Method for measuring relative movement of bones, method for obtaining and positioning axis of rotation of joint

Abstract

The application discloses a kind of bone relative motion measurement method, joint rotation axis acquisition and positioning method, can effectively improve the effect of knee joint replacement surgery, by the present application to measure a-MSA or i-MSA before operation to determine the position of rotation axis, then the prosthesis rotation axis is installed to the position in operation, can effectively reduce the dissatisfaction rate of knee joint replacement patient.And the present application is easy to implement, suitable for large-scale promotion.

Description

Technical Field

[0001] This invention relates to the fields of biomechanics and surgery, specifically to a method for measuring relative motion of bones and a method for obtaining and locating the rotation axis of a joint. Background Technology

[0002] Total knee arthroplasty (TKA) is a very common orthopedic surgery, primarily used to treat patients with end-stage knee osteoarthritis (OA). However, surveys show that 8-25% of patients are currently dissatisfied with the surgical outcome. To improve surgical results, researchers have conducted numerous studies over the past two decades. The knee joint rotation axis is considered a crucial factor affecting surgical outcomes, and the design and intraoperative placement of the artificial joint in TKA must be based on the accurate positioning of the knee joint rotation axis.

[0003] To locate this axis, a clear definition of the knee joint rotation axis is needed first. However, directly applying the traditional definition of the rotation axis to the application of the knee joint leads to the following problems: For strict pivotal movements, the definition of the rotation axis is clear because there is an absolutely stable rotation axis; however, knee joint movement is primarily pivotal (flexion and extension), combined with various movements such as internal and external rotation and inversion / eversion, and these movements also exhibit individual differences. In other words, knee joint movement is complex, and there is no absolutely stable rotation axis, so the traditional definition of the rotation axis cannot be directly applied to the knee joint. Currently, many papers focus on the knee joint rotation axis, but no researcher has clearly described a precise definition of the knee joint rotation axis, leading to problems in the design and installation of artificial joints during surgery, where they cannot accurately adapt to individual needs. Summary of the Invention

[0004] To address the technical problem of inaccurate joint rotation axis positioning, which leads to poor joint replacement surgery outcomes, this invention provides a method for measuring relative bone motion and a method for acquiring and locating the joint rotation axis.

[0005] To achieve the above-mentioned technical objectives, the technical solution of the present invention is as follows:

[0006] A method for measuring relative motion of bones includes the following steps:

[0007] Step 1: Based on magnetic resonance imaging (MRI), the first image of the skeleton before movement is obtained.

[0008] Step 2: Based on MRI, a second image is obtained by imaging the bone after movement. Then, the second image is rotated so that the orientation of the bone image in the second image is the same as that in the first image. The basis for judging whether the orientation is the same is whether the feature region frame is consistent. The feature region frame is composed of multiple feature regions in the bone, and the feature region is the subcortical blood vessels of the bone.

[0009] Step 3: Measure the angle difference between the second image after rotation and before rotation, as well as the displacement distance between the second image after rotation and the first image, and calculate the relative motion value of the skeleton based on the angle difference and displacement distance.

[0010] In the MRI-based method for measuring relative bone motion, the characteristic region in step two refers to the area where blood vessels are located, which are located directly below the bone cortex and intersect with it.

[0011] In the MRI-based method for measuring relative motion of bones, step two includes a feature region framework comprising at least two feature regions located at different levels in the MRI image, with the interval between each feature region not less than a preset number of MRI layers; and the size of each feature region not exceeding a preset size limit.

[0012] A method for obtaining the most stable rotation axis of an individual includes the following steps:

[0013] Step 1: Based on the aforementioned method, or the traditional measurement method based on imaging technology to measure joint motion, obtain the 6-DOF relative motion values ​​of the bones of the individual target joint at different bending angles.

[0014] Step 2: Divide the skeleton into a 3D mesh of a preset mesh size, and randomly select a point in each mesh to form a candidate point set;

[0015] Step 3: Based on the relative motion values ​​obtained in Step 1, quantitatively evaluate the stability of each point in the candidate point set in Step 2, and select the most stable preset number of points as the most stable point group.

[0016] Step 4: Use the least squares method or gradient descent method to find a straight line that is closest to all points in the most stable point group. This line is the most stable rotation axis of the target joint of the individual.

[0017] In the method described above, step 3, the stability of the point is evaluated based on the following method:

[0018] Using the point whose stability is to be evaluated as the target point, the position coordinates of the target point at each angle are obtained based on the relative motion values ​​of the bones at various angles of the joint. Then, the average coordinates of these position coordinates are calculated, and the distance from the average coordinates to each position coordinate is measured. The root mean square or arithmetic mean of these distances is then calculated. The larger the root mean square or arithmetic mean, the worse the stability of the target point, and vice versa.

[0019] In the method described above, step 3, the preset number of points in the most stable point group is determined in the following way:

[0020] When the total grid formed by all the grids in step 2 is a standard body, the points with the best stability according to the preset ratio are selected as the most stable point group; where the standard body refers to the smallest cube that can accommodate all the bones at the distal end of the bones on the side of the joint near the human head; when the volume of the total grid is different from that of the standard body, the preset ratio of point selection is adjusted according to the inverse ratio of the volume of the total grid to that of the standard body.

[0021] A method for obtaining the average most stable axis of rotation in a population, applicable to the knee and elbow joints, includes the following steps:

[0022] Step 1), obtain the transcondylar axis (TEA) of the test joints of multiple targets;

[0023] Step 2), based on the aforementioned method, obtain the individual most stable rotation axis of all tested joints in Step 1;

[0024] Step 3) Determine the three-dimensional coordinate system of the joint: take the straight line where TEA is located as the X-axis; then draw a circle inscribed in the medullary canal of the femoral / humeral shaft at a standard length horizontal height near the TEA, and draw a perpendicular line from the center of the circle to the X-axis as the Z-axis; the Y-axis is perpendicular to both the X-axis and the Z-axis.

