A method for screw implantation path planning in orthopedic surgery based on bone mineral density integral.

Abstract

A method for planning screw implantation paths in orthopedic surgery based on bone mineral density integrals, in the field of medical device technology, includes the following steps: calculating the reference direction of the implantation path; generating the screw's conical reachable space; generating dense candidate directions radially; generating dense candidate directions circumferentially; and obtaining the optimal path through image grayscale integration. The input data for this invention are the patient's preoperative CT scan, the coordinates of the screw insertion reference point, and the screw parameters. The final task is to calculate the starting point coordinates of the optimal implantation path. This invention proposes an objective quantitative index for evaluating screw implantation stability using bone mineral density image path integration, solving problems such as poor planning path performance, poor repeatability, and poor interpretability in previous methods. This invention also proposes using the grayscale values ​​of the patient's CT image to determine whether the screw has penetrated the bone boundary on the implantation path, effectively avoiding situations where the screw penetrates the bone and damages surrounding soft tissue.

Description

Technical Field

[0001] This invention relates to screw implantation methods in the field of medical device technology, and in particular to a method for planning screw implantation paths in orthopedic surgery based on bone mineral density integrals using grayscale values ​​of patient CT images. Background Technology

[0002] Screw implantation is a common surgical requirement in orthopedic surgery, playing a vital role in various scenarios such as pelvic fracture reduction, shoulder and knee replacement surgery, and spinal internal fixation surgery. The procedure generally involves inserting a metal screw into the bone tissue to provide fixation, connection, or shaping. However, because important nerves and blood vessels are usually located around the bone, the requirements for the screw implantation path are quite stringent. Generally, the screw must not protrude beyond the bone boundary. Furthermore, for surgeries requiring prosthesis fixation, such as shoulder and knee replacement surgery, the screw length is usually fixed. Inappropriate implantation path selection can lead to complications such as secondary fractures, and the prosthesis may loosen or fall out, affecting its lifespan. Therefore, to ensure surgical success, clinicians typically plan the screw implantation path preoperatively and then implant the screws intraoperatively based on the preoperative plan. However, traditional manual planning heavily relies on the surgeon's experience, lacks objective quantitative indicators of screw retention effectiveness along the implantation path, and has poor repeatability. Existing automatic planning methods, represented by statistical models or deep learning methods, typically yield probabilistic results that cannot guarantee the most stable screw implantation effect. Furthermore, they still lack objective, quantifiable indicators of screw retention effectiveness on the implantation path that are physically interpretable. Summary of the Invention

[0003] This invention addresses the shortcomings of existing technologies by proposing a method for planning screw implantation paths in orthopedic surgery based on bone mineral density integrals. This method not only solves the problems of poor planning path performance, poor repeatability, and poor interpretability in previous methods, but also effectively avoids situations where screws penetrate the bone and damage surrounding soft tissues.

[0004] The present invention includes the following steps: Step S1, calculating the implantation path reference direction; Step S2, generating the screw cone reachable space; Step S3, generating dense alternative directions along the radial direction; Step S4, generating dense alternative directions along the circumferential direction; Step S5, obtaining the optimal path by integrating the image grayscale.

[0005] Further, in this invention, step S1 includes the following steps: step S1.1, using random sampling consistency to fit a two-dimensional plane of point cloud data near the reference point to obtain a predicted normal vector; step S1.2, starting from the reference point, forming two rays along the positive and negative directions of the normal vector, performing image grayscale path integration along the ray direction, and taking the direction corresponding to the larger integral value as the reference direction.

[0006] Furthermore, in this invention, step S2 includes the following steps: Step S2.1, starting from the reference point, advance the screw length along the reference direction by a distance, with the point being the center of the circle, and the screw length multiplied by the tangent of the angle as the radius, to obtain the reference circle; Step S2.2, with the reference point as the vertex, the reference circle as the base, and the reference direction as the central axis direction, to obtain the screw-accessible conical space.

[0007] Furthermore, in this invention, step S3 includes the following steps: Step 3.1, generating a radial vector perpendicular to the reference direction, starting from the center of the bottom circle, taking all the equal division points of the radius along the radial vector based on a preset radial resolution; Step 3.2, taking all the equal division points as the endpoints and the cone vertex as the starting point, to obtain the radial candidate directions on the generated direction vector.

