UWB-based method for elastic spatial registration of physical constraints in orthopedic surgery

Abstract

This application relates to the field of orthopedic surgical navigation technology, specifically to a method for elastic spatial registration of orthopedic surgery based on UWB positioning. The method includes: acquiring the physical spatial coordinates of intraoperative UWB positioning markers and their corresponding virtual reference point coordinates in preoperative image data; establishing an initial spatial correspondence through rigid registration and outputting the registration residual for each intraoperative UWB positioning marker; constructing a surface mesh model of the target surgical area based on preoperative image data; distinguishing between bone regions and soft tissue coverage regions within the surface mesh model; assigning differentiated tissue stiffness coefficients to different regions based on anatomical attributes; establishing the total energy function of an elastic optimization model that integrates data fitting terms, deformation smoothing terms, and physical constraint terms; and solving for the elastic displacement field. This application can adapt to actual conditions such as changes in patient position and soft tissue displacement during surgery, significantly improving the registration accuracy and stability in complex intraoperative environments.

Description

Technical Field

[0001] This application relates to the field of orthopedic surgical navigation technology, specifically to an elastic spatial registration method for physical constraints in orthopedic surgery based on UWB positioning. Background Technology

[0002] Intraoperative navigation and positioning systems in orthopedics have been widely used in clinical practice to improve surgical precision and reduce iatrogenic risks. Their core registration mechanism is primarily based on the assumption of rigid deformation. Currently, mainstream systems typically employ classic rigid registration methods such as Singular Value Decomposition (SVD), quaternion least squares, or Iterative Closest Point (ICP) algorithms. These methods match the preoperative 3D image model with intraoperatively acquired spatial markers to obtain the spatial orientation of the patient's anatomical structures in the navigation coordinate system. Under ideal conditions—where markers are firmly fixed to the target bone surface, the operating environment is stable, and tissue morphology remains consistent—this type of method can achieve high overall rigid registration accuracy.

[0003] In real clinical surgical settings, physiological activities such as changes in patient respiration, pulse, and anesthesia status, as well as surgical interventions such as traction, soft tissue incision, and positioning, all introduce multi-source dynamic disturbances. This leads to non-rigid deformation of local tissues, causing a significant deviation between the rigid deformation assumption and the actual anatomical state. Of particular note is that spatial markers commonly used for registration in clinical practice are often fixed to the skin or soft tissue surface, while the actual target of navigation is the deep skeletal structure. When relative sliding or deformation occurs between soft tissue and bone, the spatial displacement of the markers cannot accurately reflect the changes in bone posture, resulting in systematic errors and local deviations in the registration results. If the markers are sparsely distributed, locally concentrated, or unevenly positioned due to surgical approach limitations, their ability to constrain rotation, translation, and scale transformations will be further weakened, making the registration accuracy extremely sensitive to minute disturbances and severely affecting the overall stability and long-term reliability of the navigation system.

[0004] With the introduction of ultra-wideband (UWB) ranging and positioning technology into the field of surgical navigation, the system has achieved significant enhancements in wireless spatial perception and real-time dynamic tracking capabilities. However, in the complex environment of the operating room, UWB signals are susceptible to interference from factors such as surgical instruments obstructing the signal, multipath reflection, and non-line-of-sight propagation, leading to problems such as jumps in ranging data, increased noise, or decreased reliability. Existing UWB navigation systems mostly use methods such as threshold rejection, moving average, or outlier filtering to directly discard outlier measurements. While these methods can suppress error propagation to some extent, they fail to deeply explore the environmental interference characteristics and tissue state information hidden in anomalous signals. These methods only aim to eliminate anomalies and do not dynamically incorporate signal uncertainty into the deformation assessment and registration compensation system. As a result, the system cannot identify potential risk areas and is unable to achieve adaptive error control during registration, thus limiting further improvements in navigation accuracy in scenarios with significant dynamic deformation of soft tissue. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this application proposes a UWB-based method for elastic spatial registration of physical constraints in orthopedic surgery, in order to solve the problems mentioned in the background.

