Regional Cerebral Blood Flow Estimated by
133
Xenon Inhalation
BY WALTER D. OBRIST, PH.D.,* HOWARD K. THOMPSON, JR., M.D.,t
HSIOH SHAN WANG, M.D.,* AND WILLIAM E. WILKINSON, PH.D.|
Abstract:
Regional
Cerebral
Blood Flow
Estimated
by
™Xenon
Inhalation
• A method is described for estimating the clearance rate and fractional blood flow of the fast
(gray matter) compartment of the brain from the first ten minutes of 133Xe clearance curves,
following a one-minute inhalation. Computer-simulated data were used to test the adequacy of
the two-compartmental model employed, and to evaluate the stability of the parameters in the
presence of random noise. A comparison was made between this approach and the previously
reported three-compartmental analysis. Regional cerebral blood flow data were obtained on 48
young control subjects and 20 elderly demented patients. Hemispheral, regional, and test-retest
variations were determined, as well as differences between the groups.
Additional Key Words
noninvasive technique
errors of measurement
least squares curve fit
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Introduction
• An atraumatic technique for measuring regional
cerebral blood flow (rCBF) is a recognized need in
modern clinical research.1 The 133Xe inhalation
method, first introduced by Mallett and Veall,2'3 has
the distinct advantage of being noninvasive and
repeatable a number of times. A major drawback of
the method, however, is contamination of the
clearance curves by radioactivity from the scalp and
other extracerebral sources, which may give rise to
significant measurement error. In an effort to overcome this difficulty, the present authors4 proposed a
three-compartmental analysis of the curves, in which
the first two compartments represented the faster
clearing gray and white matter, while the third compartment represented the slower extracerebral tissues.
Unfortunately, adequate separation of the cerebral
and extracerebral components required extended
periods of recording (40 minutes or more). Attempts
to analyze shorter clearance curves yielded unstable
answers.
A 40-minute examination clearly limits the
usefulness of the three-compartmental analysis in
clinical situations. Not only is it untenable to assume a
steady physiological state over such a long time interval, but the patient's cooperation is taxed, and the
lengthy curve analysis is cumbersome. The present
paper describes a shorter, simpler method in which
•Department of Psychiatry, fDepartment of Medicine, and
^Department of Community Health Sciences, Duke University
Medical Center, Durham, North Carolina 27710.
Dr. Obrist is now at the Division of Neurosurgery, Hospital of
the University of Pennsylvania, Philadelphia, Pennsylvania 19104.
Dr. Thompson is now at the Baylor College of Medicine,
Houston, Texas 77025.
This investigation was supported in part by Research Grant NS
06798 from the National Institutes of Health.
Stroke, Vol. 6. May-June 1975
end-tidal air sampling
scattered radiation
133
Xe clearance is monitored extracranially for ten
minutes, following a brief one-minute inhalation.6
Although limited to blood flow estimates of the gray
matter compartment, it is believed that this shorter
method is better suited to clinical research.6
Theoretical Model
A two-compartmental exponential model is proposed in
which a faster clearing compartment, considered to be
cerebral gray matter, is separated from a slower clearing
compartment, considered to be white matter and extracerebral tissue. Such a model assumes gray matter
clearance rates that are high relative to the remaining
cerebral and extracerebral components. This assumption is
supported by the well-established difference in blood flow
between gray and white matter.' 1 * In humans this difference
is approximately fourfold,9 but because of different 133Xe
tissue solubilities, the actual clearance rate for gray matter is
seven times that for white matter. Differences of this
magnitude permit an easy separation and identification of
tissue compartments, except in certain pathological states
where compartmental boundaries may shift.10- "
Clearance rates for gray matter also are easily distinguished from extracerebral tissue, the latter having values
that are generally less than those of white matter. The low
perfusion rate of extracerebral tissue is revealed by the
prolonged washout of 133Xe following inhalation,1 a finding
consistent with blood flows reported for skin,12 resting
muscle13' " and bone.15 Isotope injections into the scalp 2 ' 5
and external carotid artery,16 however, suggest the presence
of some faster clearing extracerebral components that may
overlap with those of the white matter.
The proximity and probable overlap of white matter
and extracerebral clearance rates make it possible, under
certain conditions, to treat these tissues as a single compartment. It can be demonstrated that washout of the combined
white matter and extracerebral components can be approximated by a single exponential when the observation
period is short relative to their half-times. In order to
achieve such an approximation, curve analysis must be
245
OBRIST, THOMPSON, WANG, WILKINSON
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limited to short time intervals,17 which necessarily include
the beginning of clearance where all tissue components are
present. Thus, in the proposed two-compartmental model,
only the early portion (first ten minutes) of the clearance
curve is analyzed. In such an analysis, the fast gray matter
components are represented by the first compartment and
all other slower components, i.e., white matter and extracerebral tissue, are represented by the second compartment. As in other compartmental methods, 8 - 9 this model
assumes that the clearance rates of the fast and slow clusters
of tissues are sufficiently different to permit the desired discrimination. Only the first compartment, however, can
provide meaningful estimates of cerebral blood flow; the
second compartment is less meaningful due to extracerebral
contamination.
Because inhalation results in appreciable uptake and
washout of I33Xe throughout the body, recirculation is an
important component of the clearance curves.18 A correction
for recirculation is possible, however, from knowledge of the
arterial input, obtained by monitoring isotope concentration
in the blood or end-tidal air.3-4 Such a correction is included
in the equations below.
The equations are derived from the Fick principle and
have been described in detail, along with their underlying
assumptions, by Kety.19 For a particular tissue compartment, i,
C,(t) = f, ("Ca(u)e-K,"""du,'
(I)
where t = a given time after the beginning of inhalation,
Ci(t) = isotope concentration in the tissue at time t,
f, = blood flow per unit volume of tissue, Ki = fi/Xi, where
\i is the tissue-blood partition coefficient, and
C a (t) = isotope concentration of the arterial blood or endtidal air at time t.
