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Spectral Bias Correction in PINNs for Myocardial Image Registration of Pathological Data

Bastien C. Baluyot, Marta Varela, Chen Qin

TL;DR

This work tackles spectral bias in physics-informed neural networks (PINNs) for myocardial image registration, where high-frequency deformation details are critical for accurate biomechanical analysis in cardiomyopathies. It combines WarpPINN with Fourier Feature mappings and introduces modulation strategies based on sinusoidal representations (SIRENs) to better capture localized, high-frequency deformations while preserving myocardial incompressibility. The approach is evaluated on CMAC and ACDC datasets, showing superior registration accuracy (lower mean contour distance) and robust volume preservation, along with improvements in landmark tracking when applicable. The findings suggest that Fourier Feature encoding and SIREN-based modulation provide a scalable path toward generalizable PINN-based registration across diverse patients and cardiac pathologies, with implications for improved cardiac motion analysis and disease assessment.

Abstract

Accurate myocardial image registration is essential for cardiac strain analysis and disease diagnosis. However, spectral bias in neural networks impedes modeling high-frequency deformations, producing inaccurate, biomechanically implausible results, particularly in pathological data. This paper addresses spectral bias in physics-informed neural networks (PINNs) by integrating Fourier Feature mappings and introducing modulation strategies into a PINN framework. Experiments on two distinct datasets demonstrate that the proposed methods enhance the PINN's ability to capture complex, high-frequency deformations in cardiomyopathies, achieving superior registration accuracy while maintaining biomechanical plausibility - thus providing a foundation for scalable cardiac image registration and generalization across multiple patients and pathologies.

Spectral Bias Correction in PINNs for Myocardial Image Registration of Pathological Data

TL;DR

This work tackles spectral bias in physics-informed neural networks (PINNs) for myocardial image registration, where high-frequency deformation details are critical for accurate biomechanical analysis in cardiomyopathies. It combines WarpPINN with Fourier Feature mappings and introduces modulation strategies based on sinusoidal representations (SIRENs) to better capture localized, high-frequency deformations while preserving myocardial incompressibility. The approach is evaluated on CMAC and ACDC datasets, showing superior registration accuracy (lower mean contour distance) and robust volume preservation, along with improvements in landmark tracking when applicable. The findings suggest that Fourier Feature encoding and SIREN-based modulation provide a scalable path toward generalizable PINN-based registration across diverse patients and cardiac pathologies, with implications for improved cardiac motion analysis and disease assessment.

Abstract

Accurate myocardial image registration is essential for cardiac strain analysis and disease diagnosis. However, spectral bias in neural networks impedes modeling high-frequency deformations, producing inaccurate, biomechanically implausible results, particularly in pathological data. This paper addresses spectral bias in physics-informed neural networks (PINNs) by integrating Fourier Feature mappings and introducing modulation strategies into a PINN framework. Experiments on two distinct datasets demonstrate that the proposed methods enhance the PINN's ability to capture complex, high-frequency deformations in cardiomyopathies, achieving superior registration accuracy while maintaining biomechanical plausibility - thus providing a foundation for scalable cardiac image registration and generalization across multiple patients and pathologies.

Paper Structure

This paper contains 19 sections, 5 equations, 3 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Background
  3. Myocardial Image Registration
  4. Physics-Informed Neural Networks (PINNs)
  5. Spectral Bias in Neural Networks
  6. Methods
  7. WarpPINN
  8. Fourier Feature Mapping (FFM)
  9. Sinusoidal Representation Networks (SIRENs)
  10. Datasets
  11. Experiments and Results
  12. PINN-based Registration on ACDC Dataset
  13. Spectral Bias Correction on CMAC Dataset
  14. Evaluation of SIRENs
  15. Discussions of Results
  16. ...and 4 more sections

Figures (3)

  • Figure 1: Visualization of Reference ($\boldsymbol{R}$), Template ($\boldsymbol{T}$) and Warped Template ($\boldsymbol{T} \circ \boldsymbol{\varphi}$) images (and segmentation masks) for Patient 50 (MINF) from the ACDC dataset. Visualizations are taken at the three representative slices (basal, mid-ventricular, and apical). Glyphs are shown to visualize the magnitude and direction of the learned deformation field ($\boldsymbol{\varphi}$).
  • Figure 2: 3D visualization of the predicted deformation of the LV at ES phase for one healthy volunteer from the CMAC dataset for the WarpPINN and WarpPINN-FF models with $\lambda = 10^{5}$, $\mu = 5 \times 10^{-6}$, and $\sigma = 1$ (for WarpPINN-FF). (a) Surface colormap of the Jacobian with the wireframe showing the ground truth surface mesh at ED. (b) Predicted (green) vs. ground truth (red) landmark coordinates at ES phase, with black lines indicating tracking error.
  • Figure 3: Box plot of landmark tracking errors of various image registration methodologies for registration on one healthy volunteer from the CMAC dataset. WarpPINN-FF is evaluated with hyperparameter $\sigma = 1$. Registration performance data for the benchmark methodologies are provided in ArrMelUri:23.