The mechanics of the blood flow in a flexible tapered artery with stenosis is studied from the viewpoint of a mathematical model. The flowing blood is represented by a two-fluid model, consisting of a core region of suspension of all erythrocytes assumed to be characterized by a Casson fluid and a peripheral plasma layer free from cells of any kind as a Newtonian fluid. The moving wall of the artery is treated as an anisotropic, linear viscoelastic incompressible circular cylindrical membrane cell. The effect of the surrounding connective tissues on the motion of the artery wall is also given due attention. The unsteady flow mechanism, subjected to a pulsatile pressure gradient has been solved using the finite difference scheme by exploiting the appropriate physically realistic prescribed conditions. The present model is also employed to study the effect of taper angle, the wall deformation, the severity of the stenonis, the viscosity of the peripheral layer, and the non-Newtonian rheology of streaming blood on the dynamic flow field. Finally, the numerical illustration presented at the end of the paper provides an effective quantitative measure of the flux, the resistive impedance and the wall shear stress through their graphical representations and also a few comparisons with the existing results have been made in order to validate the applicability of the present model. 2000 Mathematics Subject Classification: 35A22; 65M06; 74-99; 76D05.

An updated numerical simulation of unsteady generalized Newtonian blood flow through differently shaped distensible arterial stenoses is developed. A shear-thinning fluid modelling the deformation dependent viscosity of blood is considered for the characterization of generalized Newtonian behaviour of blood. The arterial model is treated as two-dimensional and axisymmetric with an outline of the stenosis obtained from a three-dimensional casting of a mildly stenosed artery. The full Navier-Stokes equations governing blood flow are written in the dimensionless form and the solution is accomplished by finite time-step advancement through their finite difference staggered grid representations. The marker and cell (MAC) method comprising the use of a set of marker particles moving with the fluid is used for the purpose. Results are obtained for three differently shaped stenoses - irregular, smooth and cosine curve representations. The present results do agree well with those of existing investigations in the steady state, but contrary to their conclusions the present findings demonstrate that the excess pressure drop across the cosine and the smooth stenoses is caused by neither their smoothness nor their higher degree of symmetry relative to the irregular stenosis, but is rather an effect of area cover with respect to the irregular stenosis. This effect clearly prevails throughout the entire physiological range of Reynolds numbers. Further the in-depth study in flow patterns reveals the development of flow separation zones in the diverging part of the stenosis towards the arterial wall, and they are influenced by non-Newtonian blood rheology, distensibility of the wall and flow unsteadiness in order to validate the applicability of the present model.

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Balloon angioplasty followed by local delivery of antiproliferative drugs to target tissue is increasingly being considered for the treatment of obstructive arterial disease, and yet there is much to appreciate regarding pharmacokinetics in arteries of non-uniform disease. We developed a computational model capable of simulating drug-coated balloon delivery to arteries of heterogeneous tissue composition comprising healthy tissue, as well as regions of fibrous, fibro-fatty, calcified and necrotic core lesions. Image processing using an unsupervised clustering technique was used to reconstruct an arterial geometry from a single, patient-specific color image obtained from intravascular ultrasound-derived virtual histology. Transport of free drug was modeled using a time-dependent reaction-diffusion model and the bound, immobilized drug using the time-dependent reaction equation. The governing equations representing the transport of free as well as bound drug along with a set of initial settings and boundary conditions were solved numerically using an explicit finite difference scheme that satisfied the Courant-Friedrichs-Lewy stability criterion. Our results support previous findings related to the transport and binding of drug in arteries where tissue retention is strongly dependent on local pharmacologic properties. Additionally, modeling results indicate that non-uniform disease composition leads to heterogeneous arterial drug distribution patterns, although further validation using animal studies is required to fully appreciate pharmacokinetics in disease-laden arteries.

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