Preoperative Surgical Planning for Lumbar Spine Pedicle Screw Placement Using PointNet

Abstract

This study introduces a novel framework for defining screw trajectory that utilizes PointNet—a deep neural network trained on lumbar vertebrae point clouds—to improve the manual surgical planning procedures. The conventional architecture of PointNet was modified to accommodate various vertebral orientations and predict six values, which were reconstructed into two control points that define a linear trajectory. A custom loss function was designed to align the predicted trajectory with the ground-truth trajectory. The neural networks were trained on 4284 point clouds of vertebrae, and 28 unseen point clouds were used to evaluate the model’s performance based on translational error, angular error, and clinical accuracy. For the left pedicle, the mean translational errors were 1.5 ± 0.8 mm at the entry point and 2.3 ± 1.2 mm at the target point. For the right pedicle, the mean translational errors were 1.5 ± 0.7 mm at the entry point and 2.3 ± 1.0 mm at the target point. The mean angular error was 3.5 ± 2.3° for the left pedicle and 3.9 ± 1.7° for the right pedicle. Clinically, the network generated 52 out of 56 trajectories without medial-cortical violations of the spinal canal. The trained neural network demonstrated promising technical and clinical accuracy, generating feasible screw trajectories across various vertebral orientations. Integrating a spinal segmentation network with the proposed framework could enable fully automated surgical planning in the future.

1. Introduction

Pedicle screw placement is commonly used in surgeries for patients with conditions such as spinal scoliosis, deformities, and intervertebral disk herniations. Historically, the success of these procedures has relied heavily on the surgeon’s expertise, as freehand techniques are often employed. However, surgical navigation and robotic guidance have substantially improved outcomes, enabling safer and more precise screw insertion than traditional methods [1,2,3,4]. Pedicle screw placement is also frequently used in minimally invasive, percutaneous procedures, providing benefits such as reduced muscle and tissue damage, decreased postoperative pain, and shorter hospital stays [5,6]. Achieving successful pedicle screw placement with navigation and robotic guidance involves multiple preoperative and intraoperative steps, including a CT scan, surgical planning, and registration [7,8]. Generally, the surgical plan includes the screw’s linear trajectory, dimensions, and insertion depth. The screw’s linear trajectory is defined by two three-dimensional control points—the entry and target points, as illustrated in Figure 1. Currently, surgical planning for screw insertion is performed manually during the preoperative and intraoperative phases based on CT scans [9]. Automated, optimized surgical planning could streamline workflows, reduce radiation exposure, and minimize the risk of screw mispositioning.

Several studies have explored automated and optimized methods for surgical planning. Knez et al. developed a computer-assisted planning approach for determining pedicle screw dimensions and insertion trajectories for the thoracic spine by modeling the vertebrae and pedicles as elliptical cylinders [10]. They compared their method with manual planning performed by two surgical professionals and found that their approach aligned well with the anatomical technique by following the pedicle’s anatomical axis [11]. Cai et al. trained a deep neural network to output six regression values that define the screw’s entry and direction points, respectively [12]. They designed a U-Net-like segmentation model to reconstruct vertebrae from CT scans, connecting it to a location network for regressing the six values. They suggested that a more advanced network architecture could better extract vertebral features for the location network. Qi et al. introduced an automatic framework for determining screw trajectories by establishing a local vertebral coordinate system to align screw trajectories based on vertebrae’s anatomical and geometrical features [13]. Zhang et al. presented a planning framework for lumbar pedicle screw placement, which estimates vertebral pose using the YOLOPOSE3D network and segments vertebrae from CT volumes with 3D U-NET, maximizing the trajectory distance from avoidance areas on axial and sagittal planes [14]. Massalimova et al. adopted PointNet++ to detect the screw entry and pedicle regions for defining an initial screw trajectory. The initial trajectory is then refined through anatomically constrained optimization [15].