[0006] This application provides a method for elastic spatial registration of physical constraints in orthopedic surgery based on UWB positioning, including: Obtain the physical spatial coordinates of the intraoperative UWB positioning markers and the corresponding virtual reference point coordinates in the preoperative image data. Establish the initial spatial correspondence through rigid registration and output the registration residual of each intraoperative UWB positioning marker. A surface mesh model of the target surgical area is constructed based on preoperative imaging data. The surface mesh model distinguishes between bone areas and soft tissue coverage areas, and different tissue stiffness coefficients are assigned to different areas according to anatomical properties. A total energy function is established for an elastic optimization model that integrates data fitting terms, deformation smoothing terms, and physical constraint terms to solve for the elastic displacement field. The data fitting term drives the elastic displacement field with registration residuals to compensate for local errors caused by soft tissue slippage or local positional changes. The deformation smoothing term ensures continuous displacement changes in adjacent regions. The physical constraint term is constructed to impose anatomical prior constraints on deformation based on differences in tissue stiffness coefficients.

[0007] Furthermore, the rigid registration employs weighted singular value decomposition and iterative reweighted least squares to solve for the optimal similarity transformation, minimizing the error between the transformed intraoperative point set and the preoperative point set. The similarity transformation includes a rotation matrix. Translation vector and scale factor The resulting optimization problem can be expressed as: , , , in, The coordinates of the intraoperative UWB positioning markers are provided. The coordinates of the corresponding virtual reference point. As initial weights, output registration residuals. , This serves as an index for intraoperative UWB localization markers. This represents the total number of UWB positioning markers used during the procedure. It is the transpose of the rotation matrix. It is an identity matrix.

[0008] Furthermore, different organizational stiffness coefficients are assigned to different regions, including: For network vertices in skeletal regions, a maximum tissue stiffness coefficient is assigned; for network vertices in soft tissue-covered regions, a tissue stiffness coefficient is assigned as follows: , in, This is a modulation function based on CT values, soft tissue thickness, and patient constitution. For vertex CT value, For local soft tissue thickness, Body Mass Index (BMI) As the reference soft tissue stiffness coefficient, is the organizational stiffness coefficient of the network vertices.

[0009] Furthermore, the expression for the data fitting term is: , in, Indicates the physical space coordinates of the intraoperative UWB positioning markers; This represents the coordinates of the virtual reference point in the preoperative imaging data; Indicates the initial rigid transformation; Represents network vertices The deformation of the first The influence weight of each intraoperative UWB positioning marker point; Represents the network vertices to be solved. The elastic displacement vector; Indicates the first Dynamic reliability weights for intraoperative UWB positioning markers This indicates the fitting of intraoperative UWB positioning markers.

[0010] Furthermore, the expression for the deformation smoothing term is: , in, It is the set of all adjacent vertex pairs in the network. For network vertices The displacement vector to be determined It is the network apex The displacement vector to be determined This is the deformation smoothing term.

[0011] Furthermore, the physical constraint term The expression is: , in, The total number of grid vertices. The organizational stiffness coefficient of the network vertices. For grid vertices The displacement vector to be determined These are physical constraint terms.

[0012] Furthermore, the dynamic credibility weight is calculated as follows: , Signal quality factor The expression is: , in, For signal-to-noise ratio, This is an index of multipath interference intensity. This is a non-line-of-sight indicator. This is an empirical coefficient. The Sigmoid function maps the output to the (0,1) interval; Residual Consistency Factor The expression is: , in, Register residuals for all current marker points The standard deviation.

[0013] Furthermore, the elastic displacement field is obtained by solving sparse linear equations, including: The total energy function of the elastic optimization model is rewritten as an expression relating the elastic displacement vector. The quadratic form: , in, The left-hand side of the total energy function is... This is the transpose of the displacement vector. It is a sparse symmetric positive definite matrix. coefficient vector transpose, For constant terms; Construct sparse linear equations: , Let be the optimal elastic displacement field to be solved.

[0014] Furthermore, based on the optimal elastic displacement field, the final spatial mapping position of any point during the operation is obtained as follows: , in, For any point during the operation, Any point during the operation The vertex of the grid in which it is located. For interpolation weights, It is a rigid transformation. This represents the final spatial mapping location; Let be the optimal elastic displacement vector of vertex k in the network.

