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Intracranial aneurysms are localized dilatations of the cerebral arteries that carry a risk of rupture and subsequent subarachnoid hemorrhage, a life-threatening condition. Middle cerebral artery (MCA) aneurysms are a common type of intracranial aneurysm, and endovascular treatment using coils or flow diverters is a common intervention approach. Understanding the hemodynamics, or blood flow patterns, within MCA aneurysms and how they are affected by endovascular treatment is crucial for improving patient outcomes. This numerical study investigates the hemodynamics of blood flow within MCA aneurysms before and after endovascular treatment. Patient-specific geometric models of MCA aneurysms were reconstructed from medical imaging data. Simulations using computational fluid dynamics were conducted to examine flow characteristics, wall shear stress, and additional hemodynamic factors within the aneurysms. The study assessed and contrasted the impact of coil embolization and flow diverter placement on the hemodynamics inside the aneurysms. The findings offer a deeper understanding of the intricate flow dynamics within MCA aneurysms and illustrate the ways in which endovascular treatments can modify these dynamics.

We compare the Lattice BGK, the Multiple Relaxation Times and the Entropic Lattice Boltzmann Methods for time harmonic flows. We measure the stability, speed and accuracy of the three models for Reynolds and Womersley numbers that are representative for human arteries.

The Lattice BGK shows predictable stability and is the fastest method in terms of lattice node updates per second. The Multiple Relaxation Times LBM shows erratic stability which depends strongly on the relaxation times set chosen and is slightly slower. The Entropic LBM gives the best stability at the price of fewer lattice node updates per second.

A parameter constraint optimization technique is used to determine which is the fastest model given a certain preset accuracy. It is found that the Lattice BGK performs best at most arterial flows, except for the high Reynolds number flow in the aorta, where the Entropic LBM is the fastest method due to its better stability. However we also conclude that the Entropic LBM with velocity/pressure inlet/outlet conditions shows much worse performance.

In this research, a computational approach is applied to model the blood flow inside the MCA aneurysm when the coiling technique is used for the treatment of the patients. To this end, porous condition with different permeability factors is applied and their impacts on the hemodynamic factors of wall shear stress, pressure and oscillatory shear index. The main attention is to find how endovascular technique could efficiently decrease the risk of bleeding in MCA aneurysms. Blood hemodynamic is simulated via solving transient Navier–Stokes equations with Casson model for the non-Newtonian condition for the blood stream. Besides, the impacts of the blood hematocrit are also examined on the hemodynamic characteristics. Attained results show that the effects of coiling permeability are significant on the reduction of the blood stress on the aneurysm.

This paper presents a comprehensive hemodynamic evaluation of two endovascular techniques for treating cerebral aneurysms. Using the finite volume method, we simulated pulsatile blood flow and heat transport dynamics in two saccular aneurysms of varying sizes and shapes. We assessed hemodynamic factors under two coiling conditions with different porosities and deformation stages to identify the most effective treatment for each case. Our computational analysis reveals that stent and coiling applications are more efficient for aneurysms with low-sac volume. Notably, stent placement proves to be more effective than coiling in treating saccular aneurysms. Our findings indicate that stent-induced deformation sufficiently diverts the main blood flow, thereby reducing the risk of aneurysm rupture near the ostium region.

Hachimi-jio-gan (HJG), a chinese herbal formula, and a placebo were given to 12 healthy adults, and the changes in blood flow in the central retinal artery were observed with the latest ultrasonic diagnosis device before and after administration. After administration of HJG, the systolic flow velocity, diastolic flow velocity and mean flow velocity in the central retinal artery showed significant increases. No change was observed in vascular resistance. The subjects deemed suitable for use of HJG showed remarkable increases in blood flow. No changes in blood flow velocities and vascular resistance were observed after administration of the placebo. HJG is frequently used in the aged, often with eye diseases such as cataract. It has been reported that a decrease of blood flow in the central retinal artery becomes more marked in proportion to the progress of various eye diseases. As increases in blood flow were obvious in the cases that were treated with HJG, it is suggested that increases in blood flow in the central retinal artery due to HJG give direct evidence supporting the positive effects of HJG on eye diseases.

