A 3D numerical study of the collateral capacity of the circle of Willis with anatomical variation in the posterior circulation

Background The Circle of Willis (CoW) is the most important collateral pathway of the cerebral artery. The present study aims to investigate the collateral capacity of CoW with anatomical variation when unilateral internalcarotid artery (ICA) is occluded. Methods Basing on MRI data, we have reconstructed eight 3D models with variations in the posterior circulation of the CoW and set four different degrees of stenosis in the right ICA, namely 24%, 43%, 64% and 79%, respectively. Finally, a total of 40 models are performed with computational fluid dynamics simulations. All of the simulations share the same boundary condition with static pressure and the volume flow rate (VFR) are obtained to evaluate their collateral capacity. Results As for the middle cerebral artery (MCA) and the anterior cerebral artery (ACA), the transitional-type model possesses the best collateral capacity. But for the posterior cerebral artery (PCA), unilateral stenosis of ICA has the weakest influence on the unilateral posterior communicating artery (PCoA) absent model. We also find that the full fetal-type posterior circle of Willis is an utmost dangerous variation which must be paid more attention. Conclusion The results demonstrate that different models have different collateral capacities in coping stenosis of unilateral ICA and these differences can be reflected by different outlets. The study could be used as a reference for neurosurgeon in choosing the best treatment strategy.

Flow pattern analysis in a highly stenotic patient-specific carotid bifurcation model using a turbulence model

The aim of this study is to investigate the blood flow pattern in carotid bifurcation with a high degree of luminal stenosis, combining in vivo magnetic resonance imaging (MRI) and computational fluid dynamics (CFD). A newly developed two-equation transitional model was employed to evaluate wall shear stress (WSS) distribution and pressure drop across the stenosis, which are closely related to plaque vulnerability. A patient with an 80% left carotid stenosis was imaged using high resolution MRI, from which a patient-specific geometry was reconstructed and flow boundary conditions were acquired for CFD simulation. A transitional model was implemented to investigate the flow velocity and WSS distribution in the patient-specific model. The peak time-averaged WSS value of approximately 73Pa was predicted by the transitional flow model, and the regions of high WSS occurred at the throat of the stenosis. High oscillatory shear index values up to 0.50 were present in a helical flow pattern from the outer wall of the internal carotid artery immediately after the throat. This study shows the potential suitability of a transitional turbulent flow model in capturing the flow phenomena in severely stenosed carotid arteries using patient-specific MRI data and provides the basis for further investigation of the links between haemodynamic variables and plaque vulnerability. It may be useful in the future for risk assessment of patients with carotid disease.

How does calcification influence plaque vulnerability? Insights from fatigue analysis

Background Calcification is commonly believed to be associated with cardiovascular disease burden. But whether or not the calcifications have a negative effect on plaque vulnerability is still under debate. Methods and Results Fatigue rupture analysis and the fatigue life were used to evaluate the rupture risk. An idealized baseline model containing no calcification was first built. Based on the baseline model, we investigated the influence of calcification on rupture path and fatigue life by adding a circular calcification and changing its location within the fibrous cap area. Results show that 84.0% of calcified cases increase the fatigue life up to 11.4%. For rupture paths 10D far from the calcification, the life change is negligible. Calcifications close to lumen increase more fatigue life than those close to the lipid pool. Also, calcifications in the middle area of fibrous cap increase more fatigue life than those in the shoulder area. Conclusion Calcifications may play a positive role in the plaque stability. The influence of the calcification only exists in a local area. Calcifications close to lumen may be influenced more than those close to lipid pool. And calcifications in the middle area of fibrous cap are seemly influenced more than those in the shoulder area.

A new method for the in vivo identification of mechanical properties in arteries from cine MRI images: Theoretical framework and validation

Quantifying the stiffness properties of soft tissues is essential for the diagnosis of many cardiovascular diseases such as atherosclerosis. In these pathologies it is widely agreed that the arterial wall stiffness is an indicator of vulnerability. The present paper focuses on the carotid artery and proposes a new inversion methodology for deriving the stiffness properties of the wall from cine-MRI (magnetic resonance imaging) data. We address this problem by setting-up a cost function defined as the distance between the modeled pixel signals and the measured ones. Minimizing this cost function yields the unknown stiffness properties of both the arterial wall and the surrounding tissues. The sensitivity of the identified properties to various sources of uncertainty is studied. Validation of the method is performed on a rubber phantom. The elastic modulus identified using the developed methodology lies within a mean error of 9.6%. It is then applied to two young healthy subjects as a proof of practical feasibility, with identified values of 625 kPa and 587 kPa for one of the carotid of each subject.

