Osteotomy plane and hinge point linkage optimization method based on bone structure direction field

Abstract

This invention relates to a method for optimizing the linkage between osteotomy planes and hinge points based on bone structure orientation fields. The method involves acquiring a 3D image of the target bone and determining the target region; extracting bone structure orientation information from the target region to form an orientation field, and obtaining reliable orientation information for planning after reliability processing. Based on the bone structure orientation field, a continuous region of the main load-bearing direction is identified, and a constraint is set that the osteotomy plane must not cross this region, generating candidate osteotomy planes under this constraint. For each candidate osteotomy plane, candidate hinge points are generated within the boundary threshold range of its intersection with the bone surface. The connectivity of the hinge neighborhood is determined in three stages: before, during, and after osteotomy, and feasible hinge points are selected. The candidate osteotomy planes are cross-validated using feasible hinge points, requiring that the osteotomy plane does not cut off the main load-bearing direction or form directional opposition in the hinge neighborhood. If cross-validation fails, the osteotomy plane or hinge point is iteratively updated according to a preset set of adjusted degrees of freedom until cross-validation is successful, and finally, the osteotomy plane parameters and hinge point positions are output.

Description

Technical Field

[0001] This invention relates to medical image computing and surgical planning, specifically to a method for optimizing the linkage between osteotomy planes and hinge points based on the orientation field of bone structure. Background Technology

[0002] Current technologies, such as the osteotomy plane boundary control method, electronic device, and storage medium disclosed in CN119818146A, while providing a certain degree of control and optimization during osteotomy surgery, remain limited to the relatively simple structural constraint of osteotomy plane boundary control, primarily focusing on boundary control of robotic arm movement and precise planning of osteotomy tool position. It ensures the osteotomy tool does not exceed the prescribed safety boundary through step-by-step search and calculation of the shortest distance. This method minimizes soft tissue damage caused by tool deviation from the boundary during surgery, but neglects more complex orientation field constraints and multi-level dynamic optimization strategies. This is clearly insufficient for optimizing complex three-dimensional bone models and multi-axis collaborative operations, especially in calculating the linkage relationship between hinge points and the osteotomy plane. After all, calculating only the planar boundary lacks the integration and dynamic adjustment of the bone tissue orientation field when dealing with more complex anatomical structures.

[0003] In practice, this method may lead to error accumulation due to its inability to adapt to the orientation field of complex bone structures in real time. For example, in the problem of translating circular trajectories within the boundary of the osteotomy plane, although collisions are avoided through path planning and reverse calculation, it is still based on a one-dimensional or two-dimensional planar control strategy, which cannot fully consider the complex morphology of the bone in three-dimensional space and its impact on surgical tools. In other words, the relationship between the movement of the osteotomy tool and the hinge points is not effectively linked and synchronized, which may result in the tool being unable to perform precise operations based on the three-dimensional structure of the bone.

[0004] While the step-by-step search and safe coordinate update methods in this technology optimize the robotic arm's path selection to some extent, their handling of orientation field switching and the linkage determination between the osteotomy plane and hinge points during multiple iterations remains relatively rudimentary. Algorithm errors exist in the feasibility screening of hinge points and the dynamic updating of the intersection set, making it unable to accurately address complex adjustments caused by changes in bone structure. In the judgment process between directional bridging and planar cutting, the current technology lacks a more comprehensive orientation field reliability adjustment, which carries a risk of incomplete selection of feasible hinge points, thus affecting the overall osteotomy optimization effect. Another drawback is that the error adjustment and iterative optimization in this patent do not fully reflect the optimization of hinge point linkage. Existing robotic arm path control and safe area adjustment fail to effectively address the adjustment needs arising from the dynamic changes in the orientation field of the target bone structure, especially when facing irregular osteotomy surfaces. This may lead to failure in mutual verification between the plane and hinge points, and even with compensation through intelligent control algorithms, some accuracy loss may still occur. Summary of the Invention

[0005] The purpose of this invention is to provide an optimization method for the linkage between the osteotomy plane and the hinge point based on the orientation field of bone structure, thereby solving some of the drawbacks and shortcomings pointed out in the background art.

[0006] The present invention addresses the aforementioned technical problems by employing the following technical solution: a method for optimizing the linkage between osteotomy plane and hinge point based on bone structure orientation field, comprising: acquiring a three-dimensional image of the target bone and determining the target region; extracting bone structure orientation information of the target region to form a bone structure orientation field, and performing reliability processing to obtain reliable orientation information for planning;

[0007] Based on the bone structure orientation field, a continuous region bearing the main direction is identified, and a constraint is set that the osteotomy plane must not cross the continuous region; under the constraint, candidate osteotomy planes are generated; for each candidate osteotomy plane, hinge point candidates are generated within the boundary threshold range of its intersection line with the target bone surface, and the connectivity of the hinge neighborhood direction is judged in three stages: before, during, and after the osteotomy to screen feasible hinge points.

[0008] The candidate osteotomy plane is cross-validated using the feasible hinge point. The cross-validation includes: the osteotomy plane does not cut off the main bearing direction and does not form directional opposition in the hinge neighborhood; when the cross-validation fails, the osteotomy plane or hinge point is iteratively updated according to the preset adjustment degree set until the cross-validation passes; the osteotomy plane parameters and hinge point positions are output.

[0009] Furthermore, the credibility processing includes contradiction elimination: when the same location direction information satisfies the determination of the continuous region of the main direction under multiple main direction assumptions, the direction information is marked as unavailable, and the representative direction is determined by the neighborhood reliable direction to participate in the planning.

