Automatic detection of posterior superior alveolar artery in dental cone-beam CT images using a deeply supervised multi-scale 3D network

Abstract

Objectives

This study aimed to develop a robust and accurate deep learning network for detecting the posterior superior alveolar artery (PSAA) in dental cone-beam CT (CBCT) images, focusing on the precise localization of the centre pixel as a critical centreline pixel.

Methods

PSAA locations were manually labelled on dental CBCT data from 150 subjects. The left maxillary sinus images were horizontally flipped. In total, 300 datasets were created. Six different deep learning networks were trained, including 3D U-Net, deeply supervised 3D U-Net (3D U-Net DS), multi-scale deeply supervised 3D U-Net (3D U-Net MSDS), 3D Attention U-Net, 3D V-Net, and 3D Dense U-Net. The performance evaluation involved predicting the centre pixel of the PSAA. This was assessed using mean absolute error (MAE), mean radial error (MRE), and successful detection rate (SDR).

Results

The 3D U-Net MSDS achieved the best prediction performance among the tested networks, with an MAE measurement of 0.696 ± 1.552 mm and MRE of 1.101 ± 2.270 mm. In comparison, the 3D U-Net showed the lowest performance. The 3D U-Net MSDS demonstrated a SDR of 95% within a 2 mm MAE. This was a significantly higher result than other networks that achieved a detection rate of over 80%.

Conclusions

This study presents a robust deep learning network for accurate PSAA detection in dental CBCT images, emphasizing precise centre pixel localization. The method achieves high accuracy in locating small vessels, such as the PSAA, and has the potential to enhance detection accuracy and efficiency, thus impacting oral and maxillofacial surgery planning and decision-making.

Introduction

Maxillary sinuses, the largest paranasal sinuses, are intrabony air-filled spaces within the maxillary bones. Anatomically, the maxillary sinus has a pyramidal structure and consists of 6 walls and floors.^1–3 The blood supply to the maxillary sinus is provided by branches of the maxillary artery, namely, the posterior superior alveolar artery (PSAA), the inferior orbital artery (IOA), and the posterior lateral nasal artery.^4,5 The PSAA and IOA give rise to extraosseous and intraosseous branches that form an arterial arcade around the maxillary sinus, supplying its lateral wall and, partially, the alveolar process.^2,4,6,7

Preoperative assessment for a maxillary sinus bone graft involves identifying any inflammation or lesions that may predispose the sinus membrane to perforation.² Accurate localization of the PSAA is important to minimize the risk of arterial damage during the opening of the bony window.^2,8,9 While damage to the vessel is not typically life-threatening, it can lead to significant bleeding, necessitating haemostasis.⁹ Complications stemming from arterial bleeding can have serious implications, obstructing the surgical field and impacting the insertion and maintenance of bone graft material.^2,8,10 Moreover, numerous studies have established a clear correlation between Schneiderian membrane perforation during surgical procedures and heightened rates of implant failure. This increased failure rate is often attributed to arterial bleeding originating from the PSAA, which can disrupt the surgeon’s field of vision.^11,12 Additional reported complications include post-surgical bleeding, nasal bleeding, congestion, haematoma, empyema, and sinus infection.³ Thus, possessing knowledge about the location and course of the PSAA is necessary consideration in surgical planning.

With advances in imaging devices, such as the cone-beam CT (CBCT), it has become easier to detect the PSAA compared to the past. A 2015 study conducted by Varela-Centelles et al¹³ found that the detection rate of PSAA in the maxillary sinus reached 74.5%. In 2017, Tehranchi et al¹⁴ reported a detection rate of 87%, while in 2021, Fayek et al¹⁵ determined the rate to be 92.0%. Over time, the improved detection has enhanced the effectiveness of preoperative PSAA evaluation during surgical planning.^4,8,16 The detection and preservation of the PSAA during oral and maxillofacial surgeries, such as maxillary sinus bone grafting,^2,9,10 fracture repair,^17,18 Caldwell-luc surgery,¹⁸ maxillary osteotomy,¹⁸ and tumour resection,¹⁹ help in reducing unnecessary bleeding and preventing associated complications. However, evaluating the PSAA using CBCT is often time-consuming, cumbersome, and prone to human error.

