Morphometry of the dog pulmonary venous tree
o
R. Z. GAN, Y. TIAN, R. T. YEN, AND G. S. KASSAB
Department of Biomedical Engineering, Memphis State University, Memphis Tennessee 181V- cd
Department of AMES-Btoengineertng, Untversity of Californta, San S^«TS^W
Gan, R. Z., Y. Tian, R. T. Yen, and G. S. Kassab. Morphom
etry' of the dog pulmonary venous tree. J. Appl. Physiol 75(1)432-440, 1993.-The biophysical approach to the study of
blood flow in the pulmonary vasculature requires a detailed
description of vascular geometry and branching pattern. The
description ol the pulmonary venous morphometry in the do^
is the focus of this paper. Silicone elastomer casts of a dog lun*
were made and were used to measure the diameters, lengths
and branching pattern of the pulmonary venous vasculature'
I he anatomic data are presented statistically with a diameterdefined St rahler ordering scheme, a rule for assigning the order
numbers of the vessels on the basis of a diameter criterion The
asymmetric branching pattern ofthe pulmonary venous vascu
lature is described with a connectivity matrix. Results show
that for the dog's right pulmonary venous tree 1) a total of 11
orders of vessels lay between the left atrium and the capillary
bed; 2) the average ratios ofthe diameter, length, and number
of branches of successive orders of veins were 1.701, 1 556 and
3.762, respectively; and 3) a fractal description ofthe tree geom
etry resulted in diameter and length fractal dimensions of 2 49
and 2.99, respectively. The morphometric data were used to
compute the cross-sectional area, vascular volume, and
Poiseuillean resistance in the venous vessels.
vasculature; connectivity matrix; fractal dimension; diameterdefined St rahler system
the alveolar wall vascular space as a sheet of blood flow
ing between two membranes held apart by numerous
posts (3).
In addition to the morphological data, the elasticity of
cat pulmonary arteries and veins has been presented bv
Yen et a (24, 26). The elasticity of arterioles, venules
and capillaries has been given by Sobin et al. (17 18)'
Based on a complete set of data on the morphometry of
the cat pulmonary vascular trees and the elasticity of
these blood vessels, a theoretical analysis of the blood
flow in the cat lung was presented by Zhuang et al. (30)
and Fung et al. (4). However, the bulk of experimental
results on pulmonary blood flow in the literature avail
able for comparison to the theoretical model is from dogs
and humans. Therefore, there is an urgent need to de
velop a morphometric data base for the dog lun<r
This paper reports the detailed morphometric data ob
tained from measurement of silicone elastomer casts of a
dog pulmonary venous tree in our laboratory. The mor
phometric data for the dog arterial tree are reported sepa
rately. With these data a fractal description ofthe pulmo
nary vascular tree is presented and the Poiseuillean resis
tance, total cross-sectional area, and blood volume in the
venous vessels were computed.
THE biophysical approach to pulmonary blood circu
METHODS
lation is incomplete without quantitative information on
Preparation of pulmonary venous tree casts. The lung of
the branching pattern ofthe vascular tree and the geome
a mongrel dog weighing 25 kg was prepared by the same
try (diameters and lengths) of the vessels. In the past method reported earlier by Yen et al. (28). Briefly after
Singhal et al. (16) and Horsfield et al. (8,10) have studied the dog was anesthetized with a pentobarbital sodium
the morphometry ofthe human arterial and venous trees
solution (30 mg/kg iv), the trachea was cannulated and
in the lung. Using resin casts of human vascular trees
the lung was ventilated. After a midline incision, the
they measured the diameters, lengths, and order of all heart and lungs were exposed and the airway pressure
branches of blood vessels in the range of 13 ^m to 3 cm was held at a constant pressure of 10 cmH20 above the
tor arterial vessels and 13 urn to 1.4 cm for venous ves
pleural (atmospheric) pressure. Through a cannula in
sels.
