To address the image-assisted localization problem during robot-assisted pedicle screw implantation in spinal surgery, this paper proposes a machine learning-based pedicle screw implantation planning method. This method utilizes a convolutional neural network (CNN) to learn and train on spinal computed tomography (CT) images. By establishing a neural network model, adjustment parameters between layers within the network are determined. Feature extraction and classification of sample images are then performed, and cross-validation is used to train the sample data and verify the correctness of the CNN model. Machine learning methods are used to identify suitable image regions for pedicle screw implantation planning within the CT images, quickly locating the safe constraint area for screw implantation. Appropriate image processing methods are then used to plan the screw implantation operation. Surgeons only need to complete the final surgical task planning based on the screw implantation plan within the safe constraint area, significantly improving surgical efficiency.
1 Introduction
Pedicle screw implantation surgery is generally used to treat spinal instability and spinal cord nerve injury caused by severe thoracic and lumbar vertebral fractures. Due to the complex structure of the spinal lesion site and the presence of nerve tissue, the failure of the surgery will have irreversible consequences. At present, the screw is mainly inserted into the vertebral body through open pedicle screw implantation surgery. However, due to the possibility of transverse process missing, too large or too small, facet joint hyperplasia, convergence, or being bitten off in previous surgeries, it will be difficult to determine the entry point of the pedicle screw, and open surgery is not conducive to the healing of the patient's wound. According to foreign literature statistics, the cumulative incidence of various complications caused by traditional spinal surgery is 52.58%[1], while the incidence of nerve dura mater injury in dangerous areas such as the thoracic spine is as high as 36.4%[2]. With social development and technological progress, modern surgical techniques are developing towards minimally invasive and precise directions, and there is an urgent need for spinal surgery robot technology to meet the requirements of precise operation and safety control in modern spinal surgery. At present, our research team has successfully developed a spinal surgery robot system, which can assist doctors in completing pedicle screw implantation surgery[3]. Based on the minimally invasive spinal surgery robot system, this paper proposes a machine learning-based pedicle screw implantation planning method, which further optimizes the traditional planning method and greatly reduces the time and workload of doctors in surgical planning.
In robot-assisted pedicle screw implantation surgery, when doctors plan pedicle screw implantation, they need to repeatedly view computed tomography (CT) images on the image operation interface of the surgical navigation software and continuously adjust the position of the pedicle screw implantation in the transverse, sagittal, and coronal views of the vertebral body to complete the surgical planning. In this process, doctors need to spend a lot of time finding and determining the appropriate position for pedicle screw implantation. This not only requires doctors to be very familiar with the navigation software, but also increases the operation time, increases the workload of doctors, and is not conducive to the smooth progress of the operation. With the development of machine learning applications in various fields, the application of machine learning in the medical field has great development potential [4]. Machine learning can be used to determine the location and type of lesions [5-7]. Applying machine learning to medical images for the diagnosis of related diseases can be very helpful. For example, the Department of Medicine at Seoul National University in South Korea critically reviewed the application of machine learning classifiers in the brain structure magnetic resonance imaging of patients with mood disorders from a clinical perspective [8]; researchers at the University of Texas at Dallas studied the application of machine learning in computational cancer biology [9]. Currently, the application of machine learning in the medical field has become a research hotspot in China. For example, Nanjing University has studied the application of machine learning to classify lung cancer and normal images [10]; Shanghai Jiao Tong University has also carried out research on applying machine learning to stereo brain images [11], using machine learning methods to obtain the corresponding features of brain images, thereby proposing a new registration framework that can improve the registration accuracy of stereo brain images. Previous studies have mostly used machine learning for the segmentation of soft tissue images, but there have been no reports on its application in spinal surgery.
To address the aforementioned issues, this paper proposes a rapid robot-assisted method for pedicle screw implantation planning. First, machine learning is used to identify suitable locations for pedicle screw implantation surgery in the patient's CT images, quickly locating the safe constraint area for screw implantation. Then, screw implantation planning is performed on the located image. The surgeon only needs to complete the final surgical task planning within the safe constraint area, reducing the time and workload spent on surgical planning. Applying machine learning to pedicle screw implantation surgery enables faster determination of the surgical location, thus quickly assisting the surgeon in completing surgical planning, significantly reducing preoperative preparation time and improving surgical efficiency.
