A method for in-vivo analysis for regional arterial wall material property alterations with atherosclerosis: preliminary results

Image-Based Finite Element Modeling Approach for Characterizing In Vivo Mechanical Properties of Human Arteries

Mechanical properties of the arterial walls could provide meaningful information for the diagnosis, management and treatment of cardiovascular diseases. Classically, various experimental approaches were conducted on dissected arterial tissues to obtain their stress-stretch relationship, which has limited value clinically. Therefore, there is a pressing need to obtain biomechanical behaviors of these vascular tissues in vivo for personalized treatment. This paper reviews the methods to quantify arterial mechanical properties in vivo. Among these methods, we emphasize a novel approach using image-based finite element models to iteratively determine the material properties of the arterial tissues. This approach has been successfully applied to arterial walls in various vascular beds. The mechanical properties obtained from the in vivo approach were compared to those from ex vivo experimental studies to investigate whether any discrepancy in material properties exists for both approaches. Arterial tissue stiffness values from in vivo studies generally were in the same magnitude as those from ex vivo studies, but with lower average values. Some methodological issues, including solution uniqueness and robustness; method validation; and model assumptions and limitations were discussed. Clinical applications of this approach were also addressed to highlight their potential in translation from research tools to cardiovascular disease management.

A Pointwise Method for Identifying Biomechanical Heterogeneity of the Human Gallbladder

Identifying the heterogeneous biomechanical property of human gallbladder (GB) walls from non-invasive measurements can have clinical significance in patient-specific modeling and acalculous biliary pain diagnosis. In this article, a pointwise method was proposed to measure the heterogeneity of ten samples of human GB during refilling. Three different points, two on the equator of GB body 90° apart and one on the apex of GB fundus, were chosen to represent the typical regions of interest. The stretches at these points were estimated from ultrasound images of the GB during the bile emptying phase based on an analytical model. The model was validated against the experimental data of a lamb GB. The material parameters at the different points were determined inversely by making use of a structure-based anisotropic constitutive model. This anisotropic model yielded much better accuracy when compared to a number of phenomenologically-based constitutive laws, as demonstrated by its significantly reduced least-square errors in stress curve fitting. The results confirmed that the human GB wall material was heterogeneous, particularly toward the apex region. Our study also suggested that non-uniform wall thickness of the GB was important in determining the material parameters, in particular, on the parameters associated with the properties of the matrix and the longitudinal fibers—the difference could be as large as 20–30% compared to that of the uniform thickness model.

A Framework for Local Mechanical Characterization of Atherosclerotic Plaques: Combination of Ultrasound Displacement Imaging and Inverse Finite Element Analysis

Biomechanical models have the potential to predict plaque rupture. For reliable models, correct material properties of plaque components are a prerequisite. This study presents a new technique, where high resolution ultrasound displacement imaging and inverse finite element (FE) modeling is combined, to estimate material properties of plaque components. Iliac arteries with plaques were excised from 6 atherosclerotic pigs and subjected to an inflation test with pressures ranging from 10 to 120 mmHg. The arteries were imaged with high frequency 40 MHz ultrasound. Deformation maps of the plaques were reconstructed by cross correlation of the ultrasound radiofrequency data. Subsequently, the arteries were perfusion fixed for histology and structural components were identified. The histological data were registered to the ultrasound data to construct FE model of the plaques. Material properties of the arterial wall and the intima of the atherosclerotic plaques were estimated using a grid search method. The computed displacement fields showed good agreement with the measured displacement fields, implying that the FE models were able to capture local inhomogeneities within the plaque. On average, nonlinear stiffening of both the wall and the intima was observed, and the wall of the atheroslcerotic porcine iliac arteries was markedly stiffer than the intima (877 ± 459 vs. 100 ± 68 kPa at 100 mmHg). The large spread in the data further illustrates the wide variation of the material properties. We demonstrated the feasibility of a mixed experimental–numerical framework to determine the material properties of arterial wall and intima of atherosclerotic plaques from intact arteries, and concluded that, due to the observed variation, plaque specific properties are required for accurate stress simulations.

