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Am J Physiol Heart Circ Physiol 293: H1987-H1996, 2007. First published June 29, 2007; doi:10.1152/ajpheart.00018.2007
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Influence of residual stress/strain on the biomechanical stability of vulnerable coronary plaques: potential impact for evaluating the risk of plaque rupture

Jacques Ohayon,1,2 Olivier Dubreuil,3 Philippe Tracqui,2 Simon Le Floc'h,2 Gilles Rioufol,3 Lara Chalabreysse,3 Françoise Thivolet,3 Roderic I. Pettigrew,1 and Gérard Finet3

1National Institutes of Health, National Heart, Lung, and Blood Institute, Pettigrew's Laboratory, Bethesda, Maryland; 2Laboratory Techniques de l’Imagerie de la Modélisation et de la Cognition-Institut de Mathématiques de Grenoble, DynaCell, Centre National de la Recherche Scientifique Unité Mixte de Recherche 5525, Institut de l'Ingénierie et de l'Information de Santé (In3S), Grenoble; and 3Department of Hemodynamics and Interventional Cardiology, Hospices Civils de Lyon and Claude Bernard University, Lyon1; Institut National de la Santé et de la Recherche Médicale E0226 Unit, Lyon, France

Submitted 5 January 2007 ; accepted in final form 20 June 2007


   ABSTRACT
TOP
 ABSTRACT
MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 GRANTS
 REFERENCES
 
In a vulnerable plaque (VP), rupture often occurs at a site of high stress within the cap. It is also known that vessels do not become free of stress when all external loads are removed. Previous studies have shown that such residual stress/strain (RS/S) tends to make the stress distribution more uniform throughout the media of a normal artery. However, the influence of RS/S on the wall stress distribution in pathological coronaries remains unclear. The aim of this study was to investigate the effects of RS/S on the biomechanical stability of VPs. RS/S patterns were studied ex vivo in six human vulnerable coronary plaque samples. Because the existence of RS/S can only be assessed by releasing it, the opening angle technique was the experimental approach used to study the geometrical opening configurations of the diseased arteries, producing an arterial wall in a near-zero stress state. Reciprocally, these opening geometries were used in finite element simulations to reconstruct the RS/S distributions in closed arteries. It was found that the RS/S 1) is not negligible, 2) dramatically affects the physiological peak stress amplitude in the thin fibrous cap, 3) spotlights some new high stress areas, and 4) could be a landmark of the lipid core's developmental process within a VP. This study demonstrates that plaque rupture is not to be viewed as a consequence of intravascular pressure alone, but rather of a subtle combination of external loading and intraplaque RS/S.

atherosclerosis; zero-stress state; lipid core; plaque growth; finite element analysis

RUPTURE OF VULNERABLE atherosclerotic plaque is recognized as the trigger event for acute coronary syndrome (8). The characteristics of a vulnerable plaque (VP) are now well-defined, thanks to numerous pathological studies (13, 56). Such plaques have a large extracellular lipid core and a thin fibrous cap. VPs may be clinically detected with the aid of various techniques as follows: intravascular ultrasound (3, 25, 48), optical coherence tomography (19, 29), computed tomography (14, 44), or magnetic resonance imaging (38). Detecting VPs is a major issue, since it could lead to the development of specific treatment strategies for the prevention of acute thrombotic accidents (26, 45). Unfortunately, prediction of plaque rupture appears to be far less precise (54), notably because the intraplaque stress distribution is a hidden variable that escapes direct observation. Therefore, in addition to known geometrical and morphological characteristics such as fibrous cap thickness and lipid core, other variables must be taken into consideration to extend our knowledge of the VP rupture process. In this context, biomechanical studies of VP stress and strain distributions is of major interest, since it is now established that mechanical stress affects several cellular processes, including macrophage migration, plaque remodeling through metalloproteinase production, and modulation of plaque angiogenesis, which are central to the plaque's vulnerability status (4, 18, 30, 55).

It is well-known that most biological tissues, including arterial walls, are not free of stress when all external loads are removed (16, 21, 50, 52). The stresses and strains that remain in a vessel free of external load (i.e., at zero blood pressure) are termed "residual" and noted here as RS/S. In normal vessels, RS/S proved to be important in determining the wall stress distribution under physiological pressure (16, 22, 46). Indeed, previous studies (7, 22, 50, 52) demonstrated that RS/S tends to smooth the circumferential stress distribution throughout the thickness of a normal artery wall.

