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Evaluation of Portal Circulation in Hepatic Cirrhosis
Vol. 57, No.5
GASTROENTEROLOGY
Printed in U.S.A .
Copyright C 1969 by The Williams & Wilkins Co.
EVALUATION OF PORTAL CffiCULATION IN HEPATIC CIRRHOSIS A new method using xenon 133 DONALD 0 . CASTELL, M.D., NORMAN D . GRACE, M.D., MARTIN THoMAS C. CHALMERS, M .D., AND EDWARD W . MooRE, M.D.
H. WENNAR, M.D.,
Metabolic and Gastrointestinal Research Unit of the Medical Services, Lemuel Shattuck Hospital, Department of Public Health, Commonwealth of Massachusetts, and the Department of Medicine and Physiology, Tufts University Medical School, Boston, Massachusetts
A method for estimating portal circulation using xenon 13 3 given rectally with monitoring of radioactivity over the precordium is presented. This test is easily performed and provides a reproducible objective end point. The portal circulation time can be estimated "visually" from the initial tracing, or can be "calculated" from a semilogarithmic plot of precordial radioactivity against time. The slope of appearance of precordial radioactivity is also obtained by the latter method . Xenon 133 portal circulation time studies were performed in 39 cirrhotic patients. Values obtained in 11 patients with portacaval shunts were significantly different from values obtained in 28 nonshunted cirrhotics by each of three methods of evaluation. The possibility that this test can identify patients having an occluded portacaval shunt is suggested by the results obtained in 1 patient showing a marked difference before and after a shunt and the discovery of a thrombosed shunt in another patient initially studied because of a prolonged xenon 133 circulation time. brachial artery after giving Na 24 rectally. 4 Ether5 and radioactive krypton 6 ' 7 have been given intrasplenically and their appearance in expired air has been used as a measurement of portal circulation time. Similarly, radioactive iodine has been given by splenic injection and the portal circulation time estimated from its appearance over the precordium. 8 Certain difficulties are encountered with each of these techniques. With ether, there is lack of an objective end point. Variable rectal absorption of Na 2 4 may occur. Intrasplenic injection constitutes a potential risk to the patient. Xenon 133 is a highly diffusible ga~ which is readily measured, biologically and chemically inert, and almost completely cleared by the lungs in a singlE transit. 9 It has therefore been widely used in studies of blood flow in various or-
Several techniques have been used for estimation of "portal circulation time," including the appearance of rectally administered ether in expired air/ -3 and the appearance of radioactivity over the Received December 26, 1968. Accepted June 23, 1969. A preliminary report of this work was presented at the meeting of the American Association for the Study of Liver Diseases in November 1968, in Chicago. Address requests for reprints to: Dr. Norman D. Grace, Lemuel Shattuck Hospital, 170 Morton Street, Boston, Massachusetts 02130. This investigation was supported by Grants AM07417, AM-05424, and AM-11243 from the National Institute of Arthritis and Metabolic Diseases, United States Public Health Service. Dr. Moore was the recipient of Research Career Development Award 6-K3-GM-11,386,01A1 from the National Institute of General Medical Sciences, United States Public Health Service. 533
534
Vol . 57, No. 5
CASTELL ET AL.
T- th . pae presen t stu d"1es m gans. 1 0 ~ 1 6 m tients with cirrhosis, it will be shown that portal circulation may be studied by intrarectal administration of this isotope with measurement of radioactivity counting over the precordium. The end point, or " portal circulation time," is readily and objectively identified. This may be of clinical value in determining the patency of portacaval shunts.
Methods A total of 53 studies were made in 39 hospitalized patients with cirrhosis. These included 20 males and 19 females ranging in age from 26 to 65 years (mean, 50.6 years) . Diagnoses were made by biopsy in 33 patients and by clinical and laboratory findings in the remainder. The biopsy was not always done at the time of the study, but in some of the severe cirrhotics it was done from an earlier admission. One patient studied both before and after a portacaval shunt is included in two groups of subjects. The patients were divided into three groups: (1) 12 patients with "mild" cirrhosis, (2) 16 patients with " severe" cirrhosis, and (3) 12 patients with surgical portacaval shunts. Prior to testing, the nonshunted patients were independently classified by two physicians as having clinicaliy mild or severe cirrhosis on the basis of the following five criteria : splenomegaly, ascites, visible abdominal collaterals and prothrombin tim~ encephalopathy, greater than 3 sec above control levels. 17 A patient was graded with a clinical score of from 0 to 5, achieved by adding 1/2 point for every positive finding noted by each of the two observers (table 1). A patient was classified as having severe cirrhosis if two findings or more were present. The xenon 133 test was performed as follows. Following defecation (without enema) the patient was placed in the right lateral decubitus position and a polyethylene tube (9-mm outer diameter) was inserted approximately 12 em into the rectum. A shielded l-inch Nal scintillation probe was then placed about 6 inches anterior to the precordium. Xenon 133 (500 !!C) in 3 ml of saline was given intrarectally through polyethylene tubing (2 mm outer diameter) contained within the rectal tube. To minimize contamination of the room, the patient's expired air was collected in a large disposable rubber bag, and the room was well ventilated. The appearance of the
isotope at the heart was measured with a Picker no. 600-046 rate meter and a permanent record obtained with a Picker no. 600-091 chart recorder. Maximum counting ( ')', 81 kev) was achieved with a 640-kev setting and window setting between 70 and 90 kev, using a 3-sec time constant. Two methods were used to estimate portal circulation time: " visual" from the observed tracing, representing the point at which a steady rise in precordial radioactivity occurred, and "calculated" by techniques outlined in the "Appendix." Visual estimations were determined blindly by two different observers (D . 0 . C. and N. D. G.); and the resulting mean value was then compared with the corresponding calculated values obtained by a third observer (E. W. M .). Calculated circulation time was obtained from the semilogarithmic plot of precordial radioactivity (y axis) against time (x axis) and represented the point of intersection of an early stable phase (i .e. , presumably representing intraluminal colonic radioactivity) and the exponential curve which followed (i.e., the precordial blood radioactivity) . The slope (k) of the blood exponential phase was calculated for each study by least squares regression analysis. The presumed physical significance of the exponential slope is given in the "Appendix."
Results Sample Tracings Two tracings of precordial radioactivity following rectal instillation of xenon 133 are shown in figure 1. Data at the top of the figure were obtained in a patient with a surgical portacaval shunt; the data below were obtained in a patient with severe cirrhosis. Note the slight rise in precordial radioactivity immediately following intrarectal administration of the isotope. This was observed in virtually all patients and presumably resulted from diffusion of gas into the splenic flexure or transverse colon. Following this plateau of radioactivity, a sharp curvilinear rise of radioactivity was observed ("precordial exponential phase") ; this represented the visual end point for estimated portal circulation time. Note that the circulation time was shorter in the shunted patient (14 sec) than in the patient with severe cirrhosis (43 sec) . fu addition, the rate of
TABLE
Patient
Total clinical sco rea
M i ld ci rrhosis D. G . F. 0. M.M . J. w. L.M. A. K. R. M. A. H. J. 0 . E. D. J.D . A.M. Mean
1. Cli nical features and xenon 13 3 portal circulation studies
Splenomegaly
Ascites
Abdominal collaterals
Encephalopathy
Abnormal prothrombin Visual CT' time 6
SE
sec
sec
(1.)
