Compartment model analysis of intravenous contrast‐enhanced dynamic computed tomography in hepatic hemodynamics: A validation study using intra‐arterial contrast‐enhanced computed tomography

To verify the utility of the 2‐in‐1‐out‐compartment model analysis (CMA) of intravenous contrast‐enhanced dynamic computed tomography (IV‐CT) for evaluating hepatic arterial and portal venous flow using intra‐arterial contrast‐enhanced CT (IA‐CT).


INTRODUCTION
E VALUATION OF PORTAL blood flow is important for the diagnosis and treatment of hepatocellular carcinoma (HCC), because portal blood flow in HCC is reduced as the grade of malignancy increases. 1 However, portal blood flow cannot be evaluated separately and independently by intravenous contrast-enhanced computed tomography (IV-CT) that is commonly used in clinical practice. 1 In contrast, intra-arterial contrast-enhanced CT (IA-CT), such as CT during arterioportography (CTAP) and CT during hepatic arteriography (CTHA), has been regarded as the gold standard for evaluating liver hemodynamics, 1-5 because arterial and portal blood flows can be separated physiologically. However, this technique is invasive. 2,3 Therefore, liver perfusion study using IV-CT has been proposed in clinical practice, because arterial and portal blood flows can be separated by computation without invasive procedures. Various useful tissue hemodynamic parameters can be quantitatively obtained from a CT perfusion study. Several studies have shown that the parameters obtained from a CT perfusion study correlate well with the presence and range of tumor vessels. [6][7][8] Although CT perfusion studies are known to be useful in the assessment of hepatic perfusion associated with disease severity in patients with chronic liver disease, 9,10 earlier detection of liver malignancies, 8 and evaluation of treatment effects in HCC, 11,12 no validation study has been conducted to date between IA-CT and a liver perfusion study using IV-CT.
Furthermore, the 2-in-1-out-compartment model analysis (CMA) has been adapted to study liver perfusion. [13][14][15] The movement of the contrast medium between pharmacokinetic compartments in the liver can be expressed using quantitative parameters, such as the arterial inflow velocity constant (k 1a ), portal venous inflow velocity constant (k 1p ), and venous outflow constant (k 2 ), in this model. Because the CMA in liver perfusion is more complex than the 1-in-1-out-compartment model used in other non-hepatic tissues, the parameters should be determined by non-linear procedures such as curve fitting of the time-density curve (TDC) using the non-linear least square method. 16,17 Appropriate limits for perfusion parameters should be determined in these procedures to avoid a local minima problem that could cause the computation to stop at an unreasonable answer because of false-best curve fitting. 18 However, details regarding this procedure have not been verified in comparison to the arterial and portal venous flows observed by IA-CT.
Therefore, the purpose of this study was to verify the utility of the CMA of IV-CT for evaluating hepatic arterial and portal venous flows in comparison to IA-CT with special emphasis on parameter limits during curve-fitting procedures.

Patient characteristics
This retrospective study was approved by the Institutional Review Board of Shinshu University School of Medicine (Matsumoto, Japan), and informed consent was obtained from all patients included in this study. We included 38 consecutive patients (25 men and 13 women; mean age, 74 years) who were radiologically diagnosed as having classical HCC and underwent both IV-CT and IA-CT (CTAP and CTHA) within 30 days as part of the preoperative evaluation for surgical resection or transarterial chemoembolization between 2008 and 2013 at our hospital. Seven patients had hepatitis B virus infection, 19 had hepatitis C virus infection, one had both hepatitis B and C virus infection, two had alcoholic or nonalcoholic steatohepatitis, one had primary biliary cirrhosis, and eight had neither hepatitis B nor hepatitis C liver cirrhosis. Eventually, 51 HCCs radiologically diagnosed using IA-CT (decreased portal venous flow on CTAP, and increased arterial flow, washout, corona, and capsular enhancement on CTHA) with a maximum diameter of more than 2 cm (mean, 2.4 cm) in the patients were evaluated in this study. Additionally, 11 consecutive patients (7 men and 11 women; mean age, 70 years) who were histologically diagnosed as having other hepatic malignant lesions including 4 early HCCs (eHCC), 3 cholangiolocellular carcinomas (CoCC), 1 mixed HCC, and 3 cholangiocellular carcionomas (CCC) were included in this study according to the same inclusion criteria as the patients with HCC. In overall 49 patients, 19, 22, and 8 were diagnosed as cirrhosis, chronic hepatitis, and normal liver clinically or histologically if available.

