CN115568942B - Multi-vertebral body combined constraint pedicle screw optimal trajectory planning method and device - Google Patents

Abstract

The present invention relates to a method for planning the optimal trajectory of pedicle screws with joint constraints of multiple vertebrae, comprising the following steps: determining the safe screw placement area for each vertebrae, obtaining the entry point range of the screw trajectory on each vertebrae; using the entry point range of the screws on each vertebrae, calculating the optimal form of the connecting rod; determining the range of motion of the multi-axial screw cap; using the avoidance area of vertebrae screw placement, the position of the connecting rod and the range of motion of the multi-axial screw cap to form the constraints of the clinically effective screw placement trajectory, and then determining the optimal trajectory of the pedicle screws of each vertebrae under the joint constraints. The present invention can accurately and quickly calculate the clinically effective three-dimensional placement path of the pedicle screws.

Description

Optimal trajectory planning method and device for pedicle screws with multi-vertebral joint constraints

Technical Field

The invention relates to the technical field of spinal pedicle screw placement, and in particular to a method and a device for optimal trajectory planning of pedicle screws with multi-vertebral joint constraints.

Background Art

Image-guided (robot-assisted) pedicle screw placement can improve the accuracy of screw placement. Compared with manual screw placement, image-guided (robot-assisted) screw placement has a higher accuracy rate. However, current commercial robotic navigation systems generally lack automation. The physician must manually plan the direction and position of the screw trajectory on the CT or CBCT image.

The current screw trajectory planning mainly uses a manual drag-and-drop strategy on CBCT images to obtain the screw trajectory. This process interrupts the workflow and may cause errors. Therefore, computer-aided planning methods have become a viable alternative. For example, the relationship between vertebral bone density and screw placement trajectory is revealed from different angles, and the screw trajectory is planned based on the correlation. A 3D planning system is used to find and optimize the screw trajectory through bone mechanical properties or bone density characteristics derived from CT images. The screw trajectory is optimized according to CT images and vertebral geometric characteristics, such as finding the optimal screw trajectory by constructing multi-angle projections and marking avoidance areas on the projection surface. Screw trajectory planning is performed by constructing a vertebral and screw trajectory atlas and then aligning the atlas to the target vertebra. A method for automatic segmentation and trajectory planning of vertebral bodies and pedicles based on pedicle geometric characteristics. Vertebral segmentation and screw trajectory planning are performed using artificial intelligence methods.

However, in practice, it is usually necessary to process multiple vertebrae at the same time. In this case, the ipsilateral screw needs to be connected to a rigid connecting rod to achieve the ultimate goal. Therefore, in addition to the constraints on the placement of a single vertebral screw, it is also necessary to have a good understanding of the mutual constraints between the screws of different vertebrae on the same side. However, so far, traditional screw trajectory planning methods are all for single vertebrae, and do not consider the situation of multi-vertebral constraints.

Summary of the invention

In view of the above problems, the purpose of the present invention is to provide a method and device for optimal trajectory planning of pedicle screws with multi-vertebral joint constraints. The method provides an effective method for determining the range of screw entry points and connecting rod design for multi-vertebral joint screw placement, and can accurately and quickly calculate the clinically effective three-dimensional placement path of pedicle screws.

To achieve the above object, the present invention adopts the following technical solutions:

The optimal trajectory planning method for pedicle screws with multi-vertebral joint constraints described in the present invention comprises the following steps:

Determine the safe screw placement area for each vertebral body and obtain the entry point range of the screw trajectory on each vertebral body;

The optimal shape of the connecting rod is calculated using the range of screw entry points on each vertebral body;

Determine the range of motion of the multi-axis nail nut;

The avoidance area of vertebral screw placement, the position of the connecting rod and the range of motion of the multi-axial screw cap are used to form the constraints of the clinically effective screw placement trajectory, and then the optimal trajectory of the pedicle screw of each vertebra under the combined constraints is determined.

