Numerical analysis of flow through a severely stenotic carotid artery bifurcation

The results of computational simulations may supplement MR and other in vivo diagnostic techniques to provide an accurate picture of the hemodynamics in particular vessels, which may help demonstrate the risks of embolism or plaque rupture posed by particular plaque deposits. In this study, a model based on an endarterectomy specimen of the plaque in a carotid bifurcation was examined. The flow conditions include steady flow at Reynolds numbers of 300, 600, and 900 as well as unsteady pulsatile flow. Both dynamic pressure and wall shear stress are very high, with shear values up to 70 N/m2, proximal to the stenosis throat in the internal carotid artery, and both vary significantly through the flow cycle. The wall shear stress gradient is also strong along the throat. Vortex shedding is observed downstream of the most severe occlusion. Two turbulence models, the Chien and Goldberg varieties of k-epsilon, are tested and evaluated for their relevance in this geometry. The Chien model better captures phenomena such as vortex shedding. The flow distal to stenosis is likely transitional, so a model that captures both laminar and turbulent behavior is needed.     

3D computational parametric analysis of eccentric atheroma plaque: influence of axial and circumferential residual stresses

Plaque rupture plays a role in the majority of acute coronary syndromes. Rupture has usually been associated with stress concentrations, which are mainly affected by the plaque geometry and the tissue properties. The aim of this study is to evaluate the influence of morphology on the risk of plaque rupture, including the main geometrical factors, and to assess the role of circumferential and axial residual stresses by means of a parametric 3D finite element model. For this purpose, a 3D parametric finite element model of the coronary artery with eccentric atheroma plaque was developed. Healthy (adventitia and media in areas without atheroma plaque) and diseased (fibrotic and lipidic) tissues were considered in the model. The geometrical parameters used to define and design the idealized coronary plaque anatomy were the lipid core length, the stenosis ratio, the fibrous cap thickness, and the lipid core ratio. Finally, residual stresses in longitudinal and circumferential directions were incorporated into the model to analyse the influence of the important mechanical factors in the vulnerability of the plaque. Viewing the results, we conclude that residual stresses should be considered in the modelling of this kind of problems since they cause a significant alteration of the vulnerable plaque region limits. The obtained results show that the fibrous cap thickness and the lipid core length, in combination with the lipid core width, appear to be the key morphological parameters that play a determinant role in the maximal principal stress (MPS). However, the stenosis ratio is found to not play a significant role in vulnerability related to the MPS. Plaque rupture should therefore be observed as a consequence, not only of the cap thickness, but as a combination of the stenosis ratio, the fibrous cap thickness and the lipid core dimensions.     

Mechanical stresses in carotid plaques using MRI-based fluid-structure interaction models

Risk assessment in patients with carotid atherosclerosis relies on the degree of luminal stenosis. Incorporating morphological information on plaque composition obtained noninvasively through the use of magnetic resonance imaging (MRI) could include other variables besides the degree of stenosis into carotid plaque risk assessment. Knowledge of the morphologic composition of the plaque allows determination of mechanic stresses exerted on the protective fibrous cap, which may be of importance in the assessment of plaque vulnerability. Based on image processing of transverse MRI scans, longitudinal 2D fluid-structure interaction (FSI) simulations of carotid atherosclerotic plaques were performed facilitating in-vivo estimation of longitudinal internal fibrous cap stresses. The FSI simulation combined finite element analysis (FEA) with computational fluid dynamics (CFD) simulations of blood-flow variables. Preliminary results from two symptomatic patients revealed longitudinal stress levels (max. 254.1 and 143.2 kPa) approaching established criteria for plaque rupture at known predilection sites of plaque rupture. Determination of longitudinal fibrous cap stresses may prove useful in assessing plaque vulnerability and improve risk stratification in patients with carotid atherosclerosis.     

A nonlinear axisymmetric model with fluid-wall interactions for steady viscous flow in stenotic elastic tubes.

