Inverse Problem Regularization for 3D Multi-Species Tumor Growth Models

TL;DR

This paper develops a novel multi-stage inverse problem approach to calibrate a complex 3D multi-species tumor growth PDE model from single MRI scans, enabling stable estimation of tumor parameters and species.

Contribution

It introduces a two-stage regularization method for inverse modeling of glioblastoma growth from clinical MRI data, addressing ill-posedness and enabling multi-species parameter estimation.

Findings

Stable estimation of non-observable tumor species achieved.

Improved calibration accuracy over unregularized methods.

Effective application to clinical MRI data demonstrated.

Abstract

We present a multi-species partial differential equation (PDE) model for tumor growth and a an algorithm for calibrating the model from magnetic resonance imaging (MRI) scans. The model is designed for glioblastoma (GBM) brain tumors. The modeled species correspond to proliferative, infiltrative, and necrotic tumor cells. The model calibration is formulated as an inverse problem and solved a PDE-constrained optimization method. The data that drives the calibration is derived by a single multi-parametric MRI image. This a typical clinical scenario for GBMs. The unknown parameters that need to be calibrated from data include ten scalar parameters and the infinite dimensional initial condition (IC) for proliferative tumor cells. This inverse problem is highly ill-posed as we try to calibrate a nonlinear dynamical system from data taken at a single time. To address this ill-posedness, we split the inversion into two stages. First we regularize the IC reconstruction by solving a single-species compressed sensing problem. Then, using the IC reconstruction, we invert for model parameters using a weighted regularization term. We construct the regularization term by using auxiliary 1D inverse problems. We apply our proposed scheme to clinical data. We compare our algorithm with single-species reconstruction and unregularized reconstructions. Our scheme enables the stable estimation of non-observable species and quantification of infiltrative tumor cells.