IA-CT protocol
CTAP and CTHA were performed using Aquilion 16 (TOSHIBA Medical Systems, Ootawara, Japan) in the angiography room. All the patients underwent single phasic CTAP first and 2 to 3 phasic CTHA.
In the CTAP scan, 5 μg of prostaglandin E1 (Liple; Mitsubishi Tanabe Pharma Corporation, Osaka, Japan) was injected into the superior mesenteric artery immediately before the injection of contrast medium. CTAP scanning began 30 s after the injection of an infusion of 300 mgI/mL iodine contrast agent (Omnipaque; Daiichi Sankyo, Tokyo, Japan) (50 mL) + saline (25 mL) at 1.8 mL/s through a catheter placed in the superior mesenteric artery. CTAP images were acquired for 1-mm-thick sections including the whole liver.
The first phase of CTHA scanning began 10 s after starting the injection of 300 mgI/mL iodine contrast agent (Omnipaque; Daiichi Sankyo) (30 mL) at 1 mL/s through a catheter placed in the common or proper hepatic artery. The infusion was continued throughout scanning. The second and the third phase scanning began 30 s after the end of contrast agent infusion and 30 s after the end of second phase scanning. All phase of CTHA images were acquired for 1-mm-thick sections including the whole liver.

Image analysis of IA-CT (CTAP and CTHA)
Four regions of interest (ROIs) were located at the hepatic artery, portal vein, liver, and hepatic malignant lesions manually on the IA-CT images by boardcertificated radiologists (D.K.: 10 years of experience; A. Y.: 17 years of experience) in consensus (Fig. 1). The ROI for the hepatic malignant lesions was set as large as possible including the maximum cross-sectional area of the lesion on CTHA and CTAP. The ROI for the liver parenchyma was set as large as possible avoiding major hepatic vessels such as hepatic arteries, hepatic veins, and portal veins at the same slice as the targeted hepatic malignant lesion on CTHA and CTAP. The ROI for the hepatic artery was set as large as possible including the arterial lumen at the proximal portion of hepatic artery on CTHA. The ROI for the portal vein was set as large as possible including the portal venous lumen at the main trunk of the portal vein on CTAP. As the gold standard for arterial and portal blood flows of the lesion and liver, we calculated the normalized enhancement on CTHA (nCTHA) and on CTAP (nCTAP) of lesions and the liver, respectively. These parameters were calculated as follows: CTAP Lesion , CTAP Liver , and CTAP PV are the CT values in the lesion, liver, and portal vein on CTAP, respectively. Similarly, CTHA Lesion, CTHA Liver , and CTHA HA are the CT values in the lesion, liver, and hepatic artery on CTHA, respectively ( Fig. 1A and 1B). The preconCT Lesion , preconCT Liver , preconCT PV , and preconCT HA are the CT values in the lesion, liver, portal vein, and hepatic artery on pre contrast CT, respectively. The CT value of Figure 1 Method of setting the regions of interestComputed tomography (CT) values in arterial and portal venous input functions, the lesion, and liver are measured as the CT during hepatic arteriography (CTHA HA , CTHA Lesion , and CTHA Liver , respectively; A) and CT during arterioportography (CTAP PV , CTAP Lesion , and CTAP Liver , respectively; B). CT values in the lesion, liver, aorta, and portal vein at scan time t are measured as C t[Lesion] (t), C t[Liver] (t), C a (t), and C p (t), respectively, on intravenous multiphasic dynamic contrast-enhanced CT (C: arterial phase and D: portal venous phase). The calculated perfusion parameter maps of classical hepatocellular carcinoma (HCC) and surrounding liver parenchyma (dashed squares in D) are also shown (E: k 1a , F: k 1p , and G: k 2 ). Note that increased k 1a and k 2 , and decreased k 1p in HCC compared to surrounding liver are quantitatively shown on parameter maps. [Color figure can be viewed at wileyonlinelibrary.com] Validation of hepatic CT perfusion study 831 Hepatology Research 2018; 48: 829-838 abdominal aorta was used for approximated preconCT HA to avoid partial volume effect because of small target area on images.