The method for optimal trajectory planning of pedicle screws with multi-vertebral joint constraints is preferably implemented by determining the safe screw placement area for each vertebral screw and obtaining the entry point range of the screw trajectory on each vertebra by:

The optimal path for pedicle screws is:

The safe area for vertebral screw placement is:

Where M is a point on the avoidance area, _M0 is the entry point of the optimal screw trajectory; ρ is the safe distance from the screw to the avoidance area, and is the unit direction vector of the screw trajectory; Special symbols represent any;

Formula (2) is transformed radially to simplify it into a cylinder with the optimal screw trajectory as the center line, specifically:

Z ² +Y ² =(d-ρ) ² (4)

0≤X≤L

in, is a unit vector orthogonal to (α, β, γ); is a unit vector orthogonal to (α, β, γ); is the space transformation matrix; L is the screw length; is the shortest distance from the optimal screw trajectory to the avoidance area; is the safe nail placement area; ρ is the safe distance from the screw to the avoidance area; L is the screw length; X, Y, Z are the original coordinates;

The entry point range of the screw trajectory is:

Z ² +Y ² =(d-ρ) ² (6)

in, It is the range of entry points of the screw trajectory.

In the method for planning optimal pedicle screw trajectories with multi-vertebral joint constraints, preferably, the optimal shape of the connecting rod is a curve that conforms to the natural curvature of the spine and is located as close as possible to the plane in the direction of all ipsilateral optimal screw trajectories; the shape of the optimal connecting rod includes its position and shape, specifically:

Assuming M ₀ (x, y, z) is the optimal screw trajectory entry point position on the same side of all vertebrae, the optimal connecting rod position is expressed as:

AX+BY+CZ+D＝0 (7)

Therefore, the optimal screw trajectory under the connecting rod constraint is expressed as:

in, A, B, C, D are the parameters of the plane where the connecting rod is located; L′ is the length of the nail cap; (α _nut , β _nut , γ _nut ) is the unit direction vector of the nail cap; ω is the maximum angle that the nail cap can form with the nail;

Assume that the best plane of the known connecting rod is P:

AX+BY+CZ+D＝0 (11)

Taking this plane as the XOZ plane, a new spatial coordinate system {i _T ,j _T ,k _T } can be constructed, then:

Among them, N ₀ , N _x and N _z are points on the optimal plane P, and Perpendicular to Then the coordinates of the nail cap on the optimal plane P are:

in, For the general Coordinates are converted to Space transformation matrix on coordinates; is the coordinate of the nail cap in the spatial coordinate system {i _T ,j _T ,k _T }; since the optimal plane P is defined as the XOZ plane of the spatial coordinate system {i _T ,j _T ,k _T }, then y _T = 0, therefore, the shape of the connecting rod is obtained by least squares fitting:

In summary, the optimal position and shape of the connecting rod are:

Among them, x _Tl and z _Tl are the coordinates of the nail cap in the new coordinate system; x _ol , y _ol and z _ol are the coordinates of the nail cap in the original coordinate system; is the curve parameter of the curve where the nail cap is located.

In the method for optimal trajectory planning of pedicle screws with multi-vertebral joint constraints, preferably, the range of motion of the screw cap of the multi-axis screw is determined by:

Assuming the length of the screw cap is L’, the parametric equation of the screw cap is expressed as:

(x,y,z)＝t(α _nut ,β _nut ,γ _nut )+Mnut (19)

s.t.0<t<L′

Among them, (α _nut ,β _nut ,γ _nut ) is the unit direction vector of the nail cap, M _nut is the position of the nail cap, and t represents the unknown number of the nail cap length;

The movable range of the nail cap is:

in is the unit direction vector of the screw; _M0 is the entry point of the optimal screw trajectory; ω is the maximum movable angle between the screw cap and the screw.

The multi-vertebral joint-constrained pedicle screw optimal trajectory planning device of the present invention comprises:

The first processing unit is used to determine the safe screw placement area for each vertebral body and obtain the entry point range of the screw trajectory on each vertebral body;

A second processing unit is used to calculate the optimal shape of the connecting rod using the entry point range of the screws on each vertebral body;

The third processing unit is used to determine the range of movement of the nail head of the multi-axis nail;

The fourth processing unit is used to form clinically effective screw insertion trajectory constraints using the avoidance area of vertebral screw placement, the position of the connecting rod and the range of motion of the multi-axial screw cap, and then determine the optimal trajectory of the pedicle screws of each vertebra under the combined constraints.

The computer storage medium of the present invention stores a computer program thereon, and when the computer program is executed by a processor, the steps of the method for optimal trajectory planning of pedicle screws with multi-vertebral joint constraints are implemented.

