CN113940752A - Multi-angle projection-based optimal path planning method for pedicle screws - Google Patents
Multi-angle projection-based optimal path planning method for pedicle screws Download PDFInfo
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- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
- A61B34/00—Computer-aided surgery; Manipulators or robots specially adapted for use in surgery
- A61B34/10—Computer-aided planning, simulation or modelling of surgical operations
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- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
- A61B34/00—Computer-aided surgery; Manipulators or robots specially adapted for use in surgery
- A61B34/20—Surgical navigation systems; Devices for tracking or guiding surgical instruments, e.g. for frameless stereotaxis
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
- G06N20/00—Machine learning
- G06N20/10—Machine learning using kernel methods, e.g. support vector machines [SVM]
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T7/00—Image analysis
- G06T7/0002—Inspection of images, e.g. flaw detection
- G06T7/0012—Biomedical image inspection
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T7/00—Image analysis
- G06T7/30—Determination of transform parameters for the alignment of images, i.e. image registration
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- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
- A61B34/00—Computer-aided surgery; Manipulators or robots specially adapted for use in surgery
- A61B34/10—Computer-aided planning, simulation or modelling of surgical operations
- A61B2034/107—Visualisation of planned trajectories or target regions
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- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
- A61B34/00—Computer-aided surgery; Manipulators or robots specially adapted for use in surgery
- A61B34/20—Surgical navigation systems; Devices for tracking or guiding surgical instruments, e.g. for frameless stereotaxis
- A61B2034/2046—Tracking techniques
- A61B2034/2065—Tracking using image or pattern recognition
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T2207/00—Indexing scheme for image analysis or image enhancement
- G06T2207/10—Image acquisition modality
- G06T2207/10072—Tomographic images
- G06T2207/10081—Computed x-ray tomography [CT]
Abstract
The invention provides a pedicle screw optimal path planning method based on multi-angle projection, which comprises the following steps: s1: performing simulated two-dimensional projection of the pedicle images at a plurality of angles to obtain a plurality of two-dimensional projection images; s2: determining a safe screw placing area in each two-dimensional projection image, and then calculating the placing track of the optimal pedicle screw in the projection image; the optimal pedicle screw implantation track is located in the safe screw implantation area, and S3: and reconstructing to form a three-dimensional optimal path of the pedicle screw by using the two-dimensional projection images of a plurality of angles. The optimal path for the pedicle screw is planned by adopting a method of calculating the optimal trajectory of the screw on a plurality of two-dimensional projection planes and then reconstructing into a three-dimensional screw trajectory, so that the optimal three-dimensional path for the pedicle screw can be accurately and quickly calculated.
Description
Technical Field
The invention belongs to the field of medicine, and particularly relates to a pedicle screw optimal path planning method based on multi-angle projection.
Background
The placement of pedicle screws in the spine is a common procedure for the treatment of various spinal injuries, tumors, deformities and degenerative diseases. Screws must be placed accurately through the stenotic passage of the pedicle, which is near the spinal cord, the dural sac, the nerve roots and the blood vessels, and improper placement of screws can lead to neurological complications including paralysis, blood loss, death, and the like. The internal spinal fixation operation in China is about 58 thousands of cases per year, wherein the implantation of the pedicle screws accounts for more than 65 percent. Relevant studies have confirmed that spinal surgery is at high risk, with post-operative complications at a risk of 16.4%. Related researches show that the dislocation rate of the lumbar pedicle screw implantation is 5-41%, and related literature reports that the accuracy of manual screw implantation can be as low as 68.1%. In recent decades, with the great progress of surgical techniques and technologies, the Spine pedicle screw implantation operation enters a Minimally Invasive age, and the popularity of Minimally Invasive Spinal Surgery (MISS) is also increasing. Over the past decade, robotic systems have played a tremendous role in the surgical field, and innovative applications in surgery have been vigorously developed. Early applications of robotic systems in these areas stimulated innovative applications of surgical robots in other surgical branch areas, including the field of spinal surgery. The development of surgical robotics in the field of spinal surgery has expanded the field of vision for spinal surgery, making it suitable for many complex spinal surgeries. The working phases of robot-assisted spinal surgery mainly include: registering and fusing the preoperative image and the intraoperative image; planning the position of the pedicle screw; the screw channel locates and implants the screw. In recent years, researchers at home and abroad make many relevant researches on the field to obtain many valuable research results.
