In this chapter we have presented mathematical modeling approaches to biological pattern
formation. While reaction-diffusion models are appropriate to describe the spatio-temporal …

We propose a multiscale model for tumor cell migration in a tissue network. The system of
equations involves a structured population model for the tumor cell density, which besides …

This volume collects ten surveys on the modeling, simulation, and applications of active
particles using methods ranging from mathematical kinetic theory to nonequilibrium …

Epithelial to mesenchymal transition (EMT) is a complex biological process that plays a key
role in cancer progression and metastasis formation. Its activation results in epithelial cells …

Generating MR-derived growth pattern models for glioblastoma multiforme (GBM) has been
an attractive approach in neuro-oncology, suggesting a distinct pattern of lesion spread with …

We present a numerical scheme for solving a parameter estimation problem for a model of
low-grade glioma growth. Our goal is to estimate the spatial distribution of tumor …

Cells move by run and tumble, a kind of dynamics in which the cell alternates runs over
straight lines and re-orientations. This erratic motion may be influenced by external factors …

When it comes to the human brain, models that closely mimic in vivo conditions are lacking.
Living neuronal tissue is the closest representation of the in vivo human brain outside of a …

Starting from kinetic transport equations and subcellular dynamics we deduce a multiscale
model for glioma invasion relying on the go-or-grow dichotomy and the influence of …

Glioma is a broad class of brain and spinal cord tumors arising from glia cells, which are the
main brain cells that can develop into neoplasms. They are highly invasive and lead to …