Co-registration of pre- and post-stent intravascular OCT images for validation of finite element model simulation of stent expansion

Abstract

Intravascular optical coherence tomography (IVOCT) provides high-resolution images of coronary calcifications and detailed measurements of acute stent deployment following stent implantation. Since pre- and post-stent IVOCT image “pull-back” acquisitions start from different locations, registration of corresponding pullbacks is needed for assessing treatment outcomes. In particular, we are interested in assessing finite element model (FEM) prediction of lumen gain following stenting, requiring registration. We used deep learning to segment calcifications in corresponding pre- and post-stent IVOCT pullbacks. We created 1D representations of calcium thickness as a function of the angle of the helical IVOCT scans. Registration of two scans was done by maximizing the cross correlation of these two 1D representations. Registration was accurate, as determined by visual comparisons of 2D image frames. We used our pre-stent calcification segmentations to create a lesion-specific FEM, which took into account balloon size, balloon pressure, and stent measurements. We then compared simulated lumen gain from FEM analysis to actual stent deployment results. Actual lumen gain across ~200 registered pre and post-stent images was 1.52 ± 0.51, while FEM prediction was 1.43 ± 0.41. Comparison between actual and FEM results showed no significant difference (p < 0.001), suggesting accurate prediction of FEM modeling. Registered image data showed good visual agreement regarding lumen gain and stent strut malapposition. Hence, we have developed a platform for evaluation of FEM prediction of lumen gain. This platform can be used to guide development of FEM prediction software, which could ultimately help physicians with stent treatment planning of calcified lesions.

1. INTRODUCTION

Major calcifications are of great concern when performing percutaneous coronary intervention (PCI) because they can hinder stent deployment. Approximately 700,000 PCIs are performed each year to open up obstructed coronary arteries.¹ Calcified plaques are found in 17% to 35% of patients undergoing PCI.^2–4 Calcifications can lead to stent underexpansion and strut malapposition, which in turn can lead to increased risk of thrombosis and in-stent restenosis.^5–10

Intravascular optical coherence tomography (IVOCT) has significant advantages for characterizing coronary calcification compared to other imaging modalities commonly used by interventional cardiologists. Although clinicians routinely use x-ray angiography to describe the vessel lumen for treatment planning, angiography does not provide specific information regarding vascular wall composition except in the case of severely calcified lesions.¹¹ Intravascular ultrasound (IVUS) can identify the location of a coronary calcification but cannot assess the thickness because the radiofrequency signal is reflected from the calcium tissue interface giving an acoustic shadow.¹² IVOCT, however, provides the location and often the thickness of a calcification.¹³ Our group has proposed multiple plaque characterization approaches on IVOCT images, including machine^14,15 and deep learning^16–20 methods as well as image registration.²¹

In this paper, we develop a co-registration method to register intravascular optical coherence tomography (IVOCT) images obtained before and after stenting. This is done to aid analysis of stent deployment, especially with regards to finite element modeling. Registration before and after stenting images will facilitate the computation of lumen gain, a metric of stent quality. We will use finite element model (FEM) to predict the lumen gain after applying post-stenting pressures. FEM results are compared to measured stent deployments in some elegant ex vivo experiments. The influence of the calcium on the stenting outcome was evaluated in terms of lumen gain. This work could provide insights for pre-clinical planning for complicated lesions.

2. METHODS

Image processing and learning techniques are applied to perform semantic segmentation of pixels in IVOCT images as calcified plaque, lumen, or other. The deep learning model trained on the in vivo data is used to classify the images from the ex vivo experiment before and after stenting. Calcification attributes are computed from the classified images. We create 1D representations of calcium thickness as a function of the angle of the IVOCT scan. The classified images are used to build the finite element model.