[0025] Step 4) Determine the medial and lateral sagittal coordinate systems: The medial sagittal plane is a plane perpendicular to the X-axis and passing through the medial condyle of the femur / humerus, and the lateral sagittal plane is a plane perpendicular to the X-axis and passing through the lateral condyle of the femur / humerus. On the medial sagittal plane, a two-dimensional coordinate system is established with the medial condyle of the femur / humerus as the origin and the Y-axis and Z-axis as the coordinate axes; this is called the medial sagittal coordinate system. On the lateral sagittal plane, a two-dimensional coordinate system is established with the lateral condyle of the femur / humerus as the origin and the Y-axis and Z-axis as the coordinate axes; this is called the lateral sagittal coordinate system.

[0026] Step 5): The individual most stable rotation axis of each tested joint intersects the medial sagittal plane at a point. The anteroposterior position of the intersection point in the medial sagittal plane coordinate system, i.e., the Y-axis coordinate, is represented by the parameter medial-anteroposterior (M-AP), and the mesiodistal position, i.e., the Z-axis coordinate, is represented by the parameter medial-mesiodistal (M-PD). The anteroposterior position of the intersection point of the individual most stable rotation axis with the lateral sagittal plane, i.e., the position on the Y-axis, is represented by the parameter lateral-anteroposterior (L-AP), and the mesiodistal position, i.e., the position on the Z-axis, is represented by the parameter lateral-mesiodistal (L-PD). The average value of each of the four parameters is taken as the population average relative position relationship between the individual most stable rotation axis and the TEA, thereby obtaining the population average most stable rotation axis.

[0027] In the method described above, in step 3, the standard length is the distance between the inner and outer condyles of the TEA × a, where a is a coefficient with a value of 0.44 to 1.0.

[0028] A method for locating the rotation axis of a knee joint in the real world includes the following steps:

[0029] Step ①: For the target knee joint, first take a CT or MRI of the knee joint, and obtain the individual's most stable rotation axis based on the aforementioned method, or obtain the population's average most stable rotation axis based on the aforementioned method, or obtain the rotation axis using the traditional method as the target rotation axis, and then locate the projection of the target rotation axis in this direction on the horizontal / coronal plane.

[0030] Step 2: Locate the posterior condylar axis (PCA) on the imaging image, and then measure the distances between the horizontal projection of the target rotation axis and the two intersections of the medial and lateral sides of the bone cortex and the PCA, respectively, as the medial anterior-posterior distance and the lateral anterior-posterior distance;

[0031] Step 3: Find the common tangent of the distal boundaries of the medial and lateral femur on the imaging image as the mandibular axis. Then measure the distance between the coronal projection of the target rotation axis and the two intersections of the medial and lateral cortical bone and the mandibular axis, respectively, as the medial mesial-distal distance and the lateral mesial-distal distance.

[0032] Step 4: Locate the PCA (proximal condyle) of the actual knee joint. Based on the medial anterior-posterior distance obtained in Step 2, find the parallel line corresponding to this distance anterior to the PCA. Draw a straight line in the mesiodistal direction through the intersection of this parallel line and the medial bone surface of the knee joint as the medial mesiodistal running line. Simultaneously, based on the lateral anterior-posterior distance obtained in Step 2, find the parallel line corresponding to this distance anterior to the PCA. Draw a straight line in the mesiodistal direction through the intersection of this parallel line and the lateral bone surface of the knee joint as the lateral mesiodistal running line. Then, locate the condylar axis of the actual knee joint and, based on the medial condyle obtained in Step 3... Find the parallel lines corresponding to the proximal-distal and lateral proximal-distal distances above the condylar axis. Then, draw two straight lines in the anterior-posterior direction through the intersections of these two parallel lines with the medial and lateral bone surfaces of the knee joint, respectively, as the anterior-posterior running lines for the medial and lateral sides. The intersection of the proximal-distal running lines and the anterior-posterior running lines on the medial side of the knee joint is the position where the target rotation axis exits the medial cortex of the knee joint; the proximal-distal running lines and the anterior-posterior running lines on the lateral side of the knee joint are the positions where the target rotation axis exits the lateral cortex of the knee joint. Use these two intersection points as the installation positions for the knee joint prosthesis rotation axis.

[0033] The technical advantage of this invention lies in its ability to effectively improve the rotational stability of the prosthesis in knee replacement surgery, thereby improving surgical outcomes. By using this invention to determine the position of the rotation axis preoperatively through a-MSA or i-MSA measurements, and then installing the prosthesis rotation axis into that position during surgery, the dissatisfaction rate of knee replacement patients can be effectively reduced. Furthermore, this invention is easy to implement and suitable for large-scale promotion. Attached Figure Description

[0034] Figure 1 This diagram illustrates the standardized method for describing the spatial location of the rotation axis near the knee joint in this invention. AD is a three-dimensional diagram showing the medial and lateral sagittal planes determined based on the distal femoral anatomy. EF is a diagram showing the establishment of two-dimensional coordinate systems on the medial and lateral sagittal planes to describe the rotation axis position. In the diagram, TEA is the X-axis, Z-axis is the line connecting the midpoint of TEA to the center of the inscribed circle of the distal femoral medullary canal, and Y-axis is perpendicular to both X and Z axes. The sagittal planes containing the medial and lateral condyles of TEA are the medial and lateral sagittal planes, respectively.

[0035] Figure 2 These are MRI images of the knee joint in patients with end-stage osteoarthritis (OA), where Figure A is the horizontal plane and Figure B is the coronal plane.