0 0 0 }1 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
1 0 0 1 0 0 0 0 0 0 0 0
45 26 33 38 32 38 27 35 43 25 30 26 33.4 2.7
38 .5 28.2 27.5 33.5 22.5 26 .0 24 .0 28 .0 37.5 23 .0 26 .7 25 .5 29 .3 1.7
0.040 0 .096 0.044 0.112 0.050 0.031 0.075 0 .071 0.036 0.030 0.065 0.060 0.058 0.008
4 3 3 2}1 3 2 2}1 2 2}1 3}1 3 2 4 3 3 3
1 1 }1 1 1 1 }1 1 }1
1
0 0 }1 }1 1 1
1 % 1 0 1 1 1 1 }1 1 1 1 1 1
1 0 }1 0 0 0 0 0 1 }1 }1 1 }1 }1 0 0
0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0
1 1 1 1 1 1 1 0 0 1 1 0 1 1 1 1
56 86 52 44 47 33 59 52 35 44 53 65 48 35 43 40 49.5 3.2
55.0 71.0 36.0 40 .0 34 .0 29.5 54.0 33.5 25.5 46.3 55 .0 45.5 25 .0 24.0 30 .0 32.5 39.9 3.4
0.027 0.032 0.029 0.029 0.035 0.032 0.009 0.022 0.025 0 .019 0.011 0.018 0.098 0.146 0.079 0.071 0.043 0.009
2 1}1 0 2 1 2 2}1 1 1 0 2
0 }1 0 1 0 0 }1 0 0 0 1
}1 0 0 0 0 0 0 0 0 0 0
}1 0 0 0 0 0 0 0 0 0 0
0 0 0 0 1 1 1 1 0 0 0
1 1 0 1 0 1 1 0 1 0 1
14 34 23 32 34 16 18 27 26 36 24 25.8 2.1
9.5 28 .0 28.5 22 .5 40.0 16.0 18.2 15.5 23.0 31.0 24.8 23.4 2.5
0.125 0.070 0.050 0.065 0.048 0.131 0. 110 0.092 0.098 0.118 0.060 0.094 0.010
1
1
SE
Portacaval shunt M . C. P.R. K. R. K. s. R. R. W.B. M.W. B. C. M.L . R.E. B. C. Mean
Slope
1 0 0 1}1 0 0 0 0 0 0 0 0
SE
Severe cirrhos is A.M. M. R. G . S. K. s. R. B. V. R. J. G. B . A. R.F . P. 0 . B. M. E. H . N.L . J _K . M.P. E. K. Mean
Calculated CT'
The patient received }1 point for every finding noted to be present by each of two observers. Greater than 3 sec above the control value. ' CT, circulation time. 535
a
b
536
CASTELL ET AL.
rise in radioactivity was more acute in the shunted patient.
Portal Circulation Time Circulation times for each of the three groups of patients obtained by the visual method are shown in figure 2. The 12 patients with mild cirrhosis had a mean circulation time of 33.4 ± 2.7 (SE) sec, whereas the 16 patientS with severe cirrhosis had a mean circulation time of 49.5 ± 3.2 sec. This difference was significant (P < 0.01). Mean circulation time in 11 patients with a surgical portacaval shunt was 25.8 ± 2.1 sec, which was significantly less than that observed in patients with severe cirrhosis (P < 0.001) and those with mild cirrhosis (P < 0.02) . One shunted patient with a markedly prolonged circulation time was not included in the calculation and is presented separately below. Calculated circulation times are also shown in figure 2. Mean values were similar to those obtained visually in each of the three groups. Mean portal circulation time was 29.3 ± 1.7 sec"in the group with mild cirrhosis. For the group with severe cirrhosis, mean circulation time was 39.9 ± 3.4 sec, and for the shunted pa-
Vol . 57, No. 5
tients, the mean value was 23.4 ± 2.5 sec. The difference between the circulation time for the shunted patients and those with severe cirrhosis was significant (P < 0.001) as was the difference between patients with mild and severe cirrhosis (P < 0.01). As shown in figure 3, there was a linear relationship between values obtained by the two techniques (r = +0.86). The fact that calculated values were usually less
33 FIG. 1. Sample tracings of precordial radioactivity following rectal administration of xenon' at the arrow (reading from right to left) . Above, from a patient with a surgical portacaval shunt (circulation time, 14 sec) , and below, from a patient with severe cirrhosis (circulation time, 43 sec).
90
VISUAL
CALCULATED
80 UJ
70
z 0 ;::
60
....~
~ ~
.......
...J
a:
30
0
0..
20
.
~ ...
I
~ ~ 50
:::> <..>
a:40 0
0 0 0
~
~.....
••• •
0 00 0
~
ti1
ffi
0
•o
&
10 OL--T--~-r--
PCS PCS • PC Shunt
537
EVALUATION OF PORTAL CIRCULATION
November 1969
SC
L--r--~~--
MC
SC • Severe Cirrhosis
PCS
sc
MC
MC • Mild Cirrhosis
FIG. 2. Portal circulation times for the three groups of patients obtained by both the calculated method (left) and the visual method (right).
than visually estimated values may reflect difficulties in identifying the early phase of the exponential rise in precordial radioactivity with the visual method. The data in figure 2 are in qualitative agreement with the equations and predictions developed in the theoretical section ("Appendix"). As expected, the shortest circulation times were observed in patients with surgical shunts, whereas the longest circulation times were seen in the patients with severe cirrhosis and presumed increased hepatic resistance. Patients with mild cirrhosis showed intermediate values.
Characteristics of the Precordial Exponential Phase A plot of precordial radioactivity (counts per minute) against time would be expected to yield a straight line on a semilogarithmic plot (equation 4, "Appendix"). This was found to be the case in all studies. The resulting slope (k) presumably represents the ratio: FlowNolume of isotope distribution. Observed values for k for the three groups of patients are shown in figure 4. As predicted from theory, the mean observed slope was greatest in the shunted group, lowest in the group with severe cirrhosis, and intermediate in the group with mild cirrhosis. Mean values for the shunted pa-
tients were significantly different from those obtained in both the severe (P < 0.01) and mild (P < 0.05) cirrhotic group. As shown in figure 4, k values in 4 patients with severe cirrhosis were 3 to 4 times those in the remaining 12 patients and were comparable to those seen in patients with surgical shunts. These same 4 patients also had circulation times shorter than most of the other patients with severe cirrhosis and comparable to those in the shunted group. The findings in these 4 patients, therefore, suggest the possibility of the presence of spontaneous portasystemic shunts in some patients with severe cirrhosis. The relationship between circulation time and slope (k) is given by equation 9, "Appendix." A plot of circulation time 0(71)
"'
60
z 0 ;::
50
/
:::E
0/10.