[0008] Furthermore, in this invention, step S4 includes the following steps: step S4.1, calculating a rotation matrix based on a preset circumferential resolution and a reference direction; step S4.2, applying the rotation matrix to a radial vector to obtain a new radial vector; step S4.3, obtaining a mirror candidate direction based on S3, repeating S4 until the radial vector rotates one full circle to obtain dense candidate directions within the conical space.

[0009] Furthermore, in this invention, step S5 includes the following steps: Step S5.1, traversing the candidate directions, discarding candidate directions that may penetrate the bone boundary, and leaving the valid candidate directions; Step S5.2, for all valid candidate directions, converting from three-dimensional space back to image space according to a preset integral resolution, reading the gray value of the three-dimensional image, performing bone density path integration to represent the bone density at that point, and taking the maximum value as the densest screw implantation direction.

[0010] Compared with existing technologies, this invention has the following beneficial effects: First, this invention proposes an objective quantitative index for evaluating screw implantation stability using path integration of bone density images, solving problems such as poor planning path performance, poor repeatability, and poor interpretability in previous methods. Second, this invention proposes using the grayscale values ​​of the patient's CT images to determine whether the screw has penetrated the bone boundary on the implantation path, effectively avoiding situations where the screw penetrates the bone and damages surrounding soft tissue. Third, compared with traditional manual planning methods, this invention takes only seconds, is highly efficient, and while there are slight differences depending on the specific surgery, it significantly outperforms traditional manual planning. Attached Figure Description

[0011] Figure 1 This is a flowchart of the present invention;

[0012] Figure 2 This refers to the screw-shaped conical movable space constructed in Embodiment 1 of the present invention;

[0013] Figure 3 This is a path planning diagram of Embodiment 1 of the present invention;

[0014] Figure 4 This is a path planning diagram of Embodiment 2 of the present invention;

[0015] Among them, 1. reference direction, 2. radial vector, 3. new radial vector obtained after one rotation matrix operation, 4. included angle generated by circumferential resolution, 5. endpoint of generated dense candidate directions, 6. center of cone base, 7. circumference of base reference circle, 8. cone angle, 9. screw insertion reference point, 10. scapula in Example 1, 11. planned path of the first screw in Example 1, 12. planned path of the second screw in Example 1, 13. artificial glenoid prosthesis in Example 1, 14. pelvis in Example 2, 15. planned path of the first screw in Example 2, 16. planned path of the second screw in Example 2, 17. planned path of the third screw in Example 2. Detailed Implementation

[0016] The embodiments of the present invention will be described in detail below with reference to the accompanying drawings. These embodiments are based on the technical solutions of the present invention and provide detailed implementation methods and specific operation processes. However, the scope of protection of the present invention is not limited to the following embodiments.

[0017] Example 1

[0018] The patient suffered a shoulder fracture and required glenoid replacement surgery. This glenoid prosthesis contains two fixation screws; if the implantation path is not ideal, loosening is likely. The input data for this invention includes the patient's preoperative CT scan, the coordinates of the screw insertion reference point (generally located on the outer surface of the bone), and screw parameters such as screw diameter *r* and length *l*. The final task is to calculate the coordinates of the starting point of the optimal implantation path. The flowchart of this invention is shown below. Figure 1 Its features include the following steps: calculating the implantation path reference direction, generating the screw cone reachable space, generating dense alternative directions radially, generating dense alternative directions circumferentially, and obtaining the densest implantation path by integrating the image grayscale.

[0019] The first step is to calculate the reference direction for the implantation path. First, a three-dimensional model of the lesion is reconstructed based on the patient's preoperative CT threshold segmentation. Then, using the least squares method, the normal vector of the point cloud distribution near the needle insertion point is fitted at the reference point, denoted as v. n But v nThe orientation of the reference vector has two possibilities: pointing outwards or inwards at the reference point. However, the actual requirement for this step is that the normal vector points inwards. Therefore, a correction mechanism is needed to ensure that the obtained normal vectors all point inwards. The correction principle is as follows: the density of human bone is generally much greater than that of the tissues outside the bone, and this is reflected in CT imaging as the gray value of the corresponding pixel of bone being much greater than the gray value of the corresponding pixel of other tissues, denoted as p. Therefore, this characteristic can be used to identify whether the reference direction points inwards. If not, correction is performed. The correction method is as follows: taking the reference point on the outer surface of the bone as the starting point, two rays are formed along the positive and negative directions of the reference vector. The same number of evenly distributed points are taken at a certain distance from the reference point on each ray. The coordinates of these points are mapped to the CT image coordinate system, and the gray value of the pixel at that position is taken and summed. If the direction corresponding to the larger value is the opposite direction of the reference vector, then the reference vector is negative, as shown in the following formula (1-3).