Visualizing the stress distribution within vascular tissues using intravascular ultrasound elastography: a preliminary investigation

A methodology for computing the stress distribution of vascular tissue using finite element-based, intravascular ultrasound (IVUS) reconstruction elastography is described. This information could help cardiologists detect life-threatening atherosclerotic plaques and predict their propensity to rupture. The calculation of vessel stresses requires the measurement of strain from the ultrasound images, a calibrating pressure measurement and additional model assumptions. In this work, we conducted simulation studies to investigate the effect of varying the model assumptions, specifically Poisson's ratio and the outer boundary conditions, on the resulting stress fields. In both simulation and phantom studies, we created vessel geometries with two fibrous cap thicknesses to determine if we could detect a difference in peak stress (spatially) between the two. The results revealed that (i) Poisson's ratios had negligible impact on the accuracy of stress elastograms, (ii) the outer boundary condition assumption had the greatest effect on the resulting modulus and stress distributions and (iii) in simulation and in phantom experiments, our stress imaging technique was able to detect an increased peak stress for the vessel geometry with the smaller cap thickness. This work is a first step toward understanding and creating a robust stress measurement technique for evaluating atherosclerotic plaques using IVUS elastography.

Passive biaxial mechanical properties and in vivo axial pre-stretch of the diseased human femoropopliteal and tibial arteries

Surgical and interventional therapies for atherosclerotic lesions of the infrainguinal arteries are notorious for high rates of failure. Frequently, this leads to expensive reinterventions, return of disabling symptoms or limb loss. Interaction between the artery and repair material likely plays an important role in reconstruction failure, but data describing the mechanical properties and functional characteristics of human femoropopliteal and tibial arteries are currently not available. Diseased superficial femoral (SFA, n = 10), popliteal (PA, n = 8) and tibial arteries (TA, n = 3) from 10 patients with critical limb ischemia were tested to determine passive mechanical properties using planar biaxial extension. All specimens exhibited large nonlinear deformations and anisotropy. Under equibiaxial loading, all arteries were stiffer in the circumferential direction than in the longitudinal direction. Anisotropy and longitudinal compliance decreased distally, but circumferential compliance increased, possibly to maintain a homeostatic multiaxial stress state. Constitutive parameters for a four-fiber family invariant-based model were determined for all tissues to calculate in vivo axial pre-stretch that allows the artery to function in the most energy efficient manner while also preventing buckling during extremity flexion. Calculated axial pre-stretch was found to decrease with age, disease severity and more distal arterial location. Histological analysis of the femoropopliteal artery demonstrated a distinct sub-adventitial layer of longitudinal elastin fibers that appeared thicker in healthier arteries. The femoropopliteal artery characteristics and properties determined in this study may assist in devising better diagnostic and treatment modalities for patients with peripheral arterial disease.

Biomechanics of atherosclerotic coronary plaque: site, stability and in vivo elasticity modeling

Coronary atheroma develop in local sites that are widely variable among patients and are considerably variable in their vulnerability for rupture. This article summarizes studies conducted by our collaborative laboratories on predictive biomechanical modeling of coronary plaques. It aims to give insights into the role of biomechanics in the development and localization of atherosclerosis, the morphologic features that determine vulnerable plaque stability, and emerging in vivo imaging techniques that may detect and characterize vulnerable plaque. Composite biomechanical and hemodynamic factors that influence the actual site of development of plaques have been studied. Plaque vulnerability, in vivo, is more challenging to assess. Important steps have been made in defining the biomechanical factors that are predictive of plaque rupture and the likelihood of this occurring if characteristic features are known. A critical key in defining plaque vulnerability is the accurate quantification of both the morphology and the mechanical properties of the diseased arteries. Recently, an early IVUS based palpography technique developed to assess local strain, elasticity and mechanical instabilities has been successfully revisited and improved to account for complex plaque geometries. This is based on an initial best estimation of the plaque components' contours, allowing subsequent iteration for elastic modulus assessment as a basis for plaque stability determination. The improved method has also been preliminarily evaluated in patients with successful histologic correlation. Further clinical evaluation and refinement are on the horizon.

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.

