Deep learning-based key point detection algorithm assisting vessel centerline extraction

Introduction

Ischemic stroke is the second leading cause of death worldwide (1). Atherosclerotic plaque is a major risk factor for ischemic stroke. Previously, the degree of stenosis caused by plaque was used to predict the risk of stroke; however, recent studies suggest that vulnerable plaque identification may provide a more effective method (2-4). Magnetic resonance vessel wall imaging (MR-VWI) is important in identifying vulnerable plaque that conventional luminal imaging tends to underestimate (5). The automated quantitative analysis of plaque morphology (6,7) and plaque enhancement (8-10) using MR-VWI has been shown to be effective in assessing plaque (11).

The rapid and accurate extraction of vessel centerlines assists in the assessment of vulnerable plaque, thereby enabling effective ischemic stroke prediction. Centerline extraction assists in the quantification of plaque morphology (12,13), and methods such as Hough transform-based algorithms (14), the improved Dijkstra’s algorithm (12), and deep learning-based algorithms (15,16) have been employed. However, these algorithms struggle with vessels that have significant curvature, tiny diameters, or bifurcations, such as the carotid siphon (16,17). Given the significant burden of ischemic stroke and the rapid increase in the number of ischemic stroke patients, there is an urgent clinical need for rapid and accurate vessel centerline extraction to aid in the preliminary screening and diagnosis of this condition.

Key point detection addresses these challenges by focusing on anatomical landmarks crucial for accurate centerline extraction. Key points are anatomical landmarks selected based on clinical needs and experience. These landmarks are often found in vessels prone to errors during vessel centerline extraction, such as tiny vessels, vessel bifurcations, and tortuous vessels. Current methods include semi-automatic (16-18) and fully automatic methods. Several fully automated methods have been proposed, such as using U-Net to identify ostium points for assisting artery extraction (19), applying deep learning algorithms for artery bifurcation detection (20), and employing automated algorithms for landmark detection on the distal femur bone (21). Despite these innovations, challenges remain, especially in vessel bifurcation and in specific anatomical contexts like the carotid artery.

To enable rapid and accurate vessel centerline extraction, this study proposed and validated an optimized deep learning-based key point detection algorithm. Given the rising incidence of ischemic stroke, this innovation aimed to improve the accuracy and efficiency of vessel analysis and facilitate the automated assessment of stroke-related risks. We present this article in accordance with the TRIPOD+AI reporting checklist (available at https://qims.amegroups.com/article/view/10.21037/qims-24-1949/rc).

Methods

Study population

The study was conducted in accordance with the Declaration of Helsinki (as revised in 2013). The study was approved by the Institutional Ethics Board of the Shenzhen Institutes of Advanced Technology (No. SIAT-IRB-180315-H0228), and the requirement of individual consent for this retrospective analysis was waived. All participating hospitals were informed and agreed the study. From May 2017 to January 2022, 539 patients with cerebrovascular disease were randomly selected from multiple centers.

MR-VWI scans were obtained using a head-and-neck joint scan. Image quality was classified into the following four grades: grade 1: unclear boundaries of the vessel lumen and outer wall, with severe artifacts, making interpretation impossible; grade 2: some clear boundaries, with slight artifacts, but interpretation remains impossible; grade 3: clear boundaries, with slight artifacts, allowing for interpretation and analysis; and grade 4: clear boundaries, with no artifacts, allowing for interpretation and analysis. To be eligible for inclusion in the study, the subjects had to have undergone T1-weighted plain scans. Subjects with an image quality below grade 3 were excluded from the study.

Image acquisition

The images were acquired using a Tl-weighted three-dimensional (3D) variable flip angle fast spin-echo sequence on multiple devices, including devices from United Imaging Healthcare Co., Ltd. (Shanghai, China), Philips Healthcare (Best, the Netherlands), and Siemens Healthineers (Erlangen, Germany). For further details, see Table 1.

