pulsatile flow

Murray’s law, as the best-known optimal relationship between bifurcation calibers, is obtained based on the assumption of steady-state Poiseuille blood flow and is mostly accurate in small vessels. In middle sized and large vessels such as the aorta and coronary arteries, the pulsatile nature of the flow is dominant and deviations from Murray law have been observed. In the present study, a general scaling law is proposed, which describes the optimum relationship between the characteristics of bifurcations and pulsatile flow. This scaling law takes into account the deviations from Murray law in large vessels, and proposes optimal flow (i.e. less flow resistance) for the full range of the vascular system, from the small vessels to large ones such aorta. As a general scaling law, it covers both symmetrical and asymmetrical bifurcations. One of the merits of this scaling law is that bifurcation characteristics solely depend on the Womersley number of parent vessels. The diameter ratios suggested by this scaling law are in acceptable agreement with available clinical morphometric data such as those reported for coronary arteries and aortoiliac bifurcations. A numerical simulation of pulsatile flow for several Womersley numbers in bifurcation models according to the proposed scaling law and Murray law has been performed, which suggests that the general scaling law provides less flow resistance and more efficiency than Murray law in pulsatile flow.

In this study, comprehensive numerical simulations were conducted to examine laminar pulsatile developing flows through flat channels. The developing velocity fields and the hydrodynamic entry length were explored for the Reynolds numbers from 20 to 200, and the low and intermediate non-dimensional pulsation frequency or the Womersley number (1.08 ≤Wo≤ 8.86). For all simulations, the pulsating amplification factor was considered from zero to one, (0 ≤A≤ 1), and to achieve more practical and relevant outcomes, time-dependent parabolic inlet velocity profiles were applied. The outcomes reveal that for the higher values of the pulsation frequency or the Womersley number (6 ≤ Wo ≤ 8.66), the maximum pulsatile entranced length during a cycle is close to the inlet length of the mean component of the flow. On the other hand, for the rest of the Womersley number range (1.08 ≤ Wo < 6), and high amplification factor (0.5 ≤ A), the value of the entrance length increases and is significantly different from the development length of the steady component. Moreover, the results demonstrate that the entry length correlates with the Womersley number through a power-law function, whilst it has linear correlations with the Reynolds number and the amplification factor. Further, using the result of the accomplished numerical study, a practical correlation of the entrance length is offered to be used in the design phase for any type of pulsatile flow through the flat channels.

The presented paper aims at comparison of modelling approaches to a pulsatile fluid flow in aorta-like tube; it investigates their influence on the shape of the velocity profiles and waveforms, and consequently on wall shear stress. Comparisons of computational results between rigid and compliant tubes with laminar and low Re turbulent models of fluid are presented. The results were validated with PIV experimental data through the velocity profile in the half-length section of the tube for both cases (rigid and compliant) and the overall agreement was very good, almost perfect for the rigid case. Frequency of the pulse pump in the experimental circuit was 1Hz, the diameter of the tube ~ 20 mm, and maximum deformation of the compliant tube during a period was 12%. The turbulent model improved the agreement with the experimental data by flattening the velocity profiles in both cases, but the effect was much more pronounced for the compliant tube, especially during the deceleration phase. This work confirms the hypothesis stated by Brindise and Vlachos (2018) that a longer deceleration phase triggers transition to turbulence. We put foundations for extension of this hypothesis to compliant tubes where this conclusion was confirmed for physiological Reynolds and Womersley numbers. The main outputs of this study are: (i) the length of deceleration phase should be considered (in addition to the geometry or severity of stenosis) in decision whether fluid simulations should be performed with or without laminar flow assumption; (ii) for fluid simulations of blood vessels considering their compliance, a special care should be devoted to time synchronization between BCs to prevent unphysiological waveforms.

