been grounded via theNMR
apparatus. Inthis way aconsiderable reductionofthenoise level
isobtained.
Otherexperimental conditionswerethesameasinChapter5.
6.2.2
Heat pulse flow
measurements
Heatpulse flowmeasurements havebeencarried outwithathermoelectricmethod asdescribed elsewhere [2].Heatisapplied locally
to the stem during a few seconds.Theheatflowsintothestemin
all directions. Part of the heat reachesthexylemvessels andis
transported downstream with themovingwater.Thusthe temperature
rise (measuredby apair ofintegrated circuittemperature sensors)
will be higher downstream than it is upstream. Time ofoccurence
(b) and magnitude (c)of the maximum in the temperature between
pointsupstream anddownstreambothdepend onthe flowrate.Wehave
taken tga=c/b as ameasure of flowrate.A sensordesignhasbeen
used with a flatsurface andadistancebetweenheater andeachof
the two i.c.'s is10mm.Thesensingelementismounted ononeleg
of a thermally isolating clip.Theother legoftheclipbears aV
groove for correct positioning ofthesensoronthestem.Toreach
anoptimumheattransferbetweenheater and flowingwater,thesensor
was positioned as near aspossible ataxylemvesselbundle (This
iseasily accomplished inthecaseofacucumber).
Durationofheatingwas 10s,withacurrentof0.5 A inaheating
elementwith 0.5 ohm resistance,allowing arepetitiontimeofabout
4 min. attheobserved flowrates.Otherexperimental conditionswere
thesame asin[2].
6.2. 3 Balance transpiration
flowrate
measurements
The transpiration rate of the pot plant has been measured by
weighing on an electrical differential top balance (Mettler,type
108
PE-11 in combination with BE-13). The output of the balance was
recorded on a strip chart recorder. The transpiration rate ata
particular timewasdetermined fromtheslopeoftherecord atthat
time.Topreventevaporationofwater fromthe soilinthepot,the
soilsurfacewascoveredwithaluminium foil.
6.2. 4 Cross-sectional
area
Cross-sectional areasAofthe flowconducting elementshavebeen
calculated frommicroscopicmeasurements assumingthevessels tobe
unobstructed capillaries. Measurements have been carried out in
radial sections taken from those stem partswhichwerepositioned
intheNMRr.f.coil andintheheatpulsesensor.
6.2.5
Plant
material
Measurements have been carriedoutonanintactcucumberplant,
potted inaplastic container,placed onthetopbalance.Theplant
was illuminated with two 400W Na-lamps at about 2m above soil
surface.TheNMR r.f.coilwassituatedontheplantstem at0.75m
above the soil surface,whereas theheatpulse sensorwasclampsed
onthestemat~ 1.25 mabovethesoilsurface.
6.3 RESULTS
Figs.1and2presents respectively themeanlinear flowvelocity
v asmeasuredwithNMR andtg a asobtainedbytheheatpulsemethod,
bothplottedversusthevolume flowrateQ_measuredwiththeweight
balance anddefined astheweightlossperunittime.IntheseFigures
we will take Q„ as the reference.AshasbeenshowninChapter5,
flowrate andwatercontentoftheplanttissue aremutuallycoupled.
However, deviations of Q R fromthetrueactualvolume flowratedue
tothesevariations inthewatercontenthavenotbeenconsidered.
To obtainvariations invandQ_ theilluminatingNa-lampshave
beenswitched offandon,warmwaterhasbeenaddedtothesoiland,
at last, leaves havebeencutoff fromthestem. InFig.1aswell
as Fig.2we have indicated from which procedure the datapoints
have been obtained. Theresponseofvasmeasured withNMRoneach
processhasthesame shapeasthatgiven inChapter 5 (Figs.6and8 ) .
109
10
15
*•Q Bft»m»3/s)
Fig. 1 Plot of v as obtained by NMR method versus Q R as measured with the
balance method for an intact cucumber plant.For the explanation of curves
a and b see text.The flowhasbeen varied by: (o)lamps off, (x)lamps
on again plus adding warm water, (A) lamps off again,and (+)cutting
off leaves fromplant stem.
0
5
10
15
*-aB(mm3/s)
Fig. 2 Plot of tga as obtained with the heat pulse method versus Qfias measured
with the balance method. See legend ofFig. 1for other conditions.
110
Ashasbeen statedinChapter4 (Section4.5.2.1)theamountof
flowingwaterV(mm3)inther.f.coilisobtained fromtheNMRflow
measurements byeither plotting s (t max )< thesignalheightofthe
maximum, versus t„ or
viaaplotof3[S(t
).tL vmax'
]/3tmaxversus
J/
max
*
max
t .InFig.3theNMRsignals offlowing water inthecucumber
plant arerepresented asaplotofS(t )vs. t . I n thisFig.
the difference inS(t )between the"lamps off"and"lampson"
data points,ashasbeen observed inagherkin plant (Chapter5,
Fig.9)isabsent.Thismaybeduetothetimelagbetweenthemoment
ofswitchingthelampsonagainandthefirst flowmeasurement after
switchingthelampson,whichhasbeen~15min.Apart fromthedata
points obtained after cuttingoffleaves fromthestem,denotedwith
(+)inFig.3,thedata points showalinear relationship between
S(t )andt x , whenplottedinasemilog fashion.Extrapolation
of this plot tot m = = 0 yields S(0)=9±0.5 (arb.units), whichhas
been foundbycalibration (Section6.2.1)tocorrespondwithanamount
of flowingwaterinthecoilV=3.2±0.4mm 3 .ViaLff =7.24mm,itis
possible tocalculate theeffective cross-sectional area available
for flowviaeqn.6.3,andviaegn.6.2thevolume flowrateQ.From
eqn.6.3wefoundA^.^0.4410.06mm 2 .
t
S(tmax)(arb.units)
10^
tmax(s)
Fie. 3 Semilog plot of S(t
)vs. t
of flowing water in cucumber plant stem
r
max
max
°
asmeasured with theNMR method. V denotes the amount orvolume of flowing
water measured in the r.f. coil. See legend ofFig. 1forother conditions.
