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Abstract
Bifurcation detection in coronary arteries is significant since it influences the treatment strategy selection and optimization. Bifurcations are also reliable landmarks for image registration. Intravascular optical coherence tomography (IVOCT) is a high-resolution imaging modality that is very useful in percutaneous coronary intervention stenting optimization. We present a bifurcation identification method utilizing pullback characteristics for IVOCT, which can effectively identify the bifurcations with a small size. The longitudinal view of the pullback will appear as an outward discontinuity in the bifurcation area. By detecting this discontinuity, bifurcation can be identified with high accuracy. We also use the normal vectors method to extract the ostium of bifurcation. We compare the proposed method with the widely-used distance transformation method by clinical 5302 IVOCT images from 22 pullbacks. The average metrics of true positive rate (TPR), true negative rate (TNR), positive predictive value (PPV), and negative predictive value (NPV) for the proposed method are 86.97%, 98.50%, 85.56%, and 98.67%, respectively. TPR, PPV, and NPV by the proposed method are improved by 40.24%, 9.31%, 3.90%, and TNR is on par compared with the distance transformation method. Especially in the small bifurcation identification, TPR of the proposed method is 64.71% higher than the distance transformation method with a bifurcation area ratio less than 0.2.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Nowadays, the coronary artery disease (CAD) is the main reason of morbidity and mortality in the world [1]. Percutaneous coronary intervention (PCI) with stenting can be used to treat CAD by opening coronary stenosis, which will increase the coronary blood flow [2]. However, stenting at the bifurcation may partially obstruct the blood flow to small bifurcations [3], which will cause poor outcomes. Such poor outcomes often include the bifurcation lesions, low patency rates, late restenosis, and acute thrombosis [4–6]. Compared with intravascular ultrasound (IVUS), intravascular optical coherence tomography (IVOCT) is a high-resolution imaging modality based on an intravascular catheter for viewing the cross-section of blood vessels. The analysis of IVOCT images can provides information for many application areas, including lesion characteristics assessment, fractional flow reserve analysis and PCI stenting optimization [7–12]. Vascular bifurcations in the cardiovascular are significant since they influence the strategy of pre- and post-stenting to a large extent. Vascular bifurcation are also reliable landmarks for image registration. Therefore, bifurcation identification in IVOCT images is meaningful.
Some automatic bifurcation identification methods have been reported so far. Wang et al. presented a distance transformation method to realize bifurcation identification [13]. In this method, the center of the main blood vessel is firstly extracted to establish a distance map with the distance from the main lumen center to the lumen contour as a reference, and bifurcations can be detected by morphological methods. However, the distance transformation method cannot identify small bifurcations where the distance to lumen center is lower than the given threshold. And the morphological operation for denoising can probably remove the region of small bifurcation. At the same time, this method is not accurate enough for the segmentation of bifurcation ostium in the cross-sectional image. Based on the distance transformation method [13], Cao et al. presented a normal vector method to detect bifurcation ostium. In this method, the normal vector of the blood vessel contour is extracted and the included angle between the normal vectors calculated. Then they performed differential operation to the included angles to determine the two ostium points between the main blood vessel contour and the bifurcation contour, which greatly improved the segmentation accuracy of the bifurcation [14]. Since the bifurcation identification in the normal vector method is based on the distance transformation method, this method still cannot handle small bifurcations.
In addition, many scholars utilized machine learning and deep learning methods to identify bifurcations. Macedo et al. presented a bifurcation detecting method based on supervised machine learning and selected features with orthogonal least squares [15]. Miyagawa et al. presented a bifurcation detecting method using convolutional neural networks (CNN) with transfer learning [16]. Porto et al. presented a bifurcation detecting method using support vector machine and artificial neural network models [17]. Huang et al. proposed a bifurcation detecting method based on multi-modal information, which is realized by a CNN framework combining the information from IVOCT and intravascular ultrasound (IVUS) images [12]. This multi-modal approach shows the best performance among all CNN methods. However, the acquisition of both IVOCT and IVUS images in the same coronary vessel of a patient is not clinically realistic and the performance of the network using only IVOCT images is largely reduced. All these CNN methods require a large amount of data with high quality for training and none of these methods utilizes open-source datasets, which reduce the reproducibility.
