Bulletin of Mathematical Biology

, Volume 49, Issue 3, pp 257-277

First online:

A study on the non-linear flow of blood through arteries

  • J. C. MisraAffiliated withDepartment of Mathematics, Indian Institute of Technology
  • , S. I. SinghAffiliated withDepartment of Mathematics, Indian Institute of Technology

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The pulsatile flow of blood through arteries is investigated in this paper by treating the blood vessel as a thin-walled anisotropic, non-linearly viscoelastic, incompressible circular cylindrical shell; nonlinearities of the flow of blood are also paid due consideration. The displacement components of the vessel wall are obtained from the equations of equilibrium which have been linearized by employing the principle of superimposition of a small deformation on a state of known finite deformation. The influence of the wall deformation on the flow properties of blood, has been accounted for by considering suitably formulated continuity conditions. A finitedifference scheme is employed for solving the flow equations together with the boundary and initial conditions by using the locally measured values of pressure and pressure gradient. Numerical results obtained for the velocity profile of blood flowing in a canine middle descending thoracic aorta have been presented through figures.