Ill
The slopeoftheplotinFig.3yields adecaytimeT=0.38s.In
Chapter4, Section 4.5.2.1we have pointed out that (i)TS3T2 if
T!=T2, or (ii)T=T2 ifT!>>T2,or (iii)T2<T<3T2 whenTi>T2,where
T] and T 2 are the spin-lattice and spin-spin relaxationtimes,
respectively. From aplotofS(t , ) . t = „vs.t ,_,(incombination
iflciX
IUclX
IUclX
withthevalue ofT,thedecaytimeobtained fromS(t „)vs.t „)
IUclX
the ratio T x /T 2 can be estimated from the point where the slope
9[S(t ).t ]/3t
becomes zero (Chapter4, Section 4.5.2.1).
H13.X
IH3.X
fflclX
For the data of Fig.3 this point in such aplot is foundtobe
~ 0.5 s (The curve is rather flat). Thisvalue is~ 1.4 timesthe
decay timeT,indicating thatT X >2T 2 andT 2 isthereforeonly slightly
largerthanT (Chapter4,Section4.5.2.1).WhenTj>2T2 eqn.6.1 is
not longervalid, andvhastobecorrected according tothevalues
of Tj and T 2.From the abovementioned considerationsweestimate
T2~0.4-0.45 s and T!~1.0-1.5s. Corrections onvinagreementwith
these values of T1 and T 2 (see Fig.11 of Chapter4) results in
Fig. 1inatransitionofthestraightline atob.Lineb isgiven
by Q=0.49v, yielding an effective cross-sectional area forflow
AB_N=0.49mm2, where B-N denotes that the cross section has been
obtained fromcombinedbalance andNMRmeasurements.
Therelative largedeviationofthedatapointsdenotedwith (+)
in Fig.1 from line a can beexplained usingFig.3.Thesepoints
have been obtained by cutting off leaves from the stem. Fig.3
clearly shows that thisresults inadecreaseofS(t x ) forthese
points, indicating that atthatmomenttheamountof flowingwater
in the coil has decreased, due to a decrease inconductingxylem
vessels. Thus, the deviationofthesepoints inFig.1from linea
reflects a decreased value of the effective cross-sectional area
forthe flowingwater,justasexpected.
Themicroscopically determined cross-section ofthexylemvessels
yieldsA=0.92±0.04mm 2 .Thoughthedistribution ofvessel radiiat
the position of the NMR r.f. coil (Fig.4)andatthepositionof
the heat sensor are slightly different, thecross-sectional areas
areequalwithinexperimentalerror.
IUclX
112
Jnumber of vessels
50
100
150
— » .R(yum)
Fig. 4 Distribution of xylem vessel radii in the cucumber plant stem at the
position of theNMR r.f. coil.
6.4
DISCUSSION
Whenwecompare thevalue ofthecross-sectional areaofthexylem
vessels asfound from inspectionby amicroscope (A=0.92±0.04 mm 2 )
withthevalues oftheeffectivecross-sections asfound fromv(Q R )
(Fig.1) (AB_N=0.49mm 2 ) and the value found with NMR alone
(ANM_=0.44±0.06mm 2 )we observe good agreement between thelatter
values, whereas the former is about twotimeshigher.Thisisnot
very surprising, because thecross-section for flowmaynotbethe
sameasthemicroscopically measured area,duetoe.g. astationary
boundary layerofwater atthewalls ofvessels [3],orduetononconductingvessels [4-8].TheagreementbetweenA__N andA N M R isan
argumentinfavorofthereliability ofthisvalue oftheeffective
A
cross-sectional area available for flow. That
NMI tends to be
slightly lowerthanA__Nmaybeexpected fromthe followingconsiderations: as has beenstated inChapter 5thevalueofT 2 of flowing
water in aparticularxylem elementstrongly dependsontheradius
Rofthatelement;bydecreasingRthevalueofT 2 will alsodecrease.
Thisresults inadecrease oftheheightoftheNMR signal att ,„.
73
max
In addition, when we assume Pouiseille flow,themeanlinear flow
velocity depends onR2.Thus,there isadistribution ofvalues for
v,resulting inaspread oft
(eqn.6.1).However,thespread in
1S
tm=„ partly compensatedbythecorrelationbetweenvandT 2 via
113
R: when v is small due toasmallvalueofR,T 2 isdecreased and
the shift of t
tohighervalues duetosmallervispartlycompensated due to the shift in t
tolowervaluesbythedecrease
ofT 2 (see Chapter4, Fig.11).Indeed, ithasbeenobserved that
theNMR signals offlowingwaterinplantstemsarehardlybroadened
with respect to thesignalsofflowingwater inaglasscapillary.
This may also becaused duetothe factthatthevolume flowrateQ
depends onR 4 , resulting inthelargestcontributiontothesignal
ofwater inthevesselswiththelargestvaluesofR,v andT 2 •
Comparing the data of Fig.1with those of Fig.2 (keeping in
mindthatthedatapoints inFig.1havetobeconsidered asgrouped
around curve b, as argued above), we find a linear relationship
betweenvandQ inFig.1,whereas theplotoftg a vs.Q R exhibits
somewhat more scatter, in particular for higher values of Q D
(Q_>7mm 3 /s). For these larger values ofQ_ thewater flowcanbe
considered asaflowofcoolant,resulting inasmaller increaseof
themagnitude oftheheatpulse signal ascompared tothatatlower
flowvelocities.Fig.2also showsastrongcorrelationbetweenthe
relationship oftgaandQ R andtheprocessbywhichthe flowvelocity
has been varied. Thismaybeexplainedby theadditional variation
inthewatercontentwhenvarying thewater flow (seeChapter 5).
