Parameter estimation techniques for transport equations with application to population dispersal and tissue bulk flow...

Area of Science:

• Mathematical modeling
• Computational biology
• Applied mathematics

Background:

• Transport equations are crucial for modeling various physical and biological processes.
• Accurate estimation of model parameters (coefficients, boundary, and initial data) is essential for reliable predictions.
• Existing methods may have limitations in handling complex biological systems.

Purpose of the Study:

• To develop novel, robust techniques for estimating parameters in parabolic distributed models, specifically transport equations.
• To validate the performance of these estimation schemes through biological applications.
• To provide convergence results for the proposed cubic spline approximation methods.

Main Methods:

• Development of estimation schemes based on cubic spline approximations.
• Mathematical analysis to provide convergence results for the approximation methods.
• Application and testing of the developed techniques on two distinct biological problems.

Main Results:

• Successfully developed and demonstrated techniques for estimating coefficients, boundary data, and initial data for transport equations.
• Convergence properties of the cubic spline approximation-based estimation schemes were established.
• The methods showed effective performance in modeling sucrose transport in brain white matter and insect dispersal patterns.

Conclusions:

• The proposed cubic spline approximation techniques offer a reliable approach for parameter estimation in transport equations.
• These methods have practical utility in analyzing complex biological transport phenomena.
• The study contributes to advancing computational methods in mathematical biology and biophysics.