Impact of metabolic syndrome on re-stenosis development: role of drug-eluting stents

Metabolic syndrome (MetS) is defined as a cluster of numerous cardiovascular risk factors, which encompasses obesity, dyslipidaemia, insulin resistance and hypertension. Patients with MetS are more prone to developing cardiovascular events than other patients. To date, several approaches such as physical exercise, dietary control and invasive and non-invasive therapeutic interventions for dyslipidaemia, hypertension and insulin resistance have been used to manage MetS. However, there is a progressive elevation in the incidence of fatal and non-fatal cardiovascular events due to the increased prevalence of obesity and diabetes. Percutaneous coronary intervention has emerged over the last few years as an effective revascularisation strategy for those with coronary artery disease, in parallel with the development of effective anti-platelet medications and newer drug-eluting stents. In recent years, considerable research efforts have been undertaken to elucidate the pathophysiology of re-stenosis and develop strategies to prevent re-stenosis following percutaneous transluminal coronary angioplasty and stent implantation. Although the rate of stent re-stenosis and target-lesion revascularisation has been reduced, there is little information in the literature on the outcome of MetS in the pathophysiology of re-stenosis. In this review article, we summarise the recent development and progress on re-stenosis and the role of drug-eluting stents, particularly in MetS.

Effect of calcification on the mechanical stability of plaque based on a three-dimensional carotid bifurcation model

Background

This study characterizes the distribution and components of plaque structure by presenting a three-dimensional blood-vessel modelling with the aim of determining mechanical properties due to the effect of lipid core and calcification within a plaque. Numerical simulation has been used to answer how cap thickness and calcium distribution in lipids influence the biomechanical stress on the plaque.

Method

Modelling atherosclerotic plaque based on structural analysis confirms the rationale for plaque mechanical examination and the feasibility of our simulation model. Meaningful validation of predictions from modelled atherosclerotic plaque model typically requires examination of bona fide atherosclerotic lesions. To analyze a more accurate plaque rupture, fluid-structure interaction is applied to three-dimensional blood-vessel carotid bifurcation modelling. A patient-specific pressure variation is applied onto the plaque to influence its vulnerability.

Results

Modelling of the human atherosclerotic artery with varying degrees of lipid core elasticity, fibrous cap thickness and calcification gap, which is defined as the distance between the fibrous cap and calcification agglomerate, form the basis of our rupture analysis. Finite element analysis shows that the calcification gap should be conservatively smaller than its threshold to maintain plaque stability. The results add new mechanistic insights and methodologically sound data to investigate plaque rupture mechanics.

Conclusion

Structural analysis using a three-dimensional calcified model represents a more realistic simulation of late-stage atherosclerotic plaque. We also demonstrate that increases of calcium content that is coupled with a decrease in lipid core volume can stabilize plaque structurally.

Identification of heterogeneous elastic properties in stenosed arteries: a numerical plane strain study

Assessing the vulnerability of atherosclerotic plaques requires an accurate knowledge of the mechanical properties of the plaque constituents. It is possible to measure displacements in vivo inside a plaque using magnetic resonance imaging. An important issue is to solve the inverse problem that consists in estimating the elastic properties inside the plaque from measured displacements. This study focuses on the identifiability of elastic parameters, e.g. on the compromise between identification time and identification accuracy. An idealised plane strain finite element (FE) model is used. The effects of the FE mesh of the a priori assumptions about the constituents, of the measurement resolution and of the data noise are numerically investigated.

On the potential of a new IVUS elasticity modulus imaging approach for detecting vulnerable atherosclerotic coronary plaques: in vitro vessel phantom study

Peak cap stress amplitude is recognized as a good indicator of vulnerable plaque (VP) rupture. However, such stress evaluation strongly relies on a precise, but still lacking, knowledge of the mechanical properties exhibited by the plaque components. As a first response to this limitation, our group recently developed, in a previous theoretical study, an original approach, called iMOD (imaging modulography), which reconstructs elasticity maps (or modulograms) of atheroma plaques from the estimation of strain fields. In the present in vitro experimental study, conducted on polyvinyl alcohol cryogel arterial phantoms, we investigate the benefit of coupling the iMOD procedure with the acquisition of intravascular ultrasound (IVUS) measurements for detection of VP. Our results show that the combined iMOD-IVUS strategy: (1) successfully detected and quantified soft inclusion contours with high positive predictive and sensitivity values of 89.7 ± 3.9% and 81.5 ± 8.8%, respectively, (2) estimated reasonably cap thicknesses larger than ∼300 µm, but underestimated thinner caps, and (3) quantified satisfactorily Young's modulus of hard medium (mean value of 109.7 ± 23.7 kPa instead of 145.4 ± 31.8 kPa), but overestimated the stiffness of soft inclusions (mean Young`s moduli of 31.4 ± 9.7 kPa instead of 17.6 ± 3.4 kPa). All together, these results demonstrate a promising benefit of the new iMOD-IVUS clinical imaging method for in vivo VP detection.