The distance transformation method provides an intuitive idea that the distance from the center of the main vessel to the bifurcation contour is always larger than the distance to the contour of the main vessel [13]. However, a suitable threshold of distinguishing the main vessel contour from the bifurcation contour is difficult to chosen when the bifurcation size is small. The reason is that the elliptical lumen shape will interfere the identification result if the given threshold is too small. Whereas, by using the pullback image sequence instead of just using a single cross-sectional image, we can find that the contour of the bifurcation suddenly expands outward in longitudinal sectional image along pullback, even if the size of the branch is small. If we detect the outward discontinuity of the contour through the pullback direction, we can identify genuine bifurcations and get rid of the interference from the elliptical lumen shape.
In this paper, we present a bifurcation identification method utilizing pullback characteristics for IVOCT. The proposed method can effectively identify the bifurcations with a small size. The lumen contour in the cross-sectional image just reaching the bifurcation will abruptly shift outward in the bifurcation part. Consequently, the longitudinal view of the pullback will appear an outward discontinuity in the bifurcation direction, as called the pullback characteristics. Utilizing the pullback characteristics, we process all cross-sectional images along the pullback direction respectively to detect bifurcations. The proposed method can utilize the information from adjacent images and is more sensitive to the small bifurcations. In addition, we use the included angle between the normal vectors and the vectors pointed to the main lumen center to extract the ostium points. By fitting a quadratic curve with mean coordinates values of adjacent contour points, we can calculate each normal vector with noise resistance, thereby improving the accuracy of ostium points extraction.
2. Methods
The proposed bifurcation detection method consists of four main steps: lumen segmentation, lumen center extraction, bifurcation image identification, and bifurcation ostium detection, as shown in Fig. 1.
2.1 Data acquisition
The IVOCT images dataset contains 6210 frames from 22 patients with 88 bifurcations, which is selected for processing and analysis from the IVOCT images database of Chinese PLA General Hospital (Beijing, China). This database was approved by the independent ethics committee of Chinese PLA General Hospital, Beijing, China (2017 ethical examine 035). The raw data is acquired by the IVOCT system (F1, Nanjing Forssmann Medical Technology Co., China) for post-processing and frame analysis. The axial spatial resolution of this IVOCT is less than 20 µm and the transverse spatial resolution is less than 100 µm. We manually excluded 908 frames with plastic tube capturing at the end of pullbacks or extremely bad quality, thus generated a total of 5302 frames for evaluation. Manual bifurcation identification and segmentation work is carried out by doctors with rich experiences in the lumen segmentation and bifurcation identification.
2.2 Lumen segmentation
We applied a lumen segmentation method that is presented in our previous work [18]. The method detects these A-lines shared by multiple connected regions and utilizes the uniqueness of vascular wall on A-lines to remove connected regions generated by blood artifacts. The method can effectively remove the artifacts and extract the lumen contour with high accuracy.
2.3 Main lumen center extraction
To precisely generate the longitudinal sectional image, we need to extract the lumen center in the main vessel. We constructed a distance map to compute the inscribed circle center of the lumen contour based on distance transformation methods [13,19]. The grayscale value of each pixel in the distance map is the smallest distance from the lumen contour to this pixel. The values of these pixels outside the lumen contour are set to zero. The pixel with the maximum grayscale value can be defined as the main lumen center, which is also the center of the maximum inscribed circle in the lumen area. This method can extract the lumen center effectively even if the lumen shape can significantly deviate from circular shape, as shown in the left subimage of Fig. 2(a). However, if the bifurcation size is too large, the main lumen center will be incorrectly extracted as shown in the right subimage of Fig. 2(a). Since the position of the center of the main lumen changes very little, we applied a median filtering to main lumen center sequences of the whole IVOCT pullback to make sure the extracted center belongs to the main vessel. Figure 2(b) shows the main lumen center extraction result after a median filtering.
Fig. 2. (a) Extracted main lumen centers on part of an IVOCT pullback and an incorrect main lumen center is extracted when lumen has a huge bifurcation. Ox and Oy are the coordinate values of main lumen centers. The yellow circle is the maximum inscribed circle in the lumen area. The red points are the centers of inscribed circle, which can be treated as the main lumen center. (b) The coordinates of main lumen centers and corrected main lumen center in the same image after a median filtering.
