Randomness-aware multiscale models of glioma invasion and treatment

In this work, we develop a stochastic multiscale model for glioma growth and invasion in the brain, incorporating the effects of therapeutic interventions. The model accounts for tumor cell migration influenced by brain tissue heterogeneity and anti-crowding mechanisms, while explicitly addressing treatment-related uncertainties through stochastic processes. Starting from a microscopic description of individual cell dynamics, we derive the corresponding system of macroscopic random reaction-diffusion-taxis equations governing cell density and tissue evolution. Finally, we conduct several numerical experiments to assess the efficacy of different treatment protocols, evaluated with respect to both established and newly proposed clinical criteria and measurable outcomes.

💡 Research Summary

The paper presents a comprehensive stochastic multiscale framework for modeling glioma invasion and radiotherapy response. Starting from a microscopic description, the authors model the binding and unbinding of two classes of membrane receptors—those that attach to extracellular matrix fibers (y₁) and those mediating cell‑cell adhesion (y₂). These dynamics follow simple mass‑action kinetics and are coupled to the macroscopic tissue volume fraction Q(t,x) and tumor cell density M(t,x). Radiation effects are incorporated through the classic linear‑quadratic (LQ) survival fractions S_Q and S_M, which depend on dose d_r and radiosensitivity parameters ρ₁, ρ₂ for healthy and tumor cells respectively.

By assuming equal detachment rates, the total bound receptor concentration y = y₁ + y₂ is reduced to a single ODE whose steady state y* depends on Q and M. The deviation z = y* – y drives a term G(z,Q,M) that captures how gradients of tissue fibers and tumor density bias cell motion. This microscopic state feeds directly into the mesoscopic kinetic transport equation (KTE) for the cell density p(t,x,v,z). The KTE includes (i) a transport term for constant‑speed motion, (ii) a drift term ∂_z(G p) reflecting the receptor‑mediated bias, (iii) a turning operator L