Study of pressure applied to blood vessels using a mathematical model

Document Type : Research Paper


Department of Mathematic, Faculty of Education, Kufa University, Iraq


In this paper we present a dynamic model of the heart’s pumping blood. To predict blood flow and pressure applied to the area of blood vessels (arteries - veins - capillaries). The fluid dynamics model is derived from the continuum equation and the Navier-Stokes equations. For an incompressible Newton flow through a network of cylindrical vessels. This paper combined a model of pressure applied to the walls of blood vessels with a (regular - turbulent) flow model of blood, and the viscoelastic deformation of the walls (arteries - veins - capillaries) was studied with different blood density and prediction of the effect of the thickness of the rubber wall on the flow and the resulting pressure on the blood vessels. The results of this study show that the viscous elastic wall of the blood vessels allows more physiological prediction of pressure and vascular deformation, and that blood flow with varying intensity is more in the aorta than in the rest of the vessels, and this is subject to wide dilation.


[1] T.A. Al-asadi and A.J. Obaid, Object-based image retrieval using enhanced SURF, Asian J. Info. Tech. 15(16) (2016) 2756–2762.
[2] L.H. Back, Y.I. Cho, D.W. Crawford and R.F. Cuffel, Effect of mild atherosclerosis on flow resistance in a coronary artery casting of man, J. Biomech. Engin. 106(1) (1948) 48–53.
[3] O. Buyukdagli and S. Yeralan, How do weights affect faculty performance evaluations, Sustainable Engin. Innov. 2(2) (2020) 89–101.
[4] G. Lakshmi, M. Ghonge and A.J. Obaid, Cloud based IoT smart healthcare system for remote patient monitoring, EAI Endorsed Trans. Pervasive Health Tech. (2021).
[5] C.H. Liu and S.C. Niranjan, Airway mechanics, gas exchange and blood flow in a nonlinear model of the normal human lung, J. Appl. Physio. 84 (1998) 1447–1469.
[6] Kh.S. Mekheimer and M.A. El Kot, Mathematical modeling of unsteady flow of Sisko fluid through an anisotropically tapered elastic arteries with time-variant overlapping stenosis, Appl. Math. Model. 36(11) (2012) 5393–5407.
[7] E. Ryzhii and M. Ryzhii, Modeling of Heartbeat Dynamics with a System of Coupled Nonlinear Oscillators, In: T.D. Pham, K. Ichikawa, M. Oyama-Higa, D. Coomans and X. Jiang (eds) Biomedical Informatics and Technology, ACBIT 2013, Communications in Computer and Information Science, Springer, Berlin, Heidelberg, 404 (2014) 67–75.
[8] D.S. Sankar and Y. Yatim, Comparative Analysis of Mathematical Models for Blood Flow in Tapered Constricted Arteries, Abstr. App. Anal. 2012 (2012) 235960.
[9] M. Schumacher and R.S. Tubbs, Anatomy, Imaging and Surgery of the Intracranial Dural Venous Sinuses, Elsevier, Amsterdam, 2020.
[10] S.R. Shah and R. Kumar, Mathematical Modeling of Blood Flow With the Suspension of Nanoparticles Through a Tapered Artery With a Blood Clot, Front. Nanotech. 2(14) (2020).
[11] B.H. Yang, H.H. Asada and Y. Zhang, Cuffless continuous monitoring of blood pressure using hemodynamic model, Home Autom. Health. Consortium Progress Rep. (2–3) (1999).
Volume 13, Issue 1
March 2022
Pages 1341-1350
  • Receive Date: 08 July 2021
  • Revise Date: 28 August 2021
  • Accept Date: 16 September 2021