CN113940752B - Multi-angle projection-based pedicle screw optimal path planning method - Google Patents

Abstract

The present invention provides a multi-angle projection-based optimal path planning method for pedicle screws, comprising the following steps: S1: perform simulated two-dimensional projection on pedicle images at multiple angles to obtain multiple two-dimensional projection images; S2: determine a safe screw placement area in each two-dimensional projection image, and then calculate the optimal placement trajectory of the pedicle screw in the projection image; the optimal placement trajectory of the pedicle screw is located in the safe placement area; The present invention uses the method of calculating the optimal screw trajectory on multiple two-dimensional projection surfaces, and then reconstructing the three-dimensional screw trajectory to plan the optimal insertion path of the pedicle screw, and can accurately and quickly calculate the optimal three-dimensional insertion path of the pedicle screw.

Description

An optimal path planning method for pedicle screws based on multi-angle projection

technical field

The invention belongs to the field of medicine, in particular to a multi-angle projection-based optimal path planning method for pedicle screws.

Background technique

The placement of spinal pedicle screws is a common procedure for the treatment of various spinal traumas, tumors, deformities and degenerative diseases. Screws must be accurately placed through the narrow passage of the pedicle, which is close to the spinal cord, dural sac, nerve roots, and blood vessels. Improper screw placement can lead to neurological complications, including paralysis, blood loss, and death. There are approximately 580,000 spinal internal fixation operations per year in my country, of which pedicle screw implantation accounts for more than 65%. Relevant studies have confirmed that the risk of spinal surgery is high, and the risk of postoperative complications is 16.4%. Related studies have shown that the misplacement rate of lumbar pedicle screw placement ranges from 5% to 41%, and related literature reports that the accuracy of manual screw placement can be as low as 68.1%. In recent decades, with the great advances in surgical technology and technology, spinal pedicle screw placement has entered the era of minimally invasive surgery, and minimally invasive spine surgery (Minimally Invasive Spine Surgery, MISS) has become increasingly popular. In the past decade, robotic systems have played a huge role in the field of surgery, and innovative applications in surgery have also flourished. Early applications of robotic systems in these areas stimulated innovative applications of surgical robotics in other branches of surgery, including spine surgery. The development of surgical robot technology in the field of spinal surgery has expanded the field of vision of spinal surgery, making it suitable for many complex spinal surgery. The working stages of robot-assisted spinal surgery mainly include: registration and fusion of preoperative images and intraoperative images; pedicle screw position planning; screw channel positioning and screw implantation. In recent years, domestic and foreign researchers have done a lot of related research in this field and obtained many valuable research results.

In the field of spine surgery, the real-time image navigation system improves the safety and accuracy of spine surgery. The application of high-quality CT image registration and stereotaxic 3D cameras enables timely 3D mapping of the spine during surgery and real-time tracking of surgical instruments. In most cases, MISS internal fixation with percutaneous pedicle screws is guided by intraoperative fluoroscopy, which can achieve high accuracy of pedicle screw fixation, but this method will expose surgeons and patients to radiation for a long time. The application of CT-based navigation system can reduce the risk of radiation exposure of surgeons and patients by more than 90% during the operation, and at the same time, it can ensure higher accuracy of pedicle screw fixation. Spinal surgery usually uses percutaneous pedicle screw fixation. The application of navigation system makes the operation process have high reliability and safety. Many studies have shown that the current navigation system based on CT images has high reliability and can be applied to most spinal surgery. It can reduce surgery-related complications, including the rate of reoperation.

Robotic systems are widely used in the field of spine surgery due to their precision, reliability, and effectiveness during surgical procedures and their ability to perform quickly. Combined with a navigation system, the robotic system could theoretically ensure a more precise surgical path and reduce soft tissue damage. Pedicle screw fixation is a typical application for robotic systems. Several related studies have shown that the accuracy of robotic system-assisted pedicle screw fixation is superior to fluoroscopy-guided pedicle screw fixation, and several systematic reviews and meta-analyses have been published comparing robot-assisted and traditional pedicle screw placement, showing that the effect of robot-assisted screw placement is better than traditional manual screw placement. Reports have clearly pointed out that the accuracy of robotic system placement of pedicle screws is generally high, as high as 94%-98%. In addition, robot-assisted spinal surgery can overcome the psychological barriers and physical fatigue of surgeons during surgery, and provide better clinical and surgical results. However, although image-guided robotic surgery is safer and more efficient, there are still deficiencies in preoperative pedicle screw trajectory planning. First, current commercial robotic surgery systems generally lack automation, requiring doctors to manually plan the direction and posture of screw trajectories on preoperative or intraoperative images. Second, image-guided robotic systems require accurate registration between surgical plans and in situ images. Image registration for robotic surgery is a challenging task.