Arteries with high-grade stenoses may compress under physiologic conditions due to negative transmural pressure caused by high-velocity flow passing through the stenoses. To quantify the compressive conditions near the stenosis, a nonlinear axisymmetric model with fluid-wall interactions is introduced to simulate the viscous flow in a compliant stenotic tube. The nonlinear elastic properties of the tube (tube law) are measured experimentally and used in the model. The model is solved using ADINA (Automatic Dynamic Incremental Nonlinear Analysis), which is a finite element package capable of solving problems with fluid-structure interactions. Our results indicate that severe stenoses cause critical flow conditions such as negative pressure and high and low shear stresses, which may be related to artery compression, plaque cap rupture, platelet activation, and thrombus formation. The pressure filed near a stenosis has a complex pattern not seen in one-dimensional models. Negative transmural pressure as low as -24 mmHg for a 78 percent stenosis by diameter is observed at the throat of the stenosis for a downstream pressure of 30 mmHg. Maximum shear stress as a high as 1860 dyn/cm2 occurs at the throat of the stenoses, while low shear stress with reversed direction is observed right distal to the stenosis. Compressive stresses are observed inside the tube wall. The maximal principal stress and hoop stress in the 78 percent stenosis are 80 percent higher than that from the 50 percent stenosis used in our simulation. Flow rates under different pressure drop conditions are calculated and compared with experimental measurements and reasonable agreement is found for the prebuckling stage.     

Mechanical action of the blood onto atheromatous plaques: influence of the stenosis shape and morphology

The vulnerability of atheromatous plaques in the carotid artery may be related to several factors, the most important being the degree of severity of the endoluminal stenosis and the thickness of the fibrous cap. It has recently been shown that the plaque length can also affect the mechanical response significantly. However, in their study on the effect of the plaque length, the authors did not consider the variations of the plaque morphology and the shape irregularities that may exist independently of the plaque length. These aspects are developed in this paper. The mechanical interactions between the blood flow and an atheromatous plaque are studied through a numerical model considering fluid–structure interaction. The simulation is achieved using the arbitrary Lagrangian–Eulerian scheme in the COMSOL TM commercial finite element package. The stenosis severity and the plaque length are, respectively, set to 45% and 15 mm. Different shapes of the stenosis are modelled, considering irregularities made of several bumps over the plaque. The resulting flow patterns, wall shear stresses, plaque deformations and stresses in the fibrous cap reveal that the effects of the blood flow are amplified if the slope upstream stenosis is steep or if the plaque morphology is irregular with bumps. More specifically, the maximum stress in the fibrous cap is 50% larger for a steep slope than for a gentle slope. These results offer new perspectives for considering the shape of plaques in the evaluation of the vulnerability.     

Computational study of pulsatile blood flow in prototype vessel geometries of coronary segments

The spatial and temporal distributions of wall shear stress (WSS) in prototype vessel geometries of coronary segments are investigated via numerical simulation, and the potential association with vascular disease and specifically atherosclerosis and plaque rupture is discussed. In particular, simulation results of WSS spatio-temporal distributions are presented for pulsatile, non-Newtonian blood flow conditions for: (a) curved pipes with different curvatures, and (b) bifurcating pipes with different branching angles and flow division. The effects of non-Newtonian flow on WSS (compared to Newtonian flow) are found to be small at Reynolds numbers representative of blood flow in coronary arteries. Specific preferential sites of average low WSS (and likely atherogenesis) were found at the outer regions of the bifurcating branches just after the bifurcation, and at the outer-entry and inner-exit flow regions of the curved vessel segment. The drop in WSS was more dramatic at the bifurcating vessel sites (less than 5% of the pre-bifurcation value). These sites were also near rapid gradients of WSS changes in space and time – a fact that increases the risk of rupture of plaque likely to develop at these sites. The time variation of the WSS spatial distributions was very rapid around the start and end of the systolic phase of the cardiac cycle, when strong fluctuations of intravascular pressure were also observed. These rapid and strong changes of WSS and pressure coincide temporally with the greatest flexion and mechanical stresses induced in the vessel wall by myocardial motion (ventricular contraction). The combination of these factors may increase the risk of plaque rupture and thrombus formation at these sites.     

Local critical stress correlates better than global maximum stress with plaque morphological features linked to atherosclerotic plaque vulnerability: an in vivo multi-patient study

Background  

It is believed that mechanical stresses play an important role in atherosclerotic plaque rupture process and may be used for better plaque vulnerability assessment and rupture risk predictions. Image-based plaque models have been introduced in recent years to perform mechanical stress analysis and identify critical stress indicators which may be linked to rupture risk. However, large-scale studies based on in vivo patient data combining mechanical stress analysis, plaque morphology and composition for carotid plaque vulnerability assessment are lacking in the current literature.     