[0010] Furthermore, the constraint of not crossing the continuous region is determined by the crossing certificate: if there is a continuous chain formed by the continuous region of the main bearing direction on both sides of the candidate osteotomy plane, a crossing certificate containing the set of intersection points of the continuous chain and the candidate osteotomy plane is generated and the candidate osteotomy plane is determined to be invalid, and the plane adjustment direction is limited according to the set of intersection points.

[0011] Furthermore, the three-stage determination adopts directional bridging mutual verification: before the resection, it is determined whether the hinge point candidate is a directional bridging position; during the resection, it is determined whether the directional paths on both sides of the osteotomy plane within the preset rotation range can still be connected through the directional bridging position; after the resection, it is determined whether the connection is restored. If the mutual verification fails, the hinge point or osteotomy plane is adjusted first, depending on whether the reason is the disappearance of the bridging or the cutting of the plane.

[0012] Furthermore, the set of intersection points is used to determine the forbidden region, and the adjustment direction of the candidate osteotomy plane is limited to normal adjustment to avoid the forbidden region or tangential adjustment along its boundary, and the topological relationship of the forbidden region remains unchanged during the iteration process.

[0013] Furthermore, the crossing certificate is used to trigger the adjustment priority: when the number of intersection points remains constant in continuous iterations, the hinge points are adjusted first; when the number of intersection points changes, the candidate osteotomy planes are adjusted first until a valid candidate osteotomy plane is obtained.

[0014] Furthermore, the directional bridging position is determined as follows: when there is a directional path from the hinge point candidate to the hinge point candidate along the main bearing direction on both sides of the osteotomy plane, it is determined to be a directional bridging position; otherwise, it is discarded.

[0015] Furthermore, the cut-off determination includes: discretizing the preset rotation range into multiple rotation positions and updating the bridging state one by one; when the first occurrence of a failure to connect the directional paths on both sides of the osteotomy plane via the directional bridging position, recording the corresponding rotation position as a fracture event; and based on the fracture event, limiting the subsequent discrete interval or adjusting the candidate positions of the hinge point.

[0016] Furthermore, when the mutual verification fails, a constraint to maintain provability is introduced: when the hinge point is adjusted first due to the disappearance of the bridging, the osteotomy plane remains unchanged; when the osteotomy plane is adjusted first due to the plane cutting, the hinge point candidate is limited to the candidate set of the directional bridging position determined in the previous round.

[0017] Furthermore, based on the fracture event, a restricted area constraint is applied to the subsequent rotation position: the rotation position corresponding to the fracture event is set as the center of the restricted area, and the subsequent discrete rotation positions avoid the restricted area; when the fracture event remains unchanged in the iteration, the restricted area is expanded and the candidate position of the hinge point is adjusted; when the fracture event changes, the restricted area is shrunk and the discrete interval is refined.

[0018] The beneficial effects of this invention are as follows: By utilizing the orientation field of the bone structure, continuous regions along the main bearing direction are identified, and constraints are set based on these regions to prevent the osteotomy plane from crossing them, thereby ensuring the mechanical stability of the bone structure. The method generates candidate osteotomy planes and performs multi-stage judgments on hinge points, combined with an orientation bridging and mutual verification mechanism, effectively screening feasible hinge points to ensure that the continuity of the bone structure is not disrupted during rotation. In particular, in the event of a fracture, a dynamic adjustment strategy is adopted to flexibly adjust the positions of the hinge points and the osteotomy plane, avoiding crossing restricted areas and optimizing the final solution.

[0019] By introducing crossing certificates and restricted area constraints, this method ensures that the adjustment of the osteotomy plane always meets mechanical requirements, avoiding instability or irreversible situations. It dynamically adjusts priorities based on changes in the intersection point set during iteration, making hinge point or osteotomy plane adjustments more rational and efficient. Through this flexible optimization and adjustment, it provides precise and reliable planning schemes for complex orthopedic surgeries, significantly improving surgical outcomes and reducing postoperative complications. Attached Figure Description

[0020] Figure 1 This is a logic judgment diagram of the bone structure orientation field and osteotomy plane optimization method of the present invention; Figure 2 This is a diagram showing the distribution of the orientation field confidence index r and the threshold filtering effect in Embodiment 1 of the present invention; Figure 3 This is a statistical chart showing the determination of candidate osteotomy plane crossing certificates and the size of the intersection point set in Embodiment 1 of the present invention; Figure 4 This is a schematic diagram illustrating the determination of the forbidden region Z and the small step size update of the osteotomy plane normal in Embodiment 1 of the present invention; Figure 5 This is a heatmap showing the change of Conn in the directional bridging connectivity determination during the midpoint stage as a function of rotation angle in Embodiment 2 of the present invention. Figure 6 The first fracture angle in Embodiment 2 of the present invention Distribution and statistical chart of the number and duration of fracture events; Figure 7 This is a schematic diagram of the forbidden zone constraint and discrete adaptive effect driven by the fracture event in Embodiment 2 of the present invention. Detailed Implementation

[0021] The specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0022] Combined with appendix Figure 1This invention relates to an optimization method for the linkage between the osteotomy plane and hinge point based on the orientation field of bone structure. Three-dimensional image data can be acquired using computed tomography (CT) or magnetic resonance imaging (MRI), with CT data having high spatial resolution being preferred to ensure the integrity of bone structural details. The acquired two-dimensional tomographic sequence is input into an image processing system for reconstruction to obtain the three-dimensional volume data of the target bone. Subsequently, bone tissue segmentation processing is performed on the three-dimensional volume data to remove soft tissue and background areas, thereby determining the three-dimensional spatial range of the target bone, which is then defined as the target region.

