Modelling of blood circulation in the liver

Jennifer Siggers (Imperial College London)

Thursday 5th November, 2009 14:00-15:00 326, Maths Department


Blood flow in the liver has several unique features compared with other organs in the body. The liver is made up of functional units called lobules, and blood flows across these from the arterial to the venous system. At the same time, substances contained in the blood (such as oxygen, other nutrients and drugs) are exchanged with the liver cells. There are very few previous models of the blood flow in the liver, and each of them is based on different modelling principles. In this talk I will present a new model of the flow in a lobule. We treat the small vessels as a porous medium, and exploit the regularity of the typical architecture of the arterial and venous systems. We discuss three ways of analysing the model; two are analytical and one is numerical. In formulating the model, we made several idealisations, and we investigate their validity by considering adaptations to account for new features. High-resolution images of the small vessels reveal their orientation appears to be directed preferentially towards the veins, and we adapt the model to account for this. In the second modification, we use a non-Newtonian model of the blood that accounts for its shear-thinning behaviour. In the third adaptation, we investigate the effect of compliance of the tissue due to changes in pressure within the tissue. The latter modification is particularly relevant in the case of small-for-size liver syndrome, which occurs when a patient has a liver of too small mass for their own body weight and is frequently associated with liver transplants and partial resections of livers. The syndrome causes pressures in the liver to rise, which may lead to deformation of the tissue and hence changes in the resistance of the vessels. A better understanding of this may lead to improved treatment of the syndrome. We conclude with a discussion of other potential applications of the model.

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