Image preprocessing

As Figure 1A shows, 32 points from the common carotid artery to the intracranial arterial terminus, including points at vessel bifurcation and carotid siphon, were manually annotated by four experienced radiologists with 5–10 years of experience, using Plaque Analysis (uOmnispace, MR Plaque Analysis, United Imaging Healthcare). The radiologists checked and verified each other’s annotations, and if any differences in opinion arose, reached an agreement via negotiation. The analysis for each subject took half an hour. Cropping, rotations, scaling, and random mirroring were employed to avoid model overfitting, and improve the adaptive capacity of the neural networks. Cropping involved extracting the upper or lower part of the image, and the central part along the Y-axis to generate an additional batch of incomplete scan images. Together, the original and cropped images formed the augmented dataset, which tripled the amount of study data. In addition to rotations and scaling, the images were also randomly mirrored. The same process was applied to ground truth to ensure its accuracy. By doing this, the total training set increased to 1,296. Image intensity value normalization was employed to reduce the morphometric errors and speed up the training. Since maximum-minimum normalization is susceptible to limit values, zero-mean normalization with truncation was applied to eliminate the influence of outliers on the input data. The intensity value I(x) at each voxel was normalized by subtracting the mean µ, and dividing it by the standard deviation σ; that is, I′(x)=I(x)−μσ. The upper truncation bound was a random number between 0.95 and 0.999, and the lower truncation bound was 0.01.

Figure 1 Key points and sampling range. (A) The 32 points selected for the experiment. (B) Sampling range. BA, basilar artery; LACA, left anterior cerebral artery; LCCA, left common carotid artery; LECA, left external carotid artery; LICA, left internal carotid artery; LMCA, left middle cerebral artery; LPCA, left posterior cerebral artery; LVA, left vertebral artery; RACA, right anterior cerebral artery; RCCA, right common carotid artery; RECA, right external carotid artery; RICA, right internal carotid artery; RMCA, right middle cerebral artery; RPCA, right posterior cerebral artery; RVA, right vertebral artery.

Sampling

To control the graphics memory and ensure data diversity in the engineering process, random sampling with a sliding window was applied. The entire image was covered to avoid information loss. Sampling points were randomly selected within a specific range, and an image block of 144×160×128 voxels centered on the sampling points was cropped. The sampling range was chosen as a rectangular block of 3/8–5/8 in the X-axis, 1/4–3/4 in the Y-axis, and 1/9–8/9 in the Z-axis direction (see Figure 1B) to prevent any loss of valid information due to the sampling points appearing at the edges of the image.

Detection framework

The images of 432, 55, and 52 subjects were used for the training, testing and evaluation, respectively. The main workflow of the network is illustrated in Figure 2. The preprocessed image served as input, and the network was supervised by 32 Gaussian heatmaps (the grey value was 255 in the center, and close to 0 at the edges). The point with the highest confidence in the k-th Gaussian heatmap represents the k-th key point. The actual Gaussian heatmaps were generated by placing a 3D Gaussian kernel at the center of each ground truth key point. For the Gaussian kernel, the parameters are set to σ =2, and cut =3 for the cut-off threshold. Thus, the radius of the Gaussian kernel was 3σ=6. The outputs also comprised Gaussian heatmaps for each channel, and peaks were identified in the outputs to obtain the coordinates of the predicted points. Each output heatmap possessed a single maximum, as each Gaussian map contained only one key point, and according to the properties of the Gaussian function, it had only one maximum value. Commonly used deep-learning networks for key point detection in medical images with Gaussian heatmaps include the U-Net and convolutional neural network (22). However, the 3D V-Net network was chosen for this experiment, as it can directly use volume convolution, thus preserving and using the information contained in the whole volume very well.

Figure 2 Flowchart of the experiment.

The main structure of the network is shown in Figure 3. The network comprised a compression path and a decompression path. The two paths were connected by a skip connection to address the gradient vanishing issue. Residual units were used to improve the propagation of information between deeper and shallower layers to minimize information loss. Each stage comprised 1–3 convolutional layers, and a size of 5×5 and stride of 1 filter were applied to all the convolutional layers to extract features. A 2×2×2 convolutional kernel with a stride of 2 was employed for both the downsampling and upsampling. A 1×1×1 kernel size was used beyond the last stage to produce outputs of the same size as the input images. The rectified linear unit function was used as the activation function to enhance the network’s efficiency and learning capacity by addressing the vanishing gradient problem and introducing sparse activations to help the network adapt better to complex patterns in the data. The 145 epochs were run at a learning rate of 10⁻³ and had a batch size of 32. The experiments were conducted on a system with the following hardware configuration: central processing unit (CPU): Intel ® Xeon ® Silver 4110 CPU @ 2.10 GHz, memory: 128 GB; and graphic processing unit (GPU): 24 GB NVIDIA TITAN RTX. The deep-learning framework PyTorch (version 1.10.1+cu111) was used, and computations were accelerated using CUDA (version 12.0) for the GPU processing.

Figure 3 Diagram of the V-Net network structure.