Previous research has used spinal CT volumes to segment vertebrae through machine learning techniques, importing the binary segmentation directly into neural networks designed to generate screw trajectories. Alternatively, screw trajectories have been derived from rule-based algorithms that utilize segmented vertebrae. In computer graphics, there are algorithms capable of creating triangular meshes from three-dimensional scalar voxel fields, such as segmented vertebrae in CT scans [16,17]. Using this approach, triangular mesh data of vertebrae can be generated. By randomly sampling points on the mesh surface, a three-dimensional point cloud can be formed. Separately, Qi et al. developed a deep neural network, PointNet, designed to train on unordered point cloud data, achieving permutation invariance through a symmetric function that aggregates features from individual points [18]. PointNet’s architecture effectively captures and interprets global geometrical features within point clouds for applications like object classification and segmentation. However, it does not explicitly model local geometrical features.

In this study, we propose a novel framework for preoperative pedicle screw planning that utilizes the deep neural network PointNet. We conducted both clinical and technical evaluations of this framework to assess its accuracy in surgical planning procedures. The framework utilizes point cloud data generated from segmented lumbar vertebrae in CT volumes. The trained neural network outputs two control points, defining the predicted trajectory of the pedicle screw within the CT volume’s coordinate system. The primary contributions of this study are as follows:

• Modification of the PointNet architecture to optimize for determining the pedicle screw trajectories.
• Development of a loss function tailored for linear screw trajectories.

2. Materials and Methods

Our framework comprises three main steps for preoperative lumbar pedicle screw placement planning, as illustrated in Figure 2.

• Training Data Preparation and Preprocessing: Training data included polygonal models of each vertebra along with control points for the screw trajectory, which were created and preprocessed.
• Data Augmentation: We enhanced the robustness of the neural network by increasing the variety of vertebral models using three-dimensional affine rotation transformations. A total of 2048 points were sampled from the surface of each augmented vertebra model to form a point cloud.
• Neural Network Architecture and Training: The neural network was created by modifying the standard PointNet architecture and was trained with a customized loss function to align the predicted trajectory with the ground-truth trajectory. The network’s output was then used to calculate entry and target points for screw insertion.

The following sections provide detailed explanations of each step, as well as specifics on training and evaluation metrics.

2.1. Training Data Generation and Preprocessing

To create the point cloud inputs for the neural network, each vertebra in the lumbar spine CT scan was segmented and processed, as shown in Figure 3. The segmented binary volume was converted into a polygonal mesh using the Flying Edge algorithm [16]. Each pedicle label included two three-dimensional control points—an entry point and a target point—that defined a straight-line trajectory in three-dimensional space. This approach is consistent with a prior method used for defining preoperative surgical planning data for pedicle screw placement in surgical navigation systems [19]. Furthermore, to minimize positional biases, we translated the center of vertices in each vertebra model to the origin of the coordinate system, where N is the number of vertices (1). The same transformation was applied to the control points associated with each vertebra.

$$\begin{gathered} Label=\left[\begin{array}{c}Entry\\ Target\end{array}\right]=\left[\begin{array}{c}\left(x_e,y_e,z_e,1\right)\\ \left(x_t,y_t,z_t,1\right)\end{array}\right] \\ Vertices=\left[\begin{array}{c}\begin{array}{c}{V}_1\\ V_2\end{array}\\ ⋮\\ V_N\end{array}\right]=\left[\begin{array}{c}\begin{array}{c}\left(V_{1x},V_{1y},V_{1z},1\right)\\ \left(V_{2x},V_{2y},V_{2z},1\right)\end{array}\\ ⋮\\ \left(V_{Nx},V_{Ny},V_{Nz},1\right)\end{array}\right] \\ Center={\left[{\displaystyle \frac{\sum _{i=1}^N{V}_{ix}}{N}},{\displaystyle \frac{\sum _{i=1}^N{V}_{iy}}{N}},{\displaystyle \frac{\sum _{i=1}^N{V}_{iz}}{N}}\right]}^T \\ Centered Vertices={\left[\left[\begin{array}{cc}I& -Center\\ 0& 1\end{array}\right]V^T\right]}^T \\ Centered Label={\left[\left[\begin{array}{cc}I& -Center\\ 0& 1\end{array}\right]{Label}^T\right]}^T \end{gathered}$$

(1)

2.2. Data Augmentation

The initial number of lumbar vertebrae models was insufficient to ensure the robustness of the trained neural network. Furthermore, because the orientation of each lumbar vertebra may vary during CT scans, a data augmentation process was implemented to improve model robustness and account for the rotational diversity of vertebrae, as illustrated in Figure 4.