Theresults obtainedwiththeheatpulsemethod canbepresented
in terms of timeofoccurenceofthemaximum (b),magnitudeofthe
maximum (c)inthetemperature difference ortga(sb/c)[2].Ineither
caseonlyarelative difference insignalparametercanbeachieved.
Whether these signal parameters arerelated tovorQispresently
unclear. By considering the striking agreement inthebehaviour of
3
v and tg a in Figs. 1 and 2 respectively, atQ=7
R mm /s and at
QB=5.5mm 3 /s, we expect that tga isprobably closely related to
thelinear flowvelocity.However,we should notethattheheatpulse
method generates signals thatmainly reflectthewater flowinthe
xylemelements orxylemvesselbundlenearthesensor andthuschanges
ine.g.theeffectivecross-sectional areaandQarenotnecessarily
reflected bythesesignals.
114
6.5 ACKNOWLEDGEMENT
We are indebted to Mr.J.Reinders who has performed the NMR
experiments and to Mr.J.G. Kornet of the Technical and Physical
Engineering Research Service (TFDL), who has performed the heat
pulse measurements. The top balance was made available by
Dr. H.C.M.deStigter of the Centre for Agro-Biological Research
(CABO).TheplantmaterialwasagiftofDr.A.P.M.denNijsofthe
Institute of Horticultural Plant Breeding (IVT). The microscope
wasmade availablebyDr.R.W. denOuter ofthedepartmentofPlant
Cytology and -Morphology.
REFERENCES
1. M.A.Hemminga,P.A.deJager,J.Magn.Reson.37 (1980),1.
2. K. Schurer,H.Griffioen,J.G.Kornet,G.J.W.Visscher,Neth.J.Agric.
Sci. 27 (1979),136.
3. B.Huber,in"Handb.Pflanzenphysiol." (W.Ruhland,ed.),Vol.Ill,p.p.
511-513(Springer-Verlag,Berlin,1956).
4. M.H.Zimmermann,C.L.Brown,"Trees:StructureandFunction"(Springer-Verlag,
NewYork,1971).
5. M.H.Zimmermann,J.McDonough,in"PlantDisease"(J.G.Horsfall,E.B.Cowling,
eds.),Vol.3,p.p.117-140(AcademicPress,London,1978).
6. M.H.Zimmermann,Can.J.Bot.56 (1978),2286.
7. J.A.Petty,J.Exp.Bot.29 (1978),1463.
8. A.A.Jeje,M.H.Zimmermann,J.Exp.Bot.30(1979),817.
115
BRIEF COMMUNICATION
7. [ ' H ] S P I N - E C H O N U C L E A R M A G N E T I C R E S O N A N C E
IN P L A N T T I S S U E
I. THE EFFECT OF M N ( I I ) AND WATER CONTENT IN WHEAT LEAVES
H. VAN As, W. P.A. VAN VLiET.t AND T. J. SCHAAFSMA, Department of
Molecular Physics, Agricultural University, DeDreijen 6,6700 EP
Wageningen, The Netherlands
ABSTRACT The effect of age-dependent Mn(II)-gradients, as observed by electron paramagnetic resonance (EPR), on the ('H)NMR spin-spin relaxation time (7"2) was studied in wheat
leaves. Anon-exponential T2spin-echodecay wasalwaysobserved, revealing the presence ofat
least twodifferent fractions of non- (or slowly) exchanging water inthe leaves. Noeffect of the
Mn(II)-concentration on T2 of the separate water fractions (covering -90% of the total water
content) has been found. From theseobservations weconclude that Mn(ll) ispresent in bound
form. The dependence of T2on water content can be explained with a two-state model,
demonstrating theoccurrenceof fast exchange within each of the twoslowly exchanging water
fractions.
7.1
INTRODUCTION
Proton-spin-latticc (7",) and Proton-spin-spin (T2) relaxation times have been widely used for
the study of the physical properties of water in biological systems (1-4) and a relationship
between 7",,T2 and water content has been demonstrated (1, 5, 6, 7). The interpretation of the
results is complicated by the complexity of the specimen. The main difficulties arise from the
fact that to the measured parameters (7",, T2) contributions may be made by factors not
directly related to the physical properties of water. It is well-known, that plants contain
Mn(II) and other paramagnetic metalions as a constituent of the photosynthctic unit (8).
These paramagnetic centers may shorten the relaxation time of water protons, obscuring the
correlation between Tu T2 and water content.
Fedotov et al. (4) have shown that there is no, or only a small, effect of paramagnetic ions
on 7", of water in intact tissues of bean and crinum leaves, nor is there one in potato tuber.
Samuilov et al. (9), using the Overhauser effect have found no effect of paramagnetic ions in
seeds of Welsh onions, peas, broad beans and sunflower. According to Hazlewood et al. (2)
t H . van As and T. J. Schaafsma weredeeply saddened by the death of W. P. A. van Vliet on July 5, 1980.
BlOPHYS. J. © Biophysical Society
Volume 32 December 1980 1043 1050
Reprinted with permission.
116
the relaxation mechanism in skeletal muscle is insignificantly affected by paramagnetic
impurities. Stout et al. (10) suggest, however, that in ivy bark T2of extracellular water is
shortened by paramagnetic ions in the cell walls. In aqueous suspensions of chloroplasts
Wydrzynski et al. (19) concluded that 7", and T2 are largely determined by manganese, bound
in the chloroplast membrane.
Here, we report the results of measurements on leaves of summer wheat, type S E L T E P .
Using EPR, we detected Mn(II)-gradients in the leaves, changing sign upon maturation. The
effect of these gradients on the spin-spin relaxation time T2 of tissue water was investigated as
a check on the correlation between T2and water content. This research is part of a program
aimed at the use of spin-echo N M R techniques to measure transport and exchange of water in
plant stems (11, 18) and tissues.