Loss function

A loss function was employed to evaluate the deviation between the outputs and the ground truth, and to guide the optimization of the model. The following two loss functions were tested: the mean squared error (MSE) and the MSE². Foreground weighting was introduced as a weighting factor in the loss function to amplify the loss and increase the penalty, which was defined as the number of background voxels divided by the number of foreground voxels; that is, weight=backpixelforepixel. The MSE, which was also called the L2 loss function, assumed that the error followed a Gaussian distribution, and was defined as:

MSE=1N∑k=1N(yk−y^k)2[1]

where yk and y^k denote the Gaussian heatmaps of the ground truth and prediction, respectively. Due to its simplicity and effectiveness, the MSE is commonly used in various regression tasks. However, we found that training failed to converge with the MSE. Switching to the MSE² resolved this issue, improving both convergence and speed. The primary reasons for using the MSE² were: (I) increased gradient magnitude: the MSE² produces larger gradients, which leads to more substantial parameter updates during backpropagation, which accelerates convergence, especially when dealing with small errors where MSE gradients might be too weak; (II) enhanced stability: the MSE² places more emphasis on minimizing larger errors, stabilizing the training process by ensuring significant corrections are prioritized; and (III) balanced performance: the use of the MSE² ensures faster convergence without compromising accuracy, leading to an overall more efficient training process.

This study showed that the model trained with MSE² converged effectively and efficiently, demonstrating that the adjustment of the loss function significantly improved the accuracy of vessel centerline extraction (see Figure 4). Thus, foreground weighting combined with the MSE² was chosen as the loss function.

Figure 4 The MSE and MSE2 loss. (A) The lack of convergence of the loss function during the training epochs with MSE. (B) The convergence behavior of the loss function during the training epochs with MSE2. The green line represents the validation loss, the orange line represents the training loss, and the red line represents the fitting curve of the training loss. MSE, mean squared error.

Evaluation metrics

After obtaining the coordinates of the key points by identifying the maximum value in the output heatmap, we set the evaluation criteria for key point detection. A grayscale threshold of 40 was applied to the outputs to determine whether the key point was successfully detected. The points with a grayscale value above 40 were classified as detected, and otherwise, the points were classified as undetected. The Euclidean distance between the key points and ground truth was calculated, and a threshold was set to discern whether the key point had been misidentified. Due to the intricate geometry of the vessels, the distance threshold was determined by point-by-point testing, and adjusted to ensure it was applicable to various situations. For easily detectable points, the threshold was 4 pixels. For vessels with extensive tortuosity, and a large diameter and length, the thresholds were relaxed. After repeated testing, an 8-pixel cube was drawn with the predicted point as its center, and the threshold was relaxed to 25 pixels. The predicted point was considered correct if both of the following conditions were met: (I) the cube intersected with the blood vessel in which it was situated; and (II) the relaxed threshold was met.

Centerline extraction was performed for the two groups. In group 1, the centerline was extracted based on the distance field, connecting and extending the segment centerlines, and aligning them with the vessel lumen’s center using the vessel wall segmentation result. In group 2, this process was enhanced by incorporating key point detection, which assisted in centerline extraction at junctions and the connection of segment centerlines. The average centerline distance (ACD) was employed to assess the difference between the predicted centerline and ground truth. The ACD was expressed as follows:

ACD(X,Y)=∑x∈Xminy∈Yd(x,y)/|X|[2]

where X represents the ground truth, Y represents the predicted centerline, and d(x, y) represents a 3D matrix consisting of the Euclidean distances between X and Y.

Results

In total, 539 subjects (age range, 11–94 years; mean age: 56±14 years; female: 164; male: 374) were included in the study. The training, testing, and evaluation datasets comprised the data of 432, 55, and 52 subjects, respectively. The average detection accuracy of the algorithm for the 32 target points was 88.99%, with 3.644 undetected points and 0.150 erroneously detected points. The average accuracy of the algorithm for points in the internal carotid artery and middle cerebral artery was 95.4%. More specifically, the accuracy of the algorithm at the sharp bend of the carotid siphon section reached 97%. Notably, the accuracy of the algorithm for 18 points exceeded 90%. Table 2 shows the accuracy of the algorithm for the points near the carotid siphon sections, which were all above 90%. Table 3 shows the accuracy of the algorithm for the remaining points; notably, the accuracy of the algorithm was below 80% for 5 points.

By using key point detection to assist in centerline extraction (see Figure 5A,5B), the anterior curvature of the carotid siphon was effectively traced, addressing the issue of the C5 segment of the internal carotid artery being missed. The yellow arrows in Figure 5A,5B indicate the anterior curvature of the carotid siphon. In Figure 5A, the red marks indicate the detected vessel centerline; the first row of images shows the centerline extraction results without key point detection; the anterior curvature of the carotid siphon was skipped and could not be traced; while the second row of images shows the centerline extraction results using key point detection; the anterior curvature of the carotid siphon was successfully traced with the valid information provided by key point detection. In Figure 5B, the left images show that the centerline was extracted without key point detection, and the carotid siphon was skipped, resulting in the wrong centerline; the right images show the centerline extracted using key point detection; the centerline at the carotid siphon was correctly traced.

