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

• URL: http://arxiv.org/abs/2407.03292v2
• Date: Tue, 9 Jul 2024 13:05:32 GMT
• Title: Biomechanics-informed Non-rigid Medical Image Registration and its Inverse Material Property Estimation with Linear and Nonlinear Elasticity
• Abstract summary: 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. Two sets of experiments have been conducted, using pairs of undeformed and deformed MR images from clinical cases of prostate cancer biopsy.
• Score: 11.39300419376046
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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.

Related papers

• Adjoint Method versus Physics-Informed Neural Networks in PDE-Constrained Inverse Problems [48.470700002941136]
  Inverse problems governed by partial differential equations (PDEs) are central to computational mechanics and are commonly solved by adjoint-based optimization.<n> physics-informed neural networks (PINNs) have emerged as a flexible alternative.<n>We present a fair comparison of adjoint optimization and PINNs for PDE-constrained inverse problems.
  arXiv  Detail & Related papers  (2026-06-10T17:07:09Z)
• Comparing Physics-Informed and Neural ODE Approaches for Modeling Nonlinear Biological Systems: A Case Study Based on the Morris-Lecar Model [0.0]
  This study systematically evaluates the performance of PINNs and NODEs across three canonical bifurcation regimes.<n>Results indicate that PINNs tend to achieve higher accuracy and robustness in scenarios involving stiffness or sensitive bifurcations.
  arXiv  Detail & Related papers  (2026-03-27T18:53:53Z)
• Physics-Informed Linear Model (PILM): Analytical Representations and Application to Crustal Strain Rate Estimation [0.0]
  We investigate a physics-informed linear model (PILM) that uses linear combinations of basis functions to represent solutions.<n>The PILM provides an analytically solvable framework applicable to linear forward and inverse problems, underdetermined systems, and physical regularization.
  arXiv  Detail & Related papers  (2025-07-16T13:23:39Z)
• High precision PINNs in unbounded domains: application to singularity formulation in PDEs [83.50980325611066]
  We study the choices of neural network ansatz, sampling strategy, and optimization algorithm.<n>For 1D Burgers equation, our framework can lead to a solution with very high precision.<n>For the 2D Boussinesq equation, we obtain a solution whose loss is $4$ digits smaller than that obtained in citewang2023asymptotic with fewer training steps.
  arXiv  Detail & Related papers  (2025-06-24T02:01:44Z)
• Physics-informed Neural Network Estimation of Material Properties in Soft Tissue Nonlinear Biomechanical Models [2.8763745263714005]
  We propose a new approach which relies on the combination of physics-informed neural networks (PINNs) with three-dimensional soft tissue nonlinear biomechanical models. The proposed learning algorithm encodes information from a limited amount of displacement and, in some cases, strain data, that can be routinely acquired in the clinical setting. Several benchmarks are presented to show the accuracy and robustness of the proposed method.
  arXiv  Detail & Related papers  (2023-12-15T13:41:20Z)
• Lie Point Symmetry and Physics Informed Networks [59.56218517113066]
  We propose a loss function that informs the network about Lie point symmetries in the same way that PINN models try to enforce the underlying PDE through a loss function. Our symmetry loss ensures that the infinitesimal generators of the Lie group conserve the PDE solutions. Empirical evaluations indicate that the inductive bias introduced by the Lie point symmetries of the PDEs greatly boosts the sample efficiency of PINNs.
  arXiv  Detail & Related papers  (2023-11-07T19:07:16Z)
• Physics-informed UNets for Discovering Hidden Elasticity in Heterogeneous Materials [0.0]
  We develop a novel UNet-based neural network model for inversion in elasticity (El-UNet) We show superior performance, both in terms of accuracy and computational cost, by El-UNet compared to fully-connected physics-informed neural networks.
  arXiv  Detail & Related papers  (2023-06-01T23:35:03Z)
• Deep learning for full-field ultrasonic characterization [7.120879473925905]
  This study takes advantage of recent advances in machine learning to establish a physics-based data analytic platform. Two logics, namely the direct inversion and physics-informed neural networks (PINNs), are explored.
  arXiv  Detail & Related papers  (2023-01-06T05:01:05Z)
• Identifiability and Asymptotics in Learning Homogeneous Linear ODE Systems from Discrete Observations [114.17826109037048]
  Ordinary Differential Equations (ODEs) have recently gained a lot of attention in machine learning. theoretical aspects, e.g., identifiability and properties of statistical estimation are still obscure. This paper derives a sufficient condition for the identifiability of homogeneous linear ODE systems from a sequence of equally-spaced error-free observations sampled from a single trajectory.
  arXiv  Detail & Related papers  (2022-10-12T06:46:38Z)
• NeuralSI: Structural Parameter Identification in Nonlinear Dynamical Systems [9.77270939559057]
  This paper explores a new framework, dubbed NeuralSI, for structural identification. Our approach seeks to estimate nonlinear parameters from governing equations. The trained model can also be extrapolated under both standard and extreme conditions.
  arXiv  Detail & Related papers  (2022-08-26T16:32:51Z)
• Learning Physics-Informed Neural Networks without Stacked Back-propagation [82.26566759276105]
  We develop a novel approach that can significantly accelerate the training of Physics-Informed Neural Networks. In particular, we parameterize the PDE solution by the Gaussian smoothed model and show that, derived from Stein's Identity, the second-order derivatives can be efficiently calculated without back-propagation. Experimental results show that our proposed method can achieve competitive error compared to standard PINN training but is two orders of magnitude faster.
  arXiv  Detail & Related papers  (2022-02-18T18:07:54Z)
• A deep learning driven pseudospectral PCE based FFT homogenization algorithm for complex microstructures [68.8204255655161]
  It is shown that the proposed method is able to predict central moments of interest while being magnitudes faster to evaluate than traditional approaches. It is shown, that the proposed method is able to predict central moments of interest while being magnitudes faster to evaluate than traditional approaches.
  arXiv  Detail & Related papers  (2021-10-26T07:02:14Z)
• Data-driven generation of plausible tissue geometries for realistic photoacoustic image synthesis [53.65837038435433]
  Photoacoustic tomography (PAT) has the potential to recover morphological and functional tissue properties. We propose a novel approach to PAT data simulation, which we refer to as "learning to simulate" We leverage the concept of Generative Adversarial Networks (GANs) trained on semantically annotated medical imaging data to generate plausible tissue geometries.
  arXiv  Detail & Related papers  (2021-03-29T11:30:18Z)
• Physics-Informed Neural Networks for Nonhomogeneous Material Identification in Elasticity Imaging [0.0]
  We apply Physics-Informed Neural Networks (PINNs) for solving identification problems of nonhomogeneous materials. By employing two neural networks in our model, we extend the capability of material identification of PINNs to include nonhomogeneous material parameter fields.
  arXiv  Detail & Related papers  (2020-09-02T23:37:36Z)
• Provably Efficient Neural Estimation of Structural Equation Model: An Adversarial Approach [144.21892195917758]
  We study estimation in a class of generalized Structural equation models (SEMs) We formulate the linear operator equation as a min-max game, where both players are parameterized by neural networks (NNs), and learn the parameters of these neural networks using a gradient descent. For the first time we provide a tractable estimation procedure for SEMs based on NNs with provable convergence and without the need for sample splitting.
  arXiv  Detail & Related papers  (2020-07-02T17:55:47Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.