CN115568942A - Method and device for optimal trajectory planning of pedicle screws with combined constraints of multiple vertebral bodies - Google Patents

Method and device for optimal trajectory planning of pedicle screws with combined constraints of multiple vertebral bodies Download PDF

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CN115568942A
CN115568942A CN202211259373.1A CN202211259373A CN115568942A CN 115568942 A CN115568942 A CN 115568942A CN 202211259373 A CN202211259373 A CN 202211259373A CN 115568942 A CN115568942 A CN 115568942A
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CN115568942B (en
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张蕴显
赵经纬
杨智
何达
刘波
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Capital Medical University
Beijing Jishuitan Hospital
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Beijing Jishuitan Hospital
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    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
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    • A61B17/56—Surgical instruments or methods for treatment of bones or joints; Devices specially adapted therefor
    • A61B17/58—Surgical instruments or methods for treatment of bones or joints; Devices specially adapted therefor for osteosynthesis, e.g. bone plates, screws or setting implements
    • A61B17/68—Internal fixation devices, including fasteners and spinal fixators, even if a part thereof projects from the skin
    • A61B17/70—Spinal positioners or stabilisers, e.g. stabilisers comprising fluid filler in an implant
    • A61B17/7074—Tools specially adapted for spinal fixation operations other than for bone removal or filler handling
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    • A61B17/58—Surgical instruments or methods for treatment of bones or joints; Devices specially adapted therefor for osteosynthesis, e.g. bone plates, screws or setting implements
    • A61B17/68—Internal fixation devices, including fasteners and spinal fixators, even if a part thereof projects from the skin
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    • A61B17/58—Surgical instruments or methods for treatment of bones or joints; Devices specially adapted therefor for osteosynthesis, e.g. bone plates, screws or setting implements
    • A61B17/68—Internal fixation devices, including fasteners and spinal fixators, even if a part thereof projects from the skin
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Abstract

本发明涉及一种多椎体联合约束的椎弓根螺钉最优轨迹规划方法，包括如下步骤：确定每个椎体置钉的安全置钉区域，获取每个椎体上螺钉轨迹的入点范围；利用每个椎体上螺钉的入点范围，计算连接杆的最优形态；确定多轴钉钉帽的活动范围；利用椎体置钉的规避区域、连接杆位置及多轴钉钉帽的活动范围形成临床有效螺钉置入轨迹的约束条件，然后确定出每个椎体在联合约束条件下的椎弓根螺钉最优轨迹。本发明能够准确、快速的计算出椎弓根螺钉的临床有效三维置入路径。

Figure 202211259373

The invention relates to a method for planning optimal trajectory of pedicle screws combined with multiple vertebral bodies, comprising the following steps: determining the safe screw placement area for each vertebral body, and obtaining the entry point range of the screw trajectory on each vertebral body ; Calculate the optimal shape of the connecting rod by using the range of the entry point of the screw on each vertebral body; determine the range of motion of the multi-axial screw cap; use the avoidance area of the vertebral body, the position of the connecting rod and the position of the multi-axial screw cap The range of motion forms the constraints of the clinically effective screw placement trajectory, and then the optimal trajectory of the pedicle screw for each vertebral body under the joint constraints is determined. The invention can accurately and quickly calculate the clinically effective three-dimensional insertion path of the pedicle screw.

Figure 202211259373

Description

Multi-vertebral body combined constraint pedicle screw optimal trajectory planning method and device
Technical Field
The invention relates to the technical field of spinal pedicle screw implantation, in particular to a multi-vertebral body combined constraint pedicle screw optimal trajectory planning method and device.
Background
Image-guided (robotic-assisted) pedicle screw placement may improve the accuracy of screw placement. Image-guided (robot-assisted) screw placement has a higher accuracy than manual screw placement. However, current commercial robot navigation systems are generally lacking in automation. The physician must manually plan the direction and location of the screw trajectory on the CT or CBCT image.