In the field of spinal surgery, a real-time image navigation system improves the safety and accuracy of spinal surgery. The application of the high-quality CT image registration and the three-dimensional stereotactic camera can carry out three-dimensional mapping on the spine in time during operation and track surgical instruments in real time. In most cases, MISS internal fixation of percutaneous pedicle screw placement employs intraoperative fluoroscopic guidance methods that enable pedicle screw fixation with high accuracy, but which expose surgeons and patients to radiation for long periods of time. The application of the CT-based navigation system can reduce the radiation exposure risk of surgeons and patients in the operation process by more than 90%, and can ensure higher accuracy of pedicle screw fixation. The spine surgery usually adopts percutaneous pedicle screw fixation, and the application of navigation system makes the operation process have higher reliability and security, and many studies show that, current CT image-based navigation system has higher reliability, can be applied to most spine surgery, can reduce operation-related complications, including reoperation rate, etc.
Robotic systems have found widespread use in the field of spinal surgery due to their accuracy, reliability, and effectiveness during surgery and their ability to perform quickly. In combination with a navigation system, the robotic system can theoretically ensure a more accurate surgical path and reduce soft tissue damage. Pedicle screw fixation is a typical application of robotic systems. Several related researches show that the accuracy of the pedicle screw internal fixation operation assisted by the robot system is superior to that of pedicle screw internal fixation under perspective guidance, and a plurality of system reviews and meta analyses comparing robot assistance and traditional pedicle screw implantation have been published, which show that the effect of robot-assisted nail implantation is better than that of traditional free-hand nail implantation, and reports clearly indicate that the accuracy of pedicle screw implantation by the robot system is generally higher and reaches 94% -98%. In addition, the robot-assisted spinal surgery can overcome the psychological obstacles and physical fatigue of surgeons during the surgery, and provide better clinical and surgical effects. However, despite the safety and efficiency of image-guided robotic surgery, there are still deficiencies in preoperative pedicle screw trajectory planning. First, current commercial robotic surgical systems are generally lacking in automation, requiring a physician to manually plan the direction and pose of the screw trajectory on the pre-or intra-operative images. Second, image guided robotic systems require accurate registration between the surgical plan and the in situ image. Whereas image registration for robotic surgery is a challenging task.
Disclosure of Invention
Aiming at the technical problems in the prior art, the invention provides a pedicle screw optimal path planning method based on multi-angle projection, which is characterized in that the optimal path of a pedicle screw is planned by adopting a method of calculating the optimal path of the screw on a plurality of two-dimensional projection surfaces and then reconstructing into a three-dimensional screw path, so that the optimal three-dimensional embedding path of the pedicle screw can be accurately and quickly calculated.
The technical scheme adopted by the invention is as follows: a pedicle screw optimal path planning method based on multi-angle projection comprises the following steps:
s1: performing simulated two-dimensional projection of the pedicle images at a plurality of angles to obtain a plurality of two-dimensional projection images;
s2: determining a safe screw placing area (such as a set vertebral body avoiding area, and the area outside the safe screw placing area) in each two-dimensional projection image, and then calculating an optimal pedicle screw placing track on each projection image;
s3: and reconstructing to form a three-dimensional optimal path of the pedicle screw by using the two-dimensional projection images of a plurality of angles.
Further, in step S1, the number of the two-dimensional projection images is at least two. The two-dimensional projection image may employ two-dimensional projection images projected orthogonally, or two or more two-dimensional projection images projected non-orthogonally. Increasing the number of two-dimensional projection images may improve the accuracy of the final three-dimensional pedicle screw optimal path, but the corresponding amount of computation may increase.