7.2
MATERIALS AND METHODS
Plant
Material
Wheat variety SELTEP, was grown under a 16-h light (23°)/8-h dark (20°C) cycle. No special culture
was used. Proton spin-spin relaxation measurements were carried out using leaves in different stagesof
maturation and at different positions in the plants. Leaves were cut transversally in ~2 cm sections for
NMR and EPR measurements. EPR signal amplitudes were not affected by waiting periods of ~2 h
after segmentation.
EPR
Measurements
Room temperature EPR spectra were obtained using a Varian E-3 spectrometer (Varian Associates,
Instrument Div., Palo Alto, Calif). Samples were contained in a quartz tube, 0.8 mm id., permitting
reproducible sample positioning. Using standard precautions, the EPR signal amplitude of a 0.175 mM
MnCL solution was reproducible within 3%.Instrument settings: 100 kHz modulation amplitude, 10G;
microwave power, 40 mW;timeconstant, 0.3 s;scan rate, 250 G/min.
NMR
Measurements
The experiments were carried out with a home-built 15-MHz spin-echo spectrometer, equipped with a
Newport 7-in electromagnet (Newport Laboratories, Inc., Santa Ana, Calif.) (11), a home-made
transmitter/receiver coil of the solenoid-type, with a length of 5 mm and a diameter of 11 mm. The
spin-spin relaxation time T2 was measured by the Carr-Purcell-Meiboom-Gill (CPMG) method (12).
Because of the inhomogeneity and the size of the samples a time-dependent baseline ("baseline drift")
must beexpected (13, 14). A first order correction for this phonomena was made by the following pulse
sequence:
90? - T - ( - 180° - 2T)„ - 5T, - 9 0 ° , - r - ( - 1 8 0 ° - 2T)„ - 57V
Bysubstracting the twoCPMG-decays, the effect of missettings in the 180°pulses wasdiminished. The
CPMG T2 decay was measured by sampling the height of the echoes. The time 2T was set on 1.6ms.A
graphical method as outlined by Hazlewood et al. (2) was used to analyze the data. The error in T2 was
evaluated at ±8%.All NMR experiments were made at probe temperature (29°C).
Water Content
Water content was determined by weighing freshly excised samples, drying until constant weight in an
oven at 90°C, followed by reweighing.
Manganese
Determination
The total manganese content in the wheat leaf segments was determined by atomic absorption
spectroscopy. Measurements were made with a Perkin-Elmer HGA-74 type 460 atomic absorption
BRIIJ COMMUNICATION
117
spectrophotometer (Perkin-Elmer Corp., Instrument Div., Norwalk, Conn.). Dried leaf segments were
digested with 100^ilconcentrated HCI0 4 at =150°C. Digested samples wereevaporated and dissolvedin
100/Aconcentrated HCI.Thefinalvolume was brought to 100mlbyadding distilled water. Standards
at 0.02, 0.06,and0.10 ppm Mnwere prepared inanacidified water medium.
7.3
RESULTS AND DISCUSSION
EPR signals are easily detected in wheat leaves. Two types of spectra can be discerned: (a) a
sextuplet hyperfine structure, typical for Mn(ll), and (b) a weak peak close to the center of
the manganese multiplet.
Mn(II) ( p p m )
125
0.5
1.0
rel. leaf position
FIGURE 1 Mn(ll) inppm ofdry matter vs.theposition intheleaf.Therelative position isdefined as the
ratio of thedistance from the base of the leaf and the total leaf length. The results aregiven for three
wheal leaves in different stages of maturation: (O) very young, not full-grown (eighth leaf of a total of
eight, growth stage of the wheat, after the decimal code of Zadoks et al. (20, 17);(A) young, nearly
full-grown (ninth ofa total often, growth stage 19); ( • ) old,full-grown (sixth ofa total often, growth
stage 19). Mn(ll) ismeasured by EPR.
VAN As ET At. /'H/Spin-Echo NMR inPlant Tissue
118
Fig. 1 represents the resultsof Mn(II) EPR measurements for three wheat leavesin various
stages of growth. For very young leaves the Mn(II) signal decreases from base to top; upon
maturation this Mn(II) gradient reverses sign.
We measured T2, Mn(II), and water content of wheat leaves at various positions between
the base and the top of the leaf, using spin-echo NMR, EPR, and drying to constant weight,
respectively (Fig. 2). Invariably, a nonexponential T2 decay was observed, indicating that
there are several fractions of tissue water with distinguishable revalues. Because of the
limited signal-to-noise ratio we have used two water fractions, constituting 90% of the total
tissue water fordata fitting. The resulting ^-valuesof the two fractions differ bya factor of3.
The ratio between the amplitudes of the slowest and the fastest relaxing water fractions varies
from 1 to 2 for young vs.old leaves. Considerable scatter in the T2-valuesof the two separate
fractions occurs due to a strong correlation between the fitting parameters (amplitudes and
relaxation times). A mean effective relaxation rate R2 isdefined by:
R2 ~ PaT-2l + PbT-2l
(1)
Here Pa and Pb designate the two fractions of tissue water. In solution, R2 is linearly
dependent on the Mn(II)-concentration, but such linear relationship does not obtain in either
type of leaf (Fig. 2) for R2 of the separate fractions.
In older leaves, the sign of the Mn(II) gradient is reversed compared with younger leaves
(Fig. 1), but the dependence of the R2 curve on the position in the leaf does not change.
Evidently, the effect of the Mn(II) gradient measured by EPR isnot reflected inthe R2 values
of tissue water determined by NMR. This indicates that Mn(II) is present in bound form
inaccessible to water on the timescale of our experiments. This is not in conflict with the fact
Mn(ll) has been detected by EPR by Meirovitch and Poupko (15) and by other authors.
Siderer et al. (16) have observed Mn(II) EPR signals in lettuce chloroplasts similar to our
experimental results on intact tissue. Mn(II)-concentrations (Figs. 1and 2) are calculated
from the EPR spectra using aqueous MnCl2 solutions for calibration. Whether these Mn(II)
signals inwheat leaves have the full possible intensity or only 9/35 of the total intensity (Ms=
±1/2 transitions) (15, 16)cannot bedecided from the observed spectra.