MRI-based fatigue analysis predicts plaque vulnerability: A study comparing symptomatic and asymptomatic individuals

BACKGROUND: Rupture of atheromatous plaque in the carotid artery often leads to thrombosis and subsequent stroke. The mechanism of plaque rupture is not entirely clear but is thought to be a multi-factorial process involving thinning and weakening of the fibrous cap and biomechanical stress as the trigger leading to plaque rupture. As the cardiovascular system is a classic fatigue environment, the weakening of plaque leading to rupture may be a fatigue process, which is a symptomatically quiescent but potentially progressive failure process. In this study, we used a fatigue analysis based on in vivo magnetic resonance imaging (MRI) to investigate the rupture initiation location, crack propagation path and fatigue life within plaques of asymptomatic and symptomatic individuals. METHODS: Forty non-consecutive subjects (20 symptomatic and 20 asymptomatic) underwent high-resolution multi-sequence in vivo MRI of the carotid bifurcation. Fatigue analysis was performed based on the plaque geometry derived from in vivo MRI of the carotid artery at the point of maximum stenosis. Paris’ Law in fracture mechanics is adopted to determine the fatigue crack growth rate. Incremental crack propagation was dynamically simulated based on stress distributions. Plaque initiation location, crack propagation path and fatigue cycle of symptomatic and asymptomatic individuals were compared. RESULTS: Cracks were often found to begin at the lumen wall at areas of stress concentration. The preferred rupture direction was radial from the lumen center. The crack initially advanced slowly but accelerated as it developed, depending on plaque morphology. The fatigue cycles of symptomatic plaques were significantly less than those in the asymptomatic group (2.3 ± 0.9 vs 3.1 ± 0.7 (x106); p = 0.003). CONCLUSIONS: The number of cycles to rupture in symptomatic patients was higher than those predicted in asymptomatic patients by fatigue analysis, suggesting the possibility that plaques with a less fatigue life may be more prone to be symptomatic and rupture. If further validated by large-scale longitudinal studies, fatigue analysis based on high resolution in vivo MRI could potentially act as a useful tool for risk assessment of carotid atheroma.

Impact of coronary tortuosity on coronary pressure: Numerical simulation study

Background: Coronary tortuosity (CT) is a common coronary angiographic finding. Whether CT leads to an apparent reduction in coronary pressure distal to the tortuous segment of the coronary artery is still unknown. The purpose of this study is to determine the impact of CT on coronary pressure distribution by numerical simulation. Methods: 21 idealized models were created to investigate the influence of coronary tortuosity angle (CTA) and coronary tortuosity number (CTN) on coronary pressure distribution. A 2D incompressible Newtonian flow was assumed and the computational simulation was performed using finite volume method. CTA of 30°, 60°, 90°, 120° and CTN of 0, 1, 2, 3, 4, 5 were discussed under both steady and pulsatile conditions, and the changes of outlet pressure and inlet velocity during the cardiac cycle were considered. Results: Coronary pressure distribution was affected both by CTA and CTN. We found that the pressure drop between the start and the end of the CT segment decreased with CTA, and the length of the CT segment also declined with CTA. An increase in CTN resulted in an increase in the pressure drop. Conclusions: Compared to no-CT, CT can results in more decrease of coronary blood pressure in dependence on the severity of tortuosity and severe CT may cause myocardial ischemia.

Utility of magnetic resonance imaging-based finite element analysis for the biomechanical stress analysis of hemorrhagic and non-hemorrhagic carotid plaques

Background: Biomechanical stress analysis has been used for plaque vulnerability assessment. The presence of plaque hemorrhage (PH) is a feature of plaque vulnerability and is associated with thromboembolic ischemic events. The purpose of the present study was to use finite element analysis (FEA) to compare the stress profiles of hemorrhagic and non-hemorrhagic profiles. Methods and Results: Forty-five consecutive patients who had suffered a cerebrovascular ischemic event with an underlying carotid artery disease underwent high-resolution magnetic resonance imaging (MRI) of their symptomatic carotid artery in a 1.5-T MRI system. Axial images were manually segmented for various plaque components and used for FEA. Maximum critical stress (M-CstressSL) for each slice was determined. Within a plaque, the maximum M-CstressSL for each slice of a plaque was selected to represent the maximum critical stress of that plaque (M-CstressPL) and used to compare hemorrhagic and non-hemorrhagic plaques. A total of 62% of plaques had hemorrhage. It was observed that plaques with hemorrhage had significantly higher stress (M-CstressPL) than plaques without PH (median [interquartile range]: 315 kPa [247-434] vs. 200 kPa [171-282], P=0.003). Conclusions: Hemorrhagic plaques have higher biomechanical stresses than non-hemorrhagic plaques. MRI-based FEA seems to have the potential to assess plaque vulnerability.