Current screw trajectory planning mainly uses a manual drag-and-drop strategy on CBCT images to obtain screw trajectories. This process interrupts the workflow and may lead to errors. Computer-aided planning methods therefore become a viable alternative. For example, the relationship between the bone density of the vertebral body and the screw placing track is revealed from different angles, and the screw track is planned according to the related relationship. The screw trajectory is found and optimized by CT image derived bone mechanics properties or bone density properties using a 3D planning system. And optimizing the screw track according to the CT image and the geometrical characteristics of the vertebral body, for example, finding the optimal screw track by constructing multi-angle projection and marking an avoidance area on a projection plane. Screw trajectory planning is performed by constructing a vertebral body and screw trajectory atlas and then registering the atlas to the target vertebral body. A vertebral body and vertebral pedicle automatic segmentation and trajectory planning method based on geometrical characteristics of vertebral pedicle. And carrying out vertebral body segmentation and screw trajectory planning by an artificial intelligence method.
In practice, however, it is often necessary to treat multiple vertebral bodies simultaneously. In this case, the ipsilateral screw needs to be connected with a rigid connecting rod to achieve the final purpose. Thus, in addition to constraining the placement of individual vertebral screws, a good understanding of the relative constraining relationships between different vertebral screws on the ipsilateral side is also desired. However, the conventional screw trajectory planning method is aimed at a single vertebral body so far, and the condition of multi-vertebral body constraint is not considered.
Disclosure of Invention
Aiming at the problems, the invention aims to provide a multi-vertebral body combined constraint optimal trajectory planning method and device for pedicle screws, the method provides an effective method for determining a screw-in point range and designing a connecting rod for multi-vertebral body combined screw placement, and can accurately and quickly calculate a clinically effective three-dimensional placement path of the pedicle screws
In order to realize the purpose, the invention adopts the following technical scheme:
the invention relates to a multi-vertebral body combined constraint pedicle screw optimal trajectory planning method, which comprises the following steps:
determining a safe screw placing area of each vertebral body screw placing, and acquiring an in-point range of a screw track on each vertebral body;
calculating the optimal form of the connecting rod by utilizing the range of the entry point of the screw on each vertebral body;
determining the moving range of the multi-axis nail cap;
and forming a constraint condition of a clinically effective screw placing track by utilizing the avoidance area of the vertebral body screw placing, the position of the connecting rod and the moving range of the multi-axis screw cap, and then determining the optimal track of the pedicle screw of each vertebral body under the combined constraint condition.
The optimal path planning method for the multi-vertebral body combined constraint pedicle screw preferably determines a safe screw placing area of each vertebral body screw placing, and the acquisition of the range of an entry point of the screw path on each vertebral body is realized by the following method:
the optimal path of the pedicle screw is as follows:
Figure BDA0003890807600000021
the safe screw-placing area of the vertebral body screw-placing is as follows:
Figure BDA0003890807600000022
where M is a point on the avoidance region, M 0 A nail insertion point for an optimal screw trajectory; rho is the safe distance from the screw to the avoidance area, and rho is greater than 0;
Figure BDA0003890807600000023
is a unit direction vector of the screw trajectory;
Figure BDA0003890807600000024
any is denoted for a special symbol;
carrying out radial transformation on the formula (2) to simplify the formula into a cylinder taking the optimal screw track as a central line, specifically:
Figure BDA0003890807600000025
z 2 +Y 2 ＝(d-ρ) 2 (4)
0≤X≤L
wherein,
Figure BDA0003890807600000031
an orthogonal unit vector of (α, β, γ);
Figure BDA0003890807600000032
Figure BDA0003890807600000033
an orthogonal unit vector of (α, β, γ);
Figure BDA0003890807600000034
is a spatial transformation matrix; l is the screw length;
Figure BDA0003890807600000035
the shortest distance from the optimal screw track to the avoidance area is obtained;
Figure BDA0003890807600000036
Figure BDA0003890807600000037
a safe nail placing area; rho is the safe distance from the screw to the avoided area; l is the screw length; x, Y, Z is the original coordinate;
the range of the nail penetration point of the screw track is as follows:
Figure BDA0003890807600000038
z 2 +Y 2 ＝(d-ρ) 2 (6)
wherein,
Figure BDA0003890807600000039
is the range of the nail penetration point of the screw track.