2.1. Calcification segmentation and measurements

We applied a deep learning segmentation model trained on pre-stent data set to segment both pre- and post-stent images in the (r, θ) representation. Figure 1 shows the (r, θ) representation in (A), the corresponding manually annotated label in (B), and the segmentation results in (C). We concatenated labels across the whole pull back (540 labels) to form one large 2-D array as in figure 2. Then we computed the calcification thickness for each A-line, indicated by the orange arrow, in both pre- and post-stent.

Figure 1.

Automated segmentation results. Images are: (A) is the IVOCT image, (B) is the ground truth annotation, and (C) is the corresponding automatic segmentation result. The white region is the calcifications. This example shows good agreement between manual and automated assessments. Lumen is shown in gray and calcification in white.

Figure 2.

Calcification thickness quantification. (A) The original spiral data set is rather arbitrarily split into (r, θ) label frames. The orange arrow represents a single A-line. The thin orange line crossing the calcification (white) represents one A-line. (B) We concatenated labels to form one large 2-D array.

2.2. Co-registration framework

We created 1D representations of calcium thickness as a function of the angle of the helical IVOCT scan. Figure 3 shows calcification thicknesses as a function of A-line position (angle) for pre-stent (A) and post-stent (B). The horizontal axis is the A-line position (angle) across the concatenated data along the entire pull back. The vertical axis represents the calcification thickness associated with its A-line. We normalize these graphs so that their maximum value is one. The pre-stent image is the fixed image. We compute the cross-correlation between the pairs of 1D graphs. The location of the maximum values of the cross-correlation indicates the time lead or lag. We align the graphs and the corresponding IVOCT scans.

Figure 3.

Calcification thicknesses as a function of A-line position (angle) for (A) pre-stent. (B) post stent pullback. When a calcification is extremely thick and its back border was not clear due to attenuation, the maximum thickness was limited to 1 mm.

2.3. Finite element model construction

We constructed lesion-specific finite element models from IVOCT images. To create a finite element mesh, there were several steps. They are as follows: (1) Process images using the semantic segmentation deep learning as above. (2) Manually correct labels if necessary. (3) Reconstruct the surface from segmentation results by computing a triangular approximation of the interfaces between different materials. (4) Smooth the generated surfaces to eliminate any staircase-like surfaces. (5) Generate the FEM mesh where the volume enclosed by the generated surface is filled with tetrahedron, using Amira software 6.5 (Thermo Fisher Scientific, Waltham, MA, USA).

Other details of finite element modeling follow. The stent was made of 316 L stainless steel, which was described as a perfect linear elastoplastic material with a Young’s modulus of 190 GPa, Poisson’s ratio of 0.3, and yield strength of 207 MPa. 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

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

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

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

where I₁ and I₂ are the first and second invariants of the Cauchy–Green deformation tensor, λ₁, λ₂, and λ₃ are the principal stretches. The coefficients C_ij are adopted from the literature.^{21, 22} In addition, perfect plastic behavior was prescribed for fibrotic plaque with a yield stress of 0.07 MPa and a corresponding yield strain of 34%.²⁴

Symmetric constraints were enforced at both ends of the artery. The stent was first crimped from its nominal diameter of 3.00 mm to mimic its catheter delivery state and plastic deformation.²³ At the stenotic location, the stent was radially expanded to a diameter of 3mm to push the stenotic lesion outwards.²⁵ After unloading the displacement of the balloon, the stent recoiled to its final deployment shape. A frictionless contact was enforced between the stent and the lesion.²⁶ 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

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

where ∇ is the Laplace operator, σ is the Cauchy stress tensor, ρ is the density, b is the body force, and a is the acceleration.²⁷

