The Comparative Anal/sis of Isotope
Clearance Curves in Normal and
Ischemic Brain
BY J. ESMOND REES, M.R.C.P., J. W. D. BULL, F.R.C.P.,
G. H. DU BOULAY, F.F.R., JOHN MARSHALL, F.R.C.P., R. W. ROSS RUSSELL, F.R.C.P.,
AND LINDSAY SYMON, F.R.C.S.
Abstract:
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The
Comparative
Analysis of
Isotope
Clearance
Curves in
Normal and
Ischemic Brain
• The regional cerebral blood flow has been measured by intracarotid
183
Xenon in ten normal subjects, ten with miscellaneous cerebral ischemic
lesions, eight with transient ischemic attacks and seven with completed strokes.
The data have been examined by the stochastic and two-compartmental
methods of analysis and by reference to the slope of the initial two minutes of
the clearance curves. In normal unanesthetized normocapnic subjects the
correlation between the results obtained by each of these methods is high. In
ischemic lesions the correlation is less god. All three methods, however, are
liable to miss, or to misrepresent the significance of, disturbances which can be
demonstrated when the proportion and rate of perfusion of gray and white
matter are separately estimated.
ADDITIONAL KEY WORDS
transient ischemic attacks
• An essential characteristic of a stroke is the
focal nature of the underlying ischemia. For
this reason, methods which measure blood flow
through the entire cerebral hemisphere, though
contributing much to our knowledge of the
general hemodynamic changes encountered in
vascular disease, do not permit the study of
focal disturbances within the hemisphere. The
introduction of methods of measuring regional
flow in animals by the use of "^Krypton 1 ' 2 and
later in man by means of intracarotid 133 Xenon
and multiple external detectors8 and the ability
to distinguish between flow through gray and
white matter by two-compartmental analysis of
the isotope clearance curves4 were, therefore,
significant advances in the study of the
hemodynamic changes which
accompany
strokes.
The isotope clearance curves obtained
From the Institute of Neurology, National Hospitals
for Nervous Diseases, Queen Square, London, WC1N
3BG, England.
This work was supported by a grant from the
National Fund for Research into Crippling Diseases.
444
cerebral blood flow
strokes
when the brain is monitored by highly
collimated external detectors after the injection
of m X e n o n into the internal carotid artery can
be analyzed in a number of ways. If the aim of
studying focal disturbances of flow in patients
with strokes is to be attained, it is essential that
the indications for and limitations of the
various methods of curve analysis should be
clearly understood. It was to facilitate this
understanding that the present study was
undertaken.
The methods of curve analysis employed
in the study were: (1) The stochastic method
or "height-over-area" ( H / A ) method as it is
frequently called. (2) Two-compartmental
analysis to give flow through gray (Fg) and
flow through white (Fw) matter and the
proportion of gray and white matter beneath a
detector (Wg:Ww). This makes it possible to
estimate a mean flow which takes into account
the proportion of gray and white matter—
weighted mean flow ( F ) . (3) Flow initial
(F[init]) determined by the slope of the first
two minutes of the clearance curve.
Stroke, Vol. 2, Sepf«mb«r-Ocfober 1971
ANALYSIS OF ISOTOPE CLEARANCE CURVES
The Stochastic Method
The mathematical derivation of the stochastic
method has been previously elucidated.5"7 The
equation
CBF = -r— x X brain,
where
H
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is the height of the clearance curve
and A the area underlying it, involves the use
of a X value for whole brain. The solubility
coefficient for 1S8Xenon in brain has been
established8"10; at a hemoglobin concentration
of 15 gm/100 ml blood it is 1.5 in gray matter
and 0.8 in white matter. A homogenate of
whole brain gave a solubility coefficient of
1.08, indicating the proportion of gray to white
matter in whole brain to be 60:40. The
application of the stochastic method to the
calculation of regional cerebral blood flow
(rCBF) assumes that this gray:white ratio
holds for all areas. Anatomical dissection of
blocks of cerebral tissue as would be monitored
by well-collimated external detectors has
shown that the proportion of gray matter varies
from 7 8 % in the anterior temporal region to
34% in the posterior frontal region.11 The
application of the stochastic method to rCBF
calculation, therefore, involves a considerable
and perhaps generally unjustifiable assumption.
