Method and device for finding the center of rotation of a hip joint, surgical planning system

Abstract

Provided are a method and device for finding the center of rotation of a hip joint, a surgical planning system, and a storage medium. A sphere is fitted by taking a set of points on the joint surface of a hip joint model, and the center of the sphere is taken as the center of rotation of the hip joint, wherein the sphere fitting is performed using a nonlinear optimization method in a manner that minimizes an error function, and the weight is updated in each iteration, wherein the sphere and the corresponding points are matched by minimizing the weighted sum of squares of the difference between the Euclidean distance of each point to the center of the sphere and the radius of the sphere based on a weighted least squares method. The weight is the inverse of the Euclidean distance from the corresponding points to the center of the fitted sphere. The sphere center point to be estimated and the radius variable are expressed as a vector, and the Levenberg-Marquardt nonlinear optimization method is used to obtain the sphere center point expressed as a vector and the radius R thereof. Thus, the fitting can be performed accurately and stably while taking into account measurement errors caused by, for example, joint surface wear.

Description

Technical Field

[0001] This invention relates to a data fitting technique based on a skeletal model, and in particular to a method and apparatus for finding the rotation center of the acetabulum, a surgical planning system, and a storage medium. Background Technology

[0002] Total hip arthroplasty (THA) can be performed using computer-aided robotic surgical guidance systems to plan and execute the procedure consistently and repeatably. For example, by utilizing patient-specific information gathered from preoperative CT scans, surgeons can flexibly adjust the plan preoperatively and intraoperatively to achieve proper hip biomechanical reconstruction for each patient with correctly placed and positioned acetabular prostheses. This placement is achieved using various parameters such as the acetabular rotation center, syndesmotic anteversion, hip joint length, and syndesmotic offset.

[0003] The center of rotation of the acetabulum can be defined as the center of a fitted sphere on the articular surface of a three-dimensional acetabular model. This sphere can be fitted by searching and collecting points on the acetabular joint surface on a CT scan. In an ideal model with a smooth acetabular joint surface, a sphere with only four well-distributed points would fit perfectly. However, actual point selection often introduces measurement errors. For example, in real life, the joint surface may also show wear, resulting in errors, which is also part of the morphology of the diseased bones captured by the CT scan.

[0004] Under these conditions, to improve the accuracy of the search points, several fitting points and a precise and stable fitting method must be used. While nonlinear least squares fitting can be considered as a solution to this type of problem, it may still be unreliable if the points have measurement errors, because this method assumes the data is accurate and error-free. Therefore, it is better to use a method that takes into account measurement errors in the data.

[0005] The information in this background section is intended only to enhance the understanding of the overall background of the invention and is not necessarily to be construed as an admission or in any way implying that the information constitutes prior art known to those skilled in the art. Summary of the Invention

[0006] To address the aforementioned problems, the present invention aims to provide a method for finding the best possible fit for a search ball using weighted least squares, thereby taking into account measurement errors caused by joint surface wear, and obtaining the rotation center of the acetabulum with accurate and stable fitting.

[0007] According to one aspect of the present invention, a method for finding the rotation center of the acetabulum is provided, characterized in that the method includes the following steps: taking a set of n points on the surface of the acetabular joint of a three-dimensional model to fit a sphere, and taking the center point of the sphere as the rotation center of the acetabulum, wherein, so that the error function E(x c y c , z c The method of minimizing R) employs a nonlinear optimization approach for spherical fitting, updating the weights in each iteration. The error function E(x) for the set of n points... c y c , z c R) is defined as:

[0008]

[0009] Among them, w i The weights assigned to the i-th point, where i = 1, 2, 3, ..., n represent the point indices, and x... i y i z i Let x be the coordinates of the i-th point in a three-dimensional coordinate system. c y c z c Let R be the coordinates of the estimated center of the sphere, R be the radius of the sphere, and E be the error magnitude used to evaluate the matching degree. Based on the weighted least squares method, the sphere is matched to the corresponding points by minimizing the weighted sum of squared differences between the Euclidean distance from each point to the center of the sphere and the radius of the sphere. The weights w are... i Calculated as the reciprocal of the Euclidean distance from each corresponding point to the center of the fitted sphere:

