Optical Coherence Tomography-Based Modeling of Stent Deployment in Heavily Calcified Coronary Lesion

Abstract

In this work, a heavily calcified coronary artery model was reconstructed from optical coherence tomography (OCT) images to investigate the impact of calcification characteristics on stenting outcomes. The calcification was quantified at various cross sections in terms of angle, maximum thickness, and area. The stent deployment procedure, including the crimping, expansion, and recoil, was implemented. The influence of calcification characteristics on stent expansion, malapposition, and lesion mechanics was characterized. Results have shown that the minimal lumen area following stenting occurred at the cross section with the greatest calcification angle. The calcification angle constricted the stretchability of the lesion and thus resulted in a small lumen area. The maximum principal strain and von Mises stress distribution patterns in both the fibrotic tissue and artery were consistent with the calcification profiles. The radially projected region of the calcification tends to have less strain and stress. The peak strain and stress of the fibrotic tissue occurred near the interface with the calcification. It is also the region with a high risk of tissue dissection and strut malapposition. In addition, the superficial calcification with a large angle aggregated the malapposition at the middle of the calcification arc. These detailed mechanistic quantifications could be used to provide a fundamental understanding of the role of calcification in stent expansions, as well as to exploit their potential for enhanced pre- and post-stenting strategies.

Introduction

Severe calcification is a great concern when implementing a stenting intervention. Stenting outcomes are affected by heterogeneous material properties of the plaque, which is composed by the dense calcification, lipid pool, and fibrotic tissue. Variations in the mechanical behaviors and compositions raise challenges in surgical planning and outcomes assessment [1–3]. Specifically, heavily calcified plaque imposes a larger resistance force on the stent expansion [4], which is commonly associated with both stent underexpansion and malapposition. Pre- and/or post-stenting strategies such as atherectomy and post-dilatation have become necessary in dealing with severely calcified plaques [5,6].

Characteristics of calcification can be assessed with intravascular ultrasound (IVUS) and optical coherence tomography (OCT) images [7]. Compared with the IVUS, OCT images can better detect the thickness, as well as the sharp corner of the calcified region [8,9]. The coronary artery calcium score [10] has been widely used for risk prediction of coronary heart disease [11,12]. It has been reported that a severe calcification led to a higher rate of major adverse cardiac events in patients [13]. Based on the retrospective study of the IVUS and OCT images, Pregowski et al. showed that the lesion with a higher calcium score often required postballoon dilatation, and the balloon pressure depended on the cross-sectional area of calcification [5]. Another OCT image analysis showed that the stent expansion was related to the angle and the cross-sectional area of the calcification, rather than its thickness [6]. An in vitro study showed that a high volume percentage of the calcification diminished the stretch capability of the lesion [14]. For a severely calcified lesion, atherectomy was required to remove a portion of the calcification to facilitate the stent expansion [15]. The efficacy of this surgical technique need to be further investigated since the two year outcomes following the atherectomy is controversial [16]. Malapposition of the stent strut, which refers to as the incomplete contact of the stent strut with the vessel wall, has a direct impact on the thrombus formation and delays healing [17,18]. Alegría-Barrero et al. showed that the occurrence of the malapposition is related to the angle of the superficial calcification rather than the depth or thickness of the calcification [19]. It should be noted that the aforementioned calcification characteristics were generally measured from the cross section with the greatest calcification angle prior to stenting. The exact location of the minimal lumen area and malapposition in relation to the maximum calcification angle has never been identified. In addition, the reported statistical relationship from retrospective studies has not yet been tested in one single lesion.

Finite element modeling has been used as an effective approach to quantify the stent implantation in the calcified lesion. Karimi et al. reported that a stiffer plaque induced higher stresses in the stent [20]. Morlacchi further showed that the stent fracture associated with the calcification in lesion [21]. Pericevic et al. illustrated that the calcified plaque helped to keep a low stress level in the arterial tissue [22]. Zhao et al. further demonstrated that calcified plaque resulted in a small lumen size even though it mitigated the tissue prolapse [23]. Recently, patient-specific models of coronary arteries were developed based on CT angiography and OCT images for comparing stent designs and strategies [24,25]. Existing stylized and image-based models are not pertinent to the correlation between the calcification characteristics and stenting performances. In our previous work, we systematically studied stylized calcification models, and observed that stent expansion was the most sensitive to the calcification angle, and the circumferential stretch ratio of either the calcified or fibrotic tissue remains constant regardless of the calcification characteristics [4]. These observations require to be validated in patient-specific calcification models.

