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This paper presents a numerical solution to the problem of time-dependent blood flow via a w-shaped stenotic conduit, driven by pulsatile pressure gradient. The problem is formulated in cylindrical coordinates by employing the theoretical model of tangent hyperbolic fluid. The electro-osmotic effects are also taken into consideration. To simplify the non-dimensional governing equations of the flow problem, a mild stenosis assumption is utilized and the impact of the blood vessel wall is mitigated by employing a radial coordinate transformation. An explicit finite difference method is used to solve the resulting nonlinear system of differential equations, considering the auxiliary conditions specified at the boundary of the blood channel. After obtaining the numerical solution to the problem, an examination is carried out for various flow variables, such as axial velocity, temperature field, mass concentration, skin friction, Nusselt number, and Sherwood number. These results are presented graphically, and a concise explanation is provided using physical facts. An increase in flow rate and blood velocity leads to a rise in response, while an increase in stenosis height, Weissenberg number, and power-law exponent leads to a reverse response. Furthermore, the temperature field is significantly affected by the Brinkman number and the Prandtl number.

In this paper, the lattice Boltzmann (LB) method is used in order to simulate non-Newtonian blood flows in deformable vessels. Casson's rheological model is adopted and a local correction to the relaxation time is implemented in order to modify the viscosity. The hyperelastic, hardening and anisotropic behavior of a flexible arterial wall is discussed and a closed-form solution is used to predict the deformed configuration of the vessel. A partitioned staggered-explicit strategy to couple the LB method and such analytical prediction is proposed.

The study of biological fluids in the presence of a magnetic field is known as biomagnetic fluid dynamics (BFD). The research work in BFD has been rapidly growing due to its applications in developing magnetic devices used for cell separation, targeted drug delivery and cancer tumor treatment. This study aims to examine the biomagnetic fluid flow with pulsatile conditions through a channel when subjected to a magnetic field that varies in space. The nondimensional continuity and momentum equations are solved with the effect of the magnetic field added as a body force. A two-dimensional computational model is developed using the finite volume method and is implemented on a staggered grid system with the help of the semi-implicit fractional step method. The code is written using MATLAB. Numerical simulations are performed by varying the Magnetic, Reynolds and Womersley numbers. Pulsatile flow results indicate the periodic growth and decay of vortices near the source of the magnetic field. With an increase in the magnetic number from 100 to 150, 250 and 500, the maximum vorticity increases by 48.04%, 149.84% and 402.68%. A similar relation is found when varying the Reynolds number, while almost no change is found when varying the Womersley number.

Blood flow in distensible arteries is nonlinear and time-dependent. The radial motion of the wall alters the dimension and geometry of the flow field. The nonlinear pulsating flow processes are successfully computed by mapping the wavy flow field to a fixed domain and by casting the geometric, kinematic and dynamic parameters of the flow into a dimensionless form of the Navier–Stokes equations. The complexity of the equations is compensated by a significant advantage in finite difference solutions. It is accomplished by using a fixed regular mesh network to model time-dependent irregular meshes in the physical domain for boundary layer development and vortices in pulsatile flows.

The present study deals with an appropriate mathematical model describing blood flow through a constricted artery that is used to analyze the physiological flow field. The time-variant geometry of the arterial segment having an overlapping type of constriction in the arterial lumen — which frequently occurs in diseased arteries, causing flow disorder and leading to malfunction of the cardiovascular system — is framed mathematically. Blood flow contained in the stenosed artery is treated as non-Newtonian (having shear-dependent viscosity) and is considered to be two-dimensional. The motion of the arterial wall and its effect on local fluid mechanics are not ruled out from the present pursuit. The flow analysis applies the time-dependent, two-dimensional incompressible nonlinear Navier–Stokes equations for non-Newtonian fluids. The flow field can be obtained by first transforming radial coordinates with the use of appropriate boundary conditions, and then adopting a suitable finite difference scheme numerically. The unsteady response of the system and the influence of the arterial wall distensibility, the non-Newtonian rheology of blood, and the presence of stenosis on the important aspects of the physiological flow phenomena are quantified in order to indicate the susceptibility to atherosclerotic lesions and thereby validate the applicability of the present theoretical model.

