Abstract
A convenient geometrical description of the microvascular network is necessary for computationally efficient mathematical modelling of liver perfusion, metabolic and other physiological processes. The tissue models currently used are based on the generally accepted schematic structure of the parenchyma at the lobular level, assuming its perfect regular structure and geometrical symmetries. Hepatic lobule, portal lobule, or liver acinus are considered usually as autonomous functional units on which particular physiological problems are studied. We propose a new periodic unit-the liver representative periodic cell (LRPC) and establish its geometrical parametrization. The LRPC is constituted by two portal lobulae, such that it contains the liver acinus as a substructure. As a remarkable advantage over the classical phenomenological modelling approaches, the LRPC enables for multiscale modelling based on the periodic homogenization method. Derived macroscopic equations involve so called effective medium parameters, such as the tissue permeability, which reflect the LRPC geometry. In this way, mutual influences between the macroscopic phenomena, such as inhomogeneous perfusion, and the local processes relevant to the lobular (mesoscopic) level are respected. The LRPC based model is intended for its use within a complete hierarchical model of the whole liver. Using the Double-permeability Darcy model obtained by the homogenization, we illustrate the usefulness of the LRPC based modelling to describe the blood perfusion in the parenchyma.
Highlights
The liver as a vital organ plays in the human body a fundamental role in its numerous functions
The liver parenchyma at the mesoscopic level with characteristic lengths 100μm is constituted by functional units which are defined in terms of the principal microvascular vessels associated with portal vein (PV), hepatic vein (HV), and hepatic artery (HA)
We introduced a parameterized geometrical model of the liver parenchyma unit, the liver representative periodic cell (LRPC), which comprises two functional liver units—the portal lobule and the acinus
Summary
The liver as a vital organ plays in the human body a fundamental role in its numerous functions. Any disease or pathological state of the liver tissue can cause serious health problems, even death of the patient and needs to be appropriately treated. The understanding of liver perfusion on the multiple scales is crucial for the surgical treatment as the liver resection, transplantation and for understanding how the liver perfusion is modified by diffuse parenchymatous diseases such as cirrhosis, steatohepatitis, sinusoidal obstruction syndrome (last two are connected with modern chemotherapies regiment), etc [1, 2].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
