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Mathematical modeling of liver fibrosis

1. Mathematical Biosciences Institute & Department of Mathematics, The Ohio State University, Columbus, OH 43210, USA
2. Department of Mathematics, The Penn State University, University Park, PA 16802, USA

Fibrosis is the formation of excessive fibrous connective tissue in an organ or tissue, which occurs in reparative process or in response to inflammation. Fibrotic diseases are characterized by abnormal excessive deposition of fibrous proteins, such as collagen, and the disease is most commonly progressive, leading to organ disfunction and failure. Although fibrotic diseases evolve in a similar way in all organs, differences may occur as a result of structure and function of the specific organ. In liver fibrosis, the gold standard for diagnosis and monitoring the progression of the disease is biopsy, which is invasive and cannot be repeated frequently. For this reason there is currently a great interest in identifying non-invasive biomarkers for liver fibrosis. In this paper, we develop for the first time a mathematical model of liver fibrosis by a system of partial differential equations. We use the model to explore the efficacy of potential and currently used drugs aimed at blocking the progression of liver fibrosis. We also use the model to develop a diagnostic tool based on a combination of two biomarkers.

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