Influence of microcalcifications on vulnerable plaque mechanics using FSI modeling

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1 Journal of Biomechanics 41 (2008) Influence of microcalcifications on vulnerable plaque mechanics using FSI modeling Danny Bluestein a,, Yared Alemu a, Idit Avrahami b,e, Morteza Gharib b, Kris Dumont a, John J. Ricotta c, Shmuel Einav a,d a Department of Biomedical Engineering, Stony Brook University, Stony Brook, NY , USA b Aeronautics and Bioengineering, California Institute of Technology, Pasadena, CA, USA c Department of Surgery, Stony Brook University Hospital, Stony Brook University, Stony Brook, NY , USA d Department of Bioengineering, Tel Aviv University, Tel Aviv, Israel e Afeka College of Engineering, Tel Aviv, Israel Accepted 25 November 2007 Abstract Sudden heart attacks remain one of the primary causes of premature death in the developed world. Asymptomatic vulnerable plaques that rupture are believed to prompt such fatal heart attacks and strokes. The role of microcalcifications in the vulnerable plaque rupture mechanics is still debated. Recent studies suggest the microcalcifications increase the plaque vulnerability. In this manuscript we present a numerical study of the role of microcalcifications in plaque vulnerability in an eccentric stenosis model using a transient fluid structure interaction (FSI) analysis. Two cases are being compared (i) in the absence of a microcalcification (ii) with a microcalcification spot fully embedded in the fibrous cap. Critical plaque stress/strain conditions were affected considerably by the presence of a calcified spot, and were dependent on the timing (phase) during the flow cycle. The vulnerable plaque with the embedded calcification spot presented higher wall stress concentration region in the fibrous cap a bit upstream to the calcified spot, with stress propagating to the deformable parts of the structure around the calcified spot. Following previous studies, this finding supports the hypothesis that microcalcifications increase the plaque vulnerability. Further studies in which the effect of additional microcalcifications and parametric studies of critical plaque cap thickness based on plaque properties and thickness, will help to establish the mechanism by which microcalcifications weaken the plaque and may lead to its rupture. r 2007 Elsevier Ltd. All rights reserved. Keywords: Vulnerable plaque; Atherosclerosis; Fibrous cap; Rupture; Microcalcification; Numerical modeling; FSI 1. Introduction Sudden heart attacks remain the primary cause of death in the United States: over 1.4 million incidences are reported annually, more than half of which prove fatal. Stenotic plaques cause symptoms that are treatable by angioplasty/percutaneous coronary interventions. However, it is the asymptomatic vulnerable plaques that cause most heart attacks and strokes. Vulnerable plaques are inflamed, active, and growing lesions, which are prone to complications such as rupture, luminal and mural Corresponding author. Tel.: ; fax: address: danny.bluestein@sunysb.edu (D. Bluestein). thrombosis, intraplaque hemorrhage, and rapid progression to stenosis. Although the disruption of an atherosclerotic plaque is considered to be the most frequent cause of heart attack and sudden cardiac death, the mechanisms responsible for the sudden conversion of a rupture-prone plaque to a life-threatening atherothrombotic lesion are not yet fully understood (Fuster et al., 2005). The importance of stress/strain distribution is now well recognized in vascular pathophysiology, specifically in the mechanisms of plaque rupture. The interaction between the luminal flow field and the arterial wall mechanics is crucial to understand the role of flow-induced mechanisms that may lead to plaque rapture. Numerical simulations using advanced fluid structure interaction (FSI) approaches /$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi: /j.jbiomech