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.

Methods

206 slices of in vivo magnetic resonance image (MRI) of carotid atherosclerotic plaques from 20 patients (age: 49–71, mean: 67.4; all male) were acquired for model construction. Modified Mooney-Rivlin models were used for vessel wall and all plaque components with parameter values chosen to match available data. A morphological plaque severity index (MPSI) was introduced based on in vivo plaque morphological characteristics known to correlate with plaque vulnerability. Critical stress, defined as the maximum of maximum- principal-stress (Stress-P₁) values from all possible vulnerable sites, was determined for each slice for analysis. A computational plaque stress index (CPSI, with 5 grades 0–4, 4 being most vulnerable) was defined for each slice using its critical stress value and stress interval for each CPSI grade was optimized to reach best agreement with MPSI. Correlations between CPSI and MPSI, plaque cap thickness, and lipid core size were analyzed.

Results

Critical stress values correlated positively with lipid core size (r = 0.3879) and negatively with cap thickness (r = -0.3953). CPSI classifications had 71.4% agreement with MPSI classifications. The Pearson correlation coefficient between CPSI and MPSI was 0.849 (p < 0.0001). Using global maximum Stress-P₁ value for each slice to define a global maximum stress-based CPSI (G-CPSI), the agreement rate with MPSI was only 34.0%. The Pearson correlation coefficient between G-CPSI and MPSI was 0.209.

Conclusion

Results from this in vivo study demonstrated that localized critical stress values had much better correlation with plaque morphological features known to be linked to plaque rupture risk, compared to global maximum stress conditions. Critical stress indicators have the potential to improve image-based screening and plaque vulnerability assessment schemes.

Vulnerable atherosclerotic plaque elasticity reconstruction based on a segmentation-driven optimization procedure using strain measurements: theoretical framework

It is now recognized that prediction of the vulnerable coronary plaque rupture requires not only an accurate quantification of fibrous cap thickness and necrotic core morphology but also a precise knowledge of the mechanical properties of plaque components. Indeed, such knowledge would allow a precise evaluation of the peak cap-stress amplitude, which is known to be a good biomechanical predictor of plaque rupture. Several studies have been performed to reconstruct a Young's modulus map from strain elastograms. It seems that the main issue for improving such methods does not rely on the optimization algorithm itself, but rather on preconditioning requiring the best estimation of the plaque components' contours. The present theoretical study was therefore designed to develop: 1) a preconditioning model to extract the plaque morphology in order to initiate the optimization process, and 2) an approach combining a dynamic segmentation method with an optimization procedure to highlight the modulogram of the atherosclerotic plaque. This methodology, based on the continuum mechanics theory prescribing the strain field, was successfully applied to seven intravascular ultrasound coronary lesion morphologies. The reconstructed cap thickness, necrotic core area, calcium area, and the Young's moduli of the calcium, necrotic core, and fibrosis were obtained with mean relative errors of 12%, 4% and 1%, 43%, 32%, and 2%, respectively.

An inverse method for imaging the local elasticity of atherosclerotic coronary plaques

The rupture of thin-cap fibroatheroma (TCFA) plaques is a major cause of acute coronary events. A TCFA has a trombogenic soft lipid core, shielded from the blood stream by a thin, possibly inflamed, stiff cap. The majority of atherosclerotic plaques resemble a TCFA in terms of overall structural composition, but have a more complex, heterogeneous morphology. An assessment of the material distribution is vital for quantifying the plaque's mechanical stability and for determining the effect of plaque-stabilizing pharmaceutical agents. We describe a new automated inverse elasticity method, intravascular ultrasound (IVUS) modulography, which is capable of reconstructing a heterogeneous Young's modulus distribution. The elastogram (i.e., spatial strain distribution) of the plaque is the input for the method, and is measured using the clinically available technique, IVUS elastography. Our method incorporates a novel divide-and-conquer strategy, allowing the reconstruction of TCFAs as well as heterogeneous plaques with localized regions of soft, weakened tissue. The method was applied to ex vivo elastograms, which were simulated from the cross sections of postmortem human coronary plaques. To demonstrate the clinical feasibility of the method, measured elastograms from human atherosclerotic coronary arteries were analyzed. One elastogram was measured in vitro; the other, in vivo. The method approximated the true Young's modulus distribution of all simulated plaques, while the in vitro reconstruction was in agreement with histology. In conclusion, the IVUS modulography in combination with the IVUS elastography has strong potential to become an all-encompassing modality for detecting plaques, for assessing the information related to their rupture-proneness, and for imaging their heterogeneous elastic material composition.

