92
133
Xenon Inhalation Method
Analysis of Reproducibility: Some of Its Physiological Implications
URS W. BLAUENSTEIN, M.D.,
JAMES H. HALSEY, J R . ,
M.D.,
EDWIN M. WILSON, D . S C , EDWARD L. WILLS, P H . D . , AND JARL RISBERG, P H . D .
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SUMMARY Regional cerebral blood flow (rCBF) was
simultaneously measured at seven locations in each hemisphere by the
Obrist '"xenon inhalation method. In each of 35 healthy righthanded subjects two rest measurements were performed on consecutive days. The data analysis comprises the two-compartmentally
derived parameters for flow (f,), relative tissue weight (w,), and fractional flow (FF,) respectively of the first compartment, and in addition the initial slope index (ISI). At each detector location the
coefficient of variation (C.V.) of the change from first to second
measurement was on average 10.4% (ISI), 14.2% (f,), 7.2% (w,), and
2.9% (FF,) respectively. However, when each regional measurement
was expressed as a percentage of its hemispheric mean, the C.V. of
the intermeasurement change was on average 4.4% (ISI), 7.0% (f,),
7.7% (w,), and 1.9% (FF,) respectively; that of the hemispheric means
of ISI, f,, and FF, was found to be distinctly larger, whereas that of
w, was about equal in size. The interhemispheric coefficient of variation for the change of the hemispheric means from first to second
measurement was only 2.3% (ISI), 4.4% (f,), 1.6% (w,), and 1.1%
(FF,) respectively.
The findings suggest that (1) the variability of rCBF from subject
- to subject and in consecutive measurements in the same subject is to a
substantial degree of physiological origin, and that (2) there are two
determinants of rCBF which may operate independently: a determinant of the hemispheric mean level, probably a single determinant for
both hemispheres, and a set of determinants for each separate region
superimposed on the hemispheric mean level.
Introduction
system, interfere with the methodologically inherent
variance of rCBF data rendering difficulties in distinguishing
between physiological changes of rCBF and the error of
measurement. The present analysis of reproducibility deals
with physiological implications of rCBF variation.
133
THE NONINVASIVE xenon inhalation technique permits simultaneous bilateral measurements of regional cerebral blood flow (rCBF) serially in patients as well as in
healthy volunteers. It is a useful tool to investigate rCBF
behavior in man under physiological and pathological conditions, particularly during neuropsychological tests.
In the assessment of rCBF by the 133xenon inhalation technique the reproducibility of rCBF determinations from subject to subject and of subsequent measurements in the same
subject is of considerable interest. It is not only a matter of
methodological validation but also a critical issue in the
evaluation of physiological fluctuations of rCBF in man at
rest and under test conditions. It is well recognized that
functional changes within the normal brain related to mental
and physical activity can be quantitated by rCBF determination.1"8 The sometimes rather small changes of rCBF,
however, accompanying spontaneous or induced alterations
of brain activity may at least partially be obscured by
methodological errors of measurement or by more general
changes of the blood supply to the brain reflecting nonspecific effects of environmental factors or of the test stimuli
applied. In the investigation of normal rCBF behavior an
analysis of reproducibility offers some insight into the
relative contribution of various determinants of rCBF.
Since the introduction of the atraumatic 133xenon inhalation technique a decade ago for measuring rCBF by extracranial recording,10' " many efforts have been undertaken to
estimate the range of reproducibility achieved by this
method, done mainly in comparison with the data obtained
by the well-established intracarotid injection technique.12"24
Numerous physiological variables, however, influencing
rCBF, e.g., arterial Pco 2 , neuronal activity and metabolic
rate of the brain, and activity stage of the reticular activating
From the Stroke Acute Care Research Unit, Department of Neurology,
University of Alabama Medical Center, Birmingham, Alabama 35294.
Supported in part by NINCDS Grants NS 08802 and NS 11109.
Dr. Blauenstein was supported by the Swiss Biologico-Medical Scholarship
Foundation.
Methods
In each of 35 healthy right-handed volunteers (one
woman, 34 men; mean age 24 ± 6 [SD] years, ranging from
18 to 43 years), two rest measurements were made on consecutive days. For the time of each session starting 15
minutes prior to the measurement the subjects were requested to relax, keeping the eyes closed but not asleep. It is
recognized that the physical rest requested may have been
only a random event in regard to brain activity being merely
modified by physical and psychic relaxation.
rCBF was measured by the Obrist 13axenon inhalation
method.24'25 The measurement procedure and the technical
specifications of our system are described in detail
elsewhere.24-M Seven detectors consisting of Nal (TI)
crystals (%" diameter X 3A" long) with %" I.D. X 1" lead
collimators each were placed perpendicularly to the side of
the subject's head covering homologous regions in both
hemispheres in the approximate locations shown in the
sketch of figure 1. The calculation of the rCBF values was
based upon the two-compartment model developed by
Obrist and co-workers. 24 ' 25 No energy discrimination was
used. The pulse-height analyzers were set to record both
gamma and x-ray radiation, i.e., from 20 to 100 kev. In the
present study only the parameters of the first compartment
enclosing mainly the fast clearing component of rCBF are
taken in consideration: f, (ml/100 gm per minute): flow of
the first compartment, derived from the clearance constant
k, using a standard blood-tissue partition coefficient X, of
0.8; w, (%): relative tissue weight of the first compartment;
FF, (%): fractional (relative) flow of the first compartment.
FF, is defined by Obrist24 as the fractional flow for the first
compartment, expressed as a percentage of the total blood
133
XENON INHALATION METHOD/Blauenstein el al.
flow in the tissue under observation: FF, = -—*-— < 100,
F, + F2
where F, and F2 respectively represent the total flow of the
first and of the second compartment respectively. This is not
equivalent to tissue weight, being influenced by both the size
of the compartment and of its blood flow. Additionally to
these flow parameters rCBF was calculated as initial slope
index (ISI) derived from the initial slope of the clearance
curve between the second and the third minute. The principles of calculation and the rationale of the ISI developed
by Risberg and collaborators in our laboratory have recently
been published.27 The arterial carbon dioxide tension was estimated from the end-tidal points of the capnographic recordings (Beckman LB-2) of the expired air sample. The
blood pressure was measured by auscultation; the mean
arterial blood pressure (MABP) was calculated as diastolic
pressure plus one-third of the pulse pressure.
93
INITIAL SLOPE INDEX
AVERAGE HEMISPHERIC PATTERN OF
FLOW DISTRIBUTION (MEAN + C.V.%)
t
CV % OF ORIGINAL DATA
CV % Of HPFD VALUES
MEAN OLEFT DRIGHT HEMISPHERE
FIRST REST MEASUREMENT N=35
HEMISPHERIC
MEAN
LEFT RIGHT
4 9 8 SOI
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Results
Tables 1 through 7 summarize the results of the 70 rCBF
measurements in the 35 subjects.
