Atalla Ashraf, Jeremic Aleksandar
Department of Electrical & Computer Engineering, McMaster University, Hamilton, ON, Canada.
Annu Int Conf IEEE Eng Med Biol Soc. 2010;2010:746-51. doi: 10.1109/IEMBS.2010.5626318.
Capillary - tissue fluid exchange is controlled by the blood pressure in the capillary and the osmotic pressure of blood (pressure of the tissue fluid outside the capillaries). In this paper, we develop a mathematical model to simulate the movement of bacteria into and within a capillary segment. The model is based on Fokker-Planck equation and Navier-Stocks equations that accounts for different boundary conditions. Also, we model the transportation through capillary walls by means of anisotropic diffusivity that depends on the pressure difference across the capillary walls. By solving the model with a numerical method, it was possible to predict the concentration of bacteria at points within the capillary. However, numerical analysis consumes computational time and resources. To efficiently simulate the bacterial clearance, we propose a segmentation model that is based on breaking the capillary network into smaller sections with pre-defined properties in order to reduce the overall computational time. The proposed model shows a great reduction in computational time and provides accurate results when compared to the numerical analysis.
毛细血管 - 组织液交换受毛细血管中的血压和血液渗透压（毛细血管外组织液的压力）控制。在本文中，我们开发了一个数学模型来模拟细菌进入毛细血管段并在其中移动的过程。该模型基于福克 - 普朗克方程和纳维 - 斯托克斯方程，并考虑了不同的边界条件。此外，我们通过依赖于毛细血管壁两侧压力差的各向异性扩散率来模拟通过毛细血管壁的传输。通过用数值方法求解该模型，可以预测毛细血管内各点的细菌浓度。然而，数值分析消耗计算时间和资源。为了有效地模拟细菌清除，我们提出了一种分段模型，该模型基于将毛细血管网络分解为具有预定义属性的较小部分，以减少总体计算时间。与数值分析相比，所提出的模型显示出计算时间大幅减少，并提供了准确的结果。