Surrounding tissues affect the passive mechanics of the vessel wall: theory and experiment

The stress and strain in the vessel wall are important determinants of vascular physiology and pathophysiology. Vessels are constrained radially by the surrounding tissue. The hypothesis in this work is that the surrounding tissue takes up a considerable portion of the intravascular pressure and significantly reduces the wall strain and stress. Ten swine of either sex were used to test this hypothesis. An impedance catheter was inserted into the carotid or femoral artery, and after mechanical preconditioning pressure-cross-sectional area relations were obtained with the surrounding tissue intact and dissected away (untethered), respectively. The radial constraint of the surrounding tissue was quantified as an effective perivascular pressure on the outer surface of the vessel, which was estimated as 50% or more of the intravascular pressure. For carotid arteries at pressure of 100 mmHg, the circumferential wall stretch ratio in the intact state was approximately 20% lower than in the untethered state and the average circumferential stress was reduced by approximately 70%. For femoral arteries, the reductions were approximately 15% and 70%, respectively. These experimental data support the proposed hypothesis and suggest that in vitro and in vivo measurements of the mechanical properties of vessels must be interpreted with consideration of the constraint of the surrounding tissue.

Quantifying effects of plaque structure and material properties on stress distributions in human atherosclerotic plaques using 3D FSI models

BACKGROUND

Atherosclerotic plaques may rupture without warning and cause acute cardiovascular syndromes such as heart attack and stroke. Methods to assess plaque vulnerability noninvasively and predict possible plaque rupture are urgently needed.

METHOD

MRI-based three-dimensional unsteady models for human atherosclerotic plaques with multi-component plaque structure and fluid-structure interactions are introduced to perform mechanical analysis for human atherosclerotic plaques.

RESULTS

Stress variations on critical sites such as a thin cap in the plaque can be 300% higher than that at other normal sites. Large calcification block considerably changes stress/strain distributions. Stiffness variations of plaque components (50% reduction or 100% increase) may affect maximal stress values by 20-50%. Plaque cap erosion causes almost no change on maximal stress level at the cap, but leads to 50% increase in maximal strain value.

CONCLUSIONS

Effects caused by atherosclerotic plaque structure, cap thickness and erosion, material properties, and pulsating pressure conditions on stress/strain distributions in the plaque are quantified by extensive computational case studies and parameter evaluations. Computational mechanical analysis has good potential to improve accuracy of plaque vulnerability assessment.

Local maximal stress hypothesis and computational plaque vulnerability index for atherosclerotic plaque assessment

It is believed that atherosclerotic plaque rupture may be related to maximal stress conditions in the plaque. More careful examination of stress distributions in plaques reveals that it may be the local stress/strain behaviors at critical sites such as very thin plaque cap and locations with plaque cap weakness that are more closely related to plaque rupture risk. A "local maximal stress hypothesis" and a stress-based computational plaque vulnerability index (CPVI) are proposed to assess plaque vulnerability. A critical site selection (CSS) method is proposed to identify critical sites in the plaque and critical stress conditions which are be used to determine CPVI values. Our initial results based on 34 2D MRI slices from 14 human coronary plaque samples indicate that CPVI plaque assessment has an 85% agreement rate (91% if the square root of stress values is used) with assessment given by histopathological analysis. Large-scale and long-term patient studies are needed to further validate our findings for more accurate quantitative plaque vulnerability assessment.

