Mathematical Models of Brain Morphogenesis

尽管有许多关于大脑形态发生的推测性论文，特别是皮层折叠，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的力学原理和最先进的结构、微观结构和力学性能的实验测量，结合生长和重塑的精确、定量描述。与实验相结合，这些模型将被用来检验这样一种假设，即机械应力、粘弹性特性和发育中的大脑生长的时空变化会产生可观察到的形状变化。该项目关注大脑发育的两个特定阶段，在这两个阶段，形式的巨大变化是显而易见的：(1)早期的神经管扩张和分化为大脑的初级囊泡（前脑、中脑和后脑）；(2)大脑皮层折叠后期（回旋发生）。脑形成的非线性三维连续力学的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，大脑生长和发育的数学模型将被建立和测试。大脑的形状与其功能密切相关，但驱使大脑形成最终形状的机制却鲜为人知。该项目侧重于两个似乎特别重要的阶段：(1)早期发育阶段，此时大脑的三个主要部分出现；(2)发育后期，大脑外表面折叠成一个卷曲的图案。人们提出了许多关于大脑发育过程的有根据的猜测，但没有一个有令人信服的证据支持。假设的机制将在定量的、精确的、计算机模拟中描述，结果将被客观地评估。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、物理上合理的理解。这些信息对于了解正常的大脑是至关重要的。此外，许多脑残障和疾病，如精神分裂症、癫痫和智力迟钝都与异常的脑形状有关。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.