The intraplaque distribution of RS/S and its effects on the stress field in atherosclerotic coronary plaques, on the other hand, have never been studied in detail. As a result, they are largely ignored in structural analyses intended to predict plaque rupture location (5, 15, 27, 33, 36, 42). To date, no data are available on RS/S patterns in human coronary plaques. Williamson's group (57), however, did some elegant computations based on the finding that RS/S produces lower radial stress gradients at physiological arterial pressure in healthy arteries. Their plaque rupture location prediction calculations were initiated by introducing optimal radial distributions of residual strain in various arterial segments. However, this approach lacks experimental validation and might fail when the structural heterogeneity of the VP is taken into consideration.

The present study was therefore designed to assess both RS/S and its impact on the in vivo stress distribution in human vulnerable coronary plaques. Stress distribution is often employed to predict plaque rupture, by correlating high-stress sites to vulnerable regions (5, 15, 27, 33, 36, 42). It is therefore legitimate to expect that taking account of RS/S in structural analysis will improve prognosis of plaque rupture.


   MATERIALS AND METHODS
TOP
 ABSTRACT
 MATERIALS AND METHODS
RESULTS
 DISCUSSION
 GRANTS
 REFERENCES
 
Materials

The study was approved by the Human Investigation Committee of our institution. Six pathological epicardial coronary artery samples with VP were selected from several arterial segments obtained from one explanted human heart after heart transplantation and three nontransplanted donor hearts. These hearts were held in physiological saline solution at a temperature of 4°C. Samples had been removed within 24 h after transplantation or 6 h after patient's death. The epicardial coronary arteries were either left anterior descending, right coronary, or left circumflex artery and were dissected over a few centimeters (see Table 1).


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  		Table 1. Origin of the hearts and coronary vulnerable plaques

 
Experimental Design

Each sample was sectioned transversally by lancet into 2- to 5-mm-thick segments (Fig. 1A), excised within the bifurcation-free area. Immediately following excision, the coronary sample was immersed in Ca2+-free Krebs-Henseleit buffer [composition (in mM): 11 D-glucose, 4.7 KCl, 120 NaCl, 25 NaHCO3, 1.2 KH2PO4, 1.2 MgSO4, and 0.026 EDTA (28)] at room temperature (22°C); such a bath prevents any precontraction of the artery. A digital image of the coronary sample in the unloaded state was taken following 15 min incubation in the Krebs-Henseleit solution (SONY 3CCD color video camera, model DXC-950P; SONY, Tokyo, Japan), with a 25-mm f2.8 C35858 lens (Century Precision Optics; Fig. 1A). In a second step, each arterial segment was sectioned radially in the middle of the presumed healthy arc (Fig. 1B) and photographed in the zero-stress state 3 h after each radial cut, according to Rehal et al.'s (47) protocol. The image was then digitized (PDB 5.01 1999 software; SAMBA, Grenoble, France) and saved to a computer for image processing with ImageJ software (ImageJ, NIH, Bethesda, MD). The opening angle of each segment was measured from digital image segmentation (Fig. 1B).


Figure 1
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  		Fig. 1. Description of the protocol performed on specimen I to obtain the geometry of the macroscopic zero-stress configuration. A: isolated left anterior descending coronary sample of 4 mm length. B: zero-stress configuration obtained 3 h after radial sectioning of the healthy arc. The opening angle was measured as 143°. C: macroscopic histological observation of the same sample in B enabling the contours of the plaque constituents to be defined. D: microscopic histological view of the thin fibrous cap, from which the cap thickness (CTh) was approximated (CTh close to 94 µm). LC, lipid core; CF, cellular fibrosis.

 
Histopathology

Each open segment was fixed in a mix of ethyl alcohol, formalin, and acetic acid for 48 h and then decalcified with 10% nitric acid and included in paraffin. Cross sections (4 µm) were sliced by microtome and colored with hematoxylin-phloxine-saffron. Anatomopathological analysis of the wall was performed under optical microscopy (LEICA type; Fig. 1, C and D). These histological observations served to validate both plaque component contour detection and fibrous cap thickness as initially measured from image analysis. For immunohistochemical staining, macrophages were detected by monoclonal anti-human-CD68 antibody (Invitrogen), according to the manufacturer's specifications. Briefly, the slides were deparaffinized, enzyme-digested, immersed in H2O2 solution, and then blocked with normal serum before incubation with CD68 antibody (1:300; Dako, Glostrup, Denmark). Staining was revealed by peroxidase-conjugated secondary antibody and visualized with diaminobenzidine chromogen.