;=
0/
G--: 0: <.>
.
u~ 0
..."'
/
/ x.
30
/eo
~xj:t(x .,I
20
//
...J
u
/
10
/
...J
•
:X
•
• •• •
r•+0.86 o • PC Shunt X • Mild Cirrhosis
0
0
/ /~1:1
<(
u
0//
X
<(
:::>
/
/
40
<(
...J
-
/
• • Severe
0 0
10
.
Revre11ion
30
20
40
50
60
70
80
90
VISUAL CIRCULATION TIME, (sec.)
FIG. 3. The relation of calculated to visual circulation time for each of the 39 patients.
E3 •!
0.140
Mean 2 S.E.
0.120 0.100 0.080 0.060
~ 0 0
0.040 0.020 0~----------------
PC Shunt
Severe Cirrhosis
Mild Cirrhosis
FIG. 4. Values for the slope (k) of precordial radioactivity with time for the three groups of patients. As predicted, the patients with portacaval shunts have larger values than both groups of nonshunted cirrhotics.
538
CASTELL ET AL.
against k would be expected to give a rectangular hyperbola and plot of the reciprocal of circulation time (1/CT) against k should be linear. This appeared to be the case, since a linear correlation (r +0.612) was observed between 1/CTand k.
Reproducibility Studies Xenon 133 studies were repeated in 9 of the patients after an interval of from 2 to 28 days. As shown in figure 5, there was high correlation between first and second tests for both time and slope. Studies of Special Note Two patients of particular interest were studied. One patient with a surgical portacaval shunt was hospitalized for recurrent gastrointestinal hemorrhage 3 years after surgery. Duplicate xenon 133 portal circulation studies revealed a markedly prolonged circulation time with a very low slope, suggesting thrombosis of the shunt. Splenic pulp pressure was 600 mm H20, and splenoportography revealed large tortuous collateral vessels without visualization of the inferior vena cava. The diagnosis of a thrombosed shunt was confirmed at laparotomy. Esophageal varices were VISUAL
60
~
/
111 TEST C.T. (sec .)
40
'"'·
/ /
/
/
r•+0.78
20 40 60 0 2"4 TEST C.T. (sec . )
20
0
/ .-
/
r•+0.97
0 0.080
/'
//
/ / /
/ /
/ / .
;(•
20
. ....
CALCULATED
.
/
/
40
60
/
/ ./
0.060 /
1'1 TEST
/ /
0.040
. .. ./. /
/
/
/
0 .020 /
/
r•+0 .89
0 0
0 .050 0.10 2"4 TEST k
FIG. 5. Reproducibility of the xenon 133 portal circulation test in 9 patients. The relation between values obtained during initial and repeat testing for both visual and calculated circulation times and slope (k) is shown. The broken lines indicate the 1: 1 regression line.
Vol. 57, No. 5
believed to have been the source of the hemorrhage. Measurement of portal circulation time was made in another patient, both preceding and following an end-to-side portacaval shunt (patient included in both groups above). The calculated circulation time preoperatively was 40 sec with a slope of 0.029. Postoperatively, the calculated circulation time was 22.5 sec with a slope of 0.065. The visual circulation time showed a similar change. There was, thus, approximately a 50% reduction in circulation time with a corresponding increase in the slope of the isotope appearance.
Discussion A number of techniques have been used in the past to estimate portal circulation time. One of the earliest methods involved rectal administration of ether, referred to as "the rectum-to-lung time." Newman and Cohen' showed that the time required to detect the intrarectally administered ether in the patients' expired air was longer in patients with cirrhosis (and probable portal hypertension) than in normal subjects. A similar observation was made by Giges and Teschan, 2 who noted a consistent decrease in the circulation time in cirrhotic patients after a surgical portacaval shunt. Waldstein et al. 3 suggested that this test might be a simple method for determining the patency of a portacaval shunt. Deterling et al. 4 reported the use of Na24 administered rectally as a test of portal circulation time. The end point was the appearance of a sharp rise in radioactivity over a brachial artery. A consistent decrease in the circulation time was observed in 16 cirrhotic patients after portacaval shunt surgery. The appearance time of ether in the expired air has been measured following its injection into the spleen. 5 Prolonged circulation times were found in cirrhotic patients when compared with normal subjects. Mter injection of 113 1 albumin into the spleen, Schwartz and Greenlaw8 found decreased time of appearance of
Novemb er 1969
EVALUATION OF PORTAL CIRCULATION
radioactivity at the precordium in patients having portacaval shunts. The use of radioactive gas (krypton 80 ) to measure portal circulation time in dogs has been reported by Lombardo et al. 6 ' 7 These workers reported a definite decrease in the circulation time of Kr 85 from the spleen to the expired air after performing portacaval shunts. Xenon, a rare gas, is biologically inert and freely diffusible in body tissues. After entry into the blood stream it is rapidly eliminated from the body in expired air, with approximately 95% of injected xenon passing into the alveoli during the first cycle through the lung. 9 The radioactive isotope Xe 133 is a fission product of uranium 235 which has a physical half-life of 5.27 days and decay emission of a 350kev {3-ray and an 81-kev -y-ray. The biological half-life of the isotope administered by various routes is a matter of minutes. 10' 11 We have found a half-life of approximately 15 min for pelvic radioactivity after the xenon 133 rectal test. Xe 133 has been used as a biologic tracer to measure blood flow in various organs, including brain/ 2 uterus, 13 muscle, 11 lungs, 9 kidney, 14 heart, 15 and skin. 16 A significant difference in both circulation time and rate of appearance of isotope at the precordium was observed for cirrhotic patients with portacaval shunts and nonshunted cirrhotics (both mild and severe). As predicted from our theoretical considerations, portal circulation time was prolonged in patients with severe cirrhosis, and this was associated with a reduction in rate of appearance of isotope at the precordium. Similarly, patients with surgical shunts showed a rapid rate of appearance at the precordium and a diminished circulation time. As predicted, patients with mild cirrhosis showed intermediate values. Thus, there was a close qualitative correspondence between observation and theory. Using the xenon 133 method, an estimation of portal circulation time can be made simply by visual inspection of the tracing or can be obtained from the semi-
539
logarithmic plot of precordial activity. The visual and calculated circulation times represent two methods for analyzing the data. The circulation time calculated from the semilogarithmic plot of the data is more time-consuming but allows for the estimation of the slope parameter of precordial radioactivity. However, the visual method is simple and direct and may have more appeal for the clinician. The data suggest that xenon 133 may offer a rapid and easily performed method of studying portal circulation in cirrhotic patients. The results obtained in 1 patient before and after a surgical portacaval shunt and in 1 patient with documented thrombosis of a shunt suggest that the xenon 133 portal circulation may be useful in the diagnosis of portacaval shunt occlusion.