Original Data: First and Second Measurement
Table 1 shows the mean with coefficient of variation
(C.V. = standard deviation, expressed as a percentage of
the mean) of each of the seven regions studied and
of the hemispheric mean respectively, listed separately for
the left side and the right side and for the first and second
measurements respectively. As indicated by both ISI
and f,, the clearance rate throughout the hemisphere is not
homogeneous, corroborating the findings of other authors.4' •*• "• "• »• *• ffl The rCBF values are the highest frontally and the lowest temporo-occipitally (figs. 1 and 2). Temporally, where the rCBF is expected to be the lowest, there is
in our system no detector available. Table 2 depicts the
mean of each regional value expressed as percentage of its
hemispheric mean, comprising the average hemispheric
pattern of flow distribution for the four parameters. Figures
1 through 4 illustrate the results of the first measurement.
The pattern of ISI differs distinctly from that of f,: the
regional percentage values of ISI are higher parietotemporo-occipitally and lower in the frontal and Rolandic
regions. The pattern of the relative tissue weight w, is the
reverse of that of the ISI and f,. Apparently the anterior
regions of the hemispheres are characterized by a high
clearance rate and a small relative tissue weight of the first
(fast) compartment, whereas the posterior regions reveal low
clearance rates but large relative tissue weights. This reverse
relationship is a feature of the hemispheric pattern of the
parameters. Regionally the relationship between clearance
rates and relative tissue weight of the first compartment is
not reverse. ISI and w, disclose a positive correlation for al)
regions. Their correlation coefficients range from 0.45 to
3.72 (p < 0.006). f, and w, reveal a weak positive correlation
3nly for a few regions during the first measurement.
Contrary to ISI, f|, and w,, respectively, the FF, pattern
itays practically uniform throughout the entire hemisphere.
While those differ from one another and from region to
•egion, the FF, is characterized by a fairly consistent size,
-urthermore it varies the least among subjects as indicated
FIGURE 1. (A) Prefrontal, (B) precentral, (C) inferior frontal, (D)
Rolandic, (E) centrotemporal, (G) parietal, (H) temporo-occipital,
and (HM) hemispheric mean.
by the smallest coefficient of variation among the four rCBF
parameters. The unique feature of FF, is a consistent finding
in various aspects of the analysis of reproducibility to be
shown below.
For each of the seven pairs of homologous regions there is
a strong to almost complete interhemispheric correlation of
the rCBF parameters for both the first and the second
measurement (table 3).
Though the coefficients of variation of the means of the
regional and hemispheric mean values respectively are large,
the interhemispheric differences are statistically significant
for a few regions as evaluated by the paired t-test (table 1).
Remarkably the most consistent interhemispheric asymmetry is found inferior frontally, i.e., between Broca's area
of the dominant hemisphere and the homologous region of
the minor hemisphere, with the higher values on the right
side. This statistically significant asymmetry is revealed by
all four rCBF parameters for both the first and the second
measurement. It is recognized that in our sample of righthanded subjects the left hemisphere is usually dominant for
speech.
Looking at the mean interhemispheric difference of each
homologous pair of the seven regions and of the hemispheric
mean respectively (table 4) there is an obvious discrepancy
between the regional interhemispheric differences and that
of the hemispheric means. For example, the mean interhemispheric difference of the prefrontal region in absolute
values of ISI is maximally 6.2 units (mean + 2 SD) or
11.7% compared with 1.9 units or 3.8% for the hemispheric
mean. In the 70 measurements the interhemispheric differences of the hemispheric means, expressed as percentage of
the mean of the left and right hemispheric mean, exceeded
Downloaded from http://stroke.ahajournals.org/ by guest on June 18, 2017
Left
Right
Left
Right
Left
Right
Left
Right
Left
Right
Left
Right
Left
Right
Left
Right
50.lt
47.6
47.9
50.4
50.6
48.4
48.6
46.7
46.8
49.8
51.5fff
53.7
53.5
51.8
52.1
50.1
15.6
15.1
15.4
15.4
15.2
15.9
16.2
16.5
15.5
15.6
15.1
16.9
15.6
13.7
14.9
15.0
C.V.
49.5
49.4
53.3
52.2f
51.3
51.5
49.7
50.9tt
47.6
47.8
49.7
50.5f
48.0
47.6
45.9
46.4
Mean
ISI
(unit9 Of ISI)
#2
14.8
12.6
12.9
12.8
14.5
13.4
12.6
13.4
11.9
12.5
13.8
12.2
13.7
13.8
12.8
12.3
C.V.
71.6
71.3
70.9
70.9
69.0
68.8
68.4
69.0
61.8
61.1
73.8f
80.5
81.0
76.7
76.5
72.1
14.8
15.1
15.1
16.3
13.5
14.4
15.2
15.5
14.3
13.8
13.6
15.1
14.1
11.8
13.2
13.7
69.6
70.1
66.6
68.lt
66.6
66.4
60.7
60.4
69.8
70.1
72.4f
79.5
78.4
75.3
74.9
70.7
Left
Right
Left
Right
Left
Right
Left
Right
Left
Right
Left
Right
95.5
95.4
101.1
100.9
97.2
96.7
93.7
93.6
102.8ft
4.8
3.9
4.6
3.6
3.3
4.9
5.4
4.8
5.2
3.3
3.2
3.7
3.3
5.5
C.V.
ISI
103.9
103.9
100.6
102.6ft
96.5
96.4
100.9
101.8f
97.2
96.2
93.1
93.6
105.5ft
107.9
Mean
#2
5.3
3.2
2.5
4.2
3.4
4.8
5.3
4.9
5.1
5.3
4.8
4.5
3.6
3.0
C.V.
5.4
112.9
113.0
107.5
106.6
101.3
103.1
99.5
98.8
96.9
96.2
96.1
96.2
86.7
85.6
4.7
5.3
4.9
5.9
6.6
5.4
5.3
4.7
6.8
4.8
5.9
5.7
5.9
C.V.
Mean
#i
113.7
112.0
108.0
106.8
101.2 ,
103.4f
99.8
100.0
95.4
97.2f
95.4
94.9
87.1
86.3
Mean
#2
*The hemispheric pattern expresses each regional value as a percentage of its hemispheric mean.
Significance of the interhemispherio difference: tp <0.05; ttO.OOl < p <0.01; t t t p = 0.0001 (paired t-teat).
Right
Temporo-occipital Left
Parietal
Centro temporal
Rolandic
Inferior frontal
Precentral
Prefrontal
Mean
107.8
106.7
104.0
103.9
100.7
#i
5.8
5.4
5.5
4.3
3.8
5.2
4.6
5.9
6.5
5.3
4.8
4.7
5.3
7.0
C.V.
TABLE 2 Average Hemispheric Pattern of Flow Distribution Derived From the Individual Patterns*
15.2
13.5
11.8
14.0
13.0
12.0
11.8
13.6
12.5
12.5
13.4
12.5
12.4
13.6
11.9
12.0
fi
(ml/100 gm/min)
#1
#2
Mean
C.V.
Mean
C.V.
Mean arterial Pcoi (mm Hg): #1 - 39.4 ± 2.9 SD; #2 = 39.6 ± 2.9 SD.
Mean MABP (mm Hg): # 1 - 93.2 ± 11.8 SD; # 2 - 91.2 =fc 11.2 SD.
