Fully Automatic Calibration of Tumor-Growth Models Using a Single mpMRI Scan

Abstract

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.

Quantitative in vivo imaging to enable tumor forecasting and treatment optimization

“…Mathematical models of cancer define a forward problem, whose solution provides state variables (e.g., tumor cell density). In general, these models are parameterized by unknown biophysical parameters (and possibly initial conditions) that typically manifest substantial variability across subjects [68,75,98]. The estimation of these unknown variables (also called inversion variables) should be patient-specific and can be mathematically posed as an inverse problem, which aims at optimizing an objective function constrained by the model.…”

“…Biophysical inversion is a promising strategy to calibrate predictive models of cancer, but also presents several challenges. Complex, typically nonlinear and time-dependent, PDE-based models often result in ill-conditioned and non-convex optimization problems, which require sophisticated numerical algorithms to stabilize the inversion, such as multiresolution continuation, parameter continuation, and regularization schemes [29,98,99,104]. Data scarcity can exacerbate the ill-posedness.…”

Multiatlas Calibration of Biophysical Brain Tumor Growth Models with Mass Effect

“…In [7], the authors consider a Bayesian framework for estimating model parameters but do not consider mass effect and use a single seed for tumor initial condition. The absence of mass effect in the tumor models allows for the use of simiplistic precancer brain approximations through deformed templates (computed by deformable registration) [7] or simple tissue replacement strategies [16]. Other than those works, the current state of the art for single-scan biophysicallybased tumor characterization is GLISTR [15].…”

“…The mismatch terms are balanced by a regularization term on the inverted initial condition (IC). O is an observation operator that defines the clearly observable tumor margin (see §II-D for its definition; for additional details see [16]). Following [5], we introduce two additional constraints to our optimization problem-Eq.…”

“…The observation operator can be interpreted as complete uncertainty of tumor observation in this region. Hence, the tumor profile in the peritumoral edema is governed solely by the model dynamics, and not fitted to arbitrary values (see [16] for more details).…”