CN118177965B - Track planning method of osteotomy robot - Google Patents
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Abstract
The invention provides a track planning method of an osteotomy robot, which belongs to the technical field of track planning and comprises the following steps: CT scanning is carried out on bones through medical imaging equipment, three-dimensional model data of the bones are obtained, and three-dimensional reconstruction is carried out on the three-dimensional model data by utilizing a reconstruction algorithm, so that a three-dimensional bone model is obtained; defining a target area in a three-dimensional skeleton model according to osteotomy requirements, extracting three-dimensional point cloud data of the target area, wherein the three-dimensional point cloud data comprises position information; searching an osteotomy line in a target area according to osteotomy requirements and a track planning algorithm, and obtaining position information of the osteotomy line; mapping the position information of the osteotomy line to a mechanical arm coordinate system of the osteotomy robot to obtain a track plan. The invention can ensure high precision and controllability of osteotomy operation in cosmetic surgery, and provides safer and more accurate cosmetic treatment for patients.
Description
Technical Field
The invention belongs to the technical field of track planning, and particularly relates to a track planning method of an osteotomy robot.
Background
With the development of cosmetic medical images and computer-aided cosmetic technologies, digital cosmetic technologies represented by three-dimensional facial design software and image navigation technologies have begun to be popularized clinically. Traditional cosmetic surgical protocols are accomplished by manual measurement of facial CT or MRI images, and the practice of the protocol is also accomplished by only manual measurement. Errors accumulate in the layers of these manual operations, ultimately leading to a large difference between the post-operative effect and the design. In recent years, the application of preoperative three-dimensional facial design software avoids the precision loss in the traditional manual scheme design, so that the beauty scheme in the brain of a doctor can be accurately expressed on an image, and even can be expressed on a facial model in a three-dimensional printing mode. However, this perfect solution lacks a good measure, supervision and execution means when it is performed intraoperatively, wherein facial osteotomy is an especially typical surgical task. The facial osteotomy is a key link of the cosmetic operation, and the osteotomy position not only can influence the damage degree of surrounding tissues, but also can determine the accuracy of the postoperative facial contour and the postoperative recovery.
Therefore, in most cosmetic design software, osteotomies are planned and simulated as an important step. How to improve the accuracy of three-dimensional reconstruction and planning of osteotomy lines becomes a highly desirable problem.
Disclosure of Invention
In view of the above, the present invention provides a trajectory planning method for an osteotomy robot, which combines a medical imaging technique and a precise algorithm, and can ensure high precision and controllability of osteotomy operation in a cosmetic operation, thereby providing safer and more precise cosmetic treatment for patients.
The technical scheme of the invention is realized as follows: the invention provides a track planning method of an osteotomy robot, which comprises the following steps:
S1, CT scanning is carried out on bones through medical imaging equipment, three-dimensional model data of the bones are obtained, and three-dimensional reconstruction is carried out on the three-dimensional model data by utilizing a reconstruction algorithm, so that a three-dimensional bone model is obtained;
S2, defining a target area in a three-dimensional skeleton model according to osteotomy requirements, extracting three-dimensional point cloud data of the target area, wherein the three-dimensional point cloud data comprise position information;
S3, searching an osteotomy line in a target area according to osteotomy requirements and a track planning algorithm, and obtaining position information of the osteotomy line;
and S4, mapping the position information of the osteotomy line into a mechanical arm coordinate system of the osteotomy robot to obtain a track plan.
Based on the above technical solution, preferably, the osteotomy requirement includes an osteotomy depth, an osteotomy direction, an osteotomy length, and an osteotomy site.
Based on the above technical solution, preferably, step S1 includes:
S11, CT scanning is carried out on bones through medical imaging equipment to obtain actual projection data, preprocessing is carried out on the acquired actual projection data, and the preprocessing comprises scattering correction and noise suppression;
S12, based on the preprocessed actual projection data, performing initial reconstruction on bones by using a back projection algorithm to obtain initial three-dimensional model data;
S13, estimating the absorption coefficient distribution of each position of bones according to the initial reconstructed image, and obtaining the simulated projection data of the initial reconstructed image according to the absorption coefficient distribution;
S14, establishing an optimization model, setting an objective function, and taking simulated projection data of an initial reconstructed image as an initialization model parameter X of the optimization model;
S15, carrying out iterative optimization by adopting an adaptive learning rate optimization algorithm, updating a model parameter X by utilizing a parameter updating formula in each iteration, and updating simulation projection data according to the new model parameter X so as to optimize an objective function;
s16, outputting the optimized three-dimensional model data when the iteration stop condition is reached;
And S17, carrying out post-processing and visualization on the optimized three-dimensional model data to obtain a three-dimensional bone model.