serted into the main pulmonary artery, the pulmonary
The only other species besides humans for which de
blood
vessels were perfused with a low-viscosity (20 cp)
tailed morphometric data for the pulmonary circulation
silicone
elastomer freshly catalyzed with 3% tin octate
have been published is the cat. Yen et al. (28, 29) made
(stannous
2-ethyl hexoate) and 5% ethyl silicate The
silicone elastomer casts of the cat arterial and venous
elastomer
was
drained from a cannula inserted into the
trees to measure the diameters, lengths, and number of
branches of arteries and veins. Arterioles and venules left atria After perfusion at a pressure of 34 cmH20 for
were measured by optical sectioning of thick histological 20 min, the atrial cannula was closed and the perfusion
sections. The alveolar capillary network in humans and pressure was lowered and maintained at 3 cmH20. In this
condition, the fluid pressure in the capillary blood vessels
^^investigated
by Weibel
and Fun8
andnetwork
Sobin was lower than the airway pressure and hence the capil
U, 3). I he structure
of the (21)
pulmonary
alveolar
cannot easily be modeled by a system of branching and lary vessels were collapsed, separating the arterial and
venous trees. After 2-3 h the silicone elastomer was com
interconnecting tubes. Instead of large meshworks made
of very short segments, it is more suitable to consider pletely hardened, and the lung was frozen for 2 wk to
increase the strength ofthe elastomer. The lung was then
432 0161-7567/93 $2.00 Copyright c 1993
the American Physiological Society
MORPHOMETRY OF PULMONARY VENOUS TREE
17
10
(29./67,
SY ,63.185
l 32, 66)
itf.V"!^
l24,\86)
FIG. 1. Sketch of pulmonary subtree with diameter and length measurements in If) «m«nit. <3;„„iQ ,
corroded with a 10% KOH solution for several days. On
dissolution the capillary vessels disappeared, and casts of
the arterial and venous trees were obtained.
upper, middle, and lower lobes was trimmed into several
main trees. Small subtrees, with the largest branch hav
ing a diameter of 600-800 jum, were cut o^"-^
from the main tree. Some small trees wei.
icfi vessel selected as samples to be measured in detdirThTrestof
the small trees were further pruned to remove sub-sub
trees with a diameter of <200 „m. Each tree was then
viewed under the dissection microscope for measure
ment. The remaining main trees were also pruned and
measured. The diameter was measured at the midpoint
of each vessel segment from the grabbed image. The
length was measured between bifurcation points alon*
dicular to the longitudinal axis ofthe vess
the centerhne. The branching pattern of each pulmonary"
tance equal to that from one side of the
venous tree was sketched with its measured diameters
other, a measure of the vessel diameter
and lengths. Figure 1 shows an example of a recon
1 was cali- structed pulmonary venous subtree.
lits. In the
Assignment of order numbers to venous branches. Two
of the best-known mathematical models of treelike
branching systems in physiology are Weibel's genera
tions model (21) and Strahler's orders model (29). Weibel (21) grouped the human airways in generations by
Ms millions of assuming a symmetrical branching pattern. The trachea
IS d*3c;,0'n;:itcirl ltQnni.ntm» C\ 4.U- _* _1. j 1 i /.. .
chi'° 1U" x> """ o" un uowii unetree. ine generation
scheme was also used for the pulmonary arterial and ve-
434
MORPHOMETRY OF PULMONARY VENOUS TREE
Dn.min - [U>«-i+ «)„.,) + (Z)„ - 5DJJ/2
and
(/)
Di.max = KD„ + SDJ + (Dn + .-5D„ + ,)]/2 (2)
where D
;lnd
A,.maI are me
the minimum and
maximum
«.<,].
"".maxof "*•=
mari'mnm
values,£•",""
of the~ range
diametersminimum
around Dand
, respectiveT
•en,™': H^B&SISS&a?' ;" Sf W« •**• sy,
stage 2. D: diamettr-dSWI S" n , ' s'Sge '•C: 'Slril,ller °"fers.
designated order fo el^ """ "" EilCh 'l'""1'" "•>—„,.,
BD. DE. and DP. ~2ZSSS&!SS?JSSr * *C-
mmMm
ir the bronchial tree and the pulmonarv arteries and
oraers
Begingenerati,°nS
at the smallest vessels
and countStrahTer
upward In
S^S thn
apProach'
smau
cnanges
one
iterations
his method, the smallest vessels are defined as order1
ar.
j ' . ™ ? in Dn: after
r
■■ " or two
* •■
» . «Finallv
»si
two order 1 vessels join to form a larger vessel of order 2*
and so on toward the main trunk. Strahler- me hod has noeodvXer ra"geS °f V6SSelS " SUCC6SSiVe £*«E5.
teantSSwa^SS
vers^-The
i&ja) is called Horsfield s method
of orderingfi™
which
ordert'thePrdeoS^tnnldy' "* haVe USed the DDS »>«hod to
conventional Strahler system. When two vess'efs o d,/
ma n "he*" ""*'' ^ °r<ier of the ™othe vessel rt
"fter all theXf S* °f *! ,arger dau»h<" vessel.