[0023] By analyzing the voxel grayscale variation trend, the dominant orientation of the local structure is determined. The dominant orientation is used to characterize the spatial arrangement direction of bone trabeculae or bone cortex. For each local spatial unit within the target area, its principal orientation vector is calculated, and all local principal orientation vectors are organized in three-dimensional space to form a continuously distributed bone structure orientation field. The bone structure orientation field is used to describe the overall orientation distribution of the internal structure of the target bone, providing a structural basis for subsequent planning.

[0024] For each local principal direction vector, a neighborhood consistency check is performed to determine whether there are significant discontinuities or abnormal deviations between it and surrounding direction vectors. When a direction information exhibits abrupt changes or fails to form a stable direction trend within its neighborhood, it is marked as unusable direction information. Direction information located in image boundary regions or regions affected by artifacts is also removed. Direction information that is not removed is confirmed as reliable direction information.

[0025] Spatial analysis of the orientation field within the target area identifies regions with high consistency and directional continuity. These regions represent the primary load-bearing directions of the trabeculae or cortex, typically the main load-bearing directions of the bone. When generating candidate osteotomy planes, based on the orientation field information within the target bone, planes that optimize osteotomy results and hinge point locations are prioritized without traversing continuous regions of the primary load-bearing directions.

[0026] Each candidate osteotomy plane is positionally optimized based on its intersection with the target bone surface, ensuring that the impact of the osteotomy on the bone structure is minimized without violating constraints. For each candidate osteotomy plane, hinge point candidates are generated within the boundary threshold range of its intersection with the target bone surface. The positions of the hinge point candidates are optimized based on the relative position of the intersection between the osteotomy plane and the bone surface, the local characteristics of the bone structure orientation field, and the mechanical load requirements.

[0027] In the pre-resection stage, it is first determined whether the hinge point candidate is located at a directional bridging position that can connect both sides of the osteotomy plane; in the mid-resection stage, it is checked whether the hinge point candidate can maintain directional consistency within the preset rotation range to ensure that the bone structure does not experience unacceptable fractures after rotation; in the post-resection stage, it is determined whether the direction near the hinge point has returned to consistency after rotation to ensure that the position of the hinge point can still maintain the stability of the structure after osteotomy.

[0028] Check for any directional discontinuities on either side of the osteotomy plane. If the osteotomy plane cuts off the main load-bearing direction, the plane is deemed unsuitable and requires adjustment. Secondly, determine if the osteotomy plane creates directional opposition. Directional opposition refers to the directional paths on either side of the osteotomy plane exhibiting opposite directions in the hinge region. This can cause unstable mechanical loads on the bone tissue during rotation, thus affecting postoperative outcomes. If the osteotomy plane exhibits directional opposition with the area around the hinge point, the plane is also deemed unsuitable.

[0029] If the above mutual verification fails, iterative updates are performed according to a preset set of adjustment degrees of freedom. The set of adjustment degrees of freedom includes rotation of the plane normal vector, translation of the plane, and fine-tuning of the hinge point position. These adjustments are made step by step through optimization algorithms until the mutual verification conditions are met, that is, the osteotomy plane does not cut off the main load-bearing direction and does not form directional opposition in the hinge neighborhood.

[0030] When the directional information at a certain location within the target area satisfies the criteria for a continuous region under multiple principal direction settings, it indicates a contradiction in the directional information, and therefore, this directional information is marked as unusable. These contradictory directional information are caused by image noise, artifacts, or segmentation errors. To ensure the stability and reliability of the planning process, all directional information marked as unusable will not participate in subsequent planning calculations.

[0031] For regions containing rejected directional information, compensation is made using directional information already deemed reliable within the neighborhood. This compensation process follows the neighborhood consensus principle, where directional information within the neighborhood is used to vote and determine a representative direction for that location. This representative direction is considered the most reliable direction for that location and is used in subsequent osteotomy plane and hinge point planning.

[0032] If a continuous chain formed by a continuous region along the main bearing direction exists on both sides of the candidate osteotomy plane, it is considered that the plane has engaged in an undesirable interaction with the continuous region. Therefore, a crossing certificate is generated, containing a set of intersection points between the continuous chain and the candidate osteotomy plane. This set of intersection points is used to determine whether the osteotomy plane violates the constraints.

[0033] If the set of intersection points between a candidate osteotomy plane and a continuous region along the principal load-bearing direction is confirmed to exist, the candidate osteotomy plane is deemed invalid. This means that the osteotomy plane crosses a continuous region along the principal load-bearing direction, causing mechanical instability or damage to the bone structure, and therefore the plane does not meet the design requirements.

[0034] The plane adjustment direction should avoid crossing the area where the intersection set is located, to ensure that the new position after the candidate osteotomy plane adjustment will not cross the continuous area of ​​the main bearing direction again.

[0035] After generating the crossing certificate and confirming the intersection set, the forbidden adjustment region is determined using the intersection set. The forbidden adjustment region refers to the area where the candidate osteotomy plane intersects with the continuous region of the main load-bearing direction. These regions constrain the adjustment of the osteotomy plane. To ensure that the osteotomy plane does not cross the continuous region of the main load-bearing direction, the forbidden adjustment region serves as a restriction condition for plane adjustment, preventing re-entry into these regions during the plane adjustment process.

