Error analysis of the quantification of hepatic perfusion using a dual-input single-compartment model

Abstract

We performed an error analysis of the quantification of liver perfusion from dynamic contrast-enhanced computed tomography (DCE-CT) data using a dual-input single-compartment model for various disease severities, based on computer simulations. In the simulations, the time-density curves (TDCs) in the liver were generated from an actually measured arterial input function using a theoretical equation describing the kinetic behavior of the contrast agent (CA) in the liver. The rate constants for the transfer of CA from the hepatic artery to the liver (K1a), from the portal vein to the liver (K1p), and from the liver to the plasma (k2) were estimated from simulated TDCs with various plasma volumes (V0s). To investigate the effect of the shapes of input functions, the original arterial and portal-venous input functions were stretched in the time direction by factors of 2, 3 and 4 (stretching factors). The above parameters were estimated with the linear least-squares (LLSQ) and nonlinear least-squares (NLSQ) methods, and the root mean square errors (RMSEs) between the true and estimated values were calculated. Sensitivity and identifiability analyses were also performed. The RMSE of V0 was the smallest, followed by those of K1a, k2 and K1p in an increasing order. The RMSEs of K1a, K1p and k2 increased with increasing V0, while that of V0 tended to decrease. The stretching factor also affected parameter estimation in both methods. The LLSQ method estimated the above parameters faster and with smaller variations than the NLSQ method. Sensitivity analysis showed that the magnitude of the sensitivity function of V0 was the greatest, followed by those of K1a, K1p and k2 in a decreasing order, while the variance of V0 obtained from the covariance matrices was the smallest, followed by those of K1a, K1p and k2 in an increasing order. The magnitude of the sensitivity function and the variance increased and decreased, respectively, with increasing disease severity and decreased and increased, respectively, with increasing stretching factor except for V0. Identifiability analysis showed that the identifiability between K1p and k2 was lower than that between K1a and k2 or between K1a and K1p. In conclusion, this study will be useful for understanding the accuracy and reliability of the quantitative measurement of liver perfusion using a dual-input single-compartment model and DCE-CT data.