Comparing the effects of linear and one-term Ogden elasticity in a model of glioblastoma invasion.

Abstract

Our modelling of brain mechanics is based on observations of Budday and colleagues [6], who analyzed the elastic properties of human brain tissue samples under multiple loading modes. Using these data, Budday et al. determined a realistic constitutive model for brain tissue mechanics. In these studies, they found that compression and shear responses were best modelled by a non-linear one-term Ogden elasticity model, although other elasticity models are possible as well. Here we analyze the role of the elasticity model of brain tissue on the invasion speed of glioma and the resulting tissue deformation (mass effect). We present a one dimensional continuum model that couples cell dynamics to tissue mechanics. Since the mechanics of glioma-compromised brain tissue is not clear, for comprehensive studies, we incorporate both elastic and viscoelastic versions of two brain tissue elasticity models - the commonly employed linear model and the experimentally determined one-term Ogden model. For each elasticity model we identify travelling wave solutions in one dimension and calculate the corresponding invasion speeds. We find that the invasion speed is, in fact, independent of the chosen elasticity model. However, the deformations of the brain tissue, and resulting stress, between the linear and one-term Ogden models are drastically different: the Ogden model shows two orders of magnitude less deformation and three orders of magnitude less stress as compared to the linear model. Such a discrepancy might be relevant when looking at glioma-induced health complications.

Statement of significance

Cancers arising from glial cells, known as gliomas, form in the spine and the brain. The spread of glioma is not fully understood, although recent studies have highlighted the role of tissue mechanics as a main factor in the invasion process. We present a one dimensional continuum model framework of glioma invasion that incorporates proliferation and invasion of glioma cells, as well as mass effects by coupling cell dynamics to tissue mechanics. We explore both elastic and viscoelastic versions of two brain tissue elasticity models - the commonly employed linear model and the experimentally determined one-term Ogden model. This is the first time the one-term Ogden model has been incorporated into a model of glioma invasion. We show that although the choice of elasticity model does not affect the invasion speed, the deformation and stress generated in the tissue are significantly different with the Ogden model producing three orders of magnitude less deformation and stress as compared to the linear model. Such a discrepancy might be relevant when looking at glioma-induced health complications.