Developing mathematical models for understanding the fundamental mechanics of the healthy brain under high-rate loading

了解健康大脑的机制是开发有效保护产品的必要条件。在研究大脑力学时，数学模型是至关重要的，甚至是必不可少的，因为实验观察活体大脑反应所需的物理传感器通常不可能正确地仪器和校准，因为大脑的柔软，头骨封闭的性质。因此，拟议的研究是开发新的数学模型，以了解健康大脑在高速率负荷期间的基本力学，揭示大脑的机械动力学如何从组织水平（毫米）到细胞水平（微米）受到影响。 从长远来看，PI计划通过计算机模型来代表健康的人类头部，以了解各种类型负载的机械效应，并开发有效的大脑保护。虽然这可能需要数年时间才能实现，但重要的是要开始克服将大脑表示为具有复杂解剖特征的软、粘弹性、非线性和各向异性固体的挑战。在短期内（未来5年），PI提出了符合长期目标的三个目标： 1)开发一个新的人类头部模型，包括脑回/脑沟，详细的海马组件，脑血管系统和纤维束。这将是一个最先进的有限元头部模型，具有非线性，粘弹性和各向异性的大脑和前所未有的详细物理学，这将有助于许多收集头部加速度数据的学者了解开发保护产品所需的全面组织级力学，例如头盔和汽车中的安全功能。 2)对现实世界的事件进行数学模拟，以获得对高速率负荷下健康大脑的新理解。这将克服打破各种研究阵营的障碍的挑战，例如那些致力于减少旋转冲击造成的大脑压力的人，以及那些致力于减少爆炸物造成的大脑压力的人，因为拟议的研究专门研究了可能在外部看起来非常不同的情况下的基本大脑力学。 3)创建新的细胞级数学模型，以了解健康大脑的细胞级组件如何响应动态负载。这将促进该领域对基本脑力学的理解，因为文献在很大程度上缺乏这种更精细的模型，因为开发细胞级几何形状，材料参数和边界/加载条件的挑战。结合目标1，本研究将为脑力学的组织和细胞尺度的研究提供一种新的途径。

Understanding the mechanics of the healthy brain is required for developing effective protection products. In studying brain mechanics, mathematical models are critical, even essential, because the physical sensors needed to experimentally observe live-brain responses are often impossible to properly instrument and calibrate, due to the soft, skull-enclosed nature of the brain. Hence, the proposed research is to develop novel mathematical models to understand the fundamental mechanics of the healthy brain during high-rate loading, revealing how the brain's mechanical dynamics are affected from the tissue level (millimeters) down to the cellular level (microns). In the long term, the PI plans to represent the healthy human head via in silico models to understand the mechanical effects of various types of loading and develop effective brain protections. Although this may take years to realize, it is important to begin overcoming the challenges of representing the brain as a soft, viscoelastic, nonlinear, and anisotropic solid that has complex anatomical features. In the short term (next 5 years), the PI proposes three objectives that fit into the long-term goal: 1) Develop a new human head model that includes the gyri/sulci, detailed hippocampal components, brain vasculature, and fiber tracts. This will be a state-of-the-art finite element head model with a nonlinear, viscoelastic, and anisoptric brain and unprecedentedly detailed physics, which will help many scholars who collect head acceleration data understand comprehensive tissue-level mechanics needed to develop protection products, such as helmets and safety features in cars. 2) Conduct mathematical simulations of real-world events to gain novel understanding of the healthy brain under high-rate loading. This will overcome the challenges of breaking the barriers of various research camps, such as those who work on reducing brain strains from rotational impacts and those who work on reducing brain pressures from explosives, because the proposed research specifically investigates fundamental brain mechanics in scenarios that may externally look vastly different. 3) Create novel cellular-level mathematical models to understand how cellular-level components of the healthy brain respond to dynamic loading. This will promote the field's understanding of fundamental brain mechanics as the literature largely lacks such finer-level models because of the challenges of developing cellular-level geometries, material parameters, and boundary/loading conditions. Combined with Objective 1, the research will provide a new approach connecting tissue and cellular scales in brain mechanics.