Regional material property alterations in porcine femoral arteries with atheroma development

We have developed a novel methodology that permits assessment of regional vascular mechanical property alterations in the presence of atheroma in vivo employing a Yucatan miniswine model with induced lesions. Femoral arteries were imaged with intravascular ultrasound. Image data were segmented and, following three-dimensional reconstruction, underwent finite element and sensitivity analysis with optimization to identify regions with altered vascular mechanical properties. All regions were compared to histological analysis. In 12 animals with 8 weeks of endothelial cell denudation and high cholesterol diet (induced atherosclerosis), the elastic modulus initially decreased with early lesion development and then increased with increasing fibrosis-(elastic modulus-all values x10(4)Pa-mean+/-SEM) histologically normal (non-denuded control segment) elements 9.73+/-0.01, fatty elements 9.53+/-0.01, fibrofatty elements 9.41+/-0.03, and fibrous elements 9.68+/-0.02 (all p<0.001 vs. normal elements). Wall thickness, however, increased with atheroma formation. These data demonstrate decreasing vascular material properties with early lesions, followed by an increase as lesions progress. This methodology permits determination of areas with early atheroma development, follow atheroma progression, and potentially evaluate interventions aimed at decreasing atheroma load and normalizing vascular material properties.

Hemodynamics and wall mechanics in human carotid bifurcation and its consequences for atherogenesis: investigation of inter-individual variation

Finite element simulations of fluid-solid interactions were used to investigate inter-individual variations in flow dynamics and wall mechanics at the carotid artery bifurcation, and its effects on atherogenesis, in three healthy humans (normal volunteers: NV1, NV2, NV4). Subject-specific calculations were based on MR images of structural anatomy and ultrasound measurements of flow at domain boundaries. For all subjects, the largest contiguous region of low wall shear stress (WSS) occurred at the carotid bulb, WSS was high (6-10 Pa) at the apex, and a small localized region of WSS > 10 Pa occurred close to the inner wall of the external carotid artery (ECA). NV2 and NV4 had a "spot" of low WSS distal to the bifurcation at the inner wall of the ECA. Low WSS patches in the common carotid artery (CCA) were contiguous with the carotid bulb low WSS region in NV1 and NV2, but not in NV4. In all three subjects, areas of high oscillatory shear index (OSI) were confined to regions of low WSS. Only NV4 exhibited high levels of OSI on the external adjoining wall of the ECA and CCA. For all subjects, the maximum wall shear stress temporal gradient (WSSTG) was highest at the flow divider (reaching 1,000 Pa/s), exceeding 300 Pa/s at the walls connecting the ECA and CCA, but remaining below 250 Pa/s outside of the ECA. In all subjects, (maximum principle) cyclic strain (CS) was greatest at the apex (NV1: 14%; NV2: 11%; NV4: 6%), and a second high CS region occurred at the ECA-CCA adjoining wall (NV1: 11%, NV2: 9%, NV4: 5%). Wall deformability was included in one simulation (NV2) to verify that it had little influence on the parameters studied. Location and magnitude of low WSS were similar, except for the apex (differences of up to 25%). Wall distensibility also influenced OSI, doubling it in most of the CCA, separating the single high OSI region of the carotid bulb into two smaller regions, and shrinking the ECA internal and external walls' high OSI regions. These observations provide further evidence that significant intra-subject variability exists in those factors thought to impact atherosclerosis.

Porcine carotid arterial material property alterations with induced atheroma: an in vivo study

OBJECTIVE

A novel methodology has been developed to evaluate regional alterations in arterial wall material properties with induced atheroma in an animal model.

METHODS

Atheromatous lesions (fatty, fibro-fatty, and fibrous) were induced in the carotid arteries of a Yucatan miniswine model by endothelial cell denudation and high cholesterol diet. The images at base line and 8 weeks after denudation were obtained using intravascular ultrasound (IVUS) imaging along with hemodynamic data. Finite element analysis (FEA) along with optimization was employed to assess regional alterations in elastic modulus in the presence of atheroma confirmed by histology.

RESULTS

In animals with 8 weeks of induced atherosclerosis, the elastic modulus increased-(elastic modulus-all values x 10(4) Pa, mean+/-S.D.) normal elements (9.34+/-0.36) compared to abnormal elements (9.52+/-0.36) (p<0.05 versus normal elements). Wall thickness increased with atheroma formation. These data demonstrate stiffening vascular wall elastic modulus with lesion progression. This is different from the behavior of femoral arteries, where the elastic modulus decreases with early stages of atheroma development followed by an increase as lesions progress.

CONCLUSIONS

This methodology permits determination of areas with early atheroma development, follow atheroma progression, and potentially evaluate interventions aimed at decreasing atheroma load and normalizing vascular material properties.