The computer device described in the present invention includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the steps of the method for optimal trajectory planning of pedicle screws with multi-vertebral joint constraints are implemented.

The present invention adopts the above technical solution, which has the following advantages:

The present invention provides an effective method for determining the range of screw insertion points and the design of connecting rods for multi-vertebral joint screw placement, and can accurately and quickly calculate the clinically effective three-dimensional placement path of pedicle screws.

BRIEF DESCRIPTION OF THE DRAWINGS

Various other advantages and benefits will become apparent to those of ordinary skill in the art by reading the detailed description of the preferred embodiments below. The accompanying drawings are only for the purpose of illustrating the preferred embodiments and are not to be considered as limiting the present invention. Throughout the accompanying drawings, the same reference numerals are used to represent the same components. In the accompanying drawings:

FIG1 is a schematic diagram of the movable range of a screw of the present invention;

FIG. 2 is a schematic diagram of an optimal form of a connecting rod of the present invention.

DETAILED DESCRIPTION

The exemplary embodiments of the present invention will be described in more detail below with reference to the accompanying drawings. Although the exemplary embodiments of the present invention are shown in the accompanying drawings, it should be understood that the present invention can be implemented in various forms and should not be limited by the embodiments described herein. On the contrary, these embodiments are provided in order to enable a more thorough understanding of the present invention and to fully convey the scope of the present invention to those skilled in the art.

The present invention provides a method for planning the optimal trajectory of pedicle screws with joint constraints of multiple vertebrae, by determining the safe area for screw placement of each vertebrae, obtaining the entry point range of the screw trajectory on each vertebrae; using the entry point range of the screw on each vertebrae, calculating the clinically effective position of the connecting rod; determining the range of motion of the multi-axial screw cap; using the avoidance area of vertebral screw placement, the position of the connecting rod and the range of motion of the multi-axial screw cap to form the constraint conditions of the optimal screw placement trajectory, and then calculating the effective screw trajectory of each vertebra under the joint constraint conditions. The present invention provides an effective method for determining the range of entry points and the design of the connecting rod for joint screw placement of multiple vertebrae, and can accurately and quickly calculate the clinically effective three-dimensional placement path of pedicle screws.

The method for optimal trajectory planning of pedicle screws with multi-vertebral joint constraints provided by the present invention comprises the following steps:

S1. Determine the safe screw placement area for each vertebral body and obtain the entry point range of the screw trajectory on each vertebral body;

S2. Calculate the optimal shape of the connecting rod using the range of screw entry points on each vertebral body;

S3, determine the range of motion of the multi-axis nail cap;

S4. Use the avoidance area of vertebral screw placement, the position of the connecting rod and the range of motion of the multi-axial screw cap to form the constraints of the clinically effective screw placement trajectory, and then determine the optimal trajectory of the pedicle screws of each vertebra under the combined constraints.

In the above embodiment, preferably, determining the safe screw placement area for each vertebral body and obtaining the entry point range of the screw trajectory on each vertebral body is achieved by:

The optimal path for pedicle screws is:

The safe area for vertebral screw placement is:

Where M is a point on the avoidance area, M ₀ is the entry point of the optimal screw trajectory; ρ>0, is the safe distance from the screw to the avoidance area; is the unit direction vector of the screw trajectory; Special symbols represent any;

For the safety of screw placement and the simplicity of calculation, formula (2) can be transformed radially to simplify it into a cylinder with the optimal screw trajectory as the center line, specifically:

Z ² +Y ² =(d-ρ) ² (4)

0≤X≤L

in, is a unit vector orthogonal to (α, β, γ); is a unit vector orthogonal to (α, β, γ); is the space transformation matrix; L is the screw length; is the shortest distance from the optimal screw trajectory to the avoidance area;

is the safe nail placement area; ρ is the safe distance from the screw to the avoidance area; L is the screw length; X, Y, Z are the original coordinates;

Among them, the entry point range of the screw trajectory is:

Z ² +Y ² =(d-ρ) ² (6)

in, It is the range of entry points of the screw trajectory.