Figure 5 Results of centerline extraction with and without key point detection. (A) Vessel extraction with and without key point detection. The yellow arrows indicate the anterior curvature of the carotid siphon; the red marks indicate the detected vessel. (B) Vessel centerline extraction at the carotid siphon with and without ley point detection. The orange arrows indicate the carotid siphon. (C) The ACD with and without key point detection. ACD, average centerline distance; LICA, left internal carotid artery; RICA, right internal carotid artery.

The ACD used to quantitatively characterize the extraction performance was significantly reduced. The results showed that in the left carotid artery, the ACD without key point detection was 0.456±0.345 mm, while the ACD with key point detection was 0.426±0.350 mm. In the right carotid artery, the ACD without key point detection was 0.529±0.334 mm, while the ACD with key point detection was 0.484±0.321 mm. In Figure 5C, the blue box indicates left carotid centerline extraction with key point detection, the red box indicates left carotid centerline extraction without key point detection, the yellow box indicates right carotid centerline extraction with key point detection, and the green box indicates right carotid centerline extraction without key point detection.

Additionally, the time required for key point localization was significantly reduced when the algorithm was used. As Figure 6 shows, a total of 13 datasets were tested. The orange curve represents manual localization, which had an average time of 319.843±6.434 seconds, while the blue curve represents automatic localization, which had an average time of only 2.046±0.315 seconds. This represents a substantial reduction in time, emphasizing the efficiency of the proposed method. Additionally, the time required for processing and predicting each image using the algorithm was only 7.46 seconds.

Figure 6 Comparison of the time required for the manual and automatic key point localization.

Discussion

A V-Net-based deep learning–method was proposed to automatically localize vessel key points on MR-VWI. The results showed that using this key point detection as an assisting step significantly improved the accuracy of vessel centerline extraction. Key point detection showed good consistency with the ground truth, particularly at the sharp corner of the siphon section, where 97% accuracy was achieved, and the accuracy of 18 points surpassed 90%. For the most critical vessel segments (i.e., the internal carotid artery and middle cerebral artery), the accuracy of the algorithm reached 95.4%. The tortuous blood vessels cause great difficulties in centerline extraction, but this algorithm has great potential to improve the accuracy of centerline extraction for tortuous blood vessels. This method enables the automated key point localization of major intracranial and carotid arteries, ensuring the accurate identification of the C5 segment of the internal carotid artery during centerline extraction. Additionally, this method significantly reduced the time required to detect the 32 key points, improving the efficiency of key point detection.

The algorithm integrates clinical needs and engineering realities, resulting in some effective improvements. An appropriate slider for the sampling was chosen to ensure the variety of the input data while controlling the graphic memory, and to speed up computations while minimizing information loss. Defining a good loss function is important, especially at arterial bifurcations (23). We combined the MSE² and foreground weighting to improve both the convergence speed and learning efficiency. We also proposed a truncation algorithm during normalization that set random truncation limits, achieving grey-value randomness and improving model robustness.

To reduce errors, Gaussian heatmaps were used along with dynamically adjusted evaluation criteria. Jiang et al. found Gaussian heatmaps improved the V-Net’s performance (18). Weng et al. used Gaussian heatmaps (24) to detect key points in the lung and obtained good results. A point cannot be represented by an isolated pixel on the image; rather, it must be represented by a group of discrete points. Thus, the algorithm used a Gaussian function centered on the marked point, filling the buffer within a specified radius with gradients, creating an enlarged representation of the point, which effectively reduced the error. For vessels with extensive tortuosity, and a large diameter and length, the proper range of the points is also broader; thus, fixed detection criteria can misclassify clinically valid points as errors, reducing detection accuracy. To address this issue, the algorithm dynamically adjusted the evaluation criteria and effectively improved the point detection accuracy.