3. EXPERIMENTAL METHODS

3.1. Ex-vivo experimental data

All ex-vivo cadaveric hearts were first CT scanned to choose a good candidate that has large deposits of calcium. PCI was then performed using an 8-Fr guiding catheter. We deployed a 3.0 mm diameter stent (Xience Sierra [3.0 mm diameter, 18 mm long], Abbott Vascular, Santa Clara, CA) using a non-compliant balloon dilated to its nominal pressure. This was followed by post-dilations at 3.5, 4.0 and 4.5 mm, each at the following balloon pressures: 10, 20, and 30 atm, for a total of 11 pullbacks (1 pre-stenting pullback; 1 post stenting pullback; and 9 post-stenting pullbacks). Maximal balloon pressure and maximal balloon size were recorded. IVOCT was performed after stent implantation. A 2.7-Fr IVOCT catheter (Dragonfly or Dragonfly JP; Abbott Vascular, Santa Clara, CA) was advanced proximal to the lesion, and automated pullback was performed with contrast injection through the guiding catheter. IVOCT images were recorded and analyzed using the IVOCT console. All IVOCT images were manually labeled by two skilled cardiologists from the Cardiovascular Imaging Core Laboratory, Harrington Heart and Vascular Institute, University Hospitals Cleveland Medical Center, Cleveland, OH, USA.

3.2. Finite element model experiment

A calcified coronary plaque model was reconstructed based on 280 OCT images with a pixel size of 9.76 μm and spacing of 200 μm, as illustrated in Fig. 1(a). OCT images were acquired from a stent implantation experiment in a cadaveric coronary artery (left anterior descending artery, 63-year-old male). The cadaveric heart was acquired from Restore Life U.S. (Elizabethton, TN). The institutional review board of University Hospital 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 automated method. Then the results were minimally edited manually using the commercial software AMIRA (Thermo Fisher Scientific, Waltham, MA, USA).

4. RESULTS

The qualitative results show the ability of the deep learning model to classify calcifications in IVOCT images while producing a smooth segmentation of the overall image. All predicted images for all training sets were compared with their corresponding manual segmentation. In Figure 1, segmentation of the lumen and the calcification are shown. Both lumen and calcification regions show good agreement with the ground truth labels. Figure 5 shows that calcification thickness graphs are much better aligned following registration (B) as compared to before registration (A). Blue is the pre-stent pullback while the orange is the post stent. The dark blue region is where the two pullbacks align.

Figure 5.

Calcification thicknesses as a function of frame number. (A) representing the calcification thickness for the pre-stent. (B) is for the post stent and (C) after registration. Blue is the present pullback while the orange is the post stent.

Figure 6 shows the anatomical representation of IVOCT images before (A and C) and after (B and D) stenting. A and C are the same pre-stent image frame. The unregistered post-stent image frame B has the same frame number as A. We can see that the image frame in D matched the one in C after the registration.

Figure 6.

Automatic registration of IVOCT images. A and C are the same pre stent image. C is the unregistered post-stent image frame with the same frame number as A (images A and B has frame number of 243 in the pre- and post-stent respectively). D is the registered image frame corresponding to C.

Additionally, in a sequence of registered images, we compared the frames before and after the corresponding image (Figure 7). We found that each frame matched its corresponding image better than the frame before and the frame after. This suggests that the accuracy of our registration is within 1 frame interval (±200 μm).

Figure 7.

Qualitative analysis of registered pre- and post-stent IVOCT image datasets suggests z-registration accuracy is within 1 IVOCT frame interval (±200 μm). We visually compared registered pre- and post-stent IVOCT image pairs, as well as images located immediately before and after within the registered datasets.

The performance of the finite element model was measured by comparing the lumen area from the IVOCT experiment and the predicted lumen area from the FEM. Table 1 shows FEM predictions of the lumen gain as compared to actual lumen gain from IVOCT measurements. The FEM results agree well with the measurement from the IVOCT images.

Table 1.

Average lumen gain across the registered stenting area.

	Lumen gain (mean ± SD)
Actual measurement	1.52 ± 0.51
FEM prediction	1.43 ± 0.41

The upper panel in Figure 8 shows the registered pre-stent IVOCT image with post-stent images at different pressure steps. The lower panel shows the corresponding FEM predictions at the same pressure steps as the upper panel.