IV-CT protocol
Intravenous multiphasic contrast-enhanced CT including the whole liver was performed using a 64-row CT scanner (Light Speed VCT; GE Healthcare Japan, Tokyo, Japan) at precontrast and 22, 28, 34, 40, 46, 52, 58, 90, and 210 s after the start of an injection of 370 mgI/mL iodine contrast agent (Iopamiron; Bayer Healthcare, Tokyo, Japan) (100 mL) at 3 mL/s through a 22-gauge catheter in the median cubital vein. Scan parameters were as follows: scan range, 25 cm caudal from the upper diaphragm; tube voltage, 120 kVp; tube current, 300 mA (22 s through 58 s, and 210 s) or 500 mA (precontrast and 90 s); matrix, 512 × 512 pixels; field of view, 320 × 320 mm; and reconstruction thickness, 2.5 mm. The median (interquartile range) effective dose was 48.9 mSv (range, 48.2-48.9). This IV-CT protocol was similar to the one described in a previous report. 19

CMA of IV-CT
To analyze the hemodynamics of the liver and various hepatic malignant lesions quantitatively using the CMA of IV-CT, four ROIs were located at the aorta, portal vein, liver, and hepatic malignant lesions manually on the IV-CT images at each contrast-enhanced phase by board-certificated radiologists as mentioned before (D. K.: 10 years of experience; A.Y.: 17 years of experience) in consensus (Fig. 1). The ROI for the hepatic malignant lesions was set as large as possible including the maximum cross-sectional area of the lesion. The ROI for the liver parenchyma was set as large as possible avoiding major hepatic vessels such as hepatic arteries, hepatic veins, and portal veins at the same slice as the targeted hepatic malignant lesion. The ROI for the aorta was set as large as possible including the aortic lumen at the same slice as the targeted hepatic malignant lesion. The ROI for the portal vein was set as large as possible including the portal venous lumen at the main trunk of the portal vein. The contrastenhanced effects in the ROIs were calculated by subtracting the CT values on postcontrast IV-CT images from the CT values on precontrast images. Because the contrast-enhanced effect and concentration of the iodine contrast medium in the tissue were linearly correlated, the obtained time-concentration curves (TCCs) were applied into the CMA described by the following differential equation: where C a (t), C p (t), and C t (t) represent the contrast medium concentrations in the aorta, portal vein, and target tissue (liver or hepatic malignant lesion) at the time t. Two inflow rate constants, arterial inflow velocity constant (k 1a ) and portal venous inflow velocity constant (k 1p ), and one outflow velocity constant (k 2 ) were included in the model. τ a and τ p are the delay parameters representing the physical transit time of the contrast medium from the aorta and portal vein, respectively, to the target tissue. The differential equation as mentioned before was solved and five perfusion parameters in hepatic malignant lesion and the liver (k 1a , k 1p , k 2 , τ a , and τ p ) were obtained with the curve-fitting technique using the nonlinear least square method with various parameter limits (Figs. 1E, 1F, and 1G). The calculation was performed five times for each revised upper k 2 limit (≦0.01, ≦0.015, ≦0.020, ≦0.025, ≦0.030, ≦0.035, ≦0.040, ≦0.045, ≦0.050, ≦0.060, ≦0.070, ≦0.10, ≦0.50, and ≦1.00) by using MATLAB 2015b (Mathworks, Natick, MA, USA). The lower k 2 limit was fixed as zero. The limits for k 1a and k 1p were not specified (0 ≦k 1a ≦1, 0 ≦k 1p ≦1).
The Pearson's correlation coefficient between normalized enhancement on IA-CT and perfusion parameters obtained from the CMA of IV-CT (k 1a and k 1p ) in lesions and background liver parenchyma was used as a measure of accuracy of the CMA of IV-CT in the evaluation of arterial and portal venous flows. Perfusion parameters were calculated according to various upper k 2 limits. The difference in the mean accuracy of CMA of IV-CT according to various upper k 2 limits was compared statistically using an analysis of variance (ANOVA) and multiple comparison.
