Three-dimensional imaging and computational modelling for estimation of wall stresses in arteries

Dynamic Clustering and Scaling Behavior of Active Particles under Confinement

A systematic investigation of the dynamic clustering behavior of active particles under confinement, including the effects of both particle density and active driving force, is presented based on a hybrid coarse-grained molecular dynamics simulation. First, a series of scaling laws are derived with power relationships for the dynamic clustering time as a function of both particle density and active driving force. Notably, the average number of clusters N¯ assembled from active particles in the simulation system exhibits a scaling relationship with clustering time t described by N¯∝t-m. Simultaneously, the scaling behavior of the average cluster size S¯ is characterized by S¯∝tm. Our findings reveal the presence of up to four distinct dynamic regions concerning clustering over time, with transitions contingent upon the particle density within the system. Furthermore, as the active driving force increases, the aggregation behavior also accelerates, while an increase in density of active particles induces alterations in the dynamic procession of the system.

Computer Modeling of Carotid Endarterectomy With the Different Shape Patches and Prediction of the Atherosclerotic Plaque Formation Zones

The article describes a method for constructing geometric models of the carotid bifurcation and computer simulation of endarterectomy surgery with the patches of various configurations. The purpose of this work is to identify the areas of the greatest risk of restenosis in the constructed models and to conduct a comparative analysis of risk factors when using the patches of different widths and shapes. The method is demonstrated on a reconstructed model of a healthy vessel. Its building is based on a preoperative computed tomography study of a particular patient's affected vessel. The flow in the vessel is simulated by computational fluid dynamics using data from the patient's ultrasound Doppler velocimetry. Risk factors are assessed through the hemodynamic indices on the vessel wall associated with Wall Shear Stress. The distribution of risk zones in the healthy vessel, presumably leading to its observed lesion (plaque), is analyzed. Comparative evaluation of 10 various patches implantation results is carried out and the optimal variant is determined. The proposed method can be used to predict the hemodynamic results of surgery using patches of various sizes and shapes.

[Computer modeling of the area of carotid endarterectomy with patches of various forms]

OBJECTIVE

To describe geometric models of carotid artery bifurcation and computer modeling of carotid endarterectomy (CEA) with patches of various configurations.

MATERIAL AND METHODS

The method was demonstrated on a reconstructed model of intact vessel based on preoperative CT of the affected vessel in a certain patient. Blood flow is modeled by computational fluid dynamics using Doppler ultrasound data. Risk factors were assessed considering hemodynamic parameters of vascular wall associated with WSS.

RESULTS

We studied hemodynamic results of 10 virtual CEA with patches of various shapes on the example of a reconstructed intact artery in a particular patient. Patch implantation is aimed at prevention of carotid artery narrowing since simple suture without a patch can reduce circumference of the artery by 4-5 mm. This result adversely affects blood flow. On the other hand, too wide a patch creates aneurysm-like deformation of internal carotid artery bulb. It is not optimal due to a large recirculation zone. It was found that patch width approximately equal to 3 mm ensures an optimal hemodynamic result. Deviations from this median value, both upward and downward, impair hemodynamics while the absence of a patch results the worst result.

CONCLUSION

The proposed computer modeling technique is able to provide a personalized patch selection for CEA with low risk of restenosis in long-term follow-up period.

Role of intraluminal thrombus in abdominal aortic aneurysm ruptures: A hemodynamic point of view

PURPOSE

Intraluminal thrombus (ILTs) are found in most abdominal aortic aneurysms (AAAs) of clinically relevant size; however, the role of ILTs in AAA ruptures remains unclear. This study investigated the role of the presence and thickness of ILTs in AAA ruptures by analyzing the hemodynamic environment in ruptured AAAs (RAAAs).

METHODS

Three-dimensional reconstructions from computed tomography scans were performed, and 13 RAAA cases were categorized into a no-ILT group, a thin-layered ILT group (thickness < 3 mm), and a thick-layered ILT group. The hemodynamic features of the RAAAs were assessed using computational fluid dynamics simulation.