[0036] Planar adjustments can be made along the normal direction, but it must be ensured that the adjusted plane no longer crosses the spatial boundaries of the restricted area. Normal adjustment refers to displacement or rotation along the plane's perpendicular direction, ensuring that the plane does not coincide with the restricted area after adjustment. Alternatively, tangential adjustments can be made along the boundary of the restricted area. Tangential adjustment means that the plane moves along the boundary of the restricted area during adjustment, thus ensuring that the plane does not cross the restricted area and maintains the stability of the skeletal structure.

[0037] During the iterative adjustment process, the topological relationship of the forbidden region must remain unchanged. This means that no matter how the plane is adjusted, the shape, position, and boundary of the forbidden region will not change, to ensure the stability and accuracy of the optimization process.

[0038] After the crossing certificate is generated, the change in the number of intersection points triggers an adjustment priority. When the number of intersection points remains constant during continuous iterations, it indicates that the adjustment of the current candidate osteotomy plane has reached its limit, and the crossing problem cannot be solved by adjusting the plane. At this point, the position of the hinge point is adjusted first. By adjusting the position of the hinge point, the relative relationship between the plane and the bone structure can be changed, thereby avoiding further crossing of the restricted area. Adjusting the hinge point helps optimize the rationality of the osteotomy plane while maintaining the mechanical stability of the bone structure.

[0039] When the number of intersection points changes, it indicates a new change in the interaction between the current osteotomy plane and the continuous region along the main load-bearing direction, leading to new crossing problems. In this case, the candidate osteotomy plane is adjusted first, changing its position and angle to reduce or eliminate the intersection point set, ensuring the plane does not cross the continuous region along the main load-bearing direction. During the adjustment process, the validity of the plane adjustment is continuously assessed using the intersection point set from the crossing certificate until a valid candidate osteotomy plane that satisfies all constraints is obtained.

[0040] The three-stage determination uses directional bridging for mutual verification to ensure the rationality and stability of the osteotomy plane. In the pre-osteotomy stage, it is determined whether the hinge point candidate is a directional bridging location. A directional bridging location is one where the region of the hinge point candidate is connected to both sides of the osteotomy plane via the main direction of the bone structure. If the hinge point does not meet this condition, it is determined to be an infeasible hinge point and will not participate in subsequent operations.

[0041] By simulating rotation, the orientation of the bone structures on both sides of the osteotomy plane is checked to see if a stable directional bridge can be formed through the hinge point candidate. If a fracture occurs within the rotation range, preventing the connection of directional paths on both sides of the osteotomy plane through the hinge point candidate, the bridging is deemed to have failed.

[0042] If directional connectivity can be restored after rotating the osteotomy plane, the mutual verification is considered successful; otherwise, the mutual verification is considered unsuccessful.

[0043] If the bridging disappears, the position of the hinge point is adjusted first, and the directional bridging is re-established by moving the hinge point to ensure the continuity of the bone structure. If the plane cuts off the main load direction, the position or angle of the osteotomy plane is adjusted first to avoid further cutting off the main load path of the bone structure.

[0044] Along the bone structure on both sides of the osteotomy plane, check if there is a continuous directional path that can reach the hinge point candidate position. If there is a directional path in the bone structure on both sides of the osteotomy plane that can smoothly connect to the hinge point candidate position without significant deviation or breakage, then the hinge point candidate is considered to meet the requirements of directional bridging and is determined to be a directional bridging position.

[0045] If a hinge point candidate cannot connect the continuous regions of the main bearing directions on both sides of the osteotomy plane through a directional path, or if there is a break in the directional path or inconsistency in the direction, then the directional bridging condition is not met. In this case, the hinge point candidate will be eliminated and will no longer participate in the subsequent optimization and adjustment process.

[0046] The cut-off determination process is mainly used to determine whether the directional paths on both sides of the osteotomy plane can remain connected through directional bridging positions within a preset rotation range. The preset rotation range is discretized into multiple rotation positions, and the bridging state is updated one by one. The osteotomy plane is rotated step by step at certain rotation intervals, and it is detected in real time whether the directional paths after rotation can still connect the bone structure directions on both sides of the osteotomy plane through the determined directional bridging positions. When the directional paths on both sides of the osteotomy plane cannot be connected through the directional bridging positions at a certain rotation position, a bridging failure event is considered to have occurred, and this rotation position is recorded as a marker of the failure event.

[0047] Based on the recorded fracture events, the subsequent rotational discrete intervals are further restricted. That is, during subsequent rotations, the rotation interval is reduced or the candidate hinge point positions are adjusted to avoid the occurrence of fracture events.

[0048] In cases where mutual verification fails, a provability constraint is introduced to ensure stability and operability during the adjustment process. When a bridging is determined to have disappeared, the position of the hinge point is adjusted first, while the osteotomy plane remains unchanged. This is because the disappearance of a bridging usually indicates an inappropriate hinge point position; therefore, adjusting the hinge point position restores directional connectivity without changing the position of the osteotomy plane, thus avoiding unnecessary disturbance to the established bone structure.

[0049] When it is determined that the osteotomy plane cuts off the main load-bearing direction, the position of the osteotomy plane should be adjusted first. In this case, when adjusting the plane, it is necessary to ensure that the hinge point is still within the candidate set of the directional bridging positions determined in the previous round. This is to ensure that the adjusted osteotomy plane does not affect the validity of the hinge point, and that the hinge point remains within a reasonable directional bridging position range, avoiding the failure or instability of the hinge point position due to plane adjustment.

[0050] The rotational position corresponding to the fracture event is designated as the center of the restricted area. This restricted area indicates that subsequent rotational positions are not allowed to enter this region. The purpose of the restricted area is to prevent the osteotomy plane from continuing to traverse the continuous area along the main load-bearing direction, thereby ensuring that adjustments to the plane do not cause new fracture problems.