2.4 Bifurcation identification
When the IVOCT pullback reaches the bifurcation, the lumen contours on corresponding cross-sectional images will be enormously influenced by the bifurcation structure. The carina bifurcation angle is the most influential feature of bifurcation structure [20]. Palinggi et al. measured the carina bifurcation angle α in a lot of quantitative coronary angiography data and find α is all in the range of 10.57 to 95.06 degrees with the median value of 39.41 degrees, which means that α is usually less than 90 degrees [21]. Since α is often less than 90 degrees, the lumen contour in the cross-sectional image just reaching the bifurcation will abruptly shift outward in the branch part. If α is small, the abrupt part reverts smoothly. These two cases are shown in Fig. 3(a). Therefore, we can identify the beginning of a bifurcation by detecting the contour discontinuities along the pullback direction. We utilized the discontinuities on lumen contour caused by bifurcations between adjacent pullback frames and proposed a novel algorithm to identify bifurcation images.
Fig. 3. Main workflow of bifurcation identification. (a) Structure characteristics of coronary vessels. The yellow arrows are indications of the frames. The blue lines are the indications of lumen contours. (b) An IVOCT pullback sequence. θ is the included angle between the sliding longitudinal view and the horizontal plane, which are denoted by the frames and the purple arrows respectively. The red frame and the yellow frame show the section planes of images with bifurcation in the last frame. The green frame shows the sliding longitudinal view of an image without bifurcations in the last frame. The blue frame shows the sliding longitudinal view of an image without bifurcations in the last frame which occasionally captures the bifurcation. The intersectional lines of the section planes and frames are marked with corresponding colors. (c1) ∼ (c4) Sliding longitudinal view in (b). The blue and green curves are the upper and lower contour respectively. (d1) ∼ (d4) Corresponding difference curves of the upper and lower bounds in (c).
In order to show the discontinuity of the lumen contour caused by bifurcation starting, we generated an adjacent longitudinal view for each cross-sectional image to be identified. Here a cross-sectional image is called as a frame. We determined the number of frames used to generate a longitudinal view and the orientation of longitudinal sections first. To limit the range of bifurcation identification on the pullback and decrease the calculation burden, we selected the previous n frames including this frame to be identified to generate a longitudinal view which can display the outward discontinuity in Fig. 3(b). Ideally, the value of n should be greater than the ratio of the ostium distance of the bifurcation in the longitudinal direction to the distance between frames. The diameter of the bifurcation vessel cannot be larger than the diameter of the main vessel, so we took the diameter of the main vessel as the reference value of the diameter of the bifurcation vessel and calculate n. Because the longitudinal ostium distance will increase as the carina angle decreasing and the size of the carina angle cannot be predicted, we need to increase the value of n appropriately. If n is too small, the outward discontinuity on the bifurcation beginning will fall outside the longitudinal view that we cannot identify all consecutive bifurcation images with the same bifurcation. A suitably larger n is robust in the proposed method, but the calculation burden will be increased. In our method, we selected n = 15.