Effect of continuous arterial blood flow in patients with rotary cardiac assist device on the washout of a stenosis wake in the carotid bifurcation: a computer simulation study

In recipients of rotary blood pumps for cardiac assist, the pulsatility of arterial flow is considerably diminished. This influences the shear stress patterns and streamlines in the arterial bed, with potential influence on washout and plaque growth. These effects may be aggravated in the recirculation area of stenoses, and therefore, exclude patients with atherosclerosis from the therapy with these devices. A numerical study was performed for the human carotid artery bifurcation with the assumption of a massive stenosis (75% reduction of cross-section area) in the carotid bulb. Four different flow time patterns (no support to full pump support) were applied. Flow patterns and particle residence time within the recirculation region were calculated, once within the relevant volume behind the stenosis and and once within a small region directly at the posterior heel of the stenosis. The flow patterns showed a considerable radial vorticity behind the stenosis. Mean particle residence time in the whole recirculation region was 15% less for high pump support (nearly continuous flow) compared to the natural flow pattern (0.19s compared to 0.22s), and nearly identical for the small heel region (0.28 to 0.27s). The flow simulation demonstrates, that even in the case of a pre-existing stenosis, the local effects of continuous flow on particle residence times are rather minimal (as was shown previously for intact arterial geometries). Therefore, from the point of macroscopic flow field analysis, continuous flow should not enhance the thromboembolic risk in ventricular assist device recipients.     

Carotid arterial plaque stress analysis using fluid–structure interactive simulation based on in-vivo magnetic resonance images of four patients

The rupture of atherosclerotic plaques is known to be associated with the stresses that act on or within the arterial wall. The extreme wall tensile stress (WTS) is usually recognized as a primary trigger for the rupture of vulnerable plaque. The present study used the in-vivo high-resolution multi-spectral magnetic resonance imaging (MRI) for carotid arterial plaque morphology reconstruction. Image segmentation of different plaque components was based on the multi-spectral MRI and co-registered with different sequences for the patient. Stress analysis was performed on totally four subjects with different plaque burden by fluid–structure interaction (FSI) simulations. Wall shear stress distributions are highly related to the degree of stenosis, while the level of its magnitude is much lower than the WTS in the fibrous cap. WTS is higher in the luminal wall and lower at the outer wall, with the lowest stress at the lipid region. Local stress concentrations are well confined in the thinner fibrous cap region, and usually locating in the plaque shoulder; the introduction of relative stress variation during a cycle in the fibrous cap can be a potential indicator for plaque fatigue process in the thin fibrous cap. According to stress analysis of the four subjects, a risk assessment in terms of mechanical factors could be made, which may be helpful in clinical practice. However, more subjects with patient specific analysis are desirable for plaque-stability study.     

Effects of varied lipid core volume and fibrous cap thickness on stress distribution in carotid arterial plaques

The rupture of atherosclerotic plaques is known to be associated with the stresses that act on or within the arterial wall. The extreme wall tensile stress is usually recognized as a primary trigger for the rupture of the plaque. The present study used one-way fluid-structure interaction simulation to investigate the impacts of fibrous cap thickness and lipid core volume to the wall tensile stress value and distributions on the fibrous cap. Von Mises stress was employed to represent the wall tensile stress (VWTS). A total of 13 carotid bifurcation cases were manipulated based on a base geometry in the study with varied combinations of fibrous cap thickness and lipid core volume in the plaque. Values of maximum VWTS and a stress value of VWTS_90, which represents the cut-off VWTS value of 90% in cumulative histogram of VWTS possessed at the computational nodes on the luminal surface of fibrous cap, were used to assess the risk of plaque rupture for each case. Both parameters are capable of separating the simulation cases into vulnerable and more stable plaque groups, while VWTS_90 is more robust for plaque rupture risk assessment. The results show that the stress level on the fibrous cap is much more sensitive to the changes in the fibrous cap thickness than the lipid core volume. A slight decrease of cap thickness can cause a significant increase of stress. For all simulation cases, high VWTS appears at the fibrous cap near the lipid core (plaque shoulder) regions.     