Finite element modelling and simulations in cardiovascular mechanics and cardiology: A bibliography 1993–2004

The paper gives a bibliographical review of the finite element modelling and simulations in cardiovascular mechanics and cardiology from the theoretical as well as practical points of views. The bibliography lists references to papers, conference proceedings and theses/dissertations that were published between 1993 and 2004. At the end of this paper, more than 890 references are given dealing with subjects as: Cardiovascular soft tissue modelling; material properties; mechanisms of cardiovascular components; blood flow; artificial components; cardiac diseases examination; surgery; and other topics.

Assessment of vulnerable plaque composition by matching the deformation of a parametric plaque model to measured plaque deformation

Intravascular ultrasound (IVUS) elastography visualizes local radial strain of arteries in so-called elastograms to detect rupture-prone plaques. However, due to the unknown arterial stress distribution these elastograms cannot be directly interpreted as a morphology and material composition image. To overcome this limitation we have developed a method that reconstructs a Young's modulus image from an elastogram. This method is especially suited for thin-cap fibroatheromas (TCFAs), i.e., plaques with a media region containing a lipid pool covered by a cap. Reconstruction is done by a minimization algorithm that matches the strain image output, calculated with a parametric finite element model (PFEM) representation of a TCFA, to an elastogram by iteratively updating the PFEM geometry and material parameters. These geometry parameters delineate the TCFA media, lipid pool and cap regions by circles. The material parameter for each region is a Young's modulus, EM, EL, and EC, respectively. The method was successfully tested on computer-simulated TCFAs (n = 2), one defined by circles, the other by tracing TCFA histology, and additionally on a physical phantom (n = 1) having a stiff wall (measured EM = 16.8 kPa) with an eccentric soft region (measured EL = 4.2 kPa). Finally, it was applied on human coronary plaques in vitro (n = 1) and in vivo (n = 1). The corresponding simulated and measured elastograms of these plaques showed radial strain values from 0% up to 2% at a pressure differential of 20, 20, 1, 20, and 1 mmHg respectively. The used/reconstructed Young's moduli [kPa] were for the circular plaque EL = 50/66, EM = 1500/1484, EC = 2000/2047, for the traced plaque EL = 25/1, EM = 1000/1148, EC = 1500/1491, for the phantom EL = 4.2/4 kPa, EM = 16.8/16, for the in vitro plaque EL = n.a./29, EM = n.a./647, EC = n.a./1784 kPa and for the in vivo plaque EL = n.a./2, EM = n.a./188, Ec = n.a./188 kPa.

Assessment of a technique to determine the mechanical properties of coronary arteries using mock arteries

Heart disease is the leading cause of death in the western world, and percutaneous transluminal coronary angioplasty (PTCA) and stent deployment are standard procedures used to reopen and/or stabilize blocked coronary arteries. Despite considerable improvements in these techniques, restenosis is still a long term problem, with patients requiring repeated procedures. Hence, further investigation of the mechanisms that contribute to arterial wall remodelling may help to improve the success of percutaneous coronary interventions (PCI). The aim of this study was to assess a measurement technique for its ability to determine the compliance of mock arteries using different balloon catheters during a standard angioplasty procedure. Pressure-volume (PV) curves were used to determine the combined mechanical response of the system, the balloon catheters and mock arteries in real time. The validity of subtracting the system compliance from the PV curves containing the system, balloon and/or mock artery was assessed using two-independent measurement techniques to determine the balloon inflation volume. Eighteen balloon catheters from four different manufactures were inflated inside three mock arteries with differing compliances (high, medium, low) and the resulting PV curves were recorded. The compliances of the three mock arteries were then determined from the PV curves. The results were compared to reference values of the three mock arteries, which were determined from one of the independent mechanical tests. Corrections for each balloon catheter type and each individual balloon catheter were studied. A correlation coefficient of 0.99 between the two-independent volume measurement techniques confirmed the validity of subtracting the system compliance. The compliance values for the high, medium and low compliant mock arteries, obtained by using the different balloon catheters, varied between 4 and 12, 3 and 9 and, 2 and 5 (microl/bar) mm(-1), respectively. Standard deviation varied from 0.1 up to 2.1 (microl/bar) mm(-1). This was equivalent to a mean variation factor (root mean square/mean) of 29%, which reduced to 12% with correction. The system was always able to detect differences between mock arteries in spite of the large variation with different balloon catheters. The study has shown that it is possible to determine compliances of different mock arteries using different balloon catheters. However, the determined compliances needed to be corrected for different mechanical properties of the balloons used.