Multiscale modelling and mathematical methods for brain development, trauma, and diseases

人脑是一个极其复杂的器官，是终极智力自我中心主义的对象，也是永无止境的科学挑战的源泉。在基本功能层面上，许多科学研究的目标是了解860亿个神经元与100万亿个连接相互作用所产生的功能。从这个角度来看，这个问题包括将脑细胞的生化和电生理行为与连接细胞网络的整体行为联系起来。最终目标是将由此产生的宏观电生理行为转化为功能维度，在功能维度中可以建立与神经元反应和最终行为的直接关系。尽管对我们的大脑如何运作有着巨大的兴趣和重大的研究计划，但相对而言，我们对大脑在物理和机械层面上的功能知之甚少。最近的研究发现直接将主要的大脑发育、机制和疾病与大脑在细胞和组织水平上的机械反应联系起来。各种因素导致了这种知识贫乏的状态。首先，大脑是一个完全封闭的器官，很难从物理上进行探测。其次，作为固体，它是非常柔软的，它的机械反应很大程度上受到流体相和在细胞和细胞外基质中发现的多个带电分子的影响。一个整体的数学分析需要一个完全耦合的多场理论，这需要校准和实验验证。此外，大多数脑病取决于许多不同的因素，他们的物理表现可能很容易被忽视，因为他们把重点放在遗传和细胞功能上，作为主要的驱动因素。尽管如此，过去十年在脑力学的不同领域取得了根本性的进展，并揭示了脑力学特别令人兴奋的原因之一是它涉及到极端的尺度：与神经外科相关的极端软尺度；头骨：与头骨相关的极其坚硬的鳞片；极慢的量表与大脑发育有关，极快的量表与创伤性脑损伤有关；轴突内极小尺度的蛋白质聚集导致细胞死亡，而大脑本身相对极大规模的神经退化过程发生。一个数学理论需要在一个统一的理论中协调所有这些不同的尺度。提出的研究目标是发展数学理论和工具来解决与脑力学有关的许多问题。它将使用大脑功能的基本物理原理来解决在正常和病理情况下出现的一些问题和挑战。在数学层面上，它需要固体、流体、电化学和机电组件的耦合，以及生长和重构的理论。我的目标是建立一个连接分子、细胞、组织和器官尺度的脑力学的通用多尺度理论框架。利用这些理论，我将解决一些情况和病理中的基本问题，其中力学发挥着关键作用，建模可以提高我们的理解和预测能力。这些疾病包括大脑发育、脑折叠、颅骨生长、脑外科手术、创伤性脑损伤、脑肿胀和神经退行性疾病。

The human brain is an organ of extreme complexity, the object of ultimate intellectual egocentrism, and a source of endless scientific challenges. At the basic functional level, the goal of many scientific enquiries is to understand the functions that result from the interaction of about 86 billion neurons with 100 trillion connections. From this perspective, the problem consists of connecting the biochemical and electrophysiological behavior of brain cells with the overall behavior of networks of connected cells. The ultimate goal is to translate the resulting macroscopic electrophysiological behavior into the functional dimension where direct relations can be established with neuronal response and, ultimately, behavior. Despite an overwhelming interest and major research initiatives on how our brain operates, comparatively little is known about how the brain functions at the physical and mechanical levels. Recent findings have directly linked major brain development, mechanisms, and diseases to the mechanical response of the brain both at the cellular and tissue levels. Various factors contribute to this poor state of knowledge. First, the brain is a fully enclosed organ that is particularly difficult to probe physically. Second, viewed as a solid, it is extremely soft and its mechanical response is heavily influenced by a fluid phase and multiple charged molecules found in its cells and in the extracellular matrix. A holistic mathematical analysis requires a fully coupled multi-field theory, which needs to be calibrated and validated experimentally. Further, most brain pathologies depend on many different factors and their physical manifestation may be conveniently ignored by focusing on genetics and cellular function as the primary driver. Nonetheless, the last decade has seen fundamental advances in different areas of brain mechanics and has revealed that one of the reasons that brain mechanics is particularly exciting is that it involves extreme scales: the extremely soft scale associated with neurosurgery; the extremely hard scale associated with the skull; the extremely slow scale associated with brain development and, the extremely fast scale associated with traumatic brain injury; the extremely small scales of protein aggregation within axons leading to cell death and the relatively extremely large scale of the brain itself where neuro-degeneratives processes take place. A mathematical theory needs to reconcile all these different scales within a unified theory.The objective of the proposed research is to develop the mathematical theory and tools to approach many questions related to brain mechanics. It will use the basic physical principles underlying brain function to address a number of problems and challenges appearing in normal and pathological situations. At the mathematical level, it requires the coupling of solid, fluid, electrochemical, and electromechanical components together with a theory of growth and remodelling. My aim is to build a general multiscale theoretical framework of brain mechanics linking molecular, cellular, tissue, and organ scales. Using these theories, I will tackle a number of fundamental questions in situations and pathologies where mechanics play a key role and where modeling can improve our understanding and predicting capabilities. These include brain development, brain folding, skull growth, brain surgery, traumatic brain injury, brain swelling, and neuro-degenerative diseases.