  We present a 3D fully-automatic method for the calibration of partial
differential equation (PDE) models of glioblastoma (GBM) growth with mass
effect, the deformation of brain tissue due to the tumor. We quantify the mass
effect, tumor proliferation, tumor migration, and the localized tumor initial
condition from a single multiparameteric Magnetic Resonance Imaging (mpMRI)
patient scan. The PDE is a reaction-advection-diffusion partial differential
equation coupled with linear elasticity equations to capture mass effect. The
single-scan calibration model is notoriously difficult because the precancerous
(healthy) brain anatomy is unknown. To solve this inherently ill-posed and
ill-conditioned optimization problem, we introduce a novel inversion scheme
that uses multiple brain atlases as proxies for the healthy precancer patient
brain resulting in robust and reliable parameter estimation. We apply our
method on both synthetic and clinical datasets representative of the
heterogeneous spatial landscape typically observed in glioblastomas to
demonstrate the validity and performance of our methods. In the synthetic data,
we report calibration errors (due to the ill-posedness and our solution scheme)
in the 10\%-20\% range. In the clinical data, we report good quantitative
agreement with the observed tumor and qualitative agreement with the mass
effect (for which we do not have a ground truth). Our method uses a minimal set
of parameters and provides both global and local quantitative measures of tumor
infiltration and mass effect.