just one vessel branch (Fig 20 constituting
method. The definition of vessels of 0X1 f 11 5
description of pulmonary vZus vess Is or M and hu'
mans by Yen etal (97 9«^ E»„« iL , . ? dCS ana nu"
h1Im!Vi0U?Udi? °n PuIm°nary arteries and veins of
fi ten
; ^etf ral.
f us,
a n29)
d have
c o - shown
w o r kthat
e r sStrahler's
( 8 , T omethnd
L°d
an
unsatisfactory
of thpnicely
QtraMn,
« u '
tt:^te.
aSy?metric feature
bifurcations
However
when t daugh vessel0 are nfsmafirlLTthTar5
ent but are assigned two different order numbers or when
a long vein has many small branches suchTha, the ma n
be In ePi?hrS T* bUt h aSSi«ned a fi«° order num
present study. Thus, our measured diameters of nrHor 1
vessels were greater than those measured by Yenet a
Counting of branches. Because a venous tree of the dL
Dns> hA meter-def™e° Strahler ordering scheme
In the
the DDS
Dn?"system,
'"troduced
vessel
^ Kassab
diameteretisal.
the(12,
man13)
focus
3S55BS3SI
MORPHOMETRY OF PULMONARY VENOUS TREE
3. ,2
-hod to cJ*V&^JZ£^£>«" Ration' J done first for „
ary venous tree. nes m tne PuIm°- sively proceeds to n = n -1 '"'
In general, vessels of order „ may snrW ^ *_ .... ^includes all the missing 8ubSS, t!' ~ J***?0"
«w oi oraers n + 1 n + 9 t«*U 1- —. ves" UI mzact vessels in ordpr n (M \ ■ . uuraoei
ssels 3*1 Ti tow atthWhen ^ nUmber 0f Crit"ia "SSSKftfflEl ^°rph°10^ 04). Th,
m - 1. •. 2 and 7 Jh.T '., 6 numbers of orders geneity, self-similaritv «^w fge degree of hetero-
-fordermctr/aS
ftCt
T
£
"°
^^SSWJWSr*
-nffnrk,«i "Iuerm tne missing subtrees of the mensinn ;« „.«*.i • , s l°'. **'• rne conceDt of di.
' ■■ 1 * - . . . ^
„tal
, description ofthe do*? n U?
S ^'t0
S t make
S & s i aS S
rlfrac"
MORPHOMETRY OF PULMONARY VENOUS TREE
TABLE 1. Experimental measurements of diameter and
length of vessels in each order of dog venous tree
Diameter, nm
Length, mm
No. of vesse
Order
rder
Means
measured ' Means t SD "t^Sf
Means ± SD± SDmeasured
11
10
9
8
7
fi
6
5
4
3
2
1
8,450±250
2
34.40
i
4,480±235
6
o
20.516±9.805 fi
2,775±354
20 1 4 . 7 6 5 ± 7 . 9 8 9 1 3
™
1,826+137
28
■8 1 2 . 6 5 3 + 6 . 6 2 4 1 9
1.167±113
55
.l 3
, 737±101
J, ±S1S0J1 ? 1i 6l 168
8 8 . 51. 41 89 ±
0±
5 3. 3. 56041 3 ?8
4 4 441±70
1 ± 7 0 3 2 0320 2 . 9 7 5 ± 1 . 8 5 4 1 0 9
251±39
2 5 1 ± 3 9 4 9491
1 1.767,1.201 212
1 4142±24
2±24
9 7 9979 1 . 0 9 3 ± 0 . 8 2 1
937
7 8 ±78±14
14
1 , 1 21,122
2
0.683±0.434
229
29±12
2
9 ± 1 2 2 , 2,407
407 0.401±0,248 j-lS
Mean t S.D.
Values were obtained at pleural pressure = 0 cmH.,0 (atmospheric)
airway pressure = 10 cmH20. and pulmonary venous pressure "3
1 _ D = log (total size of object for order n)
log(average size of object for order n) (4)
The fractal dimension is then obtained from plotting on
logarithmic scales for both axes, the total size versus the
average size of the object.
RESULTS
Our data of the pulmonary venous tree in the do*'s
right lung show that there is a total of 11 orders of pulmo
nary veins lying between the capillaries and the left
atrium. Table 1 shows our experimental results of the
means ± SD of the diameters and lengths of vessel
branches as well as the number of vessels measured,
irom these data, the relationship between the mean di
ameter of vessels in each order and the order number is
shown in Fig. 4, and the relationship between the mean
5 - Mean ± S.D.
