Biomechanics-informed Non-rigid Medical Image Registration and its Inverse Material Property Estimation with Linear and Nonlinear Elasticity

TL;DR

This paper introduces a physics-informed neural network approach for biomechanically constrained non-rigid medical image registration and tissue property estimation, comparing linear and nonlinear elasticity models using clinical MRI data.

Contribution

It develops a PINNs-based registration algorithm that generalizes to nonlinear elasticity and formulates inverse problems for tissue property estimation, with extensive experimental validation.

Findings

Nonlinear elasticity shows no significant advantage over linear models in displacement accuracy.

PINNs can effectively solve both registration and inverse parameter estimation problems.

The method is validated on clinical prostate MRI data with accurate results.

Abstract

This paper investigates both biomechanical-constrained non-rigid medical image registrations and accurate identifications of material properties for soft tissues, using physics-informed neural networks (PINNs). The complex nonlinear elasticity theory is leveraged to formally establish the partial differential equations (PDEs) representing physics laws of biomechanical constraints that need to be satisfied, with which registration and identification tasks are treated as forward (i.e., data-driven solutions of PDEs) and inverse (i.e., parameter estimation) problems under PINNs respectively. Two net configurations (i.e., Cfg1 and Cfg2) have also been compared for both linear and nonlinear physics model. Two sets of experiments have been conducted, using pairs of undeformed and deformed MR images from clinical cases of prostate cancer biopsy. Our contributions are summarised as follows. 1) We developed a learning-based biomechanical-constrained non-rigid registration algorithm using PINNs, where linear elasticity is generalised to the nonlinear version. 2) We demonstrated extensively that nonlinear elasticity shows no statistical significance against linear models in computing point-wise displacement vectors but their respective benefits may depend on specific patients, with finite-element (FE) computed ground-truth. 3) We formulated and solved the inverse parameter estimation problem, under the joint optimisation scheme of registration and parameter identification using PINNs, whose solutions can be accurately found by locating saddle points.