RESULTS

The thin- and thick-layered ILT groups showed significant differences in aneurysm diameters (P < 0.05). The three types of AAAs ruptured at different flow regions, with different hemodynamic features: (a) the no-ILT AAAs ruptured at regions of flow recirculation where velocity and wall shear stresses (WSSs) were close to zero; (b) the thin-layered ILT AAAs ruptured at sites at which the dominant flow impinged the wall; and (c) the thick-layered ILT AAAs ruptured at the border of the dominant flow channel and recirculation zone where the flow velocity and pressure changed dramatically.

CONCLUSIONS

Hemodynamic characteristics influence the rupture mechanisms of particular AAAs differently on the basis of the presence and thickness of ILTs. Recirculation flows and low WSSs may have negative effects by inducing local rupture or positive effects by promoting the formation of thin-layered ILTs. However, eccentrically located thick-layered ILTs may increase the rupture risk of small AAAs because of their location in the sac lumen, which results in chaotic flow patterns and rapid increases in flow resistance.

Vascular Endothelial Cell Behavior in Complex Mechanical Microenvironments

The vascular mechanical microenvironment consists of a mixture of spatially and temporally changing mechanical forces. This exposes vascular endothelial cells to both hemodynamic forces (fluid flow, cyclic stretching, lateral pressure) and vessel forces (basement membrane mechanical and topographical properties). The vascular mechanical microenvironment is "complex" because these forces are dynamic and interrelated. Endothelial cells sense these forces through mechanosensory structures and transduce them into functional responses via mechanotransduction pathways, culminating in behavior directly affecting vascular health. Recent in vitro studies have shown that endothelial cells respond in nuanced and unique ways to combinations of hemodynamic and vessel forces as compared to any single mechanical force. Understanding the interactive effects of the complex mechanical microenvironment on vascular endothelial behavior offers the opportunity to design future biomaterials and biomedical devices from the bottom-up by engineering for the cellular response. This review describes and defines (1) the blood vessel structure, (2) the complex mechanical microenvironment of the vascular endothelium, (3) the process in which vascular endothelial cells sense mechanical forces, and (4) the effect of mechanical forces on vascular endothelial cells with specific attention to recent works investigating the influence of combinations of mechanical forces. We conclude this review by providing our perspective on how the field can move forward to elucidate the effects of the complex mechanical microenvironment on vascular endothelial cell behavior.

Investigation of Ultrasound-Measured Flow Velocity, Flow Rate and Wall Shear Rate in Radial and Ulnar Arteries Using Simulation

Parameters of blood flow measured by ultrasound in radial and ulnar arteries, such as flow velocity, flow rate and wall shear rate, are widely used in clinical practice and clinical research. Investigation of these measurements is useful for evaluating accuracy and providing knowledge of error sources. A method for simulating the spectral Doppler ultrasound measurement process was developed with computational fluid dynamics providing flow-field data. Specific scanning factors were adjusted to investigate their influence on estimation of the maximum velocity waveform, and flow rate and wall shear rate were derived using the Womersley equation. The overestimation in maximum velocity increases greatly (peak systolic from about 10% to 30%, time-averaged from about 30% to 50%) when the beam-vessel angle is changed from 30° to 70°. The Womersley equation was able to estimate flow rate in both arteries with less than 3% error, but performed better in the radial artery (2.3% overestimation) than the ulnar artery (15.4% underestimation) in estimating wall shear rate. It is concluded that measurements of flow parameters in the radial and ulnar arteries with clinical ultrasound scanners are prone to clinically significant errors.

The simulation of magnetic resonance elastography through atherosclerosis

The clinical diagnosis of atherosclerosis via the measurement of stenosis size is widely acknowledged as an imperfect criterion. The vulnerability of an atherosclerotic plaque to rupture is associated with its mechanical properties. The potential to image these mechanical properties using magnetic resonance elastography (MRE) was investigated through synthetic datasets. An image of the steady state wave propagation, equivalent to the first harmonic, can be extracted directly from finite element analysis. Inversion of this displacement data yields a map of the shear modulus, known as an elastogram. The variation of plaque composition, stenosis size, Gaussian noise, filter thresholds and excitation frequency were explored. A decreasing mean shear modulus with an increasing lipid composition was identified through all stenosis sizes. However the inversion algorithm showed sensitivity to parameter variation leading to artefacts which disrupted both the elastograms and quantitative trends. As noise was increased up to a realistic level, the contrast was maintained between the fully fibrous and lipid plaques but lost between the interim compositions. Although incorporating a Butterworth filter improved the performance of the algorithm, restrictive filter thresholds resulted in a reduction of the sensitivity of the algorithm to composition and noise variation. Increasing the excitation frequency improved the techniques ability to image the magnitude of the shear modulus and identify a contrast between compositions. In conclusion, whilst the technique has the potential to image the shear modulus of atherosclerotic plaques, future research will require the integration of a heterogeneous inversion algorithm.

