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

We developed techniques for estimating the coefficients, boundary data, and initial data associated with transport equations (or more generally, parabolic distributed models). Our estimation schemes are based on cubic spline approximations, for which convergence results are given. We discuss the performance of these techniques in two investigations of biological interest: (1) transport of labeled sucrose in brain tissue white matter, (2) insect dispersal that cannot be modeled by a random diffusion mechanism alone.