To achieve data augmentation, a three-dimensional rotation operation using affine transformation was applied [20]. Within a range of −30° to +30°, three random integers were selected, and sequentially used to construct a 3 × 3 rotation matrix based on Euler angles in the z-y-x order (2). A total of 51 different rotation matrices were generated for each vertebra model and its associated control points, including the identity matrix (3). Subsequently, 2048 points were sampled from the surface of each vertebra model, creating a point cloud, which was then used as input for the neural network (Figure 4).

$$\begin{gathered} \gamma ,\beta ,\alpha \in \mathbb{Z}[-30, 30] \\ R=R_x\left(\alpha \right)·R_y\left(\beta \right)·R_z\left(\gamma \right) \end{gathered}$$

(2)

$$\begin{gathered} Augmented Vertices={\left[\left[\begin{array}{cc}R& 0\\ 0& 1\end{array}\right]{Centered Verteces}^T\right]}^T \\ Augmented Label= \\ {Augmented Label=\left[\left[\begin{array}{cc}R& 0\\ 0& 1\end{array}\right]{Centered Label}^T\right]}^T \end{gathered}$$

(3)

2.3. Training of the Neural Network and Determination of Screw Trajectory

The primary function of the PointNet neural network is to classify point clouds into distinct categories and perform segmentation [18]. In this study, we leveraged PointNet’s ability to capture and interpret the geometric features of point clouds for preoperative surgical planning. To achieve this, we modified the conventional PointNet architecture and developed a custom loss function to optimize the alignment of the predicted screw trajectories with the ground truth.

Figure 5 illustrates both the conventional PointNet architecture and the modified version used in this study, with alterations applied exclusively to the classification framework. As noted in the Data augmentation section, vertebral orientations in CT scans are not uniform. Consequently, the neural network must generate varying outputs for the same vertebra presented in different orientations. To address this, we excluded the input and feature transformations from the conventional architecture, which are typically employed to ensure consistent results across varying orientations.

Moreover, in the conventional PointNet classification architecture, the output typically consists of scores for k classes. In contrast, the output layer of the modified network was adjusted to regress six values. These values were subsequently reconstructed into two three-dimensional control points that define a linear screw trajectory, as shown in Figure 5.

Figure 6 depicts the augmented ground-truth labels, denoted as $P_{1 true}$ and $P_{2 true}$, alongside the predicted points, denoted as $P_{1 predict}$ and $P_{2 predict}$. These are used to visualize the loss measurement for machine learning. The two three-dimensional lines, $l_{predict}$ and $l_{true}$, are defined as follows:

$$\begin{gathered} l_{predict}=P_{1 predict}+{\lambda }_p\overrightarrow{u_p} \\ {l}_{true}=P_{1 true}+{\lambda }_t\overrightarrow{u_t} \end{gathered}$$

(4)

where ${\lambda }_p, {\lambda }_t\in \mathbb{R}$ and $\overrightarrow{u_p}$, $\overrightarrow{u_t}$ are the unit vector of $\overrightarrow{P_{1 predict}{P}_{2 predict}}$ and $\overrightarrow{P_{1 true}{P}_{2 true}}$, respectively. As shown in Figure 6, $D_1$ and $D_2$ are the Euclidean distances $\overline{P_{1 true}{P_1}^{\prime }}$ and $\overline{P_{2 true}{P_2}^{\prime }}$, respectively, where ${P_1}^{\prime }$ and ${P_2}^{\prime }$ are on the $l_{predict}$. The perpendicular points of ${P_1}^{\prime }$ and ${P_2}^{\prime }$ onto $l_{true}$ are equal to $P_{1 true}$ and $P_{2 true}$ respectively. To calculate ${P_1}^{\prime }$ and ${P_2}^{\prime }$, we first determine the perpendicular points $P_{1 perpendicular}$ and $P_{2 perpendicular}$ (5). After calculating these points, we use trapezoidal similarity to compute the Euclidean distances $\overline{{{P_1}^{\prime }P}_{1 predict}}$ and $\overline{{{P_2}^{\prime }P}_{2 predict}}$ (6) and then calculate ${P_1}^{\prime }$ and ${P_2}^{\prime }$ accordingly (7). The total loss function $\mathcal{L}$ is defined as the sum of $D_1$ and $D_2$ (8).

