Particle-fluid suspension model of blood flow through stenotic vessels with applications

The present study deals with the problem of blood flow through stenotic vessels when blood is represented by a particle-fluid suspension model, i.e. a suspension of red blood cells in plasma. The expressions for the dimensionless resistance to flow, the wall shear stress, and the shearing stress on the wall at the maximum height of the stenosis are derived. The results obtained in the analysis are discussed in brief, both qualitatively and quantitatively by comparison with other theories. It is observed that the magnitudes of the blood flow characteristics significantly increase with an increase in the red cell concentration. The importance of the decreasing vessel diameter is also pointed out. Finally, to observe the biological relevance of the analysis, the results obtained are used to compute the blood flow characteristics for normal and diseased blood using the experimental data from published literature and results are compared with those computed using the present theoretical approach.     

Steady flow of couple stress fluid through tubes of slowly varying cross-sections--application to blood flows

Steady laminar flow of a non-Newtonian fluid based on couple stress fluid theory, through narrow tubes of varying cross-sections has been studied theoretically. Asymptotic solutions are obtained for the basic equations and the expressions for the velocity field and the wall shear stress are derived for a general cross-section. Computation and discussions are carried out for the geometries which occur in the context of physiological flows or in particular blood flows. The tapered tubes and constricted tubes are of special importance. It is observed that increase in certain parameters results in erratic flow behaviour proximal to the constricted areas which is further enhanced by the increase in the geometric parameters. This elucidates the implications of the flow in the development of vascular lesions.     

Shear targeted drug delivery to stenotic blood vessels

In this review we focus on shear targeted drug delivery as a novel strategy to selectively deliver drugs to sites of vascular obstruction. We review the physics of stenotic (abnormally narrowed) blood vessels, while focusing mainly on the hemodynamics and transport phenomena at these sites. We then discuss how the local abnormal levels of shear stress, which can mechanically activate platelets, can be leveraged for localized drug delivery. We describe the development of Shear Activated Nano-particle Aggregates (SA-NPAs) that are designed to release and localize their nanoparticle drug carriers at sites of vascular stenosis. We present results in a variety of in vivo models, demonstrating the superiority of SA-NPAs carrying a thrombolytic drug compared to conventional treatment with the free drug. We also describe, shear-stress sensitive lenticular liposomes, which also show selective release under stenotic flow conditions. We then discuss limitations of both technologies, challenges in this new field and potential future applications. Altogether, we believe that mechano-sensitive therapeutics may offer a potential new approach for treatment of cardiovascular diseases.     

A model for blood flow through a stenotic tube

This article deals with the introduction of the modified Casson's fluid model as the true representation for the blood for the steady laminar flow through a small diameter artery with axi-symmetric identical double stenoses in series. The governing equations are solved by using the finite element method. The results for the velocity profiles, the pressure and the wall shear stress distributions in addition to the location and length of the flow reversal zones have been brought out and discussed in reference to the severity of the disease. It has been observed that the non-Newtonian nature of the blood helps in reducing the magnitude of the peak wall shear stress at the throat and the length of the reversed flow regions in the post stenotic dilatation.     

Peristaltic flow of a couple stress fluid in an asymmetric channel

This paper presents an analysis of the peristaltic flow of a couple stress fluid in an asymmetric channel. The asymmetric nature of the flow is introduced through the peristaltic waves of different amplitudes and phases on the channel walls. Mathematical modelling corresponding to a two-dimensional flow has been carried out. The flow analysis is presented under long wavelength and low Reynolds number approximations. Closed form solutions for the axial velocity, stream function and the axial pressure gradient are given. Numerical computations have been carried out for the pressure rise per wavelength, friction forces and trapping. It is noted that there is a decrease in the pressure when the couple stress fluid parameter increases. The variation of the couple stress fluid parameter with the size of the trapped bolus is also similar to that of pressure. Furthermore, the friction force on the lower channel wall is greater than that on the upper channel wall.     