Further, in step S1, the pedicle is repositioned to be parallel to the upper lamina or disc plane. Usually, the posture of the pedicle on the CT image will have different degrees of deflection, so the posture of the pedicle needs to be corrected before the pedicle is subjected to two-dimensional projection of multiple angles, so as to increase the accuracy of the optimal pedicle screw placement track calculated on the two-dimensional projection.
Further, in step S2, the vertebral body avoiding area is simplified to be boundary points on both sides of the pedicle, and the optimal pedicle screw placement trajectory is a straight line, as follows:
ω.x+b＝0
where ω and b are parameters of a straight line,
the clinical constraint condition of the implantation track of the pedicle screw is that the straight line is in the pedicle and does not pass through the vertebral body evasion area,
setting a point set T ═ { X, Y }, wherein X is a point on a vertebral body avoidance area, Y ∈ { +1, -1} is a class mark, and +1 and one 1 represent two sides of a vertebral pedicle,
the geometric interval from T to the line ω. x + b ═ 0 is:
the minimum separation of T to this line is defined as:
the optimal pedicle screw placement trajectory is then:
the constrained objective function is constructed as an unconstrained lagrangian objective function using the lagrangian multiplier method:
wherein alpha is Lagrange multiplier and is more than or equal to 0. The specific solution can refer to the solution process of the linear SVM algorithm in detail.
Further, in step S3, a back-projection algorithm is used to reconstruct the estimated nail placement path in the two-dimensional projection into a three-dimensional spatial path.
Further, in step S3, the process of reconstructing the two-dimensional projection image to form the three-dimensional projection image is as follows: reconstructing a three-dimensional image layer by adopting a filtering back projection algorithm, namely reconstructing to form a three-dimensional optimal path of the pedicle screw, wherein the filtering back projection algorithm is shown as the following formula:
where i is the ith layer of the three-dimensional projection image, piθ(s) represents the projection of the ith layer at an angle theta, | omega | is a ramp filter, fi(x, y) is a three-dimensional image containing the screw trajectory;
projection P at angle thetaθAs shown in the following formula:
Pθ＝∑i∑j∑klθ(i，j，k)ρθ(i，j，k)，
where ρ isθ(i, j, k) is the CT value of the voxel (i, j, k) where the ray intersects the projected object, lθ(i, j, k) is the length of the ray through the voxel, θ represents the projection angle;
in fact, fi(x, y) is a binary three-dimensional image containing only the screw trajectoryAnd the image value at the screw track is 1, and the other values are 0, the filtering process is omitted during reconstruction, and the filtering back projection algorithm is simplified as follows:
the working principle is as follows: theoretically, the optimal three-dimensional pedicle screw trajectory is known, the vertebral body is subjected to multi-angle projection around the pedicle, the projection of the optimal pedicle screw imbedding trajectory can be obtained on the two-dimensional projection plane of each angle, and on the contrary, the optimal pedicle screw trajectory on the two-dimensional projection is known, and the three-dimensional optimal pedicle screw imbedding trajectory can also be obtained by reconstructing the projection of the optimal pedicle screw trajectory of different angles.
Compared with the prior art, the invention has the beneficial effects that:
the optimal path for the pedicle screw is planned by adopting a method of calculating the optimal trajectory of the screw on a plurality of two-dimensional projection planes and then reconstructing into a three-dimensional screw trajectory, so that the optimal three-dimensional path for the pedicle screw can be accurately and quickly calculated.
According to the invention, according to the clinical practical situation, the posture of the pedicle is corrected to enable the pedicle to be parallel to a Y coordinate axis, two-dimensional projection images of orthogonal projection and a vertebral body evasion area to be simplified into boundary points at two sides of the pedicle, and a method of reconstructing a three-dimensional image layer by using a filtering back projection algorithm and neglecting a filtering process during reconstruction is adopted, so that the calculated three-dimensional optimal pedicle screw embedding track can meet the clinical use requirement on the premise of ensuring, the calculated amount is reduced as much as possible, and the operation time is saved.