In this work, an OCT-based finite element model was constructed to quantify the stent implantation in a heavily calcified lesion. The characteristics of the calcification, such as the cross-sectional area, angle, and maximum thickness, were quantified at various cross sections. The relationship between these calcification characteristics and stent expansion were obtained. The influence of the calcification on the malapposition and the distributions of stress and strain were also investigated. This work could shed light on the stenting performance in the severely calcified lesion and guide the optimal stenting strategy.

Materials and Methods

Model Construction.

A calcified coronary plaque model was reconstructed based on 131 OCT images with a pixel size of 12.5 μm and spacing of 200 μm, as illustrated in Fig. 1(a). OCT images were acquired from a stent implantation experiment in a de-identified cadaver coronary artery (left anterior descending artery, 63-year-old male). The cadaver heart was acquired from Restore Life U.S. (Elizabethton, TN). CWRU's IRB determined that this activity was not human subject research and did not require approval. Calcified and fibrotic plaque in each image was first labeled using the commercial software amira (Thermo Fisher Scientific, Waltham, MA). The calcification was labeled as a gray value of 2, and the fibrotic plaque was labeled as a gray value of 1. The inner and outer contour lines of each OCT image were extracted using the commercial software mimics (Materialize NV, Leuven, Belgium). The 3D model of plaque, consisting of both calcified and fibrotic tissue, was generated by connecting all contour lines using commercial software hypermesh (Altair engineering, Troy, MI). The artery model was generated by offsetting the out surface of the plaque with a uniform thickness of 0.75 mm adopted from the literature [26], as shown in Fig. 1(b). The artery was adopted as a length of 26 mm. The calcified plaque had a length of 13 mm. A Z-axis along the axial direction and originating from the left end of the artery was used to identify the locations of cross sections of the lesion. The plaque located from the Z-coordinates of 6.6 mm to 19.6 mm. Three representative calcified cross sections were chosen as the Z-coordinate of 9 mm, 11 mm, and 17 mm, as depicted in Figs. 1(c)–1(e). A commercial express stent (Boston Scientific, Natick, MA) was applied to expand the stenotic artery as shown in Fig. 1(f). It has a nominal diameter of 3 mm, thickness of 0.13 mm, and length of 16 mm.

Fig. 1.

(a) Reconstruction of two-component plaque model; (b) cut view of three-dimensional artery model with its axial location labeled by Z-coordinate; representative cross section of the stenotic artery at Z-coordinate of (c) 9 mm, (d) 11 mm, and (e) 17 mm; and (f) express stent

Material Properties.

The stent was made of 316 L stainless steel, which was described as a perfect linear elastoplastic material with Young's modulus of 190 GPa, Poisson's ratio of 0.3, and yield strength of 207 MPa [26]. The mechanical behaviors of lesions were described using a hyperelastic constitutive model. The strain energy density function U was defined by a reduced third-order polynomial

$$U=\sum _{i,j=1}^3{C}_{ij}{(I_1-3)}^i{(I_2-3)}^j$$ (1)

$$I_1={\lambda }_1^2+{\lambda }_2^2+{\lambda }_3^2$$ (2)

$$I_2={1/\lambda }_1^2+{1/\lambda }_2^2+{1/\lambda }_3^2$$ (3)

where I ₁ and I ₂ are the first and second invariants of the Cauchy–Green deformation tensor, λ ₁, λ ₂, and λ ₃ are the principal stretches. The coefficients $C_{ij}$ are adopted from the literature [23,26], as summarized in Table 1. In addition, a perfect plastic behavior was prescribed for the fibrotic plaque with the yield stress of 0.07 MPa and the corresponding yield strain of 34% [27].

Table 1.

Material coefficients

	C 10 (MPa)	C 01 (MPa)	C 11 (MPa)	C 20 (MPa)	C 02 (MPa)	C 30 (MPa)	C 03 (MPa)
Artery	0.10881	−0.101	−0.1790674	0.0885618	0.062686
Fibrotic tissue	0.04				0.003		0.02976
Calcification	−0.49596	0.50661	1.19353	3.6378		4.73725

Finite Element Model.

