MESH-FREE HIGH-RESOLUTION SIMULATION OF CEREBROCORTICAL OXYGEN SUPPLY WITH FAST FOURIER PRECONDITIONING.
MESH-FREE HIGH-RESOLUTION SIMULATION OF CEREBROCORTICAL OXYGEN SUPPLY WITH FAST FOURIER PRECONDITIONING.
复制标题
通过快速傅立叶预处理对脑皮质供氧进行无网格高分辨率模拟。
DOI：
10.1101/2023.01.09.523320
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发表时间：
2023
期刊：
影响因子：
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通讯作者：
Linninger,AndreasA
中科院分区：
文献类型：
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作者：
Ventimiglia,Thomas;Linninger,AndreasA
从血管到皮层脑组织的氧气转移是一类具有混合域特征的问题的代表。组织氧浓度的大规模有效计算取决于血管的管状网络耦合到组织网格的方式。对于非常密集的脑微血管系统来说，用连续网格明确地解决组织和血管系统之间的界面的模型是非常昂贵的。我们提出了混合域无网格技术，其中血管解剖网络（货车）表示为薄有向图，用于血氧对流，周围的血管外组织表示为三维体素的笛卡尔网格，氧气通过扩散传输。我们分裂的网络和组织网格的Schur补充方法的区域分解，以获得一个简化的系统方程组的组织氧浓度在稳态。使用笛卡尔网格可以使用基于快速傅里叶变换的Poisson求解器近似求解相应的矩阵方程，该求解器可以作为Krylov子空间迭代的有效预处理器。该方法的性能使得能够在不需要超级计算机的情况下，对解剖学上精确的血管网络进行皮质氧灌注的稳态模拟，分辨率低至1微米。
Oxygen transfer from blood vessels to cortical brain tissue is representative of a class of problems with mixed‐domain character. Large‐scale efficient computation of tissue oxygen concentration is dependent on the manner in which the tubular network of blood vessels is coupled to the tissue mesh. Models which explicitly resolve the interface between the tissue and vasculature with a contiguous mesh are prohibitively expensive for very dense cerebral microvasculature. We propose amixed‐domain mesh‐freetechnique whereby a vascular anatomical network (VAN) represented as a thin directed graph serves for convection of blood oxygen, and the surrounding extravascular tissue is represented as a Cartesian grid of 3D voxels throughout which oxygen is transported by diffusion. We split the network and tissue meshes by the Schur complement method of domain decomposition to obtain a reduced set of system equations for the tissue oxygen concentration at steady state. The use of a Cartesian grid allows the corresponding matrix equation to be solved approximately with a fast Fourier transform‐based Poisson solver, which serves as an effective preconditioner for Krylov subspace iteration. The performance of this method enables the steady‐state simulation of cortical oxygen perfusion for anatomically accurate vascular networks down to single micron resolution without the need for supercomputers.