[0051] When the fracture event remains unchanged during the iteration process, it indicates that the current rotational position has stabilized and is unavoidable. At this point, the restricted area needs to be expanded to further eliminate all rotational positions that could lead to fracture. Simultaneously, the candidate hinge point locations also need to be adjusted to ensure that within the new restricted area, the selection of the hinge point effectively prevents the fracture event from occurring.

[0052] When the fracture event changes, the restricted area shrinks accordingly. This means that at the new rotation position, the osteotomy plane regains connectivity, thereby reducing the original risk of fracture. At this point, the reduced restricted area allows for more precise selection of the rotation position through finer rotation intervals.

[0053] Example 1:

[0054] The orthopedics department of a top-tier hospital plans to perform a high tibial osteotomy on a patient with right knee varus deformity. The patient is a 45-year-old male, 172cm tall and weighing 78kg, who has experienced exacerbated medial compartment pain due to long-term running. Preoperative lower limb alignment analysis indicated an internal mechanical axis deviation of approximately 8.5°. The surgeon's goal is to correct the alignment to an external deviation of approximately 2.0°, while preserving as much of the continuous load-bearing trabecular bone below the tibial plateau as possible to avoid postoperative collapse or instability risks caused by cutting off the continuous load-bearing area at the osteotomy site.

[0055] The image input was knee joint CT reconstructed volumetric data, with voxel sizes of 0.6mm × 0.6mm × 0.8mm, 420 slices, and a reconstruction range extending 120mm downward from the upper edge of the tibial plateau. The target region of the proximal tibia was segmented and a surface mesh was generated, with approximately 185,000 points and 360,000 triangular faces. The planning system sampled voxel points within the target region and constructed a orientation field, with approximately 92,000 sampling points. Simultaneously, a bidirectional mapping from the bone surface to the volumetric data was established for subsequent calculation of the intersection line between the osteotomy plane and the bone surface.

[0056] At each sampling point, the gray-level gradient is statistically analyzed using a cubic window with a radius of 2.4 mm, and a structure tensor is constructed. The gradient is obtained using a 3D Sobel operator and then smoothed once using Gaussian smoothing with a smoothing kernel standard deviation of 1.0 mm. The structure tensor is defined as follows:

[0057]

[0058] in For the first in the window The gradient vector of an individual element. The number of voxels in the window. Perform eigenvalue decomposition to obtain and corresponding feature vectors and with As a candidate for the local principal direction.

[0059] To quantify the credibility of a direction, a credibility index is defined:

[0060]

[0061] At a point in the medial bearing area below the tibial plateau, the following was calculated: , , ,but:

[0062]

[0063] System set threshold ,when When the direction of this point is marked as low confidence, it does not directly participate in the determination of the continuous region, but is completed by interpolation of the confidence direction of the neighborhood. Figure 2 The direction field reliability index is given. The distribution difference between the continuous region and the non-load-bearing region in the main load-bearing direction is indicated, and the threshold value is marked. .

[0064] Conflict elimination is performed on the direction information. The system introduces two primary direction settings at the same location, and takes... and As candidates, both settings are checked to see if they satisfy the continuity rule in the determination of the continuous region in the main bearing direction. If both settings can form a continuous chain and both satisfy the continuous region determination, the location direction is marked as unusable and removed from subsequent planning. Then, a set of reliable points within a 4.8mm radius neighborhood is used. The representative direction is used as a substitute direction, and the representative direction is normalized after weighted average:

[0065]

[0066] Weight Take the value as inversely proportional to the distance and with confidence level Proportional, making the closer and more reliable direction a better fit. They made even greater contributions. Figure 2 The corresponding output also provides statistical results of the proportion of conflict points, which is used to explain that conflict elimination will mark the direction information of this proportion as unavailable and hand it over to the neighboring representative direction to complete it, thereby improving the stability and verifiability of the direction field at the boundary of the bearing area.

[0067] The system identifies continuous regions along the main bearing direction in a reliable orientation field. Sampling points are treated as graph nodes; if the distance between two points does not exceed 1.2 mm and the directional angle does not exceed 15°, an edge is established to form a directional connected graph. A seed point set is set for the bearing area below the inner platform, and connected regions are expanded to obtain the continuous region along the main bearing direction. Its coverage volume accounts for approximately 18.6% of the target area. To ensure that the osteotomy plane does not cross this continuous area, the system introduces a crossing judgment for candidate osteotomy planes. If there are crossings on both sides of the plane... The resulting continuous chain is then judged as an invalid candidate surface.

[0068] Candidate osteotomy planes are generated through parametric sampling. The plane is written as:

[0069]

[0070] in For unit normal vector, The system uses the clinically commonly used starting plane as the center and samples 5 angle positions in the left and right coronal and sagittal directions around the normal direction, with an angle step of 2°. It also samples 3 offset positions in the translation direction, forming a set of 75 candidate osteotomy planes.

[0071] For each candidate osteotomy plane, the system first calculates its intersection with the bone surface mesh and projects the intersection back into the volume data to determine the area the plane passes through in the volume data. Then, a crossing certificate determination is performed. If there are cross-cutting areas on both sides of the candidate plane... The resulting continuous chain, the system constructs a set of intersection points. Each intersection point is a voxel location where the continuous chain intersects the plane, defined as:

[0072]

[0073] when Furthermore, when the intersection point covers the through chain reaching both sides of the plane, a crossing certificate is generated and the candidate plane is determined to be invalid. Figure 3 This shows the size of the set of intersections of 75 candidate osteotomy planes. The statistics and the correspondence between the crossing certificate triggers are presented, with candidate faces that trigger the crossing certificate marked in red and those that do not trigger it marked in blue. The results for both types of candidate faces are also provided. Mean reference line.