Addendum When this paper was presented before the American Association for the Study of Liver Disease, the comment was offered that "11 % of inferior mesenteric veins drain into the renal vein." According to Gray 18 10% of the inferior mesenteric veins drain into the juncture of the splenic and superior mesenteric vein or directly into the superior mesenteric vein. No reference was made concerning drainage into the renal vein. Although the specific site of drainage from the inferior mesenteric vein is variable, all blood, nevertheless, drains into the portal rather than the systemic circulation. Appendix W. M .) If it is assumed that absorption of isotope from rectal lumen to portal blood is extremely rapid, the rate of appearance of isotope at the heart is a function of portal blood flow. The number of counts per minute at the heart (cpm) is a direct function of the moles of isotope at the heart (E.
(Q):
cpm"' Q If C is the concentration of isotope at the heart (moles per milliliter) and F is flow
540
CASTELL ET AL.
Vol. 57, No. 5
rate, in milliliters per second: dQ = FC dt
D V = CT (1)
Since the number of moles of isotope is equal to concentration times volume, i.e., Q = C . V, where V is the volume of isotope distribution: dQ = F ·Q
v
dt
dQ=Fdt
Q
v
(2)
but flow rate (F) is a direct function of velocity ( V): F"'V
F =X . V
(7)
where X is a proportionality constant with the dimension of milliliters per centimeter. Substituting 6 in 7:
F
(3)
=
1 X·D · CT
(8)
But, from equation 5:
Integrating,
F
(4)
Since cpm "' Q, a plot of cpm against time on semilogarithmic paper should yield a straight line with slope (k) equal to FIV: F k=-
v
(5)
If there is little resistance to portal flow, as in patients with functioning portacaval shunts, the ratio F/V (i.e., the slope) would be expected to be high. In patients with severe cirrhosis (i.e., high hepatic resistance) the slope would be expected to be low. A reduction in slope in such patients would presumably reflect both a decrease in flow rate (F) and increase in volume of distribution of isotope (V). Normal subjects and patients with mild cirrhosis would presumably show intermediate values. As shown in figure 4, the results obtained in this study are in close agreement with theoretical predictions. The time required for first appearance of isotope at the heart following intrarectal instillation, circulation time ( CT), would be expected to be related to the slope (F /V), since both are a function of flow rate (F). That this is the case is indicated by the following. Consider flow along a tube at velocity (V) over a distance (D). Then: CT =
or
(6)
D
V
=
k · volume
Therefore, 1
k · volume = X·D· CT or X·D 1 k = -- · volume CT
(9)
The relationship between slope (k) and circulation time ( CT) ls given by equation 9. A plot of CT against k should be a rectangular hyperbola while a plot of k against 1/CT should be linear with a slope of X· D/volume. Circulation time would be expected to be prolonged in patients with severe cirrhosis and presumably high hepatic resistance, and would be expected to be short in patients with functioning portacaval shunts. Normal subjects and patients with mild cirrhosis might be expected to show intermediate values. Again, the observed results (figure 2) show close agreement with theory. REFERENCES 1. Newman, H. F., and J . B. Cohen. 1949. Estimation of the portal circulation time in man. J. Lab . Clin. Med. 34: 674-676. 2. Giges, B., and P . E . Teschan . 1952. The portal circulation time in cirrhosis of the liver following portacaval anastomosis. J. Lab. Clin. Med. 40: 357-540. 3. Waldstein, S. S. , B. T . Forsyth, and E. S. Jahnke. 1954. An evaluation of the rectum-to-lung
November 1969
4.
5.
6.
7.
8.
9.
10.
EVALUATION OF PORTAL CIRCULATION
ether time test in shunt operations for portal hypertension and in liver disease. Gastroenterology 26: 781-788. Deterling, R. A., S. R. Powers, and S. B. Bhonslay. 1954. The use of radioactive sodium in the determination of patency of portacaval shunts. Surg. Forum 5: 193-200. Gilsanz, V., A. Vergara, and M. Gallego. 1957. A new method for determining the portal circulation time. Arch. Intern. Med . (Chicago) 99: 428-430. Lombardo, C. R., R. T. L. Long, E . Braunwald, and A. E. Morrow. 1959. The measurement of portal-systemic circulation time: a new method for detecting esophageal varices and determining patency of a portacaval anastomosis. Surg. Forum 10: 275-277. Long, R. T. L., C. R. Lombardo, and E. Braunwald. 1960. Use of radioactive krypton and cardio-green dilution curves in the detection of experimental portal-systemic venous shunts. Ann. Surg. 151: 146-152. Schwartz, S. 1., and R. H. Greenlaw. 1961. Evaluation of portal circulation by percutaneous splenic isotope injection. Surgery 50: 833-841. Bentivoglio, L. G., F. Beerel, A. C. Bryan, P . B. Stewart, B. Rose, and D. V. Bates. 1963. Regional pulmonary function studied with xenon 13 3 in patients with bronchial asthma. J. Clin. Invest. 41: 1193-1200. Hoedt-Rasmussen, K. 1965. Regional cerebral flow in man measured externally following
11.
12. 13.
14.
15.
16.
17.
18.
541
intra-arterial administration of Kr85 or Xe 133 dissolved in saline. Acta Neural. Scand . 41 : Suppl. 14: 65-68. Lassen, N. A., I. F. Lindbjerg, and 0. Munck. 1964. Measurement of blood flow through skeletal muscle by intramuscular injection of xenon 133 • Lancet 1: 686-689. McHenry, L. C., Jr., 1966. Cerebral blood flow. New Eng. J. Med. 274: 82-86. Lysgaard, H., and H. LeFeure. 1965. Myometrial blood flow in pregnane~ measured with xenon 133 • Acta Obstet. Gynec. Scand. 44: 401-407. Ladefoged, J. 1966. Measurements of the renal blood flow in man with the xenon 133 washout technique. Scand . J . Clin. Lab. Invest. 18: 299-315. Pitt, A., G. C. Friesinger, and R. S. Ross. 1966. Right and left myocardial blood flow determined by the Xe 133 method. Clin. Res. 14: 258. Sejrsen, P. 1966. Cutaneous blood flow studied by Kr 85 and Xe 133 intraarterially injected and epicutaneously applied in man. Scand. J. Clin. Lab. Invest. 17: 186-220. Grace, N.D., D. 0. Castell, and M. H. Wennar. 1969. A comparison of the oral fructose and ammonia tolerance tests in cirrhosis. Arch. Int. Med. In press. Gray, H. 1959. In C. M. Goss [ed.], Anatomy of the human body, Ed. 27, p . 764. Lea and Febiger, Philadelphia.