[0036] Figure 3This is a schematic diagram illustrating the relative motion measurement principle of the present invention, where A represents the initial state of the rigid body's motion; B represents the final state of the rigid body's motion; Figures C and E illustrate the relative motion measurement principle of a two-dimensional rigid body; Figures C, D, and E illustrate the measurement principle of a three-dimensional rigid body. In the figures, M is the moving rigid body, F is the fixed rigid body, and P and P' are points on the moving rigid body before and after its motion. V and V' represent the displacement vectors of the points, and θ is the rotation angle of the moving rigid body M.

[0037] Figure 4 The diagram shows the forward and reverse directions of rotation in the coronal, sagittal, and horizontal planes, as well as the characteristic region framework (CAF) composed of multiple subcortical vessels (SCVS). AD represents the coronal plane, EH the sagittal plane, and IL the horizontal plane. Small circles in the diagram represent the SCVS selected as the characteristic region, T represents the tibia, P the patella, Fm the femur, and Fb the fibula.

[0038] Figure 5 This diagram illustrates the changes in subcortical vessels (SCVS) after movement. Image A shows a coronal MRI image of the knee joint before rotation / translation, with SCVS highlighted by small circles. Image B shows a coronal image after rotating Image A 0.5° in the sagittal plane; the SCVS have changed at this point. Image C shows an image obtained by displacing Image A perpendicularly to the coronal plane by 0.5 mm; the SCVS have also changed. Images DF are similar to images A and C, except the tibia and femur are replaced with "aquarium stones." A rotation of 0.5° or a displacement of 0.5 mm causes significant changes in the characteristic regions.

[0039] Figure 6 This diagram illustrates the mesh setup, where AC represents a cube mesh with sides equal to the width of the bicondyle at the distal femur, with a mesh spacing of 1 mm. All mesh intersections are candidate points. In D and E, the white asterisks represent the top 0.2% of candidate points with the lowest PC values, used to determine i-MSA. Detailed Implementation

[0040] The directional concepts (inner, outer, proximal, distal, anterior, posterior) used throughout this invention are all common knowledge in the relevant professional fields. This invention describes joint direction in anatomical positions, with inner / outer being the side closer to / away from the longitudinal central axis of the human body, and proximal / distal being the side closer to the head / foot.

[0041] First, this invention no longer pursues absolute stability when searching for the knee rotation axis, but instead designs a quantitative index for the degree of stability, so that (1) the stability of different rotation axes can be compared according to the index; and (2) the most stable rotation axis can be found according to the index. Theoretically, the more stable the rotation axis of the prosthesis in knee replacement surgery (including TKA and unicompartmental knee arthroplasty (UKA)), the closer the postoperative knee joint movement is to the natural knee joint, the less discomfort the patient experiences, and the better the surgical effect.

[0042] To assess the stability of the knee joint rotation axis, the following steps are logically required: (1) Measure the relative motion values ​​of the bones on both sides of the joint when the joint is bent at different angles; (2) Take one side of the joint as the fixed bone and the other side as the moving bone, calculate the position coordinates of a point on the moving bone at any angle of joint bending based on the relative motion values, and obtain the motion trajectory of this point. The more dispersed the position coordinates of the motion trajectory, the worse the stability of this point, and vice versa; the degree of dispersion is represented by the change in position (PC value); repeat this step to obtain the PC value of each point on the moving bone; (3) If all points on a straight line are stable (the PC value is very small), then the rotation axis represented by this straight line is also stable; (4) Because the closer two points on the bone are, the more similar their motion trajectories are, and the closer their PC values ​​will be, the PC values ​​of different points on the rotation axis are continuously changing. Therefore, two standard positions (the intersection of the rotation axis and the two sagittal planes passing through the medial / lateral condyles of the femur) can be taken to reflect the stability of the entire rotation axis with their PC values. It is foreseeable that the accuracy of the stability assessment method constructed based on the above logic mainly depends on the measurement accuracy of the relative motion of the bones on both sides of the joint.

[0043] Current academic papers require relative motion measurement results to have 6 degrees of freedom (DOF), with 3 DOFs describing the 3 rotational directions in 3D space and the other 3 DOFs describing the 3 translational directions in 3D space. Therefore, the evaluation of measurement accuracy also needs to be divided into translational accuracy and rotational accuracy. The most popular technique at present is 2D-3D image matching technology based on X-ray imaging, with a translational accuracy of <1mm and a rotational accuracy of <1° [“Accuracy of mobile biplane X-ray imaging in measuring 6-degree-of-freedom patellofemoral kinematics during overground gait” (Journal of Biomechanics, Vol. 24, No. 57, pp. 152–156, 2017). Similarly, the accuracy of CT measurement technology is no less than that of X-ray imaging technology [“Implant placement accuracy in total knee arthroplasty: validation of a CT-based measurement technique” (Quant Imaging Med Surg, Vol. 2, No. 10, pp. 475–484, 2020). Both technologies have excellent accuracy, but due to the high radiation dose, they are difficult to apply on a large scale in clinical practice and are mostly used for scientific research. MRI technology is radiation-free, but the measurement accuracy reported in the literature is only 3-7 mm and 3-4° [“Development and Validation of a Subject-Specifific Moving-axis Tibiofemoral Joint Model Using MRI and EOS Imaging during a Quasi-Static Lunge” (Journal of Biomechanics, Vol. 27, No. 72, pp. 71–80, 2018)]. This invention improves the measurement accuracy of MRI to <1 mm and <1° by using the subcortical vascular segment (SCVS) as the characteristic region framework (CAF), thus providing a radiation-free measurement method.

[0044] Currently, the main traditional concepts of knee joint rotation axes in the literature include the transepicondylar axis (TEA), geometric center axis (GCA), posterior condylar axis (PCA), and Whiteside's line (WSL). Based on their definitions, these can be divided into 2D rotation axes (PCA and WSL) and 3D rotation axes (GCA and TEA). However, the 2D rotation axis definition is insufficient because it does not define the position of the rotation axis in the coronal plane, and only defines the direction of the rotation axis in the horizontal plane, without defining the anteroposterior position. Therefore, the spatial position of the rotation axis cannot be determined, making it impossible to assess its stability. The 3D rotation axis definition is sufficient; therefore, this invention calculates their stability and compares them with the i-MSA and a-MSA rotation axes proposed in this invention.