According to the optimal path planning method for the pedicle screw of the multi-vertebral body combined constraint, preferably, the optimal shape of the connecting rod is a curve which accords with the natural bending shape of the spine and is positioned on a plane which is as close to the optimal screw path directions on all the same sides as possible; the shape of the optimal connecting rod comprises the position and the shape thereof, and specifically comprises the following steps:
let M 0 (x, y, z) is the optimal screw track entry point position on all vertebral bodies ipsilateral, then the optimal connecting rod position is expressed as:
AX+BY+CZ+D＝0 (7)
Figure BDA00038908076000000310
thus, the optimal screw trajectory under the constraint of the connecting rod is expressed as:
Figure BDA00038908076000000311
Figure BDA0003890807600000041
wherein,
Figure BDA0003890807600000042
A. b, C, D is the parameter of the plane where the connecting rod is located; l' is the length of the nail cap; (alpha nut ，β nut ，γ nut ) Is a unit direction vector of the nail cap; omega is the maximum included angle which can be formed between the nail cap and the nail;
let the best plane of the known connecting rod be P:
AX+BY+CZ+D＝0 (11)
by taking the plane as an XOZ plane, a new space coordinate system { i }can be constructed T ，j T ，k T And then:
Figure BDA0003890807600000043
Figure BDA0003890807600000044
Figure BDA0003890807600000045
wherein N is 0 、N x And N z Is a point on the optimal plane P, and
Figure BDA0003890807600000046
perpendicular to
Figure BDA0003890807600000047
The coordinates of the nut on the optimal plane P are:
Figure BDA0003890807600000048
Figure BDA0003890807600000049
wherein,
Figure BDA00038908076000000410
to be composed of
Figure BDA00038908076000000411
Coordinate conversion to
Figure BDA00038908076000000412
A spatial transformation matrix on the coordinates;
Figure BDA00038908076000000413
for the head of the nail in a spatial coordinate system i T ，j T ，k T Coordinates under }; since, the best plane P is defined as the space coordinate system { i } T ，j T ，k T XOZ face of (i) }, then y T =0, therefore, the shape of the connecting rod is found by a least-squares fit:
Figure BDA00038908076000000414
in summary, the optimal position and shape of the connecting rod are obtained as follows:
Figure BDA0003890807600000051
wherein x is Tl And z Tl The coordinates of the nail cap in the new coordinate system; x is the number of ol 、y ol And z ol The coordinates of the nail cap under the original coordinate system are obtained;
Figure BDA0003890807600000054
the curve parameters of the curve on which the nail head is positioned.
The optimal trajectory planning method for the multi-vertebral body combined constraint pedicle screw is preferably realized by determining the moving range of the screw cap of the multi-axis screw in the following modes:
and if the length of the screw cap of the screw is L', the parameter equation of the screw cap is expressed as follows:
(x，y，z)＝t(α nut ，β nut ，γ nut )+M nut (19)
s.t.0＜t＜L′
wherein (alpha) nut ，β nut ，γ nut ) Is a unit direction vector of the nail head, M nut T represents the unknown number of the length of the nail head as the position of the nail head;
the movable range of the nail cap is as follows:
Figure BDA0003890807600000055
Figure BDA0003890807600000052
wherein
Figure BDA0003890807600000053
Is the unit direction vector of the screw; m 0 A nail insertion point for an optimal screw trajectory; omega is the maximum movable included angle between the screw cap and the screw.
The invention relates to a multi-vertebral body combined constraint pedicle screw optimal trajectory planning device, which comprises:
the first processing unit is used for determining a safe screw placing area of each vertebral body screw placing and acquiring an in-point range of a screw track on each vertebral body;
the second processing unit is used for calculating the optimal form of the connecting rod by utilizing the range of the entry point of the screw on each vertebral body;
the third processing unit is used for determining the moving range of the multi-axis nail cap;
and the fourth processing unit is used for forming a constraint condition of a clinically effective screw placing track by utilizing the avoidance area of the vertebral body screw placing, the position of the connecting rod and the moving range of the multi-axis screw cap, and then determining the optimal track of the pedicle screw of each vertebral body under the combined constraint condition.
The computer storage medium of the invention stores a computer program thereon, and the computer program is executed by a processor to realize the optimal path planning method steps of the pedicle screw with multi-vertebral body combined constraint.
The computer equipment comprises a memory, a processor and a computer program which is stored on the memory and can run on the processor, wherein the processor realizes the optimal path planning method steps of the pedicle screw with multi-vertebral body combined constraint when executing the computer program.
Due to the adoption of the technical scheme, the invention has the following advantages:
the invention provides an effective method for determining the range of the screw inserting point and the design of the connecting rod for the combined screw inserting of multiple vertebral bodies, and can accurately and quickly calculate the clinical effective three-dimensional inserting path of the pedicle screw.