Let N(t) represent the count rate obtained from an extracranial detector at time t. If the isotope is assumed to be
homogeneously distributed in each tissue compartment and
if differences in counting geometry are neglected, N(t) will
be proportional to a weighted sum of the isotope concentrations in the several compartments. In a twocompartmental system,
N(t) = a
(2)
where a is a proportionality constant relating units of count
rate to concentration, and Wi represents the relative tissue
weight for each compartment (2w, = 1). Substituting equation (1) into equation (2),
N(t) = « 2 w ' f l f'C.(u)e-KI'l-"du.
i - 1
(3)
•'o
If the parameters before the integral sign are represented by
a single coefficient, Pi, an equation in four unknowns can be
written:
(4)
Computer solutions for P ( , P 2 , Kt and K2 are readily obtained from equation (4) by means of an unweighted least
squares method of curve fitting. Details of the computer
analysis are given in the Appendix.
Assuming that Ki represents the gray matter clearance
246
rate, multiplication by the partition coefficient, Xg, for this
tissue20 yields gray matter blood flow, fg, in milliliters per
gram per minute. Because the partition coefficient for the
combined white matter-extracerebral compartment is unknown, a similar estimate of blood flow based on K2 is not
obtainable, nor can a determination be made of relative
tissue weight. It is possible, however, to estimate the fraction
of total blood flow accounted for by each compartment
through use of the coefficients P! and P2. Given the relation
Pi = awjfi, it follows that:
w,f,
P,
(W,/ 2 Wk)(F,/W,)
F,
(5)
Wk)(F)/Wj)1
J
- 1
in which Wi and fi are the relative tissue weights and blood
flows, respectively, for each compartment, and Wi and Fi
are the corresponding absolute weights and flows. Thus,
P,
p,
F,
= FF,,
F, + F2
(6)
where FFi is defined as the fractional flow for the first compartment (gray matter), expressed as a percentage of the
total blood flow in the tissue under observation. Although
this index is not equivalent to tissue weight, being influenced
by both the size of the compartment and its blood flow, it
nevertheless provides information about the relative contribution of the first compartment.
Methods
Analyses were carried out on two types of data: (1)
computer-synthesized curves containing both cerebral and
extracerebral components, and (2) 133Xe inhalation curves
recorded from young control subjects and elderly patients
with organic dementia. The synthetic data were used to test
the adequacy of the two-compartmental model in estimating
known parameters of the clearance curves, and to evaluate
the stability of these estimates in the presence of random
noise. The inhalation studies provided normative rCBF
data, and permitted investigation of hemispheral, regional,
and test-retest variations.
Synthetic curves were computer-generated in accordance with a three-compartmental model representing
cerebral gray matter, white matter and extracerebral tissue 1
Since blood flow in a given tissue cannot be considered
homogeneous, a Gaussian distribution of clearance rates
was assumed for each compartment. 8 A weighted sum of the
three distributions was then convoluted with a typical input
function (arterial isotope concentration) to obtain a
clearance curve that simulated an extracranial recording.
Clearance rates and weighting factors were chosen in accordance with the best available estimates from the literature,
and were varied to represent both normal and pathological
brain conditions. In some curves, random noise was added
to represent statistical variations in isotope count rate.
Details of the synthetic curve construction, along with
specific parameter values, are given in the Appendix.
Two groups of subjects were tested: 48 healthy young
volunteers with a mean age of 23.3 years (SD = 2.9), and 20
demented elderly patients with a mean age of 60.4 years
(SD = 8.9). Seven of the volunteers and four of the patients
were females. As reported elsewhere,21 clear-cut evidence of
Stroke, Vol. 6, May-June 1975
rCBF ESTIMATED BY
133
Xe INHALATION
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cerebrovascular disease was found in six of the patients; 14
were considered to have Alzheimer's disease, one confirmed
by biopsy. Five additional subjects (three controls and two
patients) were excluded from the study because of hyperventilation or inadequate counting statistics.
The procedures for 133Xe inhalation and respired air
monitoring are essentially the same as described previously.4
Tracer amounts of isotope were mixed with air in an
anesthesia machine and inhaled for one minute through a
face mask. The administered concentration was 2 mCi of
133
Xe per liter of air. This gave an estimated absorbed dose
to the lungs of approximately 100 mrads,22>23 a level considered safe for repeated exposure. A slightly higher dosage
(2.5 mCi per liter) was administered to the demented
patients in order to assure adequate count rates.
End-tidal air was used to estimate both the isotope concentration and Pco, of the arterial blood. The underlying
assumptions and limitations of this procedure are discussed
below. A continuous sample of air (1.5 liters per minute) was
drawn directly from the face mask, as shown in figure 1. The
air was passed over a scintillation detector and then through
a Godart capnograph. The capnograph was routinely
calibrated with gases of known CO2 content, and checked
against arterial Pco, determinations in six subjects. Respired
air radioactivity was recorded by a Baird-Atomic digital
ratemeter with a 0.01-minute sampling interval. Figure 2 illustrates such an air curve and its end-tidal values during
and after one minute of 133Xe inhalation. The manual selection of end-tidal peaks can be avoided by using an
automated air sampling system.24
Four Nuclear-Chicago scintillation detectors (15 mm
diameter) were placed over the precentral and parietal
regions bilaterally in all subjects except 13 of the young
volunteers, who had temporal rather than parietal
placements. The present report is limited to rCBF data from
the precentral and parietal regions, as shown in figure 1.