[0045] In order to perform the procedure accurately during surgery, it is not enough to simply locate the axis of rotation on MRI; the target axis of rotation must also be easily and precisely located intraoperatively. Commonly used anatomical landmarks for intraoperative localization include the TEA, PCA, and WSL. Numerous studies have shown that subjective differences in intraoperative localization results among different surgeons are smallest with PCA, followed by TEA, and largest with WSL [“Femoral Component Rotation in Total Knee Arthroplasty: An MRI-Based Evaluation of our Options”, The Journal of Arthroplasty, Vol. 29, No. 8, pp. 1666-70, 2014] [“Transepicondylaraxis accuracy in computer assisted knee surgery: a comparison of the CT-based measured axis versus the CAS-determined axis”, Computer Aided Surgery, Vol. 31, No. 4, pp. 200-206, 2008]. Therefore, PCA is a relatively accurate intraoperative reference. As mentioned above, the definition of PCA is insufficient to describe the position of the 3D rotation axis. Therefore, this invention further proposes the concepts of inferior condylar axis (ICA), anterior-posterior distance between medial and lateral sides, and proximal-distal distance between medial and lateral sides to enrich the definition. This allows the position of any target rotation axis to be found during surgery.

[0046] The invention will now be described using specific embodiments.

[0047] 1. Obtaining relative motion values ​​of bones

[0048] X-ray, CT, and MRI are three imaging techniques that can be used to measure relative bone motion and obtain 6DOF relative bone motion values. X-ray and CT measurement techniques have long existed and are widely used in scientific research, and will not be elaborated on here. This section mainly explains the MRI measurement method used in this embodiment (hereinafter referred to as the new MRI measurement method).

[0049] To help understand the principles of the new MRI measurement method, let's first look at the case of a two-dimensional rigid body. See [link to relevant documentation]. Figure 3The relative motion between two rigid bodies can be described by two parameters: (1) the rotation angle θ of the rigid body and (2) the displacement V of any point P on the rigid body. Since the rotation angle θ and displacement V of a two-dimensional rigid body can be directly measured on the image, the relative motion between the two rigid bodies can be obtained relatively easily. After measuring θ and V, the displacement V' of any other point P' on the rigid body can be calculated by formula (1).

[0050]

[0051] For three-dimensional rigid bodies like bones, since the entire rigid body cannot be obtained from MRI images, θ and V cannot be directly measured as in two-dimensional rigid bodies. Therefore, this embodiment uses MRI images of the bones after rotational motion to ensure that the orientation of the bones is the same in the images before and after the motion. In other words, moving the bones to the same position in two images allows them to overlap, so the rotation angle in the image is equivalent to θ in a two-dimensional rigid body. Of course, the measurement accuracy of this method depends on how precisely it is determined that the orientation of the bones before and after rotation is exactly the same. See also... Figure 4 In this embodiment, a CAF composed of multiple SCVS is used as a tool to confirm the accuracy of three-dimensional rotation alignment. After determining θ, V can be measured through some simple operations, because after rotation with θ, the translation distance of the same point in the two images is V in the two-dimensional rigid body. After completing the measurement of θ and V, the displacement V' of any other point P' on the rigid body can be calculated by formula (2).

[0052] V'=(P'-P)RxRyRz+V (2)

[0053] in

[0054]

[0055] θ = [a, b, c]

[0056] Because CAF has a significant impact on measurement accuracy, this embodiment adopts a unified standard for CAF: (1) the length / width of each feature region (SCVS) is <= 5 pixels (2.5 mm); (2) in each coordinate axis direction, the feature regions should be distributed on two different MRI slices with an interval of more than 80 slices (4 cm). See Figure 5 Under this standard, the CAF is sensitive to minute rotations of a rigid body; a rotation of 0.5° can cause a noticeable change in the CAF that is visible to the naked eye. This change is achieved through… Figure 5The AC results indicate that as long as there is a difference in a single characteristic region (SCVS), it can be determined that the rigid body has either undergone a slight rotation or a slight translation. Therefore, if the same CAF is found on the MRI images of two rigid bodies, the directional difference between the two rigid bodies will be less than 0.5°. Thus, relying on the CAF and combined with the explanation in the principle section, the rotational parameter θ of the rigid body can be accurately measured. Similarly, the CAF is also sensitive to small translations of the rigid body (a translation of 0.5 mm can cause a visually noticeable change in the CAF), so the translational parameter V of the rigid body can also be accurately measured.

[0057] The following is a supplementary explanation of the aforementioned CAF standard. Based on experience, generally speaking, the smaller the feature region, the higher the translational positioning accuracy, but the greater the difficulty of manual comparison; the larger the feature region frame, the higher the rotational accuracy, but the greater the difficulty of finding a SCVS that conforms to the standard. The CAF standard used in this embodiment is a comprehensive optimization based on experience, but modifying the feature region size parameters and feature region frame size parameters in the standard can also achieve similar measurement accuracy.

[0058] Specifically, the MRI-based method for measuring relative bone motion (i.e., the new MRI measurement method) provided in this embodiment includes the following steps:

[0059] Step 1: Based on magnetic resonance imaging (MRI), the first image of the skeleton before movement is obtained.

[0060] Step two involves creating a second image of the bone after movement using MRI. This second image is then rotated to ensure the orientation of the bone image is the same as in the first image. The alignment is determined by comparing the consistency of the feature region framework. This framework is composed of multiple feature regions within the bone, specifically the subcortical blood vessels. Each feature region is located directly beneath the cortex and intersects with the cortex, containing the blood vessels. The feature region framework includes at least two feature regions at different levels in the MRI image, with a minimum interval of 80 MRI slices between each region. Each feature region has a length / width of no more than 5 pixels.

