ORIGINAL ARTICLE 
Annals of Nuclear Medicine Vol. 13, No. 4, 215-221, 1999 
Using the spleen for time-delay correction of the input function in measuring hepatic blood flow with oxygen-15 water by dynamic PET 
Hiroki TANIGUCHI, Akihiro YAMAGUCHI, Satoshi KUNISHIMA, Toshimori KOH, Mamoru MASUYAMA, Hiroshi KOYAMA, Atsushi OGURO and Hisakazu YAMAGISHI 
First Department of Surgery, Kyoto Prefectural University of Medicine 
By the spleen, we calculated a time-delay correction of the input function for quantitation of hepatic blood flow with oxygen-15 water and dynamic positron emission tomography. The time delay (At) between the sample site and the spleen was calculated based on nonlinear multiple regression analysis when splenic blood flow was determined. Then hepatic blood flow was quantified by a method using the input function and incorporating deltat, which was assumed to be equal to the time delay between the sample site and the liver. Then hepatic arterial and portal blood flows were estimated separately as well as the delay time for passage within the organs of the portal circulation. The mean coefficient of variation and the mean sum of squares of errors decreased to about 70% when total hepatic blood flow was calculated from the results for regions of interest in three slices of the same liver segment. We concluded that using the spleen for time-delay correction of the input function for measuring hepatic blood flow by this method gave satisfactory results. 
Key words: regional hepatic blood flow, oxygen-15 water, positron emission tomography, spleen 
INTRODUCTION 
IN MEASURING cerebral blood flow by means of a [15O]-H2O bolus injection dynamic positron emission tomographic (PET) study, a time-delay correction is calculated between the brain and the arterial sampling site, usually the radial or brachial artery. Several methods have been described for accomplishing this correction,1-3 but these methods cannot be extrapolated to simultaneous quantitation of the hepatic arterial and portal blood flow, and the complexities of the liver's dual blood supply require appropriate correction. We previously have described several evolving models for quantitation of hepatic blood flow by means of [15O]-H2O dynamic 
Received November 25, 1998, revision accepted April 1, 1999. For reprint contact: Hiroki Taniguchi. M.D., First Department of Surgery, Kyoto Prefectural University of Medicine, Kawaramachi-Hirokohji, Kamigyo-ku, Kyoto 602-8566, JAPAN. E-mail: taniguchi@1surg.kpu-m.ac.jp 
PET.4,5 We also have measured splenic blood flow, because the spleen is included in images obtained during hepatic PET studies.6,7 In the present study, we performed time-delay correction of the input function by using the spleen to assess hepatic blood flow with [15O]-H20-bolus-injection dynamic PET. 
THEORY, MATERIALS AND METHODS 
Theory 
We based this study on our previous models. The original simple model may be expressed in the following three equations.4 When organs draining into the portal vein are considered to be one organ (the "portal organ"), the rate of change of the tracer in the portal organ and the liver can be expressed as Equations 1 and 2 respectively. The sum of arterial blood flow and portal blood flow represents total hepatic blood flow (Eq. 3): 
In these equations, fa and fp (mL/sec/g) represent hepatic arterial blood flow and portal venous blood flow, respectively. Ca(t), Cp(t) and Ch(t) (counts/sec/mL) are the tracer concentrations in the arterial blood, the portal organ, and the liver, respectively. Kh and Kp are the tracer's blood equilibrium partition coefficients for the liver and portal organ, respectively. In a subsequent modification the model included a coefficient for portosystemic shunting, as well as a coefficient for circulation time within the portal organ.5 The tracer concentration in the liver was also separated into arterial and portal components. The dynamics of the tracer could be explained in terms of the following four equations. Equation 1 is unchanged from the simple model. When radioactivity in the liver is separated into flow from the hepatic artery and flow from the portal vein, with Cha(t) representing the former and Chp(t) the latter, Equation 2 can be subdivided into the following two Equations, 4 and 5. Equation 5 then includes coefficients for portosystemic shunting and circulation time within the portal organ. 
In these equations,fa and E¥fp (mL/sec/g) represent tracer flows into the liver by way of the hepatic artery and from the portal circulation (portal organ), respectively. Ca(t), Cp(t), and Ch(t) (counts/sec/mL) are the tracer concentrations in the arterial blood, the portal organ, and the liver, respectively. Cha(t), and Chp(t) (counts/sec/mL) represent the radioactivities in the liver contributed by flow from the hepatic artery and flow from the portal vein, respectively. Kha, Khp, and Kp are organ-blood partition coefficients for water in the arterial component of the liver, the portal component of the liver, and the portal organ, respectively. E is the actual ratio of tracer flowing into the liver (1 minus E is therefore a shunting rate), and t (sec) is the time delay between the detection of tracer radioactivity in the portal organ and its detection in the liver. For correction of the time delay between the liver and the blood sampling site in the present, further modified model (Fig, 1), we used the spleen. The method for measuring blood flow in the spleen was based on our 6 previously reported study. 
