Mean first-passage time of cell migration in confined domains
H. Serrano, R.F. Álvarez-Estrada, G.F. Calvo
Mathematical Methods in the Applied Sciences 46, 7435-7453 (2023)
Fernández Calvo, Gabriel.
A number of key biological processes involving cell migration in which cells traverse boundaries separating well-defined tissues can be modeled in terms of mean first-passage time (MFPT) problems in confined domains. Motivated by this scenario, we consider suitable three-dimensional domains on which MFPT functions , fulfilling a Poisson-like equation and different boundary conditions on the surface enclosing, are studied. By extending methods coming from potential theory, the calculation of boils down to dealing with inhomogeneous linear integral equations having singular kernels. The latter are solved compactly and yield consistent times for several domains and homogeneous boundary conditions. Moreover, the integral equation approach allows us to analyze the MFPT with mixed (Dirichlet-Neumann) boundary conditions for the case of a closed spherical surface with Dirichlet conditions, except for a small complementary surface domain with Neumann conditions.