MULTI-SCALE HEMODYNAMIC MODEL OF THE LIVER WITH FRACTAL THEORY

The liver is an important organ for maintaining the health and normal physiological functions of the human body. Rational modeling of hepatic hemodynamics can help to better understand these changes and provide more accurate disease prediction methods. A multi-scale hepatic hemodynamic model was developed, which includes the portal vein, hepatic artery, hepatic vein, and lobular portion of the liver. The complex branching network structure in the liver was described by the fractal scale principle, and the structure of the tree-like bifurcation vascular network was modeled. The Poiseuille equation was used to describe the flow pattern of blood in the portal vein and hepatic vein vessels. For blood flow in the hepatic arterial vessels, the Forchheimer equation was used to describe the flow pattern considering its pulsatility and non-uniformity. The flow of blood through the hepatic lobules was described as the flow through the porous medium following Darcy’s Law. The accuracy of the model was verified by the consistency of the theoretical calculations with the actual data. The relationship between the structural characteristics of the hepatic vascular network and pressure drop was analyzed by the model established in this paper. As the diameter ratio decreases, the pressure drop increases in all vascular systems, but the response is most pronounced in the hepatic artery. The pressure drop in the three types of vascular networks exhibits an exponential decrease with increasing root vessel diameter. With an increase in root vessel length, the pressure drop in the vascular network increases linearly. The multi-scale liver blood flow model established in this paper can realize the pressure drop estimation of the liver vascular system by inputting the image pictures and flow data of the liver, which provides a feasible method to realize the non-invasive pressure measurement of the liver.