9 1 0 11
FIG. 4. Average diameter of vessels in each order vs. order number
FIG. 5. Average length of vessels in each order vs. order number Ifv
3KR
U.oJUb
n0?Q9nh^
+ 0.1920x°f'e,ngth
describes^results.
X repr6SentS °rder numb". thenyl
values of vessel length and the order number is depicted
in big. 5.
In Fig. 4, if y represents the logarithm ofthe diameter
and x represents the order number, then the leastsquares fit regression line is y = 1.4128 + 0.2307* The
slope gives an average diameter ratio of 1.701. Similarly
in F ig. 5, if y represents the logarithm ofthe vessel length
and x represents the order number, then the regression
te 1S
K r«?"5206 + °-1920x> y[eldinS an average length
ratio
of 1.556.
The connectivity of blood vessels of one order to an
other is expressed in the connectivity matrix for which
the component C(n,m) is the ratio ofthe total number of
vessels of order n sprung off from parent vessels of order
m to the total number of vessels of order m. To experi
mentally obtain the matrix for the average branching
pattern in the venous vasculature, we examined the
whole tree for all the branches ofthe casts of orders 1-11.
As a simple numerical example, the tree in Fig 2D is
used to calculate the element C(l,m), where m = 1 2 3
and 4. There are three vessels of order 2 that give rise to'
eight vessels of order 1 and one vessel of order 3 that
gives rise to one order 1 vessel. Thus, C(l,2) = 8/3 or 2 67
the average ofthe three ratios of 3, 3, and 2, over all order
2 vessels with a standard deviation of 0.47; likewise,
MMJ - 1/1 or 1. Because there is no order 1 vessel rising
from order 1 or 4 C(l,l) = 0 and C(l,4) = 0. By similar
reasoning the other components of C(n,m) and their
standard deviations can be derived.
The experimentally obtained connectivity matrix of
the pulmonary venous tree ofthe dog is shown in Table 2
In addition to displaying the global branching pattern of
the whole vascular tree, the connectivity matrix provides
ample information for calculating the number of
branches in each order. For instance, the last column
shows that the largest (order 11) vessels in the pulmo-
MORPHOMETRY OF PULMONARY VENOUS TREE
table 2. Connectivity matrix
1 0.690*1.207 2953±1.758 1.517±1.943 1.072±1.740 1.010±1.783 .
- 0.263±0.ol8 1.716±1.504 1.478±1.503 1.559±1 536 «»•«•J
5
3
7
0.659±0.838
1.770±1.120
1.539±L526
\
0.191±0.440
1 . 7 9 4 ± 1 . 111
L_.
0.216±0.436
2.048
0.415:
1.091±1.221 0
:i.on 1.727±1.489 0.4±0.548
'■" - - T- l ' o 6 9 L 7 2 7 ± l - 0 0 9 0 . 4 ± 0 . 5 4 8
0.143±0.3oo 1.471±0.800 1.636±0.809 0.8±0 837
0.235±0.397 1.545±0.522 0.8±0.837
0.091±0.301 2.2±0.837
0
0
0
0
0
o
0
6
Values are means ± SD. Element (n, m) in row n and colui
branches of order m to total number of branches SSm in ^VZous^
nary veins are connected to six vessels of order 10 two
vessels of order 8, and no vessels ofthe other orders The
T^aTI ?WS that n°ne of the order 9 vessels is'cor
(9 o v°vhe
°f 0rder
U>12
26isvesse*s
of ord.