[0074] There are 29 trigger traversal certificates in the initial candidate plane, with an average of There are 46. One candidate face yields three points in its intersection set. , , mm, the system locates the main risk zone of the plane crossing based on the spatial distribution of the intersection point set and uses it for subsequent adjustment of direction limits.

[0075] From the set of intersection points Determine the restricted area The system uses the projected envelope of the intersection point set as the boundary of the forbidden region in the plane parameter space, and requires that this be maintained during the iteration process. The topological relationships remain unchanged, avoiding the introduction of new crossing channels during adjustments. Forbidden adjustment regions are used to limit planar adjustments, allowing only two types of adjustments: normal adjustments that avoid the forbidden adjustment region or tangential adjustments along its boundaries. Figure 4 The diagrams of the two-dimensional projection of the intersection set, the boundary of the restricted region, and the small step update of the normal of the osteotomy plane are given to intuitively illustrate the relationship between the normal adjustment path and the risk zone avoidance under the constraint of the restricted region.

[0076] To provide an executable update rule, the system statistically calculates the centroid and distribution direction of the intersection point set as the adjustment guiding vector g. Here, g is taken as the projection direction of the first principal axis of the intersection point covariance matrix onto the current plane normal. In a simplified implementation, the gradient approximation direction from the intersection point centroid to the plane normal can also be used. The plane normal is updated and normalized as follows:

[0077]

[0078] During a certain iteration , ,Pick ,but:

[0079]

[0080] Its second norm is:

[0081]

[0082] therefore:

[0083]

[0084] The corresponding adjustment in this update can be understood as making small-step rotations in the normal direction of the osteotomy surface to reduce the risk of crossing, while avoiding the constraints of the restricted area.

[0085] The system records the number of intersection points in each iteration. And triggers priority adjustment. When The fact that the plane remains unchanged in two consecutive iterations indicates that the plane is restricted near the forbidden region. The system preferentially adjusts the hinge points to attempt to change the hinge positions within the threshold band of the intersection line, thereby altering the provability of the local directional connectivity structure. The change indicates that the planar adjustment has responded to the crossing chain, and the system will continue to adjust the osteotomy plane until a valid candidate plane is obtained.

[0086] The system sets the threshold range for generating candidate hinge points to a boundary range of 4.0 mm on both sides of the intersection line. Initially, an average of 62 hinge point candidates are generated for each candidate face. Combining crossing certificates and priority rules, the system iterates an average of 7 rounds to obtain mutually validated combinations of planes and hinge points. The average time per case is 18.4 seconds, including 9.1 seconds for orientation field construction, 7.6 seconds for candidate face determination and updating, and 1.7 seconds for hinge point adjustment. Finally, 29 invalid faces are eliminated from the 75 candidate planes, and 12 usable solutions are obtained through iterative convergence from the remaining 46, resulting in a final pass rate of 16.0%.

[0087] Table 1 below shows the impact of different directional confidence thresholds on the proportion of invalid surfaces and convergence efficiency. All results were obtained in the same hardware environment, with an 8-core 3.6GHz CPU.

[0088]

[0089] The system outputs the final osteotomy plane parameters and hinge point positions. The highest-scoring solution is selected, with its osteotomy plane normal and offset as follows: , The hinge point coordinates are mm. In the control experiment, removing the crossing certificate mechanism and disabling conflict elimination, while retaining only the basic continuum constraint, reduced the invalid candidate surface elimination rate to 21.3%. However, the proportion of continuum sections cut off in the main bearing direction during postoperative simulation increased to 27.5%, and the average number of iterations increased to 11.6. After introducing crossing certificates and conflict elimination, the risk of continuum section cutoff decreased to 6.8%, and the average time was reduced by approximately 25%, meeting the physician's dual needs for preserving the bearing area and improving planning stability.

[0090] Example 2:

[0091] A tertiary orthopedic hospital performed a high tibial osteotomy on a patient with right knee varus deformity. The procedure employed an open wedge osteotomy with progressive opening and closing rotation around the hinge point to correct the force line. The patient was a 48-year-old male who had developed medial compartment pain due to prolonged weight-bearing walking. Preoperatively, the mechanical axis was deviated medially by approximately 9%. The surgeon's planned goal was to correct the deviation to approximately 2% laterally while maintaining the continuity of the cortical bone on the hinge side, avoiding the risk of hinge-side dehiscence or opening instability due to loss of directional bridging during rotation.

[0092] The input image was knee joint CT volume data, with voxel sizes of 0.6mm × 0.6mm × 0.8mm, 400 slices, and a reconstruction range extending 110mm downward from the tibial plateau. The proximal tibia was segmented and a triangular mesh was generated, with approximately 160,000 mesh points and 320,000 triangular faces. The system sampled voxel points within the target area and extracted the bone structure orientation field, sampling approximately 80,000 points. Based on the orientation field, continuous regions bearing the principal direction were identified as the structural basis for rotational stability.

[0093] The system determines a boundary threshold band based on the intersection of the candidate osteotomy plane and the bone surface, with a width of 4.0 mm on each side of the intersection. Within this threshold band, a set of hinge point candidates is uniformly sampled, generating an average of approximately 60 hinge point candidates per candidate osteotomy plane. For each hinge point candidate, a directional bridging position determination is performed. The determination criterion is that there must be a directional path along the main bearing direction reaching the hinge point candidate from both sides of the osteotomy plane. If it is reachable from both sides, it is determined to be a directional bridging position; otherwise, it is discarded. After screening, each candidate osteotomy plane retains an average of approximately 18 directional bridging positions for subsequent three-stage mutual verification.

