Document Detail

Mathematical modeling of the circulation in the liver lobule.
MedLine Citation:
PMID:  21034152     Owner:  NLM     Status:  In-Process    
In this paper, we develop a mathematical model of blood circulation in the liver lobule. We aim to find the pressure and flux distributions within a liver lobule. We also investigate the effects of changes in pressure that occur following a resection of part of the liver, which often leads to high pressure in the portal vein. The liver can be divided into functional units called lobules. Each lobule has a hexagonal cross-section, and we assume that its longitudinal extent is large compared with its width. We consider an infinite lattice of identical lobules and study the two-dimensional flow in the hexagonal cross-sections. We model the sinusoidal space as a porous medium, with blood entering from the portal tracts (located at each of the vertices of the cross-section of the lobule) and exiting via the centrilobular vein (located in the center of the cross-section). We first develop and solve an idealized mathematical model, treating the porous medium as rigid and isotropic and blood as a Newtonian fluid. The pressure drop across the lobule and the flux of blood through the lobule are proportional to one another. In spite of its simplicity, the model gives insight into the real pressure and velocity distribution in the lobule. We then consider three modifications of the model that are designed to make it more realistic. In the first modification, we account for the fact that the sinusoids tend to be preferentially aligned in the direction of the centrilobular vein by considering an anisotropic porous medium. In the second, we account more accurately for the true behavior of the blood by using a shear-thinning model. We show that both these modifications have a small quantitative effect on the behavior but no qualitative effect. The motivation for the final modification is to understand what happens either after a partial resection of the liver or after an implantation of a liver of small size. In these cases, the pressure is observed to rise significantly, which could cause deformation of the tissue. We show that including the effects of tissue compliance in the model means that the total blood flow increases more than linearly as the pressure rises.
Andrea Bonfiglio; Kritsada Leungchavaphongse; Rodolfo Repetto; Jennifer H Siggers
Publication Detail:
Type:  Journal Article; Research Support, Non-U.S. Gov't    
Journal Detail:
Title:  Journal of biomechanical engineering     Volume:  132     ISSN:  1528-8951     ISO Abbreviation:  J Biomech Eng     Publication Date:  2010 Nov 
Date Detail:
Created Date:  2010-11-01     Completed Date:  -     Revised Date:  -    
Medline Journal Info:
Nlm Unique ID:  7909584     Medline TA:  J Biomech Eng     Country:  United States    
Other Details:
Languages:  eng     Pagination:  111011     Citation Subset:  IM    
Department of Civil, Environmental and Architectural Engineering, University of Genoa, Genoa, Italy.
Export Citation:
APA/MLA Format     Download EndNote     Download BibTex
MeSH Terms

From MEDLINE®/PubMed®, a database of the U.S. National Library of Medicine

Previous Document:  Effects of nonlinear muscle elasticity on pelvic floor mechanics during vaginal childbirth.
Next Document:  Method for testing motion analysis laboratory measurement systems.