  Our objective is the calibration of mathematical tumor growth models from a
single multiparametric scan. The target problem is the analysis of preoperative
Glioblastoma (GBM) scans. To this end, we present a fully automatic
tumor-growth calibration methodology that integrates a single-species
reaction-diffusion partial differential equation (PDE) model for tumor
progression with multiparametric Magnetic Resonance Imaging (mpMRI) scans to
robustly extract patient specific biomarkers i.e., estimates for (i) the tumor
cell proliferation rate, (ii) the tumor cell migration rate, and (iii) the
original, localized site(s) of tumor initiation. Our method is based on a
sparse reconstruction algorithm for the tumor initial location (TIL). This
problem is particularly challenging due to nonlinearity, ill-posedeness, and
ill conditioning. We propose a coarse-to-fine multi-resolution continuation
scheme with parameter decomposition to stabilize the inversion. We demonstrate
robustness and practicality of our method by applying the proposed method to
clinical data of 206 GBM patients. We analyze the extracted biomarkers and
relate tumor origin with patient overall survival by mapping the former into a
common atlas space. We present preliminary results that suggest improved
accuracy for prediction of patient overall survival when a set of imaging
features is augmented with estimated biophysical parameters. All extracted
features, tumor initial positions, and biophysical growth parameters are made
publicly available for further analysis. To our knowledge, this is the first
fully automatic scheme that can handle multifocal tumors and can localize the
TIL to a few millimeters.