Other brain areas, including four additional locations made
possible by a new 8-detector system, will be reported
separately. In 28 of the volunteers, measurements were
made on a second day within a month of the original ex-
'"Xe
off
CPM
<IO3
J
RESPIRED AIR CURVE
600
r
•= End-Tidal Volues
500
400 -
!
300 -
';
200
\
•
III
1
M-i
100
1 I. I: J
05
10
15
Minutes After Start of Inhalation
20
25
FIGURE 1
Respired air curve during and following a one-minute inhalation of
3
Xe. The curve becomes inverted when the isotope is turned off,
i.e., end-tidal values are at the trough during inhalation and at the
peak during clearance.
amination, thus providing data for test-retest comparisons.
All probes were fitted with 2 to 3 cm of lateral collimation (inside diameter = 22 mm). Low level discriminators
were set at 20 kev. Count rates from each detector were
stored in a Nuclear-Chicago multichannel analyzer, using a
six-second sampling interval. The stored digital data were
automatically punched on IBM cards for subsequent computer processing. Figure 3 presents a typical head curve
recorded from the left parietal region of a young control
subject. A minimum of 60 X 103 counts per minute (cpm)
was considered necessary at the peak of the curve for adequate signal-to-noise ratios. Extracranial monitoring was
carried out for 12 to 15 minutes, but as indicated in figure 3,
the curves were fitted only over the first ten minutes following inhalation.
Since end-tidal air is assumed to be in equilibrium with
the arterial blood at the alveolar surface, allowance should
be made for differences in arrival time of the isotope in the
brain and at the respired air detector. Based on appearance
l!!
90
80
70
Xe
off
1
FITTED HEAD CURVE
= Row Oolo
?60
I 5O
3 30
20
10 -
Valve
5
6
7
8
9
4
Minutes After Start of Inhalation
10
II
12
13
FIGURE 3
FIGURE 1
Placement of scintillation detectors over the precentral and parietal
regions (bilateral). Respired air is sampled from the face mask.
Stroke, Vol. 6, May-June 1975
Extracranially recorded head curve from the left parietal region of a
young control subject, using a six-second sampling interval. The
curve has been fitted from 1.6 to II minutes by a least squares computer method. For clarity, only every other point is plotted after 3.5
247
OBRIST, THOMPSON, WANG, WILKINSON
times, circulation from the lungs to the brain was estimated
to take six to eight seconds, while two to three seconds were
needed for the expired air to reach the monitoring probe.
This produces a net time displacement of the head curve
relative to the air curve, such that the recorded head data lag
the air data by three to six seconds. Correction for this time
displacement was achieved by subtracting a constant, delta,
from each of the head curve times.4 In the present analysis, a
delta of three seconds was used throughout.
Results
START FIT TIME
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The high isotope content of the air passages during
and immediately following 133Xe inhalation gives rise
to scattered radiation that may distort the recorded
extracranial curves. Such distortion, which is
sometimes apparent visually, can have a definite effect
on curve analysis. An attempt was madeT therefore, to
assess the influence of scattered radiation on blood
flow measurements, using computer-simulated data.
Estimates of scattered radiation were first obtained from phantoms and from four subjects in whom
isotope was introduced into the air passages (mouth,
throat and nasopharynx). Low level discriminators
were set at 20 kev and collimators at 2 cm. Depending
on head probe location, the presence of 133Xe in the
airways alone produced extracranial count rates- that
equaled 3% to 6% of those normally recorded at the
end of a one-minute inhalation.
Based on this information, a noise-free synthetic
head curve was constructed upon which scattered
radiation was added in direct proportion to the mean
air curve (both inspiratory and expiratory phases), the
latter being used to estimate the isotope content of the
air passages. The proportion of the mean air curve
that was added to the head curve was chosen to
produce a 6% increase in the extracranial count rate at
the end of inhalation. As shown in figure 4, the
Recommended
Start Fit
Time
Scattered Radiation
resulting head curve is maximally distorted when the
air counts are greatest, i.e., during the one-minute inhalation, and progressively less distorted as the
isotope leaves the air passages.
Table 1 compares the clearance rates of this synthetic curve before and after the addition of scattered
radiation. In the absence of scattered radiation, estimates of K^ approach the true value of 1.0 at early
start fit times, and then gradually decline as curve fitting begins later. This decline is attributable to the
decreasing contribution of the fastest clearing gray
matter components. In contrast, the head curve with
scattered radiation yields overestimates of Ki when
fitted during and immediately following inhalation. It
is not until the scattered radiation reaches low levels
(0.6 minute after 133Xe off) that its influence becomes
negligible, as revealed by the similarity of Ki estimates
at later start fit times. Parallel findings have been obtained from human data, i.e., appreciably higher Kx
values were found when curve fitting began during
high isotope concentrations in the respired air.
These results indicate that curve fitting should
begin early when the fastest gray matter components
are fully represented. They also indicate that start fit
times during and immediately following inhalation
give spuriously high clearance rates due to distortion
of the head curve by scattered radiation. It is concluded that the optimal start fit time is the earliest
point on the head curve where scattered radiation can
be assumed negligible. Both the synthetic and human
data suggest that such a point is reached after inhalation is over, when the mean isotope concentration in
the airways has decreased to 10% of its maximum
value (see fig. 4).
A more convenient start fit criterion used in the
present analysis is the corresponding point on the endtidal air curve, where the count rate is approximately
20% of its maximum value. Because of 133Xe recirculation, the head curve does not peak until 0.4 minute or
more after the end of inhalation. Thus, the
recommended start fit time usually falls close to the
peak of the head curve.
END FIT TIME
In accordance with the two-compartmental model
proposed above, estimation of the fast (gray matter)
TABLE 1
Estimates of K, for Different Start Fit Times: Influence of
Scattered Radiation From the Air Passages (Simulated
Data)*
05
10
15
20
25
35
Minutes after Start of Inhalation
FIGURE 4
A computer-simulated head curve, indicating the recommended
start fit lime in relation to scattered radiation from the air passages.