Contents of the invention

Aiming at the technical problems existing in the prior art, the present invention provides an optimal path planning method for pedicle screws based on multi-angle projection. The optimal trajectory of the pedicle screws is planned by calculating the optimal trajectory of the screws on multiple two-dimensional projection surfaces and then reconstructed into three-dimensional screw trajectories, so that the optimal three-dimensional insertion path of the pedicle screws can be accurately and quickly calculated.

The technical scheme adopted in the present invention is: a method for planning the optimal path of pedicle screws based on multi-angle projection, comprising the following steps:

S1: Simulate two-dimensional projections of pedicle images from multiple angles to obtain multiple two-dimensional projection images;

S2: Determine the safe screw placement area in each two-dimensional projection image (for example, set the vertebral body avoidance area, outside this area is the safe screw placement area), and then calculate the optimal pedicle screw insertion trajectory on each projection image;

S3: The three-dimensional optimal path of the pedicle screw is formed by reconstructing the two-dimensional projection images from multiple angles.

Further, in the step S1, the number of the two-dimensional projection images is at least two. The two-dimensional projected image may be two two-dimensional projected images of orthogonal projection, or two or more two-dimensional projected images of non-orthogonal projection. Increasing the number of two-dimensional projection images can improve the accuracy of the final three-dimensional optimal path of the pedicle screw, but the corresponding calculation amount will increase.

Further, in step S1, the posture of the pedicle is corrected so that it is parallel to the plane of the upper lamina or intervertebral disc. Usually, the posture of the pedicle on the CT image will have different degrees of deflection. Therefore, the posture of the pedicle needs to be corrected before the two-dimensional projection of the pedicle at multiple angles, so as to increase the accuracy of the optimal pedicle screw placement trajectory calculated on the two-dimensional projection.

Further, in step S2, the avoidance area of the vertebral body is simplified to the boundary points on both sides of the pedicle, and the optimal pedicle screw insertion trajectory is a straight line, as follows:

ω.x+b=0

Among them, ω and b are the parameters of the straight line,

The clinical constraints of the pedicle screw insertion trajectory are that the straight line is inside the pedicle and does not pass through the vertebral body avoidance area,

Set point set T={X, Y}, where X is the point on the vertebral avoidance area, Y∈{+1,-1} is the class label, +1 and -1 represent the two sides of the pedicle,

The geometric interval from T to the straight line ω.x+b=0 is:

The minimum interval of T to this line is defined as:

Then the optimal pedicle screw insertion trajectory is:

Construct the constrained objective function into an unconstrained Lagrangian objective function using the Lagrangian multiplier method:

Among them, α is the Lagrangian multiplier, and α≥0. For the specific solution, please refer to the solution process of the linear SVM algorithm in detail.

Further, in step S3, the nailing path estimated in the two-dimensional projection is reconstructed into a three-dimensional space path by using a back-projection algorithm.

Further, in step S3, the process of reconstructing the two-dimensional projection image to form the three-dimensional projection image is: using the filtered back-projection algorithm to reconstruct the three-dimensional image layer by layer, that is, to reconstruct and form the optimal path of the three-dimensional pedicle screw. The filtered back-projection algorithm is shown in the following formula:

In the formula, i is the i-th layer of the three-dimensional projection image, p _iθ (s) represents the projection of the i-th layer at an angle of θ, |ω| is the slope filter, f _i (x, y) is the three-dimensional image containing the screw trajectory;

The projection P _θ under the angle θ is as follows:

P _θ = ∑ _i ∑ _j ∑ _k l _θ (i, j, k) ρ _θ (i, j, k),

Among them, ρ _θ (i, j, k) is the CT value of the voxel (i, j, k) where the ray intersects the projected object, l _θ (i, j, k) is the length of the ray passing through the voxel, and θ represents the projection angle;

In fact, f _i (x, y) is a binary three-dimensional image containing only the screw trajectory. The image value at the screw trajectory is 1 and the others are 0. The filtering process is ignored during reconstruction, and the filtered back-projection algorithm is simplified as:

Working principle: Theoretically, the optimal three-dimensional pedicle screw trajectory is known, and multi-angle projections are made on the vertebral body around the pedicle, and the optimal projection of the pedicle screw insertion trajectory can be obtained on the two-dimensional projection surface of each angle.

Compared with prior art, the beneficial effect that the present invention has is:

The present invention uses the method of calculating the optimal screw trajectory on multiple two-dimensional projection surfaces, and then reconstructing the three-dimensional screw trajectory to plan the optimal insertion path of the pedicle screw, and can accurately and quickly calculate the optimal three-dimensional insertion path of the pedicle screw.