[0015] Furthermore, the optimal elastic displacement vector of all network vertices k is calculated to obtain the organization's average displacement; The maximum displacement vector is obtained by searching for the maximum optimal elastic displacement vector. Establish dual safety thresholds; if the average displacement or maximum displacement vector exceeds the respective set safety threshold, an alarm will be triggered.

[0016] Compared with the prior art, the advantages of this application are: This study introduces an anatomical structural partitioning and physical property modeling mechanism. The preoperative 3D model is meshed to distinguish the vertices of the skeletal region from those of the soft tissue-covered region. Differential stiffness coefficients are assigned to different regions based on image thickness information and anatomical priors. This allows the skeletal region to maintain near-rigid body characteristics during deformation, while the soft tissue-covered region is allowed to undergo restricted, small-amplitude elastic displacement, thus physically constraining the effective range and direction of deformation. Through this physical property mapping, the system achieves both tissue layer differentiation and structural constraint consistency. Even when faced with intraoperative positioning adjustments, skin traction, or slight soft tissue slippage, the registration results remain stable and reliable on the skeletal body, achieving a spatial deformation expression and mapping that conforms to actual biomechanical characteristics.

[0017] A total energy function is constructed that integrates data fitting terms, deformation smoothing terms, and physical constraint terms. This allows the deformation field to not only fit the registration error of the marker points but also avoid local distortion and unreasonable stretching. By applying different levels of deformation suppression weights to vertices in different regions during the optimization process, the displacement of the skeletal region naturally approaches zero, while the deformation of the soft tissue coverage area smoothly diffuses with the distribution of reliable points. This ensures the overall structural stability while improving local compensation capabilities, significantly enhancing the geometric consistency and structural interpretability of the deformation field.

[0018] Signal quality factors are established using signal-to-noise ratio, multipath interference intensity index, and non-line-of-sight indicator. Dynamic reliability weights are obtained, and the contribution of marker points to energy optimization is dynamically adjusted. This ensures that points with high measurement quality dominate the registration solution, while the influence of points with signal anomalies or occlusions is automatically weakened. This effectively suppresses abrupt interference caused by outliers on the overall registration field, reduces the risk of large error propagation, and ensures that the final registration result remains continuous, stable, and highly stable even in complex intraoperative environments.

[0019] By using sparse linear solutions, a unified mapping expression from rigid transformation to elastic compensation is achieved, supporting multi-round dynamic updates and real-time monitoring during surgery. It can output safety warnings and prompt recalibration based on the displacement amplitude of the soft tissue coverage area.

[0020] The method described in this application achieves precise spatial modeling of skeletal structures, adaptive compensation for local soft tissue deformation, and stable output of coordinate mapping relationships. It can maintain reliable performance under different surgical positions, different instrument interferences, and different individual patient differences, providing a safe, stable, and reliable intraoperative spatial registration technology support, and significantly improving the clinical applicability and surgical safety assurance capabilities of orthopedic navigation systems.

[0021] In summary, the UWB-based orthopedic surgical physical constraint elastic spatial registration method provided in this application achieves an organic unity of rigid consistency and local flexibility compensation by introducing an elastic deformation optimization mechanism that incorporates anatomical structure partitioning, physical stiffness constraints, and credibility weights. This effectively compensates for the deficiencies of traditional rigid registration (lacking deformation expression) and purely mathematical elastic registration (lacking physical rationality). While maintaining real-time performance, it significantly improves registration accuracy in complex deformation scenarios. It can adapt to actual conditions such as changes in body position and soft tissue displacement during surgery, significantly improving registration accuracy and stability in complex intraoperative environments. This provides a reliable technical approach and engineering foundation for orthopedic surgical navigation and precision treatment. Attached Figure Description

[0022] Figure 1 The overall flowchart of the orthopedic surgery physical constraint elastic spatial registration method based on UWB positioning provided in the embodiments of this application is as follows: Figure 2 A schematic diagram comparing the iteration curves of the method of this application with other methods, provided for embodiments of this application. Detailed Implementation

[0023] The technical solutions of this application will be clearly and completely described below with reference to the accompanying drawings of the embodiments. It should be noted that the described embodiments are only a part of this application, and not all embodiments. Other embodiments obtained by those skilled in the art based on the technical solutions of this application without creative effort are all within the protection scope of this application.