[0020] p + =p r +dv n (1)

[0021] p - =p r -dv n (2)

[0022]

[0023] Where, p r d is the reference point for needle insertion; d is the maximum distance to the point on the ray; v n This is the reference vector obtained from the preliminary estimation; p + p is the point farthest from the reference point along the positive direction of the reference vector. - p is the point furthest from the reference point along the opposite direction of the reference vector; p is the point taken on the corresponding ray; and v is the gray value of the CT image corresponding to point p.

[0024] The second step is to generate the conical reachable space for the screw. The needle insertion reference point is a fixed point, representing the final location of the screw head after implantation. However, the position of the apex is uncertain; that is, given an angle α, all possible implantation paths of the screw can form a conical space with the needle insertion reference point as its vertex. In other words, all possible implantation paths of the screw will be contained within this conical space, such as... Figure 2 The process of constructing this conical space is as follows: First, starting from the needle insertion reference point, advance the screw a distance along the reference vector direction, and take that position as the center of the cone's base. Then, based on the preset cone angle α, obtain the product of its tangent and the screw length, ltanα, as the radius of the cone's base. At this point, based on the needle insertion reference point, the center of the base, and the base radius, the conical movement space of the screw can be constructed, as follows: Figure 2 .

[0025] The third step is to generate a dense array of candidate directions along the radius of the cone's base. First, a direction perpendicular to the reference vector v is generated. n radial unit vector v r Then, starting from the center of the cone's base circle, along the radial unit vector v r The direction of travel is the radius of the base. At this point, the location is on the circumference of the conical base, and this position can be connected to the center of the base by a line segment. This is based on the preset radial resolution N. r The line segment N r Divide the cone into equal parts, taking all the division points as the endpoints and the cone vertices as the starting points. This will form a dense distribution of direction vectors along the radial direction, which can be used as alternative radial directions.

[0026] The fourth step is to generate a dense array of candidate directions along the circumference of the cone's base. The third step already generated a dense array of candidate directions along the radial vector in a certain direction on the base. To generate a dense array of candidate directions filling the entire conical space, the third step needs to be repeated in other radial directions; that is, the radial vector needs to be driven to rotate around the center of the cone's base along the circumference. For example... Figure 2 Given a circumferential resolution N c The rotation angle of a single rotation can be obtained. Then, β is combined with the normalized reference direction v n =(x,y,z) T Rotation matrix can be generated

[0027]

[0028] Then by v r =Rv r A new radial vector can be obtained, which is equivalent to rotating about the reference vector by β relative to the original radial vector.

[0029] Then repeat steps three and four until the radial vector completes one revolution.

[0030] The fifth step is to calculate the optimal implantation direction based on the bone density image path integral. After generating the candidate directions densely distributed in the screw's reachable space in the fourth step, the optimal implantation direction needs to be calculated to obtain the optimal implantation path. First, it is necessary to ensure the safety of the screw in the implantation direction, discarding candidate directions that may penetrate the bone. At this point, we still utilize the physiological characteristic from the first step that the bone density of the human body is significantly greater than that of the extraosseous tissue. We first construct the smallest cylindrical bounding box of the screw in a certain implantation direction, and then use the same rotation matrix to uniformly generate seed points on the surface of the bounding box. The coordinates corresponding to these points are transformed from the 3D model coordinate system to the CT image coordinate system, and the corresponding image grayscale values ​​are read, which reflect the bone density. If the bone density at a certain seed point is significantly lower than the bone density value, it is considered that the surface will penetrate the bone when the screw is implanted in that direction, and that direction is discarded. Finally, the remaining effective implantation candidate directions are obtained. In this method, we propose to use the bone density path integral value to objectively quantify and compare the stability performance of screws implanted in different implantation paths. A higher bone mineral density integral value along the implantation path indicates denser bone density, a lower likelihood of screw loosening, and superior performance. Specifically, in each alternative direction, starting from the vertex of the conical space, the screw tip position is obtained by advancing a distance equal to the screw length along that direction. The distance between the screw tip position and the vertex of the cone is determined according to a preset integral resolution N. i Obtain N i Divide the image into three equal parts, sum the bone density values ​​in the CT image space corresponding to these points, and the largest value is the optimal implantation direction. The corresponding cone apex and screw tip position determine the optimal implantation path. The calculation process is shown in formula (4):