[0010]

[0011] Preferably, the variable x to be estimated c y c z c R is represented as a vector:

[0012]

[0013] The Levenberg-Marquardt nonlinear optimization method is redefined as follows:

[0014]

[0015] Among them, J k (φ) is defined as E k The Jacobian matrix of (φ),

[0016]

[0017] Among them, E k (φ) represents the error function value at the k-th iteration, T represents the transpose matrix, and λ k It is a nonnegative scalar, and di ag is a matrix. The diagonal, obtained through iteration:

[0018]

[0019] Therefore, we can derive the vector The center point and radius R of a sphere are expressed in a formal way.

[0020] Preferably, in each iteration, the set of n points is randomly divided into two sub-sets with the same number of points, such that each k-th iteration will produce two sub-items.

[0021] Preferably, the points in each subset partially overlap with each other.

[0022] Preferably, the fitting is performed by searching for points on the surface of the acetabular joint using information collected from CT scans.

[0023] Preferably, the method further includes the following step: taking a point from the wear area of ​​the acetabular joint surface.

[0024] Preferably, in the weighted least squares method, a weight is assigned to each point based on its accuracy, with points with smaller errors assigned higher values ​​and points with larger errors assigned lower values.

[0025] According to another aspect of the present invention, an apparatus for finding the rotation center of the acetabulum is provided, which can realize the above-described method for finding the rotation center of the acetabulum.

[0026] According to another aspect of the present invention, a surgical planning system is provided for total hip arthroplasty using a computer-assisted robotic surgical guidance system, the computer device comprising a processor for executing multiple instructions and a memory for storing the multiple instructions, wherein the multiple instructions are loaded by the processor and executed as described above for the method of finding the center of rotation of the acetabulum.

[0027] According to another aspect of the present invention, a storage medium is provided, which is a computer-readable storage medium storing a computer program that is executed by a controller to implement the steps of the above-described method.

[0028] According to the present invention, the center of rotation of the acetabulum can be estimated well, taking into account the area of ​​bone wear and measurement errors caused by other reasons, thereby obtaining a better estimation result. Attached Figure Description

[0029] Figure 1An exemplary embodiment of searching multiple points on the acetabular joint surface according to the present invention is shown.

[0030] Figure 2 The fitted sphere on the acetabular joint surface is shown as a result of the optimization process using these multiple points. Detailed Implementation

[0031] Exemplary embodiments of the present invention will now be described in detail with reference to the accompanying drawings. The exemplary embodiments described below and illustrated in the drawings are intended to teach the principles of the invention, enabling those skilled in the art to implement and use the invention in various environments and for various applications. Therefore, the scope of protection of the invention is defined by the appended claims, and the exemplary embodiments are not intended, and should not be considered, a limiting description of the scope of protection of the invention. Techniques, methods, and devices known to those skilled in the art may not be discussed in detail, but where appropriate, such techniques, methods, and devices should be considered part of the specification. Furthermore, for ease of description, the dimensions of the various parts shown in the drawings are not necessarily drawn to actual scale. The orientations or positional relationships shown in the drawings are only for the purpose of facilitating the description of the invention and simplifying the description, and are not intended to indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the invention. Moreover, terms such as "step" are intended to distinguish different objects in a non-specific order.

[0032] In total hip replacement surgery using a computer-aided robotic surgical guidance system, a 3D bone representation of the hip (acetabulum) is useful. For this purpose, the patient can undergo computed tomography (CT), a series of X-rays, magnetic resonance imaging (MRI), and / or ultrasound imaging. For example, in preoperative planning, imaging data of the patient's acetabulum can be obtained using imaging modalities such as CT scans, ultrasound, or MRI through conventional interactive preoperative planning software. The imaging data is then transmitted digitally to a computer system, generating a corresponding 3D image model. In certain embodiments, the patient's bones can be segmented manually, semi-manually, or automatically by the user to generate a 3D model of the skeleton.