Two-Compartmental Analysis
Calculation of F giving due weight to the
proportion of gray and white matter in the
region in question can be achieved by twocompartmental analysis of the clearance
curves. This involves the assumption that the
curves can be satisfactorily resolved into two
exponentials, one representing flow through
fast-clearing tissue, believed to be gray matter
(Fg), and the other through slow-clearing
tissue, believed to be white matter ( F w ) . 1 2 3 8
The limitations of the analysis of exponential
curves representing biological data have been
studied.14 It is clear that rCBF clearance curves
represent a large number of transit times, but
that these can be satisfactorily resolved into
two exponentials in the vast majority of
cases.3' •*• 15~17 Weighted F, therefore, might
seem to offer a more accurate measure of the
rCBF than can be achieved by the stochastic
method. It is important to bear in mind,
however, that as Fg is about 80 ml/100
gm/min and Fw about 20 ml/lOOgm/min, F
is much more influenced by change in Fg than
Stroke, Vol. 2, September-October J977
in Fw and that an appreciable change in the
latter might well be concealed.
Flow Initial
The third method of curve analysis (F[init])
has been developed largely in response to the
need for the rapid estimation of rCBF during
functional studies.18 Flow is determined from
the slope of the initial two minutes of the
clearance curve. The equation is
D
F(initial) = — x X gray X 2.3 X 100
where D is the decade fall of the logarithmic
curve during the first two minutes of clearance.
The use of X gray is based on the assumption
that the early part of the curve is dominated by
clearance of gray matter. Again it takes no
account of the varying proportions of gray
matter beneath detectors overlying different
regions of the brain.
Although more than two minutes has to
be allowed for the clearance of the isotope
from the brain before a further injection can be
given, the F(init) has the advantage that it
permits the measurement of the rCBF during
hyperventilation or the inhalation of CO 2 .
F(init) has been shown to correlate poorly
with Fg, but highly (r = 0.87) with F. 1 1
Thus, each of these three methods of
curve analysis has its indications and limitations. The purpose of the present study was to
define these more closely by applying all three
to data derived from "normal" and ischemic
brain and to compare the results.
Methods
The data subjected to analysis were obtained from
ten "normal" subjects and 25 patients with focal
ischemic lesions. The "normal" group comprised
ten patients suspected of having a cerebral lesion
requiring angiography but found after full
investigation to be normal; they formed the basis
of a previous report.11 The ischemic group
comprised ten patients with miscellaneous ischemic cerebral lesions, eight patients with transient
ischemic attacks (TIAs) (focal neurological
deficits lasting less than 24 hours) and seven
patients with completed strokes (focal neurological deficits lasting more than 24 hours) believed
on clinical and angiographical grounds to be due
to infarction. All were examined immediately
prior to angiography.
In these patients, 5 to 8 mCi of 1S3Xenon
were injected by a Cordis injector triggered by the
445
REES, BULL, DU BOULAY, MARSHALL, RUSSELL, SYMON
5
6
7
IO
8
11
12
approximation this was first compared with F.
The results for 14 of the 16 detectors labeled
as in figure 1 are given in table 1. Detectors 1
and 14 were excluded, the former because in a
number of cases it was not adjacent to the skull
and the latter because it was moved from a
position immediately posterior to detector 16
to its position on figure 1 during the series. It
can be seen that a high degree of correlation,
ranging from 0.99 in areas 10 and 11 to 0.85
in area 12, existed between the two methods of
analysis for all regions. Ranking the areas
according to their correlation coefficients did
not reveal any relationship to the closeness
with which the Wg:Ww proportion in the area
approached the 60:40 assumed in the H/A
method. H/A15 flow in every region was lower
than the corresponding value for F so that the
mean flow for the entire hemisphere by H/A15
was 49.4 ml/100 gm/min, which is less than
the 53.7 for F but the difference is not
significant.
As many authors employing the H/A
method have used ten-minute clearance curves
despite the fact that these have been shown to
overestimate consistently the CBF,19 comparison was next made between F and H/A10
(table 1). This was again high in all areas,
ranging from 0.99 in area 11 to 0.84 in area
12. The mean flow for the hemisphere (52.7
ml/100 gm/min) was somewhat higher by
9
13
14
FIGURE 1
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Enumeration of detector sites.
R wave of the electrocardiogram via a catheter
introduced into the internal carotid artery to the
level of the first cervical vertebra, isotope
clearance being monitored by 16 external detectors placed against the lateral side of the skull.
