Skip to main content
SpringerLink
Log in

Performance modeling and analysis of blood flow in elastic arteries

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

Two different non-Newtonian models for blood flow are considered, first a simple power law model displaying shear thinning viscosity, and second a generalized Maxwell model displaying both shear thinning viscosity and oscillating flow viscous-elasticity. These models are used along with a Newtonian model to study sinusoidal flow of blood in rigid and elastic straight arteries in the presence of magnetic field. The elasticity of blood does not appear to influence its flow behavior under physiological conditions in the large arteries, purely viscous shear thinning model should be quite realistic for simulating blood flow under these conditions. On using the power law model with high shear rate for sinusoidal flow simulation in elastic arteries, the mean and amplitude of the flow rate were found to be lower for a power law fluid compared to Newtonian fluid for the same pressure gradient. The governing equations have been solved by Crank-Niclson scheme. The results are interpreted in the context of blood in the elastic arteries keeping the magnetic effects in view. For physiological flow simulation in the aorta, an increase in mean wall shear stress, but a reduction in peak wall shear stress were observed for power law model compared to a Newtonian fluid model for matched flow rate wave form. Blood flow in the presence of transverse magnetic field in an elastic artery is investigated and the influence of factors such as morphology and surface irregularity is evaluated.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

τ:

wall shear stress

γ:

shear rate

τγ :

yield stress

ηc :

Casson viscosity

k :

the consistency index

n :

non-Newtonian index

τ p :

shear stress of thepth element

ω:

angular velocity

R :

vessel's radius

C :

wave speed

M :

magnetic parameter (Hartmann number)

u, w :

velocity component in ther- andz-directions, respectively

P :

pressure

α:

unsteadiness parameter

\(\bar k,\bar R\) :

mean parameters

T p :

relaxation time of thepth element

ρ:

density

References

  1. Thurston G B. Rheological parameters for the viscosity, visco-elasticity and thixotropy of blood[J].Biorheology, 1979,16:149–155.

    Google Scholar 

  2. Liepsch D, Moravec S. Pulsatile flow of non-Newtonian fluid in distensible models of human arteries[J].Biorheology, 1984,21:571–583.

    Google Scholar 

  3. Rindt C C M, Van de Vosse F N, Van Steenhoven A A,et al. A numerical and experimental analysis of the human carotid bifurcation[J].J Biomechanics, 1987,20:499–509.

    Article  Google Scholar 

  4. Nazemi M, Kleinstreuer C, Archie J P. Pulsatile two-dimensional flow and plaque formation in a carotid artery bifurcation[J].J Biomechanics, 1990,23(10):1031–1037.

    Article  Google Scholar 

  5. Rodkiewicz C M, Sinha P, Kennedy J S. On the application of a constitutive equation for whole human blood[J].J Biomechanical Engg, 1990,112:198–204.

    Google Scholar 

  6. Boesiger P, Maier S E, Kecheng L,et al. Visualisation and quantification of the human blood flow by magnetic resonance imaging[J].J Biomechanics, 1992,25:55–67.

    Article  Google Scholar 

  7. Perktold K, Thurner E, Kenner T. Flow and stress characteristics in rigid walled compliant carotid artery bifurcation models[J].Medical and Biological Engg and Computing, 1994,32:19–26.

    Google Scholar 

  8. Sharma G C, Kapoor J. Finite element computations of two-dimensional arterial flow in the presence of a transverse magnetic field[J].International J for Numerical Methods in Fluid Dynamics, 1995,20:1153–1161.

    Article  MATH  Google Scholar 

  9. Dutta A, Tarbell J M. Influence of non-Newtonian behavior of blood on flow in an elastic artery model[J].ASME J Biomechanical Engg, 1996,118:111–119.

    Google Scholar 

  10. Lee R, Libby P. The unstable atheroma[J].Arteriosclerosis Thrombosis Vascular Biology, 1997,17:1859–1867.

    Google Scholar 

  11. Korenaga R, Ando J, Kamiya A. The effect of laminar flow on the gene expression of the adhesion molecule in endothelial cells[J].Japanese J Medical Electronics and Biological Engg, 1998,36: 266–272.

    Google Scholar 

  12. Rachev A, Stergiopelos N, Meister J J. A model for geometric and mechanical adaptation of arteries to sustained hypertension[J].J Biomechanical Engg, 1998,120:9–17.

    Google Scholar 

  13. Rees J M, Thompson D S. Shear stress in arterial stenoses: a momentum integral model[J].J Biomechanics, 1998,31:1051–1057.

    Article  Google Scholar 

  14. Tang D, Yang C, Huang Y,et al. Wall stress and strain analysis using a three-dimensional thick wall model with fluid-structure interactions for blood flow in carotid arteries with stenoses[J].Computers and Structures, 1999,72:341–377.

    Article  MATH  Google Scholar 

  15. Zendehbudi G R, Moayary M S. Comparison of physiological and simple pulsatile flows through stenosed arteries[J].J Biomechanics, 1999,32:959–965.

    Article  Google Scholar 

  16. Berger S A, Jou L D. Flows in stenotic vessels[J].Annual Review of Fluid Mechanics, 2000,32: 347–384.

    Article  MATH  MathSciNet  Google Scholar 

  17. Botnar R, Rappitch G, Scheidegger M B,et al. Hemodynamics in the carotid artery bifurcation: a comparison between numerical simulation and in vitro MRI measurements[J].J Biomechanics, 2000,33:137–144.

    Article  Google Scholar 

  18. Stroud J S, Berger S A, Saloner D. Influence of stenosis morphology on flow through severely stenotic vessels: implications for plaque rupture[J].J Biomechanics, 2000,33:443–455.

    Article  Google Scholar 

  19. Sharma G C, Jain M, Kumar A. Finite element Galerkin approach for a computational study of arterial flow[J].Applied Mathematics and Mechanics (English Edition), 2001,22(9):1012–1018.

    MATH  Google Scholar 

  20. Milnor W R.Hemodynamics[M]. 2nd edition. Williams and Wilkins, Baltimore, 1989.

    Google Scholar 

  21. White K C. Hemo-dynamics and wall shear rate measurements in the abdominal aorta of dogs[D]. Ph D Thesis, The Pennsylvania State University, 1991.

  22. Dutta A, Wang D M, Tarbell J M. Numerical analysis of flow in an elastic artery model[J].ASME J Biomechanical Engg, 1992,114:26–32.

    Google Scholar 

  23. Patel D J, Janicki J S, Vaishnav R N,et al. Dynamic anisotropic viscoelastic properties of the aorta in living dogs[J].Circulation Research, 1973,32:93–98.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Post-Graduate Studies and Research in Mathematics & Computer Science, S. Varshney College, 202001, Aligarh, India

    Anil Kumar & C. L. Varshney

  2. Institute of Basic Science, Khandari, 282002, Agra, India

    G. C. Sharma

Authors
  1. Anil Kumar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. C. L. Varshney
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. G. C. Sharma
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by ZHOU Zhe-wei

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kumar, A., Varshney, C.L. & Sharma, G.C. Performance modeling and analysis of blood flow in elastic arteries. Appl Math Mech 26, 345–354 (2005). https://doi.org/10.1007/BF02440085

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02440085

Key words

Chinese Library Classification

2000 Mathematics Subject Classification

2000 Mathematics Subject Classification

Search

Navigation