Drawings
Various other advantages and benefits will become apparent to those of ordinary skill in the art upon reading the following detailed description of the preferred embodiments. The drawings are only for purposes of illustrating the preferred embodiments and are not to be construed as limiting the invention. Like reference numerals refer to like parts throughout the drawings. In the drawings:
FIG. 1 is a schematic view of the range of motion of the screw of the present invention;
figure 2 is a schematic view of the preferred form of the connecting rod of the present invention.
Detailed Description
Exemplary embodiments of the present invention will be described in more detail below with reference to the accompanying drawings. While exemplary embodiments of the invention are shown in the drawings, it should be understood that the invention can be embodied in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art.
The invention provides a multi-vertebral body combined constraint optimal trajectory planning method for pedicle screws, which comprises the steps of determining a safe region for placing screws on each vertebral body, and obtaining an entry point range of the trajectory of the screws on each vertebral body; calculating the clinical effective position of the connecting rod by using the range of the entry point of the screw on each vertebral body; determining the moving range of the multi-axis nail cap; and forming constraint conditions of an optimal screw placing track by utilizing the avoidance area of the vertebral body screw placing, the position of the connecting rod and the moving range of the multi-axis screw cap, and then calculating the effective screw track of each vertebral body under the combined constraint conditions. The invention provides an effective method for determining the range of the screw inserting point and the design of the connecting rod for the combined screw inserting of multiple vertebral bodies, and can accurately and quickly calculate the clinical effective three-dimensional inserting path of the pedicle screw.
The invention provides a multi-vertebral body combined constraint pedicle screw optimal trajectory planning method, which comprises the following steps:
s1, determining a safe screw placing area of each vertebral body screw placing, and acquiring an in-point range of a screw track on each vertebral body;
s2, calculating the optimal form of the connecting rod by using the range of the entry point of the screw on each vertebral body;
s3, determining the moving range of the multi-axis nail cap;
and S4, forming a constraint condition of a clinically effective screw placing track by utilizing the evaded area of the vertebral body screw placing, the position of the connecting rod and the moving range of the multi-axis screw cap, and then determining the optimal track of the pedicle screw of each vertebral body under the combined constraint condition.
In the above embodiment, preferably, the safe screw-placing area of each vertebral body screw-placing is determined, and the range of the point of entry of the screw track on each vertebral body is obtained by:
the optimal path of the pedicle screw is as follows:
Figure BDA0003890807600000071
the safe screw-placing area of the vertebral body screw-placing is as follows:
Figure BDA0003890807600000072
where M is a point on the avoidance region, M 0 A nail insertion point for an optimal screw trajectory; rho is greater than 0 and is the safe distance from the screw to the avoidance area;
Figure BDA0003890807600000073
a unit direction vector of the screw trajectory;
Figure BDA0003890807600000074
any is denoted for a special symbol;
for the safety of nail placement and the simplicity of calculation, the formula (2) can be subjected to radial transformation to simplify the transformation into a cylinder taking the optimal screw track as a central line, specifically:
Figure BDA0003890807600000075
z 2 +Y 2 ＝(d-ρ) 2 (4)
0≤X≤L
wherein,
Figure BDA0003890807600000076
an orthogonal unit vector of (α, β, γ);
Figure BDA0003890807600000077
Figure BDA0003890807600000078
an orthogonal unit vector of (α, β, γ);
Figure BDA0003890807600000079
is a spatial transformation matrix; l is the screw length;
Figure BDA00038908076000000710
the shortest distance from the optimal screw track to the avoidance area is obtained;
Figure BDA00038908076000000711
Figure BDA0003890807600000081
a safe nail placing area; rho is the safe distance from the screw to the avoidance zone; l is the screw length; x, Y, Z is the original coordinate;
wherein, the nail penetration point range of screw track is:
Figure BDA0003890807600000082
z 2 +Y 2 ＝(d-p) 2 (6)
wherein,
Figure BDA0003890807600000083
is the range of the nail penetration point of the screw track.