Their position was recorded radiographically and
related to the clinoparietal line on the skull
radiograph so that topographical localization
could be achieved. Full details of the method are
given in a previous report.11
Results
Theoretically, the H/A method requires that
the clearance curve be recorded to infinity, but
as a 15-minute curve gives a reasonable
TABLE 1
Correlation* Between F and H/ A*,
Ar m a
2
3
4
5
6
7
8
9
10
11
12
13
15
16
Mean
446
%
Wg
65
50
62
52
40
46
42
63
55
74
53
52
74
65
•?
H/A u
H/Alt and H'mit) in Ten "Normal"
r
H/A*
Cases
r
F(lnlt)
r
H/A,i and Fflnlt)
0.94
0.77
0.96
0.96
0.89
0.93
0.88
0.84
0.97
0.93
0.92
0.87
0.90
0.87
62.5
55.1
51.4
56.7
52.8
45.4
48.7
53.6
50.9
62.5
60.0
49.9
53.0
49.5
56.5
49.9
47.0
53.8
46.2
38.5
41.9
50.7
45.5
60.8
56.4
45.1
51.2
46.2
0.93
0.97
0.96
0.96
0.97
0.97
.9
0.98
0.99
0.99
0.85
0.95
0.96
0.94
60.1
52.6
50.6
57.5
49.6
41.3
44.7
54 3
49.1
63.1
59.6
48.3
54.3
49.2
0.95
0.97
0.98
0.96
0.95
0.93
0.95
0.98
0.98
0.99
0.84
0.95
0.95
0.94
76.3
64.5
61.2
71.6
68.5
53.5
62.4
65.3
66.1
68.2
78.2
63.9
60.9
55.0
0.85
0.83
0.96
0.97
0.87
0.95
0.81
0.96
0.96
0.95
0.87
0.90
0.95
0.90
53.7
49.4
—
527
—
65.0
—
Strok; Vol. 2, SepfemW-Ocfob.r J977
ANALYSIS OF ISOTOPE CLEARANCE CURVES
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FIGURE 2
Pattern of rCBF as revealed by: (a) Fg, (b) Fw, (c) ~F, (d)
H/A10 than by H/A15, so that it approximated closely to the value obtained by F. It
seems, therefore, that in normal brain the use
of a A. of 1.08 in the calculation of rCBF on the
assumption that the Wg:Ww proportion is
60:40 in all areas does not introduce an
appreciable error.
CORRELATION BETWEEN F AND F(INIT)
Correlations between F and F(init) were
calculated for the 14 areas as before (table 1)
and ranged from 0.97 in area 5 to 0.81 in area
8, which is only minimally less good than the
correlation between F and H/A15. The flow as
calculated by F(init) was higher in each region
than the value obtained by F, giving a mean
flow for the whole hemisphere of 65.0 as
against 53.7, but again the difference does not
reach the level of significance.
Finally, correlations between H/A15 and
F(init) were calculated and ranged from 0.97
in area 10 to 0.77 in area 3, which is
Strok; Vol. 2, Sep»«mber-Octob»r 1971
H/A15.
marginally less close than the correlations
between F and H/A15 and F and F(init).
REGIONAL PATTERNS OF BLOOD FLOW
It has been shown previously that blood flow
through the hemisphere is not homogeneous
but follows a consistent regional pattern.11 Fg
is significantly higher at the 0.1% level than
mean flow for the hemisphere in areas 2 and 6
(fig. 2) and significantly lower at the same
level of significance in areas 15 and 16. Fw is
significantly higher in areas 11 and 12 and
lower in areas 5 and 10 (p < 0.001). When
these patterns were combined in a weighted
mean flow, significantly high flow at the 0.1%
level in areas 2, 11 and 12 and significantly
low flow in area 16 remained; the high Fg in
area 6, the low Fg in area 15 and the low Fw
in areas 5 and 10 were lost and significantly
low flow in areas 7 and 8 not present in either
Fg or Fw emerged. Similar patterns were also
found for F(init). 11
447
REES, BULL, DU BOULAY, MARSHALL, RUSSELL, SYMON
TABLE 2
Correlations Between F, H/Au and F(init) in Ten Cases with Ischemic Lesions
Arma
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1
2
3
4
5
6
7
8
9
10
11
12
13
15
16
%
_
Wg
T
40
55
65
52
59
63
52
50
74
74
62
53
65
46
42
'
H/A,,
36.0
36.5
33.8
31.6
26.2
31.4
30.3
27.2
34.9
30.3
36.4
29.7
25.5
27.9
25.5
36.0
36.5
35.1
31.5
28.8
29.9
27.1
28.0
32.8
29.3
36.9
33.3
26.0
24.8
24.0
r
F(lnlt)
r
H/Au anri F(Intt)
0.94
0.96
0.89
0.86
0.89
0.98
077
0.67
0.93
0.98
0.87
0.85
0.95
0.89
0.83
38.8
41.4
39.6
37.0
33.4
38.5
31.7
32.1
34.1
38.0
42.0
36.5
30.2
28.2
27.9
0.77
0.92
0.56
0.57
0.55
0.95
075
0.63
075
0.87
0.80
0.50
0.83
0.84
077
0.90
0.97
0.67
0.87
0.89
0.96
0.98
0.82
0.92
0.89
0.94
071
0.84
0.82
0.97
TABLE 3
Areas Showing Abnormal rCBF by Different Methods of Curve Analysis in Patients with
TIAs
Cat* no.