Significance of the interhemispheric difference: tp <0.05; ttO.OOl < p <0.01; t t t p - 0.0001 (paired t-test).
Hemispheric mean
Temporo-occipital
Parietal
Centro temporal
Rolandic
Inferior frontal
Pre central
Prefrontal
Mean
#1
96.5
97.0
98.2
98.9
90.5
90.0
107.4
107.3
97.5
96.2f
105.9
108.3f
8.3
8.8
6.8
6.1
7.0
6.3
8.1
8.3
96.0
97.0f
96.9
98.2f
91.1
91.2
108.4
107.8
98.0
96.9
105.0
106.1
9.8
6.9
6.3
7.6
7.9
9.0
9.0
8.7
8.7
8.9
100.3
100.5
100.0
100.7f
98.0
98.0
100.2
100.3
99.8
99.4
100.5
100.5
2.6
1.4
1.8
1.2
1.4
2.6
2.2
2.0
2.0
1.4
1.3
1.9
1.7
2.7
101.lt
101.7
93.5
94.2
91-8ftt
8.2
8.9
7.0
6.8
7.4
8.4
6.7
6.5
9.6
8.8
92.7ft
C.V.
#2
99.8
100.2
99.7
100.1
98.3
98.3
100.9
100.6
100.0
99.3f
99.9
100.2
100.7ft
#2
78.5
78.lt
77.2
77.7ft
77.2
77.7f
76.1
76.2
78.1
78.1
77.4
77.0
77.3
77.8
77.4
77.6
101.5
FF,
3.5
3.5
3.0
2.7
3.9
3.5
4.1
3.8
3.5
3.2
3.8
3.5
3.6
3.7
3.1
3.0
Mean
Mean
FFi
(%)
C .V.
Mean
#i
77.5tff
75.2
75.5
76.9
77.3
76.6
76.5
77.1
77.4
76.7
77.0ft
77.9
77.0
77.4f
76.7
78.1
Mean
C.V.
#2
10.6
11.8
8.9
7.4
11.0
10.6
10.9
11.7
9.0
7.7
9.5
10.0
12.1
12.2
8.1
7.9
C.V.
#1
Mean
46.8
46.5
42.3
41.9
45.4
45.9
43.2
43.3
39.4
39.3
42.4f
39.7ft
41.5
49.9f
41.9
40.4
Mean
#2
C.V.
10.9
11.6
9.7
8.9
12.1
11.3
12.1
12.2
8.5
8.5
10.6
10.4
10.4
11.8
11.9
11.6
C.V.
(%:i
Mean
#i
38.6
45.8
46.0
41.7
41.3
45.2
46.5ft
42.9
43.0
42.4f
38.7
41.2
41.5
42.0
40.3
39.8f
Mean
#1
2.1
1.6
1.2
2.0
1.8
2.7
2.4
2.0
1.6
1.9
1.2
1.2
2.2
2.2
C.V.
3.6
3.7
3.0
3.0
3.8
3.9
3.8
3.8
3.3
2.9
3.7
3.9
3.8
4.1
3.1
3.1
C.V.
TABLE 1 Mean Values of Four CBF Parameters for Seven Cerebral Regions and the Hemispheric Mean Bilaterally in SB Normal Righl-Handed Subjects,'Listed Separately for
the First ( # 1) and the Second ( # 2) Rest Measurement
•<
jo
jo
Tl
m
50
z
>
J
<-*
Z
o
<
O
m
3
3
XENON INHALATION METHOD/Blauenstein et al.
95
TABLE 3 Inierhemispheric Correlation of Four CBF Parameters Listed Separately for First (#1) and Second (#2) Measurement
(N = 35)
HPFD values
Original data
ISI
Prefrontal
Precentral
Inferior frontal
Rolandic
Centro temporal
Parietal
Temporo-occipital
Hemispheric mean
FFi
fi
ISI
#i
#2
#l
#2
#1
#2
#i
#2
0.95
0.98
0.97
0.95
0.96
0.97
0.93
0.99
0.95
0.95
0.96
0.97
0.96
0.94
0.96
0.99
0.90
0.92
0.88
0.83
0.88
0.86
0.75
0.99
0.82
0.85
0.86
0.91
0.91
0.85
0.87
0.97
0.96
0.95
0.97
0.97
0.93
0.96
0.87
0.99
0.97
0.96
0.95
0.97
0.95
0.91
0.92
0.98
0.91
0.91
0.93
0.92
0.89
0.85
0.73
0.97
0.93
0.92
0.90
0.88
0.88
0.87
0.76
0.97
#i
#2
0.75*
0.48ft 0.41 f
0.34f 0.28
0.31
0.40f
0.18
0.38f
0.08
0.22
0.22
0.06
-0.12
0.45tf
0.75*
0.58ft 0.84*
0.24
#2
#l
0.58ft 0.65*
0.52ft 0.51ft
0.54ft
0.44ft 0.45ft
0.54ft 0.73*
FFi
wi
fi
#1
#2
0.93*
0.90*
0.94*
0.95*
0.91*
0.88*
0.80*
0.94*
0.93*
0.93*
0.94*
0.93*
0.86*
0.90*
#2
#1
0.51ft 0.65*
0.64* 0.48ft
0.82*
0.74*
0.43f
0.33f
0.44ft
0.70*
0.52ft
0.51ft
0.56ft
0.50ft
Probability of the correlation coefficients: original data: p = 0.0001 for each of the coefficients; HPFD values: *p = 0.0001; tp = 0.05; ffO.OOl <p <0.01 .
Downloaded from http://stroke.ahajournals.org/ by guest on June 18, 2017
the 3% limit only in six measurements. Four ranged from
3.1% to 3.3%, and two reached 4.2% and 5.4%, respectively.
The two cerebral hemispheres have apparently in most of the
instances a very similar hemispheric mean level of each of
the four rCBF parameters (ISI, f,, w,, and FF,) in common
independently of the regional interhemispheric and the interregional hemispheric differences respectively. Though the
mean hemispheric CBF reveals large fluctuations from subject to subject and in subsequent measurements in the same
subject, it varies bilaterally in the same direction and by the
same order of magnitude.
(1) There is a distinct and consistent hemispheric pattern
of distribution of each of the four rCBF parameters (table
2). It is different for each of the parameters. The pattern of
ISI, fi, and w, respectively is characterized by marked interregional differences whereas that of FF, is largely even
throughout the hemisphere. The hemispheric pattern of flow
distribution is bilaterally similar except for the inferior frontal region, where a consistent interhemispheric asymmetry is
revealed by the HPFD values of all four rCBF parameters
for both the first and the second measurement as it is by the
original data.
(2) The coefficients of variation of the HPFD values
(table 2) are distinctly different from those of the original
data (table i), being approximately 70% (ISI), 61% (f,), 25%
(w,), and 48% (FF,) respectively smaller as illustrated in
figures 1 to 4 for the first measurement.
(3) The interhemispheric correlation of the HPFD values
is remarkably weakened or lost and differs much more from
region to region than that of the original data for ISI, f,, and
FF,, whereas the interhemispheric correlation of w, is about
equal for both the original data and the HPFD values (table 3).