In vivo serial MRI-based models and statistical methods to quantify sensitivity and specificity of mechanical predictors for carotid plaque rupture: location and beyond

It has been hypothesized that mechanical risk factors may be used to predict future atherosclerotic plaque rupture. Truly predictive methods for plaque rupture and methods to identify the best predictor(s) from all the candidates are lacking in the literature. A novel combination of computational and statistical models based on serial magnetic resonance imaging (MRI) was introduced to quantify sensitivity and specificity of mechanical predictors to identify the best candidate for plaque rupture site prediction. Serial in vivo MRI data of carotid plaque from one patient was acquired with follow-up scan showing ulceration. 3D computational fluid-structure interaction (FSI) models using both baseline and follow-up data were constructed and plaque wall stress (PWS) and strain (PWSn) and flow maximum shear stress (FSS) were extracted from all 600 matched nodal points (100 points per matched slice, baseline matching follow-up) on the lumen surface for analysis. Each of the 600 points was marked "ulcer" or "nonulcer" using follow-up scan. Predictive statistical models for each of the seven combinations of PWS, PWSn, and FSS were trained using the follow-up data and applied to the baseline data to assess their sensitivity and specificity using the 600 data points for ulcer predictions. Sensitivity of prediction is defined as the proportion of the true positive outcomes that are predicted to be positive. Specificity of prediction is defined as the proportion of the true negative outcomes that are correctly predicted to be negative. Using probability 0.3 as a threshold to infer ulcer occurrence at the prediction stage, the combination of PWS and PWSn provided the best predictive accuracy with (sensitivity, specificity)?=?(0.97, 0.958). Sensitivity and specificity given by PWS, PWSn, and FSS individually were (0.788, 0.968), (0.515, 0.968), and (0.758, 0.928), respectively. The proposed computational-statistical process provides a novel method and a framework to assess the sensitivity and specificity of various risk indicators and offers the potential to identify the optimized predictor for plaque rupture using serial MRI with follow-up scan showing ulceration as the gold standard for method validation. While serial MRI data with actual rupture are hard to acquire, this single-case study suggests that combination of multiple predictors may provide potential improvement to existing plaque assessment schemes. With large-scale patient studies, this predictive modeling process may provide more solid ground for rupture predictor selection strategies and methods for image-based plaque vulnerability assessment.     

External triggers of onset of myocardial infarction-an update

Coronary heart disease is one of the leading causes of death in both industrialised and developing countries. About two thirds of all coronary deaths occur outside the hospital and before any medical care can be reached. Therefore, the prevention of coronary events appears to be of utmost importance. Rupture of an atherosclerotic plaque and subsequent coronary thrombosis is the most common underlying pathophysiological mechanism of coronary events. External stresses or 'triggers' imposing on coronary plaques may precipitate plaque rupture. External triggers include physical activity, various emotional stresses, eating, environmental factors, and sexual activity. The increased relative risk of myocardial infarction may be induced by external triggers via the activation of internal triggering mechanisms such as biomechanical and hemodynamic stresses and changes in platelet aggregability and blood viscosity. Recent prospective studies have confirmed the results of earlier retrospective studies and have, similarly, shown the importance of external triggers in increasing the risk of myocardial infarction and other coronary events. Particularly, sedentary individuals with underlying coronary heart disease appear to be at risk when exposed to external triggers. Regular physical activity, on the other hand, is a protective factor against the increased risk associated with external triggers. However, health education needs to be provided about the risks associated with strenuous exercise in untrained individuals. Apart from lifestyle factors, pharmacological protection of the population at risk during vulnerable periods plays an important role as well. Medication such as beta-blockers and aspirin may lower the increased risk of coronary events during exposure to external triggers. Also, further research is needed with regard to psychosocial stressors and their potential role as external triggers of myocardial infarction and other coronary events.     

Steady flow and wall compression in stenotic arteries: a three-dimensional thick-wall model with fluid-wall interactions.

Severe stenosis may cause critical flow and wall mechanical conditions related to artery fatigue, artery compression, and plaque rupture, which leads directly to heart attack and stroke. The exact mechanism involved is not well understood. In this paper a nonlinear three-dimensional thick-wall model with fluid-wall interactions is introduced to simulate blood flow in carotid arteries with stenosis and to quantify physiological conditions under which wall compression or even collapse may occur. The mechanical properties of the tube wall were selected to match a thick-wall stenosis model made of PVA hydrogel. The experimentally measured nonlinear stress-strain relationship is implemented in the computational model using an incremental linear elasticity approach. The Navier-Stokes equations are used for the fluid model. An incremental boundary iteration method is used to handle the fluid-wall interactions. Our results indicate that severe stenosis causes considerable compressive stress in the tube wall and critical flow conditions such as negative pressure, high shear stress, and flow separation which may be related to artery compression, plaque cap rupture, platelet activation, and thrombus formation. The stress distribution has a very localized pattern and both maximum tensile stress (five times higher than normal average stress) and maximum compressive stress occur inside the stenotic section. Wall deformation, flow rates, and true severities of the stenosis under different pressure conditions are calculated and compared with experimental measurements and reasonable agreement is found.     