Feasibility Study of Ex Ovo Chick Chorioallantoic Artery Model for Investigating Pulsatile Variation of Arterial Geometry

Despite considerable research efforts on the relationship between arterial geometry and cardiovascular pathology, information is lacking on the pulsatile geometrical variation caused by arterial distensibility and cardiomotility because of the lack of suitable in vivo experimental models and the methodological difficulties in examining the arterial dynamics. We aimed to investigate the feasibility of using a chick embryo system as an experimental model for basic research on the pulsatile variation of arterial geometry. Optical microscope video images of various arterial shapes in chick chorioallantoic circulation were recorded from different locations and different embryo samples. The high optical transparency of the chorioallantoic membrane (CAM) allowed clear observation of tiny vessels and their movements. Systolic and diastolic changes in arterial geometry were visualized by detecting the wall boundaries from binary images. Several to hundreds of microns of wall displacement variations were recognized during a pulsatile cycle. The spatial maps of the wall motion harmonics and magnitude ratio of harmonic components were obtained by analyzing the temporal brightness variation at each pixel in sequential grayscale images using spectral analysis techniques. The local variations in the spectral characteristics of the arterial wall motion were reflected well in the analysis results. In addition, mapping the phase angle of the fundamental frequency identified the regional variations in the wall motion directivity and phase shift. Regional variations in wall motion phase angle and fundamental-to-second harmonic ratio were remarkable near the bifurcation area. In summary, wall motion in various arterial geometry including straight, curved and bifurcated shapes was well observed in the CAM artery model, and their local and cyclic variations could be characterized by Fourier and wavelet transforms of the acquired video images. The CAM artery model with the spectral analysis method is a useful in vivo experimental model for studying pulsatile variation in arterial geometry.

Haemodynamics and Flow Modification Stents for Peripheral Arterial Disease: A Review

Endovascular stents are widely used for the treatment of peripheral arterial disease (PAD). However, the development of in-stent restenosis and downstream PAD progression remain a challenge. Stent revascularisation of PAD causes arterial trauma and introduces abnormal haemodynamics, which initiate complicated biological processes detrimental to the arterial wall. The interaction between stent struts and arterial cells in contact, and the blood flow field created in a stented region, are highly affected by stent design. Spiral flow is known as a normal physiologic characteristic of arterial circulation and is believed to prevent the development of flow disturbances. This secondary flow motion is lost in atheromatous disease and its re-introduction after endovascular treatment of PAD has been suggested as a method to induce stabilised and coherent haemodynamics. Stent designs able to generate spiral flow may support endothelial function and therefore increase patency rates. This review is focused on secondary flow phenomena in arteries and the development of flow modification stent technologies for the treatment of PAD.

Asymmetric radial expansion and contraction of rat carotid artery observed using a high-resolution ultrasound imaging system

