Strategies to tackle ill-posed inverse problems in biological systems
Abstract
Solving inverse problems are an essential part of finding unmeasurable properties in biological systems as the interested properties are represented as parameters in a mathematical model. However, most inverse problems in mathematical models based on experimental data are ill-posed. The first part of this thesis is dedicated to investigating the causes of the ill-posedness and to provide theoretical strategies to tackle the issues caused by the ill-posedness. The second part introduces three projects as three chapters that use the suggested strategies. Each chapter shows how a mathematical model based on physiological knowledge and physical law is constructed and is used to explain the mechanism that cannot be simulated by experimental data. Moreover, they demonstrate how each strategy suggested in the first part is applied and its results are interpreted in terms of biology.
Degree
Ph.D.
Advisors
Molkov, Purdue University.
Subject Area
Applied Mathematics
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