The models of the microcirculation of blood and interstitial fluid in the human liver
lobule are developed based on the classical hexagon model of Kiernan. Both blood and
interstitial flows in the lobule are treated as flows in porous medium connected via the
fenestrated membrane of sinusoids. Several important physiological components are developed
and included in the models. The lobule with tissue elasticity shows that the
pressure-flux relationship is non-linear and the poroelastic model has more compliance
than the solid elastic model. Models of the interstitial flow in both a single lobule and
the whole liver are also developed. The results show that our models can predict the
amount of interstitial fluid drainage including the ascites. From the parameter studies,
we find that the permeabilities of the sinusoids and the interstitial space, and the portal
pressure are the most important factors on ascites production.
We further investigate the oxygen transportation and uptake by liver cells using the
advection–diffusion equations and Michaelis-Menten kinetics. The studies show that the
main mechanism of oxygen transportation within the sinusoids is advection; however,
the transportations within the interstitial space and across the fenestrated endothelial
cells are mainly from diffusion process. The effect of the arrangement of the vessels and the geometry of the lobule on blood
perfusion and oxygen distribution is also studied. The results show that the classical
hexagonal lobule with the vascular septa provides the optimal perfusion compared to
other geometries of the lobule.
In summary, this thesis contributes to the development of mathematical models of several
important features in the liver microcirculation such as the tissue elasticity, the
interstitial flow, the oxygen distribution, and the arrangement of the vessels in the lobule.