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Mathematical modeling of liver tumor

William Weens 1, 2 
Abstract : As recently demonstrated for liver regeneration after drug-induced damage, organization and growth processes can be systematically analyzed by a process chain of experiments, image analysis and modeling [43]. The authors of [43] were able to quantitatively characterize the architecture of liver lobules, the repetitive functional building blocks of liver, and turn this into a quantitative mathematical model capable to predict a previously unrecognized order mechanism. The model prediction could subsequently be experimentally validated. Here, we extend this model to the multi-lobular scale, guided by experimental findings on carcinogenesis in liver [15]. We explore the possible scenarios leading to the different tumor phenotypes experimentally observed in mouse. Our model considers the hepatocytes, the main cell type in liver, as individual units with a single cell based model and the blood vessel system as a network of extensible objects. Model motion is computed based on explicit discretized Langevin equation and cell interactions are either Hertz or JKR forces. The model is parameterized by measurable values on the cell and tissue scale and its results are directly compared to the experimental findings. In a fundamental first step we study if Wnt and Ras signaling pathways can explain the observation of [15], that instantaneous proliferation in mutated mice can only be observed if around 70% of the hepatocytes become APC depleted. In a second step, we show a sensitivity analysis of the model on the vessel stiffness and relate it to a tumor phenotype (experimentally observed) where the tumor cells are well differentiated. We integrate in a third step the destruction of vasculature by tumor cells to relate it to another experimentally observed tumor phenotype characterized by the absence of blood vessels. Finally, in the last step we show that effects that are detectible for small tumor nodules and reflect properties of the tumor cells, are not reflected in the tumor shape or phenotype at tumor sizes exceeding half of the lobule size.
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Submitted on : Monday, January 21, 2013 - 5:34:58 PM
Last modification on : Friday, February 4, 2022 - 3:20:51 AM
Long-term archiving on: : Monday, April 22, 2013 - 3:56:58 AM

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  • HAL Id : tel-00779177, version 1

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William Weens. Mathematical modeling of liver tumor. Numerical Analysis [math.NA]. Université Pierre et Marie Curie - Paris VI, 2012. English. ⟨NNT : ⟩. ⟨tel-00779177⟩

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