2 Machine Learning Models
2.1 Convolutional Neural Networks
The most common machine learning models and methods currently include autoencoders[12], restricted Boltzmann machines[13], deep belief networks[14], and convolutional neural networks (CNNs)[15]. Among them, CNN is one of the machine learning models under supervised learning and has very strong adaptability. This algorithm is particularly suitable for mining local features of data, extracting global training features and classifying them. It is widely used in image recognition and classification. Therefore, this paper uses convolutional neural networks to recognize spinal CT images. CNN is essentially a multi-layer supervised learning neural network, mainly divided into input layer, hidden layer and output layer. Among them, the convolutional layer and pooling layer in the hidden layer are the core modules for realizing feature extraction of convolutional neural networks. The lower layers of the convolutional neural network are composed of convolutional layers and pooling sampling layers alternately, extracting features layer by layer; the higher layers are composed of fully connected layers and logistic regression classifiers. The input of the first fully connected layer is the feature image obtained by the lower convolutional layer and subsampling layer after extracting features from the input image. The final output layer is a classifier. Before the classifier, logistic regression, softmax regression, or even support vector machine activation functions are typically used to activate the features extracted from the fully connected layer, thereby classifying the input image.
2.2 Convolutional Neural Network Model Design
The convolutional neural network architecture used in this paper is shown in Figure 1. The entire convolutional neural network has 8 layers, mainly divided into input layers, hidden layers, and output layers. Among them, the hidden layers are mainly divided into the first 5 convolutional layers and the last 3 fully connected layers.
Figure 1. Convolutional Neural Network Architecture
2.2.1 Input Layer
The input layer primarily takes labeled sample images as input to the entire convolutional neural network and serves as the label for the final fully connected layer. The sample images, processed by the network, produce a feature vector at the final layer. This feature vector is compared with the labels to calculate the loss function, which in turn adjusts the parameters of each layer. In this paper, the input image size is 255×255 pixels.
2.2.2 Hidden Layer
Convolutional layers 1 and 2 perform similar operations, including convolution, normalization, and activation. Pooling layers 1 and 2 follow the convolutional layers, and the last three convolutional layers perform similar operations, including convolution and activation. The roles of convolutional and pooling layers are: firstly, to preserve invariance, including rotation, translation, and scaling; secondly, to reduce parameters and computational cost while preserving features, achieving dimensionality reduction, preventing overfitting, and improving generalization ability. Multi-layered convolution and pooling operations can increase the depth of the entire convolutional neural network and reduce the number of parameters. Simultaneously, different convolutional and pooling layers can provide different receptive fields, capable of sensing features at different scales. A neuron in a multi-layered hidden layer is obtained by multiplying multiple neurons in the previous layer by their weights and adding a bias, resulting in weight sharing and expanding the local receptive field. During the learning process, the weights and biases are iteratively adjusted in reverse to find the optimal solution for the output function, thus minimizing the final loss function. To prevent the network gradient from decreasing or even vanishing, fully connected layers and regression layers are required after passing through certain convolutional layers. The image operation process of hidden layer 1 is shown in Figure 2. The image operations of other hidden layers are similar, except for the size of the convolution kernel.
Figure 2 Image computation of hidden layer 1
In hidden layer 1, the convolution operation uses three convolution kernels, each 11×11 pixels in size, with a stride of 4×4 pixels. Larger kernels and strides result in smaller output feature sizes, which helps to speed up the first layer's convolution operation. The size of the output feature map after convolution and pooling operations can be obtained using formulas (1) and (2), resulting in a final output feature map size of 64×64 pixels. The number of output feature maps is set to 96.
Where Nh and Nw are the length and width of the output data; Ih and Iw are the length and width of the input data; Ph and Pw are the length and width of the padding; Kh and Kw are the length and width of the convolution kernel; and Sh and Sw are the length and width of the convolution stride.
