Technical Note: PDE-constrained Optimization Formulation for Tumor Growth Model Calibration

TL;DR

This paper presents a PDE-constrained optimization approach using advanced algorithms for calibrating tumor growth models based on imaging data, focusing on efficient solution methods for inverse problems involving nonlinear PDEs.

Contribution

It introduces a PDE-constrained optimization framework with a globalized inexact Newton method and adjoint-based gradient and Hessian computations for tumor model calibration.

Findings

Effective solution algorithms for nonlinear PDE inverse problems

Implementation of adjoint methods for gradient and Hessian calculations

Demonstration of the approach on tumor growth model calibration

Abstract

We discuss solution algorithms for calibrating a tumor growth model using imaging data posed as a deterministic inverse problem. The forward model consists of a nonlinear and time-dependent reaction-diffusion partial differential equation (PDE) with unknown parameters (diffusivity and proliferation rate) being spatial fields. We use a dimension-independent globalized, inexact Newton Conjugate Gradient algorithm to solve the PDE-constrained optimization. The required gradient and Hessian actions are also presented using the adjoint method and Lagrangian formalism.