The latter was estimated from the mean 123Xe concentration of the
respired air sampled at the mouth. Analysis of this curve is
presented in table I.
248
Scattered
radiation
Stai•t of curve fit (minutei)
0.1
0.6
1.1
1.6
2.1
1.6
None
1.000 0.999 0.995 0.982 0.958 0.930
6 % at 133Xe 1.163 1.124 1.032 0.988 0.961 0.933
off (1 min)
*Based on a noise-free synthetic head curve. True value of Ki =
1.0. End fit time = 1 1 minutes.
Stroke, Vol. 6, May-June 1975
rCBF ESTIMATED BY l u Xe INHALATION
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clearance rate requires that curve analysis be limited
to short time intervals at the beginning of washout.
Computer-synthesized head curves were utilized to
assess the influence of curve length on Ki estimates,
and to aid in the selection of an optimum analysis interval. The stability of Kj estimates was evaluated by
the addition of random noise to the synthetic curves.
Three types of head curve, representing normal,
low and high cerebral blood flows, were synthesized
from the input function of a one-minute t33Xe inhalation. A family of 50 curves was generated for each
blood flow by adding random noise to simulate^
Poisson distribution of count rates. This permittetl^Stimation of both the mean and standard deviation of
K] at each blood flow level. The average peak
amplitude of the curves was 60 X 103 cpm. Curve fitting began at a constant 1.6 minutes in accordance
with the start fit criterion recommended above (20%
point on the descending end-tidal air curve). The end
of curve fitting was varied from 7 to 15 minutes after
the start of inhalation.
Figure 5 presents a comparison of the true and
computed K, values at five different end fit times. It is
•True Volues of K|
•Computer Estimates (MeantS O )
1.40
High CBF
1.30
1.20
1.10
1.00
.90
Low CBF
.60-
clear that early end fit times yield unstable estimates
of K, (large SDs), while late end fit times result in underestimates of K, (low mean values). The increased
SD at early end fit times is attributable to the smaller
number of data points available for curve fitting. The
decreased mean at late end fit times is attributable to
the relatively greater contribution of slow extracerebral components. As might be expected, Kj estimates for the high CBF are consistently less than the
true value, due to the rapid clearance of fast tissue
components prior to curve fitting.
These results suggest that the best end fit time is
11 minutes, a point where the mean and SD of Ki have
optimal values. At this time, the high and normal
CBFs are underestimated by 5% and 2%, respectively,
while the low CBF is overestimated by 1%. Although
ending the curve fit too early increases the variance of
the estimates and ending it too late increases the bias,
the precise end fit time does not appear to be critical
within a range of 9 to 13 minutes.
SIGNAL-TO-NOISE RATIO
It is well known that the reliability of radioisotope
measurements depends on count rate, the higher rates
giving more stable values. An attempt therefore was
made to assess the magnitude of errors in Ki as a function of counting statistics.
A computer-simulated head curve representing
normal cerebral blood flow was generated at five
different amplitudes, such that its peak counts ranged
from 20 X 103 to 100 X 103 cpm. Fifty curves were
then generated for each amplitude by adding random
noise. Start and end fit times were held constant at 1.6
and 11 minutes, respectively, as recommended above.
Table 2 presents the mean and SD of Kj at each
amplitude level. Whereas the mean Ki value remains
constant across amplitude, the SD decreases with increasing count rate. Of particular interest is the finding that the SD of K.! is inversely proportional to the
square root of the count rate. Specifically, while the
count rate increases by a factor of four (from 20 X 103
to 80 X 103), the SD of K, decreases by a factor of two
(from 0.052 to 0.025).
The present findings indicate the importance of
adequate counting statistics in providing stable estimates of Ki. Assuming a Gaussian distribution, Ki
TABLE 2
9
II
13
15
End of Curve Fit (Minutes)
Effect of Counf Rate on Means and SDs of K, (Simulated
Data)*
Counts per min X 10i(peak of head curv
FIGURES
Computer estimates of the fast compartment clearance rate (K,) at
three different blood flow levels and at five different end fit times.
Dots represent the mean, and vertical bars indicate the SD for 50
computer-simulated head curves that differ only in random noise.
The known true values of K, are indicated by the dashed lines, and
correspond to high, normal and low gray matter blood flows of 104,
80 and 56 ml/100 gm per minute, respectively.
Stroke, Vol. 6, May-June 1975
Mean
SD
20
40
60
80
100
0.981
0.052
0.979
0.036
0.980
0.029
0.981
0.025
0.980
0.023
*Each statistic is based on 50 synthetic curves that differ only
in random noise. True value of Ki = 1.0. Start fit time = 1 . 6
minutes. End fit time = 1 1 minutes.
249
OBRIST, THOMPSON, WANG, WILKINSON
TABLE 3
Comparison of Two-Compartmental and Three-Compartmental Analyses: Clearance Rates for Parietal
Curves
Subject
and side
ES
LB
JM
JB
BL
Left
Right
Left
Right
Left
Right
Left
Right
Left
Right
Mean
K,
K,
Ki
Two comp. *
Three comp.t
Two comp.
Three comp.
Three comp.
0.952
0.945
0.836
0.885
0.837
0.839
0.806
0.805
0.703
0.638
0.917
0.947
0.878
0.826
0.841
0.845
0.806
0.786
0.709
0.610
0.111
0.102
0.095
0.095
0.102
0.102
0.088
0.092
0.092
0.091
0.172
0.193
0.183
0.149
0.137
0.150
0.136
0.130
0.146
0.131
0.025
0.026
0.026
0.024
0.015
0.018
0.021
0.022
0.034
0.037
0.825
0.817
0.097
0.153
0.025
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*End of curve fit for two-compartmental analysis = 1 1 minutes.
tEnd of curve fit for three-compartmental analysis = 41 minutes.
values can be expected to vary from the mean by as
much as ±10% (two SDs) at 20 X 103 cpm, while at
60 X 103 cpm, the comparable variation is only 6%.
Since increasing the count rate beyond this level
reduces the SD by progressively smaller amounts, the
higher doses of 133Xe required to produce additional
counts do not seem justified. For this reason, a peak
count rate of 60 X 103 cpm was obtained in the present study.