Srinidhi et al. achieved 78% accuracy in detecting vessel junctions (25); Weng et al. achieved 80.58% accuracy in detecting pulmonary artery key points (24). The automatic point detection algorithm proposed in this study focused on the vessels from the common carotid artery to the intracranial arterial terminus. Our algorithm achieved an accuracy of about 87% at the junctions, with a maximum accuracy of 98%, and an average accuracy of 88.99%, all of which are better than the accuracy rates achieved by the two above-mentioned algorithms. This may be because the above-mentioned improvements enhanced the performance of the algorithm. However, the influence of vascular anatomy also needs to be taken into account. The retinal blood vessels are much finer, and have more complex crossings than the head and neck arterial vessels, and the lungs include airways and blood vessels, which are confounding factors that can lead to less accurate algorithms. Thus, the advantage of the algorithm proposed in this study needs further evaluation. Most traditional methods of centerline extraction are semi-automatic and require the manual selection of seed points (17,23,26). Conversely, the method proposed in this study is fully automated and can further reduce labor costs. The centerline extraction method proposed by Zhou et al. (12) can only evaluate intracranial vessel segments, but arterial plaque is a diffuse disease that requires the quantitative analysis of whole brain plaques. Thus, both intracranial vessels and carotid arteries were included in this study to achieve a more comprehensive plaque analysis. Diedrich et al. (13) compared various loss functions and selected one that performed well in the carotid siphon, but it was prone to losing smaller arteries in the vicinity of larger ones. This algorithm achieved an accuracy of 0.97 at the sharp corners of the siphon section without any omissions.

This study had some limitations. Detection accuracy in certain areas (e.g., bifurcation and distal points) could still be improved. Possible reasons for this include an unbalanced voxel distribution due to the target point representing only a small fraction of all voxels. Additionally, downsampling might have led to the loss of small details, leading to a decrease in the detection rate of the bifurcation points and distal points. The application of key point detection during auxiliary centerline extraction led to a decrease in the ACD in the mean, median, and minimum values, but not in the maximum value. The poor recognition of some challenging points might have led to significant errors in the ACD. Further, our hypothesis as to why the MSE² shows better convergence speed and performance than the MSE remains untested and unvalidated. Future studies should further investigate and validate this hypothesis.

Conclusions

Overall, our algorithm enabled the fully automated extraction of key points in the head and carotid arteries. Vessel centerline extraction had a higher level of accuracy using key point detection. This improvement will enhance the clinical efficiency of arterial plaque diagnosis. Our algorithm could be applied in future research to achieve more accurate lumen and vessel wall segmentation, further aiding in plaque diagnosis. The proposed enhancements could also be applied to key point detection and centerline extraction in other medical images, thereby advancing the use of key point detection algorithms across various medical imaging domains. This study has significant clinical implications for the prevention and treatment of ischemic stroke.

Acknowledgments

The authors would like to thank the Guangdong Second Provincial General Hospital, the Jiangsu Provincial People’s Hospital, the Nanjing Drum Tower Hospital, the Peking University Shenzhen Hospital, the Tongji Hospital, the Subei People’s Hospital of Jiangsu province, and the Shenzhen Hospital of Southern Medical University for providing the image dataset.

Footnote

Reporting Checklist: The authors have completed the TRIPOD+AI reporting checklist. Available at https://qims.amegroups.com/article/view/10.21037/qims-24-1949/rc

Funding: The study was partially support by the National Key Technology Research and Development Program of China (Nos. 2023YFC3402800 and 2023YFC3402802), the Natural Science Foundation of Guangdong Province (Nos. 2023B1515020002 and 2024B1515040018), the Key Laboratory for Magnetic Resonance and Multimodality Imaging of Guangdong Province (No. 2023B1212060052), the Central Guidance for Local Science and Technology Development Project (No. ZYYD2023D02), the Incubation Fund of Yan’an People’s Hospital (No. 2023PY-03), and the Guangdong Innovation Platform of Translational Research for Cerebrovascular Diseases.

Conflicts of Interest: All authors have completed the ICMJE uniform disclosure form (available at https://qims.amegroups.com/article/view/10.21037/qims-24-1949/coif). W.S., X.Y., and Y.M. report that they are employed by Shanghai United Imaging Healthcare Co., Ltd. The other authors have no conflicts of interest to declare.

Ethical Statement: The authors are accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved. The study was conducted in accordance with the Declaration of Helsinki (as revised in 2013). The study was approved by the Institutional Ethics Board of the Shenzhen Institutes of Advanced Technology (No. SIAT-IRB-180315-H0228), and the requirement of individual consent for this retrospective analysis was waived. All participating hospitals were informed and agreed with the study.

Open Access Statement: This is an Open Access article distributed in accordance with the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International License (CC BY-NC-ND 4.0), which permits the non-commercial replication and distribution of the article with the strict proviso that no changes or edits are made and the original work is properly cited (including links to both the formal publication through the relevant DOI and the license). See: https://creativecommons.org/licenses/by-nc-nd/4.0/.

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