Recent advancements in deep learning-based techniques have demonstrated great potential in medical and dental imaging applications.^20–22 Notably, digital architecture, such as 3D U-Net,^23,24 3D V-Net,²⁵ 3D Attention U-Net,^26,27 and 3D Dense U-Net²⁸ have demonstrated excellent performance in medical imaging, even with limited training data.²⁴ While structural properties can facilitate extraction of the medium to large vessels, accurately detecting small blood vessels remains challenging.²⁹ The reliability of small vessel detection is hindered by variations in image quality, which renders manual labelling time-consuming and introduces errors in segmentation. Although many studies have been conducted on anatomical characteristics, such as the prevalence, diameter, and location of the PSAA,^{2–4,6,7,14–16,30,31} research on deep learning-based PSAA extraction has not yet been conducted. Automatic detection of certain processes through deep learning may have clinical utility, as it can alleviate the burden of cumbersome and potentially forgettable processes and minimize human errors.

This study aimed to propose a method for locating the PSAA in CBCT images using deep learning and identify a robust deep learning network for this task. Automatic detection of the PSAA before surgery has the potential to reduce complications by preventing rupture of the artery during surgery. The findings of this study may contribute to the development of a reliable and efficient method for PSAA detection using CBCT, thus, benefiting both clinicians and patients.

Methods

Patient selection and data preparation

This study was conducted retrospectively from data obtained for clinical purposes. It was approved by the Institutional Review Board of Seoul National University Dental Hospital, Seoul National University (No. ERI23007). The ethics committee approved the waiver for the informed consent because this was a retrospective study. The study was performed according to the Declaration of Helsinki.

Dental CBCT images of 300 patients who visited the Seoul National University Dental Hospital for clinical reasons between 2016 and 2020 were collected for this study. Patients’ data were obtained using the CS9300 Cone Beam Computed Tomography system manufactured by Carestream Health in New York, United States, operating at 80 kVp, 8 mA, and with a 24 s exposure time. The CBCT dimensions were 841 × 841 × 289 pixels, with voxel sizes of 0.2 × 0.2 × 0.2 mm³, and 16-bit depth.

All personal information including the patient’s name and chart number was anonymized and encrypted. The maxillary sinus sizes, shapes, and pathological conditions varied among the patients. Low-quality images with severe artefacts, haziness, or distortion, images in which the PSAA is undetectable, and abnormal defects, such as fracture lines, and benign and malignant lesions in the maxilla, were excluded. Finally, the dental CBCT images from 150 patients were included in this study.

The PSAA was manually annotated by an oral and maxillofacial surgeon with 16 years of experience using the imaging software (3D Slicer for Windows 10, Version 5.0.2; MIT, Cambridge, MA, United States). For each dental CBCT image, a sphere was drawn along the centre of the PSAA seen in each slice of the coronal plane, the sphere was overlapped, and interpolation was performed on the connection part. Labelling was performed using Gaussian and median smoothing functions while checking whether the size and shape of blood vessels were reflected in the cross-section (Figure 1). To ensure the accuracy of ground truth labelling and minimize systematic errors, we performed intra-observer validation on 20% of the cases under the same conditions at 3-month interval. The mean intra-observer variability on the test dataset was 1.731 ± 2.323 mm mean absolute error (MAE).

Figure 1.

The posterior superior alveolar artery (PSAA) captured using dental cone beam computed tomography (CBCT). (A) The axial plane of CBCT. The annotated PSAA is shown. (B) The spheres centred on the centre of the PSAA. (C) The coronal plane of CBCT. (D) The sagittal plane of CBCT.

We constructed a dataset of 300 right-sided CBCT volumes using CBCT images obtained from 150 patients. These were created by horizontally flipping the original images along the centreline, effectively generating mirrored versions of the left side. Subsequently, we divided this dataset into training, validation, and test sets, following a 6:2:2 ratio. To avoid including redundant left-right pairs from the same patient, we implemented careful measures during the initial dataset division. Specifically, we allocated individuals to the training and test sets right from the outset, ensuring a balanced distribution of 150 individuals into training, validation, and test sets, with a ratio of 90, 30, and 30 individuals, respectively. The left and right maxillary sinus areas were cropped to a $200\times 200\times 288$ region of interest (ROI), and ROIs were resized to$\mathrm{ }128\times 128\times 288$. Zero padding was performed to maintain the input volume of the same length for all patients with regions of different lengths.²² As part of the preprocessing phase, we utilized an algorithm designed to automatically crop the sinus area from dental CBCT images.