After convolution, the data needs to be normalized. The purpose of normalization is twofold: firstly, to avoid the problem of a smaller gradient due to a larger output of the next activation operation during the learning process of the convolutional neural network. Because in machine learning, the smaller the gradient, the slower the learning rate. If the previous convolutional layers are not normalized, the shallow network will basically not learn, while the deep network will keep learning. Secondly, to prevent the model's generalization ability from decreasing due to different data distributions or different distributions of training and test data during training. The normalization range needs to be adjusted accordingly to adapt to the activation function. Since the activation function used below is ReLU, the normalization range is 0 to 1. The normalization process is as follows: first, the mean and variance of the input feature map are calculated using formulas (3) and (4), and then the data is standardized according to formula (5).
In order to keep the current output unchanged during forward propagation, assume training parameters y and B so that the output of the feature map remains unchanged and only the training parameters are recorded, as shown in formula (6).
After normalization, the resulting feature map needs to undergo activation operations, i.e., nonlinear operations. Adding nonlinear units using activation functions can reduce network overfitting during the learning process. Commonly used activation functions include Sigmoid, Tanh (hyperbolic tangent), ReLU (Rectified Linear Units), and ELU (Exponential Linear Units). This paper uses the ReLU function, as shown in Figure 3. By normalizing the data to 0 to 1, the gradient of the ReLU function is avoided when the x value is less than 0.
ReLU function: y = max(0, x)
Figure 3 ReLU excitation function
2.2.3 Output Layer
The final classification layer, or output layer, transforms the features learned by the learning network into feature vectors according to the classification categories of the training samples. Since this paper classifies samples into 8 categories, the feature vector obtained by the output layer is 8-dimensional, with each dimension revealing the probability of a sample image belonging to that category. A final fully connected layer is added before the output layer, and a softmax activation operation is performed to obtain the final feature vector, i.e., the fully connected layer 8. This final 8-dimensional feature vector is obtained by convolutional operations on the feature maps learned by the preceding neural network (4096 feature maps in this paper). The last layer is the classification function. The classification function is mainly used to calculate the test accuracy and loss value to measure the accuracy of the entire convolutional neural network. The network diagram of the output layer is shown in Figure 4.
Figure 4. Schematic diagram of the output layer network
2.3 Loss Function Calculation and Backpropagation Algorithm Parameter Adjustment
2.3.1 Calculation of the loss function
This paper's convolutional neural network addresses an 8-category classification problem, so the final output layer should have 8 neurons. The neuron corresponding to the true category of the sample outputs a probability value close to 1, while the neurons outputting the non-true category should output a probability value close to 0. The sum of the probabilities of the 8 categories equals 1. The activation function used in the final fully connected layer of this convolutional neural network is Softmax, defined as shown in equation (7).
Where nL is the number of neurons in layer L, i.e., the output layer; zL is the value of the i-th neuron; and aL is the value of the i-th neuron after activation.
After activation, the output value of aL is guaranteed to be in (0, 1), and the normalization factor of the activation function ensures that the sum of all output neurons is 1. For the Softmax activation function, this paper selects the log-likelihood function as the loss function, defined as shown in formula (8).
Where W and b are the weights and biases in the convolution operation, respectively; yk represents whether the theoretical output is consistent with the actual output. Assuming that the actual output of the training sample is of class i, the value of yk is as shown in formula (9).
Formula (8) can be transformed into formula (10), where i is the actual class of the training sample.
2.3.2 Backpropagation Algorithm Parameter Adjustment
Adjusting weights and biases using the backpropagation algorithm is a key step in enabling convolutional neural networks to obtain the optimal solution during the learning process. The loss function obtained through forward propagation is optimized using a specific method, iteratively calculating the derivative of the loss function with respect to the weights and biases of each layer in reverse propagation, and then updating it. After multiple iterations, the final loss function is minimized, thus achieving the optimal output function. When propagating the loss function backward, the gradient expression with respect to the weights W and biases b must first be obtained. The gradient calculation of W is shown in equation (11).
Wherein, the value of the i-th neuron in the L-th layer is:
Therefore, the gradient of the final loss function with respect to W is:
Similarly, the gradient calculation for the bias b can be obtained as shown in formula (14).
Based on the gradient of the obtained weights and biases, a learning rate is introduced, which can correct the weights W and biases b in the direction of the gradient. The corrected expressions are shown in formulas (15) and (16).