Considering the maximum element size of 0.15 mm, the artery was meshed with 175,130 linear wedge elements (C3D6), and the plaque was meshed with 108,158 linear tetrahedral elements (C3D4). The calcification component was assigned as the average gray value larger than 1.5. The stent was meshed with 274,068 linear hexahedral elements (C3D8R) with the maximum element size of 0.02 mm. Specifically, there are six elements along the stent thickness, and three elements along the strut width. Symmetric constraints were enforced at both ends of the artery. The stent was first crimped from its nominal diameter of 3 mm to 1 mm to mimic its catheter delivery state, along with the plastic deformation of the stent [26]. At the stenotic location, the stent was radially expanded to a diameter of 3 mm to push the stenotic lesion outwards [28]. After unloading the displacement of the balloon, the stent recoiled to its final deployment shape. The stenting procedure is shown in Fig. 2. A frictionless contact was enforced between the stent and the lesion [22]. The model was solved using commercial software abaqus (Dassault Systèmes Simulia Corp., Providence, RI). The mechanics of stenting was governed by the dynamic equilibrium equation [29]

$$\nabla \mathbf{\sigma }+\rho \mathbf{b}=\rho \mathbf{a}$$ (4)

Fig. 2.

Stenting procedure (a) crimped stent at the diseased lesion, (b) fully expanded stent, and (c) stent recoil

where $\nabla$ is the Laplace operator, σ is the Cauchy stress tensor, ρ is the density, b is the body force, and a is the acceleration. The modeling framework was validated in our previous experiment [28].

Characterization of Calcification and Lumen Area.

Thirteen cross sections of the stenotic lesion, from the Z-coordinates of 7 mm to 19 mm with a spacing of 1 mm, were used to depict the calcification characteristics (i.e., the angle, maximum thickness, and cross-sectional area) and the corresponding lumen area. These quantities were measured using an open source image processing program ImageJ [30]. Specifically, the angle and the maximum thickness of the calcification were illustrated in Fig. 1(d). The calcification angle θ was formed by a vertex (i.e., the geometric center of the artery) and two radii of the artery tangent to both circumferential edges of the calcification. The thickness of the calcification δ was measured along the radial line. A linear correlation was performed to calculate the Pearson correlation coefficient r as the following:

$$r=\frac{\sum (x-\mu x)(y-\mu y)}{\sqrt{\sum {(x-\mu x)}^2\sqrt{\sum {(y-\mu y)}^2}}}$$ (5)

where μx and μy are the means of x and y variables [31]. There is a strong linear dependence between x and y if r is close to 1 or −1.

Results

Prior to stenting, the characteristics of the calcification in terms of angle, maximum thickness, and area at various cross sections are depicted in Fig. 3. The calcification angle varied from 68.4 deg to 235.3 deg. The maximum thickness of the calcification varied from 0.58 mm to 1.22 mm. The calcification area altered from 0.64 mm² to 2.86 mm². The calcification area was correlated with its angle and maximum thickness with Pearson correlation coefficients of 0.669 and 0.641, respectively. The correlation coefficient between the calcification angle and maximum thickness was less than 0.1, indicating a minimal correlation between these two variables. The original lumen area spanned from 0.945 mm² to 2.273 mm². Following the stent deployment, the lumen area increased to the range from 4.25 mm² to 4.72 mm² (Fig. 4). It is clear that stent implantation improved the uniformity of the lumen significantly. In addition, the stent-induced lumen gain was negatively associated with the calcification angle (r = −0.66, p = 0.013), calcification area (r = −0.60, p = 0.031), or percentage area of calcification (r = −0.72, p < 0.01), while the relationship between the stent expansion and the thickness (r = 0.017, p = 0.95) of the calcification is relatively weaker.

Fig. 3.

Characteristics of the calcification

Fig. 4.

Relationship between stent-induced lumen gain and (a) calcification angle and (b) calcification area

Following stenting, the distributions of maximum principal strain and von Mises stress in the artery are shown in Fig. 5(a). The corresponding distributions in the fibrotic tissue are shown in Fig. 5(b). A red dashed line is drawn to show the interfacial location of the calcification. It divides the lesion into an upper right portion and a lower left portion. Specifically, the lower left portion was underneath the calcification as illustrated in Fig. 5(c). Lighter levels of stress and strain were observed in the artery underneath the calcification (i.e., lower left portion of the artery) compared with the upper right portion. The same trend was also observed in the fibrotic tissue. The peak maximum principal strain and von Mises stress occurred near the boundary of calcification (i.e., the dashed line). The peak maximum principal strain and von Mises stress in the artery were 0.65 and 0.46 MPa, respectively. In the fibrotic tissue, they were 1.71 and 0.15 MPa, respectively. Much smaller strains (i.e., 0.084 to 0.25) and larger stresses (up to 3.69 MPa) were observed in the calcification itself. Moreover, the representative strain profile along the circumference of the lumen at the Z-coordinate of 9 mm is depicted in Fig. 6. This circumference line plot is the radial projection of calcification and fibrotic tissue. It started from one edge of the calcification tangent to the radius of the artery (∼point 1 in Fig. 6(a)) and followed the circumference clockwise. It is clear that the maximum principal strains projected from the calcification are less than 0.2, while those projected from the fibrotic tissue vary between 0.2 and 0.8, which is considerably higher than that of the calcification.