GASTROENTEROLOGY
Printed in U.S.A .
Copyright C 1969 by The Williams & Wilkins Co.
EVALUATION OF PORTAL CffiCULATION IN HEPATIC CIRRHOSIS A new method using xenon 133 DONALD 0 . CASTELL, M.D., NORMAN D . GRACE, M.D., MARTIN THoMAS C. CHALMERS, M .D., AND EDWARD W . MooRE, M.D.
H. WENNAR, M.D.,
Metabolic and Gastrointestinal Research Unit of the Medical Services, Lemuel Shattuck Hospital, Department of Public Health, Commonwealth of Massachusetts, and the Department of Medicine and Physiology, Tufts University Medical School, Boston, Massachusetts
A method for estimating portal circulation using xenon 13 3 given rectally with monitoring of radioactivity over the precordium is presented. This test is easily performed and provides a reproducible objective end point. The portal circulation time can be estimated "visually" from the initial tracing, or can be "calculated" from a semilogarithmic plot of precordial radioactivity against time. The slope of appearance of precordial radioactivity is also obtained by the latter method . Xenon 133 portal circulation time studies were performed in 39 cirrhotic patients. Values obtained in 11 patients with portacaval shunts were significantly different from values obtained in 28 nonshunted cirrhotics by each of three methods of evaluation. The possibility that this test can identify patients having an occluded portacaval shunt is suggested by the results obtained in 1 patient showing a marked difference before and after a shunt and the discovery of a thrombosed shunt in another patient initially studied because of a prolonged xenon 133 circulation time. brachial artery after giving Na 24 rectally. 4 Ether5 and radioactive krypton 6 ' 7 have been given intrasplenically and their appearance in expired air has been used as a measurement of portal circulation time. Similarly, radioactive iodine has been given by splenic injection and the portal circulation time estimated from its appearance over the precordium. 8 Certain difficulties are encountered with each of these techniques. With ether, there is lack of an objective end point. Variable rectal absorption of Na 2 4 may occur. Intrasplenic injection constitutes a potential risk to the patient. Xenon 133 is a highly diffusible ga~ which is readily measured, biologically and chemically inert, and almost completely cleared by the lungs in a singlE transit. 9 It has therefore been widely used in studies of blood flow in various or-
Several techniques have been used for estimation of "portal circulation time," including the appearance of rectally administered ether in expired air/ -3 and the appearance of radioactivity over the Received December 26, 1968. Accepted June 23, 1969. A preliminary report of this work was presented at the meeting of the American Association for the Study of Liver Diseases in November 1968, in Chicago. Address requests for reprints to: Dr. Norman D. Grace, Lemuel Shattuck Hospital, 170 Morton Street, Boston, Massachusetts 02130. This investigation was supported by Grants AM07417, AM-05424, and AM-11243 from the National Institute of Arthritis and Metabolic Diseases, United States Public Health Service. Dr. Moore was the recipient of Research Career Development Award 6-K3-GM-11,386,01A1 from the National Institute of General Medical Sciences, United States Public Health Service. 533
534
Vol . 57, No. 5
CASTELL ET AL.
T- th . pae presen t stu d"1es m gans. 1 0 ~ 1 6 m tients with cirrhosis, it will be shown that portal circulation may be studied by intrarectal administration of this isotope with measurement of radioactivity counting over the precordium. The end point, or " portal circulation time," is readily and objectively identified. This may be of clinical value in determining the patency of portacaval shunts.
Methods A total of 53 studies were made in 39 hospitalized patients with cirrhosis. These included 20 males and 19 females ranging in age from 26 to 65 years (mean, 50.6 years) . Diagnoses were made by biopsy in 33 patients and by clinical and laboratory findings in the remainder. The biopsy was not always done at the time of the study, but in some of the severe cirrhotics it was done from an earlier admission. One patient studied both before and after a portacaval shunt is included in two groups of subjects. The patients were divided into three groups: (1) 12 patients with "mild" cirrhosis, (2) 16 patients with " severe" cirrhosis, and (3) 12 patients with surgical portacaval shunts. Prior to testing, the nonshunted patients were independently classified by two physicians as having clinicaliy mild or severe cirrhosis on the basis of the following five criteria : splenomegaly, ascites, visible abdominal collaterals and prothrombin tim~ encephalopathy, greater than 3 sec above control levels. 17 A patient was graded with a clinical score of from 0 to 5, achieved by adding 1/2 point for every positive finding noted by each of the two observers (table 1). A patient was classified as having severe cirrhosis if two findings or more were present. The xenon 133 test was performed as follows. Following defecation (without enema) the patient was placed in the right lateral decubitus position and a polyethylene tube (9-mm outer diameter) was inserted approximately 12 em into the rectum. A shielded l-inch Nal scintillation probe was then placed about 6 inches anterior to the precordium. Xenon 133 (500 !!C) in 3 ml of saline was given intrarectally through polyethylene tubing (2 mm outer diameter) contained within the rectal tube. To minimize contamination of the room, the patient's expired air was collected in a large disposable rubber bag, and the room was well ventilated. The appearance of the
isotope at the heart was measured with a Picker no. 600-046 rate meter and a permanent record obtained with a Picker no. 600-091 chart recorder. Maximum counting ( ')', 81 kev) was achieved with a 640-kev setting and window setting between 70 and 90 kev, using a 3-sec time constant. Two methods were used to estimate portal circulation time: " visual" from the observed tracing, representing the point at which a steady rise in precordial radioactivity occurred, and "calculated" by techniques outlined in the "Appendix." Visual estimations were determined blindly by two different observers (D . 0 . C. and N. D. G.); and the resulting mean value was then compared with the corresponding calculated values obtained by a third observer (E. W. M .). Calculated circulation time was obtained from the semilogarithmic plot of precordial radioactivity (y axis) against time (x axis) and represented the point of intersection of an early stable phase (i .e. , presumably representing intraluminal colonic radioactivity) and the exponential curve which followed (i.e., the precordial blood radioactivity) . The slope (k) of the blood exponential phase was calculated for each study by least squares regression analysis. The presumed physical significance of the exponential slope is given in the "Appendix."
Results Sample Tracings Two tracings of precordial radioactivity following rectal instillation of xenon 133 are shown in figure 1. Data at the top of the figure were obtained in a patient with a surgical portacaval shunt; the data below were obtained in a patient with severe cirrhosis. Note the slight rise in precordial radioactivity immediately following intrarectal administration of the isotope. This was observed in virtually all patients and presumably resulted from diffusion of gas into the splenic flexure or transverse colon. Following this plateau of radioactivity, a sharp curvilinear rise of radioactivity was observed ("precordial exponential phase") ; this represented the visual end point for estimated portal circulation time. Note that the circulation time was shorter in the shunted patient (14 sec) than in the patient with severe cirrhosis (43 sec) . fu addition, the rate of
TABLE
Patient
Total clinical sco rea
M i ld ci rrhosis D. G . F. 0. M.M . J. w. L.M. A. K. R. M. A. H. J. 0 . E. D. J.D . A.M. Mean
1. Cli nical features and xenon 13 3 portal circulation studies
Splenomegaly
Ascites
Abdominal collaterals
Encephalopathy
Abnormal prothrombin Visual CT' time 6
SE
sec
sec
(1.)