To generate a longitudinal section containing bifurcation, we need to choose longitudinal orientations θ between the sliding longitudinal view and the horizontal plane as shown in Fig. 3(b). We constructed a section plane by main lumen center and the contour point farthest from the main lumen center, as called the outermost point. The reason is that if a bifurcation exists, the outermost point must be the vertex of bifurcation contour in a frame. θ can be calculated as:
where Ox and Oy are the coordinate values of main lumen center and C0x and C0y are the coordinate values of the outermost point. And we have a relationship as:The determination of θ and n is used to generate a longitudinal section with the frame to be identified and its adjacent frames. An intersectional line with the section plane will be extracted on each frame. We arranged these frames along the pullback and generating a longitudinal view as shown in Fig. 3(c). It should be noted that a longitudinal view containing n frames can only identify whether the last frame contains bifurcation because θ is different in each frame. If a bifurcation exists in a frame, the lumen contour will abruptly shift outward in previous n frames. This feature will be displayed by the corresponding longitudinal view as an outward discontinuity in the longitudinal lumen contour, as shown in Figs. 3(c1) and (c3). We extracted the upper and lower longitudinal lumen contour respectively to locate the bifurcation part. After that, we applied a differential operation to these two contour curves and obtain the contour difference curves shown in Figs. 3(d1) and (d3). The abscissa of Fig. 3(d) is the distance to the starting position of IVOCT pullback. The difference of the distance from the lumen contour to the lumen center between two adjacent contour points ΔRi can be expressed as
where i is the frame number. Ri is the distance from the contour point to the main lumen center in the longitudinal view. The difference curve will generate an obvious positive peak ΔRmax in Figs. 3(d1) and (d3). If ΔRmax is larger than a given threshold ΔRth, this longitudinal view can be identified to contain bifurcation area and the position of ΔRmax is the bifurcation starting.If the last frame of the sliding longitudinal view is out of the range of the bifurcation, the outermost point in this frame will be unpredictably determined and θ will also be unpredictably selected. In general, the corresponding sliding longitudinal view will not display the bifurcation even if a bifurcation exists in its previous n frames as shown in the green frame of Figs. 3(b) and (c2). The difference curve is flat as shown in Fig. 3(d2), which represents the bifurcation ending. The sliding longitudinal view has a possibility to capture the bifurcation as shown in the blue frame of Figs. 3(b) and (c4) even through no bifurcation occurs in the last frame. Contrary to the outward discontinuity created at the lumen contour when the IVOCT pullback into the bifurcation, the lumen contour creates an inward discontinuity when the IVOCT pullback leaves the bifurcation area if the carina angle is large. The longitudinal view with blue frame in Fig. 2(c4) shows the inward discontinuity. We applied a differential operation to this inward discontinuity, and the peaks with negative values on the difference curve are shown in Fig. 2(d4). If the value of this negative peak on the difference curve is lower than -ΔRth, its position is the bifurcation ending. The frames after the bifurcation ending and before another bifurcation starting will be classified to no bifurcations.
2.5 Bifurcation ostium detection
The ostium points of a bifurcation can be located by the greatest curvature changing of the lumen contour based on the normal vector method [14,22]. We calculated the normal vectors and the vectors pointed to the lumen center, thus to convert the curvature into an included angle in global view. However, if we simply choose adjacent contour pixels to calculate normal vectors, the result will be interfered by the rough contour at the pixel scale shown in Fig. 4(a). The ostium points of a bifurcation will be inaccurately located. The reason is that the included angle between the normal vectors and the vectors pointed to the main lumen center will be interfered by the inaccurate normal vectors and the ostium points are determined by the differential curve of the included angle as shown in Fig. 4(c). To solve this problem, we calculated the mean coordinates of the adjacent five consecutive pixels on both sides of the pixel where the normal vector to be calculated. Then we constructed a quadratic curve based on the coordinates value of the pixel where the normal vector to be calculated and two mean coordinate values to calculate the normal vectors as shown in Fig. 4(b). Two bifurcation ostium points are detected by applying a differential operation on the included angle sets, as shown in Fig. 4(d).
Fig. 4. The comparison of normal vector extraction and ostium point detection between (a) the original normal vector method and (b) the method after our improvement. And the differential curve of the included angles between the normal vector and the vector pointed to the main lumen center with (c) the original normal vector method and (d) the method after our improvement. Blue points are the outermost points and green points are the extracted ostium points.