Fig. 5.

The distribution of von Mises stress (top) and maximum principal strain (bottom) in (a) artery and (b) fibrotic tissue; (c) the calcification location with relation to the artery

Fig. 6.

Circumference plot of the maximum principal strain at the z-coordinate of 9 mm (left) with its cross section profile (right)

The stent malapposition is characterized in Fig. 7. The malapposition was identified as the radial gap between strut and the lumen which was larger than 0.05 mm. The number of malapposed struts of the stent was observed ranging from 4 to 13 within the segment of the stenotic lesion (i.e., z-coordinates of 7 mm to 19 mm). The total number of struts of the express stent is 20 at each cross section. This means that the percentage of the malapposed struts varied from 20% to 65%. The same three cross sections in Fig. 1 (i.e., z-coordinates of 9 mm, 11 mm, and 17 mm) were used to illustrate the malapposition location denoted by *. It generally occurred close to the interface between the calcification and the fibrotic tissue, where the peak strain existed in the fibrotic tissue. In the cases of calcification with a large angle (Fig. 7(b)), the malapposition also occurred at the center of the calcification. Less malapposed struts were observed when a thicker fibrotic tissue was above the calcification, also referred to as deep calcification (Fig. 7(c)). It is interesting to see that a small calcification angle of 68.43 deg at the z-coordinate of 15 mm corresponds to the most malapposed struts (Fig. 7(e)). This could be explained by the abrupt changes in calcification angles in the neighboring cross sections (Fig. 3). Specifically, the calcification angle is 123 deg and 124 deg for z-coordinate of 14 mm and 16 mm, respectively.

Fig. 7.

Malapposition of stent struts. (a) Number of malapposition at each location, as well as three representative cross sections at the z-coordinate of (b) 9 mm, (c) 11 mm, and (d) 17 mm; (e) the cross section with most malapposed stent strut at the z-coordinate of 15 mm.

Discussion

In this work, the OCT-based stenotic artery was reconstructed to investigate the impact of calcification characteristics on stenting outcomes in terms of lumen gain, tissue mechanics, and malapposition. Following the stenting, the lumen gain was found to be negatively associated with the calcification angle. A large calcification angle reduced the stretchability of the lesion, leading to stent underexpansion. The stress and strain patterns in both the artery and fibrotic tissue were associated with the calcification profile. The calcification mitigated the stress and strain in the artery or fibrotic tissue radially projected from the calcification. The peak stress and strain in the fibrotic tissue occurred near the calcification interface. This implied a higher risk of strut malapposition and tissue dissection, as clinically reported near the calcification edges [32]. For a large calcification angle, malapposition was also observed at the projected location from the center of the superficial calcification due to the high rigidity.

The stent deployment improved the uniformity of the lumen size along the axial direction. We found that the lumen gain was negatively correlated with the calcification angle. This implied that the stent-induced minimal lumen area occurred near the cross section with the largest calcification angle, regardless of the original luminal pattern. This agrees with the retrospective study of OCT images by Kobayashi et al. [6]. Their observation was based on the peak calcification angles of many clinical cases. It is important to note that our observations are based on the heterogeneous cross section profiles of one single stenotic artery. The implication of our observation is that clinical strategies would be more effective by targeting the large calcification angle, rather than the minimal lumen size.

The sensitivity of the lumen area to the calcification angle could be further explained by the strain distributions of the lesion. The calcified tissue led to relatively lower strains due to the calcification rigidity, which inhibited the circumferential stretch capacity of the lesion. The larger the calcification angle, the more constraints on the lesion stretch along the circumferential direction, which resulted in a smaller lumen gain (i.e., stent underexpansion). This is consistent with our previous study using stylized models [4]. The in vitro experiment of the calcified carotid artery also demonstrated that calcification volume was negatively associated with the stretch capability of the lesion [14]. It was reported that the lumen gain was also related to the calcification area [6], which was measured at the cross section with the greatest calcification angle. In this work, we focused on using calcification characteristics from various cross sections of one single lesion. Generally, the cross section with the greatest calcification angle was not the one with the greatest calcification area. This is a different characterization approach compared to the clinical literature.

