Mathematical modelling of microcirculation in a poroelastic model of the liver, and its application to the study of ascites

The liver performs many vital functions in the body and has a natural ability to regenerate itself, except in the case of repeated or severe damage often caused by liver diseases. Damage due to liver disease occurs in the form of scarring of healthy liver tissue, a process known as fibrosis. Chronic fibrosis can lead to liver cirrhosis, a condition that is irreversible and often requires liver transplantation. Cirrhosis manifests itself in the form of increased tissue stiffness and decreased tissue permeability, which then leads to a marked decrease in blood perfusion and functioning of the liver tissue. As a homeostatic response, hepatic portal blood pressure also increases, which then leads to an increased outflow of excess interstitial fluid across the surface of the liver and into the surrounding peritoneal cavity. The abnormal accumulation of fluid in the peritoneal cavity is known as ascites and is characterised by large abdominal girth, abdominal pain and discomfort. The aim of this thesis was to model the microcirculation of blood and interstitial fluid in the liver, so as to investigate the changes in vasculature that lead to impaired blood perfusion and the formation of ascites. To that end, we have developed a dual-porosity, dual-permeability deformable model of the liver tissue using the Biot theory of poroelasticity. We then used the model as part of a compartmental model of the peritoneal cavity and investigated the effect of liver disease (fibrosis/cirrhosis) on the accumulation of fluid in the peritoneal cavity. By varying the degree of liver tissue stiffness, we simulated and compared different stages of liver fibrosis, as well as predicted the severity of the resulting ascites. This makes our model an improvement on the current literature, with the aim of future use in informing and improving disease treatment strategies.Open Acces

Modelling bispecific monoclonal antibody interaction with two cell membrane targets indicates the importance of surface diffusion

We have developed a mathematical framework for describing a bispecific monoclonal antibody interaction with two independent membrane-bound targets that are expressed on the same cell surface. The bispecific antibody in solution binds either of the two targets first, and then cross-links with the second one whilst on the cell surface, subject to rate-limiting lateral diffusion step within the lifetime of the monovalently engaged antibody-antigen complex. At experimental densities, only a small fraction of the free targets is expected to lie within the reach of the antibody binding sites at any time. Using ordinary differential equation and Monte Carlo simulation-based models, we validated this approach against an independently published anti-CD4/CD70 DuetMab experimental data set. As a result of dimensional reduction, the cell surface reaction is expected to be so rapid that, in agreement with the experimental data, no monovalently bound bispecific antibody binary complexes accumulate until cross-linking is complete. The dissociation of the bispecific antibody from the ternary cross-linked complex is expected to be significantly slower than that from either of the monovalently bound variants. We estimate that the effective affinity of the bivalently bound bispecific antibody is enhanced for about four orders of magnitude over that of the monovalently bound species. This avidity enhancement allows for the highly specific binding of anti-CD4/CD70 DuetMab to the cells that are positive for both target antigens over those that express only one or the other We suggest that the lateral diffusion of target antigens in the cell membrane also plays a key role in the avidity effect of natural antibodies and other bivalent ligands in their interactions with their respective cell surface receptors

Modelling Afferent Nerve Responses to Bladder Filling

A sensation of fullness in the bladder is a regular experience, yet the mechanisms that act to generate this sensation remain poorly understood. This is an important issue because of the clinical problems that can result when this system does not function properly. The aim of the study group activity was to develop mathematical models that describe the mechanics of bladder filling, and how stretch modulates the firing rate of afferent nerves. Several models were developed, which were qualitatively consistent with experimental data obtained from a mouse model

Modelling Afferent Nerve Responses to Bladder Filling

A sensation of fullness in the bladder is a regular experience, yet the mechanisms that act to generate this sensation remain poorly understood. This is an important issue because of the clinical problems that can result when this system does not function properly. The aim of the study group activity was to develop mathematical models that describe the mechanics of bladder filling, and how stretch modulates the firing rate of afferent nerves. Several models were developed, which were qualitatively consistent with experimental data obtained from a mouse model