Image-based Parameter Optimization of a mechanically-coupled Brain Tumor Growth Model

Glioblastoma (GBM) is the most frequent malignant brain tumor in adults. Its growth is characterized by infiltration of surrounding healthy tissue, and the formation of a necrotic core. GBM presents with varying degree of mass-effect which results in healthy-tissue deformation, midline shift or herniation. Biomechanical forces, such as those resulting from displacive tumor growth, shape the tumor environment, contribute to tumor progression [1] and may affect treatment response and outcome. We hypothesize that different growth “phenotypes” can be distinguished by mathematical models that estimate the forces responsible for tissue displacement. However, most approaches for estimating brain tumor growth parameters from patient imaging do not account for the tumor’s mass-effect. We have previously developed a mechanically–coupled reaction-diffusion model [2] that captures three dominant aspects of macroscopic GBM growth: (a) tumor cell proliferation, (b) the diffuse invasion of the growing tumor into surrounding healthy tissue, and (c) the resulting mass effect. Here, we propose an optimization approach to estimate three patient-specific parameters of this model: tumor cell proliferation rate, cell motility, as well as a coupling coefficient that links local tumor cell concentration to tumor-induced mechanical strains. The forward problem is solved using the Finite Element Method. The inverse problem is formulated as a PDE constrained optimization problem that aims at minimizing the difference between observed and predicted tumor cell distribution and induced displacements. Target fields are inferred from magnetic resonance (MR) images at different observation time points. The efficient solution of the inverse problem relies on the adjoint method and FENICS dolphin-adjoint [3] for its implementation. Performance of the parameter estimation approach was evaluated on synthetic data generated by solving the forward problem on a brain atlas. MR images from the public TCGA-GBM data set were used for tests on clinical data. References [1] R. K. Jain et al. Annu. Rev. Biomed. Eng. 16.1 (2014), pp. 321–346. [2] D. Abler and P. Büchler. CMBBE. Ed. by A. Gefen and D. Weihs (2018), pp. 57–64. [3] P. Farrell, et al. SIAM J. Sci. Comput 35.4 (2013), pp. C369-C393