2 1112 D. Bluestein et al. / Journal of Biomechanics 41 (2008) showed critical regions for wall buckling, high shear stress and recirculation distal to the constriction (throat) region (Tang et al., 1999, 2001, 2002, 2004a, c). These regions were presented as possible sites for thrombosis, atherosclerosis, and plaque rupture. The results of these studies were verified through experimental observations and MRI scans (Tang et al., 1999, 2001, 2002). Recent modeling that integrates lipid core indicates 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, calcium content, and FSIs (Tang et al., 2004b, c, 2005). FSI simulation of a moderate carotid stenosis (30 70%) with a thin fibrous cap indicated a high risk for plaque rupture (Li et al., 2006). In a parametric study (Finet et al., 2004), the critical plaque cap thickness was determined based on plaque properties and thickness. In another study (Zohdi et al., 2004), a mathematical description of plaque growth, lipid deposition and monocyte activity was used to study growth and rupture as the result of critical hydrostatic pressure, while ignoring flow-induced wall shear stress. Another study which excluded fluid flow, considered plaque rupture as the result of fatigue based on crosssection of arterial plaque geometry (Versluis et al., 2006). The shear stress-dependent growth was described using FSI coupling in arterial stenosis after vein grafting. Maximum and minimum stresses were found near the interface region of the graft and host artery (Chun et al., 2003). Recent modeling for performing intravascular ultrasound elastography of human atherosclerotic coronary arteries has been proposed to identify high-strain regions containing plaques that show the hallmarks of vulnerable plaques (Baldewsing et al., 2004). Calcification is commonly found in atherosclerosis, but the role of calcification in plaque rupture is still unknown. Some studies indicate beneficial effects in stabilizing the plaque (Cheng et al., 1993; Huang et al., 2001), whereas others suggest its deleterious effects on plaque vulnerability. Larger superficial calcification attenuates the stress, with stress concentration depending on the distribution of the lipid core and calcification. Many of the features of plaque development and progression that occur in human plaques are similarly observed in murine plaques (Breslow, 1996), specifically in a transgenic ApoE-deficient mice model. In this mouse model calcium deposits were observed along the aorta at the shoulders of raised plaques. Plaque rupture can be induced (Gough et al., 2006), but appears otherwise to occur only rarely spontaneously. The exact mechanisms of the attenuation or increase of stress by surface calcification are unclear (Imoto et al., 2005). A new hypothesis for vulnerable plaque rupture due to stress-induced debonding around cellular microcalcifications embedded in thin fibrous caps was recently offered by some of the current authors (Vengrenyuk et al., 2006). It indicated local stress concentration around these minute spherical inclusions that predict a nearly two-fold increase in interfacial stress. The existence of these cellular-level microcalcifications was also confirmed in autopsy specimens of coronary atheromatous lesions using in vitro imaging techniques (Vengrenyuk et al., 2006). In order to better understand the contribution of mechanical factors to plaque vulnerability, and to examine whether an inclusion of a calcified spot attenuates or increases the stresses in the cap, the present study investigates the role of the lipid core and of a calcification spot in the vulnerable plaque mechanics. FSI simulation under physiological flow dynamics was conducted in a 3D numerical model of an eccentric arterial stenosis with a vulnerable plaque lesion, using hyperelastic material properties for its various components. Fig. 1. Models of vulnerable plaques: (a) 3D perspective of the studied geometry; dimensions of the models and the location of the calcification spot for the two cases studied, (b) severe stenosis and (c) mild stenosis. Table 1 The four Mooney Rivlin coefficients (c 1, c 2, D 1 and D 2 ) for the material properties of the different tissues composing the wall structures (r wall ¼ 1120 kg/m 3 ) Tissue Material property c 1 (Pa) c 2 (Pa) D 1 (Pa) D 2 (Pa) Vessel wall Lipid core Calcification 92, ,

3 D. Bluestein et al. / Journal of Biomechanics 41 (2008) Ux=Uy=0 Ux=Uy=Uz=0 τ z =0 parabolic inlet flow Q(t) fluid-structure interface V f =U s, τ f =σ s Fig. 2. Applied boundary conditions: (a) inlet velocity coronary waveform and (b) schematic description of boundary conditions application for FSI simulation. Fig. 3. Typical numerical mesh: severe stenosis central axial cross-section of the solid model with a magnified view on the stenosis region, showing the lipid core, the fibrous cap, and the microcalcification embedded within the fibrous cap.