0 0 0 }1 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
1 0 0 1 0 0 0 0 0 0 0 0
45 26 33 38 32 38 27 35 43 25 30 26 33.4 2.7
38 .5 28.2 27.5 33.5 22.5 26 .0 24 .0 28 .0 37.5 23 .0 26 .7 25 .5 29 .3 1.7
0.040 0 .096 0.044 0.112 0.050 0.031 0.075 0 .071 0.036 0.030 0.065 0.060 0.058 0.008
4 3 3 2}1 3 2 2}1 2 2}1 3}1 3 2 4 3 3 3
1 1 }1 1 1 1 }1 1 }1
1
0 0 }1 }1 1 1
1 % 1 0 1 1 1 1 }1 1 1 1 1 1
1 0 }1 0 0 0 0 0 1 }1 }1 1 }1 }1 0 0
0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0
1 1 1 1 1 1 1 0 0 1 1 0 1 1 1 1
56 86 52 44 47 33 59 52 35 44 53 65 48 35 43 40 49.5 3.2
55.0 71.0 36.0 40 .0 34 .0 29.5 54.0 33.5 25.5 46.3 55 .0 45.5 25 .0 24.0 30 .0 32.5 39.9 3.4
0.027 0.032 0.029 0.029 0.035 0.032 0.009 0.022 0.025 0 .019 0.011 0.018 0.098 0.146 0.079 0.071 0.043 0.009
2 1}1 0 2 1 2 2}1 1 1 0 2
0 }1 0 1 0 0 }1 0 0 0 1
}1 0 0 0 0 0 0 0 0 0 0
}1 0 0 0 0 0 0 0 0 0 0
0 0 0 0 1 1 1 1 0 0 0
1 1 0 1 0 1 1 0 1 0 1
14 34 23 32 34 16 18 27 26 36 24 25.8 2.1
9.5 28 .0 28.5 22 .5 40.0 16.0 18.2 15.5 23.0 31.0 24.8 23.4 2.5
0.125 0.070 0.050 0.065 0.048 0.131 0. 110 0.092 0.098 0.118 0.060 0.094 0.010
1
1
SE
Portacaval shunt M . C. P.R. K. R. K. s. R. R. W.B. M.W. B. C. M.L . R.E. B. C. Mean
Slope
1 0 0 1}1 0 0 0 0 0 0 0 0
SE
Severe cirrhos is A.M. M. R. G . S. K. s. R. B. V. R. J. G. B . A. R.F . P. 0 . B. M. E. H . N.L . J _K . M.P. E. K. Mean
Calculated CT'
The patient received }1 point for every finding noted to be present by each of two observers. Greater than 3 sec above the control value. ' CT, circulation time. 535
a
b
536
CASTELL ET AL.
rise in radioactivity was more acute in the shunted patient.
Portal Circulation Time Circulation times for each of the three groups of patients obtained by the visual method are shown in figure 2. The 12 patients with mild cirrhosis had a mean circulation time of 33.4 ± 2.7 (SE) sec, whereas the 16 patientS with severe cirrhosis had a mean circulation time of 49.5 ± 3.2 sec. This difference was significant (P < 0.01). Mean circulation time in 11 patients with a surgical portacaval shunt was 25.8 ± 2.1 sec, which was significantly less than that observed in patients with severe cirrhosis (P < 0.001) and those with mild cirrhosis (P < 0.02) . One shunted patient with a markedly prolonged circulation time was not included in the calculation and is presented separately below. Calculated circulation times are also shown in figure 2. Mean values were similar to those obtained visually in each of the three groups. Mean portal circulation time was 29.3 ± 1.7 sec"in the group with mild cirrhosis. For the group with severe cirrhosis, mean circulation time was 39.9 ± 3.4 sec, and for the shunted pa-
Vol . 57, No. 5
tients, the mean value was 23.4 ± 2.5 sec. The difference between the circulation time for the shunted patients and those with severe cirrhosis was significant (P < 0.001) as was the difference between patients with mild and severe cirrhosis (P < 0.01). As shown in figure 3, there was a linear relationship between values obtained by the two techniques (r = +0.86). The fact that calculated values were usually less
33 FIG. 1. Sample tracings of precordial radioactivity following rectal administration of xenon' at the arrow (reading from right to left) . Above, from a patient with a surgical portacaval shunt (circulation time, 14 sec) , and below, from a patient with severe cirrhosis (circulation time, 43 sec).
90
VISUAL
CALCULATED
80 UJ
70
z 0 ;::
60
....~
~ ~
.......
...J
a:
30
0
0..
20
.
~ ...
I
~ ~ 50
:::> <..>
a:40 0
0 0 0
~
~.....
••• •
0 00 0
~
ti1
ffi
0
•o
&
10 OL--T--~-r--
PCS PCS • PC Shunt
537
EVALUATION OF PORTAL CIRCULATION
November 1969
SC
L--r--~~--
MC
SC • Severe Cirrhosis
PCS
sc
MC
MC • Mild Cirrhosis
FIG. 2. Portal circulation times for the three groups of patients obtained by both the calculated method (left) and the visual method (right).
than visually estimated values may reflect difficulties in identifying the early phase of the exponential rise in precordial radioactivity with the visual method. The data in figure 2 are in qualitative agreement with the equations and predictions developed in the theoretical section ("Appendix"). As expected, the shortest circulation times were observed in patients with surgical shunts, whereas the longest circulation times were seen in the patients with severe cirrhosis and presumed increased hepatic resistance. Patients with mild cirrhosis showed intermediate values.
Characteristics of the Precordial Exponential Phase A plot of precordial radioactivity (counts per minute) against time would be expected to yield a straight line on a semilogarithmic plot (equation 4, "Appendix"). This was found to be the case in all studies. The resulting slope (k) presumably represents the ratio: FlowNolume of isotope distribution. Observed values for k for the three groups of patients are shown in figure 4. As predicted from theory, the mean observed slope was greatest in the shunted group, lowest in the group with severe cirrhosis, and intermediate in the group with mild cirrhosis. Mean values for the shunted pa-
tients were significantly different from those obtained in both the severe (P < 0.01) and mild (P < 0.05) cirrhotic group. As shown in figure 4, k values in 4 patients with severe cirrhosis were 3 to 4 times those in the remaining 12 patients and were comparable to those seen in patients with surgical shunts. These same 4 patients also had circulation times shorter than most of the other patients with severe cirrhosis and comparable to those in the shunted group. The findings in these 4 patients, therefore, suggest the possibility of the presence of spontaneous portasystemic shunts in some patients with severe cirrhosis. The relationship between circulation time and slope (k) is given by equation 9, "Appendix." A plot of circulation time 0(71)
"'
60
z 0 ;::
50
/
:::E
0/10.