TWO-COMPARTMENTAL VERSUS THREE-COMPARTMENTAL ANALYSIS
Whereas the present two-compartmental model treats
the slowly perfused white matter and extracerebral
tissue as a single compartment, the previously
described three-compartmental model4 attempts to
distinguish between these two types of tissue. Since
both methods assume that the faster clearing gray
matter can be adequately separated from other
tissues, it is of interest to compare the clearance rates
obtained by each.
Extracranial monitoring was carried out for 40
minutes in five volunteer subjects, following one
minute of 133Xe inhalation. The resulting clearance
curves were subjected to both a two-compartmental
and three-compartmental analysis. Except for
differences in curve length appropriate to the particular method, data for the two analyses were identical.
Table 3 presents the clearance rates obtained by
each method for the left and right parietal regions. It
is apparent that the Kl values are in close agreement,
thus lending support to the validity of the fast tissue
compartment. In contrast, K2 is consistently lower in
the two-compartmental analysis, suggesting that the
second compartment includes both the intermediate
and slow clearing tissues represented by K2 and K3 in
the three-compartmental analysis.
HEALTHY Y O U N G ADULTS
Tables 4, 5 and 6 summarize the statistical findings on
the young control group for both the clearance rate
(Ki) and fractional flow (FFO of the first compartment. Whereas between-subject variations in K, are
generally large (SD > 10% of the mean), individual
differences in FFi are much smaller (SD < 5% of the
mean). An equivalent gray matter blood flow (fg) is
presented for each Ki value, assuming a partition
coefficient of 0.8. Corrections for arterial Pco, (shown
TABLE 4
Laterality Differences in Fast Compartment Clearance Rate (KJ and Fractional Flow (FFX): Comparison
of Right and Left Precentral Values in 48 Young Controls
K,
Mean
Right precentral
Left precentral
Difference
Correlation coefficient
(right versus left)
SD
0.933
0.935
-0.002
0.105
0.107
0.043
0.917
Equivalent f8*
SD
Mean
74.6
74.8
-0.2
8.4
8.6
3.4
ft,
Mean
SD
0.917
0.919
*fe = Ki X X, X 100 = gray matter blood flow in milliliters per 100 gm per minute, assuming \ g
corrected to 40 mm Paco2, right fe = 80.8 and left fB = 81.0.
250
0.027
0.027
0.011
0.765
0.763
+ 0.002
0.8. When
Stroke, Vol. 6, May-June 1975
rCBF ESTIMATED BY
133
Xe INHALATION
Regional Differences in Fast Compartment Clearance Rate (Kt) and Fractional Flow (FFi): Comparison
of Right Precentral and Parietal Values in 35 Young Controls
Equivalent
Mean
Ki
Mean
SD
0.102
Right precentral
0.934
Right parietal
0.103
0.827
Difference
0.060
+ 0.107t
Correlation coefficient
(precentral versus parietal)
0.829
74.7
66.2
+ 8.5f
u*
FFi
SD
Mean
SD
8.2
8.2
4.8
0.764
0.747
0.027
0.030
0.018
+ 0.017f
0.813
0.829
*In milliliters per 100 gm per minute. When corrected to 40 mm Paco», precentral fg = 81.1 and parietal fE
71.8.
tStatistically significant difference by paired / test (P < 0.001).
Downloaded from http://stroke.ahajournals.org/ by guest on June 15, 2017
in the footnotes) are based on the blood flow response
to 5% inhaled CO 2 in a subsample of 12 subjects. The
mean Paco2 for the entire group was 38.4 mm Hg. A
correction factor of 5.0% change in fg per millimeter
change in Paco 2 was applied.
As indicated in table 4, there was no systematic
K^ difference between the left and right precentral
regions (mean difference = — 0.002), and the two
sides were highly correlated (product-moment correlation = 0.917). The SD of the difference, however,
was 0.043, or approximately 5% of the mean Ki value.
Assuming that the Ki differences are normally distributed and that the obtained SD approximates the
true value, side-to-side differences in K, greater than
10% (two SDs) can be considered statistically significant at the 0.05 level. A similar lack of systematic
difference and a high correlation between sides was
found for F F L Because of the small side-to-side variation, FFi differences of only 3% can be considered
significant.
In contrast to the overall agreement between
sides, a systematic regional difference in Kj was obtained, as shown in table 5. Thirty-two of 35 subjects
had greater Ki values for the precentral than the
parietal region, the mean difference being highly
significant. Fractional flow also differed significantly,
and in the same direction. The two regions tended to
vary together, as revealed by the moderately high correlation coefficients for both K, and FFj.
Table 6 presents the test-retest findings for the
precentral region. Neither Id nor FF; yielded
systematic day-to-day differences (mean = — 0.007
and +0.003, respectively). However, the SD of the Ki
difference was 0.066, or approximately 7% of the
mean value. These differences could not be accounted
for by inter-test variations in arterial Pco2. Based on
the assumptions made previously, a day-to-day
difference in K, of at least 14% (two SDs) was considered necessary to be statistically significant. A
moderately high test-retest correlation was computed
for Ki, similar in magnitude to the inter-regional
value. The relatively low correlation for FF : may
reflect differences in compartmental size due to
variations in probe placement between tests.