$$\begin{gathered} {\theta }_1={\mathit{cos}}^{-1}\left({\displaystyle \frac{\overrightarrow{P_{1 true}{P}_{2 true}}·\overrightarrow{P_{1 true}{P}_{1 predict}}}{\left|\overrightarrow{P_{1 true}{P}_{2 true}}\right|\left|\overrightarrow{P_{1 true}{P}_{1 predict}}\right|}}\right), \\ {\theta }_2={\mathit{cos}}^{-1}\left({\displaystyle \frac{\overrightarrow{P_{2 true}{P}_{1 true}}·\overrightarrow{P_{2 true}{P}_{2 predict}}}{\left|\overrightarrow{P_{2 true}{P}_{1 true}}\right|\left|\overrightarrow{P_{2 true}{P}_{2 predict}}\right|}}\right) \\ {P}_{1 perpendicular}=P_{1 true}+\left|\overrightarrow{P_{1 true}{P}_{1 predict}}\right|\mathit{cos}{\theta }_1{\displaystyle \frac{\overrightarrow{P_{1 true}{P}_{2 true}}}{\left|\overrightarrow{P_{1 true}{P}_{2 true}}\right|}} \\ {P}_{2 perpendicular}=P_{2 true}+\left|\overrightarrow{P_{2 true}{P}_{2 predict}}\right|\mathit{cos}{\theta }_2{\displaystyle \frac{\overrightarrow{P_{2 true}{P}_{1 true}}}{\left|\overrightarrow{P_{2 true}{P}_{1 true}}\right|}} \end{gathered}$$

(5)

$$\begin{gathered} \overline{{P_1}^{\prime }{P}_{1 predict}}={\displaystyle \frac{\overline{P_{1 predict}{P}_{2 predict}} \overline{P_{1 true}{P}_{1 perpendicular}}}{\overline{P_{1 perpendicular}{P}_{2 perpendicular}}}} \\ \overline{{P_2}^{\prime }{P}_{2 predict}}={\displaystyle \frac{\overline{P_{2 predict}{P}_{1 predict}} \overline{P_{2 true}{P}_{2 perpendicular}}}{\overline{P_{2 perpendicular}{P}_{1 perpendicular}}}} \end{gathered}$$

(6)

$$\begin{gathered} P_1^{\prime }=P_{1 predict}-\overrightarrow{u_p}{\displaystyle \frac{\mathit{cos}{\theta }_1}{\left|\mathit{cos}{\theta }_1\right|}}\overline{{P_1}^{\prime }{P}_{1 predict}} \\ {P}_2^{\prime }=P_{2 predict}+\overrightarrow{u_p}{\displaystyle \frac{\mathit{cos}{\theta }_2}{\left|\mathit{cos}{\theta }_2\right|}}\overline{{P_2}^{\prime }{P}_{2 predict}} \end{gathered}$$

(7)

$$\mathcal{L}=D_1+D_2=\overline{{P_1}^{\prime }{P}_{1 true}}+\overline{{P_2}^{\prime }{P}_{2 true}}$$

(8)

The two predicted control points were used to define the entry and target points of the screw trajectory. Expanding the predicted control points in both directions results in at least two intersection points on the surface of each vertebra model, as shown in Figure 7. The posterior apex of these intersections was designated as the entry point of screw trajectory while the target point was positioned 45 mm from the entry point, along the direction of $\overrightarrow{P_{1 predict}{P}_{2 predict}}$.

2.4. Data Acquisition and Training Configuration

In this study, 84 vertebrae from 17 lumbar spine CT volumes were segmented for the training dataset, while 28 vertebrae from six additional CT volumes were used for the experimental dataset. CT scans were performed using two scanners: the Philips Iqon Spectral CT (Philips, Amsterdam, The Netherlands) and the Toshiba Aquilion One Vision Edition CT (Toshiba, Tokyo, Japan) at Gyeongsang National University Changwon Hospital. The in-plane voxel size ranged from 0.244 to 0.350 mm, with a slice thickness of 2 mm. Each slice had a resolution of 512 × 512 pixels. The dataset included 14 male and nine female participants, aged between 22 and 57 yr (mean = 43, median = 46). Lumbar vertebrae segmentation was performed using the 3D Slicer software (version 5.2.2, www.slicer.org) [21]. Following data augmentation, a total of 4284 point clouds representing vertebrae and corresponding ground-truth labels were generated and used for training.

