Mathematical Modeling of Blood Flow Through Human Femoral Arteries and the Analysis of Model Parameters

• Published in: International journal of applied and computational mathematics 2022-02, Vol.8 (1), Article 30
• Main Authors: Karthik, A., Radhika, T. S. L., Praveen Kumar, P. T. V.
• Format: Article
• Language: English
• Subjects: Applications of Mathematics; Applied mathematics; Arteries; Blood flow; Blood vessels; Computational mathematics; Computational Science and Engineering; Flow velocity; Mathematical and Computational Physics; Mathematical Modeling and Industrial Mathematics; Mathematical models; Mathematics; Mathematics and Statistics; Newtonian fluids; Non Newtonian fluids; Nuclear Energy; Operations Research/Decision Theory; Original Paper; Parameter identification; Shear rate; Simulation; Statistical analysis; Statistical models; Theoretical; Veins & arteries; Viscosity; Wall shear stresses
• ISSN: 2349-5103; 2199-5796
• DOI: 10.1007/s40819-021-01228-7

In this work, we propose mathematical models for blood flow through human femoral arteries, fit statistical models to the data generated by simulations and identify model parameters that are significant on the blood flow. It is known that blood is a complex fluid whose viscosity varies with the shear rate, and this biophysical parameter, i.e., the blood viscosity is a critical determinant of friction against the vessel walls. Thus, we built two mathematical models; one describes blood as a Newtonian fluid (model-1) that defines viscosity as a constant and the other as a non-Newtonian fluid (model-2) that describes viscosity as a function of shear rate. The models developed incorporating the salient features of arterial blood flow consisted of three sets of parameters called the fluid parameters (to describe blood), the flow parameters (to describe the nature of blood flow), and the material and geometric parameters (to describe the nature of arteries). With the help of publicly available data on the human femoral artery for both male and female populations with different ages ranging from 19 years to 60+ , we carried out simulations using the developed models. Later, we performed statistical analysis of the data generated through simulations and identified the potential predictor variables on the two physical quantities computed: the wall shear stress and the volumetric flow rate. An interesting idea in this study is that we projected these models to describe the different states of health of human arteries: model-1 for “healthy,” model-2 for “transient,” and that with large values of a non-Newtonian parameter for the “unhealthy.”