[0024] In practical scenarios of orthopedic spinal surgery navigation, taking the registration of UWB positioning markers deployed on the surgical area and bone surface with virtual reference point coordinates in preoperative image data as an example, the coordinate data of the physical space and the image model of the virtual space are acquired simultaneously to form multimodal intraoperative registration data. During the data registration process, the correlation between the physical coordinate points and the virtual reference point coordinates of the anatomical points in the image is realized. All spatial registrations are transformed into multimodal feature vectors that integrate geometric coordinates, registration residual information, and tissue attributes. These multimodal features are mapped to a deformation parameter space with biomechanical constraints. After deep fusion of a physical prior-based elastic optimization model and dynamic confidence weights, the complex deformation relationship between the bone region and the surrounding soft tissue coverage area is effectively captured. Then, the stiffness of the bone region in the deformation field is constrained to lock its rigid transformation properties, and the elastic displacement of the soft tissue coverage area is solved through optimization methods. Combined with the anatomical coordinate system defined in the preoperative images, a high-fidelity spatial mapping relationship with biomechanical rationality can be directly output, realizing real-time and accurate registration of intraoperative navigation coordinates.

[0025] The method described in this application involves deploying a UWB (Ultra-Wideband) positioning base station network in the patient's surgical area to track surgical instruments and UWB positioning markers placed on the patient's body surface in real time; receiving UWB positioning data through a processor and performing compensation processing, converting the compensated coordinates to a navigation display terminal, and issuing warnings in case of abnormalities; finally, the navigation display terminal is used to present the compensated surgical navigation image in real time to assist doctors in performing precise operations.

[0026] Please see Figure 1 This document outlines a procedure for elastic spatial registration of physical constraints in orthopedic surgery based on UWB localization, comprising the following steps: S101, obtain the physical spatial coordinates of the intraoperative UWB positioning markers and the corresponding virtual reference point coordinates in the preoperative image data, establish the initial spatial correspondence through rigid registration, and output the registration residual of each intraoperative UWB positioning marker; S102, construct a surface mesh model of the target surgical area based on preoperative image data, distinguish between bone areas and soft tissue coverage areas in the surface mesh model, and assign differentiated tissue stiffness coefficients to different areas according to anatomical properties; S103, establish the total energy function of the elastic optimization model that integrates data fitting terms, deformation smoothing terms, and physical constraint terms, and solve for the elastic displacement field; wherein, the data fitting term drives the elastic displacement field with registration residuals to compensate for local errors caused by soft tissue sliding or local positional changes; the deformation smoothing term ensures continuous displacement changes in adjacent regions; the physical constraint term is constructed to impose anatomical prior constraints on deformation based on the differences in tissue stiffness coefficients.

[0027] In step S101, a preset rigid registration initialization algorithm is used to spatially align the intraoperative UWB positioning marker set with the preoperative virtual point set, and obtain the overall rotation, translation and optional scale parameters so that the two form a preliminary match in the overall spatial distribution. At the same time, the registration error of each marker point is output for subsequent elastic compensation and reliability assessment.

[0028] Let the set of physical space coordinates of the N UWB positioning markers acquired during the procedure be . , It is the first The physical spatial coordinates of each UWB positioning marker point, and the corresponding set of virtual reference point coordinates in the preoperative imaging data are: , It is the first The coordinates of a virtual reference point. Rigid registration aims to solve for an optimal similarity transformation (including the rotation matrix). Translation vector ,scale The goal is to minimize the error between the transformed intraoperative point set and the preoperative point set. This problem can be formulated as a weighted least squares optimization problem, with the optimality problem expressed as: , The constraints are: , , in, The coordinates of the intraoperative UWB positioning markers are provided. The coordinates of the corresponding virtual reference point. As initial weights, output registration residuals. , This serves as an index for intraoperative UWB localization markers. This represents the total number of UWB positioning markers used during the procedure. It is the transpose of the rotation matrix. It is an identity matrix.