1
2
3
4
5
6
7
8
Total
*
I
i
I
1
1
I
1
1
Fw
Wg
7
—
7
7
—
—
15
—
—
1,15
—
Fg
F(lntt)
H/A u
—
12
3
—
—
3
—
—
3
—
—
3
—
10
16
—
11
—
—
—
10
1,5
12
3
1
6
3
—
10
—
—
—
—
—
—
11
2
2
significant increase, | significant decrease at 1 in 1,000 level.
The regional pattern of flow as calculated
by H/A15 was determined in the present
study. There was high flow (p < 0.001) in
areas 2, 11 and 12 and lowflowin areas 7 and
8. Comparison with F shows the same regional
448
pattern of distribution except that the low flow
in area 16 was lost. The same result was
obtained with H/A 10.
In general, therefore, in "normal" subjects
who were normocapnic H/A15 or H/A10
Strokm, Vol. 2, Stptamber-Octobmr 1971
ANALYSIS OF ISOTOPE CLEARANCE CURVES
provided a satisfactory method of determining
rCBF which compared well with the more
complicated estimation of weighted mean flow.
The varying proportions of gray and white
matter present in different regions of the
hemisphere did not appreciably influence the
accuracy of the results.
CORRELATION BETWEEN H/A15 and 7
IN ABNORMAL CASES
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Attention was next turned to the problem of
whether the assumption of a gray: white
proportion of 60:40 adversely affected the
analysis of data from patients with focal
cerebral ischemia. Data from ten patients with
miscellaneous ischemic cerebral lesions in
whom two-compartmental analysis had shown
disturbance of the normal Wg:Ww ratio due to
infarction of gray or white matter were
examined. Correlations between rCBF for 15
areas (detector 1 was included in this series)
as determined by H/A15 and F were calculated, the results being given in table 2. They
ranged from 0.98 in areas 6 and 10 to 0.67 in
area 8. Correlation between F and F(init)
ranged from 0.95 in area 6 to 0.5 in area 12,
which is much less satisfactory. This is
probably due to the use of the fixed X gray in
the calculation of F(init), clearly inappropriate
if any large infarct of gray matter is present.
COMPARISON OF FG, FW AND WG WITH
H/A15, F and F(INIT)
In order to examine further the relationship
between the different methods of clearance
curve analysis, comparison of these methods
was made in individual cases in a series of
eight patients who had experienced TIAs.
Abnormalities of flow and of gray:white ratio
may persist as long as 90 days after a TIA. 20
The data from eight patients of this type were
analyzed by the various methods (table 3 ) . All
patients had shown some abnormality on twocompartmental analysis, three having disturbance of Fg, one of Fw, and six of Wg. F
revealed only three of these abnormalities,
F(init) two when Fg was predominantly
involved and H/A15 two.
The reasons for these discrepancies can
best be illustrated by reference to individual
cases. Case 5 showed a low Fg and an
increased Wg in area 3, indicating nonperfu-
TABLE 4
Areas Showing Distvrbance of rCBF by Different Methods of Curve Analysis in Patients with Completed Strokes
Cote no.
l
2
3
4
5
6
7
Total
I
!