According to the actual clinical situation, the present invention adopts the method of correcting the posture of the pedicle so that it is parallel to the Y coordinate axis, two two-dimensional projection images of the orthogonal projection, simplifying the vertebral body avoidance area to the boundary points on both sides of the pedicle, reconstructing the three-dimensional image layer by layer with a filter back projection algorithm, and ignoring the filtering process during reconstruction. On the premise that the finally calculated three-dimensional optimal pedicle screw placement trajectory can meet the clinical use requirements, the amount of calculation is reduced as much as possible and the operation time is saved.

Description of drawings

Fig. 1 is the structural representation of the embodiment of the present invention;

Fig. 2 is the pedicle CT image of the embodiment of the present invention;

Fig. 3 is the two-dimensional projection image of the pedicle CT image of the embodiment of the present invention;

Fig. 4 is a two-dimensional projection image of the optimal pedicle screw placement trajectory of the embodiment of the present invention;

Fig. 5 is a reconstructed three-dimensional projection image of an embodiment of the present invention.

Detailed ways

In order to enable those skilled in the art to better understand the technical solution of the present invention, the present invention will be described in detail below in conjunction with the accompanying drawings and specific embodiments.

Embodiments of the present invention provide a method for optimal path planning of pedicle screws based on multi-angle projection, as shown in Figure 1, which includes the following steps:

S1: Adjust the CT image of the pedicle, and correct the posture of the pedicle so that it is parallel to the Y coordinate axis, as shown in Figure 2. Usually, the posture of the pedicle on the CT image will have different degrees of deflection. Therefore, the posture of the pedicle needs to be corrected before the two-dimensional projection of the pedicle at multiple angles, so as to increase the accuracy of the optimal pedicle screw placement trajectory calculated on the two-dimensional projection. When the pedicle deflection angle is small and does not affect the calculation of the optimal pedicle screw placement trajectory, posture correction may not be performed.

Perform two-dimensional projections from multiple angles on the pedicle CT images to form multiple two-dimensional projection images; the number of the two-dimensional projection images is at least two. Clinically, two two-dimensional projection images of orthogonal projection are generally used. In this embodiment, two orthogonal two-dimensional projection images are selected for two-dimensional projection at multiple angles based on clinical practice. Figure 3(a) is a two-dimensional projection image in the direction of the Y coordinate axis, and Figure 3(b) is a two-dimensional projection image in the direction of the X coordinate axis. Increasing the number of two-dimensional projection images can improve the accuracy of the final three-dimensional optimal path of the pedicle screw, but the corresponding calculation amount will increase.

S2: Determine the vertebral body avoidance area in each two-dimensional projection image, and the vertebral body avoidance area is simplified to the boundary points on both sides of the pedicle; then calculate the optimal pedicle screw insertion trajectory.

The optimal pedicle screw insertion trajectory is a straight line, as follows:

ω.x+b=0

Among them, ω and b are the parameters of the straight line.

When pedicle screws are actually placed clinically, the pedicle screws usually pass through the pedicle, so the vertebral body avoidance area on the two-dimensional projection image can be simplified to the boundary points on both sides of the pedicle, and clinical constraints are added according to the actual clinical situation. The clinical constraint condition is that the straight line is within the pedicle and does not pass through the vertebral body avoidance area.

We took the boundary points on both sides of the pedicle as points in the avoidance area of the vertebral body, and calculated the optimal pedicle screw placement trajectory on the two-dimensional projection image.

Set the point set T = {X, Y}, where X is the point on the vertebral avoidance area, Y∈{+1,-1} is the class label, +1 and -1 represent the two sides of the pedicle,

The geometric interval from T to the straight line ω.x+b=0 is:

The minimum interval of T to this line is defined as:

Then the optimal pedicle screw insertion trajectory is:

Construct the constrained objective function into an unconstrained Lagrangian objective function using the Lagrangian multiplier method:

Among them, α is the Lagrangian multiplier, and α≥0. For the specific solution, please refer to the solution process of the linear SVM algorithm in detail.

Through calculation, the optimal trajectory of pedicle screw placement is shown in Figure 4(a) and Figure 4(b).

S3: The three-dimensional projection image is formed by reconstructing the two-dimensional projection image from multiple angles, and the optimal trajectory of the pedicle screw in the two-dimensional projection image is reconstructed to form a three-dimensional optimal path of the pedicle screw.

In this embodiment, a ray-driven projection algorithm of parallel light is used to reconstruct the two-dimensional projection into a three-dimensional projection.