When all manganese ispresent as Mn(II) ina bound form, allowingtheobservation ofonly
the - 1/2 z i 1/2 EPR transitions, the amount of manganese deduced from atomic absorption
and EPR measurements should be in a ratio of ~4. We observed a ratio of ~8. However,
manganese is not necessarily present as Mn(II). In dark-adapted chloroplasts Wydrzynski et
al. (19) have found that only part of the bound manganese is present as Mn(II).
Because Mn(ll) had noeffect on the spin-spin relaxation time of >90% of the total water,
we will now consider the relationship between T2 of the water protons and the total water
content in the two fractions. Separate /?2-values for the two fractions indicate that 90%of the
total water ispresent in twoslowly exchanging fractions. For a model with twostates aand b,
slow exchange isdefined by the condition:
ra' + Tb> « (Tl) < - {T°2b)\
(2)
neglecting thechemical shift difference between the twostates; T„,rbare the lifetimes of water
molecules in states a and b. and J?,,, T\b are the spin-spin relaxation times of water in the
BRIEF COMMUNICATION
119
very young wheat leaf
.i
Mn(ll)(p,p.m.)(a)
°/o dry matter (o)
R2(S-')(D)
young wheat leaf
Mn(lI)(ppm)(A)
•/. dry matter (o)
R2(s-')(o)
25-
25
Jf
.J'
20
20
t »-i
t-f
..i'f
15
ttW-V-f
10
0
0.5
rel. leaf position
1.0
0
0.5
rel leaf position
10
FIGLRI: 2 Mn(II), percent of dry matter, and spin-spin relaxation rate R2 as function of the leaf position
for the very young (a) and the young (b) wheat leaf of Tig. 1. Mn(ll) is measured by FiPR. The spin-spin
relaxation rate isgiven as the weighted average.
absence of exchange. The existence of fast exchange between two subfraclions within each
fraction is indicated by the dependence of R2 o n l n c dry matter/water ratio (Fig. 3).
For a two-state, fast-exchange model (1, 17), the observed single relaxation rate R2 is the
weighted average of the separate rates of two fractions consisting of "bound" and "free"
water, yielding:
K 2 ( = T2') = T2}+ Ph(T2'h-
r2».
where subscripts band/refer to "bound" and "free," respectively; Ph is the mole fraction of
the "bound" fraction. The magnitude of Pb is proportional to the ratio between the tissue dry
weight and the water weight, at least in the high water content region. Thus, in the two-state,
fast-exchange model there isa linear dependence of R2 on the ratio between tissue dry weight
VAN As KT AL. pHjSpin-Echo NMR in Plant Tissue
(3)
120
R2(s-')
40-
30
/
20
/
/°
/
/
/
/
10
/
° A J"
/
.^6a*te
0
0.2
0.4
weight dry matter
weight water
FIGURE 3 Proton relaxation rate R2 in the wheat leavesof Fig. 2A (A) and B (O) as a function of water
content. A nonexponential 7Vdccay was observed. The two fractions given here account for >907i of the
tissue water.
and water weight in the high water content region as experimentally observed for both
separate R2ain wheat leaves (Fig. 3).
Therefore, we conclude that >90% of the total water is present in two slowly exchanging
fractions within which there are fast-exchanging subfractions. Since the relaxation rate of the
separate fractions varies inversely with water content, inthis system the water content may be
measured using T2 values.This isnot always possible (5) sincevariations of the exchange rate
between different water fractions and of the dry matter structure may disturb the predicted
linear dependence of R2 on the ratiodry tissue weight and water weight.
7.4
CONCLUSIONS
(a) Wheat leaf containsage-dependent Mn(II) gradients. Part of the manganese isobservable
by EPR. (b) The Mn(II)-concentration docs not affect the spin-spin relaxation time T2 of
water fractions representing >90% of the total water content of the leaf, (c) From aand bwe
conclude that the measured Mn(II) is present in bound form, (d) >90% of the total water is
BRIRF C O M M U N I C A T I O N
121
present intwo fractions exhibiting slow exchange on the T2 timescale. Within these fractions
there arc fast-exchanging subfractions. (e) The relaxation rate of these twoseparate fractions
varies inversely with water content, in agreement with the predictions from asimple two-state
fast-exchange model.
We arc indebted to Mr. P. A. de Jager for general technical assistance and to Mr. R.M.J. Pennders of the Institute
for Atomic Sciences in Agriculture for making available the atomic absorption spectrometer. Stimulating discussions
with Mrs. \.van Leeuwen are gratefully acknowledged.
Receivedfor publication 10June19H0
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18.
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ZIMMERMAN, J. R., and W. E.BRITTIN. 1957. Nuclear magnetic resonance studies inmultiple phase systems:
lifetime of a water molecule in an adsorbing phase on silica gel.J.Phys. Chem. 61:1328-1333.
HEMMINGA, M. A., and P.A.DE JAGER. 1980. The study of flow bypulsed nuclear magnetic resonance. II.
Measurements offlow velocities usingarepetitive pulse method. J. Magn. Reson. 37:1-16.
19. WYDRZYNSKI, T. J., S. B. MARKS, P. G. SCHMIDT, GOVINDJEE, and H. S. GUTOWSKY. 1978. Nuclear magnetic
relaxation by the manganese in aqueous suspensions of chloroplasts. Biochemistry. 17:2155-2162.
20. ZADOKS, J.C ,T. T. CHANG, and C. F.KONZAK. 1974.Adecimal code for the growth stages ofcereals. Weed
Res. 14:415^121.