Based on the above technical solution, preferably, step S12 includes:
the actual projection data after preprocessing is expressed as:
where P (θ, s) represents projection data at an angle θ and a distance s, f (x, y) is an absorption coefficient of a bone site, μ (x, y) is an absorption coefficient distribution, λ 1||f(x,y)||p is an Lp norm regularization term for controlling the overall smoothness of the absorption coefficient f (x, y), Is a gradient regularization term for controlling the local smoothness of the absorption coefficient f (x, y);
performing back projection operation according to the projection data P (theta, s), and back projecting the projection data onto a two-dimensional plane;
and filtering, superposing and interpolating the data obtained by back projection to obtain initial three-dimensional model data.
Based on the above technical solution, preferably, the objective function is:
F＝min||W×(P-AX)||2+γR(μ)+εS(μ)
In the formula, P is actual projection data, A is a system matrix, X is a model parameter of an optimization model, mu is absorption coefficient distribution corresponding to X, W is a weight matrix, R is a regularization matrix, S is a regularization matrix of introduced prior information, gamma is a regularization parameter of a data fitting term, and epsilon is a regularization parameter of the introduced prior information.
Based on the above technical solution, preferably, the parameter update formula is:
Where m t and v t are estimated variables of the first moment and the second moment, respectively, m hat and v hat are estimated values after correcting the deviation, X is a model parameter of the optimization model, g t is a gradient of the current iteration, α is a learning rate, β 1 and β 2 are super parameters, and ζ is a constant.
Based on the above technical solution, preferably, step S3 includes:
S31, randomly selecting a point from the three-dimensional point cloud data as a root node of a first state tree, and finding a point closest to the root node of the first state tree as a root node of a second state tree, wherein the first state tree is in a starting state, and the second state tree is in a target state;
s32, randomly sampling a point in the three-dimensional point cloud data as a target node, and then respectively finding a first node and a second node which are closest to the target node in a first state tree and a second state tree;
s33, expanding from the first node and the second node to the target node according to the constraint condition to obtain a new first node and a new second node; wherein the constraint conditions comprise osteotomy depth constraint, osteotomy direction constraint and osteotomy length constraint;
s34, if no collision exists between the new first node and the new second node and the constraint condition is met, connecting the new first node and the new second node; otherwise, exchanging the states of the first state tree and the second state tree, and returning to the step S32;
s35, repeating the steps S32-S34 until the first state tree and the second state tree are connected;
s36, when the first state tree and the second state tree are connected, a path is extracted from the initial state to the target state, and the path is the osteotomy line;
s37, extracting position information of the osteotomy line according to the three-dimensional bone model.
Based on the above technical solution, preferably, the mathematical expression of the osteotomy depth constraint is as follows:
Wherein A is an amplitude parameter, sigma is a control parameter, For the position vector of the new node,As a position vector of the initial node,D max represents the maximum osteotomy depth, which is the normal vector in the depth direction.
Based on the above technical solution, preferably, the mathematical expression of the osteotomy direction constraint is as follows:
In the method, in the process of the invention, As the normal vector of the new node,In order to cut the bone direction vector,Is the maximum allowable direction deviation angle.
Based on the above technical solution, preferably, the mathematical expression of the osteotomy length constraint is as follows:
In the method, in the process of the invention, Representing the Euclidean distance between the new node and the nearest node, N is the number of blended components in the Gaussian mixture model, ω i is the weight of each blended component, κ i 2 is the standard deviation of each blended component, and L max is the maximum osteotomy length.
Compared with the prior art, the method has the following beneficial effects:
(1) According to the method, the target area is determined in the three-dimensional model in advance and the track planning is carried out, so that the operation time in the operation can be reduced; the accurate track planning and robot assisted surgery can realize the minimally invasive surgery, reduce the damage to surrounding tissues and accelerate the postoperative rehabilitation of patients; the accuracy and controllability of the operation can be improved through accurate three-dimensional model reconstruction and track planning;
(2) The reconstruction algorithm provided by the invention can reduce scattering and noise interference in CT scanning images through pretreatment of scattering correction and noise suppression, improve image quality and accuracy, obtain simulated projection data according to absorption coefficient distribution by estimating absorption coefficient distribution of each position of bones, realize quantitative analysis of bone tissue density and components, and provide more accurate and clearer bone structure information for optimized three-dimensional model data;
(3) According to the invention, through the steps of state tree construction, target node selection and expansion, collision detection and connection and the like, an algorithm can accurately extract an osteotomy line of a bone structure, the accuracy and the safety of operation planning and operation are ensured, constraint conditions such as osteotomy depth constraint, osteotomy direction constraint, osteotomy length constraint and the like are included in the algorithm, the constraint conditions ensure the rationality and feasibility of the osteotomy line, unnecessary errors and risks are avoided, the position information of the osteotomy line is extracted according to a three-dimensional bone model, and accurate bone structure position data is provided.