In this equation, fs(mL/sec/g) represents splenic blood flow, and Ks is the spleen-blood equilibrium partition coefficient for the tracer. Ca(t) and Cs(t) (counts/sec/mL) are the tracer concentrations in the arterial blood and the spleen, respectively. When a new coefficient [deltat (sec)] for the time delay between the spleen and sample site is introduced in Equation 7, the expression becomes 
As the input function, the following two equations were applied when the splenic blood flow was estimated: 
where tmax is the time when the radioactivity concentration in the blood sample is maximum. The terms deltat, fs, and Ks were calculated by using the radioactivity concentration in the arterial blood sample and the time-activity curve for the spleen in Equation 8 and Equation 9 by the simplex method, a nonlinear least-squares method. Because the spleen usually is included in the imaging field for hepatic PET, the assumption that At is nearly equal to the time delay between the liver and the blood sampling site permits substitution of the following Equations for the hepatic input function: 
We therefore arrived at At by first calculating the splenic blood flow, and we quantified the hepatic blood flow by using the input functions and value for At (Fig. 2). 
PATIENTS AND METHODS 
In 88 patients (48 men and 40 women), regional hepatic blood flow was measured simultaneously in all four liver segments (lateral, medial, anterior, and posterior) by using PET, after informed consent was obtained. The patients ranged in age from 29 to 79 years with a mean age of 57.9 years. All the patients had normal liver function; their liver biopsy specimens or resected liver being diagnosed histologically as normal. Serial measurements were performed in fasted patients in the supine position in a whole-body PET scanner (HEADTOME III SET-120W, Shimadzu, Kyoto, Japan). Performance characteristics of the PET system in this study were set to obtain an image resolution of 8.2 mm in full width at half-maximum (FWHM) and a slice thick-ness of 11 mm (direct) and 13 mm (cross-plane) FWHM. The matrix size of the image was 128 x 128 with a 2-mm pixel size. The slice interval of the planes was 15 mm. After an intravenous bolus injection of 20 mCi (370 MBq) of the radioisotope [150]-H2O produced in a medical cyclotron (BC-1710, Japan Steel Works, Muroran, Japan), 12 PET measurements were acquired at serial 5-sec intervals for 1 min, and another 8 measurements were obtained every 30 seconds for the next 4 min. Emission data for three slices at each 1.5-cm thickness were collected simultaneously. The physical decay of 150 was corrected every 2.5 sec. Regions of interest (ROIs) were defined to correspond to the liver segments and the spleen in the PET images (Fig. 3) with reference to computed tomographic images at corresponding levels. In the current study, the specific gravity of the liver and spleen was assumed to be 1. Blood samples were taken from the left brachial artery at 10, 15, 20, 25, 30, 35, 60, 120, 180, and 240 sec after the beginning of the emission scan, to yield a total of 10 samples in a 4-min period. Radioactivity counts in the blood samples were measured immediately in a precalibrated well counter (MINAXI-gamma Packard Japan; 
Tokyo). Results for the three models were compared by coefficient of variation, which was calculated using the standard deviation and the mean hepatic blood flow of three ROIs set for three serial slices in the same liver segment [coefficient of variation (CV) = 100 x standard deviation/mean], and from the sum of the squares of the errors (SSE) of each result. Hepatic blood flow was assumed to be uniform within the same liver segment. The previously reported result obtained with the simple model4 was derived from fa, fp, Kp, and Kh with the solution (Eq, 11) of Equations 1 , 2, and 3 and the simplex method. 
The result with the modified model in a previous report5 was obtained by deriving fa and Kha by the simplex method and with the solution (Eq. 12) of Equations l, 4, 5, and 6 during the arterial phase (from the beginning of scanning to the maximum point of the time-activity curve of the spleen), and determining fp. Kp, Khp, and E from the beginning of scanning to the time when scanning was complete by using the data already determined (fa and Kha). In these two methods, values were approximated by the simplex method with Equation 9 as the input function. In the new method, the splenic blood flow and lit were calculated with these input functions (Eq. 9) by the simplex method. Then, with the new input functions including At (Eq. 10), hepatic blood flow was calculated in the same manner as in the modified method; specifically fa and Kha were calculated by the simplex method from the beginning of scanning to the time of maximal activity in the spleen. Finally, fp, Kp, Khp, and E were calculated by the simplex method from the beginning of scanning to the time of its completion by using the data already determined. The time delay correction for hepatic blood flow was therefore performed by using the splenic result, which is available on the same slice as the liver data. Data processing was performed by means of a specially developed software program on a personal computer (PC-LW2634A, NEC, Tokyo, Japan). Statistical evaluation was performed with Microsoft Excel 97 (Japan Microsoft, Tokyo). 