All statistical analysis was performed using MATLAB 2015b (Mathworks). Probability values less than 0.05 were considered statistically significant.
The scatter plots of obtained perfusion parameters (k 1a , k 1p , and k 2 ) according to hepatic pathology are shown in  Previous studies have reported the usefulness of CMA using IV-CT, because it enables separate and quantitative evaluation of arterial and portal venous blood flows in the liver. Van Beers, et al. and Ronot, et al. reported significant changes in perfusion parameters, especially portal venous flow, among patients with cirrhosis compared to those without cirrhosis using the same compartmental model we used in this study. 9, 10 Koh, et al. evaluated arterial and portal perfusion in the liver and HCC by using CMA. They noted that the portal perfusion fraction in the HCC was lower than the normal value, and the HCC appeared hypodense on the portal venous and delayed phases. They concluded that this observation was consistent with the finding that portal perfusion progressively decreases with increasing dedifferentiation of regenerating, dysplastic, and HCC nodules. [1][2][3]15 However, a direct comparison between the perfusion parameters obtained from the CMA of IV-CT and IA-CT findings, especially in portal venous blood flow, has not been reported before. Miyazaki, et al. reported that hepatic arterial perfusion determined from the CMA of IV-CT was similar to that determined from the CMA of IA-CT, even though portal venous blood flow was not validated using CTAP in their study. 20 Therefore, we believe our study is the first to validate the appropriateness of estimating hepatic portal blood flow via the CMA of IV-CT using CTAP. Our results will have significant clinical relevance in the application of the CMA of IV-CT as a less-invasive substitutional method to IA-CT in liver imaging.
However, non-linear parameter estimation, such as the least square method in curve fitting, is needed to determine the perfusion parameters in the CMA. One of the problems in non-linear parameter estimation is that of a local minima that causes the calculation to converge not at a global optimum solution, but at a local optimum solution. To avoid convergence at the local Figure 3 The box plot showing the mean correlation coefficients between the normalized enhancement in computed tomography during hepatic arteriography (nCTHA) and hepatic arterial inflow velocity (k 1a ) of the liver and hepatic lesions according to various upper outflow velocity constant (k 2 ) limits. The best mean correlation coefficient of 0.65 is observed when the upper k 2 limit is set to 0.035. A significant decrease in concordance rate is observed when the upper k 2 limit is set to lower than 0.02 or higher than 0.1. [Color figure can be viewed at wileyonlinelibrary.com] Figure 4 The box plot showing the mean correlation coefficients between the normalized enhancement in computed tomography during arterioportography (nCTAP) and the hepatic arterial inflow velocity (k 1p ) of the liver and hepatic lesions according to various upper outflow velocity constant (k 2 ) limits. The best mean correlation coefficient of 0.69 is observed when the upper k 2 limit is set to 0.045. A significant decrease in concordance rate is observed when the upper k 2 limit is set to lower than 0.03 or higher than 0.07. [Color figure can be viewed at wileyonlinelibrary.com] minima, setting appropriate parameter limits is necessary. 18 However, previous studies have not mentioned taking precautions to avoid such a situation within the context of a perfusion study. Our results showed that an appropriate evaluation of arterial and portal venous hepatic flows was possible when the upper limit of k 2 was set neither too low nor too high. The k 2 represents venous out flow during tissue perfusion; therefore, a high k 2 correlates with rapid wash out of the contrast medium, resulting in a steep decrease in the TCC between early-and late-phase imaging. 16 Our results showed that the mean correlation coefficient between k 1a and nCTHA was relatively good (higher than 0.4) regardless of the k 2 limit. In contrast, the mean correlation coefficient between k 1p and nCTAP was significantly poor when the upper k 2 limit was lower than 0.03 or higher than 0.07. According to these results, the estimation of k 1p can be more easily affected by the k 2 limit than by the k 1a . In other words, the local minima problem can have a significant influence on the calculation of k 1p . When an unreasonably higher k 2 value was allowed in the calculation, the TCC of the HCC, which is likely to show more rapid decrease than that of the surrounding liver parenchyma, might be erroneously fitted as the local optimum solution by the TCC of the portal venous vein, resulting in an unreasonably higher k 1p than the actual portal venous blood flow in the HCC. However, when only an unreasonably lower k 2 value was allowed in the calculation, the TCC of the surrounding liver parenchyma, which is likely to show a slower decrease than that of the HCC, might be erroneously fitted as the local optimum solution by the TCC of the artery, resulting in an unreasonably lower k 1p than the actual portal venous blood flow in the surrounding liver parenchyma.