To detect the centre of the PSAA using CBCT, a heatmap-based detection method was adopted to transfer each centreline of the PSAA into a heatmap.³² Coordinates of the centreline pixel $C_i$ is represented by a Gaussian heatmap $H_i$, which is considered as a probability of a centreline pixel in the range [0, 1] as shown in Figure 2. The probability of a pixel is 1.0 at the centre of a heatmap. The probability of a pixel decreases below 1.0 as it moves further from the centre. The Gaussian distribution is defined as:

$$H\left(C_{i,}{\sigma }_i\right)=\frac{\phi }{{\sigma }_i\sqrt{2}}\mathrm{e}\mathrm{xp}(-\frac{{‖x-C_i‖}_2^2}{2{\sigma }_i^2}),$$

where $\phi$ is the scale factor to define the size of a heatmap, empirically set as 5. The $\sigma$ is a standard deviation, which is the hyper-parameter to determine the sharpness of the Gaussian distribution. Centreline pixels with a lower $\sigma$ show a much sharper distribution than a higher $\sigma$ at the centre of a heatmap. CBCT images were used as input volumes and stacked heatmaps of centreline pixels were used as ground truth volumes for network training.

Figure 2.

A coronal slice of the posterior superior alveolar artery (PSAA) is shown in (A) CBCT images. The ground truth segmentation mask of (B) the PSAA, (C) converted to heatmap train data with label. The segmented label is converted into a heatmap where the centre pixel is 1, and decreases as it moves further away from the centre. Abbreviation: CBCT = computed tomography.

Deeply supervised multi-scale 3D network

The proposed deeply supervised multi-scale 3D network (3D U-Net MSDS) had a 3D encoder and decoder architecture consisting of 3D convolution blocks, multi-scale inputs, and deep supervisions.³³

In the proposed 3D U-Net MSDS, 3D convolution blocks were comprised of a 3 × 3 × 3 convolution, batch normalization, and rectified linear unit at the encoder part. After repeating the 3D convolution block twice, a 2 × 2 × 2 max-pooling operation for extracting down-sampled feature maps. To alleviate volumetric information loss due to max-pooling operations, the multi-scale inputs down-sampled by 2 × 2 × 2 average pooling from the original input were merged at each level of layer in the encoder parts. The number of feature maps of 3D convolution blocks gradually increased from 32 to 64, 128, and 256 at the encoder part of 3D U-Net MSDS. Similar to the encoder structure, 2 3D convolution blocks, and a 3D transposed convolution were used for extracting feature maps and up sampled at each level of the decoder. The 3D transposed convolution had a 2 × 2 × 2 convolution with a stride of 2. Skip connections were used to concatenate feature maps of each level of layers in the encoder with the corresponding up-sampled feature maps. To mitigate the vanishing problem for encouraging backpropagation of the gradient flow,³³ a deep supervision layer was embedded, which concatenated feature maps generated from output maps at every level of the layers in the decoder. The output activation was a linear function for regressing a heatmap. The number of feature maps of 3D convolution blocks gradually decreased from 256 to 128, 64, and 32 at the decoder part of the 3D U-Net MSDS (Figure 3).

Figure 3.

The 3D U-Net architecture with multiscale deep supervision. It combines the benefits of the 3D U-Net architecture, and the use of multiscale input and deep supervision, to enhance network performance.

The proposed networks were trained using RMSProp optimizer and mean squared error loss function. An initial learning rate was set to start at 10⁻³ and decrease to the minimum learning rate of 10⁻⁶ by reducing the learning rate by half when there is no performance improvement for 5 epochs in the validation dataset. The maximum training epoch was set to 300 with a batch size of 1, and training was terminated when there was no performance improvement in the validation dataset during 45 epochs. The proposed networks were implemented using Python3 and TensorFlow on Ubuntu 16.04 and an NVIDIA RTX A6000 graphic card. Data augmentation was performed to increase the variation of the actual training dataset, using rotation, Gaussian noise, and brightness. By increasing the variation of the training dataset in this way, overfitting can be reduced, and the model can perform better in practice.^21,34

Performance evaluation

The performance of the centre pixel of the blood vessel was compared using 3D U-Net MSDS in conjunction with other networks, such as 3D V-Net,²⁵ 3D Attention U-Net,²⁶ and 3D Dense U-Net.²⁸