[0094] The system employs a three-stage directional bridging mutual verification strategy: pre-cut, during-cut, and post-cut. In the pre-cut stage, the directional connectivity graph is used to verify whether candidate hinge points satisfy the directional bridging position determination and to form a verifiable candidate set. In the during-cut stage, the connectivity status of the directional paths on both sides of the osteotomy plane is updated within a preset rotation range, determining whether they can still be connected via the directional bridging position. In the post-cut stage, after rotating back to the initial or near-initial posture, connectivity is again determined to verify whether the bridging is recoverable. If mutual verification fails, the failure is categorized according to the reason: when the bridging disappears, the hinge point position is adjusted first; when the plane cuts off the directional path, the osteotomy plane posture is adjusted first.

[0095] The system is set to rotate within the opening range. arrive And the rotation range is discretized into a set:

[0096] Δ , Δ

[0097] Pick Δ Thirteen sampling points were obtained at that time. Around the hinge axis and with hinge point Update any point for the center of rotation The pose is represented by a simplified rotation:

[0098]

[0099] in For the axis The rotation matrix of the system in each... Calculate the connectivity determination function at the location The value is 1 when the directional bridging position can connect the directional paths on both sides of the osteotomy plane; otherwise, it is 0. Figure 5 The set of discrete angles for bridging positions in each direction during the interception stage is given. Below The heatmap shows that each row corresponds to a directional bridging position, and each column corresponds to a rotation angle sampling point. The position =0 is used to mark the angle at which a fracture event occurs.

[0100] The mid-stage records the fracture event, when it first occurs The fracture angle is defined as follows:

[0101]

[0102] If the connected sequence of a candidate hinge point is such that all values ​​from 0° to 6° are 1, while the value at 7° becomes 0, then... =7°. Figure 6 The initial fracture angle is given. The distribution statistics are presented, and the number of fracture events and fracture duration are overlaid and displayed. Fracture duration is measured by the number of consecutive fracture angle increments. The average number of fracture events is 1.5, and the average fracture duration is 2.2 angle increments. The concentration is mainly in the 6° to 9° range, thus supporting the judgment that a medium opening angle is a high-risk angle region for bridging instability. Meanwhile, the example sequence first shows 0 at 7°. =7° is used to illustrate the reproducibility of the definition of the fracture angle.

[0103] When the reason for mutual verification failure is determined to be the disappearance of the bridging, the system prioritizes adjusting the candidate hinge point position while keeping the osteotomy plane unchanged to satisfy the provability constraint and avoid new unprovable paths caused by plane changes. The adjustment method is to fine-tune the hinge point position along the tangential direction of the intersection line within the threshold band, with a step size of 1.0 mm, and then re-execute the pre- and mid-cut determination. When the reason for mutual verification failure is determined to be a plane cutting direction path, the system prioritizes adjusting the osteotomy plane and restricts the hinge point candidate to be located within the candidate set of the direction bridging position determined in the previous round, thereby ensuring that there are still provable candidates as anchor points in each plane adjustment. Through the above strategies, the system reduces the average number of retry attempts for mutual verification failure from 3.1 times to 1.8 times and controls the elimination ratio of invalid candidate combinations to within 45%.

[0104] The system sets the rotational position corresponding to the fracture event as the center of the restricted area and applies avoidance constraints to subsequent discrete sampling, defining the restricted area width parameter. The subsequent sampling angle is required to satisfy:

[0105]

[0106] Under this constraint, the restricted area corresponds to .when °、 °、 When the angle is 7°, only the 7° angle point is disabled, reducing the number of available points from 13 to 12. When the fracture event remains constant throughout continuous iterations, the restricted area is expanded and the hinge point candidate positions are adjusted. Expanding from 1° to 2° disables three angle points from 6° to 8°, increasing the number of available points to 10. This reduces redundant sampling in high-risk angle regions and lowers false positives and computational waste. When the fracture event changes during iteration, the restricted area is narrowed and the discrete interval is refined. Restored to 1° and The angle was refined from 1° to 0.5° to improve the accuracy of fracture boundary positioning. Figure 7 It indicated that The avoidance effect of expanding the restricted area width from 1° to 2° with ° as the center is given, and a comparison of the changes in the number of available sampling points is provided. At °, there are 12 points available. At °, there are 10 available points, which is used to illustrate that expanding the restricted area will reduce the sampling density of high-risk corner areas, thereby improving computational efficiency.

[0107] The system compares the same case under two settings. A fixed Δ is used when there are no restricted areas. Full-range sampling resulted in significant fluctuations in fracture event localization across different iterations, Δ The standard deviation is approximately The average processing time was 22.6 seconds, and the average number of iterations was 9.3. When there are forbidden zones and adaptive discretization constraints, The standard deviation decreased to 0.4°, the average time decreased to 17.8s, and the average number of iterations decreased to 6.7. Figure 7 The comparison information on the right shows the stability and time consumption of fracture event detection under different discrete intervals. The stability is based on... The standard deviation is used to illustrate that while refining the discrete interval can improve stability, it also increases the time consumption, while the adaptive strategy can reduce the time consumption while improving stability.

[0108] Table 2 below compares the stability and time consumption of fracture event detection under different discrete intervals. The stability is expressed as follows: Standard deviation is expressed.