3. Classification of spinal bone CT image samples
3.1 Sample classification criteria
Machine learning is divided into supervised learning and unsupervised learning. Supervised learning uses existing training samples to train an optimal model. This paper uses supervised learning, so sample classification is necessary. For spinal CT images, the transverse section is very suitable for determining whether pedicle screw implantation is appropriate. The transverse section allows for rapid localization of the safe constraint area for pedicle screw implantation, and its features are relatively clear, making it suitable for sample image classification. To ensure that the final classified samples have distinct features between classes and to obtain the desired classification, the following classification criteria are adopted.
Figure 5. Sample feature distribution
Figure 6. Features contained in each sample image
As shown in Figure 5, the features of the cross-sectional image of the spine are divided into 9 regions, each containing one feature. Samples are classified based on whether they contain all 9 features or a combination of several features from those 9. Features 7, 8, and 9 are the precision features for sample classification. This paper classifies images containing the precision features and other features as target images, and images not containing all the precision features as non-target images. Further subdividing non-target images based on the presence of different other features improves the learning efficiency and accuracy of convolutional neural networks in machine learning. As shown in Figure 6, the sample images are divided into 8 categories based on whether they contain features 1 through 9.
Figure 7. Effects of different filtering processes
Because sample images are affected by factors such as CT scan angle and scanning jitter during acquisition, certain preprocessing is required before image classification after establishing classification criteria. To reduce the noise impact of jitter on sample images, image denoising is necessary. Common denoising methods include mean filtering and median filtering. Figure 7 shows the results of denoising noisy images using mean filtering and median filtering, respectively.
To address the issue of sample image position shifts caused by different scanning angles, the grid should be translated during the segmentation of feature regions to accurately capture and classify the images. When creating the grid, the center of the largest connected region in the image is first located, corresponding to the center of the spinal cord within the spine. This location is then used as the center to create the grid for segmenting the feature regions. Through this image preprocessing, eight categories of sample images are obtained, as shown in Figure 8. Sample 1 is the target image, and the rest are non-target samples.
Figure 8 Sample classification results
3.1 Sample Image Training and Result Analysis
3.2.1 Training Methods
The main training methods for convolutional neural networks include cross-validation, hold-out, and bootstrap. Cross-validation, also known as K-fold cross-validation, divides the dataset into K equal subsets, with no overlap between subsets. During each training iteration, K-1 subsets are used as the training set, and the remaining subset is used as the test set. The entire dataset can be trained and tested K times, and the final loss is the average of these K training iterations. Empirically, K is usually set to 10. Cross-validation is suitable for small datasets. Hold-out divides the dataset into two disjoint subsets, one as the training set and the other as the test set. The loss value obtained from the test set is used as the test error. This method is suitable for large datasets. Bootstrap assumes a dataset contains m samples. The training set is obtained by randomly drawing m samples with replacement, and the samples not included in the training set are used as test values. This method is suitable for small datasets but has drawbacks, such as the potential for introducing estimation bias. In summary, since the sample dataset used in this paper is relatively small, and cross-validation is more suitable for training with smaller datasets, this paper adopts cross-validation as the training method, as shown in Figure 9.
Figure 9. Cross-validation training principle
Training process
After preparing the training images and defining the network model, the next step is to continuously train the network model using the training images as input to obtain the final optimized output model. During training, some parameters need to be set, as shown in Table 1. Because this paper uses cross-validation, the entire training process requires 10 iterations. After each complete training run, the loss value and accuracy of the test sample set are recorded. The entire training cycle is 150, meaning it has undergone 150 iterations. Furthermore, the initial learning rate is 0.0001, and it decreases to 0.2 times the original rate every 15 cycles. Because the model parameters are gradually optimized during training, a large learning rate can cause fluctuations in the backpropagation adjustment of weights and biases, preventing the model from achieving optimality. The network is trained using a GPU with a minimum batch size of 128.
Figure 10. Model changes during network training.