The purpose of this study was to investigate the effect of the De-Qi sensations of acupuncture (sourness-distension and distension-numbness) stimulation. Fifty-two healthy medical student volunteers were given acupuncture at the Hoku (LI-4) acupoint as they were resting. During a test that lasted 30 minutes, their skin blood flow was measured at the Quchi (LI-11) acupoint and their palm temperature was measured. Our results indicated that acupuncture increased blood flow when the De-Qi sensation occurred. If the needle was twirled a few minutes thereafter and the De-Qi feeling again occurred, the same blood flow increase was seen again. If the needle was not twirled, but the test person felt soreness, numbness and heat sensation within a few minutes after needle insertion, the same blood flow increase was also seen. After acupuncture, Quchi did not show continuous increase of blood flow as did Hoku. Hoku acupuncture also increased palm temperature suggesting that the blood flow increased from cutaneous vessel vasodilation. In conclusion, when the test person felt the sore and numb De-Qi sensation, there was an increase of blood flow at the acupuncture points. Thus, our results suggest that increased flow may be one of the mechanisms accounting for meridian system responses during acupuncture.

The biological flow characteristics inside a microchannel were investigated experimentally using a micro-particle image velocimetry (micro-PIV) method. The main objectives of this study were to understand the blood flow in micro-domain blood vessels and to identify the feasibility of nano-scale fluorescent particles for velocity measurement. The flow field was analyzed with a spatial resolution of 1K×1K pixels at low Reynolds number flow. To obtain the spatial distributions of mean velocity, 100 instantaneous velocity fields were captured and ensemble-averaged. As a result, for the case of blood flow, there were substantial velocity variations in the central region of micro-channel due to the presence of blood cells in the blood flow.

The large time behavior of passive contaminant in non-Newtonian peristaltic blood flow in a two-dimensional (2D) channel (capillary) has been examined in this paper. The power-law model is employed in order to highlight the non-Newtonian blood characteristic. The study was conducted using the Reynolds decomposition technique, which converts a 2D transport problem into a 1D transport model in which species concentration can be decomposed into sectional average concentration and variation from its mean value. For flow velocity, the same decomposition method is used. This allows the derivation of the dispersion coefficient and convection coefficient. Using Fick’s law, the advection–diffusion equation is modified by replacing these coefficients by their corresponding average values and analytical solutions for the mean concentration are derived. In the absence of peristalsis effects ($\gamma =0$), i.e., for the straight rigid channel, the dispersion coefficient is invariant along the channel length. With increasing modulation (peristaltic wave) parameter, $\gamma$, there is a strong elevation in advection coefficient in the initial half of the channel with a subsequent suppression in the second half of the channel, indicating that the location in the channel strongly influences advection characteristics. Advection coefficient is significantly elevated with increment in power-law rheological index (for shear-thinning fluids, $n<1$) across the channel length and exhibits an oscillatory nature due to the peristaltic waves. In the shear-thickening range ($n>1$), with progressive increase in n, an increment in peristaltic modulation parameter, $\gamma$, induces a marked reduction in the axially average relative advection coefficient. Dispersion coefficient is initially boosted along the early section of the channel with increment in modulation parameter whereas further long the channel this trend is reversed. Increasing aspect ratio and Péclet number consistently boost dispersion coefficient along the entire channel length. The study provides a solid benchmark for further generalized simulations with computational fluid dynamics.

The analysis of blood flow in the stenotic artery is imperative as the existence and progression of stenosis effectively disturbs the blood flow in the artery, which may cause vascular disease. In this study, we considered the linearized Phan-Thien–Tanner (PTT) fluid model to study the non-Newtonian nature of blood flow in the stenosed artery inclined at an angle $\gamma$. The artery is considered to have multiple stenoses and a cross-section of elliptical shape. The PTT model is appropriate for this analysis as viscoelastic properties and shear-thinning characteristics characterize it. The elliptical cross-section of the artery raises the nonlinearity of the mathematical model and makes it effortful to solve the equations analytically. The mathematical equations of the model are processed to non-dimensional form under the assumptions of mild stenosis, which help us to get the exact solutions of the equations in the elliptical domain. The analytically acquired solutions are investigated in detail by their graphical interpretation. It is analyzed that progressive height of stenosis generates the more significant disorder in the narrowed part of the channel as the velocity reverses its behavior in that region. The advancing values of the Weissenberg number, Grashof number and extensional and heat source parameters cause to lessen the axial velocity and slow the fluid flow. The rising Grashof number has nearly no impact on the velocity in the center of the channel. The wall shear stress aggrandizes with the growth of stenosis height, and its behavior for other physical constraints is similar to the flow velocity. It also has a practical enhancement in the stenotic region of the conduit. It is observed that fluid velocity and wall shear stress have larger values for zero angles of inclination than the inclination angle of $90^{\circ }$. The streamlined examination indicates the generation of the vortices in the stenotic part of the artery. Moreover, the flow velocity and wall shear stress have lower values for the nonuniform shape than for the uniform form of stenosis.