[0029] For robust solution, iterative reweighted least squares (IRLS) is employed. In each iteration, the decentralized coordinates are calculated: , ,in The weighted centroid of the intraoperative UWB positioning markers. The weighted centroid of the virtual reference point coordinates. For decentralized intraoperative UWB localization markers, Decentralized virtual reference point coordinates; construct a weighted covariance matrix. , Transpose of the coordinates of decentralized intraoperative UWB positioning markers; for the weighted covariance matrix Performing singular value decomposition, we obtain: ; in, A right singular vector matrix transpose, It is a left singular vector matrix. It is a singular value diagonal matrix. Left singular vector matrix The transpose of .

[0030] Calculate the optimal rotation matrix ; Calculate the optimal scaling factor ; Calculate the optimal translation vector Update weights Based on the current registration residual Use the Huber kernel or Tukey robust kernel to reduce the weight of large residuals.

[0031] After iterative convergence, the output is the rotation matrix after rigid registration. Translation vector and scale factor and the final registration residual of each intraoperative UWB positioning marker. .

[0032] In step S102, a surface mesh model is established for the target surgical area based on preoperative image data, and the skeletal area and the soft tissue covered area are distinguished in the surface mesh model. The skeletal area is regarded as a rigid body, which is only allowed to have minimal displacement changes, while the soft tissue covered area is regarded as an area that can undergo limited elastic deformation. Different tissue stiffness parameters are assigned to the two types of areas according to anatomical properties, so that the skeletal area remains stable in the subsequent registration process, while the soft tissue covered area can generate displacement compensation within a controlled range.

[0033] Based on the segmented preoperative CT / MRI images, the Marching Cubes algorithm was used to extract the surface mesh of the triangular facets of the target surgical region. ,in For the set of network vertices, Let be the set of edges. This is a set of facets. Using an image segmentation mask, the network vertex set is divided into subsets of vertices representing skeletal regions. and soft tissue coverage region vertex subset .

[0034] For each network vertex Assign an organizational stiffness coefficient This coefficient directly determines the ease with which displacement occurs during deformation: , in, It is a maximum tissue stiffness coefficient used to mathematically approximate indeformability. For network vertices in a soft tissue-covered region, it is the tissue stiffness coefficient of the network vertex. Based on the reference soft tissue stiffness coefficient With a modulation function Together, we determine that the modulation function takes into account the vertex CT value. Local soft tissue thickness Individual factors such as body mass index (BMI) also play a role. Generally, areas with higher density and thinner thickness have greater stiffness.

[0035] In step S103, based on the distribution of registration residuals in the rigid registration results, a total energy function of the elastic optimization model, including data fitting terms, deformation smoothing terms, and physical constraint terms, is constructed to describe and constrain the local elastic deformation process. The data fitting term drives the deformation to compensate for the observation residuals, the deformation smoothing term ensures the continuous change of displacement in adjacent regions, and the physical constraint term significantly suppresses the deformation of the skeletal region based on the difference in tissue stiffness. It is constructed to impose anatomical prior constraints on the deformation based on the difference in tissue stiffness coefficients, thus maintaining the physical rationality of the anatomical structure while ensuring the registration accuracy.

[0036] The goal is to solve for a displacement for each vertex in the mesh. This allows the deformation field defined by these displacements to smoothly compensate for the residuals and obey physical constraints. To this end, a total energy function is constructed: , in, It is a stack of vectors representing the displacements of all vertices. Hyperparameters are used to balance the weights of each energy term.

[0037] Specifically, it includes: Data fitting term This ensures that the deformation at the marker point effectively compensates for its rigid registration residual. For each intraoperative UWB positioning marker point after rigid transformation of its physical space coordinates following step S101, the marker point... , = Its deformed position is obtained by displacement-weighted interpolation of the adjacent mesh vertices.

