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

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 nonlinear elasticity theory is leveraged to formally establish the partial differential equations (PDEs) representing physics laws of biomechanical constraints 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. While the forward problem has direct clinical applications in guiding targeted biopsy and treatment, the solution to the inverse problem may open new research directions in quantifying disease-indicative mechanical properties of in vivo tissues. Two net configurations (i.e., Cfg1 and Cfg2) have also been compared for both linear and nonlinear physics models, according to whether backbones are shared between branches or not. Two sets of experiments have been conducted, using pairs of undeformed and deformed MR images from clinical cases of prostate cancer biopsy. In the first experiment, against the finite-element-computed ground-truth, the root mean squared error (rmse) of registration for surface points was reduced from \(1.83\pm 0.51\) mm without PINNs to \(1.43\pm 0.70\) mm (Cfg1, \(p=0.024\) ) and \(1.23\pm 0.69\) mm (Cfg2, \(p<0.001\) ) with linear elasticity, and to \(1.45\pm 0.84\) mm (Cfg1, \(p=0.004\) ) and \(1.24\pm 0.69\) mm (Cfg2, \(p<0.001\) ) with nonlinear elasticity, while average differences between linear and nonlinear models were not found statistically significant (e.g., \(p=0.972\) between two Cfg1s) but their respective benefits may depend on specific patients. In the second experiment, the nonlinear model exhibited evident advantages over the linear counterpart ( \(p=0.002\) ) in predicting ratios of tissue stiffness (i.e., Young’s modulus) between two subregions (i.e., peripheral and transition zones) of the prostate, with the mean average percentage error (mAPE) values being \(14.20\%\pm 14.12\%\) and \(76.28\%\pm 30.97\%\) , respectively. The codes are available at https://github.com/ZheMin-1992/Registration_PINNs .