PATIENTS WITH ORGANIC DEMENTIA
Figures 6 and 7 compare the distributions of Ki and
FFi in demented elderly patients with those of healthy
young adults. For each parameter, the mean precentral values of the two groups are significantly different,
there being little or no overlap of individual
measurements. FFi is also significantly more variable
in the patient group, the SD being more than twice
that of the normal subjects.
Discussion
The results indicate the sensitivity of computed
clearance rates to variations in the time of curve fit-
TABIE 6
Test-Retest Differences in Fast Compartment Clearance Rate ( K j and Fractional Flow (FFt): Comparison
of Right Precentral Values on Different Days in 28 Young Controls
Ki
Mean
Day 1
Day 2
Difference
Correlation coefficient
(day 1 versus day 2)
SD
0.947
0.954
-0.007
0.118
0.108
0.066
0.831
Equivalent '
SD
Mean
75.8
76.3
-0.5
9.4
8.6
5.3
0.831
FF,
SD
Mean
0.764
0.761
+ 0.003
0.027
0.024
0.023
0.608
*In milliliters per 100 gm per minute. When corrected to 40 mm Paco2, fK for day 1 = 82.0 and fK for day 2 =
82.6.
Stroke, Vol. 6. May-June 1975
251
OBRIST, THOMPSON, WANG, WILKINSON
• 48
• 20
0 8 6-
(Mean = 933 ± 1 0 5 )
YOUNG CONTROLS
DEMENTED PATIENTS (Mean = 577 ±125)
•
2
4
-
—|
2
40
1
1I
•II 1 •
III
III
INI I l l l• L.1
.50
45
.60
55
.70
.65
.80
.90
85
.75
1.00
.95
1.10
1.05
1.20
115
Clearance Rate (K,)
Downloaded from http://stroke.ahajournals.org/ by guest on June 15, 2017
FIGURE 6
Comparison of fast compartment clearance rates fKt)for the right
precentral region in young control subjects and elderly demented
patients. Group means and SDs are shown. The means correspond
to gray matter blood flows of 74.6 and 46.2 ml/100 gm per minute,
respectively, and are significantly different by the Wilcoxon twosample rank test (P < 0.001).
ting. Although Kt estimates are relatively insensitive
to end fit time within a range of 9 to 13 minutes, the
choice of start fit time is critical due to head curve distortion by scattered radiation from the air passages,
which can result in gross overestimations of K.,. In the
present study, head curve distortion was avoided by
delaying the curve fit until the isotope content of the
48 YOUNG CONTROLS
( Mean = .765 t.027)
20 DEMENTED PATIENTS (Mean = .644 ± .060)
16
14
8 12
O
o
o>
8
£ 6
4
2
2
m
.52
n .64
.60
.56
54
58
.62
.68
.66
.72
.70
76
74
.80
78
82
Fractional Flow (FF|)
Comparison of fast compartment fractional flows (FF^for the right
precentral region in young control subjects and elderly demented
patients. Both the means and SDs differ significantly (P < 0.001) by
the Wilcoxon two-sample rank lest and (he F test, respectively.
252
airways declined to low levels (20% point on the endtidal air curve). As suggested in table 1, such a delay
causes minor attenuation of Ki estimates, presumably
because of the lesser contribution of fast clearing
tissues.
Preliminary attempts to minimize head curve distortion due to scattered radiation have not yielded
practical solutions. While pulse-height discrimination
of the gamma ray peak (lower level discriminator set
at 75 kev) is able to reduce Compton scatter, such
radiation cannot be completely eliminated,25 so that
K[ estimates continue to vary with start fit time during
inhalation. Furthermore, this approach has the disadvantage of requiring increased 133Xe dosage in order to
maintain adequate count rates. Attempts to remove
scattered radiation from the head curve by computer
subtraction of respired air radioactivity have been
equally unsuccessful. The resulting K.! estimates are
unstable due to the necessity of solving for an additional unknown weighting factor in the least squares
fit. Although IV injection of the isotope26 results in
lower airway radioactivity during inspiration, head
curve distortion also occurs with this technique
because of the high 133Xe content of the expired air.
Until better procedures can be found to eliminate head
curve distortion, a delay in curve fitting appears to be
the most suitable approach.
Another advantage of a late start fit time is that
K, estimates are less sensitive to temporal displacement of the air and head curves caused by differences
in arrival time of the isotope at the respective probes.
When curve fitting begins at the start of inhalation,
precise alignment of the two curves is essential, i.e.,
errors in estimating delta (the correction for temporal
displacement) have a marked effect on computed
clearance rates. However, at the recommended later
start fit time, delta can vary by as much as 12 seconds
without affecting Kj values.
In addition to high concentrations of 133Xe in the
airways during inhalation, there is the possibility that
some of the isotope may become trapped in the air
sinuses. If washout is prolonged, the head curve could
be contaminated by such radioactivity for extended
periods of time. Gamma camera studies on two subjects showed little or no accumulation of radioactivity
in any of the air sinuses, consistent with previous
observations."
The statistical findings on young control subjects
revealed no systematic differences in Id or FF t
between the precentral regions of each hemisphere or
between tests administered on separate days, i.e., the
mean values were approximately the same. Significant
differences in both variables were obtained, however,
between precentral and parietal regions within the
hemisphere, a finding that agrees with previous observations of a higher rCBF in precentral as opposed to
postcentral areas.28
In contrast to the similarity in mean values, substantial test-retest differences in Ki were found among
Stroke, Vol. 6, May-June 1975
rCBF ESTIMATED BY
133
Xe INHALATION
Downloaded from http://stroke.ahajournals.org/ by guest on June 15, 2017
individuals, as reflected in the relatively large SD of
the difference. Thus, assuming a Gaussian distribution, day-to-day differences must exceed 14% to be
considered significant at the 0.05 level. This large testretest variation agrees with previous findings for both
the intracarotid injection technique9-29-30 and the
Kety-Schmidt nitrous oxide method,31 where shorter
inter-test intervals were employed. Such variation
suggests either gross errors of measurement or considerable fluctuation in cerebral blood flow over time.