[0038] , in, Indicates the physical space coordinates of the intraoperative UWB positioning markers; This represents the coordinates of the virtual reference point in the preoperative imaging data; Indicates the initial rigid transformation; Represents network vertices The deformation of the first The influence weight of each intraoperative UWB positioning marker point; Represents the network vertices to be solved. The elastic displacement vector; Indicates the first Dynamic reliability weights for intraoperative UWB positioning markers This indicates the fitting of intraoperative UWB positioning markers.

[0039] Deformation smoothing term This constraint ensures that the displacements of adjacent network vertices are as consistent as possible, in order to guarantee the smoothness of the deformation field and avoid local distortion.

[0040] , This is essentially based on the regularization term of the grid Laplacian operator, where, It is the set of all adjacent vertex pairs in the network. For network vertices The displacement vector to be determined It is the network apex The displacement vector to be determined This is the deformation smoothing term.

[0041] Physical constraints Based on the organizational stiffness coefficients assigned in S102, the displacement of all network vertices is penalized, but the penalty intensity varies depending on the stiffness.

[0042] , in, The total number of grid vertices. The organizational stiffness coefficient of the network vertices. For grid vertices The displacement vector to be determined These are physical constraint terms.

[0043] Due to the network vertices of the skeletal region The value is extremely large, and this term will strongly suppress its displacement. For network vertices in soft tissue-covered regions, a smaller tissue stiffness coefficient is desirable. It is allowed to produce the necessary displacements driven by the data fitting term.

[0044] S103, during the process of solving the elastic displacement field, the signal quality information provided by the UWB positioning system is simultaneously invoked to dynamically evaluate the reliability of each intraoperative UWB positioning marker. The reference information used includes signal-to-noise ratio, multipath interference intensity, presence of non-line-of-sight propagation, and the magnitude of the registration residual in the rigid registration stage. Based on the evaluation results, a corresponding confidence weight is assigned to each intraoperative UWB positioning marker. When the signal state of a marker is abnormal or has significant uncertainty, its impact on the overall result during the registration process will be automatically weakened to avoid abnormal measurement data from adversely affecting the spatial registration result.

[0045] A dynamic confidence weight was designed for each intraoperative UWB localization marker. This dynamic confidence weight combines real-time signal quality with historical registration consistency: , Signal quality factor The expression is: , in, For signal-to-noise ratio, This is an index of multipath interference intensity. This is a non-line-of-sight indicator. This is an empirical coefficient. This is the Sigmoid function, which maps the output to the (0,1) interval.

[0046] Residual Consistency Factor The expression is: , in, Register residuals for all current marker points The standard deviation of the standard deviation. Points where the registration residuals are significantly greater than the average value. The value will decrease sharply.

[0047] The final calculated dynamic credibility weight Will be directly used for data fitting terms The weighting is used to achieve adaptive suppression of outliers.

[0048] In one embodiment, the elastic displacement field is obtained by solving sparse linear equations; then the elastic displacement vector in the elastic displacement field is fused with the aforementioned rigid registration to form a final mapping relationship from the physical coordinate space of the intraoperative UWB positioning marker to the coordinates of the virtual reference point in the preoperative image data, and is used to guide the real-time display and spatial correspondence of the positions of key anatomical structures and surgical instruments in the surgical navigation system.

[0049] The total energy function Expand and rewrite as about the elastic displacement vector The quadratic form: , in, The left-hand side of the total energy function is... This is the transpose of the displacement vector. It is a sparse symmetric positive definite matrix. coefficient vector transpose, This is a constant term.

[0050] , , Contribute to the data fitting term, The coefficient matrix contributing to the data fitting term. , , To map network vertex displacements to intraoperative UWB localization markers Interpolation shift; The coefficient matrix contributing to the smoothing term. ,in Let Laplace's matrix be the grid. It is the identity matrix. For Kronecker product; The coefficient matrix contributing to the physical constraint terms. , For the first Organizational stiffness coefficients of each network vertex.

[0051] Let be the optimal elastic displacement field to be solved. , and These are the weighting coefficients. The right-hand vector contributed to the data fitting term.

[0052] The optimal elastic displacement field is obtained by solving the sparse linear equations: , Efficient numerical methods such as the preprocessed conjugate gradient (PCG) method are used for solving the problem.