The present numerical study deals with a mathematical model representing mass transfer in blood flow under stenotic condition. Streaming blood is considered as a non-Newtonian fluid characterized by Carreau fluid model and the vessel wall is taken to be flexible. The nonlinear pulsatile flow phenomenon is governed by the Navier-Stokes equations together with the continuity equation while that of mass transfer is governed by the convection-diffusion equation coupled with the velocity field. A finite difference scheme is developed to solve these equations accompanied bysuitable initial and boundary conditions. Results obtained are examined for numerical stability up to wanted degree of correctness. Various significant hemodynamic parameters are examined for additional qualitative insight of the flow-field and concentration-field over the entire arterial segment with the help of the obtained numerical results. Comparisons are made with the available results in open literature and good agreement has been achieved between these two results. Comparisons have been made to understand the effects of viscosity models for Newtonian and non-Newtonian fluids and also for rigid and flexible arteries.

In this paper analytical expressions for time-dependent velocity profiles and pressure gradient are obtained for fully-developed laminar flows with given volume flow-rate conditions in circular pipe flows with slip boundary conditions. The governing equations are solved analytically using the traditional Laplace transform method together with Mellin’s inversion formula. The evolution of velocity profiles and pressure gradient for starting and pulsatile flow with slip boundary conditions are analyzed. New simplified expressions and perspectives on velocity and pressure gradient for no-slip and slip flows are obtained from the analytical results. New scalings in starting and pulsatile flows are proposed for pipe flows with no-slip and slip boundary conditions using nondimensional numbers. Special attention is paid to the effect of slip factor and pulsatile flow frequency on the time-dependent skin-friction factor. Finally, by using the starting and pulsating flow results, analytical expressions of velocity and pressure for arbitrary inflow are obtained by approximating the arbitrary volume flow-rate by a Fourier series

Recently, due to the development of CFD techniques, many attempts have been made to simulate the initiation and progression of atherosclerosis. In recent works, various curves have been suggested to model the stenosis shape. However, little effort has been made to study the importance of the stenosis shape on the flow behavior. In this study, four types of stenosis with asteroid, Gaussian, semi-circle, and sinusoidal shapes were simulated in order to study the effect of the stenosis shape on flow behavior and diagnosis parameters. Shear stress and flow behavior were investigated in the common carotid artery with stenosis severities of 30%, 40%, and 50%. Flow was assumed to be unsteady and the inlet to be a pulsatile flow. Two cases of Newtonian and non-Newtonian fluids were simulated. The no-slip and permeable boundary conditions were imposed on the outer walls. To examine the effect of the location of stenosis, modeling was conducted at various locations. The results showed that the maximum shear stress occurs in the Gaussian stenosis at the opening of the stenosis. Semi-circle, sinus, and asteroid shapes had the next largest shear stress values. Additionally, the location of stenosis had a negligible effect on the maximum shear stress. However, flow resistance increased with increasing the stenosis’s distance from the beginning of the artery. This study indicates that stenosis shape highly affects the flow characteristics, and stenosis severity is not the only parameter that is important. Hence, the stenosis shape should be considered when simulating atherosclerosis.

A numerical study of hemodynamic parameters of pulsatile blood flow is presented in a stenotic artery with
A numerical study of hemodynamic parameters of pulsatile blood flow is presented in a stenotic artery with non-Newtonian models using ADINA. Blood flow was considered laminar, and the arterial wall was considered rigid. Studied stenosis severities were 30, 50, and 70% of the cross-sectional area of the artery. Six non-Newtonian models were used to model the non-Newtonian behavior of blood, and their results were compared with the Newtonian model. The results showed that in Power-law and Walburn-Schneck models, unlike other models, shear stress values before and after the stenosis were smaller than Newtonian models. Also, in maximum flow rate, the Carreua, generalized Power-law, Casson, and Carreua-Yasuda models showed a reduction in global importance factor of non-Newtonian behavior, and subsequently, the results approached Newtonian model. In minimum flow rate, the global importance factor of Newtonian behavior increased, which highlighted the importance of Newtonian model. In minimum flow rate, Carreua-Yasuda model was more sensitive to the non-Newtonian behavior of blood compared to Carreua, Casson, and Power-law models. Also, in that time period, Walburn-Schneck was less sensitive to the non-Newtonian behavior of blood. On the other hand, this model did not show sensitivity when the flow rate was at its peak. Power-law model overestimated the global importance factor values. Therefore, Power-law model was not suitable, because it showed extreme sensitivity to dimension. Walburn-Schneck model was not suitable too because it lacked sensitivity.