Method and system for calculating the rotation center of the femoral head

Abstract

The present invention provides a method and system for calculating the center of rotation of the femoral head. The method comprises: recording the spatial position data of multiple markers on the femoral head when the thigh is shaken; using a random sampling consensus algorithm to delete singular points in the spatial position data; using Gaussian elimination to fit the spatial position data to obtain the initial spherical center coordinates; calculating the average of the spherical center coordinates of all markers; using the average of the spherical centers as the initial value, using the Cauchy kernel function as the robust kernel function, and establishing a spherical equation based on the information of all tracking markers after deleting singular points, performing nonlinear iterative optimization, and obtaining the spherical center coordinates. The method and system for calculating the center of rotation of the femoral head provided by the present invention can accurately calculate the center of rotation of the femoral head, and is simple, convenient, and robust.

Description

Technical Field

[0001] The present invention relates to the technical field of surgical navigation systems, and in particular to a method and system for calculating the rotation center of a femoral head. Background Art

[0002] Total knee replacement (TKR) is one of the most effective surgical procedures for resolving severe knee joint lesions that affect a patient's mobility and can effectively improve their quality of life. However, traditional knee replacement surgery currently relies heavily on the clinician's experience, with a failure rate of 5% to 8% due to prosthesis loosening, dislocation, fracture, and infection. Compared to traditional knee replacement surgery, the knee replacement surgical navigation system combines computer image processing with precise robotic planning to perform intelligent force and motion analysis, assisting clinicians in completing knee replacement surgery. This system can reduce surgical injuries, shorten operative time, and improve surgical success rate and quality.

[0003] The goal of total knee replacement surgery is to completely align the patient's femoral force line with the tibial force line after surgery. Therefore, the navigation system for knee replacement surgery needs to calculate the femoral head center to obtain the femoral force line to evaluate the success of the surgery. Therefore, it is of great significance to study the calculation method and system of the femoral head rotation center. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a method and system for calculating the rotation center of the femoral head, which can accurately calculate the rotation center point of the femoral head and is simple, convenient and robust.

[0005] In order to solve the above technical problems, the present invention provides a method for calculating the rotation center of the femoral head, which includes: recording the spatial position data of multiple markers on the femoral head when the thigh is shaken; using a random sampling consensus algorithm to delete the singular points of the spatial position data; using the Gaussian elimination method to fit the initial sphere center coordinates of the spatial position data; calculating the average value of the sphere center coordinates of all markers; taking the average value of the sphere center as the initial value, using the Cauchy kernel function as the robust kernel function, and based on the information of all tracking markers after deleting the singular points, establishing a spherical equation, performing nonlinear iterative optimization, and obtaining the sphere center coordinates.

[0006] In some embodiments, the initial sphere center coordinates of the spatial position data are obtained by fitting using the Gaussian elimination method, including: fitting the initial sphere center coordinates of the spatial position data using the Gaussian elimination method according to the constructed function.

[0007] In some embodiments, the constructed function has the following form:

[0008]

[0009] Among them, x0 is the x-axis coordinate of the initial sphere center coordinate, y0 is the y-axis coordinate of the initial sphere center coordinate, z0 is the z-axis coordinate of the initial sphere center coordinate, x i is the x-axis coordinate of the spatial position data, y i is the y-axis coordinate of the spatial position data, z i is the z-axis coordinate of the spatial position data, and R is the radius of the sphere.

[0010] In some embodiments, the initial sphere center coordinates of the spatial position data are fitted using Gaussian elimination method according to the constructed function, including: fitting the initial sphere center coordinates of the spatial position data by solving a set of equations derived from the constructed function.

[0011] In some embodiments, the system of equations has the following form:

[0012]

[0013]

[0014]

[0015] Among them, (u i ,v i ,w i ) is the offset of the spatial position data, and (u0,v0,w0) is the initial value of the offset.

[0016] In addition, the present invention also provides a femoral head rotation center calculation system, which includes: one or more processors; a storage device for storing one or more programs, and when the one or more programs are executed by the one or more processors, the one or more processors implement the femoral head rotation center calculation method described above.

[0017] After adopting such a design, the present invention has at least the following advantages:

[0018] Gaussian elimination can be used to quickly obtain the approximate position of the sphere center coordinates, and then the nonlinear iterative method can be used to quickly and accurately calculate the sphere center coordinates, avoiding the defect of nonlinear iteration entering the local optimum. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] The above is only an overview of the technical solution of the present invention. In order to more clearly understand the technical means of the present invention, the present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0020] Figure 1 This is a flow chart for calculating the center of rotation of the femoral head. DETAILED DESCRIPTION

[0021] The preferred embodiments of the present invention are described below with reference to the accompanying drawings. It should be understood that the preferred embodiments described herein are only used to illustrate and explain the present invention, and are not used to limit the present invention.