[0061] Step 3: Measure the angle difference between the second image after rotation and before rotation, as well as the displacement distance between the second image after rotation and the first image, and calculate the relative motion value of the skeleton based on the angle difference and displacement distance.

[0062] This embodiment verified the overall rotational accuracy of the rigid body and the translational accuracy of the three-dimensional mesh intersections in an in vitro measurement experiment, as shown in Table 1. The results show that the translational accuracy of all tested mesh intersections is <1mm, and the rotational accuracy of the rigid body is <1°. This embodiment verified the measurement range of 0-150° rotation and 0-100mm translation, which is sufficient for knee joint measurements.

[0063] Table 1. Measurement accuracy inspection

[0064]

[0065] In the table, the asterisk (*) indicates that the measurement results in three different spatial directions are separated by the symbol " / ", representing the measurement results in the coronal plane, sagittal plane, and horizontal plane.

[0066] The # symbol in the table indicates that the measurement accuracy is the measured length / angle minus the true value; two measurers each take two measurements, for a total of four measurements; the average and standard deviation of the measurement accuracy are calculated using the four measurements.

[0067] The ^ symbol in the table indicates that a cubic mesh with a grid spacing of 1cm and a side length of 14cm is created in the measured rigid body and its surrounding space, with a total of 15 grids. 3 = 3375 grid intersections; with the grid center point as P, the other 3374 grid intersections are P'; P' has 4*3374=13496 measurement results, which are used to calculate the average and standard deviation of the measurement accuracy.

[0068] 2. A method for assessing the stability of the knee joint rotation axis

[0069] Multiple MRI scans (14 scans in total, taken at 10° intervals) were performed on a single subject with knee flexion from 0 to 130°. Using the method described earlier, the trajectory of any point on the femur relative to the tibia was obtained (the trajectory consists of 14 coordinates, representing the point's position during knee flexion from 0 to 130°). The root mean square deviation of the distances of these coordinates from the mean coordinates was used to measure the magnitude of the positional change of that point during knee flexion (referred to as positional change, PC, in this embodiment). Clearly, the smaller the PC value of a point, the more convergent its trajectory, and the more stable that point is during knee joint movement. For the axis of rotation, see [link to relevant documentation]. Figure 1 In this embodiment, two sagittal planes, inner and outer, are first determined. The rotation axis intersects these two sagittal planes at two points, inner and outer, and their PC values ​​are used to evaluate the stability of the rotation axis.

[0070] The stability evaluation method for a specific point on the skeleton (the point used as the evaluation target, hereinafter referred to as the target point) in this embodiment includes the following steps:

[0071] Step 1: Obtain MRI images of the joint from different angles on both sides of the joint of a single subject being evaluated.

[0072] Step 2: Then, according to the aforementioned method for measuring relative bone motion, obtain the relative bone motion values ​​of the joint at different angles;

[0073] Step 3: Based on the relative motion values ​​of the bones, calculate the 14 position coordinates of the target point at different knee flexion angles (0-130°, in 10° intervals), and calculate their average coordinates. This average coordinate has 14 distances from the 14 motion trajectory coordinates. Calculate the mean square error (or arithmetic mean, as experimental results show very little difference) of these distances as the PC value to evaluate the stability of the target point.

[0074] The stability evaluation method for a specific rotation axis (the rotation axis used as the evaluation target, hereinafter referred to as the target rotation axis) in this embodiment includes the following steps:

[0075] Step 1: Determine a plane that passes through the medial condyle of the knee joint and is perpendicular to the line connecting the medial and lateral condyles (TEA), called the medial sagittal plane; similarly, determine the lateral sagittal plane through the lateral condyle of the knee joint.

[0076] Step 2: The target rotation axis has two intersection points with the inner / outer sagittal plane. The PC values ​​of these intersection points are calculated using the aforementioned method to evaluate the stability of the target rotation axis.

[0077] It should be noted that although the above examples used MRI to obtain PC values ​​to assess rotational axis stability, CT can achieve the same technical effect, as CT can also acquire three-dimensional imaging images. Furthermore, two-dimensional X-ray images can be converted into three-dimensional imaging data by adding an MRI scan [“Posterolateral structures of the knee in posterior cruciate ligament deficiencies” (Am J Sports Med), Vol. 37, pp. 534–541, 2009)], thus achieving the same technical effect. Additionally, replacing the knee joint in this example with other joints would also allow for obtaining stability at each point on the bone.

[0078] 3. The concepts of individual most stable axis of rotation (i-MSA) and population average most stable axis of rotation (a-MSA), and their localization methods in radiographic images:

[0079] In knee MRI images, a 3D mesh encompassing the entire distal femur is constructed with a 1mm mesh spacing. All mesh intersections are used as a candidate point set, and the PC value for each point is calculated. A subset of points with the lowest PC values ​​(0.2%) are selected as the most stable point group. Then, a straight line passing through this point group is fitted using the least squares method (or gradient descent, with minimal difference in results) as the i-MSA (i-MSA). Figure 6 The i-MSA is the most stable axis of rotation for an individual; theoretically, placing the rotation axis of the knee replacement (TKA or UKA) prosthesis here yields the best surgical results. Because i-MSA measurement is time-consuming (40-50 minutes), it is not convenient for large-scale clinical application; therefore, this embodiment proposes the concept of a-MSA. In this embodiment, i-MSA measurements were first completed on 36 healthy subjects, and then (… Figure 1 The medial and lateral sagittal coordinate systems are established using the method shown in AD (in this embodiment, the unit length of the coordinate system is the bicondylar width (distance between the medial and lateral femoral condyles), but it can also be replaced by other units such as millimeters, height, or leg length). All i-MSA uses ( Figure 1 The method involving E and F was transformed into four parameters: medial-proximal (M-PD), medial-anteroposterior (M-AP), lateral-proximal (L-PD), and lateral-anteroposterior (L-AP). The average values ​​of the corresponding parameters in i-MSA from 36 healthy subjects were taken for each of the four parameters, resulting in the four corresponding parameters for a-MSA: M-PD = 22.2, M-AP = 15.2, L-PD = 20.3, L-AP = 17.7. Figure 1 (E, F in the image). For a new subject, only one MRI scan is needed to determine the location of the a-MSA using the medial and lateral sagittal coordinate systems. This avoids the cumbersome measurement process of the i-MSA and reduces the measurement time to 4-5 minutes.