Intimal hyperplasia developed at the end-to-side anastomosis of artery bypass is closely related to unphysiological hemodynamics. The helical flow as a normal physiological phenomenon in arteries is beneficial to endothelial damage repair. To deeply understand the physiological flow properties in a S-type bypass (StB) graft, four end-to-side bypass models including 30°, 45°, 60° conventional bypasses and a 45° StB were compared numerically under physiological pulsatile flow. The results showed that strong helical flow was observed at the distal anastomosis of StB. The distribution of hemodynamic parameters such as helicity, average wall shear stress and oscillating shear index, etc. were significantly improved at the S-type anastomosis as compared with those of three conventional models. The area-averaged normalized helicity in StB reached maxima at the moments of maximum flow rate and systolic deceleration. The hemodynamic performance in a 45° StB was improved as compared with a 30° conventional model. It is concluded that large StB anastomosis angle can be taken to achieve good hemodynamic performance while much smaller anastomosis angle has to be adopted for conventional bypass. As such, a S-type anastomosis should be a feasible choice of clinical artery bypass grafting due to its significant improvement in hemodynamic performance.

A mathematical model has been developed in this paper with an aim to study arterial blood flow in a vibration environment. Blood is treated as a couple stress fluid. Oscillatory flow in a porous channel is considered in the study, when the flow takes place under the action of an external pressure gradient. The fluid flows between two porous plates lying parallel to each other. The fluid is considered to be injected on one plate with a constant velocity. The plates are considered to be oscillating with the same frequency in their own planes. However, the plate velocity of single-harmonic oscillation is not constant. The effects of various parameters representing couple stress, suction and magnitude of the oscillating pressure gradient on the velocity profile and wall shear stress are discussed. It is found that the presence of couple stress in the fluid enhances the velocity of the fluid in both axial and transverse directions, while a reverse phenomenon is observed for the wall shear stress.

Phase Contrast Magnetic Resonance Image (PC-MRI) is an emerging noninvasive technique that contains pulsatile information by measuring the parameters of cerebrospinal fluid (CSF) flow. As CSF flow quantities are measured from the selected region on the images, the accuracy in the identification of the interested region is the most essential, and the examination requires a lot of time and experience to analyze and for accurate CSF flow assessment. In this study, a three-dimensional (3D)-Unet architecture, including pulsatile flow data as the third dimension, is proposed to address the issue. The dataset contains 2176 phase and rephase images from 57 slabs of 39 3-tesla PC-MRI subjects collected from the lower thoracic levels of control and Idiopathic Scoliosis (IS) patients. The procedure starts with labeling the CSF containing spaces in the spinal canal. In the preprocessing step, unequal cardiac cycle images (i.e., frame) and the numbers of MRIs in cases are adjusted by interpolation to align the temporal dimension of the dataset to an equal size. The five-fold cross-validation procedure is used to evaluate the 3D Attention-U-Net model after training and achieved an average weighted performance of 97% precision, 95% recall, 98% F1 score, and 95% area under curve. The success of the model is also measured using the CSF flow waveform quantities as well. The mean flow rates through the labeled and predicted CSF lumens have a significant correlation coefficient of 0.96, and the peak CSF flow rates have a coefficient of 0.65. To our knowledge, this is the first fully automatic 3D deep learning architecture implementation to segment spinal CSF-containing spaces that utilizes both spatial and pulsatile information in PC-MRI data. We expect that our work will attract future research on the use of PC-MRI temporal information for training deep models.

This article analytically investigates the interaction of pulsatile flow with peristaltic transport of a viscoelastic Maxwell fluid in a cylindrical tube. The flow is considered unsteady even in the wave frame analysis where we impose a periodic pressure gradient. This transport is studied under low Reynolds number and long wavelength approximations. The governing equations are developed up to the second-order in the Deborah number and the Womersley number. We first analyzed the impact of the pulsatile flow, of the occlusion and of the viscoelastic effects of fluid on the pressure rise and on the friction force. Physical behavior of different parameters of the problem has been graphically presented and the influence of these parameters on the mechanical efficiency has been analyzed.

