Serajelahi B, Kharche S, Goldman D
Annu Int Conf IEEE Eng Med Biol Soc. 2020 Jul;2020:2279-2282. doi: 10.1109/EMBC44109.2020.9175901.
Simulations that are meant to determine the steady-state distribution of a diffusible solute such as oxygen in tissues have typically used finite difference methods to solve the diffusion equation. Finite difference methods require a tissue mesh with enough points to resolve oxygen gradients near and between discrete blood vessels. The large number of points that are typically required can make these calculations very slow. In this paper, we investigate a numerical method known as the Green's function method which is not bound by the same constraint. The Green's function method is expected to yield an accurate oxygen distribution more quickly by requiring fewer mesh points. Both methods were applied to calculate the steady state oxygen distribution in a model simulation region. When the Green's function calculation used meshes with 1/2, 1/4 and, 1/8 of the resolution required for the finite-difference mesh, there was good agreement with the finite difference calculation in all cases. When the volume of the domain was increased 8-fold the Green's function method was able to calculate the O field in 22 minutes, whereas the finite difference calculation is expected to take approximately 1 week. The number of steps required for the Green's function calculation increases quadratically with the number of points in the tissue mesh. As a result, small meshes are calculated very quickly using Green's functions, while for larger mesh sizes this method experiences a significant decrease in efficiency.
旨在确定诸如组织中氧气等可扩散溶质稳态分布的模拟通常使用有限差分法来求解扩散方程。有限差分法需要一个具有足够点的组织网格，以解析离散血管附近和之间的氧气梯度。通常所需的大量点会使这些计算非常缓慢。在本文中，我们研究了一种称为格林函数法的数值方法，该方法不受相同约束的限制。预计格林函数法通过需要更少的网格点能够更快地得出准确的氧气分布。两种方法都应用于计算模型模拟区域中的稳态氧气分布。当格林函数计算使用的网格分辨率为有限差分网格所需分辨率的1/2、1/4和1/8时，在所有情况下与有限差分计算都有很好的一致性。当域的体积增加8倍时，格林函数法能够在22分钟内计算出氧场，而有限差分计算预计需要大约1周时间。格林函数计算所需的步数随组织网格中的点数呈二次方增加。因此，使用格林函数可以非常快速地计算小网格，而对于较大的网格尺寸，该方法的效率会显著降低。