4 1114 D. Bluestein et al. / Journal of Biomechanics 41 (2008) Methods 2.1. Model geometry Two 3D streamlined models of coronary artery with an eccentric stenosis, one severe and one mild (80% and 34% area reduction, correspondingly) were used, both containing a lipid core and a fibrous cap (Fig. 1a). For each of the stenoses models, the effect of a calcified inclusion in the fibrous cap was examined by embedding a 10mm spherical calcification spot within the fibrous cap, at mid distance downstream from the plaque shoulder and the stenosis throat (Fig. 1b). The vessel diameter was 3 mm and the wall thickness was 1 mm. The thickness of the fibrous cap at its thinnest region was about 40 and 60 mm for the severe and mild constriction cases, respectively. The lipid core at its thickest region was 1.8 and 0.5 mm for the severe and mild constriction cases, respectively. The fluid was assumed to be Newtonian with a density of r ¼ g/cm 3 and dynamic viscosity of m ¼ g/(cm s), representing human blood properties at 37 1C. Non-linear isotropic and hyperelastic material properties were assumed for the vessel s wall, lipid core, and the fibrous cap, using the Mooney Rivlin model (Rivlin, 1951). This model is based on the strain energy function W of incompressible hyperelastic body: W ¼ c 1 ði 1 3Þþc 2 ði 2 3ÞþD 1 e D 2ðI 1 3Þ 1, (1) where I 1 and I 2 are the first and second strain invariants and the coefficients c 1, c 2, D 1, and D 2 are the material s parameters. This model gives good approximation for the linear behavior of the material under small strain conditions, with the exponential term matching the stiffening effect of the material under finite strain conditions, when D 1 is proportional to the elastic modulus at zero strain (Bathe, 2002). The various material properties (Table 1) were based on values found in the literature (Huang et al., 2001; Tang et al., 2005). A typical physiological coronary flow waveform was imposed at the inlet (Fig. 2a), with a parabolic velocity profile and a stress-free boundary condition at the outlet. The inlet and outlet of the model were located at a distance of 10 diameters from the stenosis to avoid boundary conditions effects. Stress-free conditions were applied on the outer surface of the vessel s wall (du/dx ¼ 0, du/dy ¼ 0). Velocity and pressure were strongly coupled at the fluid structure interface, using direct FSI to account for the no-slip conditions on the flexible wall (Fig. 2b). The numerical simulations utilized direct strong coupling between the fluid and structure domains. Large strains and large deformations were considered. The dynamics of the flexible wall were calculated using the linear dynamics response of a system: M U þ C _U þ KU ¼ R, (2) where M, C, and K are the mass, damping and stiffness matrices; R is the vector of externally applied loads; and U; _U; and U are the displacement, velocity and acceleration vectors of the structural domain. The flow and pressure fields were calculated by solving the momentum and continuity equations in the fluid domain: rv ¼ 0, þðv V gþrv þrp ¼ mr 2 V, (4) where V is the flow velocity vector and V g is the local coordinate velocity vector, p the static pressure, and t the time. A finite-element scheme was used to solve the set of motion and fluid equations using the commercial software ADINA (ADINA R&D Inc., MA). The Arbitrary Lagrengian Eulerean (ALE) moving mesh approach was utilized for remeshing. The numerical mesh is depicted in Fig. 3, with the fluid domain, which includes the vessel s lumen, and the solid domain, which includes the wall, lipid core, and the calcification. A zoom-in depicts the mesh refinement around the microcalcification. The mesh was further refined in both the solid and fluid domain around the stenosis and in regions characterized by strong gradients and elevated stresses. Mesh convergence studies in which flow Fig. 4. Depiction of the flow field during peak flow: (a) pressure distribution and (b) velocity vector field showing the recirculation zone formed downstream the stenosis.