[0033] For example, CT images are often used as a reference for surgical planning. CT images can be imported into a virtual space, and by extracting the same feature points, the structure of the bone in the virtual CT image can be superimposed on the structure of the real bone. This allows the entire structure of the bone from the CT image to be imported into the virtual space, replacing the pose of the real bone structure in the virtual space. The main purposes of this process are: to display the overall bone structure in a virtual coordinate system; to assist surgeons in surgical planning, allowing them to place implants into a 3D model of the skeletal anatomy to specify the optimal position and alignment of the implant on the bone; and to further assist surgical robots in accurately fitting the acetabular prosthesis components to the acetabulum, i.e., simulating the placement and positioning of the prosthesis. The resulting preoperative planning data can also be used to manufacture patient-specific instruments, or loaded and read by surgical equipment, to help surgeons execute plans during surgery, and even position the surgical robot to ensure that the robot's space is within the required surgical area. The methods and equipment for establishing the acetabular coordinate system are not the focus of this invention and will not be elaborated here; they can be achieved using existing methods such as those described above.

[0034] In total hip arthroplasty systems, the location of the acetabulum's center of rotation (corresponding to the hip joint center) can be determined by fitting points collected on the acetabular articular surface of a 3D model. In a perfect system, these points should ideally belong to a sphere with its center as the acetabulum's center of rotation. However, in actual systems, these points are affected by wear areas and even the measurement process itself, leading to inaccurate point locations and measurement errors. Through careful research, the inventors have developed a new fitting method that, by considering data points with measurement errors, can accurately and stably obtain the center of a sphere as the acetabulum's center of rotation.

[0035] To more accurately obtain the acetabular rotation center, which varies from patient to patient, according to the present invention, on the articular surface of the three-dimensional acetabular model established as described above, some points that have been searched and collected (see...) are used... Figure 1 When fitting the center of a sphere to multiple black dots (as shown in the image), fitting the sphere to a set of points with measurement errors allows for a more realistic fit to the sphere and its center. This can be achieved using the Weighted Least Squares (WLS) method. In this method, each point is assigned a weight based on its accuracy. Points with smaller errors are assigned higher values, while points with larger errors are assigned lower values. The goal is to ensure that points with smaller errors have a greater impact on the final fit of the sphere, while points with larger errors have a smaller impact.

[0036] These weights will be calculated as the reciprocal of the Euclidean distance from the corresponding point to the center of the fitted sphere. This is because, due to factors such as natural wear and tear on the bones, it can be assumed that the point closest to the estimated center of the sphere is the most accurate, and therefore should have a larger weight in the final adjustment of the sphere.

[0037] The WLS method matches the sphere to points by minimizing the weighted sum of squared differences between the Euclidean distance from each point to the center of the sphere and the radius of the sphere, thus matching the sphere and the corresponding points as closely as possible. The error function E(x) for a set of n points... c y c , z c R) is defined as:

[0038]

[0039] Among them, w i The weight assigned to the i-th point, where i = 1, 2, 3, ..., n (natural numbers) represents the point's index, x i y i z i Let x be the coordinates of the i-th point in the coordinate system. c y c z c The coordinates of the estimated center of the sphere are given, R is the radius of the sphere, and E is the error magnitude, used to evaluate the degree of matching.

[0040] The weight w i The calculation method is as follows:

[0041]

[0042] Spherical fitting employs a nonlinear optimization method to make the error function E(x) c y c , z c The algorithm minimizes R (see Equation 1) and updates the weights in each iteration of the algorithm.

[0043] Therefore, the Levenberg-Marquardt (LM) method can be used as a nonlinear optimization method, which has achieved good results in nonlinear curve fitting.

[0044] The variable x to be estimated c y c z c Let R be a vector, then we can obtain:

[0045]

[0046] Therefore, when using the LM method to solve this problem, the problem can be redefined as:

[0047]

[0048] Among them, J k (φ) is defined as E k The Jacobian matrix of (φ), E k(φ) represents the error function value at the k-th (natural number) iteration, and T represents the transpose matrix.