Figure 10 shows the changes in loss and accuracy on the test set recorded during network training. As can be seen from the curves in the figure, the loss function converges rapidly at the beginning of training, then slows down and gradually approaches 0 in the middle of training. This is consistent with the optimization process of the network model, which adjusts the training parameters through backpropagation to minimize the loss function. The final loss value of the entire network stabilizes at around 0.26. The trend of the training accuracy on the test set is the same as that of the loss value, showing a gradual increase and eventually stabilizing at around 92%. Considering the changes in loss and accuracy during network model training, the model optimization effect is good, and the final model output meets the training expectations. The next step is to use the trained model for validation on the validation set. The validation set data has no overlap with the sample dataset, ensuring that the validation process is not affected by the sample data.
3.2.3 Model Validation
To validate the trained model, a validation set was formed by taking several images that did not overlap with the sample dataset. The validation dataset contained 10 images each of Sample 1 and Sample 3, which were labeled and classified using the trained model. The final classification results were compared with the labels to calculate the final prediction accuracy. Figure 11(a) shows the validation image labeled Sample 1 in the validation set. Under the trained model, the prediction results were: 9 out of 10 validation images were predicted as Sample 1, and 1 image was predicted as Sample 2, with a prediction success rate of 90%. Figure 11(b) shows the validation image labeled Sample 3 in the validation set. 8 out of 10 validation images were predicted as Sample 3, and the remaining 2 images were predicted as Sample 5 and Sample 6. From the prediction results of the validation set, it can be concluded that the network model used in this paper can effectively recognize images, with a high recognition rate for the target image, Sample 1. Through the effective recognition of Sample 1, the safe constraint area for pedicle screw implantation can be quickly located.
Figure 11. Prediction accuracy of the network model on the validation set.
3. Pedicle screw implantation assisted planning
3.1 Planning Methods for Pedicle Screw Implantation
When performing pedicle screw implantation surgery on the spine, the screw insertion point, insertion angle, and screw length vary in the cervical, thoracic, and lumbar spine. For pedicle screw implantation surgery in the lumbar spine, many well-known researchers in the medical community at home and abroad have proposed effective methods. For example, Xu et al. [16] proposed that the intersection of two perpendicular intersecting lines should be the insertion point, with the vertical line being the extension line through the interarticular space and the horizontal line being the bisector of the transverse process. Kawaguchi et al. [17] proposed that the insertion point should be located at the intersection of the vertical line along the outer edge of the superior articular process of the fixed vertebra and the bisector of the transverse process. Domestic scholars such as Shan Yunguan et al. [18] proposed the "cross" positioning method. For the 1st to 4th vertebrae, a vertical line is drawn at the midpoint of the posterior edge of the mastoid process of the articular process, and a horizontal line is drawn on the accessory process of the transverse process. The intersection of the two lines is the insertion point. For the 5th vertebra, the insertion point is at the midpoint of the deepest part between the mastoid process and the accessory process of the transverse process of the superior articular process. The above methods all use the transverse process and articular process as references. For the 1st to 3rd vertebral bodies, the inclination angle of the screw insertion ranges from 5° to 10°; for the 4th to 5th vertebral bodies, the inclination angle ranges from...
10°～15°. Only when the screw insertion depth ensures that the screw length reaches 80% of the pedicle axis length can sufficient mechanical strength be guaranteed. If it is too long, it can easily penetrate the contralateral cortex of the spine and damage other tissues. Therefore, the length is generally about 83% of the total length from the insertion point to the anterior cortex of the vertebral body. The location of the screw's termination point...
The deviation from the centerline is 1/5 of the vertebral body width. Figure 12 is a schematic diagram of pedicle screw implantation in the lumbar spine, mainly judging the appropriateness of the pedicle screw implantation plan from the transverse and sagittal planes. This paper will refer to the above-mentioned methods for selecting the screw angle, insertion depth, and insertion point, and use the target image extracted through machine learning to plan the pedicle screw implantation.
4.2 Target Image Pinning Planning
After extracting the target image using a convolutional neural network, to automatically perform coarse-graining for pedicle screw implantation, feature extraction, such as the center line of symmetry, is required. Then, based on the extracted features, the aforementioned implantation method is used to perform corresponding calculations to extract the screw path. To effectively extract features from the target image, certain image processing is necessary, including binarization, opening/closing operations, and filling. As shown in Figure 13, firstly, the original target image is binarized to separate the features of interest from the background. Then, opening operations are used to remove noise from the background region after binarization, and closing operations are used to erode the opened image to smooth it and enhance edges. Finally, filling operations are used to fill holes in connected regions to complete the image.