VAN A s ET AL. /'H/Spin-Echo NMR inPlant
Tissue
122
8
APPLICATION
OF NMR FLOW MEASUREMENTS
Based ontheresults reported inChapters4-7,wesuggestforthe
combinationofthepulsedNMRmeasurements of flowandwatercontent
the following applications inagriculture and inparticularhorticulture foruseas:
controling device for irrigation of cropfield and glasshouse
cultures.
warning device fordevelopmentofstressphenomena duetodrought,
frostordiseases.
monitoring device forscreening inplantbreeding experimentsto
selectplantswith lowenergy (lowtemperature)orlowwaterrequirements.
laboratorydevice for,e.g. studyofthewaterbalance inrelation
totheeffects ofenvironmental factors andstudyoftheblocking
phenomenon ofwatertransport incut-flowers,relevanttotenability.
Inallthesecasesthewater flowinthestemxylemvessels canserve
as aparameter for characterizing the wateruptake,transportand
storage(fructification).
The results discussed inChapters4-7 havebeenobtainedwitha
home-builtNMR spectrometer,operating at15MHz,andequippedwith
anair-cooled electromagnetwithasquareyoke (totalweight±200kg)
and either a single solenoid or Helmholtz r.f. coil. Theworking
dimensions determined by magnetandcoildimensionspermittheuse
ofobjectswith^15mmcross-section.
Inviewoftheapplications suggested above,amorepracticalNMR
instrumentshouldbe:
- portable for horticulture and field applications. This canbe
achieved by using small permanent magnets (e.g. [1]),keeping
inmind, however, that the water protons mustbe abletohave
reached Boltzmann equilibrium before entering the r.f. coil
(Section4.5.2.1). Forparameter settings seeSection4.5.3.
123
abletomeasureT 2 aswell asflowvelocities.Thisrequirestwo
differenttrainsofpulses,whichonlydiffer inthe firstpulse,
abletocompensate fordrift.Thiscanbe achievedbymakinguse
of the response oftheoff-resonance signalofstationarywater
(Section4.5.2.2).
The method has some distinct advantages alsoinmedicalapplications, in comparison with existing NMR methodsmeasuringbloodcirculation (see Section 3.5.1 and 3.5.2). The main advantage is
that the method is insensitive for a large amount of stationary
tissue water. Preliminary results of steady-state measurements in
fingers ofadultshave shownthe followingresults:
themethod issensitiveenoughtomeasure theeffectofthetwochamber heart contraction intheprofile oftheNMR signal (see
Fig.1 ) .
in
*-»
c
.a
k_
a
Of
-o
D
"5.
£
o
o
c
S?
in
T-
2
—i
1
1-
4
6
— > t(sec)
Fig. 1 NMR signal ofpulsed blood flow in finger of adult during the first seconds
after starting a (n-x)
pulse-train. Note structure of heart-beat signal
and the shape of the back-ground curve,which is similar to thatof steadystate flow. (See e.g. Fig.5,Chapter 5 ) . This signalmay also be due to
stationary water in finger-tissue,observed off-resonance (Section 4.5.2.2).
124
®
^
^
^
^
^
10
15
t (sec)—•
©
^J^U^U^
T-
5
lo
—r
t(sec)
15
Fig. 2 A Steady state *H pulsed NMR signals of blood flowing through index
finger of adult,obtained by apulse sequence ofequidistant n pulses
in combination with a linear magnetic gradient inthe direction of
flow.Time t=0 coincides with the n
pulse,wheren>4000.
B Same signal after 10 times knee-flexing. The DC-level changes sign
due to change innet flow and/or blood oxygenation.
C Same signal as inBafter \ \ min. resting period.
125
asshowninFig.2,bothheart-beat frequency,net flowandflow
during aheart-cycle canbemeasured. Changes innet flowand/or
blood oxygenation cause an off-set inDC-level,observed when
comparing Fig.2AandB.
since oxygenation results in changes inT 2 ofblood [2],which
in its turn affects thesteady state levelofthe flowing fluid
signal, effects of e.g. breathing and smokinghaveeasilybeen
detected.
sincetheT 2 ofthe fluid isstrongly related tothevesselradius,
physiological processes resulting inachangeofRwillbedetectable.This applies todefects intheblood circulation system.
In addition, the pulsedNMRmethod tomeasure flowasused inthis
Thesis [3]caneasilybecombinedwiththe "sensitive-line" imaging
method [4]to measure spatially resolved flowpatterns invarious
objects.
Obviously, for medical applications,theNMRmethodwouldbeof
considerably more interest if the instrument wouldpermittheuse
of objects with large diameters.Preferably themagnetgapshould
admit legs and arms. This does notseemtopreventapplicationin
themedical field,since instrumentswouldbe laboratory-bound.
REFERENCES
1. J.G.Shanks,F.-D.Tsay,W.K.Rhim,Am.J.Phys.48(1980),620.
2. K.R.Thulborn,J.C.Waterton,P.Styles,G.K.Radda,Biochem.Soc.Trans.
9 (1981),233.
3. M.A.Hemminga,P.A.deJager,J.Magn.Reson.37 (1980),1.
4. W.S.Hinshaw,P.A.Bottomley,G.N.Holland,Nature270 (1977),722.
126
SUMMARY
ThisThesis describestheapplicationofanon-destructive pulsed
proton NMR method mainly to measure water transport in thexylem
vessels ofplant stems and in somemodel systems.Theresultsare
equally well applicable toliquid flowinotherbiological objects
than plants, e.g. flowofblood andotherbody fluids inhumanand
animals (Chapter 8). The method isbased on apulse sequence of
equidistant n pulses in combination with a linear magnetic field
gradientG.
Following a general introduction andasurveyoftheproperties
ofwater inplants (Chapters 1and 2), thebasicNMR theory aswell
asreviewsontheapplicationofpulsedNMR tothedeterminationof
flow,diffusionandwatercontent arepresented inChapter3.