The geometry of carotid artery bifurcation is of high clinical interest because it determines the characteristics of blood flow that is closely related to the formation and development of atherosclerotic plaque. However, information on the dynamic changes in the vessel wall of carotid artery bifurcation during a pulsatile cycle is limited. This pilot study investigated the cyclic changes in carotid artery geometry caused by blood flow pulsation in rats. A high-resolution ultrasound imaging system with a broadband scanhead centered at 40 MHz was used to obtain longitudinal images of the rat carotid artery. A high frame rate retrospective B-scan imaging technique based on the use of electrocardiogram to trigger signal acquisition was used to examine precisely the fast arterial wall motion. Two-dimensional geometry data obtained from nine rats showed that the rat carotid artery asymmetrically contracts and dilates during each cardiac cycle. Systolic/diastolic vessel diameters near the upstream and downstream regions from the bifurcation were 0.976 ± 0.011/0.825 ± 0.015 mm and 0.766 ± 0.015/0.650 ± 0.016 mm, respectively. Their posterior/anterior wall displacement ratios in the radial direction were 41.0 ± 14.9% and 2.9 ± 1.6%, respectively. These results indicate that in the vicinity of bifurcation, the carotid artery favorably expands to the anterior side during the systolic phase. This phenomenon was observed to be more prominent in the downstream region near the bifurcation. The cyclic variation pattern in wall movement varies depending on the measurement site, which shows different patterns at far upstream and downstream of the bifurcation. The asymmetric radial expansion and contraction of the rat carotid artery observed in this study may be useful in studying the hemodynamic etiology of cardiovascular diseases because the pulsatile changes in vessel geometry may affect the local hemodynamics that determines the spatial distribution of wall shear stress, one of important cardiovascular risk factors. Further systematic study is needed to clarify the effects of wall elasticity, branch angle and vessel diameter ratio on the asymmetric wall motion of carotid artery bifurcation.

Secondary flow in peripheral vascular prosthetic grafts using vector Doppler imaging

Prosthetic grafts are used for the treatment of peripheral arterial disease. Re-stenosis in the distal anastomosis of these grafts is a common reason for graft occlusion. The role of local hemodynamics in development of neo-intimal hyperplasia is well known. A new graft design has been proposed for the induction of optimized spiral flow in the host vessel. The secondary flow motions induced by this graft were compared with those of a control device. Both types of grafts were connected with vessel mimic and positioned in ultrasound flow phantoms with identical geometry. Constant flow rates were applied. Data collected in the cross-sectional view distal from the graft outflow and dual-beam vector Doppler was applied to create 2-D velocity maps. A single-spiral flow pattern was found for the flow-modified graft, and double or triple spirals for the control graft. In-plane maximum velocity was greater for the flow-modified graft than for the control device.

Understanding the role of hemodynamics in the initiation, progression, rupture, and treatment outcome of cerebral aneurysm from medical image-based computational studies

About a decade ago, the first image-based computational hemodynamic studies of cerebral aneurysms were presented. Their potential for clinical applications was the result of a right combination of medical image processing, vascular reconstruction, and grid generation techniques used to reconstruct personalized domains for computational fluid and solid dynamics solvers and data analysis and visualization techniques. A considerable number of studies have captivated the attention of clinicians, neurosurgeons, and neuroradiologists, who realized the ability of those tools to help in understanding the role played by hemodynamics in the natural history and management of intracranial aneurysms. This paper intends to summarize the most relevant results in the field reported during the last years.

A Fast Method to Estimate the Wall Shear Stress Waveform in Arteries

Introduction

Ultrasound has been applied to measure vessel diameter and blood flow velocity to compute the wall shear rate (WSR) in arteries. This paper describes a fast technique to assess the WSR waveform using an image of a pulsed Doppler waveform downloaded from a modern clinical ultrasound scanner.

Methods

A walled vascular phantom has been developed to mimic the physiological condition of brachial arteries, from where measurements were made. A MATLAB program has been developed and used to compute the WSR waveform in a flow phantom from a pulsed Doppler image. The mean WSR obtained from the WSR waveform was compared with the mean WSR derived from the flow rate obtained from a timed collection method. Measurement errors in Doppler velocity estimates from ultrasound scanners were also investigated and used to determine correction factors in WSR calculations.

Results

For three different flow phantom depths, 9.5,14.5 and 19.5 mm, the mean percentage errors between the true and measured WSR were found to be 4.5% (SD = 4.0), 7.4% (SD = 5.1) and 14.2% (SD = 4.1) respectively.

Conclusions

The results demonstrated the feasibility of calculating WSR based solely on an image of the Doppler spectrum and arterial diameter measurement, which opens up the possibility of obtaining WSR estimates from generic scanners.

