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Analysis and numerical simulation of an inverse problem for a structured cell population dynamics model.
Frédérique Clément1,2, Béatrice Laroche3, Frédérique Robin1,2
1Inria, Université Paris-Saclay, France.
Mathematical Biosciences and Engineering : MBE
|May 30, 2019
Summary
This study develops a mathematical model to determine cell division and migration rates from population data. The method accurately reconstructs microscopic cell behaviors from macroscopic observations in age-structured populations.
Area of Science:
- Mathematical Biology
- Population Dynamics
- Biophysics
Background:
- Age-structured cell populations are modeled using McKendrick-VonFoerster type equations.
- Multi-type models introduce unidirectional migration between cell types, affecting boundary conditions.
- Inverse problems aim to infer microscopic parameters from macroscopic measurements.
Purpose of the Study:
- To investigate a multiscale inverse problem for age-structured, multi-type cell populations.
- To develop a method for retrieving microscopic information (division and migration rates) from macroscopic data (total cell numbers).
- To establish the well-posedness of the inverse problem for both single-type and multi-type models.
Main Methods:
- Utilizing Fredholm integral equations derived from characteristic curves.
- Employing a constructive approach to determine division rates.
- Decomposing the multi-type model into nested submodels based on unidirectional migration.
- Numerical illustrations of theoretical results.
Main Results:
- Demonstrated well-posedness of the inverse problem in the single-type case.
- Successfully deduced well-posedness for the multi-type inverse problem by leveraging unidirectional migration.
- Provided numerical validation for the developed theoretical framework.
Conclusions:
- The proposed inverse problem approach is mathematically sound for both single- and multi-type cell population models.
- The method allows for the reconstruction of crucial microscopic parameters from observable macroscopic data.
- This work offers a robust framework for analyzing complex cell population dynamics.
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