1
i
1
1
1
'g
Fw
5
17
12
F
«lnh)
H/An
2,6,10
8,12,13
13
5
8,13
13
11
12
12
12
3,10,14
16
7
10
9
16
4
7
=
—
3
10,11
4,9,15
67,10,11,12
12
—
—
—
10
5
—
—
—
4
3
10
Prerolandic
hypovascular
area
—
Normal
7
7
11
5
6
—
7
MCO prerolandic
branch
11
7
—
MCO parietal
branch
MCO prerolandic
branch
—
11
MCO* distal to
striate vessels
—
7
10
Angiogram
4
Normal
*MCO = Middle cerebral occlusion.
| significant increase
at 1 in 1,000 level.
4. significant decrease
Stroke, Vol. 2, S»pf«mbor-Oc(ofaer 197/
449
REES, BULL, DU BOULAY, MARSHALL, RUSSELL, SYMON
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sion predominantly of white matter. F(init)
failed to pick this up because, though Fg was
low, this was obscured by the increase in the
proportion of Wg.
In case 3 there was a significant increase
in Fw in areas 1 and 15, neither of which was
reflected in F or H/A15 because Fw contributes so small a proportion to the flow in an
area. A reduced Fw in area 12, significant only
at the 1 in 100 level, hence not appearing in
the table, appeared in F as significant at the 1
in 1,000 level, as the proportion of white
matter in that area is higher than elsewhere;
the same feature appeared in case 8.
A series of seven patients with completed
strokes was also examined in the same way
(table 4). The persisting clinical deficit due to
more severe ischemia was reflected in the fact
that of the seven cases, five showed abnormalities in F(init), six in H/A15, and four in F.
Again F(init) reflects most closely changes in
Fg, but may on occasion be misleading as in
case 7. Here there was no significant alteration
in Fg in any area, but F(init) showed an
increase in area 7 due to increased Wg from
loss of white matter.
Discussion
Each method of analyzing cerebral isotope
clearance curves involves assumptions due to
the facts that the proportion of gray and white
matter is different in different regions of the
brain and that these tissues have different
solubility coefficients for 138Xenon and different rates of flow. Methods of analysis which
assume only one compartment as do H/A and
F(init) and choose an average k or the A of
one compartment must introduce a degree of
error. The present study has shown that in
normal brain the results given by these
methods do not differ significantly from those
given by F. H/A15 gives a slightly, but not
significantly, lower estimate of flow than does
F; H/A10 is virtually the same as F. F(init)
on the other hand gives a higher estimate than
does F, but again this does not reach the level
of significance. In pathological circumstances
the accord of the various methods of curve
analysis was not so high, though here again the
lowest correlation coefficient for a region was
0.5. It seems, therefore, that if two-compartmental analysis were being carried out merely
to provide a weighted mean flow, it would not
450
be worth the extra work involved. But if
ischemic lesions are to be studied, twocompartmental analysis is essential, not to
provide a weighted mean flow, but to reveal the
flow disturbances occurring separately in gray
and white matter and the altered proportions of
these tissues in an area due to nonperfusion.
The present study has shown that methods of curve analysis which do not distinguish
between Fg and Fw frequently miss significant
areas of disturbance of flow; more serious is
the fact that they may on occasion give
misleading information, as when a loss of white
matter is represented as an increase in F
because of the greater proportion of tissue
clearing at the fast rate. F(init) remains
valuable as a means of assessing change in flow
following the alteration of Pac0o or blood
pressure, but does not provide an accurate
assessment of the nature of the flow disturbance. The stochastic method, despite its
sound mathematical basis, has even less to
recommend its use in the assessment of
cerebral ischemia. Two-compartmental analysis detects abnormalities in cases of cerebral
ischemia more readily than do the other
methods of analysis. The pathological basis of
these abnormalities—vascular or parenchymatous damage, structural or functional change—
has yet to be determined by extensive
clinicopathological studies. Preliminary work
suggests that the disturbances revealed by twocompartmental analysis are meaningful in
pathological terms.21 In light of the experience
gained by this study, two-compartmental
analysis of clearance curves is clearly essential
for a proper understanding of the pathophysiology of ischemic cerebral disease.
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The Comparative Analysis of Isotope Clearance Curves in Normal and Ischemic Brain
J. ESMOND REES, J. W. D. BULL, G. H. DU BOULAY, JOHN MARSHALL, R. W. ROSS
RUSSELL and LINDSAY SYMON
Stroke. 1971;2:444-451
doi: 10.1161/01.STR.2.5.444
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