Living biological tissue is a complex system, constantly growing and changing in response to external and internal stimuli. These processes lead to remarkable and intricate changes in shape. Modeling and understanding both natural and pathological (or abnormal) changes in the shape of anatomical structures is highly relevant, with applications in diagnostic, prognostic, and therapeutic healthcare. Nevertheless, modeling the longitudinal shape change of biological tissue is a non-trivial task due to its inherent nonlinear nature. In this review, we highlight several existing methodologies and tools for modeling longitudinal shape change (i.e., spatiotemporal shape modeling). These methods range from diffeomorphic metric mapping to deep-learning based approaches (e.g., autoencoders, generative networks, recurrent neural networks, etc.). We discuss the synergistic combinations of existing technologies and potential directions for future research, underscoring key deficiencies in the current research landscape.

翻译：活体生物组织是一个复杂的系统，会因外部和内部刺激而不断生长和变化。这些过程导致形状发生显著而复杂的变化。对解剖结构自然与病理（或异常）形状变化进行建模和理解具有高度相关性，可应用于诊断、预后和治疗等医疗领域。然而，由于生物组织固有的非线性特性，对其纵向形状变化进行建模并非易事。本综述重点介绍了多种现有的纵向形状变化（即时空形状建模）建模方法与工具。这些方法涵盖从微分同胚度量映射到基于深度学习的方法（如自编码器、生成网络、循环神经网络等）。我们探讨了现有技术的协同组合及未来研究的潜在方向，并强调了当前研究格局中的关键不足。