In the above embodiment, preferably, the optimal configuration of the connecting rod is a curve conforming to the natural curvature configuration of the spine and lying as close as possible to the plane in the direction of the optimal trajectory of the screws on all ipsilateral sides; the form of the optimal connecting rod comprises the position and the shape thereof, and specifically comprises the following steps:
let M 0 (x, y, z) is the optimal screw trajectory entry point position for all vertebras ipsilateral, then the optimal connecting rod position can be expressed as:
AX+BY+CZ+D＝0 (7)
Figure BDA0003890807600000084
thus, the optimal screw trajectory under the constraint of the connecting rod can be expressed as:
Figure BDA0003890807600000085
Figure BDA0003890807600000086
wherein,
Figure BDA0003890807600000087
A. b, C, D is the parameter of the plane where the connecting rod is located; l' is the length of the nail cap; (alpha nut ，β nut ，γ nut ) Is a unit direction vector of the nail cap; the omega nail cap can form a maximum included angle with the nail;
let the best plane of the known connecting rod be P:
AX+BY+CZ+D＝0 (11)
by taking the plane as an XOZ plane, a new space coordinate system { i }can be constructed T ，j T ，k T And then:
Figure BDA0003890807600000091
Figure BDA0003890807600000092
Figure BDA0003890807600000093
wherein N is 0 ，N x ，N z Is a point on the optimal plane P, the moon
Figure BDA0003890807600000094
Perpendicular to
Figure BDA0003890807600000095
The coordinates of the nut on the optimal plane P are:
Figure BDA0003890807600000096
Figure BDA0003890807600000097
wherein,
Figure BDA0003890807600000098
to be composed of
Figure BDA0003890807600000099
Coordinate conversion to
Figure BDA00038908076000000910
A spatial transformation matrix on the coordinates;
Figure BDA00038908076000000911
for the head of the nail in a spatial coordinate system i T ，j T ，k T Coordinates under }; since, the optimal plane P is defined as the space coordinate system { i } T ，j T ，k T XOZ face of (i) }, then y T =0, therefore, the shape of the connecting rod can be derived by least-squares fitting:
Figure BDA00038908076000000913
as shown in fig. 2, the optimal position and shape of the connecting rod can be summarized as follows:
Figure BDA00038908076000000912
wherein x is Tl And z Tl The coordinates of the nail cap under the new coordinate system; x is the number of ol 、y ol And z ol The coordinates of the nail cap under the original coordinate system;
Figure BDA0003890807600000103
the curve parameters of the curve on which the nail head is positioned.
In the above embodiment, preferably, the determination of the range of motion of the cap of the multi-axis nail is performed by:
if the length of the screw cap is L', the parameter equation of the screw cap can be expressed as follows:
(x，y，z)＝t(α nut ，β nut ，γ nut )+M nut (19)
s.t.0＜t＜L′
wherein (alpha) nut ，β nut ，γ nut ) Is a unit direction vector of the nail head, M nut T represents the unknown number of the length of the nail head as the position of the nail head;
then, as shown in fig. 1, the movable range of the nail head is:
Figure BDA0003890807600000104
Figure BDA0003890807600000101
wherein
Figure BDA0003890807600000102
Is the unit direction vector of the screw; m 0 A nail insertion point for an optimal screw trajectory; omega is the maximum movable included angle between the screw cap and the screw.
The invention also provides a multi-vertebral body combined constraint optimal trajectory planning device for the pedicle screws, which comprises:
the first processing unit is used for determining a safe screw placing area of each vertebral body screw placing and acquiring an in-point range of a screw track on each vertebral body;
the second processing unit is used for calculating the optimal form of the connecting rod by utilizing the range of the entry point of the screw on each vertebral body;
the third processing unit is used for determining the moving range of the multi-axis nail cap;
and the fourth processing unit is used for forming a constraint condition of a clinically effective screw placing track by utilizing the avoidance area of the vertebral body screw placing, the position of the connecting rod and the moving range of the multi-axis screw cap, and then determining the optimal track of the pedicle screw of each vertebral body under the combined constraint condition.
The invention also provides a computer storage medium on which a computer program is stored, wherein the computer program is executed by a processor to realize the optimal path planning method steps of the multi-vertebral body combined constraint pedicle screw.
The invention also provides computer equipment which comprises a memory, a processor and a computer program which is stored on the memory and can run on the processor, wherein the processor realizes the optimal path planning method steps of the multi-vertebral body combined constraint pedicle screw when executing the computer program.
Finally, it should be noted that: the above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.