Wall shear stress is decreased in the pulmonary arteries of patients with pulmonary arterial hypertension: An image-based, computational fluid dynamics study

Previous clinical studies in pulmonary arterial hypertension (PAH) have concentrated predominantly on distal pulmonary vascular resistance, its contribution to the disease process, and response to therapy. However, it is well known that biomechanical factors such as shear stress have an impact on endothelial health and dysfunction in other parts of the vasculature. This study tested the hypothesis that wall shear stress is reduced in the proximal pulmonary arteries of PAH patients with the belief that reduced shear stress may contribute to pulmonary endothelial cell dysfunction and as a result, PAH progression. A combined MRI and computational fluid dynamics (CFD) approach was used to construct subject-specific pulmonary artery models and quantify flow features and wall shear stress (WSS) in five PAH patients with moderate-to-severe disease and five age- and sex-matched controls. Three-dimensional model reconstruction showed PAH patients have significantly larger main, right, and left pulmonary artery diameters (3.5 ± 0.4 vs. 2.7 ± 0.1 cm, P = 0.01; 2.5 ± 0.4 vs. 1.9 ± 0.2 cm, P = 0.04; and 2.6 ± 0.4 vs. 2.0 ± 0.2 cm, P = 0.01, respectively), and lower cardiac output (3.7 ± 1.2 vs. 5.8 ± 0.6 L/min, P = 0.02.). CFD showed significantly lower time-averaged central pulmonary artery WSS in PAH patients compared to controls (4.3 ± 2.8 vs. 20.5 ± 4.0 dynes/cm(2), P = 0.0004). Distal WSS was not significantly different. A novel method of measuring WSS was utilized to demonstrate for the first time that WSS is altered in some patients with PAH. Using computational modeling in patient-specific models, WSS was found to be significantly lower in the proximal pulmonary arteries of PAH patients compared to controls. Reduced WSS in proximal pulmonary arteries may play a role in the pathogenesis and progression of PAH. This data may serve as a basis for future in vitro studies of, for example, effects of WSS on gene expression.

Comparison of patient-specific inlet boundary conditions in the numerical modelling of blood flow in abdominal aortic aneurysm disease

Three inlet boundary condition datasets were derived from phase-contrast MRI: (i) centre line velocity data converted to two-dimensional (2D) velocity profile using Womersley equations (Womersley), (ii) 2D velocity profile with one axial component of velocity (1CV), (iii) 2D velocity profile with three components of velocity (3CV). Computational fluid dynamics was performed using a rigid wall approach with geometry data extracted from the computed tomography dataset. Helical flow was present in the 1CV and 3CV simulations, with more complex patterns for the 3CV case. The Womersley method produced simplified flow patterns with an absence of helical flow. Mean values of quantitative indices (helical flow index, mean wall shear stress, oscillatory index) were compared with the 3CV inlet data. These were lower for both the Womersley inlet data (28%, 71%, 56%) and the 1CV inlet data (9%, 24%, 69%). It was concluded that inlet methods based on centre line velocity, such as might be obtained from Doppler ultrasound, lead to significantly simplified abdominal aortic aneurysm haemodynamics and thus are not recommended. Single velocity component (axial) data from MRI might suffice when general flow characteristics and spatial wall shear stress are required. Ideally 2D MRI velocity profiles with 3-velocity component data are preferred to fully account for helical flow.

Estimation of blood velocity, volumetric flow and wall shear rate using Doppler ultrasound

Commercial ultrasound systems can make a number of measurements related to haemodynamics which are relevant to clinical practice and to clinical research. These include maximum velocity, volumetric flow and wall shear rate. Using appropriate protocols, measurements can be made averaged over the cardiac cycle, or as a function of time through the cardiac cycle. Maximum velocity underpins most of these measurements. Maximum velocity is overestimated as a result of geometric spectral broadening, by typically up to 30%, but by much larger amounts as the angle approaches 90°. Though not used in clinical practice, a simple correction technique using a string phantom can substantially reduce these errors. For volumetric flow and wall shear rate, methods such as specialist multi-gate ultrasound systems, magnetic resonance imaging and image guided modelling are available. Before resorting to these more complex methods users might consider that, with care and attention to procedure, high quality information may be obtained using commercial ultrasound systems. Manufacturers could make more use of the colour flow image for quantification of velocity, and adopt vector Doppler techniques.