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Biomechanical constraints are increasingly being adopted in medical image registration to enforce physically plausible soft-tissue deformations. When formulating loss functions for physics-informed neural networks (PINNs)-based registration, a central design choice is whether the network should explicitly predict biophysical model parameters or implicitly infer them by enforcing their governing equations. In this study, we introduce four physics-informed regularization strategies for biomechanics-informed non-rigid point set registration: (i) stress prediction, (ii) strain prediction, (iii) stress–strain prediction, and (iv) deformation prediction. We provide a promising direction to understand and potentially utilised prior biomechanical knowledge to modern data-driven approach for motion modelling and medical image registration. On the simulation dataset, the deformation prediction strategy achieved the strongest performance, reducing the root mean square error (RMSE) from 1.748 ± 0.912 mm (FPT, without PINN) to 0.219 ± 0.057 mm ( \(-87.5\%\) ) and chamfer distance from 1.260 ± 0.913 mm to 0.194 ± 0.057 mm, without generating negative jacobian determinants. Other PINNs strategies also yielded competitive results, stress (RMSE 0.264 ± 0.098 mm), strain (0.305 ± 0.116 mm), and stress–strain (0.242 ± 0.147 mm), all of which consistently outperformed conventional baselines such as BCPD (RMSE 2.326 ± 5.811 mm) and GMM-FEM (1.528 ± 0.912 mm). On the clinical dataset, the deformation prediction strategy again obtained the lowest target registration error (TRE 4.924 ± 1.542 mm, \(-16.6\%\) vs. FPT), while maintaining a chamfer distance of 2.125 ± 0.291 mm and only negligible foldings (0.278 ± 0.312% negative Jacobians). The other PINNs variants, stress (TRE \(5.694 \pm 1.780\) mm), strain ( \(5.359 \pm 1.746\) mm), and stress–strain ( \(5.912 \pm 2.008\) mm), showed similar improvements over non-PINNs approaches, but remained slightly inferior to deformation prediction. The deformation prediction strategy was statistically significant against all methods (paired \(p<0.05\) ), except BCPD on the simulation dataset. The source codes have been released at https://github.com/Msx00/PINNs-for-Point-Set-Registration.git .

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The Impact of Biomechanical Quantities on PINNs-Based Medical Image Registration

  • 会议论文

  • 发表日期：

    2026年

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  • Shixing Ma,
  • Zhaoxi Lin,
  • Xinzhe Du,
  • Yipeng Hu,
  • Zhe Min

摘要

Biomechanical constraints are increasingly being adopted in medical image registration to enforce physically plausible soft-tissue deformations. When formulating loss functions for physics-informed neural networks (PINNs)-based registration, a central design choice is whether the network should explicitly predict biophysical model parameters or implicitly infer them by enforcing their governing equations. In this study, we introduce four physics-informed regularization strategies for biomechanics-informed non-rigid point set registration: (i) stress prediction, (ii) strain prediction, (iii) stress–strain prediction, and (iv) deformation prediction. We provide a promising direction to understand and potentially utilised prior biomechanical knowledge to modern data-driven approach for motion modelling and medical image registration. On the simulation dataset, the deformation prediction strategy achieved the strongest performance, reducing the root mean square error (RMSE) from 1.748 ± 0.912 mm (FPT, without PINN) to 0.219 ± 0.057 mm ( \(-87.5\%\) ) and chamfer distance from 1.260 ± 0.913 mm to 0.194 ± 0.057 mm, without generating negative jacobian determinants. Other PINNs strategies also yielded competitive results, stress (RMSE 0.264 ± 0.098 mm), strain (0.305 ± 0.116 mm), and stress–strain (0.242 ± 0.147 mm), all of which consistently outperformed conventional baselines such as BCPD (RMSE 2.326 ± 5.811 mm) and GMM-FEM (1.528 ± 0.912 mm). On the clinical dataset, the deformation prediction strategy again obtained the lowest target registration error (TRE 4.924 ± 1.542 mm, \(-16.6\%\) vs. FPT), while maintaining a chamfer distance of 2.125 ± 0.291 mm and only negligible foldings (0.278 ± 0.312% negative Jacobians). The other PINNs variants, stress (TRE \(5.694 \pm 1.780\) mm), strain ( \(5.359 \pm 1.746\) mm), and stress–strain ( \(5.912 \pm 2.008\) mm), showed similar improvements over non-PINNs approaches, but remained slightly inferior to deformation prediction. The deformation prediction strategy was statistically significant against all methods (paired \(p<0.05\) ), except BCPD on the simulation dataset. The source codes have been released at https://github.com/Msx00/PINNs-for-Point-Set-Registration.git .