Claims (7)

1.一种多椎体联合约束的椎弓根螺钉最优轨迹规划方法，其特征在于，包括如下步骤：1. a pedicle screw optimal trajectory planning method of multi-vertebral joint constraint, is characterized in that, comprises the steps: 确定每个椎体置钉的安全置钉区域，获取每个椎体上螺钉轨迹的入点范围；Determine the safe screw placement area for each vertebral body, and obtain the entry point range of the screw trajectory on each vertebral body; 利用每个椎体上螺钉的入点范围，计算连接杆的最优形态；Using the range of the entry point of the screw on each vertebral body, calculate the optimal shape of the connecting rod; 确定多轴钉钉帽的活动范围；Determine the range of motion of the multi-axial nail cap; 利用椎体置钉的规避区域、连接杆位置及多轴钉钉帽的活动范围形成临床有效螺钉置入轨迹的约束条件，然后确定出每个椎体在联合约束条件下的椎弓根螺钉最优轨迹。Using the avoidance area of the vertebral body screw, the position of the connecting rod and the range of motion of the multiaxial screw cap to form the constraint conditions of the clinically effective screw insertion trajectory, and then determine the maximum pedicle screw of each vertebral body under the combined constraint conditions Excellent trajectory. 2.根据权利要求1所述的多椎体联合约束的椎弓根螺钉最优轨迹规划方法，其特征在于，确定每个椎体置钉的安全置钉区域，获取每个椎体上螺钉轨迹的入点范围是通过以下方式实现的：2. The pedicle screw optimal trajectory planning method of multi-vertebral joint constraint according to claim 1, characterized in that, determine the safe screw-setting area of each vertebral body, and obtain the screw trajectory on each vertebral body The in-point scope of is achieved by: 椎弓根螺钉最优路径为：The optimal path for pedicle screws is:
Figure FDA0003890807590000011
Figure FDA0003890807590000011
 椎体置钉的安全置钉区域为：The safe nail placement area for vertebral body screw placement is:
Figure FDA0003890807590000012
Figure FDA0003890807590000012
 其中，M是规避区域上的点，M0为最优螺钉轨迹的入钉点；ρ为螺钉到规避区域的安全距离，且ρ>0；
Figure FDA0003890807590000013
为螺钉轨迹的单位方向向量；
Figure FDA0003890807590000014
为特殊符号表示任意；Among them, M is a point on the avoidance area, and M0 is the entry point of the optimal screw trajectory; ρ is the safe distance from the screw to the avoidance area, and ρ>0;
Figure FDA0003890807590000013
is the unit direction vector of the screw trajectory;
Figure FDA0003890807590000014
Denote any special symbol; 对公式(2)进行放射变换，使其简化为一个以最优螺钉轨迹为中心线圆柱体，具体为：Carry out radial transformation on the formula (2) to simplify it into a cylinder with the optimal screw trajectory as the center line, specifically:
Figure FDA0003890807590000015
Figure FDA0003890807590000015
 z2+γ2＝(d-ρ)2 (4)z 2 +γ 2 =(d-ρ) 2 (4) 0≤X≤L0≤X≤L 其中，
Figure FDA0003890807590000021
为(α,β,γ)的正交的单位向量；
Figure FDA0003890807590000022
Figure FDA0003890807590000023
为(α,β,γ)的正交的单位向量；
Figure FDA0003890807590000024
为空间变换矩阵；L为螺钉长度；
Figure FDA0003890807590000025
为最优螺钉轨迹到规避区域的最短距离；
Figure FDA0003890807590000026
Figure FDA0003890807590000027
为安全置钉区域；ρ为螺钉到避开区域的安全距离；L为螺钉长度；X、Y、Z为原始坐标；in,
Figure FDA0003890807590000021
is an orthogonal unit vector of (α, β, γ);
Figure FDA0003890807590000022
Figure FDA0003890807590000023
is an orthogonal unit vector of (α, β, γ);
Figure FDA0003890807590000024
is the space transformation matrix; L is the screw length;
Figure FDA0003890807590000025
is the shortest distance from the optimal screw trajectory to the avoidance area;
Figure FDA0003890807590000026
Figure FDA0003890807590000027
is the safe nailing area; ρ is the safe distance from the screw to the avoiding area; L is the screw length; X, Y, Z are the original coordinates; 螺钉轨迹的入钉点范围为：The entry point range of the screw trajectory is:
Figure FDA0003890807590000028
Figure FDA0003890807590000028
 z2+Y2＝(d-ρ)2 (6)z 2 +Y 2 =(d-ρ) 2 (6) 其中，
Figure FDA0003890807590000029
为螺钉轨迹的入钉点范围。in,