In the above embodiment, preferably, the optimal shape of the connecting rod is a curve that conforms to the natural curvature of the spine and is located as close as possible to a plane in the direction of all ipsilateral optimal screw trajectories; the optimal shape of the connecting rod includes its position and shape, specifically:

Assuming M ₀ (x, y, z) is the optimal screw trajectory entry point position on the same side of all vertebrae, the optimal connecting rod position can be expressed as:

AX+BY+CZ+D＝0 (7)

Therefore, the optimal screw trajectory under the connecting rod constraint can be expressed as:

in, A, B, C, D are the parameters of the plane where the connecting rod is located; L′ is the length of the nail cap; (α _nut , β _nut , γ _nut ) is the unit direction vector of the nail cap; ω is the maximum angle that the nail cap can form with the nail;

Assume that the best plane of the known connecting rod is P:

AX+BY+CZ+D＝0 (11)

Taking this plane as the XOZ plane, a new spatial coordinate system {i _T ,j _T ,k _T } can be constructed, then:

Among them, N ₀ , N _x , N _z are points on the optimal plane P, and Perpendicular to Then the coordinates of the nail cap on the optimal plane P are:

in, For the general Coordinates are converted to Space transformation matrix on coordinates; is the coordinate of the nail cap in the spatial coordinate system {i _T ,j _T ,k _T }; since the optimal plane P is defined as the XOZ plane of the spatial coordinate system {i _T ,j _T ,k _T }, then y _T = 0, therefore, the shape of the connecting rod can be fitted by the least squares method:

As shown in Figure 2, the optimal position and shape of the connecting rod are:

Among them, x _Tl and z _Tl are the coordinates of the nail cap in the new coordinate system; x _ol , y _ol and z _ol are the coordinates of the nail cap in the original coordinate system; is the curve parameter of the curve where the nail cap is located.

In the above embodiment, preferably, the activity range of the nail cap of the multi-axis nail is determined by:

Assuming the length of the screw cap is L’, the parameter equation of the screw cap can be expressed as:

(x,y,z)＝t(α _nut ,β _nut ,γ _nut )+M _nut (19)

s.t.0<t<L′

Among them, (α _nut ,β _nut ,γ _nut ) is the unit direction vector of the nail cap, M _nut is the position of the nail cap, and t represents the unknown number of the nail cap length;

Then, as shown in Figure 1, the movable range of the nail cap is:

in is the unit direction vector of the screw; _M0 is the entry point of the optimal screw trajectory; ω is the maximum movable angle between the screw cap and the screw.

The present invention also provides a multi-vertebral joint-constrained pedicle screw optimal trajectory planning device, comprising:

The first processing unit is used to determine the safe screw placement area for each vertebral body and obtain the entry point range of the screw trajectory on each vertebral body;

A second processing unit is used to calculate the optimal shape of the connecting rod using the entry point range of the screws on each vertebral body;

The third processing unit is used to determine the range of movement of the nail head of the multi-axis nail;

The fourth processing unit is used to form clinically effective screw insertion trajectory constraints using the avoidance area of vertebral screw placement, the position of the connecting rod and the range of motion of the multi-axial screw cap, and then determine the optimal trajectory of the pedicle screws of each vertebra under the combined constraints.

The present invention also provides a computer storage medium on which a computer program is stored. When the computer program is executed by a processor, the steps of the above-mentioned method for optimal trajectory planning of pedicle screws with multi-vertebral joint constraints are implemented.

The present invention also provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the above-mentioned multi-vertebral joint constrained pedicle screw optimal trajectory planning method steps when executing the computer program.

Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims (5)

