Interstitial dynamics of the poroelastic brain and cerebral vasculature in humans

中风、肿瘤和脑积水等疾病影响着全世界数百万人的大脑动态。本项目旨在推进研究脑内软组织流体相互作用的数学方法。数学模型将解决在血液和脑脊液运动的动态相互作用下的大脑变形，具有三个显著特征：软多孔脑组织的欧拉-拉格朗日移动网格公式；将脑血管系统整合到多孔的可变形细胞基质中。以及基于Krylov子空间迭代的非精确牛顿型直接数值求解算法的进展。为了解决这个项目的跨学科性质，PI组建了一个由生化工程师、两名数学家、一名神经外科医生、一名核磁共振物理学家和生物医学工程师组成的研究小组。该项目的两个主要目标是：目标#1。创建多尺度流体-结构相互作用框架，计算脑变形力学与脑脊液动力学。目标# 2。我们将结合现实的脑血管模型。现有的计算大脑大变形动力学的模型仍然不能令人满意。提出的颅内动力学整体模型解决了关键缺陷。具体目标(i)弥合医学成像和严格数学分析的最新进展之间的差距，（ii）为变形软多孔介质的流固相互作用创造新的数学公式，以及（iii）解释脑血管系统的扩张。据我们所知，以前从未尝试过从患者特定图像中获得脑、血液和脑脊液相互作用的综合多阶段模型。目前医学图像的定量分析是缓慢的，因为很少有数学方法来评估血液、脑组织和脑脊液流在三维空间和时间上的相互作用。磁共振成像、血管造影或计算机断层扫描，将推动生物和医学知识的发展，当精确预测传输现象的严格数学模型成为可能时。本研究将整合现有医学影像技术与数学建模及科学计算。PI将通过全球网络共享人脑的计算网格和大脑传输现象的符号代码。通过这种开放的互联网方法，他们将吸引越来越多的科学界的兴趣。预计该项目将为定量理解与某些类型的大脑疾病的发生和发展相关的流动物理奠定数学基础。因此，该项目是未来产生更好的诊断和新的治疗方案的先决条件。该教育计划为传播提案成果提供了具体步骤，包括通过教师研究经验（RET）开展高中数学和科学教育，以及通过本科生研究指导（REU）向少数民族和代表性不足群体推广。

CBET-0756154LinningerDiseases like stroke, tumors and hydrocephalus affect brain dynamics in millions of people worldwide. This project aims at advancing mathematical methods for studying soft tissue fluid interaction in the brain. The mathematical models will address large brain deformations in dynamic interaction with blood and cerebrospinal fluid motion with three salient features:an Euler-Lagrangian moving grid formulation for soft porous brain tissues; integration of cerebral vasculature into a porous deformable cell matrix.; and advancement of direct numerical solution algorithms based on inexact Newton-type methods with Krylov subspace iterations.For addressing the interdisciplinary nature of this project, the PI assembled a research team composed of biochemical engineers, two mathematicians, a neurosurgeon and an MRI physicist and biomedical engineer. Two major goals of the project are:Aim #1. Creation of a multi-scale fluid-structure interaction framework accounting for brain deformation mechanics with cerebrospinal fluid dynamics.Aim #2. We will incorporate realistic models of the cerebral vasculature.Existing models for computing large brain deformation dynamics are still unsatisfactory. The proposed holistic model of intracranial dynamics addresses key deficiencies. Specific aims (i) bridge the gap between recent advancements in medical imaging and rigorous mathematical analysis, (ii) create novel mathematical formulations for fluid-solid interaction for deforming soft porous media, and (iii) account for dilations of the cerebral vasculature. Comprehensive multi-phase models of brain, blood and cerebrospinal fluid interaction derived from patient-specific images have never been attempted before to the best of our knowledge. Currently quantitative analysis of medical images is slow, because there exists few mathematical methods for evaluating the interactions of blood, brain tissue and cerebrospinal fluid flow, distributed in the three-dimensional space and in time. Magnetic resonance imaging, angiography or computer tomography, will move forward biological and medical knowledge, when rigorous mathematical models to accurately predict transport phenomena become available. The proposed research will integrate existing medical imaging technology with mathematical modeling and scientific computing. The PI will share computational grids of human brains and symbolic codes for cerebral transport phenomena via the world-wide web. By this open internet approach, they will attract the interest of a growing scientific community. It is expected that this project will lay the mathematical foundations for a quantitative understanding of flow physics associated with the onset and progression of certain types of brain disorders. Thus, the project is prerequisite for generating better diagnostic and new treatment options in the future. The education plan provides specific steps for the dissemination of proposal outcomes and includes high school math and science education via the research experiences for teachers (RET), as well as outreach to minorities and underrepresented groups through undergraduate research (REU) mentorship.