Mathematical modeling of glioma invasion and therapy approaches via kinetic theory of active particles

TL;DR

A multiscale model is proposed for study the effect of combined therapies on glioma spread in the brain under the influence of vascularization, which accounts for the interplay between the different components of the neoplasm and the healthy tissue.

Abstract

We propose here a multiscale model for study the effect of combined therapies on glioma spread in the brain under the influence of vascularization. The model accounts for the interplay between the different components of the neoplasm and the healthy tissue and it investigates and compares various therapy approaches. Precisely, these involve radio- and chemotherapy in a concurrent or adjuvant manner together with anti-angiogenic therapy affecting the vascular component of the system. We assess tumor growth and spread on the basis of DTI data, which allows us to reconstruct a realistic brain geometry and tissue structure, and we apply our model to real glioma patient data. In this latter case, a space-dependent radiotherapy description is considered using data about the corresponding isodose curves.

Figures (9)

• Figure 1: Initial conditions of system \ref{['mac_set_neu']}. The five columns refer to densities of glioma, ECs, VEGFs, necrotic matter, and healthy tissue, respectively. The initial densities in the bottom row are visualized on the zoomed domain $\bar{\Omega}=[-35, 5] \times [-15, 25]$.
• Figure 5: Experiment (A). Numerical simulation of system \ref{['mac_set_neu']} with the parameters listed in Table 1 and without any treatment.
• Figure 6: Experiment (B). Differences between the respective solution components of Model \ref{['mac_set_neu']} and of the analogous one with equation \ref{['Comp1']} (first and second column) or equation \ref{['Comp2']} (third and fourth column) for ECs at 18 weeks (upper row), 24 weeks (middle row), and 30 weeks (lower row).
• Figure 7: Experiment (C). Numerical simulation of system \ref{['mac_set_neu']} with the parameters listed in Table 1 and for the therapeutic plan schematized in Figure \ref{['therapy_plan_scheme1']}.
• Figure 8: Differences between experiment (C) and experiment (D). Differences between the respective solution components of system \ref{['mac_set_neu']} with the two different treatment schedules sketched in Figures \ref{['therapy_plan_scheme1']} and \ref{['therapy_plan_scheme2']} at 27 weeks (first row), 30 weeks (second row), 40 weeks (third row), and 50 weeks (last row).