[0053] Based on the optimal elastic displacement field, the final spatial mapping position of any point during the operation is obtained as follows: , in, For any point during the operation, For the vertex of the grid, For interpolation weights, It is a rigid transformation. This represents the final spatial mapping location; Let be the optimal elastic displacement vector of vertex k in the network.

[0054] During continuous system operation, the elastic displacement vector of the soft tissue coverage area is monitored in real time. When the displacement amplitude of the monitored area exceeds the preset safety threshold, a prompt message is automatically issued in the navigation interface to remind the operator that the current body position may have changed significantly or the status of the marker point is abnormal, prompting a reassessment or recalibration, thereby improving the safety and reliability of the system in clinical applications.

[0055] After each frame of registration results is generated, the average tissue displacement of the current soft tissue coverage area is calculated. and maximum displacement As a monitoring indicator, Establish a dual first safety threshold Second security threshold The monitoring logic is as follows: , When an alert is triggered (Alert=True), the following actions are performed: a prominent visual warning is overlaid on the navigation interface and an audible alert is issued; the current out-of-limit displacement data and possible abnormal marker IDs are recorded. Optionally, the registration mode is automatically switched to pure rigid transformation, and the operator is notified.

[0056] The method described in this application ensures that the navigation system can degrade and proactively provide alerts in the event of unpredictable large-scale deformation or system failure, thus safeguarding the bottom line of safety during the surgical procedure.

[0057] Please see Figure 2 The iterative curves of the existing rigid registration method, the traditional TPS (thin plate spline) registration method and the method of this application clearly demonstrate the differences in recognition accuracy and computational efficiency among the various schemes.

[0058] While rigid registration schemes can achieve rapid initial alignment through global transformations such as rotation and translation, they completely ignore the local elastic deformation of biological tissues. In real-world surgical scenarios with significant soft tissue displacement, the registration residuals are difficult to further reduce. Convergence curves show that the registration residuals of rigid registration plateau after a few iterations, eventually remaining at a high level. This results in a theoretical bottleneck in navigation accuracy when facing changes in body position or tissue deformation, making it difficult to meet the requirements of high-precision surgery.

[0059] While the TPS registration scheme can achieve high theoretical alignment accuracy through mathematical deformation models, its optimization process has a large degree of freedom and weak constraints, resulting in slow convergence speed and heavy computational load. Figure 2 The convergence curves show that TPS registration requires a large number of iterations to gradually reduce the residuals, making it difficult to operate stably under the requirements of real-time operation during surgery, thus limiting its practical application value in real surgical scenarios.

[0060] In contrast, the method in this application effectively suppresses non-physical deformation of the skeletal region during the actual registration process due to the tissue stiffness prior, ensuring the biological authenticity of the deformation; while the smoothing constraint and weighting mechanism guide the optimization process to converge quickly, avoiding overfitting and local optima, and significantly improving the accuracy, real-time performance and system stability of registration in real surgical environments.

[0061] Although embodiments of this application have been shown and described, the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for elastic spatial registration of physical constraints in orthopedic surgery based on UWB positioning, characterized in that: include: Obtain the physical spatial coordinates of the intraoperative UWB positioning markers and the corresponding virtual reference point coordinates in the preoperative image data. Establish the initial spatial correspondence through rigid registration and output the registration residual of each intraoperative UWB positioning marker. A surface mesh model of the target surgical area is constructed based on preoperative imaging data. The surface mesh model distinguishes between bone areas and soft tissue coverage areas, and different tissue stiffness coefficients are assigned to different areas according to anatomical properties. A total energy function is established for an elastic optimization model that integrates data fitting terms, deformation smoothing terms, and physical constraint terms to solve for the elastic displacement field. The data fitting term drives the elastic displacement field with registration residuals to compensate for local errors caused by soft tissue slippage or local positional changes. The deformation smoothing term ensures continuous displacement variation in adjacent regions. The physical constraint term is constructed to impose anatomical prior constraints on deformation based on differences in tissue stiffness coefficients. The expression for the data fitting term is: ， in, Indicates the physical space coordinates of the intraoperative UWB positioning markers; This represents the coordinates of the virtual reference point in the preoperative imaging data; Indicates the initial rigid transformation; Represents network vertices The deformation of the first The influence weight of each intraoperative UWB positioning marker point; Represents the network vertices to be solved. The elastic displacement vector; Indicates the first Dynamic reliability weights for intraoperative UWB positioning markers The fitting of intraoperative UWB positioning markers is represented; the dynamic confidence weight is calculated as follows: ， Signal quality factor The expression is: ， in, For signal-to-noise ratio, This is an index of multipath interference intensity. This is a non-line-of-sight indicator. This is an empirical coefficient. The Sigmoid function maps the output to the (0,1) interval; Residual Consistency Factor The expression is: ， in, Register residuals for all current marker points The standard deviation.