5 parameters and stress/displacement analyses with coarser and finer meshes were tested, established that the results are independent of mesh density. For the severe stenosis geometries, the vessel with and without calcification consisted of 715,641 and 582,198 elements, respectively. The fluid domain for the severe stenosis case consisted of 173,070 elements. For the mildly stenosed geometries, vessels with and without calcification consisted of 730,908 and 310,941 elements, respectively, and the fluid domain consisted of 126,501 elements. After establishing that periodicity was achieved by the second cycle, each computation was continued for two complete coronary flow cycles using the physiologic waveform (Fig. 2a), with 1250 time-steps for each cycle. As the flow pulse propagated along the artery model it became smoother due to the wall elasticity. D. Bluestein et al. / Journal of Biomechanics 41 (2008) Results Flow and pressure fields at peak flow (t ¼ 0.35 s) are shown in Figs. 4a and b, including velocity vectors at axial and transverse cross-sections depicting the recirculation zone formed distal to the stenosis. The effect of the microcalcification is not noticeable on the transient flow field. However, marked differences were found in the stresses developing within the solid domain when the microcalcification was included in the fibrous cap. Figs. 5 and 6 show the distribution of stress and strain within the wall during peak flow at axial and transverse crosssections, respectively. The axial section (Fig. 5) crosses through the central plane (x ¼ 0 cm), and the radial (transverse) section (Fig. 6) crosses through the calcification spot location. The stresses shown are the Von-Mises stress scalar representation of the 3D stress tensor at each point: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s v ¼ 1=2 ðs 1 s 2 Þ 2 þðs 2 s 3 Þ 2 þðs 3 s 1 Þ 2, (5) where s 1, s 2, s 3 are the principal stresses. The strains shown are the first-principal stretch strain at each point. As depicted in Fig. 5, the stresses and strains in the vessel wall distal to the stenoses were similar, regardless of whether a calcified inclusion was present or not. However, marked differences are found at the proximal stenosis regions (where the microcalcification is embedded) between the two cases. In the case without the calcification, the highest stresses and strains are found at the proximal side of the stenosis, with stress and strain concentration appearing within the thin-fibrous cap around the calcified spot and propagating upstream. The maximal stresses within the fibrous cap without the calcification during peak flow for this case are s ¼ and kpa (for the severe and mild stenosis cases, respectively, Figs. 5a and b). The principal stretches at that point at peak flow are e ¼ and (for the severe and mild stenosis cases, respectively, Figs. 5c and d). Much higher stress values are found in the fibrous cap for the case with the calcification spot, with a maximal magnitude of s ¼ and kpa (for the severe and mild stenosis cases, respectively). The maximal stresses are located within the fibrous cap, proper around the calcified spot (surrounding the interface between the microcalcification and the fibrous cap, Figs. 5a and b, zoom in) almost tripling the peak Fig. 5. Distribution of stresses and strains at peak flow in the central axial cross-section of the vessel wall, showing a magnified view of the distal side of the stenosis (with a zoom-in around the microcalcification): Von-Mises effective stresses for the (a) severe, and (b) mild stenoses; strains (principal stretch) for the (c) severe, and (d) mild stenoses. stress level as compared with the case without calcification. Those elevated stresses propagate upstream towards the plaque shoulder, and circumferentially (Figs. 6a and b). The principal stretches at that point during peak flow are e ¼ and for the severe and mild stenosis cases, respectively (Figs. 6c and d). 4. Discussion Calcification is commonly found in atherosclerosis, but the role of calcification in plaque rupture is still unknown. Some studies indicate beneficial effects in stabilizing plaque specially in cases where the calcified area was big enough (Cheng et al., 1993; Huang et al., 2001),