The Siddon algorithm is the most classic algorithm in the light-driven projection method. The projection P _θ under the angle θ is shown in the following formula:

P _θ = ∑ _i ∑ _j ∑ _k l _θ (i, j, k) ρ _θ (i, j, k),

Among them, ρ _θ (i, j, k) is the CT value of the voxel (i, j, k) where the ray intersects the projected object, l _θ (i, j, k) is the length of the ray passing through the voxel, and θ represents the projection angle.

In the process of reconstructing the 2D projection image to form the 3D projection image, the filter back projection algorithm is used to reconstruct the 3D stereoscopic image layer by layer, that is, the reconstruction forms the optimal path of the pedicle screw in 3D. The filter back projection algorithm is shown in the following formula:

In the formula, i is the i-th layer of the three-dimensional projection image, p _iθ (s) represents the projection of the i-th layer at an angle of θ, |ω| is the slope filter, and f _i (x, y) is the three-dimensional image containing the screw trajectory. In fact, f _i (x, y) is a binary three-dimensional image containing only the screw trajectory. The image value at the screw trajectory is 1 and the others are 0. The filtering process is ignored during reconstruction, and the filtered back-projection algorithm is simplified as:

After the calculation of the filtered back projection algorithm, the reconstructed 3D projection image is shown in Figure 5, and the 3D optimal path of the pedicle screw is reconstructed in the image at the same time.

The present invention has been described in detail through the above examples, but the content described is only an exemplary embodiment of the present invention, and cannot be considered as limiting the implementation scope of the present invention. The protection scope of the present invention is defined by the claims. Anyone who utilizes the technical solutions described in the present invention, or those skilled in the art who are inspired by the technical solutions of the present invention, design similar technical solutions to achieve the above technical effects within the essence and protection scope of the present invention, or make equal changes and improvements to the scope of application, etc., should still belong to the scope of protection covered by the patent of the present invention.

Claims (7)

1. a pedicle screw optimal path planning method based on multi-angle projection, is characterized in that: comprise the following steps: S1: Simulate two-dimensional projections of pedicle images from multiple angles to obtain multiple two-dimensional projection images; S2: Determine the safe screw placement area in each two-dimensional projection image, and then calculate the optimal pedicle screw placement trajectory in the projection image; the optimal pedicle screw placement trajectory is located in the safe screw placement area, Based on the boundary points on both sides of the safe screw placement area, the optimal pedicle screw insertion trajectory is defined as a straight line, and the clinical constraints are that the straight line must be within the safe screw placement area and not go out of the safe screw placement area. The avoidance area of the vertebral body is simplified as the boundary points on both sides of the pedicle, and the optimal pedicle screw insertion trajectory is a straight line, as follows: ω.x+b=0 Among them, ω and b are the parameters of the straight line, The clinical constraints of the pedicle screw insertion trajectory are that the straight line is inside the pedicle and does not pass through the vertebral body avoidance area, Set the point set T = {X, Y}, where X is the point on the vertebral avoidance area, Y∈{+1,-1} is the class label, +1 and -1 represent the two sides of the pedicle, The geometric interval from T to the straight line ω.x+b=0 is: The minimum interval of T to this line is defined as: Then the optimal pedicle screw insertion trajectory is: Construct the constrained objective function into an unconstrained Lagrangian objective function using the Lagrangian multiplier method: Among them, α is the Lagrangian multiplier, and α≥0; S3: The three-dimensional optimal path of the pedicle screw is formed by reconstructing the two-dimensional projection images from multiple angles. 2. The multi-angle projection-based optimal path planning method for pedicle screws according to claim 1, wherein in step S1, the number of the two-dimensional projection images is at least two. 3. The method for planning optimal path of pedicle screws based on multi-angle projection according to claim 2, characterized in that in step S1, two two-dimensional projection images of orthogonal projection are formed. 4. The multi-angle projection-based optimal path planning method for pedicle screws according to claim 2, wherein in step S1, two or more two-dimensional projection images of non-orthogonal projections are formed. 5. The optimal path planning method for pedicle screws based on multi-angle projection according to claim 1, characterized in that: in step S1, the posture of the pedicle is corrected so that it is parallel to the plane of the upper lamina or intervertebral disc. 6. The optimal path planning method for pedicle screws based on multi-angle projection as claimed in claim 1, wherein in step S3, the insertion trajectory calculated in the two-dimensional projection is reconstructed by using the back-projection algorithm to form a three-dimensional optimal path for the pedicle screws. 7. The multi-angle projection-based optimal path planning method for pedicle screws according to claim 6, characterized in that: in step S3, the back-projection algorithm uses a filtered back-projection algorithm.