The detection performance was assessed based on the centre pixel. The MAE was utilized to quantify the discrepancy between the ground truth and predicted values on a point-to-point basis. The obtained MAE (mm) values were accompanied by the standard deviation (SD) errors, which were computed across all test data using the following formula:

$$\mathrm{MAE}=\frac{1}{p}\sum _{i=1}^p\left(\frac{\left|x_i-{\overline{x}}_i\right|+\left|y_i-{\overline{y}}_i\right|}{2}\right).$$

$\{x_i,y_i\}$ and $\{{\overline{x}}_i,{\overline{y}}_i\}$represent the $\{x,y\}$coordinate for the ground truth and predicted centreline, respectively. $p$ denote the total number of data points in a test data.

The mean radial error (MRE) was also evaluated to quantify network performance. MRE (mm) was defined as the absolute distance between the ground truth and predicted value using the following equation:

$$\mathrm{MRE}=\frac{1}{p}\sum _{i=1}^p\left(\sqrt{{\left(x_i-{\overline{x}}_i\right)}^2+{(y_i-{\overline{y}}_i)}^2}\right).$$

$\{x_i,y_i\}$ and $\{{\overline{x}}_i,{\overline{y}}_i\}$represent the coordinate for the ground truth and predicted centreline, respectively. $p$ denotes the total number of data points in the test data.

A successful detection rate (SDR) for each network was obtained. This SDR (%) represents the probability of successful detection when the MAE and MRE results for the prediction and the ground truth were <1, 1.5, 2, 2.5, and 3 mm, respectively. The SDR with a precision of less than a threshold value (t) mm can be expressed as:

$$\mathrm{SDR}=\frac{\#\left\{p:‖M_p‖<t\right\}\mathrm{ }}{n}\mathrm{ }\times 100\mathrm{\%}.$$

$M_p$ represents the MAE or MRE score of test data $p$, and $t$ is for the threshold value of a range of measurement values for evaluation, such as 1, 1.5, 2, 2.5, and 3 mm. $p\in n$, and n is the total number of the test data.

We used the one-way Kruskal-Wallis test tests to compare performances among 3D U-Net MSDS, 3D U-Net, 3D U-Net DS, 3D V-Net,²⁵ 3D Attention U-Net,²⁶ and 3D Dense U-Net²⁸ networks using PASW Statistics for Windows 10 (Version 18.0.0, IBM, Armonk, NY, United States) since the data did not follow a normal distribution. The statistical significance level was set to 0.05.

Results

The results in Table 1 show the detection performance of MAE and MRE by the 3D U-Net MSDS, 3D U-Net DS, 3D U-Net, 3D Dense U-Net, 3D V-Net, and 3D Attention U-Net networks. The performances were compared to a dataset with 60 CBCT volumes not used for training. The 3D U-Net MSDS network showed the lowest values of MAE and MRE for the centreline pixel detection compared to other 3D networks (P < .05).

Table 1.

The mean absolute error (MAE) and mean radial error (MRE) values from different networks (P < 0.05).

Network	MAE (mm)	MRE (mm)
3D Attention U-Net	1.012 ± 1.248	1.559 ± 1.819
3D V-Net	1.340 ± 1.594	2.102 ± 2.380
3D Dense U-Net	1.064 ± 1.472	1.700 ± 2.286
3D U-Net	1.681 ± 2.759	2.524 ± 3.987
3D U-Net DS	0.804 ± 1.068	1.292 ± 1.626
3D U-Net MSDS	0.696 ± 1.552	1.101 ± 2.270

The detection performance of the 6 networks was evaluated. The results showed that the 3D U-Net MSDS demonstrated the best performance, while the conventional 3D U-Net exhibited the worst performance. Notably, the detection performance of MAE and MRE achieved 0.696 ± 1.552 and 1.101 ± 2.270 mm, respectively, thus indicating that 3D U-Net MSDS modifications significantly enhanced the detection performance of 3D U-Net.

Tables 2 and 3 show the SDR of MAE and MRE by networks for PSAA detection, respectively. All 6 deep learning networks achieved an SDR of over 80% within 2 mm. The 3D U-Net MSDS demonstrated an accuracy of up to 86.67% within 1 mm, and an SDR of 96.67% within 2.5 mm. As shown in Table 3, the 3D U-Net MSDS demonstrated an accuracy of up to 80.00% within 1 mm, and 95.00% of SDR within 2.5 mm. The results were consistent with the MAE and MRE findings. In both the SDR of MAE and MRE, the 3D U-Net MSDS demonstrated better performance compared to the other models.