In vivo velocity vector imaging and time-resolved strain rate measurements in the wall of blood vessels using MRI

In this paper, we present a new approach for velocity vector imaging and time-resolved measurements of strain rates in the wall of human arteries using MRI and we prove its feasibility on two examples: in vitro on a phantom and in vivo on the carotid artery of a human subject. Results point out the promising potential of this approach for investigating the mechanics of arterial tissues in vivo.

Association between biomechanical structural stresses of atherosclerotic carotid plaques and subsequent ischaemic cerebrovascular events - A longitudinal in vivo magnetic resonance imaging-based finite element study

Background: High-resolution magnetic resonance (MR) imaging has been used for MR imaging-based structural stress analysis of atherosclerotic plaques. The biomechanical stress profile of stable plaques has been observed to differ from that of unstable plaques; however, the role that structural stresses play in determining plaque vulnerability remains speculative. Methods: A total of 61 patients with previous history of symptomatic carotid artery disease underwent carotid plaque MR imaging. Plaque components of the index artery such as fibrous tissue, lipid content and plaque haemorrhage (PH) were delineated and used for finite element analysis-based maximum structural stress (M-C Stress) quantification. These patients were followed up for 2 years. The clinical end point was occurrence of an ischaemic cerebrovascular event. The association of the time to the clinical end point with plaque morphology and M-C Stress was analysed. Results: During a median follow-up duration of 514 days, 20% of patients (n=12) experienced an ischaemic event in the territory of the index carotid artery. Cox regression analysis indicated that M-C Stress (hazard ratio (HR): 12.98 (95% confidence interval (CI): 1.32-26.67, pZ0.02), fibrous cap (FC) disruption (HR: 7.39 (95% CI: 1.61e33.82), p Z 0.009) and PH (HR: 5.85 (95% CI: 1.27e26.77), p Z 0.02) are associated with the development of subsequent cerebrovascular events. Plaques associated with future events had higher M-C Stress than those which had remained asymptomatic (median (interquartile range, IQR): 330 kPa (229e494) vs. 254 kPa (166-290), p Z0.04). Conclusions: High biomechanical structural stresses, in addition to FC rupture and PH, are associated with subsequent cerebrovascular events.

The mechanical triggers of plaque rupture: Shear stress vs pressure gradient

The aim of this study was to evaluate the mechanical triggers that may cause plaque rupture. Wall shear stress (WSS) and pressure gradient are the direct mechanical forces acting on the plaque in a stenotic artery. Their influence on plaque stability is thought to be controversial. This study used a physiologically realistic, pulsatile flow, two-dimensional, cine phase-contrast MRI sequence in a patient with a 70% carotid stenosis. Instead of considering the full patient-specific carotid bifurcation derived from MRI, only the plaque region has been modelled by means of the idealised flow model. WSS reached a local maximum just distal to the stenosis followed by a negative local minimum. A pressure drop across the stenosis was found which varied significantly during systole and diastole. The ratio of the relative importance of WSS and pressure was assessed and was found to be less than 0.07% for all time phases, even at the throat of the stenosis. In conclusion, although the local high WSS at the stenosis may damage the endothelium and fissure plaque, the magnitude of WSS is small compared with the overall loading on plaque. Therefore, pressure may be the main mechanical trigger for plaque rupture and risk stratification using stress analysis of plaque stability may only need to consider the pressure effect.

MRI-based measurement of carotid mechanical properties in asymptomatic patients

Arterial mechanical property may be a potential variable for risk stratification. Large artery and central arterial compliance have been shown not only to correlate well with overall cardiovascular outcome in large epidemiological studies [1, 2] but also to correlate with coronary atherosclerotic burden as measured by conventional angiography [3]. Until recently, real-time B-mode ultrasound combined with simultaneous blood pressure measurements have been used to assess large artery compliance [4]. These techniques have an excellent temporal resolution but are unable to provide adequate spatial resolution to determine changes in vessel area as opposed to diameter and make the assumption that the vessel is perfectly round. Attempts to use MR imaging to measure large artery compliance have been published previously [5]. However, they have not utilised simultaneous blood pressure measurements during sequence acquisition. We report a technique using regular and simultaneous blood pressure measurement during 2 dimensional phase contrast magnetic resonance imaging 2DPC-MRI to determine local carotid compliance.

