Amiri-Hezaveh Amirhossein, Tan Shelly, Deng Qing, Umulis David, Cunniff Lauren, Weickenmeier Johannes, Buganza Tepole Adrian
School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907 USA.
Department of Mechanical Engineering, Stevens Institute of Technology, Hoboken, NJ 07030 USA.
Int J Comput Vis. 2025;133(9):6374-6399. doi: 10.1007/s11263-025-02476-6. Epub 2025 Jun 8.
An unsupervised machine learning method is introduced to align medical images in the context of the large deformation elasticity coupled with growth and remodeling biophysics. The technique, which stems from the principle of minimum potential energy in solid mechanics, consists of two steps: Firstly, in the predictor step, the geometric registration is achieved by minimizing a loss function composed of a dissimilarity measure and a regularizing term. Secondly, the physics of the problem, including the equilibrium equations along with growth mechanics, are enforced in a corrector step by minimizing the potential energy corresponding to a Dirichlet problem, where the predictor solution defines the boundary condition and is maintained by distance functions. The features of the new solution procedure, as well as the nature of the registration problem, are highlighted by considering several examples. In particular, registration problems containing large non-uniform deformations caused by extension, shearing, and bending of multiply-connected regions are used as benchmarks. In addition, we analyzed a benchmark biological example (registration for brain data) to showcase that the new deep learning method competes with available methods in the literature. We then applied the method to various datasets. First, we analyze the regrowth of the zebrafish embryonic fin from confocal imaging data. Next, we evaluate the quality of the solution procedure for two examples related to the brain. For one, we apply the new method for 3D image registration of longitudinal magnetic resonance images of the brain to assess cerebral atrophy, where a first-order ODE describes the volume loss mechanism. For the other, we explore cortical expansion during early fetal brain development by coupling the elastic deformation with morphogenetic growth dynamics. The method and examples show the ability of our framework to attain high-quality registration and, concurrently, solve large deformation elasticity balance equations and growth and remodeling dynamics.
一种无监督机器学习方法被引入，用于在结合生长和重塑生物物理学的大变形弹性背景下对齐医学图像。该技术源于固体力学中的最小势能原理，由两个步骤组成：首先，在预测步骤中，通过最小化由差异度量和正则化项组成的损失函数来实现几何配准。其次，在校正步骤中，通过最小化与狄利克雷问题相对应的势能来强制执行问题的物理特性，包括平衡方程以及生长力学，其中预测器解定义边界条件并由距离函数维持。通过考虑几个例子突出了新求解过程的特点以及配准问题的性质。特别是，包含由多连通区域的拉伸、剪切和弯曲引起的大的非均匀变形的配准问题被用作基准。此外，我们分析了一个基准生物学例子（脑数据配准），以展示新的深度学习方法与文献中现有方法的竞争力。然后我们将该方法应用于各种数据集。首先，我们从共聚焦成像数据中分析斑马鱼胚胎鳍的再生。接下来，我们评估与大脑相关的两个例子的求解过程质量。对于一个例子，我们将新方法应用于大脑纵向磁共振图像的三维图像配准，以评估脑萎缩，其中一阶常微分方程描述体积损失机制。对于另一个例子，我们通过将弹性变形与形态发生生长动力学相结合，探索胎儿早期大脑发育过程中的皮质扩张。该方法和例子展示了我们的框架实现高质量配准的能力，同时求解大变形弹性平衡方程以及生长和重塑动力学。