[0022] The present invention proposes a femoral head center calculation method and system, which can accurately calculate the femoral head rotation center point and is simple, convenient and robust.

[0023] The confirmation of the femoral head center is the basis for the confirmation of the femoral force line and is also the premise for the prosthesis placement planning during the knee joint navigation system. The present invention provides a method and system for calculating the femoral head center of the knee joint navigation system.

[0024] A tracking marker bracket is installed on the femur. With the hip joint fixed, the thigh shaking operation is completed and the spatial position of each tracking marker in the tracking marker bracket is recorded.

[0025] First, for each marker position, the random sample consensus (RANSAC) algorithm is used to calculate the variance of different sets of markers and remove singular points.

[0026] Then for each set of tracking marker points, construct a function

[0027]

[0028] The goal is to calculate (x0, y0, z0, R) so that H is minimized.

[0029]

[0030]

[0031]

[0032]

[0033] The coordinates of the sphere center are obtained by fitting using the Gaussian elimination method. Assume:

[0034]

[0035] Simplified to get

[0036]

[0037]

[0038]

[0039] Solving the equation to get (u0, v0, w0) will give (x0, y0, z0).

[0040] Then calculate the average of the sphere centers of all tracking markers.

[0041] The average value of the center of the sphere is used as the initial value, the Cauchy Loss kernel function is used as the robust kernel function, and the information of all tracking markers after deleting the singular points is used as the basis to establish the spherical equation and perform nonlinear iterative optimization to obtain the center of the sphere.

[0042] The nonlinear least squares equation for calculating the sphere center is established as:

[0043]

[0044] The Cauchy Loss kernel function expression is: ρ(s) = log(1+s)

[0045] The advantage of the present invention is that the approximate position of the sphere center coordinates can be quickly obtained through Gaussian elimination, and then the sphere center coordinates can be quickly and accurately calculated through a nonlinear iterative method, avoiding the defect of nonlinear iteration entering a local optimum.

[0046] The above description is only a preferred embodiment of the present invention and does not limit the present invention in any form. Those skilled in the art can make some simple modifications, equivalent changes or modifications based on the technical content disclosed above, which all fall within the scope of protection of the present invention.

Claims

1. A method for calculating the rotation center of the femoral head, characterized in that: include: Record the spatial position data of multiple markers on the femoral head when shaking the thigh; Use random sampling consensus algorithm to remove singular points in spatial position data; The Gaussian elimination method is used to fit the initial spherical center coordinates of the spatial position data, including: According to the constructed function, the Gaussian elimination method is used to fit the initial sphere center coordinates of the spatial position data. The constructed function has the following form: Among them, x0 is the x-axis coordinate of the initial sphere center coordinate, y0 is the y-axis coordinate of the initial sphere center coordinate, z0 is the z-axis coordinate of the initial sphere center coordinate, x i is the x-axis coordinate of the spatial position data, y i is the y-axis coordinate of the spatial position data, z i is the z-axis coordinate of the spatial position data, and R is the radius of the sphere; Calculate the average of the sphere center coordinates of all markers; The average value of the sphere center is used as the initial value, the Cauchy kernel function is used as the robust kernel function, and the information of all tracking markers after deleting the singular points is used as the basis to establish a spherical equation, perform nonlinear iterative optimization, and obtain the sphere center coordinates, which are the rotation center of the femoral head; The nonlinear least squares equation for calculating the sphere center is established as: The Cauchy Loss kernel function expression is: ρ(s) = log(1+s).

2. The method for calculating the center of rotation of the femoral head according to claim 1, wherein: According to the constructed function, the Gaussian elimination method is used to fit the initial sphere center coordinates of the spatial position data, including: By solving the set of equations derived from the constructed function, the initial sphere center coordinates of the spatial position data are fitted.

3. The method for calculating the center of rotation of the femoral head according to claim 2, wherein: The system of equations has the following form: Among them, (u i ,v i ,w i ) is the offset of the spatial position data, and (u0,v0,w0) is the initial value of the offset.

4. A femoral head rotation center calculation system, characterized in that: include: one or more processors; a storage device for storing one or more programs, When the one or more programs are executed by the one or more processors, the one or more processors implement the method for calculating the femoral head rotation center according to any one of claims 1 to 3.

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