Hemodynamics of ulcerated plaques: before and after

The hemodynamics and fluid mechanical forces in blood vessels have long been implicated in the deposition and growth of atherosclerotic plaque. Detailed information about the hemodynamics in vessels affected by significant plaque deposits can also provide insight into the mechanisms and likelihood of plaque weakening and rupture. In the current study, the governing equations are solved in their finite volume formulation in several patient-specific stenotic geometries. Of specific interest are the flow patterns and forces near ulcerations in the plaque. The flow patterns and forces in vessels with ulcerated plaques are compared with those in stenotic vessels without evidence of ulceration and to the hemodynamics in the same vessels as they likely appeared prior to ulceration. Hemodynamics "before" and "after" hemorrhage may suggest fluid mechanical and morphological factors of diagnostic and predictive value. Recirculation zones, vortex shedding, and secondary flows are captured by both laminar and turbulent solutions. The forces on vessel walls are shown to correlate with unstable plaque deposits. Performing before and after studies of vessels in long-term radiology studies may illuminate mechanisms of hemorrhage and other vessel remodeling.     

Fluid-Structure Interaction Analysis of Pulsatile Flow within a Layered and Stenotic Aorta

In this paper, the hemodynamic characteristics of blood flow and stress distribution in a layered and stenotic aorta are investigated. By introducing symmetrical and unsymmetrical stenosis, the influence of stenosis morphology and stenotic ratio on the coupled dynamic responses of aorta is clarified. In the analysis, the in-vivo pulsatile waveforms and fully fluid–structure interaction (FSI) between the layered elastic aorta and the blood are considered. The results show that the fluid domain is abnormal in the stenotic aorta, and the whirlpool forms at the obstructed and downstream unobstructed regions. The maximum wall shear stresses appear at the throat of the stenosis. Downstream region appears low and oscillated shear stresses. In addition, along with the increase of the stenotic ratio, the amplitude of the maximum shear stress will be intensively increased and localized, and the sensitivity is also increased. In the aorta with unsymmetrical stenosis, the Von Mises stresses reach the peak value at the side with the surface protuberance, but they are reduced at the side with no protuberance. The sign variation of the layer interface shear stresses near the throat indicates the variation of the shear direction which increases the opportunity of shear damage at the transition plane. Moreover, the shear stress levels at the fluid-solid and intima-media interfaces are higher than that at the media-adventitia interface. The unsymmetrical stenosis causes higher stresses at the side with the surface protuberance than symmetrical one, but lower at the side with no protuberance. These results provide an insight in the influence of the stenosis, as well as its morphology, on the pathogenesis and pathological evolution of some diseases, such as arteriosclerosis and aortic dissection.     

In Vitro Shear Stress Measurements Using Particle Image Velocimetry in a Family of Carotid Artery Models: Effect of Stenosis Severity,Plaque Eccentricity,and Ulceration

Atherosclerotic disease, and the subsequent complications of thrombosis and plaque rupture, has been associated with local shear stress. In the diseased carotid artery, local variations in shear stress are induced by various geometrical features of the stenotic plaque. Greater stenosis severity, plaque eccentricity (symmetry) and plaque ulceration have been associated with increased risk of cerebrovascular events based on clinical trial studies. Using particle image velocimetry, the levels and patterns of shear stress (derived from both laminar and turbulent phases) were studied for a family of eight matched-geometry models incorporating independently varied plaque features – i.e. stenosis severity up to 70%, one of two forms of plaque eccentricity, and the presence of plaque ulceration). The level of laminar (ensemble-averaged) shear stress increased with increasing stenosis severity resulting in 2–16 Pa for free shear stress (FSS) and approximately double (4–36 Pa) for wall shear stress (WSS). Independent of stenosis severity, marked differences were found in the distribution and extent of shear stress between the concentric and eccentric plaque formations. The maximum WSS, found at the apex of the stenosis, decayed significantly steeper along the outer wall of an eccentric model compared to the concentric counterpart, with a 70% eccentric stenosis having 249% steeper decay coinciding with the large outer-wall recirculation zone. The presence of ulceration (in a 50% eccentric plaque) resulted in both elevated FSS and WSS levels that were sustained longer (∼20 ms) through the systolic phase compared to the non-ulcerated counterpart model, among other notable differences. Reynolds (turbulent) shear stress, elevated around the point of distal jet detachment, became prominent during the systolic deceleration phase and was widely distributed over the large recirculation zone in the eccentric stenoses.     