6 1116 D. Bluestein et al. / Journal of Biomechanics 41 (2008) Fig. 6. Distribution of circumferential (hoop) stress and strains at peak flow in a radial cross-section of the vessel which crosses through the calcification spot location: (a) Von-Mises effective stresses for the (a) severe, and (b) mild stenoses; strains (principal stretch) for the (c) severe, and (d) mild stenoses. whereas others suggest its worsening effects to plaque vulnerability (Imoto et al., 2005; Vengrenyuk et al., 2006). In our study, a single, microcalcification spot significantly augmented the stresses in the fibrous cap in regions adjacent to the calcification, thus enhancing the vulnerability of the plaque. Recent studies provided a plausible explanation of the paradox that most plaque ruptures occurred close to a region of high circumferential tensile stress, but were not necessarily located at the points of maximum stress (Maehara et al., 2002). In the new hypothesis for vulnerable plaque rupture due to stress-induced debonding around cellular microcalcifications (Vengrenyuk et al., 2006), a newly developed theoretical model predicted that a calcified macrophage or an iron deposit located at the area of high circumferential stress can intensify this stress nearly two-fold to values high enough to cause plaque rupture when the cap thickness is o65 mm. This thickness is in close agreement with the criterion for cap instability (Virmani et al., 2003). In this study we show the effect of microcalcification embedded within the fibrous cap proper on stress and strain distributions within the cap, by applying a rigorous 3D FSI analysis of the dynamic stresses developing within the ultrastructure of the vulnerable plaque. Our analysis indicated that a calcified inclusion might significantly affect the plaque stability, possibly increasing its vulnerability. For the flow domain solution, the flow was assumed laminar and Newtonian. Coronary artery dimensions were large enough to assume a Newtonian fluid, and the mean and peak Reynolds number (Re ¼ 71.5 and 108, respectively) justify neglecting turbulent effects, although some localized turbulence may arise distal to the stenosis, especially during the deceleration phase of the waveform (Einav and Bluestein, 2004). However, turbulence will have a negligible effect on the stresses distribution at the proximal side of the stenosis, where the higher stresses are found. A secondary effect of turbulence at the distal size of the stenosis may be the transmission of vibrations generated by the shed vortices that may develop in the interface between the turbulent jet and the recirculation zones (Bluestein et al., 1999) to the proximal side, potentially increasing the vulnerability of the plaque. This potential effect may require additional investigation and increased computational costs in order to solve the combined FSI transient turbulence problem. While phenomenologically similar, the current model not only replicates the conditions that underlie the new hypothesis for vulnerable plaque rupture due to stressinduced debonding around cellular microcalcifications (Vengrenyuk et al., 2006), but adds more. The geometry solved analytically by Vengrenyuk et al. (2006) was of a thin planar material with a spherical inclusion under unidirectional tension only, while ours is a 3D dynamic FSI analysis that incorporates the various components of a vulnerable plaque lesion. Notwithstanding, our simulation supports this hypothesis by showing significant increases in wall stresses developing around the calcified spot and propagating around it indicating increased vulnerability to rupture the plaque s fibrous cap. Ongoing and future studies will place a stronger focus on simulating the debonding properties of smaller calcified inclusions

7 D. Bluestein et al. / Journal of Biomechanics 41 (2008) embedded in the artery wall, adding several more calcified inclusions, perturbing material properties of the various plaque components, and incorporating anisotropic models for the various components of the vulnerable plaque. 5. Conclusions The use of a transient FSI modelling enabled to simulate the time-dependent distribution of stresses and strains developing within a vulnerable plaque, including a lipid core, fibrous cap, and a calcified inclusion. The FSI simulations show that critical stress/strain conditions are very sensitive to changes in material properties, plaque structure, lipid core and the inclusion of calcified spots. The latter may increase local stress concentrations by propagating stresses developing around it to vulnerable regions of the fibrous cap, thus increasing the risk of plaque rupture. It also underscores the importance of conducting a transient simulation to account for cyclic effects during the coronary flow cycle. The results of these simulations further support the hypothesis that local stress concentrations that arise as a result of a calcified inclusion may be the underlying mechanism that enhances the plaque vulnerability. Acknowledgments This work was performed during the term of an Established Investigator Award from the American Heart Association (DB) under Grant N from the National American Heart Association, and by the National Science Foundation under Grant no (DB). SE thanks the Drown Foundation for its support. Conflict of interest statement None of the authors of this paper have any financial and personal relationships with other people or organizations that could inappropriately influence (bias) the presented work. Appendix A. 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