[0049]

[0050] λ k It is a nonnegative scalar, and diag is a matrix. The diagonal. Through k iterations, until the k-th error E. k When (φ) is sufficiently small, a solution can be obtained, which can be expressed as:

[0051]

[0052] To avoid the algorithm falling into local minima and improve its performance, a mini-batch Levenberg-Marquardt (LM) optimization process is preferred. To achieve this, each iteration divides the set of n points into two subsets of equal size, with points randomly selected from each subset. Each k-th iteration K generates two sub-items K1 and K2, and the algorithm is then executed for each sub-item, thus avoiding local optima. For example, if 123 points are obtained through measurement, and 90 points are randomly selected twice, the resulting sets will both contain 90 points. While in extreme cases they might be completely identical, in most cases they will partially overlap.

[0053] Therefore, we can derive the vector The center point (x) of the sphere expressed in form c ,y c ,z c ) and its radius R. This center point (x) c ,y c ,z c The acetabulum is the center of rotation.

[0054] Figure 1 , Figure 2 The diagram shows the spherical surface produced by the optimization process when there are 10 points on the acetabular articular surface. Of course, the number of points is not limited to this and can be appropriately determined based on the condition of the articular surface. Generally, several dozen points are sufficient to achieve adequate accuracy, and fewer or more points may also be used. The points are generally distributed as randomly as possible across the entire acetabular surface. In this way, the method can accurately estimate the center of rotation of the acetabulum, and because it takes into account areas of bone wear, it can achieve particularly excellent estimation results.

[0055] As described above, the method for finding the center of rotation of the acetabulum according to the present invention can accurately estimate the center of rotation of the acetabulum, thereby serving as an important step in correctly aligning the implant with the patient's anatomy.

[0056] This invention also provides an apparatus for locating the rotation center of the acetabulum, comprising units for implementing the aforementioned method for locating the rotation center of the acetabulum. Each constituent unit can be implemented by a corresponding hardware or software unit; each unit can be an independent hardware or software unit, or it can be integrated into a single hardware or software unit, which is not intended to limit the invention. Specific implementations of each unit can be based on the knowledge of those skilled in the art, and will not be elaborated upon here.

[0057] Accordingly, the present invention provides a joint surgery robot for implementation based on the above-described method and apparatus.

[0058] Accordingly, the present invention provides a computer device that may include a controller or a processor, the controller and processor being used to execute a computer program stored in a memory to perform the above-described method.

[0059] Accordingly, the present invention provides a computer-readable storage medium storing a computer program thereon, which is executed by a controller to perform the above-described method. The computer program may include multiple modules, such as a series of instruction segments that perform corresponding functions, to describe the execution process of the program in a computer device. A processor may be connected to the modules for processing 3D virtual image modeling, solving vectors, etc.

[0060] Accordingly, the present invention provides a surgical navigation system or surgical planning system for finding the rotation center of the acetabulum. The system may include the aforementioned computer device, having a processor, input / output devices, network access devices, a bus, etc.; or may include the aforementioned system and execute the aforementioned method.

[0061] Although the invention has been described with reference to various specific embodiments, it should be understood that modifications can be made within the spirit and scope of the described inventive concept. Therefore, it is intended that the invention be limited to the described embodiments but will have the full scope defined by the language of the appended claims.

