Randomness-aware multiscale models of glioma invasion and treatment

TL;DR

This work addresses glioma invasion under radiotherapy by constructing a randomness-aware multiscale framework that links microscopic receptor-mediated cell dynamics to mesoscopic kinetic transport and to macroscopic random PDEs for tumor density $M(t,x)$ and healthy tissue $Q(t,x)$. A parabolic scaling yields a macroscopic system with a diffusion tensor $\\mathbb{D}_M(x)$ derived from tissue orientation, while radiotherapy introduces stochastic effects through an Ornstein–Uhlenbeck process $\xi_t$ in the operator $R_M(d_r,\xi_t)$. Numerical experiments on a 2D brain slice evaluate treatment protocols via clinically meaningful metrics: TCP, NTCP, UTCP, RECIST-based responses, and post-treatment relapse times, revealing that intermediate fractionation ($D_T\in[25,35]$, notably $D_T=30$) offers a favorable balance between tumor control and normal-tissue toxicity; imaging thresholds bias volume estimates and relapse detection. Overall, the paper provides a first systematic, randomness-aware multiscale modeling framework that connects cellular-scale stochasticity to population-level predictions, with potential to improve robustness in radiotherapy planning for glioma patients by leveraging clinically aligned evaluation criteria.

Abstract

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.

Figures (10)

• Figure 1: Definition of the initial setting. Schematic representation of the model initialization, including the radiotherapy planning volumes. The second row shows magnifications of the main area interested by the tumor mass.
• Figure 2: Tumor area contour. Identification of the tumor-occupied region in a brain slice with (solid red line) and without (dashed red line) application of the $T_2$ detection threshold. The tumor distribution results from a 12-week simulation of the model without treatment, starting from the initial conditions given in \ref{['IC_M']}–\ref{['IC_Q']}. The right plot shows a magnification of the main area affected by the tumor.
• Figure 3: Impact of the detection threshold on tumor volume quantification. Comparison of simulated mean tumor volume ($V_T$) over time with (right panel) and without (left panel) application of the $T_2$ detection threshold for the different treatment protocols. In the figure legend the number $D_T$ of days for each treatment is indicated. Mean tumor volumes were obtained by averaging the results of 200 independent simulations of the same experiment.
• Figure 4: TCP, NTCP, and UTCP. Comparison of the mean TCP (left panel), NTCP (middle panel), and UTCP (right panel) evolution over time for the different treatment protocols. In the figure legend the number of $D_T$ for each treatment is indicated. Mean values for TCP, NTCP, and UTCP were obtained by averaging the results of 200 independent simulations of the same experiment.
• Figure 5: $R$-score analysis. R-score distribution for the different treatment protocols, with $D_T$ values shown on the x-axis.

Theorems & Definitions (1)

• Remark