Non-operable glioblastoma: Proposition of patient-specific forecasting by image-informed poromechanical model

Abstract

We propose a novel image-informed glioblastoma mathematical model within a reactive multiphase poromechanical framework. Poromechanics offers to model in a coupled manner the interplay between tissue deformation and pressure-driven fluid flows, these phenomena existing simultaneously in cancer disease. The model also relies on two mechano-biological hypotheses responsible for the heterogeneity of the GBM: hypoxia signaling cascade and interaction between extra-cellular matrix and tumor cells. The model belongs to the category of patient-specific image-informed models as it is initialized, calibrated and evaluated by the means of patient imaging data. The model is calibrated with patient data after 6 cycles of concomitant radiotherapy chemotherapy and shows good agreement with treatment response 3 months after chemotherapy maintenance. Sensitivity of the solution to parameters and to boundary conditions is provided. As this work is only a first step of the inclusion of poromechanical framework in image-informed glioblastoma mathematical models, leads of improvement are provided in the conclusion.

Statement of Significance: In this study, we employ mechanics of reactive porous media to effectively model the dynamic progression of a glioblastoma. Traditionally, glioblastoma tumors are surgically removed a few weeks post-diagnosis. To address this, we focus on a non-operable clinical scenario which allows us to have sufficient time points for the calibration and subsequent validation of our mathematical model. It is paramount to underscore that the tumor’s evolution is significantly influenced by chemotherapy and radiotherapy. These therapeutic effects find incorporation within our mathematical framework. Notably, the approach we present is distinctive for two key reasons: Firstly, the mathematical model inherently captures the complex multiphase and hierarchical nature of brain tissue. Secondly, our constitutive laws factor in the ever-changing properties of cells and tissues, mirroring the local phenotypic alterations observed within the tumor. This work constitutes an initial stride towards systematically integrating multiphase poromechanics into patient-specific glioblastoma growth modeling. As we look ahead, we acknowledge areas for potential enhancement in pursuit of advancing this promising direction.