Institue of Continuum Mechanics, Leibniz University Hannover, An der Universität 1, 30823, Garbsen, Lower Saxony, Germany.
Biomech Model Mechanobiol. 2024 Dec;23(6):2091-2113. doi: 10.1007/s10237-024-01883-x. Epub 2024 Sep 30.
Dense communities of bacteria, also known as biofilms, are ubiquitous in all of our everyday life. They are not only always surrounding us, but are also active inside our bodies, for example in the oral cavity. While some biofilms are beneficial or even necessary for human life, others can be harmful. Therefore, it is highly important to gain an in-depth understanding of biofilms which can be achieved by in vitro or in vivo experiments. Since these experiments are often time-consuming or expensive, in silico models have proven themselves to be a viable tool in assisting the description and analysis of these complicated processes. Current biofilm growth simulations are using mainly two approaches for describing the underlying models. The volumetric approach splits the deformation tensor into a growth and an elastic part. In this approach, the mass never changes, unless some additional constraints are enforced. The density-based approach, on the other hand, uses an evolution equation to update the growing tissue by adding mass. Here, the density stays constant, and no pressure is exerted. The in silico model presented in this work combines the two approaches. Thus, it is possible to capture stresses inside of the biofilm while adding mass. Since this approach is directly derived from Hamilton's principle, it fulfills the first and second law of thermodynamics automatically, which other models need to be checked for separately. In this work, we show the derivation of the model as well as some selected numerical experiments. The numerical experiments show a good phenomenological agreement with what is to be expected from a growing biofilm. The numerical behavior is stable, and we are thus capable of solving complicated boundary value problems. In addition, the model is very reactive to different input parameters, thereby different behavior of various biofilms can be captured without modifying the model.
密集的细菌群落，也被称为生物膜，在我们的日常生活中无处不在。它们不仅总是围绕着我们，而且还在我们体内活跃，例如在口腔中。虽然一些生物膜对人类生活有益甚至是必要的，但另一些则可能有害。因此，深入了解生物膜非常重要，可以通过体外或体内实验来实现。由于这些实验通常既耗时又昂贵，因此，计算机模型已被证明是辅助描述和分析这些复杂过程的一种可行工具。目前的生物膜生长模拟主要使用两种方法来描述基础模型。体积方法将变形张量分为生长部分和弹性部分。在这种方法中，除非施加了一些额外的约束，否则质量不会改变。另一方面，基于密度的方法使用演化方程通过添加质量来更新生长组织。在这里，密度保持不变，不会施加压力。本工作中提出的计算模型结合了这两种方法。因此，可以在添加质量的同时捕捉生物膜内的应力。由于这种方法是直接从哈密顿原理推导出来的，因此它自动满足热力学第一和第二定律，而其他模型需要单独检查。在这项工作中，我们展示了模型的推导以及一些选定的数值实验。数值实验与预期的生长生物膜的情况表现出很好的现象学一致性。数值行为是稳定的，因此我们能够解决复杂的边值问题。此外，该模型对不同的输入参数非常敏感，因此可以在不修改模型的情况下捕捉到不同生物膜的不同行为。