2.6 Evaluation metrics
To quantitatively evaluate the accuracy of identification result of the proposed method, we calculated several metrics for both the distance transformation method and the proposed method. These metrics are widely accepted [13–17], which includes true positive rate (TPR), true negative rate (TNR), positive predictive value (PPV) and negative predictive value (NPV) as below:
where TP, FP, TN, FN denote the sample number of true positive, false positive, true negative and false negative, respectively. It should be noted that TPR is also known as sensitivity or precision. TNR and PPV are also known as specificity and recall respectively. A positive image denotes an image which contains bifurcations, and vice versa. These metrics were calculated in average based on identification results for both distance transformation method and the proposed method with clinical 5302 IVOCT frames.2.7 Parameter selection
The threshold ΔRth is the most critical parameter in the proposed method. The threshold ΔRth must be lower than the minimum distance between the main lumen contour and the outermost point in the bifurcation orientation. According to the measuring of Karanasos et al [23]., the minimum diameter of main vessel along the pullback path is 1.80 ± 0.80 mm. We chose a lower bound of the minimum diameter that is the 1.00 mm as the reference. We adjust the ΔRth by varying the range from 0.1 mm to 1 mm with a step 0.1 mm, and the precision-recall (PR) curve is plotted in Fig. 5. The generalized F score Fβ is defined as [24]:
where Fβ is a measure of a model’s accuracy on a dataset. The metrics Fβ is a way of combining TPR and PPV which are mutually restrictive. The larger Fβ, the more accuracy the bifurcation identification model is. β is the weight factor and the TPR becomes more important as β approaches 0 and vice versa. In our work, we set β = 1 since we consider TPR and PPV to be equally important. With the proposed method, the maximum value of Fβ is obtained at the ΔRth = 0.3 mm where the TPR is 86.97% and PPV is 85.56%. Therefore, we selected ΔRth = 0.3 mm and all the results in this study are based on this threshold.Fig. 5. Precision-recall (PR) curve plotted by tuning the threshold ΔRth from 0.1 mm to 1 mm with step 0.1 mm.
3. Experimental results
We compared the proposed method with the distance transformation method [13] and the ground-truth manual segmentation to evaluate the proposed method qualitatively. To focus on the ability of bifurcation identification of these methods, the same automatic lumen segmentation method [18] was applied to data. The segmentation images with different size of bifurcations are shown in Fig. 6. Those images processed by the distance transformation method shown in Figs. 6(b1) to (b4) deviate from the results of manual segmentation shown in Figs. 6(a1) to (a4). One reason is that the distance transformation method set a given threshold on the distance between the main lumen center and the lumen contour. The contour points will be classified to the bifurcations if the distance to the center is larger than this given threshold. However, the bifurcation contour near the ostium points can be lower than this given threshold so that the distance transformation method cannot correctly identify the images with bifurcations as shown in Figs. 6(b1) and (b2). The images with small bifurcations cannot be identified correctly as well by the distance transformation method as shown in Figs. 6(b3) and (b4). The corresponding 2D region generated by the distance transformation method will be misclassified as noises and removed by the given thresholds of the minimum and maximum grayscale as well as the size of 2D regions. These given thresholds cannot be tuned smaller because elliptical lumen shape will interfere the bifurcation identification result.
Fig. 6. Bifurcation identification and segmentation results of IVOCT cross-section images with different size of bifurcations using manual segmentation in (a1) ∼ (a4), using the distance transformation method in (b1) ∼ (b4) and in the proposed method (c1) ∼ (c4). The green points denote the bifurcation ostium points. There are no ostium points in (b3) and (b4) because they are classified to non-bifurcation images by the distance transformation method.
The bifurcation identification and ostium points extraction results processed by the proposed method shown in Figs. 6(c1) to (c4) were very close to the results of the manual segmentation shown in Figs. 6(a1) to (a4). By utilizing the improved normal vectors method, we focused on the changing trend of normal vectors, thus could accurately extract two ostium points, as shown in Fig.s 6(c1) and (c2). By using the pullback sequence instead of just using a single frame, we detected the outward discontinuity of the contour through the pullback direction and identify genuine bifurcations and got rid of the interference from the elliptical lumen shape as shown in Figs. 6(c3) and (c4). As shown in Fig. 7, we can observe several black holes caused by bifurcations with different size on the lumen wall with their corresponding frames. It can be noticed that the identification and segmentation results of the proposed method are in strong agreement with these black holes.
Fig. 7. A cropped 3D vessel. Cross-sectional images corresponding to the black holes appearing in 3D vessel are shown around reconstructed vessel.
All 5302 frames are included for metrics calculation. The total number of frames which contains bifurcations is 490. TPR, TNR, PPV and NPV for the proposed method are 86.97%, 98.50%, 85.56% and 98.67%, respectively. Compared with the distance transformation method, TPR, PPV and NPV by the proposed method are improved by 40.24%, 9.31%, 3.90% and TNR is 0.01% behind. The detailed result is shown in Table 1.