(2.2
X Nl0aogoSt
= 2.2 XVeSSGl
12 = 26,
where
the numb
essels of order 10 from Table 3) are connected to ve:
oi order 10, and three vessels of nrdpr Q (c\ not v ^^
Figure 8 plots the total branch length resulting from
the summation of the lengths of all vessels in a given
-der vs. the average branch length for the same order
asels on a log-log scale. Each point on the graph corre
sponds to a specific branching order. The slope of the
iSTm^
fraCtal dimensi°n
of asthe
length of*'theGS
dog^s pulmonary
venous tree
9 99branch
%T
}e 3)number
are connected
to vessels
order
9 ve
Ji1™66"is ^°m
^ ? structure
and 8 that
the Pu^onary
venous
lhe total
of branches
of each of
order
in the
system
a fractal
that provides
a mechanism
nous tree can be computed from the information given in for converting an alveolar-capillary surface area of di
rabies 2 and 3 by using Eg. 3. The computation be
mension two into a volume of dimension three. The estilrom the largest vessels of order 11, i.e., n = 11 in
Z ehd™alU|f1
°f 2fmay
^^u be
dimensi0n
fordeveloping
vesseI diameter
3, and then proceeds successively to n = W9 l 1 Ml. and
branch length
useful for
strucresults are shown in Table 3. The number'of intact ves
sels and cut-off or broken-off vessels and the total num
Zi!ZTng
ractal analysis
frf°nSof pulmonary
H°WeVer'
vasculature
°Ur aPProach
is derived from
for
ber of branches in each order are also listed in Table 3
the morphometric measurement of one dog's lung casts
which is not sufficient to complete the study of fractal
.Jhnrd!
10f.uiP
b!tWGen
the number
of branches
in geometry for the pulmonary vascular tree of the dog
each order
and the
order number
is shown
in Fig 6 F—
the logarithm of the number of branches (y) in each oiu
is plotted against the order number (x). The regression
fine is y = 6.5602 - 0.5754*, yielding an average branch
mg ratio of 3.762 over the 11 orders
JS ? ?l°tS
the total diameter
collection
of diameters-of
all vessels ^suiting
in a givenfrom
order the
vs.
ameter obtained from the regression line is 2.49.
TABLE 3. Computation of total numhor -' brands
in each order of dog's venous tree
No. of Intact No. of Cut
_V^.
Vessel,
B-ng&Sfy—fc
•
4
3
2
101
205
215
199
596
84
181
258
717
903
1,046
145
842
3,107
10,111
77,478
213,540
2,474,291
.Cor^e^otl,
197
989
3,389
10,574
78,410
214,642
2,475,933
ORDER
FIG. 6. Number of branches in each ord
represents logarithm of number of branch-
MORPHOMETRY OF PULMONARY VENOUS TREE
H o w e v e r, o u r p r e s e n t r e s u l t s s e r v e a s a f o u n d a t i o n f o r A = ( i r / 4 ) n 2 N
other
morphometric
results
to
follow.
"
K*/*)IJ*Nm
(i
On the basis of the morphometric data of the pulmo- ^f® °n u the averaSe diameter of vessels and N is the
nary venous vasculature, the total cross-sectional area ™tal number of vessels of order n. The results shown in
and vascular volume in every order can be computed fpu afe Wlth an exP°nential function,
along the venous pathway. Figure 9 shows the variation t0tal bl°°d volume of order n (V„) is given by
of the total cross-sectional area with the order number in V = A L ia \
the venous tree. The cross-sectional area of order n (A ) " K }
is defined as the product of the area of each vessel and °r
the
total
number
of
vessels
V„
=
(ir/i)DlLnNn
{6b)
,
5 where Ln is the average length of vessels of order n The
10 1 B D ?4Q calculated venous blood volumes are plotted on a logF " anthmic scale against their order number in Fig 10 It is
seen that the data may be fitted by a straight line' If y
represents ^e logarithm of the blood volume and x rep-
AVERAGE DIAMETER OF VESSELS (mm)
FIG. 7. Fractal dimension (DK) for vessel diameter (total vs average
vessel diameter) was computed from points. Each point corresponds to
specific branching order.
D =2.99
F
AVERAGE BRANCH LENGTH (mm)
FIG. 8. DF for branch length (total vs. average branch length) was
computed from points. Each point corresponds to specific branching
0
12
3
9 1 0 11 1 2
fig. 9. Computed cross-sectional area of venous branches in each
order vs order number. Uy represents cross-sectional area and x repre
sents order number, then v = 19.098 X UT*»*X describes results
1 0 11 1 2
-0.2398 + 0.0780x describes results.
MORPHOMETRY OF PULMONARY VENOUS TREE
table 4. Comparison of diameter, length, and
r, length, and ,-_ n ._ n _ ,
branching ratios and number of orders
pulmonary
-dersin in
pulmonary g °n ~ (log ^ " loS *>*) + « log DR (U)
venous tree of dog, cat, and human
Pulmonafy
,
and
'
log Ln - (log Lx - log LR) + n log LR (12)
ct forms of fifc U and 72 for the dog's venous
illustrated in Figs. 4 and 5. The diameter and
itios were calculated as 1.701 and l.SsTrespec
1.556
1.533 (4-10)
2.402 (1-3)
Human
1.682 (7-14)
1.679 (71.493
1
. 4 9(1-6)
3 ( 1 - 6 1 . 4 7 fi M .