Ultrasound biomicroscopy for longitudinal studies of carotid plaque development in mice: validation with histological endpoints

Atherosclerosis is responsible for the death of thousands of Americans each year. The carotid constriction model of plaque development has recently been presented as a model for unstable plaque formation in mice. In this study we 1) validate ultrasound biomicroscopy (UBM) for the determination of carotid plaque size, percent stenosis, and plaque development in live animals, 2) determine the sensitivity of UBM in detecting changes in blood flow induced by carotid constriction and 3) test whether plaque formation can be predicted from blood flow parameters measured by UBM. Carotid plaques were induced by surgical constriction in Apo E−/− mice. Arteries were imaged bi-weekly by UBM, at which time PW-Doppler measurements of proximal blood flow, as well as plaque length and percent stenosis were determined. Histology was performed 9 weeks post surgery. When compared to whole mount post-mortem measurements, UBM accurately reported carotid plaque length. Percent stenosis, based on transverse B-mode UBM measurements, correlated well with that calculated from histological sections. PW-Doppler revealed that constriction reduced maximum systolic velocity (v_max) and duration of the systolic velocity peak (t_s/t_t). Pre-plaque (2 week post-surgery) PW-Doppler parameters (v_max and t_s/t_t) were correlated with plaque length at 9 weeks, and were predictive of plaque formation. Correlation of initiating PW-Doppler parameters (v_max and t_s/t_t) with resulting plaque length established the degree of flow disturbance required for subsequent plaque development and demonstrated its power for predicting plaque development.     

Effect of a lipid pool on stress/strain distributions in stenotic arteries: 3-D fluid-structure interactions (FSI) models

Nonlinear 3-D models with fluid-structure interactions (FSI) based on in vitro experiments are introduced and solved by ADINA to perform flow and stress/strain analysis for stenotic arteries with lipid cores. Navier-Stokes equations are used as the governing equations for the fluid. Hyperelastic Mooney-Rivlin models are used for both the arteries and lipid cores. Our results indicate that critical plaque stress/strain conditions are affected considerably by stenosis severity, eccentricity, lipid pool size, shape and position, plaque cap thickness, axial stretch, pressure, and fluid-structure interactions, and may be used for possible plaque rupture predictions.     

Influence of arterial wall compliance on the pressure drop across coronary artery stenoses under hyperemic flow condition

Hemodynamic endpoints such as flow and pressure drop are often measured during angioplasty procedures to determine the functional severity of a coronary artery stenosis. There is a lack of knowledge regarding the influence of compliance of the arterial wall-stenosis on the pressure drop under hyperemic flows across coronary lesions. This study evaluates the influence in flow and pressure drop caused by variation in arterial-stenosis compliance for a wide range of stenosis severities. The flow and pressure drop were evaluated for three different severities of stenosis and tested for limiting scenarios of compliant models. The Mooney-Rivlin model defined the non-linear material properties of the arterial wall and the plaque regions. The non-Newtonian Carreau model was used to model the blood flow viscosity. The fluid (blood)-structure (arterial wall) interaction equations were solved numerically using the finite element method. Irrespective of the stenosis severity, the compliant models produced a lower pressure drop than the rigid artery due to compliance of the plaque region. A wide variation in the pressure drop was observed between different compliant models for significant (90% area occlusion) stenosis with 41.0, 32.1, and 29.8 mmHg for the rigid artery, compliant artery with calcified plaque, and compliant artery with smooth muscle cell proliferation, respectively. When compared with the rigid artery for significant stenosis the pressure drop decreased by 27.7% and 37.6% for the calcified plaque and for the smooth muscle cell proliferation case, respectively. These significant variations in pressure drop for the higher stenosis may lead to misinterpretation and misdiagnosis of the stenosis severity.