Drawings
FIG. 1 is a schematic structural diagram of an embodiment of the present invention;
FIG. 2 is a pedicle CT image of an embodiment of the present invention;
FIG. 3 is a two-dimensional projection image of a pedicle CT image of an embodiment of the present invention;
FIG. 4 is a two-dimensional projection image of an optimal pedicle screw placement trajectory in accordance with an embodiment of the present invention;
FIG. 5 is a reconstructed three-dimensional projection image of an embodiment of the present invention.
Detailed Description
In order to make the technical solutions of the present invention better understood, the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
The embodiment of the invention provides a pedicle screw optimal path planning method based on multi-angle projection, which comprises the following steps as shown in figure 1:
s1: the pedicle CT image was adjusted to correct the pedicle pose to be parallel to the Y coordinate axis as shown in fig. 2. Usually, the posture of the pedicle on the CT image will have different degrees of deflection, so the posture of the pedicle needs to be corrected before the pedicle is subjected to two-dimensional projection of multiple angles, so as to increase the accuracy of the optimal pedicle screw placement track calculated on the two-dimensional projection. The deflection angle of the pedicle of vertebral arch is small, and posture correction can not be carried out when the optimal pedicle of vertebral arch screw imbedding track is not influenced.
Performing two-dimensional projection of a plurality of angles on the pedicle CT image to form a plurality of two-dimensional projection images; the number of the two-dimensional projection images is at least two. Clinically, two-dimensional projection images projected orthogonally are generally used. According to clinical practice, two orthogonal two-dimensional projection images are selected when two-dimensional projection is performed at multiple angles, wherein fig. 3(a) is a two-dimensional projection image in the Y coordinate axis direction, and fig. 3(b) is a two-dimensional projection image in the X coordinate axis direction. Increasing the number of two-dimensional projection images may improve the accuracy of the final three-dimensional pedicle screw optimal path, but the corresponding amount of computation may increase.
S2: determining a vertebral body avoiding area in each two-dimensional projection image, wherein the vertebral body avoiding area is simplified into boundary points on two sides of a pedicle; and then calculating the optimal implantation track of the pedicle screw.
The optimal implantation track of the pedicle screw is a straight line as follows:
ω.x+b＝0
where ω and b are parameters of straight lines.
When the pedicle screw is clinically and actually placed, the pedicle screw usually passes through the pedicle of a vertebral arch, so that a vertebral body avoidance area on a two-dimensional projection image can be simplified into boundary points on two sides of the pedicle of a vertebral arch, clinical constraints are added according to actual clinical conditions, and the clinical constraint condition is that the straight line is in the pedicle of a vertebral arch and does not pass through the vertebral body avoidance area.
Boundary points on two sides of the pedicle of vertebral arch are used as points of a vertebral body avoidance area, and an optimal pedicle screw imbedding track on a two-dimensional projection image is calculated.
Setting a point set T ═ { X, Y }, wherein X is a point on a vertebral body avoidance area, Y ∈ { +1, -1} is a class mark, and +1 and-1 represent two sides of a vertebral pedicle,
the geometric interval from T to the line ω. x + b ═ 0 is:
the minimum separation of T to this line is defined as:
the optimal pedicle screw placement trajectory is then:
the constrained objective function is constructed as an unconstrained lagrangian objective function using the lagrangian multiplier method:
wherein alpha is Lagrange multiplier and is more than or equal to 0. The specific solution can refer to the solution process of the linear SVM algorithm in detail.
By calculation, the implantation trajectory of the optimal pedicle screw is shown in fig. 4(a) and 4 (b).
S3: and reconstructing the two-dimensional projection images of a plurality of angles to form a three-dimensional projection image, and reconstructing the embedded track of the optimal pedicle screw in the two-dimensional projection image to form a three-dimensional optimal path of the pedicle screw.