Hemispheric Pattern of Flow Distribution (HPFD): First and
Second Measurement
Expressing the regional CBF values as a percentage of
their corresponding hemispheric mean establishes a
hemispheric pattern of flow distribution (HPFD). The
average hemispheric pattern derived from each individual
hemispheric pattern of the 70 measurements reveals three
relevant findings.
TABLE 4 Interhemispheric Differences Expressed as Absolute Figures Between Homologous Regions and the Hemispheric Means
Respectively, Listed Separately for First and Second Measurement and the Original Data and the HPFD Values Respectively (N = 35)
ISI
fi
(units of index)
Mean SD
Mean
#2
#1
SD
Mean
SD
FFi
(%)
Wl
(%)
(ml/100 gm/min)
#2
#l
#1
Mean SD
#2
#2
#l
Mean
SD
Mean
SD
Mean
SD
Mean
SD
1.1
1.0
1.0
0.9
1.1
1.1
2.1
0.5
0.8
0.8
0.8
0.7
1.0
0.8
2.1
0.4
1.1
0.9
1.2
0.7
0.9
1.4
1.8
0.5
0.9
0.6
0.7
0.9
0.7
0.9
1.1
1.5
0.5
0.8
0.7
1.0
1.0
0.7
1.2
1.7
0.4
0.8
1.1
1.3
0.4
0.9
0.8
1.0
1.0
0.9
1.1
1.5
0.3
2.5
2.4
2.6
1.9
2.6
2.9
4.5
2.0
1.5
1.9
1.6
1.6
1.9
3.9
2.6
2.2
2.8
2.3
2.3
1.9
1.5
1.8
1.9
1.6
2.5
2.8
1.4
0.9
1.1
1.1
1.0
1.6
2.0
1.1
0.8
1.2
0.9
1.0
1.3
1.9
1.2
0.9
1.2
1.5
1.0
1.5
2.0
1.1
0.9
1.1
1.2
1.1
1.2
1.7
Original Data
Prefrontal
Precentral
Inferior frontal
Rolandic
Centrotemporal
Parietal
Temporo-occipital
Hemispheric mean
1.7
1.3
1.8
1.7
1.7
1.5
2.1
0.6
Prefrontal
Precentral
Inferior frontal
Rolandic
Centrotemporal
3.2
2.8
3.2
3.3
3.1
2.9
3.8
2.1
1.1
1.8
1.9
1.6
1.6
1.6
0.6
2.0
1.6
2.0
1.1
1.4
1.7
1.4
0.7
2.1
1.3
1.2
1.2
1.2
1.7
1.2
0.6
3.9
3.7
4.0
4.4
3.6
4.1
4.5
1.2
3.5
3.1
3.4
4.4
3.1
3.4
3.7
1.2
2.9
2.1
2.9
2.8
2.5
2.1
2.7
3.6
2.5
3.5
2.2
2.2
3.3
2.8
3.1
2.3
2.3
1.8
2.0
2.3
2.2
5.1
4.9
5.1
5.8
5.1
5.7
6.0
4.1
3.7
4.4
5.0
4.1
4.1
4.5
5.1
4.3
4.1
3.0
2.8
3.6
3.2
1.8
4.8
3.3
2.9
2.5
2.7
3.0
2.5
1.2
0.7
1.0
0.8
0.9
0.7
0.9
1.0
1.0
0.9
1.3
0.5
HPFD Values
Parietal
Temporo-occipital
5.9
4.5
5.6
4.7
4.1
5.0
4.5
5.1
4.3
3.4
3.7
3.2
4.1
3.4
3.2
3.3
96
STROKE
f, FLOW OF FIRST COMPARTMENT
AVERAGE HEMISPHERIC PATTERN OF
FLOW DISTRIBUTION (MEAN ± C.V.%)
J
CV % OF ORIGINAL DATA
CV % OF HPFO VALUES
MEAN OLEFT DHIGHT HEMISPHERE
FIRST REST MEASUREMENT N=35
lEMISPHERld
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70
U
A
B
C
0
E
G
H
HM
FIGURE 2. Abbreviations as in figure I.
Change of the rCBF Parameters From First to Second Measurement
Change from first to second measurement connotes the
second measurement as a percentage of the first (table 5);
100% means no change occurred.
w, RELATIVE WEIGHT OF FIRST COMPARTMENT
AVERAGE HEMISPHERIC PATTERN OF
DISTRIBUTION (MEAN 1 C.V %)
. CV % OF ORIGINAL DATA
FIRST REST MEASUREMENT N-35
HEMISPHERIC
MEAN
LEFT RIGHT
42 9 430
VOL
8, No
1, JANUARY-FEBRUARY
As listed in table 5, the mean regional change of both the
original data and the HPFD values is very small or almost
negligible. The hemispheric means of ISI and of f, show a
tendency to decrease whereas w, and FF, appear to increase
slightly. All seven regions change their rCBF parameters in
a similar range as indicated by their similar coefficients of
variation. Furthermore, there is a moderate to strong
positive interhemispheric correlation of the changes in the
original data from first to second measurement (table 6).
That of the hemispheric means is almost complete. It indicates that rCBF is changing simultaneously in both
hemispheres in the same direction. In contrast to the original
data, the interhemispheric correlation of changes of the
HPFD values is weak or lacking for ISI and FF! respectively. As depicted in table 3, mainly the interhemispheric
correlation of the HPFD values of f, is not consistent in the
two subsequent measurements, w,, however, discloses a
comparable positive correlation for both the original data
and the HPFD values.
As mentioned earlier for the subject-to-subject variation
for the first and the second measurement, respectively, the
FF, shows among the four rCBF parameters again the
smallest coefficient of variation for the change from one
measurement to the next in the same subject. The fraction of
total flow accounted for by the first compartment appears to
be fairly consistent in spite of large fluctuations of the
clearance rates and the relative tissue weights of the first
compartment both among subjects and in consecutive
measurements in the same subject.
The analysis of the intermeasurement correlation of the
rCBF parameters for each region reveals similar findings as
discussed for the interhemispheric correlation of the changes
of homologous regions (table 7).
Comparison of Intersubject and Intermeasurement Variation of the
rCBF Parameters
A characteristic feature of the rCBF behavior in the context of this study is the changing C.V. from subject to subject
and from one measurement to the next (tables 1, 2 and 5).
The coefficient of variation of the hemispheric mean of
ISI, f,, and w, is smaller for the second measurement than
for the first (subject-to-subject variation). That of FF,,
however, is similar for both measurements. The C.V. of
changes from one measurement to the next indicates that the
fluctuations of the hemispheric mean of ISI, w,, and FF,,
FF, FRACTIONAL FLOW OF FIRST COMPARTMENT
AVERAGE HEMISPHERIC PATTERN OF
DISTRIBUTION (MEAN t C.V.%)
T CV % OF ORIGINAL DATA
+ C V % OF HPFO VALUES
i MEAN OLEFT ORIGHT HEMISPHERE
B
C
D
E
G
H
FIGURE 3. Abbreviations as in figure 1.