Figure FDA0003890807590000029
It is the nail entry point range of the screw track. 3.根据权利要求2所述的多椎体联合约束的椎弓根螺钉最优轨迹规划方法，其特征在于，所述连接杆的最优形态是符合脊柱自然弯曲形态的曲线，且位于尽可能靠近所有同侧最优螺钉轨迹方向上的平面；所述最优连接杆的形态包括其位置和形状，具体为：3. The optimal trajectory planning method for pedicle screws of multi-vertebral joint constraints according to claim 2, characterized in that the optimal shape of the connecting rod is a curve that conforms to the natural curvature of the spine, and is located as far as possible Close to the plane in the direction of the optimal screw trajectory on the same side; the shape of the optimal connecting rod includes its position and shape, specifically: 设M0(x,y,z)为所有椎体同侧最优螺钉轨迹入点位置，则最优连接杆位置表示为：Let M 0 (x, y, z) be the entry point position of the optimal screw trajectory of all vertebral bodies on the same side, then the optimal connecting rod position is expressed as: AX+BY+CZ+D＝0 (7)AX+BY+CZ+D=0 (7)
Figure FDA00038908075900000210
Figure FDA00038908075900000210
 因此，在连接杆约束下的最优螺钉轨迹表示为：Therefore, the optimal screw trajectory under the constraint of the connecting rod is expressed as:
Figure FDA0003890807590000031
Figure FDA0003890807590000031
Figure FDA0003890807590000032
Figure FDA0003890807590000032
 其中，
Figure FDA0003890807590000033
A、B、C、D为连接杆所在位置平面的参数；L′为钉帽长度；(αnut,βnut,γnut)为钉帽的单位方向向量；ω为钉帽能够与钉子形成的最大夹角；in,
Figure FDA0003890807590000033
A, B, C, D are the parameters of the plane where the connecting rod is located; L′ is the length of the nut; (α nut , β nut , γ nut ) is the unit direction vector of the nut; ω is the distance between the nut and the nail maximum angle; 设已知连接杆的最佳平面为P：Let the best plane of the known connecting rod be P: AX+BY+CZ+D＝0 (11)AX+BY+CZ+D=0 (11) 以该平面为XOZ面可构建新的空间坐标系{iT,jT,kT}，则：A new space coordinate system {i T , j T , k T } can be constructed by using this plane as the XOZ plane, then:
Figure FDA0003890807590000034
Figure FDA0003890807590000034
Figure FDA0003890807590000035
Figure FDA0003890807590000035
Figure FDA0003890807590000036
Figure FDA0003890807590000036
 其中，N0、Nx和Nz为最佳平面P上的点，且
Figure FDA0003890807590000037
垂直于
Figure FDA0003890807590000038
则钉帽在最佳平面P上的坐标为:Among them, N 0 , N x and N z are points on the best plane P, and
Figure FDA0003890807590000037
perpendicular to
Figure FDA0003890807590000038
Then the coordinates of the nail cap on the best plane P are:
Figure FDA0003890807590000039
Figure FDA0003890807590000039
Figure FDA00038908075900000310
Figure FDA00038908075900000310
 其中，
Figure FDA00038908075900000311
为将
Figure FDA00038908075900000312
坐标转换为
Figure FDA00038908075900000313
坐标上的空间变换矩阵；
Figure FDA00038908075900000314
为钉帽在空间坐标系{iT,jT,kT}下的坐标；由于，定义最佳平面P为空间坐标系{iT,jT,kT}的XOZ面，则yT＝0，因此，连接杆的形状通过最小二乘法拟合得出：in,
Figure FDA00038908075900000311
for will
Figure FDA00038908075900000312
Coordinates converted to
Figure FDA00038908075900000313
Space transformation matrix on coordinates;
Figure FDA00038908075900000314
is the coordinates of the nail cap in the space coordinate system {i T , j T , k T }; since the best plane P is defined as the XOZ plane of the space coordinate system {i T , j T , k T }, then y T = 0, therefore, the shape of the connecting rod is fitted by the least square method:
Figure FDA00038908075900000315
Figure FDA00038908075900000315
 综上，得到连接杆最优位置和形状为：In summary, the optimal position and shape of the connecting rod can be obtained as:
Figure FDA0003890807590000041
Figure FDA0003890807590000041
 其中，xTl和zTl为钉帽在新坐标系下的坐标；xol、yol和zol为钉帽在原始坐标系下的坐标；
Figure FDA0003890807590000045