The strut malapposition of the stent had an adverse effect in the local fluid dynamics, especially the enlarged area of low wall shear stresses [33], which was associated with the intima hyperplasia [34]. We have observed that malapposition commonly occurred near the interface between the calcification and the fibrotic tissue. This was attributed to the material mismatch. Specifically, the stent implantation induced more stretch or strain in the fibrotic tissue, which resulted in a concave shape at the interface, and thus the malapposition (Fig. 7). For a large calcification angle, stent deployment usually did not conform to the shape of the rigid calcification. This led to malapposition happening in the middle of the calcification arc. This was clearly observed for the superficial calcification (i.e., minimal fibrotic tissue surrounding the lumen that was above the calcification). For a deep calcification, the relatively softer fibrotic tissue served as a cushion to mitigate the impact of the calcification on the malapposition. This agrees well with clinical observations that the malapposition was aggravated in the superficial calcification with a larger angle [19]. It is worth noting that the contact between the stent and the lesion at a cross section depends not only on the local cross-sectional profile of the calcification, but also on the neighboring cross sections. This has been illustrated at the cross section with the most malapposed struts (at the z-coordinate of 15 mm, Fig. 7(e)).

The influence of the calcification on the mechanics of the lesion was assessed using stress and strain distributions of the lesion. The stress and strain patterns in the lesion were consistent with the calcification profile, with the peak magnitude near the interface between the calcification and fibrotic tissue. The peak stress and strain location matched with the clinically observed tissue dissection region [32]. In addition, this implied a potential remodeling in response to abnormal stresses or strains [35]. The calcification mitigated the stress and strain in its projected lesion region. The projected fibrotic circumference has the capacity to sustain a large strain or stretch, which contributed to a larger lumen gain compared with the projected calcification portion. Our results were based on one single lesion with severe calcification. For cases with different calcification profiles, the magnitude of our results will differ, but the observed relationship is expected to be the same. Specifically, the length of the calcification has been found to have minimal impact on both the lumen gain and the malapposition [4].

In the present model, our focus is the stenting performance in the heavily calcified lesion instead of the well-studied thin-cap fibroatheroma. We have adopted a straight artery since the OCT datasets could not provide information related to artery curvature. The actual curvature could be obtained by coregistration with magnetic resonance imaging or angiogram [25]. A curved artery might aggregate the tissue stress [23,36,37] as well as the impact of the calcification. In addition, we have adopted a displacement boundary condition on the inner surface of the stent, rather than the balloon component, to save the computational cost. The modeling strategy without balloon could affect the transient behavior of stent expansion [38,39]. The heterogeneous plaque composition was also simplified as two major components (i.e., calcification and fibrotic tissue). A nonhomogeneous plaque with different material properties could lead to higher in situ stresses. The material properties of the plaque components are lacking in the literature, which are needed for a finer prediction of acute stenting outcomes. Moreover, the tissue dissection and rupture was not incorporated in this work, which is observed in some clinical cases with severe calcified lesion [40].

The aforementioned simplifications could alter the level of stent underexpansion and malapposition, as well as the peak stress/strain in the lesion. However, the stent underexpansion and malapposition in relation to the calcification angle are expected to remain, which was supported by the qualitative comparisons between our simulation results and OCT images. Both pre- and post-stenting strategies were not considered, which also facilitate a better stenting outcome. Despite these simplifications, this work demonstrates the importance of calcification on stenting outcomes, which may have significant clinical implications toward optimal stenting. Our findings from one single case need to be interpreted as hypothesis-generating study, which requires further validations by additional cases including clinical datasets.

Conclusion

The stenting performance in a heavily calcified coronary artery was investigated to delineate the influence of calcification characteristics on stent expansion, malapposition, and lesion mechanics. The calcification, fibrotic tissue, and lumen surface were reconstructed from the OCT images. The calcification was characterized by the angle, thickness and area at various cross sections along the axial direction. We found that the stent-induced lumen gain is sensitive to the calcification angle and area, and the calcification weakens the stretch capability of the lesion. Even though the calcification diminishes the lumen gain, it protects the neighboring tissue from abnormal strain and stress. Specifically, the radially projected region of the calcification tends to have less strain and stress. The peak strain and stress of the fibrotic tissue occurred near its interface with the calcification, which is also the region having a high risk of tissue dissection and strut malapposition. In addition, the contact between the stent and the lesion at a cross section depends not only on the local calcification profile, but also on the neighboring cross sections. Our mechanistic understanding of the role of calcification on the stent performances could be used to generate new hypothesis for optimizing the stent procedures.

Funding Data

• National Heart, Lung, and Blood Institute (Grant No. R01 HL143484-01; Funder ID: 10.13039/100000002).