The synthetic curve analysis offers some insight
into the relative contribution of errors of measurement. As shown in table 2, clearance curves with peak
counts of 60 X 103 cpm, which differ only in random
noise, yielded a K.! SD of 0.029, or 3% of the mean
value. Because the variances are additive, the SD of
the difference between pairs of such curves is \/2 X
(0.029) = 0.041, or 4% of the mean value. Since the
SD of the difference between precentral regions in
each hemisphere was only slightly greater (<5% of the
mean value according to table 4), it can be argued that
most of the K, variation between bilaterally
symmetrical probes was due to counting statistics. In
the case of regional (precentral versus parietal) and
day-to-day differences, however, the Ki SDs were
larger, i.e., approximately 7% of the mean value, indicating the existence of other, probably
physiological, sources of variation.
The significant difference in Ki found between
healthy young adults and demented elderly patients
agrees with previous findings of reduced gray matter
blood flow in dementia. 32 ' 33 Similarly, the significant
difference in FFi between groups is consistent with
earlier reports of decreased gray matter weight in
demented patients.34
Fractional flow was utilized in the present study
as an alternative to the concept of relative tissue
weight. Unlike the latter, it does not require assumption of partition coefficients, especially the unknown
value for the second compartment (mixed white
matter and extracerebral tissue). As indicated in equation (5), the fractional flow of a compartment, i, can
be regarded as a product of the relative tissue weight,
W|, and the ratio of compartmental blood flow tomean
blood flow, fi/f. To the extent that fj and f vary
proportionately, changes in fractional flow will reflect
alterations in tissue weight. Data from the intracarotid injection method35 yield fractional flows for
the first compartment ( F F ^ of approximately 0.80 in
normal controls (w, = 0.5, f, = 80, f = 50). This contrasts with a mean of 0.76 obtained by the present
method, the lower value being attributable to the
presence of extracerebral components. Whether FF,
can provide useful information in clinical studies
remains to be seen. Preliminary findings suggest little
variability among normal subjects, with considerably
lower and more variable values in patient groups.
Estimation of the arterial input function from
end-tidal air raises questions concerning the adequacy
Stroke, Vol. 6. May-June 1975
of the latter measurement. As previously reported,4
there is good agreement between the end-tidal and
arterial isotope curves in healthy young subjects, a
finding confirmed by subsequent studies in this
laboratory. Five elderly patients with obstructive lung
disease, however, revealed discrepancies between the
two curves, such that end-tidal 133Xe measurements
overestimated arterial concentration during inhalation, and underestimated it during clearance. Id
values based on the air curve were consistently lower
than those computed from arterial measurements.
Work is now in progress to determine the extent to
which the end-tidal curve deviates from the arterial
curve in the aging population, and to assess its influence on computed rCBF values. Preliminary findings suggest that a substantial deviation is necessary
before rCBF values are affected. Nevertheless, it may
be necessary to sample arterial blood in some cases,
particularly those with marked
respiratory
irregularities. The possibility of applying a correction
to deviant air curves also is being explored.
Except for minor differences relating to the route
of administration, intravenous injection of the
isotope26 yields data comparable to those obtained by
inhalation. In comparing the two techniques, the present authors have encountered similar limitations and
difficulties with each. The methodology developed for
inhalation, including the theoretical model and computer analysis, can be readily applied to IV injection
data.
Validation of the 133Xe inhalation method by
comparison with established rCBF techniques is
necessary before reliance can be placed on its use in
clinical research. Recently, Corbett and Eidelman36
reported excellent agreement between changes in Ki
obtained by the present method and changes in
cerebral arteriovenous O2 differences during hyperventilation. A direct comparison with the internal carotid
injection method is currently being undertaken by the
present authors in collaboration with Drs. Martin
Reivich and Herbert Goldberg at the University of
Pennsylvania (Philadelphia, Pennsylvania). In ten
patients with cerebrovascular disease, a productmoment correlation of 0.91 was obtained for gray
matter blood flow between the two methods, based on
61 pairs of regional measurements in back-to-back examinations. Although there was a tendency for the inhalation method to underestimate blood flow at very
low levels, the overall agreement between the methods
was quite good. Further studies are now in progress.
Application of the 133Xe inhalation method to
clinical research appears feasible, based on
preliminary work in several laboratories. The method
has been utilized by the present authors in studies on
normal all-night sleep37 and in preoperative and
postoperative evaluation of patients with carotid endarterectomy. 6 Recently, Rao and coworkers38 have
reported its use in serial studies on acute stroke, while
Risberg and associates39 have employed it in the in253
OBRIST, THOMPSON, WANG, WILKINSON
vestigation of functional rCBF changes during mental
activity. In each case, emphasis has been placed on
bilateral as well as serial examinations. The general
usefulness of the method in neurological and
neurosurgical research, however, remains to be determined.
Appendix
where C a (t) is a given input function (arterial isotope concentration), and
(11)
g.(x) ="
is the Gaussian disstribution with a mean of Ki and an SD of
(j,. For three compartments, the tissue isotope concentration is
CLEARANCE CURVE ANALYSIS
Head curve analysis was carried out in accordance with the
two-compartmental model given in equation (4). Let
0 = t0 < t, < t2 < . . . be equally spaced time points and let
N
(tj). j = 1, 2, . . . , be the count rate in the interval (tj „ tj).
Expressed in terms of equation (4),
1
K
N(tj) =2)
iV> du.