The clinical relevance of our study is that it will strengthen the reliability of liver perfusion CT study using the CMA for evaluating hepatic hemodynamics, especially in hepatic portal venous flow, as a lessinvasive substitutional method to CTAP. Our results will also provide practical and appropriate k 2 limits for calculating hepatic perfusion using the CMA. Our findings suggest that the upper k 2 limit should be set to between 0.03 and 0.07, because the mean correlation coefficient between the perfusion parameters and IA-CT contrasts are significantly high in both hepatic Figure 5 Scatter plots of obtained perfusion parameters (A: k 1a vs. k 2 B: k 1p vs. k 2 ) according to various hepatic pathologies are shown. The upper k 2 limit is set to 0.045. Representative cases of HCC (red arrow), eHCC (yellow arrow), and CCC (blue arrow) are shown in Figs. 1, 6, and 7, respectively. Note that the HCC tends to have higher k 1a and k 2 , and lower k 1p compared to the other pathologies. eHCC tends to have slightly higher k 1a and k 2 , and slightly lower k 1p compared to the surrounding livers. CCC tends to have lower k 1a , k 1p , and k 2 compared to the other pathologies. Liver: surrounding liver parenchyma, HCC: classical hepatocellular carcionoma, eHCC: early hepatocellular carcionoma, CoCC: cholangiolocellular carcinoma, mixHCC: mixed hepatocellular carcinoma, CCC: cholangiocellular carcinoma. [Color figure can be viewed at wileyonlinelibrary.com] arterial and portal venous flow evaluation. Furthermore, our results showed that hepatic arterial and portal venous hemodynamics could be evaluated to some extent using CMA even when using relatively low temporal resolution TCC data obtained from IV-CT, compared to the findings of previous studies 9, 10,15,20,21 This may imply that the proposed method can be an alternative to an additional dedicated perfusion study, thereby reducing the patient's additional burden and radiation exposure.
This study has some limitations. First, this study was retrospective and the number of subjects was small especially in histologically proven pathologies other than HCC. However, as shown in representative case presentations, the proposed method could properly discriminate faint portal venous supply of eHCC and prolonged or delayed enhancement of CCC by k 1a , k 1p , and k 2 . Although we did not have a case showing complete delayed enhancement in this study, quantitative classification of hepatic pathologies by CMA of IV-CT may be feasible in future. Second, the biological relevance of the k 2 limits is unknown, even though we validated both k 1a and k 1p using IA-CT. The k 2 is also expressed as the inverse of mean transit time, whose usefulness in the evaluation of liver diseases has been reported by several studies. 7,9,10,12 However, a gold standard method to validate k 2 is lacking, because it is an apparent value in the calculation of CMA. Further clinical validation of the k 2 values obtained using this method is needed in the future. Figure 6 The representative case of early hepatocellular carcinoma (eHCC). The lesion shows slightly increased nodular arterial enhancement on CT during hepatic arteriography (CTHA; A) and slightly decreased portal venous enhancement on CT during arterioportography (CTAP; B). The lesion shows weak nodular enhancement at arterial phase on intravenous-enhancement CT (C); however, 'washout' is not as obvious as that of classical hepatocellular carcinoma (HCC) shown in Fig. 1D at portal venous phase (D). The calculated perfusion parameter maps of eHCC and surrounding liver parenchyma (dashed squares in A, B, C, and D) are also shown (E: k 1a , F: k 1p , and G: k 2 ). Note that slightly increased k 1a and k 2 , and slightly decreased k 1p in eHCC compared to surrounding liver are quantitatively shown on parameter maps. [Color figure can be viewed at wileyonlinelibrary.com]