Building up a model family for inflammations

TL;DR

The paper introduces a new method using mathematical models to study inflammation mechanisms in the liver when data is limited.

Contribution

A novel approach using model families with feasible functions to study inflammation mechanisms with limited data.

Findings

Model families help understand hierarchical mechanisms in liver inflammation.

The method translates biological knowledge into mathematical constraints.

Numerical simulations align with qualitative clinical observations.

Abstract

The paper presents an approach for overcoming modeling problems of typical life science applications with partly unknown mechanisms and lacking quantitative data: A model family of reaction–diffusion equations is built up on a mesoscopic scale and uses classes of feasible functions for reaction and taxis terms. The classes are found by translating biological knowledge into mathematical conditions and the analysis of the models further constrains the classes. Numerical simulations allow comparing single models out of the model family with available qualitative information on the solutions from observations. The method provides insight into a hierarchical order of the mechanisms. The method is applied to the clinics for liver inflammation such as metabolic dysfunction-associated steatohepatitis or viral hepatitis where reasons for the chronification of disease are still unclear and time- and space-dependent data is unavailable.

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