Claims

1. A method for locating the center of rotation of the acetabulum, characterized in that, The method includes the following steps: A set of n points is selected on the wear area of ​​the acetabular joint surface of the three-dimensional model to fit a sphere, and the center point of the sphere is used as the rotation center of the acetabulum. Where, so that the error function E(x) c y c , z c The method of minimizing R) employs a nonlinear optimization approach for spherical fitting, updating the weights in each iteration. The error function E(x) for the set of n points... c y c , z c R) is defined as: Among them, w i The weights assigned to the i-th point, where i = 1, 2, 3, ..., n represent the point indices, and x... i y i z i Let x be the coordinates of the i-th point in a three-dimensional coordinate system. c y c z c Here are the estimated coordinates of the sphere's center, R is the sphere's radius, and E is the error magnitude used to assess the degree of fit. Among them, based on the weighted least squares method, the sphere is matched with the corresponding points by minimizing the weighted sum of squares of the difference between the Euclidean distance from each point to the center of the sphere and the radius of the sphere. The weight w i The calculation is the reciprocal of the Euclidean distance from each corresponding point to the center of the fitted sphere: The variable x to be estimated c y c z c R is represented as a vector: The Levenberg-Marquardt nonlinear optimization method is redefined as follows: Among them, J k (φ) is defined as E k The Jacobian matrix of (φ), Among them, E k (φ) represents the error function value at the k-th iteration, T represents the transpose matrix, and λ k It is a nonnegative scalar, and diag is a matrix. The diagonal, obtained through iteration: Therefore, we can derive the vector The center point and radius R of a sphere are expressed in a formal way.

2. The method for finding the center of rotation of the acetabulum according to claim 1, characterized in that, In each iteration, the set of n points is randomly divided into two sub-sets with the same number of points, in such a way that each k-th iteration will produce two sub-items.

3. The method for finding the center of rotation of the acetabulum according to claim 2, characterized in that, The points in each subset partially overlap with each other.

4. The method for finding the center of rotation of the acetabulum according to claim 1, characterized in that, Fitting is performed by searching for points on the surface of the acetabulum joint using information collected from CT scans.

5. The method for finding the center of rotation of the acetabulum according to any one of claims 1 to 4, characterized in that, In the weighted least squares method, each point is assigned a weight based on its accuracy; points with smaller errors are assigned higher weights, while points with larger errors are assigned lower weights.

6. A device for locating the center of rotation of the acetabulum, characterized in that, It includes the following units capable of implementing the method for finding the center of rotation of the acetabulum as described in any one of claims 1 to 5: Unit 1: On the worn area of ​​the acetabular joint surface in the 3D model, select a set of n points to fit a sphere, and use the center point of the sphere as the rotation center of the acetabulum. Unit 2: To make the error function E(x) c y c , z c The method of minimizing R) employs a nonlinear optimization approach for spherical fitting, updating the weights in each iteration. The error function E(x) for the set of n points... c y c , z c R) is defined as: Among them, w i The weights assigned to the i-th point, where i = 1, 2, 3, ..., n represent the point indices, and x... i y i z i Let x be the coordinates of the i-th point in a three-dimensional coordinate system. c y c z c Here are the estimated coordinates of the sphere's center, R is the sphere's radius, and E is the error magnitude used to assess the degree of fit. Unit 3: Based on the weighted least squares method, the sphere is matched with the corresponding points by minimizing the weighted sum of squares of the differences between the Euclidean distance from each point to the center of the sphere and the radius of the sphere. The weight w i The calculation is the reciprocal of the Euclidean distance from each corresponding point to the center of the fitted sphere: Unit 4: The variable x to be estimated c y c z c R is represented as a vector: The Levenberg-Marquardt nonlinear optimization method is redefined as follows: Among them, J k (φ) is defined as E k The Jacobian matrix of (φ), Among them, E k (φ) represents the error function value at the k-th iteration, T represents the transpose matrix, and λ k It is a nonnegative scalar, and diag is a matrix. The diagonal, obtained through iteration: Therefore, we can derive the vector The center point and radius R of a sphere are expressed in a formal way.

7. A surgical planning system suitable for total hip arthroplasty using a computer-aided robotic surgical guidance system, characterized in that, The computer device includes a processor for executing a plurality of instructions and a memory for storing the plurality of instructions, wherein the plurality of instructions are loaded by the processor and execute the steps of the method for finding the center of rotation of the acetabulum as described in any one of claims 1 to 5.

8. A storage medium, which is a computer-readable storage medium, characterized in that, The device contains a computer program that is executed by a controller to implement the steps of the method described in any one of claims 1 to 5.

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