1977
B
C
D
E
G
H
FIGURE 4. Abbreviations as in figure 1.
l33
XENON INHALATION METHOD/Blauenstein et al.
97
TABLE 5 Change of Four CBF Parameters From First to Second Measurement Expressing the Second Measuremenl as a Percentage
of the First (N = 36)
Hemispheric pattern of Sow d istribution
Orijjinal data
ISI
wi
FF i
ISI
fi
Wl
FF i
C.V.
Mean C.V.
Mean C.V.
Mean C.V.
Mean C.V.
Mean C.V.
Mean C.V.
99.9 9.6
98.5 10.2
99.5 12.0
98.2 15.0
100.6 7.2
100.0 7.6
100.7 2.7
100.4 3.1
100.2 4.1
98.9 5.1
100.8 6.4
99.4 7.4
99.5 7.1
99.2 7.2
99.8 1.9
99.6 2.1
99.7
99.6
9.1
8.8
99.4 13.0
99.2 14.4
100.8 5.9
101.0 5.4
100.4 2.5
100.4 2.4
100.0 3.1
100.1 3.5
100.6 5.4
100.3 5.6
99.7 6.4
100.2 7.0
99.5 1.3
99.7 1.3
99.9 11.8
99.6 11.1
99.2 15.2
99.4 14.8
100.2 8.8
100.4 8.3
100.6 2.9
100.2 3.2
99.9 4.8
100.0 5.4
100.1 6.9
100.6 7.7
99.1 8.9
99.6 7.7
99.8 2.0
99.5 1.7
101.0 10.2
100.8 10.5
99.5 13.8
100.4 15.4
101.9 7.6
102.3 7.2
101.2 3.1
101.0 3.0
101.2 5.8
101.2 4.1
100.7 7.5
101.5 7.9
100.8 7.7
101.6 8.5
100.4 2.0
100.3 1.9
99.8 10.8
100.6 10.2
97.7 14.9
99.9 12.9
102.3 6.0
101.4 5.4
101.6 3.3
101.1 2.3
99.9 4.5
101.0 3.2
98.7 7.1
101.2 5.3
101.2 6.7
100.5 5.7
100.7
100.4
1.8
1.5
99.8 10.8
99.2 10.9
98.5 14.3
97.7 14.6
101.7 6.4
101.6 6.4
101.1 2.5
100.7 2.5
100.0 4.1
99.5 4.1
99.6 6.8
98.9 7.2
100.7 8.1
100.9 7.6
100.2
99.9
1.8
1.6
99.4 11.8
99.6 10.1
99.6 14.5
99.7 14.1
100.7 9.3
99.2 9.6
100.4 3.5
100.5 4.0
99.5 5.2
100.0 4.5
100.7 7.1
101.2 9.1
99.6 9.9
98.2 8.7
99.5 2.7
99.8 2.8
99.8
99.6
98.9 12.3
98.8 12.8
101.5 7.8
101.1 7.4
100.9 2.2
100.7 2.5
—
—
—
—
Mean
Prefrontal
Left
Right
Precentral
Left
Right
Inferior frontal
Left
Right
Rolandic
Left
Right
Centrotemporal
Left
Right
fi
c.v.
Mean
Parietal
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Left
Right
Temporo-occipital
Left
Right
Hemispheric
mean
Left
Right
9.5
9.3
—
—
—
—
Mean change of arterial Pcoi (difference in mm Hg): 0.1 ±2.1 SD.
Mean change of MABP (in percent of MABP for the first measurement): -1.6 =fc 9.9 SD.
respectively, are smaller in subsequent measurements in the
same subject than those from subject to subject. The C.V. of
f, of the first and the second measurement respectively approximates that of the change in subsequent measurements.
The regional coefficients of variation of the original data of
ISI, f,, and FF, are similar to those of the hemispheric mean
values. The subject-to-subject fluctuations of ISI and fi are
slightly smaller for the second measurement than for the
first whereas those of w, and FF, are almost the same. The
intermeasurement fluctuations of ISI, w,, and FF, in the
same subject, however, are smaller than the subject-tosubject fluctuations for the first and second measurements
respectively; those of f, are about equal. At each detector
location the coefficient of variation of the change from first
to second measurement was on average 10.4% (ISI), 14.2%
(f,), 7.2% (w,), and 2.9% (FF,) respectively. However, when
each regional measurement was expressed as a percentage of
its hemispheric mean, the C.V. of the intermeasurement
change was on average 4.4% (ISI), 7.0% (f,), 7.7% (w,), and
1.9% (FF,) respectively; that of the hemispheric means of
ISI, f,, and FF, was found to be distinctly larger, whereas
that of w, was about equal in size (table 5). The interhemispheric C.V. for the change of the hemispheric means
from first to second measurement was only 2.3% (ISI), 4.4%
(f,), 1.6% (w,), and 1.1% (FF,) respectively.
In contrast to the behavior of the original data, the C.V.
of the HPFD values is fairly constant both among subjects
and in subsequent measurements in the same subject. Only
the HPFD values of f, show slightly larger C.V. for the
change from one measurement to the next than those from
subject-to-subject. The overall variation of the HPFD values
is remarkably smaller than that of the original data except
for w,. The C.V. of the original data of w, in subsequent
measurements approximates that of the HPFD values of w,
both for the subject-to-subject and the measurement-tomeasurement variation in the same subject.
TABLE 6 Interhemispheric Correlation of Changes of Four CBF Parameters From First to Second Rest Measurement (N = 35)
Correlation coefficient
derived from original data
Prefrontal
Precentral
Inferior frontal
Rolandic
Centrotemporal
Parietal
Temporo-occipital
Hemispheric mean
Correlation coefficient
derived from HPFD values
ISI
fi
wi
FF,
ISI
0.73*
0.84*
0.86*
0.88*
0.91*
0.83*
0.77*
0.97*
0.68*
0.76*
0.76*
0.82*
0.81*
0.69*
0.52§
0.94*
0.92*
0.81*
0.92*
0.89*
0.83*
0.81*
0.82*
0.98*
0.74*
0.78*
0.79*
0.74*
0.68*
0.66*
0.55J
0.90*
0.11
-0.03
0.30
0.47§
0.48§
-0.10
0.16
—
fi
0.09
0.04
0.01
0.28
0.07
-0.13
-0.09
—
Probability of the correlation coefficients: *p = 0.0001, tp <0.05, $0.0001 <p <0.001, §0.001 <p <0.01.
Wl
FF,
0.91*
0.92*
0.92*
0.91*
0.90*
0.88*
0.84*
0.40f
0.30
0.61t
0.35t
0.17
0.42f
0.09
—
—
98
STROKE
VOL 8, No
1, JANUARY-FEBRUARY
1977
TABLE 7 Correlation of Four CBF Parameters From First to Second Measurement for Each of the Seven Regions
and the Hemispheric Mean Bilaterally (N = 35)
ISI
Prefrontal
Precentral
Inferior frontal
Rolandic
Centro temporal
Parietal
Temporo-occipital
Hemispheric mean
Left
Right
Left
Right
Left
Right
Left
Right
Left
Right
Left
Right
Left
Right
Left
Right
0.80
0.73
0.80
0.81
0.68
0.71
0.74
0.76
0.68
0.75
0.73
0.72
0.70
0.70
0.77
0.77
Original data
Wl
f.