Finite Element Analysis

Geometry. Static finite element (FE) computations were performed using ANSYS 10 software (Ansys, Canonsburg, PA), starting with the macroscopic zero-stress geometrical configurations (Fig. 1B). The various regions of the plaque components and arterial wall were meshed with ~1,500 triangular (6-node) and quadrangular (8-node) elements. The FE models were solved under the assumption of plane and finite strains.

Material properties. The mechanical behavior of the plaque constituents was modeled using incompressible neo-Hookean isotropic materials characterized by a strain-energy function (W). Such isotropic behavior has been previously used to model the mechanical response of coronaries (34) and living cells (43). The strain-energy function is given by W = a(I1 – 3), where a is a material constant, and I1 is the first invariant of the strain tensor (23). For such incompressible material, an explicit relationship between the initial Young's modulus E and the material constant a can be obtained for small uniaxial tension or compression of the medium: E ~ 6a. Lee et al.'s (32) data for the mechanical behavior of cellular fibrosis in human atherosclerotic plaques were used, and a value of Efibrosis = 500 kPa was adopted for computation. For the artery and the lipid core, the following initial Young's moduli values were used: Ecore = 5 kPa (37) and Eartery = 150 kPa (57).

Simulations. Two kinds of simulation were performed to analyze the influence of RS/S on the spatial stress/strain distribution in the wall of the pathological artery under physiological loading.

For the first, FE simulation started off from the open (stress-free) arterial configuration. The RS/S distribution was obtained by first closing the artery, i.e., by numerically bringing the free edges together. In the absence of any blood pressure, this situation corresponds to the unloaded physiological configuration, in which residual stresses and strains persist within the arterial wall lesion. In the second step, the above load (i.e., that imposed to obtain closure) was supplemented by 120 mmHg (or 16 kPa) systolic blood pressure to obtain the loaded physiological configuration.

To compare these original results with those usually obtained when RS/S is ignored (5, 15, 27, 33, 36, 42), a second series of simulations was then performed, starting FE calculation off from the closed contours of the unloaded physiological configuration. First, the closed zero-blood-pressure configuration previously obtained after closure was assumed to be the strain-free initial state. Second, a loading pressure of 16 kPa was applied to the closed artery.

Statistical Analysis

The correlations between experimental measurement and RS/S of the unstable VP population were analyzed by simple and multiple linear regression using a commercially available software package (SigmaStat 3.5; Systat Software, Point Richmond, CA). Regressions with P < 0.05 and r2 = 0.90 were considered statistically significant.


   RESULTS
TOP
 ABSTRACT
 MATERIALS AND METHODS
 RESULTS
DISCUSSION
 GRANTS
 REFERENCES
 
Background: Idealized Case Illustrating the Importance of RS/S in Normal Artery

Because the existence of RS/S can only be assessed by releasing it, the opening angle technique is currently the only possible experimental approach to obtain the geometrical configuration of the artery sample approximating a zero-stress state. The technique, used by several authors for normal arteries (16, 22, 50, 52), proceeds as follows: a thin ring-like slice of an arterial segment is cut radially, and the arterial wall springs open into an arc. After viscoelastic dissipation, the opened configuration is totally free of stress and is therefore called the "zero-stress configuration". Figure 2 shows the three main configurations of the artery, which are the "zero-stress state", the "unloaded physiological state," and the "loaded physiological state". These idealized illustrations show that closing the zero-stress open configuration of the normal artery (Fig. 2A) generates a compression of the subintima layers and an extension of the subadventitia layers (Fig. 2B). Interestingly, pressurizing such a prestressed vessel releases the compressive stress in the subintima layers (Fig. 2C). It would be tempting to say that this prestress induced by blood pressure in a normal artery had been physiologically designed to minimize stress and strain amplitudes in the luminal wall region.


