Despite their seemingly delicate appearance, thin biological membranes fulfill various crucial roles in the human body and can sustain substantial mechanical loads. Unlike engineering structures, biological membranes are able to grow and adapt to changes in their mechanical environment. Finite element modeling of biological growth holds the potential to better understand the interplay of membrane form and function and to reliably predict the effects of disease or medical intervention. However, standard continuum elements typically fail to represent thin biological membranes efficiently, accurately, and robustly. Moreover, continuum models are typically cumbersome to generate from surface-based medical imaging data. Here we propose a computational model for finite membrane growth using a classical midsurface representation compatible with standard shell elements. By assuming elastic incompressibility and membrane-only growth, the model a priori satisfies the zero-normal stress condition. To demonstrate its modular nature, we implement the membrane growth model into the general-purpose non-linear finite element package Abaqus/Standard using the concept of user subroutines. To probe efficiently and robustness, we simulate selected benchmark examples of growing biological membranes under different loading conditions. To demonstrate the clinical potential, we simulate the functional adaptation of a heart valve leaflet in ischemic cardiomyopathy. We believe that our novel approach will be widely applicable to simulate the adaptive chronic growth of thin biological structures including skin membranes, mucous membranes, fetal membranes, tympanic membranes, corneoscleral membranes, and heart valve membranes. Ultimately, our model can be used to identify diseased states, predict disease evolution, and guide the design of interventional or pharmaceutic therapies to arrest or revert disease progression.

尽管其外观看似精致，但薄的生物膜在人体中发挥着各种关键作用，并且可以承受巨大的机械负荷。与工程结构不同，生物膜能够生长并适应机械环境的变化。生物生长的有限元模型有可能更好地理解膜形式和功能的相互作用，并可靠地预测疾病或医疗干预的影响。然而，标准连续体单元通常无法有效、准确和稳健地表示薄生物膜。此外，从基于表面的医学成像数据生成连续模型通常很麻烦。在这里，我们提出了一种使用与标准壳单元兼容的经典中表面表示的有限膜生长计算模型。通过假设弹性不可压缩性和仅膜生长，该模型先验满足零法向应力条件。为了证明其模块化性质，我们使用用户子程序的概念将膜生长模型实现到通用非线性有限元包 Abaqus/Standard 中。为了有效地检测和稳健性，我们模拟了在不同负载条件下生长生物膜的选定基准示例。为了证明其临床潜力，我们模拟了缺血性心肌病中心脏瓣膜小叶的功能适应。我们相信，我们的新方法将广泛适用于模拟薄生物结构的适应性慢性生长，包括皮肤膜、粘膜、胎膜、鼓膜、角巩膜和心脏瓣膜。 最终，我们的模型可用于识别疾病状态，预测疾病演变，并指导介入或药物疗法的设计以阻止或逆转疾病进展。