Biomechanical Constraints Assimilation in Deep-Learning Image Registration: Application to sliding and locally rigid deformations

TL;DR

This work tackles the limitation of uniform regularization in deformable image registration by introducing locally adaptive biomechanical priors learned during training. It constructs region-specific losses for local rigidity, sliding (shearing), and default pseudo-elasticity, informed by solid-mechanics concepts such as strain tensors and Jacobians, and applies a region-aware regularization mask derived from segmentation masks. Across synthetic and real 3D thoraco-abdominal CT data (notably Learn2Reg AbdomenCTCT), the approach yields substantial improvements in preserving rigid structures and modeling sliding interfaces, while maintaining or improving registration accuracy (MSE, NCC, Dice) and reducing folding, with statistical significance ($p<10^{-3}$). The method demonstrates generalization of biomechanical properties to unseen image pairs and offers a practical, plug-in strategy for physics-informed regularization in DLIR, accompanied by publicly available code. This advances physiologically plausible motion modeling in complex anatomical regions and has potential clinical impact for more accurate and interpretable registrations in thoracic and abdominal imaging.

Abstract

Regularization strategies in medical image registration often take a one-size-fits-all approach by imposing uniform constraints across the entire image domain. Yet biological structures are anything but regular. Lacking structural awareness, these strategies may fail to consider a panoply of spatially inhomogeneous deformation properties, which would faithfully account for the biomechanics of soft and hard tissues, especially in poorly contrasted structures. To bridge this gap, we propose a learning-based image registration approach in which the inferred deformation properties can locally adapt themselves to trained biomechanical characteristics. Specifically, we first enforce in the training process local rigid displacements, shearing motions or pseudo-elastic deformations using regularization losses inspired from the field of solid-mechanics. We then show on synthetic and real 3D thoracic and abdominal images that these mechanical properties of different nature are well generalized when inferring the deformations between new image pairs. Our approach enables neural-networks to infer tissue-specific deformation patterns directly from input images, ensuring mechanically plausible motion. These networks preserve rigidity within hard tissues while allowing controlled sliding in regions where tissues naturally separate, more faithfully capturing physiological motion. The code is publicly available at https://github.com/Kheil-Z/biomechanical_DLIR .

Figures (13)

• Figure 1: Possible hypotheses on the movement of different anatomical structures in medical image registration. Pseudo-elastic deformations are classically used throughout the image domain. However, it may be advantageous to consider locally more realistic biomechanical constraints on the deformed structures. (left) Locally rigid deformations can reasonably be considered in bones, as here in the ribs. (right) Sliding motion may also occur, as here at the thoracic cage boundary, next to the lungs/liver interface. Breathing indeed induces there a large up and down motion in the inner part of the thoracic cage, while the ribs are not impacted by this motion. Importantly, thoracic cage swelling also induces a small displacement of the locations where sliding phenomena occur. This motion is globally orthogonal to the large up and down motion.
• Figure 2: Measure of local deformation properties and back-propagation of their impact to favor specific bio-mechanical deformation properties using DNN-based image registration. The deformations in this figure are in 2D but the principles are the same in 3D domains. Remark that each represented vector is scaled using the multiplicative factor given at the bottom-right of each sub-figure to be visible. (Top) Strong expansion in one direction and small compression in the orthogonal direction. (Middle) Similar configuration than in the top row, but the local volume property is now preserved, meaning that $\log(det(J(x)))\approx 0$. As a consequence $loss_{Jac}$ as no regularization effect while $loss_{rigid}$ still favors locally rigid deformations (Bottom) Compressions and expansions in diagonal directions. These directions are properly captured by the eigenvectors of the strain tensor $S(x)$ and the corresponding eigenvalues reflect the levels of compression and expanion.
• Figure 3: Identification of the regions with locally-rigid or sliding deformations in a 3D volume out the Learn2Reg AbdomenCTCT dataset Zhoubing_learn2reg. (a) Segmentation labels automatically generated. (b) Derived regularization regions ($\mathcal{R}$) for rigidity,shearing and Jacobian losses. (c) Subset of projection vectors $\mathit{Strain\_Directions}$ derived for the shearing loss.
• Figure 4: Sample registration results from (a)$\mathcal{D}_{\textit{rigid}}$ and (b)$\mathcal{D}_{\textit{shearing}}$ test sets. In both cases, the first row displays the fixed and moving images. The second and third rows present the moved images on the left with the fixed target's outline, while the right side shows the deformation fields overlaid on the moving images. Notably, the rigid deformations inside the cuboids are nearly rigid, while the sliding effect is well generalized to test data.
• Figure 5: Sample registration results of a patient from the AbdomenCTCT dataset. The first row contains the fixed and moving images and the next rows display the moved image with an outline of the desired result, and the associated predicted deformation fields plotted over the moving images. We also display two regions of the obtained deformation field.