[0080] The i-MSA acquisition method provided in this embodiment includes the following steps:

[0081] Step 1: Take MRI images of the subject's joints at different angles using the aforementioned method and obtain the 6-DOF relative motion values ​​of the bones at different bending angles;

[0082] Step 2, see Figure 6The skeleton is divided into a 3D mesh of a preset mesh size, and a point is randomly selected from each mesh to form a candidate point set. Using the relative motion values ​​obtained in step 1, the PC value of all points in the candidate point set is calculated, and the points with the smallest PC value within the preset ratio are selected as the most stable point group. When the total mesh formed by all meshes is a standard cube, the preset ratio can be 0.2%. Here, a standard cube refers to the smallest cube that can accommodate all the distal bones of the bones near the head on the side of the joint. When the volume of the total mesh differs from that of the standard cube, the preset ratio for point selection is adjusted according to the inverse proportion between the volumes of the total mesh and the standard cube.

[0083] Step 3: Use the least squares method or gradient descent method to determine a straight line that is closest to all points in the most stable point group, as the i-MSA.

[0084] The a-MSA acquisition method provided in this embodiment includes the following steps:

[0085] Step 1: Obtain the i-MSA of joints from multiple subjects using the aforementioned method. Then, obtain the transcondylar axis (TEA) of the joints of the corresponding subjects.

[0086] Step 2, see Figure 1 First, determine the three-dimensional coordinate system of the joint: Use the straight line containing the TEA as the X-axis; then, draw a circumscribed circle of the femoral / humeral shaft medullary canal at a standard horizontal height proximal to the TEA, and draw a perpendicular line from the center of the circle to the X-axis as the Z-axis; the Y-axis is perpendicular to both the X-axis and Z-axis. Next, determine the medial and lateral sagittal planes: use a plane perpendicular to the X-axis and passing through the medial condyle of the femur / humerus as the medial sagittal plane, and a plane perpendicular to the X-axis and passing through the lateral condyle of the femur / humerus as the lateral sagittal plane; on the medial sagittal plane, establish a two-dimensional coordinate system with the medial condyle of the femur / humerus as the origin and the Y-axis and Z-axis as the coordinate axes, called the medial sagittal plane coordinate system; on the lateral sagittal plane, establish a two-dimensional coordinate system with the lateral condyle of the femur / humerus as the origin and the Y-axis and Z-axis as the coordinate axes, called the lateral sagittal plane coordinate system. The positions of the intersections of the i-MSA with the medial and lateral sagittal planes are described using a coordinate system with four parameters: medial-proximal (M-PD), medial-anteroposterior (M-AP), lateral-proximal (L-PD), and lateral-anteroposterior (L-AP). The average value of each of these four parameters is used as the corresponding parameter for the a-MSA. This represents the population-average relative position of the individual's most stable rotation axis to the TEA, thus obtaining the population-average most stable rotation axis. Figure 1 The distance between the TEA in D and the center of the inscribed circle of the femoral medullary cavity can be any value between 0.44 and 1 times the width of the bicondyles, as long as the value is the same in all subjects. If the multiple is less than 0.44, the inscribed circle may still be inside the knee / elbow joint and not reach the bone shaft; if the multiple is greater than 1.0, its practical value is reduced because more bone shaft needs to be exposed upwards for localization during surgery, increasing surgical trauma.

[0087] The stability of i-MSA and a-MSA in 36 healthy subjects is shown in Table 2. It can be seen that the PC value of i-MSA is significantly smaller than that of a-MSA, and the PC value of a-MSA is significantly smaller than that of TEA, while there is no significant difference in PC values ​​between GCA and a-MSA. This indicates that i-MSA is more stable than GCA, GCA is more stable than TEA, and the stability of a-MSA and GCA is similar. Furthermore, because bone defects caused by OA affect the location of GCA, GCA is generally unavailable in knee replacement patients, thus GCA has no practical surgical value. In summary, both i-MSA and a-MSA are superior to traditional rotation axes in terms of stability, and a-MSA measurement is rapid and convenient, making it easy to apply on a large scale.

[0088] The stability of the conventional 3D rotation axes (TEA and GCA) of 36 subjects is shown in Table 2 below.

[0089] Table 2. PC values ​​of a-MSA at two points on the medial / lateral sagittal plane and their comparison with TEA, GCA and i-MSA.

[0090]

[0091] *P<0.05 indicates a significant difference.

[0092] It should be noted that although the above examples used MRI to obtain i-MSA and a-MSA, CT can achieve the same technical effect as MRI, as CT can also obtain three-dimensional imaging images. Furthermore, two-dimensional X-ray images can be converted into three-dimensional imaging data by adding an MRI scan [“Posterolateral structures of the knee inposterior cruciate ligament defificiency” (Am J Sports Med), American Journal of Sports Medicine, Vol. 37, pp. 534–541, 2009)], thus achieving the same technical effect. Additionally, replacing the knee joint in this example with other joints would also allow for obtaining stability at each point on the bone, thus obtaining i-MSA; the elbow joint also has anatomical structures similar to the TEA of the knee joint (the line connecting the medial and lateral condyles of the humerus), so the method for obtaining a-MSA is also applicable to the elbow joint.