Stenosis can disrupt the normal pattern of blood flow and make the artery more susceptible to buckling which may cause arterial tortuosity. Although the stability simulations of the atherosclerotic arteries were conducted based on solid modeling and static internal pressure, the mechanical stability of stenotic artery under pulsatile blood flow remains unclear while pulsatile nature of blood flow makes the artery more critical for stresses and stability. In this study, the effect of stenosis on arterial stability under pulsatile blood flow was investigated. Fluid–structure interaction (FSI) simulations of artery stenosis under pulsatile flow were conducted. 3D idealized geometries of carotid artery stenosis with symmetric and asymmetric plaques along with different percentages of stenosis were created. It was observed that the stenosis percentage, symmetry/asymmetry of the plaque, and the stretch ratio can dramatically affect the buckling pressure. Buckling makes the plaques (especially in asymmetric ones) more likely to rupture due to increasing the stresses on it. The dominant stresses on plaques are the circumferential, axial and radial ones, respectively. Also, the highest shear stresses on the plaques were detected in $𝜃-z$ and $r-𝜃$ planes for the symmetric and asymmetric stenotic arteries, respectively. In addition, the maximum circumferential stress on the plaques was observed in the outer point of the buckled configuration for symmetric and asymmetric stenosis as well as at the ends of the asymmetric plaque. Furthermore, the artery buckling causes a large vortex flow at the downstream of the plaque. As a result, the conditions for the penetration of lipid particles and the formation of new plaques are provided.

The pulsatile flow of blood in a tapered narrow artery with overlapping time-dependent stenosis is mathematically analyzed, modeling blood as Carreau fluid. Perturbation method is employed for solving the resulting nonlinear system of equations along with the appropriate boundary conditions. The analytic solutions to the pressure gradient, velocity distribution, flow rate, wall shear stress and longitudinal impedance to flow are obtained in the asymptotic form. The variation of the aforesaid flow quantities with respect to various physical parameters such as maximum depth of the stenosis, angle of tapering of the artery, power law index, Reynolds number, pulsatile amplitude of the flow and Weissenberg number is investigated. It is found that the wall shear stress and longitudinal impedance to flow increase with the increase of the angle of tapering of the artery, the maximum depth of the stenosis and pulsatile Reynolds number and these decrease with the increase of the amplitude of the flow, power law index and Weissenberg number. The mean velocity of blood decreases significantly with the increase of the artery radius, maximum depth of the stenosis, angle of tapering of the artery.

Pulsatile flow of blood in a blood vessel having time-dependent shape (diameter) is investigated numerically in order to understand some important physiological phenomena in arteries. A smooth axi-symmetric cosine shaped constriction is considered. To mimic the realistic situation as far as possible, viscosity of blood is taken to be non-uniform, a shear-thinning viscosity model is considered and a physiologically relevant pulsatile flow is introduced. Taking advantage of axi-symmetry in the proposed problem, the stream function–vorticity formulation is used to solve the governing equations for blood flow. Effect of different parameters associated with the problem on the flow pattern has been investigated and disparities from the Newtonian case are discussed in detail.

In recent years, ventricular assist devices (VAD) have received a worldwide admissibility and have become the unrivalled tools for replacing a failed heart. Most of the newer generations of these devices, including second and third generations, are designed to produce non-pulsatile flow at constant rotational speed. Here, we have proposed the design of a VAD, which although is an axial flow type, is able to produce pulsatile flow; and this has come through by changing the rotational speed of the impeller of the pump. This pump, which has an output analogous to cardiac output, is able to produce a flow rate of approximately 6 L per minute. Designing of this pump is based on turbomachinery theories and applying computational fluid dynamics (CFD) methods. The proposed pattern of the changes of rotational speed is trapezoidal and consists of four phases. Studies of the shear stresses imposed on the blood within the pump have shown that there has been an acceptable margin of safety for this pump in terms of blood injuries such as hemolysis and thrombosis.

In vivo, endothelial cells are exposed to varying frequencies of pulsatile flow. However, little is known of how their frequency affects cell morphology and function. In this study, the effects of frequency of pulsatile flow on morphology and α_vβ₃ integrin expression of bovine aortic endothelial cells (BAEC) were investigated. BAEC were exposed to pulsatile flow at frequencies of 0.5, 1.0 and 1.5 Hz for 12 h using a newly developed flow-system. BAEC at 0.5 and 1.0 Hz elongated and oriented with the direction of flow and exhibited developed stress fibers parallel to the cell major axis, and these morphological changes were similar to these of BAEC under steady flow conditions. BAEC showed elongation but a random orientation after exposure to 1.5 Hz pulsatile flow. Fluorescent staining revealed that the expression of α_vβ₃ integrin at 1.0 Hz was significantly higher at the central regions of cells than at the upstream regions. In contrast, at 0.5 and 1.5 Hz, the expression of α_vβ₃ integrin was significantly higher at the upstream regions than at the central regions. These findings suggest that frequency of pulsatile flow play important roles in morphological changes and α_vβ₃ integrin expression in EC.