[0031]

[0032] Among them, Λ={λ1, λ2, λ3,…,λ j ,…} represent all alternative directions; ω j =1 is λ j Safety indicator, when ω j =1 represents λ j For a valid path, when ω j =0 indicates a discarded path; p j,k Representative by λ j The kth integration point on the generated screw implantation path; Representative point p j,k The corresponding grayscale value in the CT image space reflects the bone density; λ * This is the optimal implantation direction.

[0033] Finally, two of the densest implantation pathways were planned. (See details below) Figure 3 This can effectively prevent the above problems from occurring.

[0034] Example 2

[0035] The patient suffered a pelvic fracture, requiring the implantation of fixation screws to connect the bone fragments. After confirming the implantation location, this method generated multiple alternative implantation paths and calculated the optimal path, achieving effective fixation between the fractured bone fragments. See details... Figure 4 .

[0036] The above embodiments are merely illustrative of the design principles and uses of the present invention and are not intended to limit the invention. Any person skilled in the art can modify or alter the above embodiments without departing from the spirit and scope of the present invention. Therefore, all equivalent modifications or alterations made by those skilled in the art without departing from the spirit and technical concept disclosed in the present invention should still be covered by the claims of the present invention.

Claims

1. A method for planning screw implantation paths in orthopedic surgery based on bone mineral density integrals, characterized in that... Includes the following steps: Step S1: Calculate the reference direction for the implantation path; Step S2: Generate the screw-conical reachable space; Step S3: Generate dense candidate directions radially; Step S4: Generate dense candidate directions along the circumference; Step S5: Image grayscale integration yields the optimal path; Step S1 includes the following steps: Step S1.1: Fit a two-dimensional plane of the point cloud data near the reference point using random sampling consistency to obtain the predicted normal vector; Step S1.2: Starting from the reference point, two rays are formed along the positive and negative directions of the normal vector. Image grayscale path integration is performed along the ray direction, and the direction corresponding to the larger integral value is taken as the reference direction. Step S2 includes the following steps: Step S2.1: Starting from the reference point, advance the screw length along the reference direction by a distance, and take the point as the center of the circle. Multiply the screw length by the tangent of the angle to obtain the radius, and obtain the reference circle. Step S2.2: Using the reference point as the vertex, the reference circle as the base, and the reference direction as the central axis direction, the screw-reachable conical space is obtained; Step S3 includes the following steps: Step 3.1: Generate a radial vector perpendicular to the reference direction. Starting from the center of the bottom circle, take all the equal division points of the radius along the radial vector based on the preset radial resolution. Step 3.2: Using all the equally divided points as the endpoints and the cone vertices as the starting points, we obtain the radial candidate directions for generating this direction vector; Step S4 includes the following steps: Step S4.1: Calculate the rotation matrix based on the preset circumferential resolution and reference direction; Step S4.2: Apply the rotation matrix to the radial vector to obtain a new radial vector; Step S4.3: Based on S3, obtain the mirror candidate directions, repeat S4 until the radial vector rotates one full turn, and obtain the dense candidate directions in the cone space; Step S5 includes the following steps: Step S5.1: Iterate through the candidate directions, discard the candidate directions that may go out of the bone boundary, and keep the valid candidate directions. Step S5.2: For all valid candidate directions, convert from three-dimensional space back to image space according to the preset integral resolution, read the gray value of the three-dimensional image, perform bone density path integration to represent the bone density at that point, and take the largest value as the densest screw implantation direction.

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