Development of a mathematical model of ammonia metabolism in liver cirrhosis

Hepatic encephalopathy is a neuropsychiatric syndrome, which affects most patients with advanced cirrhosis. Development of the syndrome has been associated with the accumulation of ammonia (a neurotoxin) in the brain, resulting from abnormally high levels of ammonia in the bloodstream (hyperammonaemia). Blood ammonia concentration increases with the grade of cirrhosis. Hyperammonaemia has also been linked with immune dysfunctions, making the control of toxin levels in cirrhosis essential. Yet current strategies to lower ammonia concentrations are not fully effective. Elevation of blood ammonia level has been suggested to result from deranged metabolism and the development abnormal connections between gastrointestinal blood vessels and the systemic circulation (portosystemic shunting). Most of the research on hyperammonaemia has dealt with the study of metabolic derangements. On the other hand, very few studies have tried to quantify the role of portosystemic shunting. In the first part of this thesis, we test the hypothesis that haemodynamic disturbances associated with cirrhosis are sufficient to cause hyperammonaemia. As standard distributions of organ blood flow at differing grades of cirrhosis do not exist, we develop a methodology to simulate the distribution of organ blood flow. Then we construct a theoretical model, which combines distribution of organ blood flow with individual organ fluxes of ammonia. The model is used to predict arterial ammonia levels when organ blood flow is modulated. This model demonstrates that metabolic derangements are not necessary to develop hyperammonaemia, and that the development of portosystemic shunting associated with the grade of cirrhosis is sufficient to precipitate it. The model also emphasises the importance of renal ammonia production, and suggests that limiting the renal vein flux may slow down the elevation of blood ammonia concentration. Ammonia flux in the kidney depends on both the rate of ammonia production and on the balance between urinary excretion and renal vein reabsorption. In the last part of this thesis, we develop a mathematical model to investigate which transport components within the renal medulla control the rate of urinary ammonia excretion. We suggest a mechanism by which pH environment in the outer medulla could increase the rate of urinary excretion.