Amathematical treatmenthasproduced analytical expressions for
theshapeofthesignal S(t),basedonamodel inwhichthe flowing
fluid is thought toreceive aHn-T-(n-x-) pulsetrain:aVipulse
uponentering ther.f. coil followedby asequence ofequidistantn
pulsesuntil the fluid leavesthecoil; simultaneously, thismovement
ofthe fluid along amagnetic fieldgradientapplied inthedirection
of flowproduces aphase shift of the nuclear magnetizationwith
respect to the rotating frame of reference (Chapter 4 ) . Although
thismodel doesnotleadtoperfectagreementbetweentheexperimental
andtheoretical signal shape S(t),itcorrectlypredicts theeffects
of experimental parameters onS(t)via analytical expressions.The
main results from this theoretical treatment in combination with
computer simulations, which have been experimentally verified in
glasscapillary systems,are:
as long as T 2 ^HT 1( themean linear flowvelocityvcanbe found
fromthetimet
atwhich amaximum appears inthesignalshape:
v=C/t ,where C is a calibration constant,depending onG,T
Ifl3.X
andthe flowprofile. IfT 2 <%T 1 vcanonlybereliably determined
whenbothTi andT 2 ofthe flowing fluidareknown.
- T 2 andtheamountof flowingwater inthecoilV, and consequently
the volume flowrate Q,canbedetermined fromtheheightofthe
maximum S(t )and t „.Depending on thevalue ofT 2 andthe
ITlclX
IRciX
valueoftheratioT!/T2,T 2 andV are found from asemilogplot
127
ofeither S(t m a x )vs.t m a x ( T l » T 2 )or3[S(t max ).t m a x ]/3t m a xvs.
Snax < T ^ > Based onflowmeasurements inplantstemsegments (Chapter 5)it
has been suggested thatT 2 stronglydependsonthevessel diameter
for the narrow xylemcapillaries.Thisbehaviour ofT 2 canexplain
negative results inplant stems with smallvessel diameter.Under
thepresentexperimental conditions themethodhasbeen successfully
applied to Cucurbitaceae (cucumber, gherkin, pumpkin) and tomato
plants.
T 2 measurements inwheatleaveshavebeenshowntobe insensitive
to the presence of cell-bound paramagnetic ions (Chapter 7). The
magnitude of T 2 of two separate water fractions (covering~90%of
thetotalwatercontent)hasbeen foundtobeinversely proportional
to water content.Measurements of flowandwatercontenthavebeen
combined foranintactgherkinplant (Chapter 5), demonstrating that
thecombination ofbothNMRmethods results inapowerful non-invasive
method to study important parts of theplantwaterbalancesimultaneously.Theresults strongly suggestthatthemethod canbeused
as an early warning fordevelopmentofstressphenomena inplants,
duetodroughtandother factors.Fromthe flowmeasurements ithas
been shownhow inaplantsystem thevalues ofT 2 andTx ofthewater
inthexylemvesselscanbedetermined andestimated, respectively.
A comparison between the results obtained withNMR,heatpulse
and weight balance flow measurements ispresented inChapter 6.A
linear relationship between the linear flow velocity obtained by
NMR andthevolume flowratedeterminedbythebalancemethodyields
aneffectivecross-sectional areaavailable for flowof~50%ofthe
cross-sectional areaofthexylemvesselsmeasuredbyusingamicroscope. NMR measurements alone yield a slightly lower value ofthe
effective cross-sectional area. Compared with the NMRmethod,the
heatpulsemethodmonitorsonlyrelativechanges inthe flowvelocity.
Aplotofthe flowvelocityobtainedbytheheatpulsemethodversus
the volume flowrate obtained by the balance method exhibits some
unwanted experimental scatter.
Chapter 8suggests someapplications ofthepulsedNMR flowmethod,
alsotoother systems thanplants,anddefines important instrumental
requirements fortheseapplications.
128
SAMENVATTING
In ditproefschrift wordteenniet-destructieveprotonpuisNMRmethode beschreven, voor demetingvanmetnamehetwatertransport
inhetxyleemvanplantestengels eninmodelsystemenvaneenplant.
De methode is even goed toe tepassenopdemetingvanvloeistofstroming in andere biologische systemendanplanten,b.v.stroming
vanbloedenanderelichaams-vloeistoffeninmensendier (hoofdstuk 8)
De methode is gebaseerd opeenpulstreinvanequidistante n pulsen
in combinatie met eenlineairemagneetveldgradientGindestroomrichting.
Na een algemene inleiding (hoofdstuk 1)eneenoverzichtvande
fysisch-chemische eigenschappen van water inplanten (hoofdstuk 2)
wordtinhoofdstuk 3detheorievanpuisNMRbehandeld.Dithoofdstuk
bevat tevens een bespreking van de tot nu toe bekende puis NMRmethodenomstroming,diffusie enwatergehalte inbiologische systemen
temeten.
Analytische uitdrukkingen voor devormvanhetNMR signaal S(t)
werdenverkregenuitgaandevaneenmodelwaarindestromendevloeistof
depulstrein ^n-x-(n-x-) ondervindt,zodanigdatdevloeistofeen
Vi puis ondervindt op hetmoment dathetder.f. spoelinstroomt,
gevolgd dooreenreeksnpulsentotdatdevloeistofdespoelverlaat;
gelijktijdig heeft de stromingvandevloeistof inderichtingvan
demagnetischeveldgradient totgevolg datereen faseverschuiving
ontstaat van de magnetisatie ten opzichte vanhetroterendassenstelsel (hoofdstuk 4). Hoewel ditmodelniettotvolmaakteovereenstemming leidt tussen deexperimenteleentheoretischevormvande
signalen S(t), voorspellen deanalytische uitdrukkingenwelgoedde
effecten van de experimentele parameters op S(t).De voornaamste
resultaten, die ook experimenteel in glascapillair systemen zijn
geverifieerd, uit deze theoretische behandeling in combinatiemet
computersimulatieszijn:
zolangT2SST!kandegemiddeldelineaire stroomsnelheidgevonden
wordenuitt x , detijdwaarophetsignaal eenmaximumbereikt,
via v=C/t ,met Ceencalibratieconstante dievanG, Tenhet
stromingsprofielafhangt. IndienT2<1-jTikanvalleenbetrouwbaar
129
bepaaldwordenalszowelTi alsT 2 vanhetstromendewaterbekend
zijn.