;=
0/
G--: 0: <.>
.
u~ 0
..."'
/
/ x.
30
/eo
~xj:t(x .,I
20
//
...J
u
/
10
/
...J
•
:X
•
• •• •
r•+0.86 o • PC Shunt X • Mild Cirrhosis
0
0
/ /~1:1
<(
u
0//
X
<(
:::>
/
/
40
<(
...J
-
/
• • Severe
0 0
10
.
Revre11ion
30
20
40
50
60
70
80
90
VISUAL CIRCULATION TIME, (sec.)
FIG. 3. The relation of calculated to visual circulation time for each of the 39 patients.
E3 •!
0.140
Mean 2 S.E.
0.120 0.100 0.080 0.060
~ 0 0
0.040 0.020 0~----------------
PC Shunt
Severe Cirrhosis
Mild Cirrhosis
FIG. 4. Values for the slope (k) of precordial radioactivity with time for the three groups of patients. As predicted, the patients with portacaval shunts have larger values than both groups of nonshunted cirrhotics.
538
CASTELL ET AL.
against k would be expected to give a rectangular hyperbola and plot of the reciprocal of circulation time (1/CT) against k should be linear. This appeared to be the case, since a linear correlation (r +0.612) was observed between 1/CTand k.
Reproducibility Studies Xenon 133 studies were repeated in 9 of the patients after an interval of from 2 to 28 days. As shown in figure 5, there was high correlation between first and second tests for both time and slope. Studies of Special Note Two patients of particular interest were studied. One patient with a surgical portacaval shunt was hospitalized for recurrent gastrointestinal hemorrhage 3 years after surgery. Duplicate xenon 133 portal circulation studies revealed a markedly prolonged circulation time with a very low slope, suggesting thrombosis of the shunt. Splenic pulp pressure was 600 mm H20, and splenoportography revealed large tortuous collateral vessels without visualization of the inferior vena cava. The diagnosis of a thrombosed shunt was confirmed at laparotomy. Esophageal varices were VISUAL
60
~
/
111 TEST C.T. (sec .)
40
'"'·
/ /
/
/
r•+0.78
20 40 60 0 2"4 TEST C.T. (sec . )
20
0
/ .-
/
r•+0.97
0 0.080
/'
//
/ / /
/ /
/ / .
;(•
20
. ....
CALCULATED
.
/
/
40
60
/
/ ./
0.060 /
1'1 TEST
/ /
0.040
. .. ./. /
/
/
/
0 .020 /
/
r•+0 .89
0 0
0 .050 0.10 2"4 TEST k
FIG. 5. Reproducibility of the xenon 133 portal circulation test in 9 patients. The relation between values obtained during initial and repeat testing for both visual and calculated circulation times and slope (k) is shown. The broken lines indicate the 1: 1 regression line.
Vol. 57, No. 5
believed to have been the source of the hemorrhage. Measurement of portal circulation time was made in another patient, both preceding and following an end-to-side portacaval shunt (patient included in both groups above). The calculated circulation time preoperatively was 40 sec with a slope of 0.029. Postoperatively, the calculated circulation time was 22.5 sec with a slope of 0.065. The visual circulation time showed a similar change. There was, thus, approximately a 50% reduction in circulation time with a corresponding increase in the slope of the isotope appearance.
Discussion A number of techniques have been used in the past to estimate portal circulation time. One of the earliest methods involved rectal administration of ether, referred to as "the rectum-to-lung time." Newman and Cohen' showed that the time required to detect the intrarectally administered ether in the patients' expired air was longer in patients with cirrhosis (and probable portal hypertension) than in normal subjects. A similar observation was made by Giges and Teschan, 2 who noted a consistent decrease in the circulation time in cirrhotic patients after a surgical portacaval shunt. Waldstein et al. 3 suggested that this test might be a simple method for determining the patency of a portacaval shunt. Deterling et al. 4 reported the use of Na24 administered rectally as a test of portal circulation time. The end point was the appearance of a sharp rise in radioactivity over a brachial artery. A consistent decrease in the circulation time was observed in 16 cirrhotic patients after portacaval shunt surgery. The appearance time of ether in the expired air has been measured following its injection into the spleen. 5 Prolonged circulation times were found in cirrhotic patients when compared with normal subjects. Mter injection of 113 1 albumin into the spleen, Schwartz and Greenlaw8 found decreased time of appearance of
Novemb er 1969
EVALUATION OF PORTAL CIRCULATION
radioactivity at the precordium in patients having portacaval shunts. The use of radioactive gas (krypton 80 ) to measure portal circulation time in dogs has been reported by Lombardo et al. 6 ' 7 These workers reported a definite decrease in the circulation time of Kr 85 from the spleen to the expired air after performing portacaval shunts. Xenon, a rare gas, is biologically inert and freely diffusible in body tissues. After entry into the blood stream it is rapidly eliminated from the body in expired air, with approximately 95% of injected xenon passing into the alveoli during the first cycle through the lung. 9 The radioactive isotope Xe 133 is a fission product of uranium 235 which has a physical half-life of 5.27 days and decay emission of a 350kev {3-ray and an 81-kev -y-ray. The biological half-life of the isotope administered by various routes is a matter of minutes. 10' 11 We have found a half-life of approximately 15 min for pelvic radioactivity after the xenon 133 rectal test. Xe 133 has been used as a biologic tracer to measure blood flow in various organs, including brain/ 2 uterus, 13 muscle, 11 lungs, 9 kidney, 14 heart, 15 and skin. 16 A significant difference in both circulation time and rate of appearance of isotope at the precordium was observed for cirrhotic patients with portacaval shunts and nonshunted cirrhotics (both mild and severe). As predicted from our theoretical considerations, portal circulation time was prolonged in patients with severe cirrhosis, and this was associated with a reduction in rate of appearance of isotope at the precordium. Similarly, patients with surgical shunts showed a rapid rate of appearance at the precordium and a diminished circulation time. As predicted, patients with mild cirrhosis showed intermediate values. Thus, there was a close qualitative correspondence between observation and theory. Using the xenon 133 method, an estimation of portal circulation time can be made simply by visual inspection of the tracing or can be obtained from the semi-
539
logarithmic plot of precordial activity. The visual and calculated circulation times represent two methods for analyzing the data. The circulation time calculated from the semilogarithmic plot of the data is more time-consuming but allows for the estimation of the slope parameter of precordial radioactivity. However, the visual method is simple and direct and may have more appeal for the clinician. The data suggest that xenon 133 may offer a rapid and easily performed method of studying portal circulation in cirrhotic patients. The results obtained in 1 patient before and after a surgical portacaval shunt and in 1 patient with documented thrombosis of a shunt suggest that the xenon 133 portal circulation may be useful in the diagnosis of portacaval shunt occlusion.