(7)
Downloaded from http://stroke.ahajournals.org/ by guest on June 15, 2017
The desired least-squares solution is the set of parameter
values (P,, P 2 , Ki, and K2) which minimizes
n
2
h
2 [N(1J) ~ 2 Pi J Ca(u)eK i V»i du]2,
where P,(K,, K2) and P2(K,, K2) are the least squares solutions for P, and P2 in equation (8), given arbitrary but fixed
values of K, and K2. The least squares curve fit is obtained
by minimizing the function f of the two nonlinear variables,
K, and K2. This is accomplished by using a variable metric
algorithm for function minimization developed by
Fletcher.40 The algorithm requires the computation of the
gradient vector (df/3K,, 3f/dK2), as well as the value of the
function f at each iteration. Information accumulated from
all previous iterations determines both the direction and
magnitude of the next step at each stage of the iterative
process. Typically, only 8 to 12 evaluations of f and the two
derivatives are required for convergence, even with relatively
poor initial estimates of Ki and K2. For moderately fast
computers, this can be achieved in a few seconds. The computer program is written in Fortran, and is available upon
request from the authors.
CLEARANCE CURVE SYNTHESIS
The synthetic head curves were generated with a threecompartmental model that is physiologically more realistic
than the one used for analysis. While the analysis model
described by equation (4) assumes a single clearance rate for
an entire compartment, the synthesis model includes a Gaussian distribution of clearance rates for each compartment.
Thus, for a particular tissue compartment, i, the 133Xe concentration in the tissue at time t is
ar
[
Ci(t) = X, fxgi(x) ["C a (u)e xit "dudx,
254
Addition of random noise to this curve was accomplished as follows. Let N(tj) be the count rate in the interval (tj-,, tj), and assume it to be a Poisson distributed
random variable with a mean value of
t
(8)
du] 2 , (9)
(10)
(12)
where w, is the relative weight of the ith compartment
(2w, = 1).
m(tj) = «J"c(t)dt,
where tm is the start fit time, and tn is the end fit time.
Since P, and P2 are linear parameters, minimization of
the above function can be reduced to a two-variable
problem. Let
f(K,,
C(t) = 2 w,C,(t),
(13)
'j-i
where a is a proportionality constant relating units of count
rate to concentration. Computationally, use is made of the
fact that the distribution of N(tj) is approximately Gaussian
with a mean and variance both equal to m(tj). By generating
a sequence of standard normal deviates, Zj, a synthetic
clearance curve, N(tj), therefore can be constructed:
N(tj)= m(tj)+
j , j = 1, 2 . . . .
(14)
The noise-free synthetic curve in figure 4 and table 1 was obtained by setting N(tj) = m(tj).
The parameters used to construct the synthetic curves
were chosen in accordance with the best available estimates
from the literature. Although information is available for
the first and second compartments (gray and white matter),
less is known about the parameter values for the third (extracerebral) compartment. All synthetic curves were
generated from the arterial input function, C a (t), of a typical
control subject. For the "normal CBF" curves in figure 5,
the mean clearance rates (K,, K2, and K3) of the Gaussian
distributions were 1.0, 0.14 and 0.035, respectively, and the
SDs (cr,, <72, and <r3) were 0.2, 0.03 and 0.015, respectively.
Values for the relative tissue weights and partition
coefficients were w, = 0.3, w2 = 0.3, w3 = 0.4, X, = 0.8,
X2 = 1.5 and X3 = 1.0. The proportionality constant, a, was
adjusted to give the desired peak count rate. Figure 8 shows
the noise-free synthetic curve generated with these
parameter values, along with the three compartments that
comprise it.
The above values of K, and K2 and the assumed
equality of w, and w2 were based on two-compartmental
analyses of intracarotid injection curves in normal subjects,35 while K3 and w3 were based on three-compartmental
analyses of inhalation data/ The SDs, <T, and a2, were
chosen to approximate those obtained by Reivich and
coworkers8 on cats, and a3 was chosen so that the corresponding Gaussian distribution would include the
heterogeneous clearance rates of skin12 and resting
muscle.13-14 Values for X, and X2 were taken from Veall and
M alien,20 assuming a normal hematocrit. The unknown parStroke, Vol. 6, May-June 1975
rCBF ESTIMATED BY m X e INHALATION
100-
7.
„
80-
8.
9.
10.
2
4
Minutes A f t e r
Start
of I n t i a l a l i o n
11.
Downloaded from http://stroke.ahajournals.org/ by guest on June 15, 2017
Computer-simulated head curve, showing three hypothetical
compartments and their sum (total curve). The first, second and
third compartments correspond to gray matter, white matter and
exlracerebral tissue, respectively. Each compartment was generated
from a Gaussian distribution of clearance rales, representing
heterogeneous blood flow in that tissue.
tition coefficient, X3, was given a value of 1.0. The "high
CBF" curves in figure 5 were generated by increasing Ki, K2,
(7, and <72, . . . each by 30%. A corresponding downward
adjustment of 30% was used to generate the "low CBF"
curves. The other parameters, including K3 and <r3,
remained unchanged.
It should be noted that the count rate representing
arterial or end-tidal isotope concentration [Ca(t), t > 0] is
also a random process. Computer simulation studies were
carried out in which these count rates were assumed to be
Poisson distributed. The resulting variations in K, and K2 estimates were negligible (SD < 0.5% of the mean) when compared with the variations produced by random fluctuations
in head curve counts, N(tj). Consequently, arterial and endtidal count rates were treated as nonrandom functions.
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Stroke, Vol. 6, May-June 1975
Regional Cerebral Blood Flow Estimated by 133Xenon Inhalation
WALTER D. OBRIST, HOWARD K. THOMPSON, JR., HSIOH SHAN WANG and WILLIAM
E. WILKINSON
Stroke. 1975;6:245-256
doi: 10.1161/01.STR.6.3.245
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