1. A method for optimal trajectory planning of pedicle screws with multi-vertebral joint constraints, characterized in that it comprises the following steps: Determine the safe screw placement area for each vertebral body and obtain the entry point range of the screw trajectory on each vertebral body; The optimal shape of the connecting rod is calculated using the range of screw entry points on each vertebral body; Determine the range of motion of the multi-axis nail nut; The avoidance area of vertebral screw placement, the position of the connecting rod and the range of motion of the multi-axial screw cap are used to form the constraints of the clinically effective screw placement trajectory, and then the optimal trajectory of the pedicle screw of each vertebra under the combined constraints is determined; The safe screw placement area for each vertebral body is determined and the entry point range of the screw trajectory on each vertebral body is obtained by the following methods: The optimal path for pedicle screws is: The safe area for vertebral screw placement is: Where M is a point on the avoidance area, M ₀ is the entry point of the optimal screw trajectory; ρ is the safe distance from the screw to the avoidance area, and ρ>0; is the unit direction vector of the screw trajectory; Special symbols represent any; Formula (2) is transformed radially to simplify it into a cylinder with the optimal screw trajectory as the center line, specifically: Z ² +Y ² =(d-ρ) ² (4) 0≤X≤L in, is a unit vector orthogonal to (α, β, γ); is a unit vector orthogonal to (α, β, γ); is the space transformation matrix; L is the screw length; is the shortest distance from the optimal screw trajectory to the avoidance area; is the safe nail placement area; ρ is the safe distance from the screw to the avoidance area; L is the screw length; X, Y, Z are the original coordinates; The entry point range of the screw trajectory is: Z ² +Y ² =(d-ρ) ² (6) in, The range of entry points of the screw trajectory; The optimal shape of the connecting rod is a curve that conforms to the natural curvature of the spine and is located as close as possible to a plane in the direction of all ipsilateral optimal screw trajectories; the optimal shape of the connecting rod includes its position and shape, specifically: Assuming M ₀ (x, y, z) is the optimal screw trajectory entry point position on the same side of all vertebrae, the optimal connecting rod position is expressed as: AX+BY+CZ+D＝0 (7) Therefore, the optimal screw trajectory under the connecting rod constraint is expressed as: in, A, B, C, D are the parameters of the plane where the connecting rod is located; L′ is the length of the nail cap; (α _nut , β _nut , γ _nut ) is the unit direction vector of the nail cap; ω is the maximum angle that the nail cap can form with the nail; Assume that the best plane of the known connecting rod is P: AX+BY+CZ+D＝0 (11) Taking this plane as the XOZ plane, a new spatial coordinate system {i _T ,j _T ,k _T } can be constructed, then: Among them, N ₀ , N _x and N _z are points on the optimal plane P, and Perpendicular to Then the coordinates of the nail cap on the optimal plane P are: in, For the general Coordinates are converted to Space transformation matrix on coordinates; is the coordinate of the nail cap in the spatial coordinate system {i _T ,j _T ,k _T }; since the optimal plane P is defined as the XOZ plane of the spatial coordinate system {i _T ,j _T ,k _T }, then y _T = 0, therefore, the shape of the connecting rod is obtained by least squares fitting: z _Tl = fitting(θ,x _Tl ) (17) In summary, the optimal position and shape of the connecting rod are: Among them, x _Tl and z _TL are the coordinates of the nail cap in the new coordinate system; x _ol , y _ol and z _ol are the coordinates of the nail cap in the original coordinate system; θ is the curve parameter of the curve where the nail cap is located. 2. The optimal trajectory planning method for pedicle screws with multi-vertebral joint constraints according to claim 1 is characterized in that the range of motion of the screw cap of the multi-axis screw is determined by: Assuming the length of the screw cap is L’, the parametric equation of the screw cap is expressed as: (x,y,z)＝t(α _nut ,β _nut ,γ _nut )+M _nut (19) s.t.0<t<L′ Among them, (α _nut ,β _nut ,γ _nut ) is the unit direction vector of the nail cap, M _nut is the position of the nail cap, and t represents the unknown number of the nail cap length; The movable range of the nail cap is: in is the unit direction vector of the screw; _M0 is the entry point of the optimal screw trajectory; ω is the maximum movable angle between the screw cap and the screw. 3. A device for the optimal trajectory planning method of pedicle screws with multi-vertebral joint constraints according to claim 1 or 2, characterized in that it comprises: The first processing unit is used to determine the safe screw placement area for each vertebral body and obtain the entry point range of the screw trajectory on each vertebral body; A second processing unit is used to calculate the optimal shape of the connecting rod using the entry point range of the screws on each vertebral body; The third processing unit is used to determine the range of movement of the nail head of the multi-axis nail; The fourth processing unit is used to form clinically effective screw insertion trajectory constraints using the avoidance area of vertebral screw placement, the position of the connecting rod and the range of motion of the multi-axial screw cap, and then determine the optimal trajectory of the pedicle screws of each vertebra under the combined constraints. 4. A computer storage medium having a computer program stored thereon, characterized in that when the computer program is executed by a processor, the steps of the method for optimal trajectory planning of pedicle screws with multi-vertebral joint constraints described in any one of claims 1-2 are implemented. 5. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, the steps of the method for optimal trajectory planning of pedicle screws with multi-vertebral joint constraints described in any one of claims 1-2 are implemented.