0.66
0.47
0.58
0.57
0.31
0.35
0.41
0.44
0.35
0.49
0.45
0.39
0.41
0.35
0.51
0.50
0.78
0.79
0.81
0.80
0.73
0.75
0.80
0.83
0.79
0.78
0.81
0.81
0.71
0.70
0.72
0.72
HPFD values
FPi
ISI
fi
Wl
FFi
0.71
0.66
0.66
0.64
0.71
0.62
0.70
0.71
0.55
0.73
0.79
0.77
0.57
0.51
0.75
0.67
0.58*
0.37J
0.62*
0.41J
0.57*
0.49t
0.28
0.69*
0.05
0.41t
0.49f
0.23
0.51t
0.62*
—
—
0.49f
0.12
0.37J
0.39J
0.10
0.13
0.09
-0.05
-0.07
0.21
0.37J
-0.21
0.25
-0.07
0.64*
0.67*
0.64*
0.55*
0.62*
0.67*
0.61*
0.60*
0.57*
0.61*
0.46f
0.49*
0.39J
0.51f
—
—
0.15
0.37J
0.40J
0.50f
0.64*
0.66*
0.51f
0.57*
0.23
0.34J
0.60*
0.61*
0.48f
0.391
—
—
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Probability of the correlation coefficients: original data: ISI and wi: p
*p <0.001, fO.001 <p<0.01, tp <0.05.
PcOj Relationship of rCBF Parameters
The Pco2 correlation of the four rCBF parameters was
calculated separately for the first measurement, the second
measurement, and the change from first to second measurement of the 35 pairs.
First and Second Measurement
The Pco2 relationship of the original data is different for
each of the four parameters. There is a consistent moderate
correlation between Pco2 and ISI, both in regard to the
regions and to the hemispheric means. The correlation
coefficients range from 0.51 to 0.70 (p < 0.01). Though they
differ slightly from region to region, side to side, and
measurement to measurement respectively, none of them
deviates greatly. The most consistent correlation is found inferior frontally (0.59 to 0.60) and centrotemporally (0.65 to
0.69). The correlation coefficients of f,, w,, and FF, respectively to Pco2 are generally lower and reveal much larger interregional, interhemispheric, and intermeasurement
differences than those of ISI. They are often not statistically
significant. The f, of several regions fails to reach a significant correlation to Pco2 exclusively during the second
measurement. The hemispheric means of w, and FF,, however, reveal a consistent weak to moderate correlation for
both hemispheres and for both the first and second measurement (r: 0.41 to 0.56; p < 0.05); those off, show a significant
correlation only for the first measurement (r: 0.58 on the left
side, 0.62 on the right side; p < 0.01). In summary the ISI
discloses a more consistent and closer relationship to Pco2
than the compartmentally derived parameters. In the instance of ISI the Pco2 correlation may reflect a causal interaction of Pco2 upon the overall level of the clearance rate at
least as a partial determinant.
The correlation coefficients between Pco2 and the HPFD
values of the four parameters do not exceed 0.36 and reach
statistical significance only in a few instances.
Change From First to Second Measurement
Correlating the change of Pco2, i.e., the difference in
millimeters of mercury from first to second measurement in
—
—
0.0001, fi and Wi: O.OOOKp <0.05, HPFD values:
the same subject, to the change of regional CBF reveals a
lack of any systematic interrelationship. Remarkably the
changes of the hemispheric mean values are also independent of the change in Pco2. The changes of rCBF exceed disproportionally the small differences in Pco2 in subsequent
measurements in the same subject. The analysis of each
single pair of measurements in the 35 subjects indicates that
Pco2 and the hemispheric mean levels of ISI and f, are
changing randomly in either direction, i.e., in parallel or in
an inverse fashion. For example, an increase of Pco2 was accompanied by an increase of ISI in 12 subjects and by a
decrease in three subjects; a decrease of Pco2 was associated
with an increase of ISI in six subjects and with a decrease in
eight subjects. In one subject an increase of the hemispheric
mean level of ISI of about 11% occurred in spite of no
change of the systemic Pco2.
Blood Pressure Relationship of rCBF
No significant correlation between mean arterial blood
pressure and rCBF could be found, as would be expected
with intact autoregulation.
Discussion
The accumulating information about normal rCBF in
man, reported by numerous investigators, 12 '" indicates a
considerable range of rCBF fluctuations from subject to subject and in subsequent measurements in the same subject. It
comprises figures ranging from about 5% to 20%, apparently
not a major function of the method applied or the technical
specifications of equipment used. Almost always the
probable role of physiological variables influencing the
deviation of rCBF data has been mentioned. Naturally, the
interference of the methodological error of measurement
and the biological variation compromises any analysis ol
reproducibility of rCBF data obtained in vivo. Also in oui
study, designed to evaluate rCBF at rest, it cannot seriouslj
be assumed to meet steady states on the two occasions rCBI
was measured in each subject. The insistent request on the
volunteers to relax, keeping the eyes closed, but not to sleep
could not interrupt thinking. Ongoing pleasant or unpleas
133
XENON INHALATION METHOD/Blauenstein et al.
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ant thoughts of various intensity and differing degrees of
relaxation must have exerted influences upon rCBF. In spite
of these and other biological variables the summarized
results reveal enough consistency to provide meaningful interpretation.
There are obvious major differences between homologous
regions interhemispherically and between regions within the
same hemisphere in each single rCBF measurement. The interregional differences in each hemisphere, however, seem to
be balanced out to a high degree in each measurement
resulting in a hemispheric mean which approximates very
closely that of the contralateral hemisphere. Accordingly the
interhemispheric correlation of the hemispheric means
appears to be stronger than that of each single region (table
3). It is almost complete for all parameters and for both the
first and the second measurement. In turn, the two
hemispheres have the similar hemispheric mean level of each
of the four rCBF parameters in common, independently of
the regional interhemispheric and the interregional
hemispheric differences respectively. That is, the fluctuations of the mean hemispheric level from subject to subject do not influence essentially the hemispheric pattern of
flow distribution in the range observed in this study. But they
contribute substantially to the overall variation, being equal
in size and direction for both hemispheres as indicated by the
identical range for both hemispheres and their almost complete positive interhemispheric correlation. Therefore, the
fluctuations of the HPFD values describe the regionally
dependent variation of rCBF being much smaller, i.e., only
one-half to one-third of the overall variation. The regionally
dependent variation of cerebral blood flow differs from
region to region in the same hemisphere and behaves independently between homologous regions of both
hemispheres as indicated by the attenuated or abolished interhemispheric correlation (table 3) even though the regional
range of variation is similar on the left and right side (table
2). A similar behavior of the mean hemispheric level and the
HPFD values respectively is found for the changes from first
to second measurement.
Contrary to the features of ISI, f|, and FF,, the regional
variation of w, does not seem to be dominated by the fluctuations of the mean hemispheric level. The coefficient of
variation of the HPFD values is on average only 25%
smaller than that of the original data. Furthermore, the
strong positive interhemispheric correlation is present in
both the original data and the HPFD values (table 3).