Addendum When this paper was presented before the American Association for the Study of Liver Disease, the comment was offered that "11 % of inferior mesenteric veins drain into the renal vein." According to Gray 18 10% of the inferior mesenteric veins drain into the juncture of the splenic and superior mesenteric vein or directly into the superior mesenteric vein. No reference was made concerning drainage into the renal vein. Although the specific site of drainage from the inferior mesenteric vein is variable, all blood, nevertheless, drains into the portal rather than the systemic circulation. Appendix W. M .) If it is assumed that absorption of isotope from rectal lumen to portal blood is extremely rapid, the rate of appearance of isotope at the heart is a function of portal blood flow. The number of counts per minute at the heart (cpm) is a direct function of the moles of isotope at the heart (E.
(Q):
cpm"' Q If C is the concentration of isotope at the heart (moles per milliliter) and F is flow
540
CASTELL ET AL.
Vol. 57, No. 5
rate, in milliliters per second: dQ = FC dt
D V = CT (1)
Since the number of moles of isotope is equal to concentration times volume, i.e., Q = C . V, where V is the volume of isotope distribution: dQ = F ·Q
v
dt
dQ=Fdt
Q
v
(2)
but flow rate (F) is a direct function of velocity ( V): F"'V
F =X . V
(7)
where X is a proportionality constant with the dimension of milliliters per centimeter. Substituting 6 in 7:
F
(3)
=
1 X·D · CT
(8)
But, from equation 5:
Integrating,
F
(4)
Since cpm "' Q, a plot of cpm against time on semilogarithmic paper should yield a straight line with slope (k) equal to FIV: F k=-
v
(5)
If there is little resistance to portal flow, as in patients with functioning portacaval shunts, the ratio F/V (i.e., the slope) would be expected to be high. In patients with severe cirrhosis (i.e., high hepatic resistance) the slope would be expected to be low. A reduction in slope in such patients would presumably reflect both a decrease in flow rate (F) and increase in volume of distribution of isotope (V). Normal subjects and patients with mild cirrhosis would presumably show intermediate values. As shown in figure 4, the results obtained in this study are in close agreement with theoretical predictions. The time required for first appearance of isotope at the heart following intrarectal instillation, circulation time ( CT), would be expected to be related to the slope (F /V), since both are a function of flow rate (F). That this is the case is indicated by the following. Consider flow along a tube at velocity (V) over a distance (D). Then: CT =
or
(6)
D
V
=
k · volume
Therefore, 1
k · volume = X·D· CT or X·D 1 k = -- · volume CT
(9)
The relationship between slope (k) and circulation time ( CT) ls given by equation 9. A plot of CT against k should be a rectangular hyperbola while a plot of k against 1/CT should be linear with a slope of X· D/volume. Circulation time would be expected to be prolonged in patients with severe cirrhosis and presumably high hepatic resistance, and would be expected to be short in patients with functioning portacaval shunts. Normal subjects and patients with mild cirrhosis might be expected to show intermediate values. Again, the observed results (figure 2) show close agreement with theory. REFERENCES 1. Newman, H. F., and J . B. Cohen. 1949. Estimation of the portal circulation time in man. J. Lab . Clin. Med. 34: 674-676. 2. Giges, B., and P . E . Teschan . 1952. The portal circulation time in cirrhosis of the liver following portacaval anastomosis. J. Lab. Clin. Med. 40: 357-540. 3. Waldstein, S. S. , B. T . Forsyth, and E. S. Jahnke. 1954. An evaluation of the rectum-to-lung
November 1969
4.
5.
6.
7.
8.
9.
10.
EVALUATION OF PORTAL CIRCULATION
ether time test in shunt operations for portal hypertension and in liver disease. Gastroenterology 26: 781-788. Deterling, R. A., S. R. Powers, and S. B. Bhonslay. 1954. The use of radioactive sodium in the determination of patency of portacaval shunts. Surg. Forum 5: 193-200. Gilsanz, V., A. Vergara, and M. Gallego. 1957. A new method for determining the portal circulation time. Arch. Intern. Med . (Chicago) 99: 428-430. Lombardo, C. R., R. T. L. Long, E . Braunwald, and A. E. Morrow. 1959. The measurement of portal-systemic circulation time: a new method for detecting esophageal varices and determining patency of a portacaval anastomosis. Surg. Forum 10: 275-277. Long, R. T. L., C. R. Lombardo, and E. Braunwald. 1960. Use of radioactive krypton and cardio-green dilution curves in the detection of experimental portal-systemic venous shunts. Ann. Surg. 151: 146-152. Schwartz, S. 1., and R. H. Greenlaw. 1961. Evaluation of portal circulation by percutaneous splenic isotope injection. Surgery 50: 833-841. Bentivoglio, L. G., F. Beerel, A. C. Bryan, P . B. Stewart, B. Rose, and D. V. Bates. 1963. Regional pulmonary function studied with xenon 13 3 in patients with bronchial asthma. J. Clin. Invest. 41: 1193-1200. Hoedt-Rasmussen, K. 1965. Regional cerebral flow in man measured externally following
11.
12. 13.
14.
15.
16.
17.
18.
541
intra-arterial administration of Kr85 or Xe 133 dissolved in saline. Acta Neural. Scand . 41 : Suppl. 14: 65-68. Lassen, N. A., I. F. Lindbjerg, and 0. Munck. 1964. Measurement of blood flow through skeletal muscle by intramuscular injection of xenon 133 • Lancet 1: 686-689. McHenry, L. C., Jr., 1966. Cerebral blood flow. New Eng. J. Med. 274: 82-86. Lysgaard, H., and H. LeFeure. 1965. Myometrial blood flow in pregnane~ measured with xenon 133 • Acta Obstet. Gynec. Scand. 44: 401-407. Ladefoged, J. 1966. Measurements of the renal blood flow in man with the xenon 133 washout technique. Scand . J . Clin. Lab. Invest. 18: 299-315. Pitt, A., G. C. Friesinger, and R. S. Ross. 1966. Right and left myocardial blood flow determined by the Xe 133 method. Clin. Res. 14: 258. Sejrsen, P. 1966. Cutaneous blood flow studied by Kr 85 and Xe 133 intraarterially injected and epicutaneously applied in man. Scand. J. Clin. Lab. Invest. 17: 186-220. Grace, N.D., D. 0. Castell, and M. H. Wennar. 1969. A comparison of the oral fructose and ammonia tolerance tests in cirrhosis. Arch. Int. Med. In press. Gray, H. 1959. In C. M. Goss [ed.], Anatomy of the human body, Ed. 27, p . 764. Lea and Febiger, Philadelphia.