Figure 2
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  		Fig. 2. Schematic representation of the effect of residual stress on the normal in vivo blood vessel performance. A: zero-stress configuration. B: unloaded physiological configuration. C: loaded physiological configuration. P, blood pressure. Note that from state A to state B, the length of the median line stays constant.

 
Inside atherosclerotic plaques, however, the RS/S distribution is found to be more complex than in a normal artery. Plaque is a composite material made of various media, including soft atheromatous core (or lipid core), calcified tissue, cellular fibrosis, and other components, all with different mechanical properties. In spite of such material heterogeneity, the above experimental protocol can be used to release most of the RS/S in the pathological vessel. The resultant open configuration of the atherosclerotic vessel is assumed to be free of stress and has therefore been called by Matsumoto et al. (39) the "macroscopic stress-free configuration," although admittedly other lower-amplitude RS/S patterns might still be at work in the plaque even after radial sectioning (40).

Morphological Description and Zero-stress Configuration of the VP

For each specimen and from the closed cross section configurations obtained after simulating the closure of the artery, the areas of lumen (LA), lipid core (LCA), cellular fibrosis, external elastic membrane (EEMA), plaque (PA) + media (MA; where PA + MA = EEMA – LA), relative lipid core (defined as the ratio 100 x LCA/PA), and the plaque burden [PB = 100 x (PA + MA)/EEMA] were calculated (Table 1). It is to be noted that the five unstable VPs have similar cap thicknesses (mean = 89.40 ± 14.69 µm) and plaque burdens (mean = 75.24 ± 5.48%). Table 1 summarizes the amplitude of the opening angle for each specimen and the features of the three hearts from which the six specimens were taken.

Spatial RS/S Distribution in the VPs

By closing the open VPs (Fig. 3A), the RS/S in the pathological wall was calculated (Fig. 3, B and C). The effective residual strain in the thin fibrous cap appeared to be nonnegligible (close to 40% in some cases: see Fig. 3; zoom on Fig. 3B, specimen I). Thus, even under no external load (i.e., blood pressure), the plaques were subject to high stress/strain. According to our chosen stress-strain law, a linear relationship exists between effective strain and von Mises stress. The ratio of von Mises stress over effective strain gives the apparent Young's modulus, which appeared to be close to the initial Young's modulus postulated for the various constituents (Fig. 3D).


Figure 3
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  		Fig. 3. Color maps of finite element results highlighting, for specimens I, II, and III, the residual strain and stress distributions in the vulnerable coronary plaque. A: geometries, meshes, and plaque constituents of the zero-stress configurations used to initiate the numerical computations for the three first specimens. Green, lipid core; blue, cellular fibrosis; red, arterial wall. B: spatial distribution of effective mean strain ({varepsilon}eff). C: spatial distribution of von Mises stress ({sigma}VM; units are kPa; 1 kPa = 0.1333 mmHg). D: color maps giving spatial distribution of the apparent Young's modulus (Eap = {sigma}VM/{varepsilon}eff in kPa), which reflects the apparent stiffness of the tissue. Vulnerable thin fibrous cap sites of interest are zoomed for clarity.

 
Macrophage Areas and Spatial RS/S Distribution

Atheromatous plaques showed robust staining for macrophages, mainly located in the shoulders, which are regions prone to rupture. Additionally, in some cases, observations highlighted the presence of a few macrophages in the rear of the lipid core (Fig. 4).


Figure 4
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  		Fig. 4. Example of immunohistochemical staining for macrophages performed with CD68 antibodies. Notice that macrophages are mainly present in the shoulders (arrows) while some are located at the rear of the lipid core (square area).

 
Relationship Between RS/S Amplitude and Lipid Core Size

For the unstable VP population, simple and multiple linear regression analyses were carried out to look for potential correlations between the peak residual strain amplitude in the fibrous cap obtained from numerical computation on the one hand and the measured relative lipid core area and opening angle on the other. In all statistical simulations, only one linear regression proved to be significant (r2 = 0.90, P = 0.016) between the relative cross-sectional area of the lipid core on one hand and RS/S amplitude in the fibrous cap on the other (Fig. 5). Plaque burden and cap thickness were not taken into account in these statistical analyses, being similar in all five specimens (see Table 1).