Though the mean relative tissue weight of the first compartment differs distinctly from region to region revealing an
identical and consistent pattern in both hemispheres, its
large fluctuations in the sample population affect all regions
and both sides approximately to a similar degree, and
homologous regions in the same direction regardless of the
variation of the level of the hemispheric mean. A similar extraordinary behavior of w, is found for the changes from one
measurement to the next in the same subject. The particular
feature of w, is not shared by the likewise compartmentally
derived parameter f,. It seems unlikely that it is mainly due
to error of measurement. A largely fluctuating w, in turn
cannot be equated with relative tissue weight of gray matter
which represents a given anatomical structure not changing
over short time periods in healthy subjects dealt with in this
study. The w, appears to have more likely functional mean-
99
ing than an anatomical one. It describes the fraction of brain
tissue which reveals at a given time the fast clearance rate indicated by k, comprising the first compartment of the twocompartment model. Evidence supporting this view is
reported by others.29-30
The fractional flow of the first compartment reveals the
most outstanding consistency among the four rCBF
parameters. In our study FF, is very similar for all the
regions except for the Rolandic region which reveals a
slightly lower value. If FF, provides physiologically
meaningful information about the relative contribution of
the first compartment to its blood flow then it could be inferred from our results that the fraction of total blood flow
accounted for by the first compartment is quite consistent
throughout the hemisphere. Such an inference is intriguing.
Regional differences in the proportion of the relative tissue
weight of the first to that of the second compartment,
i.e., essentially the proportion of gray to white matter in the
concept of the two-compartment model, would have to be
compensated for by an inverse proportion of the clearance
constant of the first (k,) to that of the second (k2) compartment though k, and k2 are supposed to indicate clearance
rate in the corresponding compartments independently of
the proportions of relative tissue weight. In more than 300
rCBF studies at rest in patients with unilateral ischemic
cerebral infarction we encountered in a number of
measurements regional k2 values being zero resulting in a w,
of 100%. In most of these instances which were reversible in
the follow-up it could not realistically be assumed that exclusively the second compartment, i.e., white matter, was
deprived from its blood supply. The k, values merely represent the average flow in the remaining active compartments
revealing one extreme of the phenomenon of slippage which
describes the manifestation of clearance rates of tissue fractions of gray or white matter in the wrong compartment of
the two-compartment model. The pathophysiological overlap of clearance rates of different tissues is not a function of
anatomy but of the impaired tissue perfusion, hence another
way to arrive at the same conclusion as mentioned above in
the context of the discussion of w,.
The w, and FF, seem at present to be mainly descriptive in
nature. Further investigations are necessary to evaluate their
physiological meaning.
Influence of Cross-Talk Upon Interhemispheric Differences and
Variability of rCBF
The strong to almost complete interhemispheric correlation of the rCBF parameters for each of the seven pairs of
homologous regions both for the first and the second
measurement (table 3) indicates a pronounced parallelism of
rCBF variations between both hemispheres. This cannot be
accounted for by mere cross-talk from one hemisphere to
the other. Phantom studies performed in our laboratory with
diffuse and point sources indicate that in the worst instance
less than 36% of the count rate measured unilaterally
originates from the hemisphere opposite to the counting
detectors.31 This maximal order of magnitude of cross-talk
was obtained under static conditions. The impact of crosstalk upon the dynamics of clearance curves implying an essentially different situation from static conditions is not
known yet. Studies with synthetic data are underway and
100
STROKE
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will be reported later. In measurements on patients with unilateral brain infarction flow values differing interhemispherically between homologous regions by a factor as
much as 2 to 1 have been observed. The capability of the
system to detect interhemispheric differences between
homologous locations in healthy volunteers as indicated by
the data obtained in this study attenuates also the objection
of cross-talk which, however, may account for some
smoothing of the differences.
The inspection of all the individual sets of clearance
curves of each single measurement reveals unequivocally the
existence of regional interhemispheric differences. The
statistical work-up of the material shows at least a consistent
and significant asymmetry in the inferior frontal region. It
can still be argued that in spite of regional interhemispheric
differences the underlying hemispheric mean level shared by
both hemispheres is secondary to cross-talk. On the other
hand, the phenomenon of cross-talk would not distort interhemispheric equality of flow hypothetically postulated in
healthy subjects. The evidence that cross-talk does not
obscure any interhemispheric asymmetry under rest conditions in normal subjects is given by the inferior frontal
region. It remains to further investigations to design more
sensitive flow parameters and analytical methods less sensitive to cross-talk to reveal the real physiological interhemispheric asymmetries.
Influence of Systemic Arterial CO, Tension Upon rCBF Variability
Carbon dioxide is well recognized to be one of the most
powerful agents to influence CBF. From studies dealing with
cerebrovascular response to induced alterations in arterial
CO 2 tension correction factors have been derived to be
applied to values for blood flow to standardize them for an
arterial Pco 2 of 40 mm Hg.28'32"34 In the assessment of rCBF
such correction factors have logically been used to achieve
comparable data in samples of measurements obtained at
different arterial Pco 2 levels. It has to be noted, however,
that the results of experiments dealing with the evaluation of
CO 2 response, where the artificially manipulated CO 2 tension is considered to be the main variable influencing CBF,
are not necessarily applicable to flow studies where the spontaneous systemic arterial Pco 2 is only one among several
variables determining CBF. Though a Pco 2 correction factor for the standardization of rCBF measured in connection
with artificially altered CO 2 tension is meaningful, its
application as a proportionality constant to standardize
regional flow data under normal conditions is not appropriate. As Purves stated, it cannot be assumed that blood
vessels in different regions of the brain respond to increases
in arterial Pco 2 equally or even in the same direction.35 The
gray matter blood flow in response to the inhalation of carbon dioxide increases more than that of white matter,35 the
proportion of gray to white matter being furthermore
different from region to region.12- " Regional cerebral flow
expressed as percentage of the hemispheric mean does not
change its hemispheric pattern of distribution by the
application of a proportionality coefficient related to the
Pco 2 level.
The finding of a moderate correlation between Pco 2 and
ISI from subject to subject at rest and the lack of correlation
between the two variables for changes in consecutive
VOL 8, No
1, JANUARY-FEBRUARY
1977
measurements in the same subject emphasize in our opinion
the postulated presence of additional determinants of CBF
operating at the same time but counteracting one another in
different subjects on different occasions under different circumstances. At least the Pco 2 does not appear to be the
main determinant of the biological variability of rCBF under rest conditions.
Error of Measurement and Biological Variation of rCBF
In the dilemma of error of measurement and biological
variation the synthetic clearance curve analysis reported by
Obrist and colleagues2 offers a valuable tool to an estimation
of the relative contribution of errors of measurement. Obrist
and coworkers found for the clearance constant k, of the
first compartment a standard deviation of the difference
between pairs of synthetic curves of 4% of the mean values,
taking into account that the variances are additive. They
argued that most of the k[ variation between bilaterally
symmetrical probes in normal subjects, being only slightly
greater than 4%, can therefore be accounted for by counting
statistics. They noted, however, that in the case of interregional and day-to-day differences the standard deviations
of k, were larger, i.e., approximately 7% of the mean values.
