Reduced-order models (ROMs) are essential for rapid simulation of complex biomechanical systems and for bridging the gap between high fidelity models and clinical application. However, ROMs for tissue growth and remodeling (G&R) remain largely unexplored. Here, we present a Neural Ordinary Differential Equation (NODE) ROM framework that learns latent dynamics of coupled mechanical deformation and tissue growth, demonstrated in the context of skin growth during tissue expansion (TE). TE is a challenging problem involving nonlinear contact, history-dependent material behavior, and mechanobiology driven growth. The displacement field is compressed via Proper Orthogonal Decomposition (POD) into a low-dimensional latent space, and a NODE learns the resulting dynamics conditioned on patient-specific parameters. To address long-horizon error accumulation, a key challenge in autoregressive latent dynamical models, we propose a closed-loop architecture in which encoded features of the evolving growth field are fed back into the dynamics at each step. We compare feedback representations of increasing expressiveness: scalar, linear POD-based, and nonlinear CNN-based. The CNN-based growth feature feedback substantially stabilizes long-horizon rollouts. The best model captures 90.3% of validation cases within clinical tolerance based on the final skin area gain, compared to 43.7% for the open-loop baseline. Moreover, the NODE ROM achieves over 20000x the speed of full finite element simulations. More broadly, these results suggest that selectively retaining inexpensive physics of the state evolution and feeding features from these fields back into the latent dynamical system is a promising strategy for stable and accurate ROMs of G&R in biological tissues.

翻译：降阶模型对于复杂生物力学系统的快速模拟以及弥合高保真模型与临床应用之间的差距至关重要。然而，针对组织生长与重塑的降阶模型仍鲜有探究。本文提出一种神经常微分方程降阶模型框架，该框架可学习机械变形与组织生长耦合的潜在动力学，并以组织扩张过程中的皮肤生长为背景进行验证。组织扩张是一个涉及非线性接触、历史依赖性材料行为以及力学-生物学驱动生长的挑战性问题。通过本征正交分解将位移场压缩至低维潜在空间，并由神经常微分方程学习以患者特异性参数为条件的动力学演化过程。针对长时程误差累积这一自回归潜在动力学模型的关键难题，我们提出一种闭环架构，将不断演变的生长场的编码特征在每一步反馈至动力学系统。我们比较了表达能力递增的反馈表征形式：标量反馈、基于线性POD的反馈以及基于非线性CNN的反馈。基于CNN的生长特征反馈显著稳定了长时程预测轨迹。最优模型对90.3%的验证案例实现了基于最终皮肤面积增益的临床容差内预测，而开环基线模型仅为43.7%。此外，该神经ODE降阶模型的速度是完整有限元模拟的20000倍以上。更广泛而言，这些结果表明：选择性保留状态演化中廉价物理信息，并将这些场的特征反馈至潜在动力学系统，是构建生物组织生长与重塑稳定且精确降阶模型的一种有效策略。