Mathematical liver modeling: hemodynamics and function in hepatectomy. (Modèles mathématiques de l'hémodynamique et de la fonction du foie lors d'une hépatectomie)

Major liver resection is being performed to treat liver lesions or for adult-to-adult living donor liver transplantation. Complications of these surgeries are related to a poor liver function. The links between liver hemodynamics, liver volume and liver function remain unclear and are important to better understand these complications. The surgery increases the resistance to blood flow in the organ, therefore it modifies liver hemodynamics. Large modifications of the portal vein hemodynamics have been associated with poor liver regeneration. Moreover the liver receives 25% of the cardiac outflow, therefore liver surgery may impact the whole blood circulation. In this context, the first goal is to investigate with mathematical models the impact of liver surgery on liver hemodynamics. The second goal is to study the liver perfusion and function with mathematical models. The first part describes the experimental conditions and reports the measurements recorded. Then, the second part focuses on the liver hemodynamics during partial hepatectomy. On one hand, the hemodynamics during several surgeries is quantitatively reproduced and explained by a closed-loop model based on ODE. On the other hand, the change of waveforms observed after different levels of liver resection is reproduced with a model of the global circulation, including 0D and 1D equations. This may contribute to a better understanding of the change of liver architecture induced by hepatectomy. Next, the transport in blood of a compound is studied. And a pharmacokinetics model and its parameter identification are developed to quantitatively analyze indocyanine green fluorescence dynamics in the liver tissue.

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