Risberg and Ingvar23 tested the reproducibility of their multibolus technique during steady-state conditions, where
133
xenon solution was injected into the internal carotid artery
at one-minute intervals: the standard error of measurement
was found to be 4%.
In comparison the coefficients of variation of the HPFD
values of ISI and f, respectively derived from the 35 pairs of
measurements in the present study (tables 1, 2 and 5) approximate in reasonable order of magnitude the error of
measurement of about 4% quoted from the literature. Those
for ISI are only slightly larger, those for f! are about 1 '/2-fold
to two-fold greater. It is recognized, however, that the error
of measurement is operating on the original data, i.e., on
both the HPFD and the hemispheric mean values.
Subtracting the estimate of the error of measurement
quoted above from the overall variability of rCBF there still
remains a large amount of variation being mainly accounted
for by the fluctuations of the hemispheric mean level shared
by both hemispheres. The data suggest that this is
predominantly of physiological origin. It appears from the
analysis of reproducibility that the hemispheric mean flow
behaves like a separate physiological variable exhibiting its
own peculiar intrinsic characteristic, whereas the
hemispheric pattern of flow distribution seems to be determined by regionally dependent variables but not by the
hemispheric mean level of flow. The findings suggest that
there are two determinants of CBF which operate independently: a determinant of the hemispheric mean level,
probably a single determinant for both hemispheres, common to all regions, and a set of determinants for each region,
unique to the region.
The objection may be raised, however, that the lower
coefficients of variation of the HPFD values than of the
absolute regional values do not imply two separate determinants of these values, but are only an arithmetical artifact: dividing sets of numbers by their means must inevitably result in lower coefficients of variation of the
calculated ratios, in this case the HPFD. That this is not
m
X E N O N INHALATION METHOD/Blauenstein et al.
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necessarily so can be seen in the general formula for the
coefficient of variation of the ratio of two variables given
below. The comparison of the variation of the means of the
regions, the hemispheric means, and the HPFD values involves statistically both the variances and the covariances. If
a given variable behaves independently from region to
region, then each member of the sum of the covariances
equals zero. This condition apparently does not hold true for
our sample; e.g., since the variances of a given parameter for
each of the seven regions of a hemisphere are roughly similar
in size, the variance of the hemispheric mean should be oneseventh of a single regional variance. In our sample,
however, the variance of the hemispheric mean is distinctly
larger. This fact simply means that the sum of the 21
covariances for seven regions of a hemisphere is a positive
term. Since the correlation coefficient between two
variables, i.e., regions in our example, is directly proportional to their covariance, it can be concluded that one or
more positive interregional correlations are dominating in
the final term for the sum of the covariances. A similar
feature is shared by homologous regions of the two
hemispheres and by the hemispheric means respectively. In
our sample the regions obviously do not behave independently. The correlation between two regions may be
due, wholly or in part, to their common relation to one or
more other factors. In the case of the HPFD values the sum
of the regional variances equals the sum of their covariances
since by definition the hemispheric mean of the regional
HPFD values equals invariably 100%. The larger the
regional HPFD variances are, the larger the sum of their
covariances has to be regardless of the behavior of the
hemispheric mean level of the original data, and vice versa.
Though two or more regions may reveal positive correlations for their HPFD values, they have then to correlate
negatively to one or more of the remaining regions resulting
in a negative term for the sum of their covariances which is
in turn equal in size to the sum of the regional variances. If
one or more regional HPFD variances were equal to zero,
then the corresponding regional variances of the original
data would be a mere function of the fluctuations of their
hemispheric mean.
Statistically the coefficient of variation of a ratio of random variables (in our example: a region as a percentage of
its hemispheric mean) may be larger or smaller than that of
either the numerator (region X 100) or the denominator
(hemispheric mean) of the ratio depending upon their correlation.
The general formula for the coefficient of variation of the
. X,
ratio —
(= Xi/j) of two random variables X, and Xj is:
Q 2 - 2r,j • C,
where ClUi) = coefficient of variation of the ratio of X, and
Xjj C|,Cj = coefficient of variation of the variable X, and Xj
respectively, and r,j = correlation coefficient between X, and
Xj.
In our example Xui stands for the HPFD values of region
i, Xi for the original data of region i, and Xj for the
hemispheric means. Obviously if rfJ is zero then CM/J) must
101
be larger — not smaller — than either C, or Cj. Only if there
is a high correlation between Xi and Xj will the coefficient of
variation of their ratio be smaller than that of either of the
original numbers, as in our case of the regional ISI, or of
their hemispheric mean values. The correlation between the
regional ISI and their hemispheric mean determines the
range within which the regional patterns vary.
For ISI, f|, and FF, in our sample the coefficient of variation of the ratio region X 100/hemispheric mean (HPFD
values) is distinctly, i.e., 50% to 70%, smaller than that of the
denominator (hemispheric mean), whereas for w, it is only
about 25% smaller. For w, the regional independent
variability competes with that of the hemispheric mean.
This discussion concerns only the validity of the statistical
approach chosen for the data analysis. There still remains
the possibility that the sampling features of the data are not
valid, e.g., that the two-compartmental model (f,, w,, FF,)
or the derivation of the ISI is not appropriate to describe
cerebrovascular physiology. In our study it is assumed that
the definition of the flow parameters applied is useful. It is,
however, our opinion that this point deserves further
detailed analysis to evaluate the most beneficial interpretation of clearance curves.
The observation that the coefficients of variation of the
regional ISIs and their hemispheric means under rest conditions are more than twice as great as the coefficients of
variation of the regional pattern (HPFD) values reveals a
striking analogy to the model originally proposed by
Risberg and Ingvar4 in the context of brain activation
studies: The cortical flow changes which occur during mental activity appear to consist of two components: (1) a nonspecific component determined by the general level of
arousal during the tests, and probably mediated by the
reticular activating system, and (2) a specific component giving rise to a more circumscribed cortical activation due to
selective attention. The regions activated depend upon the
type of mentation going on. The same model appears to be
applicable also for rest measurements as in our sample.
The hypothesis of two determinants of CBF operating at
different sites, i.e., hemispherically and regionally respectively, offers some explanation for the phenomenon of
bilateral depression of hemispheric blood flow in patients
with unilateral cerebral infarction36"10 as it does for the
bilateral exaltation of CBF occurring with brain activation.4' 6 Unilateral infarction is attended by bilaterally
abnormal low hemispheric mean levels of CBF and a distinct
interhemispheric asymmetry of regional CBF with lower
values in the symptomatic hemisphere. Further preliminary
results of repeated measurements in healthy volunteers during mental or physical activity and of about 700 serial
measurements in 170 patients with stroke support this view.
They will be reported later.
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133Xenon inhalation method. Analysis of reproducibility: some of its physiological
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U W Blauenstein, J H Halsey, Jr, E M Wilson, E L Wills and J Risberg
Stroke. 1977;8:92-102
doi: 10.1161/01.STR.8.1.92
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