The neural network was configured using TensorFlow and Keras libraries and trained on a Windows desktop PC with the following specifications: Intel i7-13700-K CPU, 31.8 GB DDR4 RAM, and an NVIDIA GeForce RTX 4080 GPU. The neural network was implemented and trained in Python (version 3.8.10) using the TensorFlow (version 2.8.0) and Keras (version 2.8.0) libraries. Key hyperparameters included a learning rate of 0.001, a batch size of 8, 300 epochs, and a dropout rate of 0.3. The network used hyperbolic tangent activation functions for hidden layers and linear activation for the output layer. Training terminated early after 10 epochs without improvement in training loss. To determine screw trajectories bilaterally, two separate neural networks were trained for the right and left pedicles. The final validation losses were 3.23 for the left pedicle network and 4.04 for the right pedicle network.

2.5. Evaluation

The performance of the trained neural network was assessed in terms of both technical and clinical accuracy. An orthopedic surgeon labeled the desired screw trajectories on unseen lumbar vertebrae models, which served as the ground truth for calculating technical accuracy.

The technical accuracy was evaluated based on translational, and angular errors. Translational error refers to the deviation between the predicted trajectory and the ground truth at the entry and target points, computed using the same method as the distances $D_1$ and $D_2$ in Figure 6. Angular error is the angle between the predicted and ground-truth trajectory for each pedicle, calculated as follows (9):

$$\theta ={\mathit{cos}}^{-1}\left({\displaystyle \frac{\overrightarrow{P_{1 true}{P}_{2 true}}·\overrightarrow{P_{1 predict}{P}_{2 predict}}}{\left|\overrightarrow{P_{1 true}{P}_{2 true}}\right|\left|\overrightarrow{P_{1 predict}{P}_{2 predict}}\right|}}\right)$$

(9)

The Gertzbein–Robbins classification was used to assess the clinical accuracy of the predicted trajectories [22]. For this evaluation, we assumed the insertion of a screw 45 mm in length with a major diameter of 6.0 mm, represented as a cylinder model of the same dimensions (Figure 8). The predicted trajectories were classified into grades A to E based on the degree of medial-cortical violation (Figure 8a) observed in the CT scan.

• Grade A: Intrapedicular insertion
• Grade B: Violation of <2 mm
• Grade C: Violation between 2 and 4 mm
• Grade D: Violation between 4 and 6 mm
• Grade E: Violation > 6 mm

3. Results

In this study, 28 unseen lumbar vertebrae models from CT scans of six patients were used to generate bilateral pedicle screw trajectories through a trained neural network. The network generated 56 pairs of points, with screw trajectories determined for each pedicle. Figure 8 illustrates a lumbar spine with screw trajectories successfully defined by the neural network.

Translational errors are summarized in

Table 1. Translational error at the entry and target points based on the labeled trajectories.

		Left		Right
Vertebra	n	Entry (mm)	Target (mm)	Entry (mm)	Target (mm)
L1	6	1.9 ± 1.1	2.6 ± 1.6	1.1 ± 0.7	2.0 ± 0.3
L2	6	1.2 ± 0.6	1.9 ± 0.7	1.5 ± 0.9	2.0 ± 0.9
L3	6	1.5 ± 0.9	2.2 ± 1.5	1.8 ± 0.7	2.4 ± 1.4
L4	5	1.4 ± 1.0	2.4 ± 1.5	1.8 ± 0.8	3.1 ± 0.8
L5	5	1.3 ± 0.5	2.1 ± 0.9	1.2 ± 0.6	1.9 ± 1.4
Total	28	1.5 ± 0.8	2.3 ± 1.2	1.5 ± 0.7	2.3 ± 1.0

. The mean translational error for the left pedicle at the entry point was 1.5 ± 0.8 mm and 2.3 ± 1.2 mm at the target point. For the right pedicle, the corresponding errors were 1.5 ± 0.7 mm at the entry point and 2.3 ± 1.0 mm at the target point. Translational errors were 52.8% and 54.0% larger at the target point than the entry point for the left and right pedicles, respectively. Angular errors are detailed in

Table 2. Angular error between the predicted and the labeled trajectories.