The objective of this research is to predict the thermal observations for hybrid nanofluid conveying the thin film flow influenced by the suction phenomenon and slip consequences. The copper and aluminum nanoparticles are utilized to explore the hybrid nanofluid features. In addition, a uniform magnetic field perpendicular to the motion of the nanoliquid has been generated. By utilizing appropriate dimensionless quantities, partial differential equations (PDEs) are transformed into nonlinear ordinary differential equations (ODEs). The controlling method for boundary value problems (BVP4C) has been applied against the thermal profile. The coating film’s thickness has been kept fixed. The skin friction and Nusselt number distribution are calculated for blood over the shrinking sheet in the attendance of the radiation and velocity slip parameters. The effects of various variables and spray rate through coating are clearly represented. The numerical calculation is computed for assessing the wall shear force. It is observed that a dual branch has been discovered. In addition, a stability analysis has been conducted and the upper branch has been determined to be the stable branch.

This paper presents a model of nonisothermal blood flow through a diseased arterial segment due to the presence of stenosis and thrombosis. The rheological properties of the blood in the annulus are captured by utilizing micropolar fluid model. The equation describing the blood flow and heat transfer is developed under the assumption that stenosis growth into the lumen of the artery is small as compared to the average radius of the artery. Biological processes like intimal proliferation of cells or changes in artery caliber may be activated by small growths that cause moderate stenotic blockages. Closed-form solutions for temperature, velocity, resistance impedance and wall shear stress are obtained and then utilized to estimate the impact of various physical parameters on micropolar blood flow. Graphs are plotted to illustrate variations in temperature, velocity, shear stress at the wall and resistance impedance against different controlling parameters. The results are also validated via the bvp4c approach.

This paper conducts an extensive comparative analysis of numerical methods employed in modeling blood flow through arteries with Magnetohydrodynamics (MHD) and hybrid nanofluids. The study investigates the effectiveness and precision of distinct numerical approaches: Akbari Ganji’s Method (AGM), Fourth-Order Runge–Kutta (RK4), Finite Volume Method (FVM), and the Finite Element Method (FEM). These methods are essential for comprehending the intricate fluid dynamics that arise in the presence of magnetic fields and hybrid nanofluids a phenomenon relevant in numerous medical applications. Blood flow is subjected to a homogeneous magnetic field in a radial direction while the magneto-hemodynamics effect is taken into account. A variety of medical, physiological, and surgical procedures, as well as the regulation of blood pressure, heat distribution, wound healing, diagnostic imaging, and drug discovery, depend on blood flow through arteries to carry out vital functions such as oxygen and nutrition delivery, organ maintenance, and wound healing. Our findings highlight that while each method has strengths, their applicability varies based on the problem’s characteristics and computational resource constraints. This analysis aids researchers and practitioners in selecting the most suitable method for their modeling requirements, advancing numerical techniques for complex fluid dynamics involving MHD and hybrid nanofluids.

This paper introduces a groundbreaking method, Homotopy-based Fourier transform, integrating Fourier transform and Homotopy perturbation for refined nonlinear problem-solving. The modification enhances solution technique efficiency, notably accelerating convergence, particularly in solving the Korteweg–de Vries equation. Demonstrating versatility, the method effectively addresses ordinary and partial differential equations, showcasing its applicability across diverse mathematical scenarios. Moreover, the approach is extended to nonlinear dynamical systems, illustrating its robustness in handling complex dynamic behaviors. This method proves especially suitable for highly nonlinear differential equations, offering an efficient and effective tool for scientists and engineers dealing with intricate mathematical models. By significantly improving convergence rates, the Homotopy-based Fourier transform stands out as a valuable asset in unraveling the complexities of nonlinear systems across various scientific and engineering applications.

In this paper we consider the coupling between two diffusion-reaction problems, one taking place in a three-dimensional domain Ω, the other in a one-dimensional subdomain Λ. This coupled problem is the simplest model of fluid flow in a three-dimensional porous medium featuring fractures that can be described by one-dimensional manifolds. In particular this model can provide the basis for a multiscale analysis of blood flow through tissues, in which the capillary network is represented as a porous matrix, while the major blood vessels are described by thin tubular structures embedded into it: in this case, the model allows the computation of the 3D and 1D blood pressures respectively in the tissue and in the vessels.

