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

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 (K(1a)), from the portal vein to the liver (K(1p)), and from the liver to the plasma (k(2)) were estimated from simulated TDCs with various plasma volumes (V(0)s). 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 V(0) was the smallest, followed by those of K(1a), k(2) and K(1p) in an increasing order. The RMSEs of K(1a), K(1p) and k(2) increased with increasing V(0), while that of V(0) 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 V(0) was the greatest, followed by those of K(1a), K(1p) and k(2) in a decreasing order, while the variance of V(0) obtained from the covariance matrices was the smallest, followed by those of K(1a), K(1p) and k(2) 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 V(0). Identifiability analysis showed that the identifiability between K(1)(p) and k(2) was lower than that between K(1)(a) and k(2) or between K(1a) and K(1p). 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.