T 2 endehoeveelheid stromendwater indespoelV,endusookde
volumesnelheidQ,wordengevondenuitdehoogtevanhetmaximum,
S(t m ^ v ), en t „ _ . AfhankelijkvandewaardevanzowelT 2 alsde
verhouding T1/T2, worden T 2 enV gevonden door middel vaneen
semilogarithmischegrafiekvanofS(t )tegent m = v (T!>>T2)of
Gebaseerd op stromingsmetingen in segmenten vanpianteStengels
isverondersteld datdewaardevanT 2 vanhetstromendewatersterk
afhankelijk isvan de diameter van de xyleemvaten (hoofdstuk5 ) .
Deze afhankelijkheid kan een verklaring zijn voor de negatieve
resultaten die in stengelsegmentenmetkleinevatdiameterzijngevonden. Onder de huidige experimentele gegevens isdemethodetot
nu toe met succes toegepast in Cucurbitaceae (komkommer, augurk,
pompoen)entomatenplanten.
Inhetblad vantarweplanten isgevondendatdeT 2 vanheteelwateronafhankelijk isvancelgebondenparamagnetischeionen (hoofdstuk 7). Voortweeafzonderlijkewaterfracties (±90%vanhettotale
watergehalte vertegenwoordigend) is gevonden dat de waardevanT 2
omgekeerdevenredig ismethetwatergehalte.Ditsteltonsinstaat
om niet-destructief veranderingen inhet watergehalte tevolgen.
Metingenvanstromingenwatergehaltem.b.v.tweeverschillende pulstreinenzijnaaneenzelfde intacteplant (augurk)uitgevoerd (hoofdstuk 5). Uitderesultatenvandezemetingenblijktdatdecombinatie
van deze twee NMR methodenveelbelovende perspectieven biedt om
belangrijke onderdelenvandewaterbalansvaneenplantgelijktijdig
tebestuderen op eenwijze die de plant niet beinvloedt.Erzijn
bovendien sterkeaanwijzingen datdemethode gebruiktkanwordenom
hetontstaanvanstress situaties -b.v.tengevolgevandroogteof
andere factoren -indeplantvroegtijdigtesignaleren.Metbehulp
van deze stromingsmetingen wordt tevens aangetoond hoedewaarden
vanT 2 enTx vanhetxyleemwaterineenplantrespectievelijk kunnen
wordenbepaald enafgeschat.
Inhoofdstuk 6wordenderesultatenvanstromingsmetingen verkregen
metNMR-,warmtepuls-enbalansmethodenvergeleken.Vanhetlineaire
verband tussen de lineaire stroomsnelheid (bepaald metbehulpvan
NMR)endevolumesnelheid (verkregenmetbehulpvandebalansmethode)
r
130
werdheteffectieve oppervlakvandedwarsdoorsnede,datbeschikbaar
isvoor stroming,bepaald.Ditoppervlakbleek~50%tezijnvanhet
oppervlak van de xyleem vaten gezamenlijk zoals gemetenmet een
raicroscoop.DeNMR resultatenalleenleverdeneeniets lagerewaarde
opvoordeeffectieve dwarsdoorsnede vandevaten. Integenstelling
totdeNMRmethodemeetdewarmtepulsmethodealleenrelatieveveranderingen indestroomsnelheid.Eengrafiekvandestroomsnelheidsveranderingen gemeten met dewarmtepuls methode uitgezettegende
volume snelheidverkregenm.b.v.debalansmethode,vertoonteenonverwachte sterkematevanspreidingvandeexperimentelemeetresultaten.
Hoofdstuk8bevateenopsommingvanenigemogelijketoepassingen
van depuis NMR-methode, zowel in de land- en tuinbouw alsinde
medische sfeer.Tevens worden in dit hoofdstuk eenaantalbelangrijke instrumenteleeisenvoordezetoepassingengeformuleerd.
131
CURRICULUM VITAE
HendrikVanAswerd op12September 1952teHuizen (N-H)geboren.
In 1968behaalde hij hetMULO-B diploma aan de ChristelijkeULOschool GroenvanPrinsterer teHuizenenin1970hetHBS-Bdiploma
aanhetBijzonderWillemdeZwijger Lyceum teBussum.Hetzelfde jaar
begonhijdestudie scheikunde aandeVrijeUniversiteitteAmsterdam.
Na het afleggen van het kandidaatsexamen S2in1973,bereiddehij
zich bij de vakgroep Fysische Chemie, afdeling Spectroscopie van
prof.dr.ir.C.MacLean,o.l.v.dr.J.Bulthuisvoorophetdoctoraalexamen. In het kader van het bijvak KlinischeChemie werd een
6-maandsdoctoraal onderzoekverrichtaanhetAcademischZiekenhuis
teUtrecht.Nahetbehalenvanhetdoctoraalexamenindecember1976,
tradhijop1januari 1977indienstbijdeStichting ZuiverWetenschappelijk Onderzoek.Hijwerd tewerkgesteld aandeLandbouwhogeschool te Wageningen bij de vakgroep Moleculaire Fysica. Op
1 januari 1978 kwam hij voor hetzelfde onderzoek indienstvande
Landbouwhogeschool.Naasthetinditproefschriftbeschrevenonderzoek had hij als onderwijstaak het leidinggeven aan de practica
ChemischeBinding enMolecuulspectroscopie.
Met steun van de Stichting Technische Wetenschappen hoopt hij
soortgelijk onderzoek voort te zetten bij devakgroep Moleculaire
Fysica.