为钉帽所在曲线的曲线参数。Wherein, x Tl and z Tl are the coordinates of the nail cap under the new coordinate system; x ol , y ol and z ol are the coordinates of the nail cap under the original coordinate system;
Figure FDA0003890807590000045
is the curve parameter of the curve where the nail cap is located. 4.根据权利要求1所述的多椎体联合约束的椎弓根螺钉最优轨迹规划方法，其特征在于，确定多轴钉的钉帽的活动范围是通过以下方式实现的：4. the pedicle screw optimal trajectory planning method of multi-vertebral body joint constraint according to claim 1, is characterized in that, the scope of motion of the nail cap of determining polyaxial screw is realized by the following manner: 设螺钉钉帽长度为L’，则钉帽的参数方程表示为：Assuming the length of the screw cap is L', the parameter equation of the cap is expressed as: (x,y,z)＝t(αnut,βnut,γnut)+Mnut (19)(x,y,z)=t(α nut ,β nut ,γ nut )+M nut (19) s.t.0<t<L′s.t.0<t<L' 其中，(αnut,βnut,γnut)为钉帽的单位方向向量，Mnut为钉帽的位置，t表示钉帽长度的未知数；Wherein, (α nut , β nut , γ nut ) is the unit direction vector of the nut, M nut is the position of the nut, and t represents the unknown number of the length of the nut; 则钉帽的可活动范围为：Then the movable range of the nail cap is:
Figure FDA0003890807590000042
Figure FDA0003890807590000042
Figure FDA0003890807590000043
Figure FDA0003890807590000043
 其中
Figure FDA0003890807590000044
为螺钉的单位方向向量；M0为最优螺钉轨迹的入钉点；ω为钉帽与螺钉之间的最大可活动夹角。in
Figure FDA0003890807590000044
is the unit direction vector of the screw; M 0 is the entry point of the optimal screw trajectory; ω is the maximum movable angle between the nut and the screw. 5.一种多椎体联合约束的椎弓根螺钉最优轨迹规划装置，其特征在于，包括：5. A device for optimal trajectory planning of pedicle screws combined with multiple vertebral bodies, characterized in that it comprises: 第一处理单元，用于确定每个椎体置钉的安全置钉区域，获取每个椎体上螺钉轨迹的入点范围；The first processing unit is configured to determine the safe nail placement area for each vertebral body, and obtain the entry point range of the screw trajectory on each vertebral body; 第二处理单元，用于利用每个椎体上螺钉的入点范围，计算连接杆的最优形态；The second processing unit is used to calculate the optimal shape of the connecting rod by using the range of the entry point of the screw on each vertebral body; 第三处理单元，用于确定多轴钉钉帽的活动范围；The third processing unit is used to determine the range of motion of the multi-axis nail cap; 第四处理单元，用于利用椎体置钉的规避区域、连接杆位置及多轴钉钉帽的活动范围形成临床有效螺钉置入轨迹的约束条件，然后确定出每个椎体在联合约束条件下的椎弓根螺钉最优轨迹。The fourth processing unit is used to use the avoidance area of the vertebral body, the position of the connecting rod and the range of motion of the multi-axial screw cap to form the constraint conditions of the clinically effective screw insertion trajectory, and then determine the joint constraint conditions of each vertebral body. The optimal trajectory of the lower pedicle screw. 6.一种计算机存储介质，其上存储有计算机程序，其特征在于，所述计算机程序被处理器执行时实现权利要求1-4中任一项所述的多椎体联合约束的椎弓根螺钉最优轨迹规划方法步骤。6. A computer storage medium, on which a computer program is stored, characterized in that, when the computer program is executed by a processor, the pedicle of any one of claims 1-4 is realized that is jointly constrained by multiple vertebral bodies The steps of screw optimal trajectory planning method. 7.一种计算机设备，包括存储器、处理器及存储在存储器上并可在处理器上运行的计算机程序，其特征在于，所述处理器执行所述计算机程序时实现权利要求1-4任意一项所述多椎体联合约束的椎弓根螺钉最优轨迹规划方法步骤。7. A computer device, comprising a memory, a processor, and a computer program stored on the memory and operable on the processor, characterized in that, when the processor executes the computer program, any one of claims 1-4 is realized The steps of the optimal trajectory planning method for pedicle screws with combined constraints of multiple vertebral bodies described in the item.
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