Figure 13 Processing of the target image
The centerline is extracted from the processed image. Extraction of the centerline requires two centroids: one is the centroid of the spinous process anterior end, located at the centroid of the smallest connected region in the image, denoted as point A; the other is the centroid of the vertebral body, located at the centroid of the largest connected region in the image, denoted as point B. As shown in Figure 14, connecting points A and B forms the centerline. The required vertebral body insertion depth for screw implantation is located on the centerline. The center point is the location of the vertebral body at 80% of its length passing through the centerline, i.e., the location of the green dot in the figure, denoted as point C. The straight line perpendicular to the centerline from this point represents the minimum depth to which the pedicle screws on both sides should reach.
Figure 14 Feature centerline extraction
Assuming the equation of the centerline is given, then the equation passes through points A and B, which satisfies formula (17).
The line where the screw terminates intersects the center line and passes through point C. Assuming the equation of the line is given, then the equation satisfies formula (18).
After obtaining the straight line at the screw termination point, the vertebral body width L at the location of the straight line can be calculated, and the offset distance between the screw implantation termination point and point C is L/5. Given the coordinates of the termination point, the location of the termination point can be obtained by solving the equation in formula (19).
The coordinates of the two termination points on the left and right of the relative centerline are obtained by solving formula (19), and are denoted as and , respectively. For the lumbar segment, the inclination angle of the screw is 10° to 15°. This paper uses a uniform inclination angle of 15° as the standard for planning. Extend the straight line where the screw path is located to the straight line where point A is located. This straight line is perpendicular to the centerline. Assuming that it is the starting point of the termination point E1, it satisfies equation (20). Solving the equation will give S1. Similarly, S2 can be obtained.
in,;
The line connecting the endpoint and the starting point is the planned nail path. Figure 15 shows the nail path planning completed in the binary image and the original image.
Figure 15 Nail Track Planning
5. Comparative analysis with similar studies at home and abroad
The machine learning-based robot-assisted pedicle screw implantation planning method mentioned in this paper differs from existing research at home and abroad. For example, the machine learning method introduced by DeBruijne[6] is mainly applied to image diagnosis, disease prevention and risk assessment, and has conducted in-depth research on the difficulties and problems encountered in the application of machine learning methods in the medical field. The primary problem is the influence of different imaging protocols on sample data. For different spinal imaging methods, the proposed solution is conducive to the improvement of network learning in this paper. Insufficient label persuasiveness is an important problem in medical image recognition and classification. The sample image classification standard in this paper classifies the sample images well and gives the sample images strong persuasive labels, thus solving this problem. Using machine learning as a black box for diagnosis and evaluation is risky. This is because in a learning system in a high-dimensional feature space, it is easily affected by confounding factors. Solving this problem requires adding remedial measures to the system. The remedial measure of the automatic planning method proposed in this paper is the doctor's final planning, which provides a guarantee for the correctness of the machine learning classification results. Compared with Anjie's [19] study on the whole brain white matter of patients with medial temporal lobe epilepsy using machine learning, this paper not only has clear classification criteria for sample classification, but also optimizes the network architecture design according to specific samples, which greatly reduces training time and improves the accuracy of image recognition.
6 Conclusions
This paper employs machine learning to identify images of the safety constraint area for pedicle screw implantation. First, a convolutional neural network (CNN) is trained on sample images. Then, the trained model is tested and validated on a validation set of images. After obtaining the target image, image features are extracted using binarization and opening/closing operations. Finally, based on commonly used medical methods for pedicle screw implantation planning, mathematical operations are used to calculate the screw path positions and complete the screw path planning. Surgeons only need to plan the final surgical procedure based on the screw implantation plan within the safety constraint area, reducing the time and workload spent on surgical planning. Due to significant individual differences among patients and the diverse vertebral body shapes across different spinal segments, and the relatively limited sample images collected in this study, which did not cover all spinal segments, some planned screw paths showed deviations or significant errors. Therefore, further research is needed to collect more sample images for training and to improve the designed CNN to enhance its learning efficiency. (Article excerpted from *Integrated Technology*)
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