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

为了开发有效的保护产品，需要了解健康大脑的机制。在研究脑力学时，数学模型是关键的，甚至是必不可少的，因为由于大脑的柔软、头骨封闭的性质，实验观察活脑反应所需的物理传感器通常不可能正确地测量和校准。因此，这项拟议的研究旨在开发新的数学模型，以了解健康大脑在高速负荷下的基本机制，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。*长期而言，PI计划通过硅胶模型来表示健康的人头，以了解各种类型负荷的机械效应，并开发有效的脑保护措施。尽管这可能需要几年的时间才能实现，但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是很重要的。在短期内(未来5年)，PI提出了符合长期目标的三个目标：*1)开发一种新的人头模型，其中包括脑回/脑沟、详细的海马区组件、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，这将帮助许多收集头部加速度数据的学者了解开发防护产品所需的全面组织水平的力学，如头盔和汽车的安全功能。*2)对真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壁垒的挑战，比如那些致力于减少旋转撞击造成的大脑压力的人，以及那些致力于降低爆炸物造成的大脑压力的人，因为拟议中的研究专门研究了可能与外部情况截然不同的情况下的基本大脑机制。*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对动态负荷做出反应。这将促进该领域对基本脑力学的理解，因为由于开发细胞级几何图形、材料参数和边界/加载条件的挑战，文献基本上缺乏这种更精细的模型。与目标1相结合，这项研究将提供一种在脑力学中连接组织和细胞尺度的新方法。

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.