DR, diameter ratio; LR, length ratio; BR, branchine r
ratios are calculated from total number of orders exce
tively.
SSSESSSSSSgiiisF
The morphometric data ofthe pulmonau
vide three system ratios: the diameter
nchino-
ratine
TKQ
„
,.-/•
3r 2 branches in humane ««~ u_^_. ' ' v '
its, which was pointed out by
3, in response to this interpretae has 12 DDS orders compared
?
ber * ~* ""—"•"*" W1 ww order num-
K^NJBU)1-"
(7)
«r?? iSiue 3Verage branching ratio for the system
MM£" ^^ ^ l0garithm °f ^ sidfsTf
log Nn = (log ^ + log BR) - n log BR (8)
By represents the logarithm ofthe number of branches
and x represents the order number then Fn lil+Zt
least-squares fit regression line for the plotting of tt
number of branches against the order number The anti
og of the absolute value ofthe slope o"the^regression
line is defined as the average branching ratio For he
pulmonary venous tree, Eq. 8 is presented in Pig" 6 as
h2
7 °'s5.754x
and theinbranchi
s «*i
o ksminHorton
law is statistical
nature n
and
provides
formation on average-properties. It can also be applied to
measurements of vessel diameter and branch length for
Ln<T m°nary ™ous tree- Becau*e the diameter and
sels (A,) and the average length of branches (L ) in each
order are presented as n
AhZSZ Wlth ^^f'thG 3Verage *2S?5 ves
and
A.-ACDR)—1
(Q)
A^L^LR)"-'
(i0)
vhere DR and LR are the average diameter and lonarh
0
1
2
3
4
5
6
7
9
10
11
12
ORDER
each'order ^rd:' SSTkLS^T °f ~«5 bra"cheS in
branching order. 8Ch point corresP°nds to specific
440
MORPHOMETRY OF PULMONARY VENOUS TREE
AP„ = (128MnLn/^X)Q„
(23)
or
AP„ = R„Q„
(14)
where AP„ is the pressure drop at order n, nn is the appar
ent viscosity of the blood, Q„ is the total flow in order n,
and R„ is defined as Poiseuillean resistance of order n
and is given by the terms within parentheses in Eq. 13.
Obviously, the Poiseuillean resistance considers only the
morphometric aspects of the vessels.
To calculate the Poiseuillean resistance in each order,
the apparent viscosity values of blood should be esti
mated first. According to the results determined by Yen
and Fung (25) in model experiments and calculations, an
apparent viscosity of 4.0 cp is assumed in large vessels.
The apparent viscosity of blood in small vessels of orders
1-3 is obtained by interpolation as 2.5, 3.0, and 3.5 cp,
respectively.
With these data the Poiseuillean resistance from
orders 1-11 in the dog's venous tree was computed, and
the results are shown in Fig. 11. It is seen that most ofthe
resistance occurs in the small vessels of diameters <100
nm and that the resistance in the small vessels is 55%
of the cumulative Poiseuillean resistance in the venous
system.
In addition to the Poiseuillean resistance, the blood
volume distribution within the venous bed provides a
functional analysis for pulmonary circulation. The re
sults of Fig. 10 show that blood volume increases with
order number, and the average vascular volume in order
n (V„) is presented as
V„ = V^VR)'
(15)
where VR is the average volume ratio. The best fit rela
tionship between the average blood volume and the order
number is also illustrated in Fig. 10. The equations result
in the vascular volume ratio of 1.197 for the pulmonary
venous tree of the dog. The cumulative venous volume is
22 ml in the dog's right lung, where 50% of the total
venous volume resides in the largest three orders of the
venous tree.
Results obtained from measurements of vascular vol
ume in the lung (6, 9, 10, 20) are quite variable. These
wide variations may be related to the different physiologi
cal states and experimental conditions for data measure
ment. Horsfield (9) studied the cast model ofthe human
pulmonary venous tree and showed that the total venous
volume was 73 ml, compared with an arterial volume of
86 ml (excluding the main pulmonary artery). Compared
with this result, the 22-ml volume of blood in the venous
tree in the dog's right lung is reasonable.
Address for reprint requests: R. T. Yen, Dept. of Biomedical Engi
neering, Memphis State Univ., Memphis, TN 38152.
Received 27 April 1992; accepted in final form 22 February 1993.
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