An anatomic and physiological model of hepatic vascular system

Hepatic function can be characterized by the activity/time curves obtained by imaging the aorta, spleen, and liver. Nonparametric deconvolution of the activity/time curves is clinically useful as a diagnostic tool in determining organ transit times and flow fractions. The use of this technique is limited, however, because of numerical and noise problems in performing deconvolution. Furthermore, the interaction of part of the tracer with the spleen and gastrointestinal tract, before it enters the liver, further obscures physiological information in the deconvolved liver curve. In this paper, a mathematical relationship is derived relating the liver activity/time curve to portal and hepatic behavior. The mathematical relationship is derived by using transit time spectrum/residence time density theory. Based on this theory, it is shown that the deconvolution of liver activity/time curves gives rise to a complex combination of splenic, gastrointestinal, and liver dependencies. An anatomically and physiologically plausible parametric model of the hepatic vascular system has been developed. This model is used in conjunction with experimental data to estimate portal, splenic, and hepatic physiological blood flow parameters for eight normal volunteers. These calculated parameters, which include the portal flow fraction, the splenic blood flow fraction, and blood transit times are shown to adequately correspond to published values. In particular, the model of the hepatic vascular system identifies the portal flow fraction as 0.752 +/- 0.022, the splenic blood flow fraction as 0.180 +/- 0.023, and the liver mean transit time as 13.4 +/- 1.71 s. The model has also been applied to two portal hypertensive patients. The variation in some of the model parameters is beyond normal limits and is consistent with the observed pathology.