Figure 8.

The registered IVOCT images and the corresponding prediction from the FEM. The first IVOCT image in the upper panel is the pre-stent image. A2 and A3 are the post stent images at nominal and 20 atm respectively. B1 is the FE model based on the pre-stent labeled images. B2 and B3 are the simulation results that matched the procedure conditions as in A2 and A3.

We can also analyze the predictions over an entire stenting area. In Figure 9, we show two lines comparing actual measurements (dark blue) with the FEM prediction (orange) for registered pre and post-stent. In the bottom line (yellow), we show the pre-stent lumen area across all frames. Here we see our FEM model almost exactly matches the experimental data.

Figure 9.

Comparison between prediction results from the FEM after stenting with the one from the actual data.

FEM simulation of stent deployment is in Figure 10. A and B columns show stent deployment and IVOCT images at a pressure of 11-atm. Predicted lumen shape is consistent, with non-circular irregularities present at the same locations in FEM and IVOCT. Malapposed struts (red arrows) not flush with the artery wall are visible in this frame. Calcifications hinder deployment as (proximal, min, distal) IVOCT areas are (4.2, 3.11, 3.8) mm², less than the manufacturer’s predicted 7.0 mm² at 11-atm.

Figure 10.

IVOCT images and corresponding cuts of the 3D FEM show excellent correspondence of stent struts malapposition (red arrow). A and B are the registered pre and post stent image frames. C and D are the corresponding FEM prediction of stent deployment at 11 atm.

5. DISCUSSION

Deep learning calcification segmentation was an important step. We were able to quantify calcification attributes based on the automated segmentations (Figure 1). For the lumen area, the automated measurements were excellent (good precision and bias) compared to manual assessments. Segmentation errors are mostly related to calcification deposits that have small arc angles (<40°), which have less impact on clinical decision-making. Our algorithm tends to agree with manual determination of the calcification front border but has less agreement with the back border. This is due to the IVOCT signal having limited depth penetration, making determination of the calcification back border difficult even for manual assessments. This is especially the case after stenting, when calcifications will be hidden behind the stent strut shadow.

For pre and post stent registration, we created a specialized image registration method. Our solution consisted of creating 1D representations of calcium thickness as a function of the angle of the helical IVOCT scan. Qualitative analysis of registered pre- and post-stent IVOCT image datasets suggests z-registration accuracy is within 1 IVOCT frame interval (±200 μm). We visually compared registered pre- and post-stent IVOCT image pairs, as well as images located immediately before and after within the registered datasets. Qualitative features suggested that registration accuracy was within 1 frame interval. In Figure 7, this is especially apparent when considering the side branch located within the registered pair. In the bottom pre-stent image, located one frame away from the registered pair, we see that the side branch has not yet appeared, as it has in the registered pair. Moreover, in the top pre-stent, located one frame away from the registered pair, we see that the side branch is more pronounced than in the registered pair. Clearly, the best match occurs within the registered pair, suggesting that registration accuracy is within the IVOCT frame interval of one frame apart.

We quantify the accuracy of our model by computing the lumen gain and comparing it with the simulation results from the finite element model. Lumen gain, a metric of stent quality, is the ratio between the lumen area before and after stenting. In our data, comparison between actual and FEM results showed no significant difference (p < 0.001), suggesting accurate prediction of FEM modeling. In the present finite element model, 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 co-registration with the angiogram.²⁸

Our method is easy to implement and able to perform registration while requiring far less computation time to register volume pairs. The proposed framework is generic and can be used to register images from other modalities (i.e. IVUS). oving forward, we believe this platform can be used to guide development of FEM prediction software, which could ultimately help physicians with stent treatment planning for lesions containing calcifications.

Figure 4.

The finite element model with stent at the diseased lesion. The model was generated from the labeled pre-stent IVOCT volume. The artery wall (green) was generated by offsetting the out surface of the plaque with a uniform thickness of 0.75mm.