RESULTS 
Splenic blood flow was calculated in 180 ROIs (Table 1). The mean time delay between the spleen and arterial sample site was 2.38 sec. The hepatic blood flow was calculated in 588 ROIs. The actual data from a typical case are shown in Figure 4, and the results of hepatic blood flow based on each of the three models are shown in Table 2. Arterial hepatic blood flow values based on the current model were similar to those obtained with the simple model, but smaller than those obtained with the modified model. Portal hepatic blood flow values obtained with the current model were larger than those obtained with the simple model but smaller than those obtained with the modified model. CVs and SSEs are shown in Table 3. CVs of arterial blood flow based on each model were similar, but the CV for total blood flow based on the current model was smaller than that given with the others because the CV of the portal hepatic blood flow was the smallest among the models. A one-way analysis of variance (ANOVA) demonstrated a significant difference between the three models in SSEs (d.f. = 1763, p < 0.00001). In addition, significant differences were evident between models in the SSE. A p value less than 0.00001 was observed between the result obtained using the modified model and that yielded by the current model by means of a nonparametric Wilcoxon test. 
DISCUSSION 
The time required for a tracer to circulate from the injection site to the liver will differ according to the time required to reach an arterial sampling site. If the difference is large, the estimated value of the hepatic blood flow will deviate widely from the true value. In our previous models for quantitation of hepatic blood flow, we had ignored this time delay because of the already complicated model needed to reflect the dual blood supply of the liver. Although a time-delay correction is used regularly when cerebral blood flow is measured by PET, we felt that adding a new parameter for time delay to our model that was based on nonlinear multiple regression analysis as used for the brain would result in a larger error. Since the spleen usually is included in the imaging field when we quantify hepatic blood flow, we studied the possibility of using the spleen to determine the time-delay correction. Accordingly, the mean time delay between the spleen and arterial sample site was 2.38 sec, the splenic blood flow decreased slightly and the spleen-blood partition coefficient for water increased slightly. These results for splenic blood flow are in agreement with some previous reports.8-10 Our new model assumed that the time delays for the liver and spleen were almost the same. First, we attempted to calculate the time delay for the spleen in the same manner as for the brain 1,11 by nonlinear multiple regression analysis. Then the hepatic blood flow was calculated by using the time delay for the liver added to the input function (Fig. 2). The hepatic blood flow changed equally with the splenic blood flow. The results for the liver were also in agreement with some reported values.12,13 After introduction of splenic time delay into the hepatic time delay correction, we obtained smaller CVs and SSEs without using additional parameters. With the time-delay correction, the mean CV of the arterial blood flow was not different from that observed before the correction, but the CV of the portal blood flow was significantly lower when this correction was used. In particular, because the velocity of portal blood flow was low, the time delay more profoundly influenced the measurement results. We believe that this rationale explains why the CV of the portal blood flow based on the current model was smaller than that with earlier models. Furthermore, the decrease in the CV of portal blood flow decreased the CV of total blood flow. Measuring hepatic arterial and portal blood flow separately is extremely difficult. Ziegler and colleagues14 have proposed a model that is physiologic for use in measuring hepatic blood flow with [15O]-H2O by PET, but errors in the PET scanning protocol and in data accumulation limited the applicability of that study. A typical time-activity curve of the spleen and the liver (Fig. 4) shows an inflection point where time-activity in the spleen is maximum, thought to represent the first point when the radioactive water reaches the liver in the portal blood flow from the spleen. This point usually is detected within 60 sec after isotope injection. Accordingly, PET should be performed frequently in the first 60 min to detect this inflection point; otherwise separate measurement of arterial and portal blood flow cannot be performed. Moreover, the spleen provides a means of calculating the time-delay correction. In the past, the kidney was used when hepatic blood flow was measured with radioactive colloid,15 because colloids can pass through the kidneys but are trapped in the spleen. The current study demonstrates that the spleen is useful for calculation of the time-delay correction. Because in almost all cases the inflection point of the time-activity curve of the liver corresponds exactly to the peak of the time-activity curve of the spleen, we believe that our assumption is correct and that any distortion is minimum. A number of improvements have been made in our method since the first model, and we believe that the time-delay correction was made successfully, but the assumption considering the various portal organs as a single one still is required, and this point needs further consideration. 
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