Table 2.

A successful detection rate (SDR) from different networks by mean absolute error.

SDR (%)	<1 mm	<1.5 mm	<2 mm	<2.5 mm	<3 mm
3D Attention U-Net	71.67	80.00	85.00	88.33	90.00
3D V-Net	63.33	68.33	80.00	83.33	86.67
3D Dense U-Net	73.33	80.00	85.00	88.33	90.00
3D U-Net	65.00	75.00	80.00	83.33	83.33
3D U-Net DS	78.33	85.00	91.67	93.33	93.33
3D U-Net MSDS	86.67	93.33	95.00	96.67	96.67

Table 3.

A successful detection rate (SDR) from different networks by mean radial error.

SDR (%)	<1 mm	<1.5 mm	<2 mm	<2.5 mm	<3 mm
3D Attention U-Net	60.00	71.67	75.00	80.00	86.67
3D V-Net	48.33	60.00	66.67	73.33	78.33
3D Dense U-Net	61.67	73.33	78.33	81.67	85.00
3D U-Net	56.67	65.00	70.00	78.33	80.00
3D U-Net DS	68.33	76.67	81.67	85.00	91.67
3D U-Net MSDS	80.00	86.67	91.67	95.00	95.00

Figure 4 illustrates the 3D reconstruction of PSAA positions predicted by the network, offering multiple examples. In the 3D visualizations and comparison with the ground truth, areas with disconnections or multiple detections were indicated by black arrows. As a result, 3D U-Net MSDS consistently displayed lower levels of disconnection and false positives when compared to other networks.

Figure 4.

Three-dimensional (3D) reconstruction of the posterior superior alveolar artery (PSAA) for various distinct cases offering multiple examples. (A) The ground truth using the (B) 3D U-Net MSDS, (C) 3D U-Net, (D) 3D U-Net DS, (E) 3D V-Net, (F) 3D Dense U-Net, and (G) 3D Attention U-Net. The 3D U-Net MSDS shows less PSAA disconnection and fewer false positives, compared to other networks, as indicated by the black arrow.

Figure 5 is intended to provide examples of the performance of the deep learning network in various cases, including scenarios such as the presence of impacted teeth, sinusitis. Each column represents a set of these diverse cases, illustrating the performance of each network. The prediction for the PSAA by the 3D U-Net MSDS alongside the ground truth was superimposed on the CBCT images. To assess the clinical significance of the network’s performance, we employed a visualization method involving the drawing of a rectangle with a height and a width of 2 pixels. This rectangle was centred around the pixel coordinate predicted by the deep learning network and was subsequently superimposed on the CBCT images. Predicted areas are highlighted in red, ground truth areas in blue, and overlapping areas in yellow.

Figure 5.

Multiple examples of the posterior superior alveolar artery (PSAA) detection results are displayed. In (A), the original CBCT image is presented, while (B) shows the results obtained with 3D U-Net MSDS. The subsequent columns, (C) through (G), correspond to the results achieved by the following networks: (C) 3D U-Net, (D) 3D U-Net DS, (E) 3D V-Net, (F) 3D Dense U-Net, and (G) 3D Attention U-Net, respectively. Each column represents a set of diverse cases, illustrating the performance of each network. To assess the clinical significance of these performances, a rectangle with a height and width of 2 pixels is placed around the centre pixel of the PSAA for visualization. Predicted areas are highlighted in red, ground truth in blue, and overlapping areas in yellow.

The MAE and MRE values for the test dataset were plotted from the posterior to the anterior regions of the image (Figure 6). Across most networks, there was a noticeable increase in the distance between the predictions and ground truth in both the posterior and anterior regions. However, the increase in error was more pronounced in the anterior region compared to the posterior. In the midsection of the vessels, there was an overall higher level of agreement in terms of distance. Among them, the 3D U-Net MSDS demonstrated the least variation in distance between the predicted values and ground truth when compared to other networks, indicating higher performance. This pattern can be attributed to the continuous nature of blood vessel anatomy, which makes it difficult to precisely distinguish the beginning and end points of the vessels.