Vertebra	n	Left (deg)	Right (deg)
L1	6	4.4 ± 2.9	2.9 ± 0.8
L2	6	2.7 ± 1.2	3.8 ± 1.7
L3	6	3.5 ± 3.2	4.5 ± 2.2
L4	5	5.2 ± 2.1	5.3 ± 1.0
L5	5	3.1 ± 1.8	2.8 ± 1.3
Total	28	3.5 ± 2.3	3.9 ± 1.7

. The neural network for the left pedicle deviated by 3.5 ± 2.3° from the ground truth, and for the right pedicle, the deviation was 3.9 ± 1.7°.

Clinically, 52 of the 56 cylinder models along the predicted trajectories did not breach the medial wall of the pedicles. However, four trajectories showed medial-cortical violations of <2 mm, classified as grade B (

Table 3. Clinical accuracy based on Gertzbein–Robbins classification.

Grade	Left (n)	Right (n)
A	26	26
B	2	2
C	0	0
D	0	0
E	0	0
Total	28	28

). Figure 9 shows axial slices of the screw trajectories classified as grade B. The slices labeled (b), (c), and (d) in Figure 9, from the same patient, demonstrate pedicle radii < 6 mm.

4. Discussion

This study introduces a method for preoperative pedicle screw trajectory planning using a machine learning-based neural network trained on point cloud data. We evaluated the performance of the neural network by comparing screw trajectories generated by the network to manually defined trajectories for unseen vertebrae.

Preoperative trajectory planning assisted by computers offers a streamlined surgical workflow and greater planning accuracy than manual methods, which require additional steps and depend on the surgeon’s clinical experience. In contrast, our approach can reduce the time spent on manual planning by directly generating accurate screw trajectories, requiring only minor adjustments.

Previous studies have assessed various methods for computer-assisted screw trajectory planning and evaluated their frameworks. Knez et al. found that the interclass variability between surgical planning by two surgeons and parametric modeling was within the intraclass variability of individual surgeons [10,11]. Qi et al. achieved a 93% success rate in clinical evaluations of their automated path planning method [13]. Cai et al. reported a validated mean squared error of 1.340 for the six regression values in their deep neural network, which were reconstructed as 3D entry and direction points [12]. Zhang et al. observed angular deviations and point-to-point distances between manually defined trajectories and vertebral pose estimation-based trajectories for lumbar spines with scoliosis. Their angular deviations were reported as 4.77°, 5.53°, 5.19°, 4.11°, and 7.61° for L1–L5, respectively. For L1–L4, the mean minimum point-to-point distance was 0.79 mm, and the mean maximum was 2.47 mm, which were located around the middle of the trajectory and at the anterior end of the screw tip [14]. Massalimova et al. reported an entry point offset (∆EP) of 3.53 ± 1.0 mm and an angular deviation (∆θ) of 7.31 ± 3.34° using a point cloud derived from CT meshes [15]. Compared with this study, previous works incorporated deep learning techniques as submodules within a trajectory determination framework. Qi et al. utilized a deep neural network to segment individual vertebrae and subsequently established a local coordinate system for each vertebra [13]. Zhang et al. employed deep learning–based models for both vertebral segmentation and pose estimation [14]. Massalimova et al. employed PointNet++ to segment anatomical landmarks [15]. Chang et al. adopted PointNet architecture to identify entry and exit clusters of vertebrae point clouds [23]. In contrast, Cai et al. adopted a similar approach to this study, where the neural network directly predicts the screw trajectory [12].

Our findings align with results of previous studies, demonstrating that translational errors exhibited greater deviations at the anterior end of the screw trajectory than at the posterior end. Unlike previous approaches, which primarily employ machine learning as submodules for anatomical segmentation or candidate region identification, our method directly applies and evaluates a machine learning model for the screw trajectory prediction. Moreover, we trained the neural network using a novel loss function, specifically designed to accurately model the ground truth of 3D straight-line trajectories.