[0093] 4. A real-world positioning method for arbitrary rotation axes (including i-MSA and a-MSA)

[0094] This embodiment includes the following steps:

[0095] Step 1: Obtain i-MSA or a-MSA using the aforementioned method, or obtain any conventional rotation axis as the target rotation axis using conventional methods.

[0096] Step 2, see Figure 2 In step A, locate the two intersection points of the target's rotation axis with the medial and lateral sides of the femoral cortex on the horizontal image, and measure their distances to the PCA (medial anterior-posterior distance, lateral anterior-posterior distance).

[0097] Step 3, see Figure 2 In step B, similar to step 2, find the two intersection points of the target rotation axis with the medial and lateral sides of the femoral cortex on the coronal image, and measure their distances to the inferior condylar axis (ICA) (medial proximal-distal distance, lateral proximal-distal distance).

[0098] Step 4: During the surgery, locate the actual PCA (percutaneous coronary artery) of the knee joint. Based on the medial anterior-posterior distance obtained in Step 2, find a parallel line corresponding to this medial anterior-posterior distance anterior to the PCA. Then, through the intersection of this parallel line and the medial bone surface of the knee joint, draw a straight line in the mesiodistal direction as the medial mesiodistal course. The intersection of the target rotation axis and the medial cortex of the knee joint lies on this medial mesiodistal course. Simultaneously, based on the parallel line corresponding to the lateral anterior-posterior distance obtained in Step 2, through the intersection of this parallel line and the lateral bone surface of the knee joint, draw a straight line in the mesiodistal direction as the lateral mesiodistal course. The intersection of the target rotation axis and the lateral cortex of the knee joint lies on this lateral mesiodistal course. Then, locate the condylar axis (ICA) of the actual knee joint. Based on the medial proximal-distal and lateral proximal-distal distances obtained in step 3, find the corresponding parallel lines above the ICA. Through the intersections of these two parallel lines with the medial and lateral bone surfaces of the knee joint, draw two straight lines in the anterior-posterior direction as the anterior-posterior running lines for the medial and lateral sides, respectively. The intersection of the medial proximal-distal running lines and the anterior-posterior running lines is the position where the target rotation axis exits the medial cortex of the knee joint; the lateral proximal-distal running lines and the anterior-posterior running lines are the positions where the target rotation axis exits the lateral cortex of the knee joint. Use these two intersection points as the installation positions for the knee joint prosthesis rotation axis, thereby achieving the real-world positioning of the knee joint rotation axis.

[0099] This method relies on the PCA and ICA to locate the rotation axis in the real world: the PCA has been proven to be a more accurate real-world anatomical location than the TEA; this embodiment proposes the ICA based on the concept of the PCA, which theoretically has a similar real-world positioning accuracy to the PCA. Since both the PCA and ICA are located within the knee joint, it is not necessary to locate and measure the lower limb force line intraoperatively. Based on the above analysis, surgical instruments designed using this method will be simpler and have higher positioning accuracy than current instruments.

[0100] To verify the accuracy of this method, this embodiment used the a-MSA as the target rotation axis for real-world localization. Two cadaver knee joint specimens were taken, MRI was performed, and the anterior-posterior distance and proximal-distal distance of the a-MSA were measured. The knee joint was then exposed via a TKA surgical approach. Two operators each performed two measurements, and the localization results were marked with 0.5% iodine-chloroform solution after each measurement. After one operator completed two measurements, the chloroform was allowed to evaporate, and a 1% starch solution was sprayed for staining, with the staining location recorded. After one operator completed staining, the stained area was wiped with a 75% alcohol swab until colorless before the second operator could perform the measurement. The inter-operator variability and intra-operator variability (ICC) were 0.97 and 0.99, respectively.

Claims

1. A method for obtaining the most stable rotation axis of an individual, characterized in that, Includes the following steps: Step 1: Based on a skeletal relative motion measurement method, obtain the 6-DOF relative motion values ​​of the bones of an individual target joint at different bending angles. Specifically, the skeletal relative motion measurement method includes the following steps: Step 1: Based on magnetic resonance imaging (MRI), the first image of the skeleton before movement is obtained. Step two: Based on MRI, a second image is obtained by imaging the bone after movement. Then, the second image is rotated so that the orientation of the bone image in the second image is the same as that in the first image. The basis for judging whether the orientation is the same is whether the feature region frame is consistent. The feature region frame is composed of multiple feature regions within the bone. The feature region is the subcortical blood vessel of the bone. The feature region is the area where the blood vessel is located, which is close to the bone cortex and intersects with the bone cortex. Step 3: Measure the angle difference between the second image after rotation and before rotation, as well as the displacement distance between the second image after rotation and the first image, and calculate the relative motion value of the skeleton based on the angle difference and displacement distance; Step 2: Divide the skeleton into a 3D mesh of a preset mesh size, and randomly select a point in each mesh to form a candidate point set; Step 3: Based on the relative motion values ​​obtained in Step 1, quantitatively evaluate the stability of each point in the candidate point set in Step 2, and select the most stable preset number of points as the most stable point group. Step 4: Use the least squares method or gradient descent method to find a straight line that is closest to all points in the most stable point group. This line is the most stable rotation axis of the target joint of the individual.

2. The method for obtaining the most stable rotation axis of an individual according to claim 1, characterized in that, In step two, the feature region framework includes at least two feature regions located at different layers in the MRI image, and the interval between each feature region is not less than the preset number of MRI layers; the size of each feature region does not exceed the preset size limit.

3. The method for obtaining the most stable rotation axis of an individual according to claim 1, characterized in that, In step 3, the stability of the point is evaluated based on the following method: Using the point whose stability is to be evaluated as the target point, the position coordinates of the target point at each angle are obtained based on the relative motion values ​​of the bones at various angles of the joint. Then, the average coordinates of these position coordinates are calculated, and the distance from the average coordinates to each position coordinate is measured. The mean squared error or arithmetic mean of the distance from the average coordinates to each position coordinate is then calculated. The larger the mean squared error or arithmetic mean, the worse the stability of the target point, and vice versa.