Figure 5
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  		Fig. 5. Linear relationship between the relative lipid core size and the residual peak cap effective strain found for this population of similar unstable vulnerable plaques (r2 = 0.9, P < 0.02). The confidence and prediction intervals (area between the internal and external dashed lines, respectively) were also plotted. Note that the relative lipid core area is defined as the ratio of the lipid core area (LCA) over the plaque area (PA). PA is equal to LCA plus fibrosis area. PB, plaque burden.

 
To confirm and strengthen this finding, additional simulations (data not shown) were performed on a schematic plate section consisting of a lipid core embedded in a rectangular plate. Increasing lipid core sizes were considered while keeping cap thickness constant. Arterial wall closure was simulated by bending this idealized plaque by a torque applied on the two opposite ends of the plaque. The numerical results (data not shown) confirmed those obtained with real artery samples; namely, the larger the lipid core, the greater the residual strain within the cap.

Influence of RS/S on Peak Stress Amplitude

The RS/S patterns in our computations spotlighted some new zones of high stress located on the rear side of the lipid core and at the interface between the wall and the plaque fibrosis (see arrows on Fig. 6C). No such sites were apparent when RS/S was neglected (Fig. 6B). Moreover, the results presented in Figs. 6 and 7A show clearly that neglecting RS/S in structural analysis overestimates the strain/stress amplitude in the thin fibrous cap by a factor of as much as four (Figs. 6 and 7A, specimen II). Additionally, we investigated the influence of blood pressure on peak cap effective strain by comparing results obtained with and without RS/S; RS/S tended to decrease, making the strain amplitude more uniform within the artery wall, over the cardiac cycle (Fig. 7B).


Figure 6
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  		Fig. 6. Influence of residual stress/strain (RS/S) on the stress fields of the pressurized artery. A: geometries, meshes, and plaque constituents of the zero-stress configurations used to initiate the finite element computations ignoring RS/S. Green, lipid core; blue, cellular fibrosis; red, arterial wall. B: spatial distribution of {sigma}VM obtained for a systolic blood pressure of 16 kPa (120 mmHg) ignoring RS/S. C: spatial distribution of {sigma}VM obtained the same systolic blood pressure P but with RS/S included in the computation. Arrows show high-stress zones located on the rear of the lipid cores. Vulnerable thin fibrous cap sites of interest are zoomed for clarity, and the peak cap effective strain and peak {sigma}VM are specified.

 

Figure 7
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  		Fig. 7. Influence of RS/S on the peak cap effective strain of the pressurized unstable vulnerable plaques. A: comparison of systolic peak cap effective strain obtained when RS/S is considered (white bars) or neglected (black bars). A systolic blood pressure of 16 kPa was used for these simulations. The gray bars give the values of the residual peak cap effective strains for each specimen (Speci). B: in specimen II, the effect of RS/S on peak cap effective strain according to blood pressure. Note that the gray area limits the physiological pressure range.

 
Sensitivity of RS/S to the Material Properties of the Plaque Constituents

Additional computations on the five unstable VPs revealed that peak cap effective strain was not very sensitive to variations in the material properties of arterial wall components. Thus peak cap effective strain amplitude exhibited <3% variation as the stiffness of the fibrosis doubled from 500 to 1,000 kPa. On the contrary, increasing the stiffness of the core constituent from 5 kPa (lipid medium) to 500 kPa (fibrosis medium) significantly affected peak cap stress. Taking specimen I as an example, the amplitude of the residual peak stress in a given thin cap site decreased by 51%, from 218 kPa (Fig. 3C, specimen I) to 107 kPa (Fig. 8B, specimen I), when the lipid core was replaced by a fibrosis region. This drop in residual stress accordingly induced a significant increase in physiological peak cap stress amplitude, from 54 kPa (Fig. 6C, specimen I) to 81 kPa (Fig. 8C, specimen I), corresponding to a variation of 50%.


Figure 8
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  		Fig. 8. Potential impact of RS/S on lipid core shape, location, and size. A: plaque geometries, where asterisks indicate the location of the lipid core size in the real morphologies, meshes, and plaque constituents of virtual zero-stress configurations of stable plaques used to initiate finite element computation. Blue, cellular fibrosis; red, arterial wall. B: resulting spatial distribution of residual {sigma}VM. C: resulting spatial distribution of {sigma}VM obtained for a systolic blood pressure of 16 kPa (120 mmHg). Red arrows indicate the sites of zero stress/strain.

