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Identification of a chemotactic sensitivity in a coupled system
K Renee Fister1, Maeve L McCarthy
1Department of Mathematics and Statistics, Murray State University, Murray, KY 42071, USA. renee.fister@murraystate.edu
Mathematical Medicine and Biology : a Journal of the IMA
|July 18, 2008
Summary
This study recovers cell chemotactic sensitivity from experimental data, even with complex, non-linear relationships. Inverse problem techniques and Tikhonov regularization provide reliable methods for analyzing cell movement following chemical gradients.
Area of Science:
- Mathematical biology
- Cellular biophysics
- Biochemical engineering
Background:
- Chemotaxis, the directed movement of cells along chemical gradients, is crucial in biological processes like immune response and tumor development.
- Understanding and quantifying chemotactic behavior is essential for modeling and controlling these phenomena.
- Current methods often assume linear relationships, limiting their applicability to complex biological systems.
Purpose of the Study:
- To develop and validate a method for recovering chemotactic sensitivity from experimental data.
- To address the challenge of non-linear dependence of chemotactic parameters on state variables.
- To analyze the existence of solutions for the forward problem in chemotaxis.
Main Methods:
- Utilizing inverse problem techniques for parameter identification.
- Applying Tikhonov regularization to ensure stable and convergent solutions.
- Analyzing the forward problem to establish the existence of solutions.
- Exploring concentration-dependent chemotactic terms through numerical simulations.
Main Results:
- Successfully recovered chemotactic sensitivity, even with non-linear parameter dependencies.
- Demonstrated the convergence and stability of Tikhonov regularization for this inverse problem.
- Provided theoretical analysis on the existence of solutions for the forward chemotaxis model.
- Investigated the impact of concentration on chemotactic behavior via numerical results.
Conclusions:
- The developed inverse problem approach effectively identifies chemotactic sensitivity in complex scenarios.
- Tikhonov regularization offers a robust mathematical framework for analyzing chemotaxis.
- This work advances the quantitative understanding of cell migration in biological systems.
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