The mathematical analysis of the problem requires non-standard tools, since the mass conservation condition at the interface between the porous medium and the one-dimensional manifold has to be taken into account by means of a measure term in the 3D equation. In particular, the 3D solution is singular on Λ. In this work, suitable weighted Sobolev spaces are introduced to handle this singularity: the well-posedness of the coupled problem is established in the proposed functional setting. An advantage of such an approach is that it provides a Hilbertian framework which may be used for the convergence analysis of finite element approximation schemes. The investigation of the numerical approximation will be the subject of a forthcoming work.

The present investigation is devoted to study a theoretical investigation of the peristaltic flow of a couple-stress conducting fluids in a porous channel under the influence of slip boundary condition. This study is applicable to the physiological flow of blood in the micro-circulatory system, by taking account of the particle size effect. The expressions for axial velocity, pressure gradient, stream function, frictional force and mechanical efficiency are obtained under the small Reynolds number and the large wavelength approximations. Effects of different physical parameters reflecting permeability parameter, couple-stress parameter, Hartmann number as well as amplitude ratio on pumping characteristics, frictional force, mechanical efficiency and trapping of peristaltic flow pattern are studied. The computational and numerical results are presented in graphical form. On the basis of our discussion, it is concluded that pressure reduces by increasing the magnitude of couple-stress parameter, permeability parameter, slip parameter, whereas it enhances by increasing the magnitude of magnetic field and amplitude ratio.

The traditional approach to calculating stress distribution in arteries has been to assume (incorrectly) that the unloaded intact artery is stress-free. We consider the unloaded intact artery to have initial (i.e. residual) stresses and study how this affects the calculated wave speed of the arterial pulse. We use a set of equations that describe, in a simplified way, the blood flow in arteries and apply nonlinear elasticity theory to derive a formula for wave speed. We compare wave speed calculations under two assumptions (considering unloaded intact arteries as stress-free and considering these arteries to have residual stresses). We find that wave speeds calculated assuming residual stresses are more realistic. Clinical applications of this work are suggested.

The structure and the functioning of cardio-pulmonary system is complex and statistical physics appear to be suitable for their characterization. In this review, we examine scaling in cardio-pulmonary physiology. The focus will be on the interpretation of scaling behaviors and their relation to structure-function in the normal and diseased cardio-pulmonary system. First, we overview fluctuations and scaling in respiratory rate variability in terms of a neural network model. Next, we analyze fluctuations in human heartbeat dynamics under healthy and pathologic conditions using wavelets and multifractal approaches. We then discuss avalanche behavior of airway openings as well as scaling behavior of crackling sound generated during the process of airway openings. We also examine the relationship between the observed scaling properties and the design features of the pulmonary vascular tree. Finally, we show how the network failure of lung tissue structure leads to emphysema, a leading cause of respiratory disability and death worldwide.

Arterial narrowing can cause an audible whirling in the blood flow. We propose diagnosing such narrowing by simply recording that sound and analyzing its spectrum. We show how the Navier-Stokes equation for flow through a narrowing can be turned into a Schrödinger type equation. The complex eigenvalues of the latter equation give the frequencies and decay rates of the vortices present in the whirling pattern. Our diagnosis is based on understanding the relation between features in the sound spectrum and the severity of the narrowing. Today the most commonly used method of diagnosis is duplex ultrasound. In a small clinical trial our method appears to be as good as duplex ultrasound.

We have determined the wavelet phase coherence between simultaneously recorded microvascular blood flow and oxygen saturation signals from 88 healthy subjects, thus enabling us to study their common fluctuations. Measurements were taken for 30 min from the arm and leg, at two depths. In the skin, blood flow and oxygen saturation were found to be coherent both at the cardiac frequency and below 0.1 Hz down to about 0.01 Hz. Coherence in the arm extends to lower frequencies than that in the leg. From the deeper recordings, no coherence was found on either limb. The existence of coherence between skin blood flow and oxygen saturation demonstrates causal connections between them within certain frequency ranges. The method has yielded the first detailed insight into the dynamics of blood oxygenation.

The study presented in this paper is concerned with the analysis of the ultrasound Doppler signal of the arteries in the spectro-temporal domain using the wavelet packet transform. The spectro-temporal representation is obtained by the decomposition of the Doppler signal in frequency sub-band, using filter banks associated with a well chosen wavelet. It is shown that the decomposition level depends on the stationarity of the Doppler signal, and the best profile of blood flow velocity in arteries is obtained according to an appropriate choice of wavelet type.

Three types of wavelets have been tested on two Doppler signals previously recorded from the carotid and femoral arteries. The best representation is obtained when the frequency sub-bands of the filter bank associated with chosen wavelet are regularly distributed in the frequency domain and the level of decomposition is 7.