Research Center in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai, Thailand.
Center of Excellence in Mathematics, CHE, Bangkok, Thailand.
Cardiovasc Hematol Disord Drug Targets. 2020;20(1):16-30. doi: 10.2174/1871529X19666190509111336.
A mathematical model of blood flow is a way to study the blood flow behavior. In this research work, a mathematical model of non-Newtonian blood flow through different stenosis, namely bell shape and cosine shape, is considered. The physiologically important flow quantities of blood flow behavior to describe the blood flow phenomena are obtained such as resistance to flow, skin friction and blood flow rate.
Mathematical methods are used to analyze a mathematical model of blood flow through stenosed artery. The resistance to flow, skin friction and blood flow rate were obtained to describe the blood flow in stenosis. The resistance to flow is a relation between pressure and blood flow rate while the skin friction is the friction at the artery membrane. Resutls: The blood flow in cosine geometry exhibits higher resistance to flow and flow rate than in the bell geometry, while the blood flow in bell geometry gives a higher skin friction than in cosine geometry. Not only the effect of stenotic geometry was studied but also the effect of stenosis depth and stenosis height on the flow quantities Moreover, the power law index was adjusted to explore the non-Newtonian behavior. When blood exhibits Newtonian behavior, the resistance to flow and skin friction decrease but the blood flow rate increases.
The stenosed artery geometry, the stenosis length, stenosis depth and the power law index (non-Newtonian behavior) are important factors affecting the blood flow through the stenosed artery. This work provides some potential aspects to further study the causes and development of cardiovascular diseases.
血流的数学模型是研究血流行为的一种方法。在这项研究工作中，考虑了通过不同狭窄部位（即钟形和余弦形）的非牛顿血流的数学模型。获得了血流行为的生理上重要的血流参数，如流动阻力、壁面摩擦力和血流速率，以描述血流现象。
使用数学方法分析狭窄动脉中的血流数学模型。获得了流动阻力、壁面摩擦力和血流速率，以描述狭窄部位的血流。流动阻力是压力与血流速率之间的关系，而壁面摩擦力是动脉膜上的摩擦力。
与钟形几何形状相比，余弦几何形状的血流具有更高的流动阻力和血流速率，而钟形几何形状的血流产生的壁面摩擦力高于余弦几何形状。不仅研究了狭窄几何形状的影响，还研究了狭窄深度和狭窄高度对流动参数的影响，此外，还调整了幂律指数以探索非牛顿行为。当血液表现出牛顿行为时，流动阻力和壁面摩擦力减小，但血流速率增加。
狭窄动脉的几何形状、狭窄长度、狭窄深度和幂律指数（非牛顿行为）是影响狭窄动脉中血流的重要因素。这项工作为进一步研究心血管疾病的病因和发展提供了一些潜在方面。