Stress analysis of carotid atheroma in a transient ischaemic attack patient using the MRI-based fluid-structure interaction method

Rupture of atherosclerotic plaque is a major cause of mortality. Plaque stress analysis, based on patient-specific multisequence in vivo MRI, can provide critical information for the understanding of plaque rupture and could eventually lead to plaque rupture prediction. However, the direct link between stress and plaque rupture is not fully understood. In the present study, the plaque from a patient who recently experienced a transient ischaemic attack (TIA) was studied using a fluid-structure interaction method to quantify stress distribution in the plaque region based on in vivo MR images. The results showed that wall shear stress is generally low in the artery with a slight increase at the plaque throat owing to minor luminal narrowing. The oscillatory shear index is much higher in the proximal part of the plaque. Both local wall stress concentrations and the relative stress variation distribution during a cardiac cycle indicate that the actual plaque rupture site is collocated with the highest rupture risk region in the studied patient.

Stress analysis on human arterial plaques by fluid structure interactions - Multi-case study

Atherosclerotic plaque rupture has been extensively considered as the leading cause of death in the world. It is believed that high stress within plaque can be an important factor which can trigger the rupture of the plaque. High resolution multi-spectral magnetic resonance imaging (MRI) has allowed the plaque components (arterial wall, lipids, and fibrous cap) to be visualized in vivo [1]. The patient specific finite element model can be generated from the image data to perform stress analysis and provide critical information on understanding plaque rupture mechanisms [2]. The present work is to apply the procedure to a total of 14 patients (S1 ∼ S14), to study the stress distributions on carotid artery plaque reconstructed from multi-spectral magnetic resonance images, and the possible relationships between stress and plaque burdens.

Experimental measurement of the mechanical properties of carotid atherothrombotic plaque fibrous cap

Eleven carotid atherothrombotic plaque samples were harvested from patients. Three samples that were highly calcified were discarded, while eight yielded results. The elastic properties of the material were estimated by fitting the measured indentation response to finite element simulations. The methodology was refined and its accuracy quantified using a synthetic rubber. The neo-Hookean form of the material model gave a good fit to the measured response of the tissue. The inferred shear modulus μ was found to be in the range 7-100 kPa, with a median value of 11 kPa. A review of published materials data showed a wide range of material properties for human atherothrombotic tissue. The effects of anisotropy and time dependency in these published results were highlighted. The present measurements were comparable to the static radial compression tests of Lee et al, 1991 [Structure-dependent dynamic behaviour of fibrous caps from human atherosclerotic plaques. Circulation 83, 1764-1770].

Assessment of carotid plaque vulnerability using structural and geometrical determinants

Background Because many acute cerebral ischemic events are caused by rupture of vulnerable carotid atheroma and subsequent thrombosis, the present study used both idealized and patient-specific carotid atheromatous plaque models to evaluate the effect of structural determinants on stress distributions within plaque. Methods and Results Using a finite element method, structural analysis was performed using models derived from in vivo high-resolution magnetic resonance imaging (MRI) of carotid atheroma in 40 non-consecutive patients (20 symptomatic, 20 asymptomatic). Plaque components were modeled as hyper-elastic materials. The effects of varying fibrous cap thickness, lipid core size and lumen curvature on plaque stress distributions were examined. Lumen curvature and fibrous cap thickness were found to be major determinants of plaque stress. The size of the lipid core did not alter plaque stress significantly when the fibrous cap was relatively thick. The correlation between plaque stress and lumen curvature was significant for both symptomatic (p = 0.01; correlation coefficient: 0.689) and asymptomatic patients (p = 0.01; correlation coefficient: 0.862). Lumen curvature in plaques of symptomatic patients was significantly larger than those of asymptomatic patients (1.50±1.0mm-1 vs 1.25±0.75 mm-1; p = 0.01). Conclusion Specific plaque morphology (large lumen curvature and thin fibrous cap) is closely related to plaque vulnerability. Structural analysis using high-resolution MRI of carotid atheroma may help in detecting vulnerable atheromatous plaque and aid the risk stratification of patients with carotid disease.