 
Computation of RS/S Within the Associated Idealized Non-VPs

To examine whether the heterogeneous spatial distribution of RS/S may provide landmarks of initiation sites of subsequent lipid core morphogenesis, simulations were performed in associated idealized plaques obtained by replacing the lipid medium by a cellular homogeneous fibrosis (Fig. 8A). Keeping plaque area and artery opening angle constant, computation revealed a large local intraplaque zone where RS/S was close to zero (Fig. 8B). Interestingly, this area appeared to correlate very well with lipid core size, shape, and location (compare Fig. 8B with Fig. 3C). Moreover, these zero RS/S zones subsisted and remained more or less unchanged over the cardiac cycle, i.e., when the artery was pressurized (Fig. 8C).


   DISCUSSION
TOP
 ABSTRACT
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
GRANTS
 REFERENCES
 
One important issue in the prediction of vulnerable coronary plaque rupture is to determine the mechanical strain/stress in the wall of the pathological artery and, more specifically, in the fibrous cap. Because of the relative complexity of quantifying stresses and strains in pathological arteries, the influence of RS/S, generated by remodeling and plaque growth processes, is usually ignored.

This study, based on a combined experimental and computational approach, sought to infer the modification of the estimated stress field when RS/S in the vulnerable coronary plaque was taken into account. RS/S was studied ex vivo in six human vulnerable coronary plaques, using the opening angle technique. The geometrical opening configurations were taken as the zero-stress states of the pathological arteries and were employed to initiate FE computations of RS/S throughout the arterial wall and plaque.

Relation Between RS/S in VP and Lipid Core Size

Lipid core size is a well-known morphological criterion of plaque vulnerability, but no biomechanical parameter hitherto seemed able to explain this fact. The present study, however, tends to show that the size of the lipid core correlates with residual local cap stress amplitude. Thus RS/S amplitudes in a VP were found to be nonnegligible, at the same order of magnitude as those induced under pressure loading (in the 20–40% range in the case of effective strain).

Influence of RS/S on the Risk of Plaque Rupture

Peak stress would not seem to shift significantly within the fibrous cap, remaining at the place where the cap is thinnest. It may, however, be overestimated by as much as a factor of four, as seen in our simulations, if RS/S is neglected; Cheng et al.'s (5) estimates of rupture thresholds are too high and need bringing down by an equivalent factor. In addition, our study sheds light on new high-stress areas, overlooked by previous studies that failed to take account of RS/S. Such areas tend to be located at the rear of the lipid core and may additionally trigger inflammatory processes, as detailed below. Interestingly, some of our specimens presented a few macrophages in this location. Similar observations were made by Sugiyama et al. (49) and Dollery et al. (12) in their studies on human coronaries and carotids, respectively.

Potential Impact of RS/S Distribution on Lipid Core Morphology

The potential impact of mechanical stress on VP development was emphasized by some studies reporting that inflammatory process appears to be well correlated with the parietal stress/strain distribution in atherosclerotic plaques. The proposed underlying scheme is an increased proteolytic macrophage activity associated with an increased matrix metalloproteinase level (1, 9, 11, 20, 34, 35, 51, 53). Nevertheless, we still do not understand the mechanisms that determine the location at which the lipid core is initiated within the plaque. In this context, the results obtained here on idealized non-VPs associated with the six pathological coronaries (Fig. 8) highlighted a potential correlation between the location of the intraplaque area showing zero RS/S and the morphology (size and location) of the lipid core. This suggests that RS/S could be one of the control factors involved in the growth process of the lipid core. A possible scenario would be that foam cells, rich in low density lipoprotein lipids, tend to accumulate in the intraplaque area with the lowest stress/strain, thereby locally promoting lipid core development.

Such a scenario appears still more relevant in the case of hemorrhagic plaque (55), where rapid accumulation of erythrocytes may occur preferentially in such low stress/strain areas.

VP Instability Viewed as the Result of a Subtle Balance Between Intraplaque Residual Stress and External Loading

In the pathological arteries studied here, the thin cap showed an attenuation mechanism similar to that found in normal arteries. Pressurizing the artery always tends to reduce internal stress/strain. Unlike in normal arteries, however, this attenuation was suboptimal, with intraplaque stress/strain remaining high even under physiological loading.