[0109]

[0110] The system ultimately outputs the cross-validated osteotomy plane parameters, hinge point coordinates, and rotatable safety angle range. The osteotomy plane parameters of the highest-scoring scheme are selected as follows. , The hinge point coordinates are mm. The system provides a rotatable safety angle range of 0° to 10°, within which... Furthermore, the connection can be restored after the cut, thereby reducing the risk of hinge side cracking and meeting the orthopedic opening and closing requirements.

Claims

1. A method for optimizing the linkage between the osteotomy plane and hinge point based on the orientation field of bone structure, characterized in that... include: Acquire three-dimensional images of the target bone and determine the target region; The bone structure orientation information of the target region is extracted to form a bone structure orientation field, and credibility processing is performed to obtain credible orientation information for planning; Based on the bone structure orientation field, a continuous region bearing the main direction is identified, and a constraint is set that the osteotomy plane must not cross the continuous region; under the constraint, candidate osteotomy planes are generated; for each candidate osteotomy plane, hinge point candidates are generated within the boundary threshold range of its intersection line with the target bone surface, and the connectivity of the hinge neighborhood direction is judged in three stages: before, during, and after the osteotomy to screen feasible hinge points. The candidate osteotomy plane is cross-validated using the feasible hinge point, and the cross-validation includes: the osteotomy plane does not cut the main load direction and does not form directional opposition in the hinge neighborhood; When the mutual verification fails, the osteotomy plane or hinge point is iteratively updated according to the preset adjustment of the degree of freedom set until the mutual verification passes; the osteotomy plane parameters and hinge point positions are output.

2. The method for optimizing the linkage between the osteotomy plane and hinge point based on the bone structure orientation field according to claim 1, characterized in that... The credibility processing includes contradiction elimination: when the directional information at the same location satisfies the determination of the continuous region of the main direction under multiple main direction assumptions, the directional information is marked as unavailable, and the representative direction is determined by the reliable direction in the neighborhood to participate in the planning.

3. The method for optimizing the linkage between the osteotomy plane and hinge point based on the bone structure orientation field according to claim 1, characterized in that... The constraint that the candidate osteotomy plane must not cross the continuous region is determined by the crossing certificate: if there is a continuous chain formed by the continuous region of the main bearing direction on both sides of the candidate osteotomy plane, a crossing certificate containing the set of intersection points of the continuous chain and the candidate osteotomy plane is generated and the candidate osteotomy plane is determined to be invalid, and the plane adjustment direction is limited according to the set of intersection points.

4. The method for optimizing the linkage between the osteotomy plane and hinge point based on the bone structure orientation field according to claim 1, characterized in that... The three-stage determination adopts directional bridging mutual verification: before the resection, it is determined whether the hinge point candidate is a directional bridging position; during the resection, it is determined whether the directional paths on both sides of the osteotomy plane within the preset rotation range can still be connected through the directional bridging position; after the resection, it is determined whether the connection is restored. If the mutual verification fails, the hinge point or osteotomy plane is adjusted first, depending on whether the reason is the disappearance of the bridging or the cutting of the plane.

5. The method for optimizing the linkage between the osteotomy plane and hinge point based on the bone structure orientation field according to claim 3, characterized in that... The set of intersection points is used to determine the forbidden region. The adjustment direction of the candidate osteotomy plane is limited to normal adjustment to avoid the forbidden region or tangential adjustment along its boundary, and the topological relationship of the forbidden region remains unchanged during the iteration process.

6. The method for optimizing the linkage between the osteotomy plane and hinge point based on the bone structure orientation field according to claim 3, characterized in that... The crossing certificate is used to trigger the adjustment priority: when the number of intersection points remains constant in continuous iterations, the hinge point is adjusted first; when the number of intersection points changes, the candidate osteotomy plane is adjusted first until a valid candidate osteotomy plane is obtained.

7. The method for optimizing the linkage between the osteotomy plane and hinge point based on the bone structure orientation field according to claim 4, characterized in that... The directional bridging position is determined as follows: when there is a directional path that leads to the hinge point candidate from both sides of the osteotomy plane along a continuous region of the main bearing direction, it is determined to be a directional bridging position; otherwise, it is discarded.

8. The method for optimizing the linkage between the osteotomy plane and hinge point based on the bone structure orientation field according to claim 4, characterized in that... The cut-off determination includes: discretizing the preset rotation range into multiple rotation positions and updating the bridging state one by one; when the first occurrence of a directional bridging position that cannot connect the directional paths on both sides of the osteotomy plane, recording the corresponding rotation position as a fracture event; and based on the fracture event, limiting the subsequent discrete interval or adjusting the candidate positions of the hinge points.

9. The method for optimizing the linkage between the osteotomy plane and hinge point based on the bone structure orientation field according to claim 4, characterized in that... When mutual verification fails, a constraint is introduced to maintain provability: when the hinge point is adjusted first due to the disappearance of the bridging, the osteotomy plane remains unchanged; when the osteotomy plane is adjusted first due to planar cutting, the hinge point candidates are limited to the candidate set of the directional bridging positions determined in the previous round.

10. The method for optimizing the linkage between the osteotomy plane and hinge point based on the bone structure orientation field according to claim 8, characterized in that... Based on the fracture event, a restricted area constraint is applied to the subsequent rotation position: the rotation position corresponding to the fracture event is set as the center of the restricted area, and the subsequent discrete rotation positions avoid the restricted area; when the fracture event remains unchanged in the iteration, the restricted area is expanded and the candidate position of the hinge point is adjusted; when the fracture event changes, the restricted area is shrunk and the discrete interval is refined.

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