4. The method for obtaining the most stable rotation axis of an individual according to claim 1, characterized in that, In step 3, the preset number of points in the most stable point group is determined in the following way: When the total grid formed by all the grids in step 2 is a standard body, the points with the best stability according to the preset ratio are selected as the most stable point group; where the standard body refers to the smallest cube that can accommodate all the bones at the distal end of the bones on the side of the joint near the human head; when the volume of the total grid is different from that of the standard body, the preset ratio of point selection is adjusted according to the inverse ratio of the volume of the total grid to that of the standard body.

5. A method for obtaining the average most stable rotation axis of a population applicable to the knee and elbow joints, characterized in that, Includes the following steps: Step 1), obtain the transcondylar axis (TEA) of the test joints of multiple targets; Step 2), based on the method for obtaining the most stable rotation axis of an individual as described in any one of claims 1-4, obtain the most stable rotation axis of the individual for all tested joints in step 1); Step 3) Determine the three-dimensional coordinate system of the joint: take the straight line where TEA is located as the X-axis; then draw a circle within the medullary canal of the femoral / humeral shaft at a standard length horizontal height near the TEA, and draw a perpendicular line from the center of the circle to the X-axis as the Z-axis; the Y-axis is perpendicular to both the X-axis and the Z-axis. Step 4), determine the medial and lateral sagittal coordinate systems: The medial sagittal plane is a plane perpendicular to the X-axis and passing through the medial condyle of the femur / humerus, and the lateral sagittal plane is a plane perpendicular to the X-axis and passing through the lateral condyle of the femur / humerus. On the medial sagittal plane, a two-dimensional coordinate system is established with the medial condyle of the femur / humerus as the origin and the Y-axis and Z-axis as the coordinate axes; this is called the medial sagittal coordinate system. On the lateral sagittal plane, a two-dimensional coordinate system is established with the lateral condyle of the femur / humerus as the origin and the Y-axis and Z-axis as the coordinate axes; this is called the lateral sagittal coordinate system. Step 5): The individual most stable rotation axis of each tested joint intersects the medial sagittal plane at a point. The anteroposterior position of the intersection point in the medial sagittal plane coordinate system, i.e., the Y-axis coordinate, is represented by the parameter medial-anteroposterior (M-AP), and the mesiodistal position, i.e., the Z-axis coordinate, is represented by the parameter medial-mesiodistal (M-PD). The anteroposterior position of the intersection point of the individual most stable rotation axis with the lateral sagittal plane, i.e., the position on the Y-axis, is represented by the parameter lateral-anteroposterior (L-AP), and the mesiodistal position, i.e., the position on the Z-axis, is represented by the parameter lateral-mesiodistal (L-PD). The average value of each of the four parameters is taken as the population average relative position relationship between the individual most stable rotation axis and the TEA, thereby obtaining the population average most stable rotation axis.

6. The method for obtaining the average most stable rotation axis of a population according to claim 5, characterized in that, In step 3), the standard length is the distance between the inner and outer condyles of the TEA × a, where a is a coefficient with a value of 0.44~1.

0.

7. A method for locating the rotation axis of a knee joint in the real world, characterized in that, Includes the following steps: Step ①: For the target knee joint, first take a CT or MRI of the knee joint, and obtain the individual's most stable rotation axis as the target rotation axis based on the method for obtaining the individual's most stable rotation axis according to any one of claims 1-4, or obtain the population's average most stable rotation axis as the target rotation axis based on the method for obtaining the population's average most stable rotation axis according to any one of claims 5-6. Then, locate the projection of the target rotation axis in this direction on the horizontal / coronal plane. Step 2: Locate the posterior condylar axis (PCA) on the imaging image, and then measure the distances between the horizontal projection of the target rotation axis and the two intersections of the medial and lateral sides of the bone cortex and the PCA, respectively, as the medial anterior-posterior distance and the lateral anterior-posterior distance; Step 3: Find the common tangent of the distal boundaries of the medial and lateral femur on the imaging image as the mandibular axis. Then measure the distance between the coronal projection of the target rotation axis and the two intersections of the medial and lateral cortical bone and the mandibular axis, respectively, as the medial mesial-distal distance and the lateral mesial-distal distance. Step 4: Locate the PCA (proximal condyle) of the actual knee joint. Based on the medial anterior-posterior distance obtained in Step 2, find a parallel line corresponding to the medial anterior-posterior distance of the PCA. Draw a straight line in the mesiodistal direction through the intersection of this parallel line and the medial bone surface of the knee joint as the medial mesiodistal running line. Simultaneously, based on the lateral anterior-posterior distance obtained in Step 2, find a parallel line corresponding to the lateral anterior-posterior distance of the PCA. Draw a straight line in the mesiodistal direction through the intersection of this parallel line and the lateral bone surface of the knee joint as the lateral mesiodistal running line. Then, locate the mandibular axis of the actual knee joint and, based on the medial proximal-posterior distance obtained in Step 3... Find the parallel lines corresponding to the medial proximal-distal and lateral proximal-distal distances above the mandibular axis, respectively. Then, draw two straight lines in the anterior-posterior direction through the intersections of these two parallel lines with the medial and lateral bone surfaces of the knee joint, respectively, as the anterior-posterior running lines of the medial and lateral sides. The intersection of the medial proximal-distal running lines and the anterior-posterior running lines is the position where the target rotation axis exits the medial cortex of the knee joint; the medial proximal-distal running lines and the anterior-posterior running lines are the positions where the target rotation axis exits the lateral cortex of the knee joint. Use these two intersection points as the installation positions of the knee joint prosthesis rotation axis.

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