2. The method for elastic spatial registration of physical constraints in orthopedic surgery based on UWB positioning according to claim 1, characterized in that: The rigid registration employs weighted singular value decomposition and iterative reweighted least squares to solve for the optimal similarity transformation, minimizing the error between the transformed intraoperative point set and the preoperative point set. The similarity transformation includes a rotation matrix. Translation vector and scale factor The resulting optimization problem can be expressed as: ， ， ， in, The coordinates of the intraoperative UWB positioning markers are provided. The coordinates of the corresponding virtual reference point. As initial weights, output registration residuals. , This serves as an index for intraoperative UWB localization markers. This represents the total number of UWB positioning markers used during the procedure. It is the transpose of the rotation matrix. It is an identity matrix.

3. The method for elastic spatial registration of physical constraints in orthopedic surgery based on UWB positioning according to claim 1, characterized in that, Different organizational stiffness coefficients are assigned to different regions, including: For network vertices in skeletal regions, a maximum tissue stiffness coefficient is assigned; for network vertices in soft tissue-covered regions, a tissue stiffness coefficient is assigned as follows: ， in, This is a modulation function based on CT values, soft tissue thickness, and patient constitution. For vertex CT value, For local soft tissue thickness, Body Mass Index (BMI) As the reference soft tissue stiffness coefficient, is the organizational stiffness coefficient of the network vertices.

4. The method for elastic spatial registration of physical constraints in orthopedic surgery based on UWB positioning according to claim 1, characterized in that, The expression for the deformation smoothing term is: ， in, It is the set of all adjacent vertex pairs in the network. For network vertices The displacement vector to be determined It is the network apex The displacement vector to be determined This is the deformation smoothing term.

5. The method for elastic spatial registration of physical constraints in orthopedic surgery based on UWB positioning according to claim 1, characterized in that, The physical constraints The expression is: ， in, The total number of grid vertices. The organizational stiffness coefficient of the network vertices. For grid vertices The displacement vector to be determined These are physical constraint terms.

6. The method for elastic spatial registration of physical constraints in orthopedic surgery based on UWB positioning according to claim 2, characterized in that, The elastic displacement field is obtained by solving sparse linear equations, including: The total energy function of the elastic optimization model is rewritten as an expression relating the elastic displacement vector. The quadratic form: ， in, The left-hand side of the total energy function is... This is the transpose of the displacement vector. It is a sparse symmetric positive definite matrix. coefficient vector transpose, For constant terms; Construct sparse linear equations: , Let be the optimal elastic displacement field to be solved.

7. The method for elastic spatial registration of physical constraints in orthopedic surgery based on UWB positioning according to claim 6, characterized in that, Based on the optimal elastic displacement field, the final spatial mapping position of any point during the operation is obtained as follows: ， in, For any point during the operation, Any point during the operation The vertex of the grid in which it is located. For interpolation weights, It is a rigid transformation. This represents the final spatial mapping location; Let be the optimal elastic displacement vector of vertex k in the network.

8. The method for elastic spatial registration of physical constraints in orthopedic surgery based on UWB positioning according to claim 7, characterized in that, Calculate the optimal elastic displacement vector of all network vertices k to obtain the organization's average displacement; The maximum displacement vector is obtained by searching for the maximum optimal elastic displacement vector. Establish dual safety thresholds; if the average displacement or maximum displacement vector exceeds the respective set safety threshold, an alarm will be triggered.

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