Thus a subtle balance exists between RS/S and the stress induced by blood pressure. Closing the artery compresses the lipid core, which reacts and generates high RS/S by pushing against the more compliant regions of the thin fibrous cap. In contrast, blood pressure tends to extend the luminal layers and to induce an opposing stress, decreasing stress amplitude within the thin cap and, concomitantly, the risk of rupture. Thus this study shows that plaque rupture must not be viewed as a consequence of external pressure alone but rather as the result of a subtle combination of external loading and intraplaque RS/S. Moreover, the intraplaque RS/S may also affect the morphogenesis of the microvascular network within the plaque and thus the plaque stability (30, 55).

Study Limitations

This study highlights original and potentially promising concepts for improving the evaluation of VP rupture; even so, several limitations are to be pointed out at this stage in our work:

  1. ) In vivo prediction of residual stress patterns in the wall of the pathological vessel is a crucial step that remains to be achieved to diagnose accurately the degree of stability of a VP. Elastography techniques (2) appear to be very promising tools that may, in the near future, enable in vivo determination of residual stress patterns in coronary plaques. Following the elegant approach proposed by Zamir and Taber (58), such quantification can be reasonably expected from the measurement of strain distribution in the pathological coronary wall using various techniques (magnetic resonance imaging, optical coherence tomography, or intravascular ultrasound) and of the deformed contours of all the plaque constituents at a known loading pressure.
  2. ) Our model is time independent and only considers fixed (i.e., postmortem) structural features, without taking into account dynamic processes such as the modulation of cell dynamics and enzymatic activity by mechanical processes (41).
  3. ) In all the FE simulations, static loading conditions were also applied. These conditions fail to reproduce the pulsatile nature of physiological blood pressure. Thus the effects resulting from the cyclic loading imposed by blood flow in the arteries (6, 18) were not taken into account, nor were the time-dependent viscoelastic and anisotropic nonlinear elastic components of the plaque's mechanical behavior (24, 47).

Conclusion

RS/S present in a vulnerable coronary plaque dramatically influences the spatial stress distribution and spotlights some new sites of stress concentration. RS/S could play a major role in the biomechanical stability of vulnerable coronary plaque and in the growth process of the lipid core. Additionally, this study showed that plaque rupture is to be viewed as a consequence not of external pressure alone but rather of a subtle combination of external loading and intraplaque RS/S.

Further studies are needed to extend the current work to the other phases of coronary atherosclerosis progression, but the spatiotemporal evolution of residual stress may be a new paradigm and prognostic factor to consider for plaque rupture assessment and, more generally, a key element for improving our understanding of how mechanical factors modulate and control the morphobiological evolution of atheromatous plaques and their stability.


   GRANTS
TOP
 ABSTRACT
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 GRANTS
REFERENCES
 
This research was supported in part by an appointment to the Senior Fellow Program at the NIH. This program is administered by the Oak Ridge Institute for Science and Education through an interagency agreement between NIH and the United States Department of Energy. J. Ohayon, P. Tracqui, and G. Finet were supported by grants from the European Community (Disheart Cooperative Research Project 2004–2006), Agence Nationale de la Recherche (ANR 2007–2009: ATHEBIOMECH; France), Cluster I3M 2007 et Emergence 2005 Rhône-Alpes Region (France), and TERUMO France.


   ACKNOWLEDGMENTS
 
J. Ohayon would like to express his sincere gratitude to Dr. Julie Heroux [National Heart, Lung, and Blood Institute (NHLBI)], Dr. Ahmed Gharib (NHLBI) and Dr. Richard Chadwick (NINDS) at the National Institutes of Health (NIH) for helpful discussions.

Present address for G. Finet: Service d'Hémodynamique et de Cardiologie Interventionnelle, Hôpital Cardiologique, BP Lyon-Monchat, 69394 Lyon cedex 03, France (e-mail: gerard.finet@creatis.univ-lyon1.fr).


   FOOTNOTES
 

Address for reprint requests and other correspondence: J. Ohayon, National Heart, Blood and Lung Institute, NIH, Bldg. 10, 10 Center Drive, Bethesda, MD 20892 (e-mail: ohayonj2{at}mail.nih.gov)

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.


   REFERENCES
TOP
 ABSTRACT
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 GRANTS
 REFERENCES
 

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