Figure 6.

The line plots show the (A) mean absolute error (mm) and (B) mean radial error (mm) from the posterior slice to the anterior slice of the posterior superior alveolar artery (PSAA) for 3D U-Net MSDS, 3D U-Net, 3D U-Net DS, 3D V-Net, 3D Dense U-Net, and 3D Attention U-Net.

Discussion

In the field of medical imaging, deep learning technology has continuously evolved to detect and segment anatomical structures or abnormalities.^20,21,34 Deep learning technology has been extensively employed in oral and maxillofacial imaging to ensure accurate segmentation and classification of anatomical structures, such as the mandibular canal segmentation (in CBCT),³³ tooth segmentation (in CBCT),³⁵ cyst and tumour detection (in CBCT and panorama),^20,21 as well as facilitated precise age and gender estimations (in cephalogram).³⁶ Deep learning algorithms have also been utilized for the detection of tooth caries (in periapical radiograph),³⁷ apical lesions (in periapical radiograph),^37,38 and landmark identifications (in cephalogram).^39,40 Research on the use of deep learning in various aspects of maxillary sinus-related studies is ongoing. These include automatic segmentation of the sinuses,⁴¹ the diagnosis of sinusitis,⁴² and cyst detection.⁴¹ Importantly, to date, no deep learning studies have been conducted specifically on the PSAA.

Vascular structures in the maxillofacial region are often surrounded by cortical bone, such as the mandibular canal. Their characteristics are reflected in the image as density differences, which are useful for structural deep learning. Segmentation methods, commonly used for learning and detecting the 3D shape of anatomical structures, have shown success in improving the imaging of anatomical structures.⁴³ This traditional approach is based on filtering-based algorithms that extract features using the optical and spatial characteristics of blood vessels.⁴⁴ This method has been effective in detecting larger blood vessels and major anatomical structures. However, using this method to accurately identify small vessels, such as the PSAA, is challenging. The small diameter of the PSAA and its complex pathway all contribute to the difficulty. The insufficient contrast and poor continuity between the PSAA and the maxillary sinus wall further contribute to the difficulty of automatic segmentation using deep learning methods.^43–45 As such, this study employed a centreline pixel detection method to accurately locate the PSAA using CBCT.

Centreline pixel detection is a method developed to accurately identify intricate vascular structures. The method originated from the idea of centreline prediction, which was first introduced by Tetteh et al.⁴⁰ Centreline prediction involves post-processing blood vessel segmentation to locate the branching points and the skeleton of the blood vessels. For small-sized blood vessels, such as the PSAA, positional information is considered more crucial than other morphological features. In the centreline pixel detection method, the centre of the blood vessel is designated as 1 and serves as a central reference point. Deep learning algorithms are employed to locate these pixels accurately. To address the 3D nature of the PSAA and ensure accurate detection and localization, a 3D context-aware network was employed, ultimately resulting in favourable outcomes.

In this study, several widely utilized 3D networks in the field of deep learning for medical imaging were compared to the 3D U-Net MSDS. The centerline pixel detection method yielded the highest network performance (in both MAE and MRE) with the 3D U-Net MSDS, followed in decreasing order by the 3D U-Net DS, 3D Attention U-Net, 3D Dense U-Net, 3D V-Net, and conventional 3D U-Net. In particular, the 3D U-Net MSDS demonstrated the highest accuracy in the centreline pixel detection, as evidenced by a >90% SDR for both MAE and MRE within a detection range of 2 mm or less. This can be interpreted as successfully detecting the position of the vessel in over 90% of cases within a distance that is close to its diameter, which is typically around 1-2 mm for the PSAA.^15,17,30 Our results demonstrated a significant performance improvement, compared to the 3D U-Net, which showed an SDR of 80% for MAE and 70% for MRE within the same range.

One of the main advantages of the 3D U-Net MSDS is its use of a deep supervision strategy, where intermediate predictions are made at different levels of the network and are used to provide feedback to earlier layers during training. This helps to prevent the vanishing gradient problem, which can occur in deep neural networks, leading to difficulties in training.^46,47 With the deep supervision strategy, gradients are propagated back to earlier layers, allowing the network to learn more efficiently, converge faster, and ultimately, reduce false positives. Our findings indicate that the 3D U-Net DS exhibits improved performance compared to the 3D U-Net (MAE: 0.804 ± 1.068 vs 1.681 ± 2.759 mm and MRE: 1.292 ± 1.626 vs 2.524 ± 3.987 mm).