In the embodiment, the two-dimensional projection is reconstructed into the three-dimensional projection by adopting a ray-driven projection algorithm of parallel light.
The Siddon algorithm is the most classical algorithm in the light-driven projection method, and the projection P under the angle thetaθAs shown in the following formula:
Pθ＝∑i∑j∑klθ(i，j，k)ρθ(i，j，k)，
where ρ isθ(i, j, k) is the CT value of the voxel (i, j, k) where the ray intersects the projected object, lθ(i, j, k) is the length of the ray through the voxel, and θ represents the projection angle.
In the process of reconstructing the two-dimensional projection image into the three-dimensional projection image, a three-dimensional image is reconstructed layer by adopting a filtering back-projection algorithm, namely, a three-dimensional optimal path of the pedicle screw is reconstructed and formed, wherein the filtering back-projection algorithm is shown as the following formula:
where i is the ith layer of the three-dimensional projection image, piθ(s) represents the projection of the ith layer at an angle theta, | omega | is a ramp filter, fi(x, y) is a three-dimensional image containing the screw trajectory. In fact, fi(x, y) is a binary three-dimensional image only containing a screw track, the value of the image at the screw track is 1, the other value is 0, the filtering process is omitted during reconstruction, and the filtering back projection algorithm is simplified as follows:
through calculation of the filtering back-projection algorithm, a three-dimensional projection image formed by reconstruction is shown in fig. 5, and a three-dimensional optimal path of the pedicle screw is simultaneously reconstructed in the image.
The present invention has been described in detail with reference to the embodiments, but the description is only illustrative of the present invention and should not be construed as limiting the scope of the present invention. The scope of the invention is defined by the claims. The technical solutions of the present invention or those skilled in the art, based on the teaching of the technical solutions of the present invention, should be considered to be within the scope of the present invention, and all equivalent changes and modifications made within the scope of the present invention or equivalent technical solutions designed to achieve the above technical effects are also within the scope of the present invention.
Claims (8)
1. A pedicle screw optimal path planning method based on multi-angle projection is characterized by comprising the following steps: the method comprises the following steps:
s1: performing simulated two-dimensional projection of the pedicle images at a plurality of angles to obtain a plurality of two-dimensional projection images;
s2: determining a safe screw placing area in each two-dimensional projection image, and then calculating the placing track of the optimal pedicle screw in the projection image; the optimal implantation track of the pedicle screw is positioned in the safe implantation area,
s3: and reconstructing to form a three-dimensional optimal path of the pedicle screw by using the two-dimensional projection images of a plurality of angles.
2. The pedicle screw optimal path planning method based on multi-angle projection as claimed in claim 1, wherein: in step S1, the number of the two-dimensional projection images is at least two.
3. The pedicle screw optimal path planning method based on multi-angle projection as claimed in claim 2, wherein in step S1, two-dimensional projection images of orthogonal projection are formed.
4. The pedicle screw optimal path planning method based on multi-angle projection as claimed in claim 2, wherein in step S1, two or more two-dimensional projection images of non-orthogonal projection are formed.
5. The pedicle screw optimal path planning method based on multi-angle projection as claimed in claim 1, wherein: in step S1, the pedicle is repositioned to be parallel to the upper lamina or disc plane.
6. The pedicle screw optimal path planning method based on multi-angle projection as claimed in claim 1, wherein: in step S2, based on the boundary points on the two sides of the safe screw placement area, the optimal placement trajectory of the pedicle screw is defined as a straight line, and the clinical constraint condition is that the straight line needs to be in the safe screw placement area and does not pass through the safe screw placement area.
7. The pedicle screw optimal path planning method based on multi-angle projection as claimed in claim 1, wherein: in step S3, the placement trajectory calculated in the two-dimensional projection is reconstructed by using a back-projection algorithm to form a three-dimensional optimal path of the pedicle screw.
8. The multi-angle projection-based pedicle screw optimal path planning method as claimed in claim 7, wherein: in step S3, the back projection algorithm is a filtered back projection algorithm.
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