The computational time of the proposed framework was not considered as a primary metric for evaluation. This study focuses on validating the feasibility and generalization capability of the neural network itself, rather than on optimizing an end-to-end clinical workflow. The proposed framework involves manual CT segmentation of vertebrae, in contrast to previous studies that used automated segmentation via another neural network [12,13,14]. Manual segmentation inevitably involves human error, which may propagate to the neural network and affect final performance in terms of accuracy. If integrated with both segmentation and trajectory determination, computer-assisted screw trajectory planning could be incorporated directly into the surgical workflow, as mobile intraoperative CT scan devices are readily available. However, the neural network used in this study generates only two control points based on the geometrical features of each vertebra, excluding essential anatomical considerations such as the radius of the pedicle isthmus. Consequently, the network is unable to consistently avoid medial-cortical and lateral-cortical violations. In some cases, shown in Figure 9, the predicted trajectory caused a medial wall violation, but the pedicle size was thinner than the screw diameter. If performed in the human body, screw fixation could occur without damaging the medial wall due to the viscoelasticity of the bone. In addition, even if the pedicle size was smaller than the screw size, we were instructed to insert the screw laterally to reduce medial wall violation if possible. Furthermore, while previous studies have optimized pedicle screw planning by accounting for both the screw trajectory and its dimensions (e.g., diameter and length), our study focused on defining the screw trajectory, parameterized by a 3D line equation derived from the ground truth. The proposed method relies primarily on local geometric features of individual vertebrae, rather than on global spinal alignment or intervertebral relationships, which may influence optimal screw orientation in complex deformities. Additionally, augmentation was limited to rotations within ±30°, which restricts robustness to wider pose variations. Despite the data augmentation technique adopted in this study, limited dataset size may restrict the ability to fully demonstrate generalizability. Furthermore, all datasets were collected from a single medical center and an orthopedic surgeon, which may limit data diversity and acquisition-related noise variability. Also, the number of input points was uniformly sampled from each vertebral surface to construct the input point cloud, without a systematic evaluation of sampling density, which may influence both prediction accuracy and computational efficiency.

Given these limitations, we propose several directions for future research to enhance the surgical planning framework. The integration of spinal segmentation [24,25] with the neural network developed in this study could fully automate the surgical planning process, making it suitable for surgical navigation systems or robotic guidance. Such an approach could be applied intraoperatively, eliminating the need for preoperative CT scans and significantly reducing the time spent on surgical planning compared with manual methods. Accordingly, a comprehensive analysis of computational performance—from CT acquisition to final trajectory generation—will be addressed in future studies as part of a fully integrated framework. With sufficiently large and diverse datasets, more robust augmentation methods covering broader orientations, or an additional framework for orientation normalization, could be explored to improve general applicability. To further optimize surgical planning, collecting training datasets from multiple medical centers, along with parameter tuning through sensitivity analysis, could improve data diversity and generalizability. Additional patient-specific factors such as pedicle radius and safety margins [26] should be incorporated when determining the screw trajectory and dimensions. Furthermore, incorporating surrounding anatomical structures, including intervertebral disks and nerve root foramina, could provide additional anatomical constraints for safer and more clinically applicable trajectory planning. Diagnostic factors, such as osteoporosis, can also refine trajectory labeling. Preoperative screw trajectories for osteoporotic vertebrae, for instance, may require different inclinations of the screw direction on the axial plane [27].

5. Conclusions

This study proposes a framework for preoperative lumbar pedicle screw trajectory determination using the deep neural network PointNet. The major contribution of this study is the modification of the conventional architecture of PointNet and the design of a novel loss function optimized for linear screw trajectory prediction. The trained neural network generates feasible screw trajectories, even when the orientation of vertebrae differs. Additionally, it achieved promising clinical accuracy, which can be utilized in surgical navigation systems and robotic guidance. We expect that automated surgical planning will streamline the comprehensive surgical procedure by integrating another neural network for spinal segmentation. Simultaneously, the anatomical features of vertebrae should be considered in surgical planning to establish a more optimized framework.