Another advantage of the 3D U-Net MSDS is its ability to effectively learn and incorporate features at multiple scales. The path of the PSAA varies for each individual, and the surrounding anatomical structures do not appear in a consistent pattern. Therefore, multiscale learning is necessary. The network consists of multiple encoder-decoder pathways, each with a different receptive field, allowing the network to capture information details at various levels.^48,49 This enables the network to identify small and large structures in the image, and is particularly useful in medical image analysis. Our findings confirmed that the 3D U-Net DS (MAE: 0.804 ± 1.068 mm and MRE: 1.292 ± 1.626 mm) improved in performance when the multiscale strategy was applied (MAE: 0.696 ± 1.552 mm and MRE: 1.101 ± 2.270 mm). Overall, the 3D U-Net MSDS is a powerful and effective deep learning architecture for the volumetric segmentation of medical images, with the ability to capture features at multiple scales and efficiently train deep neural networks.

Our study found that the 3D U-Net MSDS outperformed all other tested networks, although all tested networks demonstrated clinically acceptable performance. Our findings affirm the efficacy of employing various 3D networks in medical imaging. These networks excel at learning and incorporating the inherent continuity present in medical image data, allowing them to probabilistically exclude non-continuous predictions. The primary difference from 2D networks lies in their ability to capture and reflect the 3D continuity of anatomical structures. This effect is particularly evident when applying the centreline pixel detection method. The choice of architecture depends on the specific requirements of the task. The specific benefits depend on the task and the dataset being used. Hence, careful experimentation and validation are necessary to determine the optimal configurations for any given application.

This study has some limitations. First, like other continuous anatomical structures, unclear structural boundaries of the PSAA resulted in a high number of false positives at the start and end points, which lowered the accuracy (Figure 6). Second, to reduce the memory requirements for handling large amounts of data, we used resized and cropped images rather than original images. This approach necessitated additional image preprocessing. Third, the generalizability of the results may be limited since the data were collected from a single type of CBCT.

To enhance the accuracy of the extended model, it would be beneficial to collect annotated data from multiple types of CBCT and different CBCT machines. Furthermore, inter-observer variability could not be assessed in this study as the annotation was performed by a single oral-maxillofacial surgeon. To further validate the generalizability of the proposed deep learning-based centre detection method, additional datasets annotated by different radiologists using diverse sources and in different clinical settings should be considered in future studies. In the future, studies to assess the performance and robustness of the method across different imaging modalities, patient populations, and pathological conditions, to ensure its reliability and applicability in real-world clinical scenarios, are warranted.

Conclusion

This study aimed to determine the most robust method and network for detecting the PSAA, an important anatomical structure that crosses the maxillary sinus. To overcome the ambiguous clarity in the cortical bone and issues associated with the low contrast of CBCT images, we introduced the centreline pixel detection method to identify the central point of the blood vessel on each coronal slice. Instead of segmentation, we compared the performance of this detection method among several 3D networks. To derive the most robust network, the 3D U-Net was customized. Our results demonstrated the superiority of the 3D U-Net MSDS compared to other networks. By combining the centreline pixel detection method and the 3D U-Net MSDS, the accuracy and efficiency of PSAA detection are enhanced. This automatic detection of PSAA could be beneficial in reducing bleeding and preventing complications in the maxillary sinus area. Further validation using larger datasets and better-designed clinical trials to validate the clinical utility of this approach is paramount.

Author contributions

J.A. Park and D. Kim contributed equally and are considered co-senior authors of this work. In addition, they had full access to all the data in the study and took responsibility for the integrity of data and accuracy of the data analysis.

Funding

This work was supported by a National Research Foundation of Korea (NRF) grant, funded by the Korean Government (Ministry of Science and Information Communication Technology) (Number: 2023R1A2C200532611).

This work was also supported by a Korea Medical Device Development Fund grant, funded by the Korean Government (Ministry of Science and Information Communication Technology; Ministry of Trade, Industry, and Energy; Ministry of Health & Welfare; Ministry of Food and Drug Safety) (Project Number: 1711194231, KMDF_PR_20200901_0011), (Project Number:1711174552, KMDF_PR_20200901_0147).

Conflicts of interest

None declared.