Influence of stenosis morphology on flow through severely stenotic vessels: implications for plaque rupture

Flow patterns and flow-related stresses contribute to the characterization of health risks, particularly the risk of plaque rupture, posed by a particular atherosclerotic stenosis. Blood flow in the presence of significant plaque deposits is investigated, and the influence of factors such as stenosis morphology and surface irregularity is evaluated. Solutions for three-dimensional, unsteady flow in these stenotic vessels are obtained for an incompressible, Newtonian fluid. The equations of motion are solved numerically using a finite volume formulation. The resulting flow patterns and shear and normal stresses are interpreted with respect to diagnostic implications, including the possibility of plaque rupture. The inadequacy of "percent stenosis" to characterize the risks posed by a particular plaque is demonstrated. Surface irregularity, stenosis aspect ratio, and the shape of the pulsatile waveform all have considerable influence on the flow field and on the stresses on the plaque. A measure of surface irregularity or plaque symmetry, in particular, may complement percent stenosis in diagnosing the risk of plaque rupture.     

A couple stress model of blood flow in the microcirculation

A simple mathematical model depicting blood flow in the capillary is developed with an emphasis on the permeability property of the blood vessel based on Starling's hypothesis. In this study the effect of inertia has been neglected in comparison with the viscosity on the basis of the smallness of the Reynolds number of the flow in the capillary. The capillary blood vessel is approximated by a circular cylindrical tube with a permeable wall. The blood is represented by a couple stress fluid. With such an ideal model the velocity and pressure fields are determined. It is shown that an increase in the couple stress parameter increases the resistance to the flow and thereby decreases the volume rate flow. A comparison of the results with those of the Newtonian case has also been made.     

Flow through zone 1 lungs utilizes alveolar corner vessels

We have previously observed flows equivalent to 15% of the resting cardiac output of rabbits occurring through isolated lungs that were completely in zone 1. To distinguish between alveolar corner vessels and alveolar septal vessels as a possible zone 1 pathway, we made in vivo microscopic observations of the subpleural alveolar capillaries in five anesthetized dogs. Videomicroscopic recordings were made via a transparent thoracic window with the animal in the right lateral position. From recordings of the uppermost surface of the left lung, alveolar septal and corner vessels were classified depending on whether they were located within or between alveoli, respectively. Observations were made with various levels of positive end-expiratory pressure (PEEP) applied only to the left lung via a double-lumen endotracheal tube. Consistent with convention, flow through septal vessels stopped when PEEP was raised to the mean pulmonary arterial pressure (the zone 1-zone 2 border). However, flow through alveolar corner vessels continued until PEEP was 8-16 cmH2O greater than mean pulmonary arterial pressure (8-16 cm into zone 1). These direct observations support the idea that alveolar corner vessels rather than patent septal vessels provide the pathway for blood flow under zone 1 conditions.     

Numerical modeling of pulsatile turbulent flow in stenotic vessels

Pulsatile turbulent flow in stenotic vessels has been numerically modeled using the Reynolds-averaged Navier-Stokes equation approach. The commercially available computational fluid dynamics code (CFD), FLUENT, has been used for these studies. Two different experiments were modeled involving pulsatile flow through axisymmetric stenoses. Four different turbulence models were employed to study their influence on the results. It was found that the low Reynolds number k-omega turbulence model was in much better agreement with previous experimental measurements than both the low and high Reynolds number versions of the RNG (renormalization-group theory) k-epsilon turbulence model and the standard k-epsilon model, with regard to predicting the mean flow distal to the stenosis including aspects of the vortex shedding process and the turbulent flow field. All models predicted a wall shear stress peak at the throat of the stenosis with minimum values observed distal to the stenosis where flow separation occurred.     

Peristaltic transport of a couple stress fluid in a uniform and non-uniform channels

The problem of peristaltic transport of a couple stress fluid in uniform and non-uniform two-dimensional channels has been investigated under zero Reynolds number with long wavelength approximation. Blood is represented by a couple stress fluid (a fluid which its particles size are taken into account, a special case of a non-Newtonian fluid). It is found that the pressure rise decreases as the couple stress fluid parameter gamma increases (i.e., small size fluid particle). So the pressure rise for a couple stress fluid (as a blood model) is greater than that for a Newtonian fluid. Also the pressure rise increases as the amplitude ratio phi increases for different values of gamma. Further, the pressure rise in the case of non-uniform geometry is found to be much smaller than the corresponding value in the case of uniform geometry. Finally, the maximum pressure rise when the mean flow rate over one period of the wave, Q = 0, increases as phi increases and gamma decreases.     

