Modeling and computation of growth in soft biological matter

软生物物质生长的建模和计算

• 批准号: 241697724
• 负责人: Professor Dr.-Ing. Paul Steinmann
• 金额: --
• 依托单位: Lehrstuhl für Technische Mechanik (LTM)
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2014
• 资助国家: 德国
• 起止时间: 2013-12-31 至 2020-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/241697724?language=en
• 关键词: Modeling; computation; growth; soft; biological

Wrinkling phenomena emerging from mechanical instabilities in inhomogeneously growing soft biological tissue can evoke a wide variety of surface morphologies. Applications range from undesired folding of asthmatic airways, via wrinkling of skin, to brain convolutions, which maximize the number of neurons and minimize their distance. Here, we study growth-induced loss of stability primarily using the example of cortical folding during brain development. On the one hand the brain still remains our least understood organ. On the other hand brain growth involves both growth-induced mechanical instabilities and mechanically-induced biological growth with a morphogenetically growing superficial gray matter layer and a stretch-induced growing white matter substrate. Using the nonlinear field theories of mechanics supplemented by the theory of finite growth, in the first phase of the project we have established a preliminary computational model of brain growth, which provides first insights into growth-induced primary and secondary instabilities: Moderate growth in the outer layer generates a regular pattern of sinusoidal wrinkles; further continuing growth induces secondary instabilities associated with advanced wrinkling modes - the surface bifurcates into increasingly complex morphologies. During the second phase of the project, we will refine our model regarding more realistic constitutive equations and growth laws. For this purpose, we will supplement our computational investigations with biomechanical testing of brain tissue. We will incorporate temporal and regional variations in material properties with close consideration of the corresponding microstructure. Such experimental studies will not only allow for realistic simulations of brain development but could also revolutionize computational modeling of brain tissue in general. Accordingly, our project related work could additionally contribute to the medical treatment of diseases such as brain tumors and the prevention of injuries such as traumatic brain injury. With our computational model we will explore major aspects of healthy and pathologic brain development. As brain structure closely correlates with brain function, malformations of cortical development are common causes of mental diseases such as epilepsy and developmental delay. The computational model can bridge the scales from largely studied disruptions on the cellular level towards form and function on the organ level. It can explain why cortical malformations emerge. Understanding the underlying mechanisms of brain development will enhance early diagnostics of cortical malformations and ultimately facilitate treatment and prevention of mental disorders.

不均匀生长的软生物组织中的机械不稳定性引起的起皱现象可以引起各种各样的表面形态。应用范围从哮喘气道的不良折叠（通过皮肤起皱）到大脑卷积（最大限度地增加神经元数量并最小化它们的距离）。在这里，我们主要使用大脑发育过程中皮质折叠的例子来研究生长引起的稳定性丧失。一方面，大脑仍然是我们最不了解的器官。另一方面，大脑生长涉及生长诱导的机械不稳定性和机械诱导的生物生长，其中包括形态发生生长的浅层灰质层和拉伸诱导生长的白质基质。利用力学的非线性场论并辅以有限生长理论，在项目的第一阶段，我们建立了大脑生长的初步计算模型，该模型为生长引起的初级和次级不稳定性提供了初步见解：外层的适度生长会产生规则的正弦皱纹图案；进一步的持续生长会引起与高级起皱模式相关的二次不稳定性——表面分叉成越来越复杂的形态。在项目的第二阶段，我们将根据更现实的本构方程和增长定律完善我们的模型。为此，我们将通过脑组织的生物力学测试来补充我们的计算研究。我们将结合材料特性的时间和区域变化，并密切考虑相应的微观结构。此类实验研究不仅可以对大脑发育进行真实模拟，而且还可以彻底改变脑组织的计算模型。因此，我们的项目相关工作还可以为脑肿瘤等疾病的治疗和创伤性脑损伤等伤害的预防做出贡献。通过我们的计算模型，我们将探索健康和病理性大脑发育的主要方面。由于大脑结构与大脑功能密切相关，皮质发育畸形是癫痫、发育迟缓等精神疾病的常见原因。计算模型可以将广泛研究的细胞水平破坏与器官水平的形式和功能联系起来。它可以解释为什么会出现皮质畸形。了解大脑发育的潜在机制将增强皮质畸形的早期诊断，并最终促进精神障碍的治疗和预防。