Modeling glioma invasion with anisotropy- and hypoxia-triggered motility enhancement: From subcellular dynamics to macroscopic PDEs with multiple taxis

Abstract

We deduce a model for glioma invasion that accounts for the dynamics of brain tissue being actively degraded by tumor cells via excessive acidity production, but also according to the local orientation of tissue fibers. Our approach has a multiscale character: we start with a microscopic description of single cell dynamics including biochemical and/or biophysical effects of the tumor microenvironment, translated on the one hand into cell stress and corresponding forces and on the other hand into receptor binding dynamics. These lead on the mesoscopic level to kinetic equations involving transport terms with respect to all considered kinetic variables and eventually, by appropriate upscaling, to a macroscopic reaction–diffusion equation for glioma density with multiple taxis, coupled to (integro-)differential equations characterizing the evolution of acidity and macro- and mesoscopic tissue. Our approach also allows for a switch between fast and slower moving regimes, according to the local tissue anisotropy. We perform numerical simulations to assess the importance of each tactic term and investigate the influence of two models for tissue dynamics on the tumor shape. We also suggest how the model can be used to perform a numerical necrosis-based tumor grading or support radiotherapy planning by dose painting. Finally, we discuss alternative ways of including cell level environmental influences in such a multiscale modeling approach, ultimately leading in the macroscopic limit to (multiple) taxis.

Multiscale modeling of glioma pseudopalisades: contributions from the tumor microenvironment

“…The no-flux boundary conditions are obtained through the upscaling procedure (as done e.g., in Corbin et al (2021) for a related problem). For the tumor diffusion tensor D T we require…”

“…glioma migration along its constituent fibers. This is a relevant information for the existing models of glioma invasion built upon ideas commonly employed within the KTAP framework and which take into account the underlying brain structure and its properties in trying to predict the tumor extent and its aggressiveness; we refer to Hillen (2006) and Corbin et al (2021) for two works where such issue is explicitly addressed. On the other hand, this could also be relevant from a biological viewpoint; indeed, to our knowledge such information is not available in the biological literature.…”

A Flux-Limited Model for Glioma Patterning with Hypoxia-Induced Angiogenesis

“…In this work, we aim to use a related approach and to extend the model in [17] such as to account for hypoxia-triggered angiogenesis and its effects on the pseudopalisade patterns. We thereby continue in the line of previous works [21][22][23][24][25][26][27][28][29][30][31] dealing with cancer cell migration in heterogeneous tissues. The deduced macroscopic system is able to generate the expected patterns; indeed, accounting for angiogenic effects leads to disruption of the garland-like structure of glioma pseudopalisades and transient behavior as consequences of proton uptake and nutrient supply by ECs forming capillaries.…”

Modeling Interactions among Migration, Growth and Pressure in Tumor Dynamics

“…Taken into account the non-uniform growth proposed in (8) and the definition of P I in terms of strains (6), the relative deformation is:…”

“…Due to the relevance of the issue together with the technical difficulties of obtaining data from in vivo experiments, mathematical modeling appears to be a useful tool to predict and anticipate tumor development. Some papers [2][3][4][5][6] highlight the challenges surrounding the dynamics of cancer and review mathematical models that attempt to respond to these concerns. From one side, research has been focused, on a large degree, on models that control growth and treatments through biochemical interactions that identify morphogens and target genes involved in deregulation and growth associated with tumor processes [4,7].…”