The importance of blood rheology in patient-specific computational fluid dynamics simulation of stenotic carotid arteries

Biomechanics and Modeling in Mechanobiology - The initiation and progression of atherosclerosis, which is the main cause of cardiovascular diseases, correlate with local haemodynamic factors such...     

Flow cytometric determination of cell proliferation in hypertensive blood vessels.

BACKGROUND: Measurement of vascular cell proliferation in animal models of hypertension is currently accomplished by demonstrating [(3)H]-thymidine ([(3)H]-dT) incorporation into DNA using autoradiography. This method, however, is labor intensive, requires radioactivity, and is limited by the inherent difficulty in discriminating labeled and unlabeled cells. To address these limitations, a flow cytometric-based method is described utilizing incorporation of 5-bromo-2'-deoxyuridine (BrdU) into DNA of nuclei isolated from blood vessels. METHODS: Pulmonary hypertension was induced in rats by exposure to 10% O(2) (hypoxia) for varying periods of time. Pulmonary arteries and aorta from rats injected with BrdU prior to sacrifice were isolated, fixed with 10% formalin, and digested with Protease XIV. The intact nuclei liberated by this treatment were successively treated with HCl/Triton X-100 and sodium borate. Processed nuclei were probed with a BrdU-specific fluorescein-conjugated antibody, and the percentage of BrdU staining cells was determined using flow cytometry. RESULTS: An approximately 20-fold increase in BrdU-positive cells at 3 days of hypoxia in pulmonary arteries (relative to control) with no change in aorta was observed. These results were similar to previous studies using [(3)H]-dT labeling. CONCLUSIONS: Flow cytometric determination of cell proliferation in blood vessels is a simple, objective technique that may facilitate measurement of cell proliferation in animal models of vascular disease.     

Effect of couple stresses on the unsteady convective diffusion in fluid flow through a channel

A generalized dispersion model is used to obtain exact solution for unsteady convective diffusion in the presence of couple stresses. The effect of the couple stress parameter 'a' on the most dominant dispersion coefficient is clearly depicted. The dimensionless mean concentration distribution is obtained as a function of dimensionless axial distance, time and 'a'. The results for 'pure convection' are also reported. It is shown that the effect of couple stress is predominant only for small values of 'a' and when a----infinity the flow characteristics tend to their equivalents in Newtonian theory. The results of Taylor's dispersion model are recovered as a particular case in the limit tau----infinity.     

Effects of couple stresses on the blood flow through an artery with mild stenosis

An analysis of the effects of couple stresses on the blood flow through thin artery in the presence of very mild stenosis has been carried out with the help of two nondimensional parameters, alpha (the length ratio parameter) and eta (the parameter characterizing the antisymmetric property of the couple stress tensor). It is shown that an increase in the couple stress (small value of alpha and eta), increases the resistance to the flow and the wall shear stress. These characteristics are further enhanced by the presence of the stenosis.     

A fluid--structure interaction finite element analysis of pulsatile blood flow through a compliant stenotic artery.

A new model is used to analyze the fully coupled problem of pulsatile blood flow through a compliant, axisymmetric stenotic artery using the finite element method. The model uses large displacement and large strain theory for the solid, and the full Navier-Stokes equations for the fluid. The effect of increasing area reduction on fluid dynamic and structural stresses is presented. Results show that pressure drop, peak wall shear stress, and maximum principal stress in the lesion all increase dramatically as the area reduction in the stenosis is increased from 51 to 89 percent. Further reductions in stenosis cross-sectional area, however, produce relatively little additional change in these parameters due to a concomitant reduction in flow rate caused by the losses in the constriction. Inner wall hoop stretch amplitude just distal to the stenosis also increases with increasing stenosis severity, as downstream pressures are reduced to a physiological minimum. The contraction of the artery distal to the stenosis generates a significant compressive stress on the downstream shoulder of the lesion. Dynamic narrowing of the stenosis is also seen, further augmenting area constriction at times of peak flow. Pressure drop results are found to compare well to an experimentally based theoretical curve, despite the assumption of laminar flow.