Table 1. Comparison of bifurcation identification results using the proposed method with distance transformation method.a
To reveal the superiority of small bifurcation identification by the proposed method, we calculated TPR for distance transformation method and the proposed method with different range of bifurcation area ratio, as shown in Fig. 8. The bifurcation area ratio is bifurcation area dividing by main vascular area. Different bifurcation area ratios are split into five ranges, which are (0, 0.2], (0.2, 0.4], (0.4, 0.6], (0.6, 0.8] and (0.8, ∞). Compared with the distance transformation method, TPR of the proposed method in these ranges are improved by 64.71%, 30.32%, 11.90%, 25.00% and 10.71% respectively. The qualitative and quantitative results manifest that the proposed method can identify the bifurcations more accurately compared to the distance transformation method, especially in the IVOCT frames with small bifurcation identification namely the bifurcation area ratio of less than 0.2.
Fig. 8. True positive rate (TPR) of distance transformation method and the proposed method with different ranges of bifurcation area ratio.
4. Discussions
The proposed method also has its limitations. The proposed method may misidentify where bifurcations ending. If a sliding longitudinal view just captures the bifurcation occasionally, we can treat the frames as the bifurcation ending when the negative peak is higher than -ΔRth on the contour difference curve shown in Fig. 3(d4). However, a small bifurcation carina angle has no inward discontinuities in longitudinal view. Namely, the negative peak is less than -ΔRth on the contour difference curve. The proposed method will fail to detect bifurcation ends and will incorrectly identify the images without bifurcation when the longitudinal view occasionally captures the beginning of an end bifurcation with a small carina angle. In the future, we will develop a new algorithm to speculate the location where the main lumen contour should be at and correctly identify the image with no bifurcations by measuring the Hausdorff distance between actual value and speculated value.
The accuracy of lumen segmentation is also very essential in this work. The lumen segmentation algorithm should have the ability to distinguish the cavity caused by bifurcations with the shadow caused by guide-wire or blood artifacts in cross-sectional images. Our segmentation method may perform a false positive segmentation on the lumen which will reduce the TPR and PPV. The lumen segmentation method should also overcome the artifacts cling to the vascular wall. Otherwise, a fake outward discontinuity could appear in the longitudinal view, which will reduce the NPV and PPV. This limitation can be addressed by developing a more accurate lumen segmentation method.
We do not compare the proposed method with the popular CNN methods mentioned in the introduction part. The reason is that the dataset is different between all the methods and the quantity of our data may not reach the convergence of these CNN model. Therefore, the results of comparison are not objective enough to improve the confidence. The proposed algorithm is light-weighted and practically applicable, and the characteristics proposed in our algorithm may inspire future approaches, especially the input feature selections of neural networks.
If multiple bifurcations are too closed along the pullback direction, multiple bifurcations of different orientations appear in a frame. In this case, the bifurcations identification by the proposed method is still feasible. Although the sliding longitudinal views may be generated in either bifurcation direction, the proposed method can correctly identify frames with multiple bifurcations.
5. Conclusions
We presented a bifurcation identification method utilizing pullback characteristics for IVOCT, which can effectively identify the bifurcations with a small size. We first applied the lumen segmentation to IVOCT frames and found the lumen center by its inscribed circle. We generated the longitudinal view by finding the outermost point in each frame. The longitudinal view of the pullback will appear an outward discontinuity in the bifurcation area. By detecting the outward discontinuity caused by bifurcation starting, bifurcation can be identified with high accuracy. We also used the normal vectors method to extract the ostium of bifurcation. We compared the proposed method and the distance transformation method on the average TPR, TNR, PPV and NPV calculated with clinical 5302 IVOCT images from 22 pullbacks. The result shows that TPR, PPV and NPV are improved, and TNR is comparable. Especially in the small bifurcation identification, TPR of the proposed method is higher 64.71% than the distance transformation method with bifurcation area ratio less than 0.2. The proposed method can offer a more robust characteristic to identify small bifurcations, which is very useful for image registration in multimodal imaging and treatment strategy selection in PCI.
Funding
National Natural Science Foundation of China (61975147, 61735011, 61635008, 61505138); Key Technologies Research and Development Program (2019YFC0120701).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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