Mathematical Models of Brain Morphogenesis

尽管有许多关于脑形态发生，特别是皮质折叠的推测性论文，但导致大脑正常和异常发育的生物力学因素在很大程度上是未知的。本研究的总体目标是建立脑形态发生的定量生物力学模型。数学模型将基于基本力学原理和最先进的结构、微观结构和机械性能的实验测量，并结合对生长和重塑的精确、定量描述。结合实验，这些模型将被用来检验这一假设，即机械应力、粘弹性特性和发育中的大脑生长的空间和时间变化会导致观察到的形状变化。该项目关注大脑发育的两个特定时期，在这两个时期，形态发生了明显的戏剧性变化：(1)神经管扩张和分化为大脑的初级小泡(前脑、中脑和后脑)的早期阶段；(2)大脑皮层折叠的后期(脑回发育)。对脑形成的非线性、三维连续介质力学进行数学和计算建模是对神经生物学中这一基本问题的经典生物学方法的必要补充。这个项目的结果将为大脑发育的生物力学机制提供基本的新见解。在这个项目中，将建立和测试大脑生长和发育的数学模型。大脑的形状与其功能密切相关，但人们对驱动大脑形成最终形状的机制知之甚少。该项目专注于两个似乎特别重要的阶段：(1)大脑三个主要部分出现的早期发育阶段；(2)大脑外表面折叠成错综复杂的图案的后期发育阶段。人们提出了许多关于大脑发育过程的有根据的猜测，但没有一个得到令人信服的证据的支持。假想的机制将在定量、精确的计算机模拟中进行描述，并对结果进行客观评估。新的实验研究将为这些计算机模型提供物理参数。目标是对驱动大脑发育的形式-功能关系有一个连贯的、物理上可信的理解。这些信息对于理解正常的大脑非常重要。此外，许多大脑残疾和疾病，如精神分裂症、癫痫和智力低下，都与大脑形状异常有关。该项目将解决解决这些问题所需的大脑发育基础知识方面的重要空白。

Despite many speculative papers on the topics of brain morphogenesis, particularly cortical folding, the biomechanical factors that are responsible for normal and abnormal brain development are largely unknown. The general objective of this research is to develop quantitative biomechanical models for brain morphogenesis. The mathematical models will be based on fundamental mechanical principles and state-of-the-art experimental measurements of structure, microstructure, and mechanical properties, combined with precise, quantitative descriptions of growth and remodeling. In conjunction with experiments, these models will be used to test the hypothesis that spatial and temporal variations in mechanical stress, viscoelastic properties, and growth of the developing brain produce observed changes in shape. This project focuses on two specific periods of brain development where dramatic changes in form are apparent: (1) the early period of expansion and differentiation of the neural tube into the primary vesicles of the brain (forebrain, midbrain, and hindbrain); and (2) the later period of folding of the cerebral cortex (gyrogenesis). Mathematical and computational modeling of the nonlinear, three-dimensional continuum mechanics of brain formation is a necessary complement to classical biological approaches to this basic problem in neurobiology. The results from this project will provide fundamental new insight into the biomechanical mechanisms of brain development.In this project, mathematical models for growth and development of the brain will be built and tested. The brain's form is closely related to its function, but the mechanisms that drive the brain into its final shape are poorly understood. The project focuses on two stages that appear particularly important: (1) the stage of early development when three primary segments of the brain emerge; (2) the stage of later development when the outer surface of the brain folds into a convoluted pattern. Many educated guesses about the process of brain development have been proposed, but none have been supported by convincing evidence. Hypothesized mechanisms will be described in quantitative, precise, computer simulations, and the results will be assessed objectively. New experimental studies will provide physical parameters for these computer models. The objective is a coherent, physically plausible, understanding of the form-function relationship that drives brain development. This information is of fundamental importance to understanding the normal brain. In addition, many disabilities and diseases of the brain, such as schizophrenia, epilepsy, and mental retardation are associated with abnormal brain shape. This project will address important gaps in the fundamental knowledge of brain development needed to address these problems.