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In order to more clearly illustrate the embodiments of the invention or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, it being obvious that the drawings in the following description are only some embodiments of the invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of a method according to an embodiment of the invention.
Detailed Description
The following description of the embodiments of the present invention will clearly and fully describe the technical aspects of the embodiments of the present invention, and it is apparent that the described embodiments are only some embodiments of the present invention, not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the present invention without making any inventive effort, are intended to fall within the scope of the present invention.
As shown in fig. 1, the present invention provides a trajectory planning method of an osteotomy robot, comprising the steps of:
S1, CT scanning is carried out on bones through medical imaging equipment, three-dimensional model data of the bones are obtained, and three-dimensional reconstruction is carried out on the three-dimensional model data by utilizing a reconstruction algorithm, so that a three-dimensional bone model is obtained;
S2, defining a target area in a three-dimensional skeleton model according to osteotomy requirements, extracting three-dimensional point cloud data of the target area, wherein the three-dimensional point cloud data comprise position information;
S3, searching an osteotomy line in a target area according to osteotomy requirements and a track planning algorithm, and obtaining position information of the osteotomy line;
and S4, mapping the position information of the osteotomy line into a mechanical arm coordinate system of the osteotomy robot to obtain a track plan.
Wherein, the osteotomy requirement comprises osteotomy depth, osteotomy direction, osteotomy length and osteotomy position.
Specifically, in an embodiment of the present invention, step S1 includes:
S11, CT scanning is carried out on bones through medical imaging equipment to obtain actual projection data, preprocessing is carried out on the acquired actual projection data, and the preprocessing comprises scattering correction and noise suppression;
S12, based on the preprocessed actual projection data, performing initial reconstruction on bones by using a back projection algorithm to obtain initial three-dimensional model data;
S13, estimating the absorption coefficient distribution of each position of bones according to the initial reconstructed image, and obtaining the simulated projection data of the initial reconstructed image according to the absorption coefficient distribution;
S14, establishing an optimization model, setting an objective function, and taking simulated projection data of an initial reconstructed image as an initialization model parameter X of the optimization model;
S15, carrying out iterative optimization by adopting an adaptive learning rate optimization algorithm, updating a model parameter X by utilizing a parameter updating formula in each iteration, and updating simulation projection data according to the new model parameter X so as to optimize an objective function;
s16, outputting the optimized three-dimensional model data when the iteration stop condition is reached;
And S17, carrying out post-processing and visualization on the optimized three-dimensional model data to obtain a three-dimensional bone model.
Wherein, step S12 includes:
the actual projection data after preprocessing is expressed as:
where P (θ, s) represents projection data at an angle θ and a distance s, f (x, y) is an absorption coefficient of a bone site, μ (x, y) is an absorption coefficient distribution, λ 1||f(x,y)||p is an Lp norm regularization term for controlling the overall smoothness of the absorption coefficient f (x, y), Is a gradient regularization term for controlling the local smoothness of the absorption coefficient f (x, y);
performing back projection operation according to the projection data P (theta, s), and back projecting the projection data onto a two-dimensional plane;
and filtering, superposing and interpolating the data obtained by back projection to obtain initial three-dimensional model data.
In this embodiment, the objective function is:
F＝min||W×(P-AX)||2+γR(μ)+εS(μ)
In the formula, P is actual projection data, A is a system matrix, X is a model parameter of an optimization model, mu is absorption coefficient distribution corresponding to X, W is a weight matrix, R is a regularization matrix, S is a regularization matrix of introduced prior information, gamma is a regularization parameter of a data fitting term, and epsilon is a regularization parameter of the introduced prior information.
The parameter updating formula is as follows:
Where m t and v t are estimated variables of the first moment and the second moment, respectively, m hat and v hat are estimated values after correcting the deviation, X is a model parameter of the optimization model, g t is a gradient of the current iteration, α is a learning rate, β 1 and β 2 are super parameters, and ζ is a constant.
The following description is given by way of a specific example:
CT scanning is performed on a body part of a patient, such as a skull, by a CT scanner, CT image data of the bone is acquired, and the data comprises density information and structural information of the interior of the bone, and is obtained by scanning the patient under different angles by X-rays. CT scanners scan body parts of a patient by emitting X-rays. X-rays are absorbed to different extents by different tissues and bones, which are recorded by the detector. The detector will record the absorption of the X-rays through the patient's body part, i.e. the actual projection data, which may be affected by scattering effects and noise, and therefore require pre-processing to improve the image quality and accuracy.
The main content of the preprocessing includes scatter correction and noise suppression.
Scatter correction: scatter refers to the deflection and scattering of X-rays inside an object, resulting in artifacts and image blurring in the CT image. The purpose of scatter correction is to reduce the impact of such scattering effects on image quality and to improve the accuracy of the image. In this embodiment, a model-assisted scatter correction algorithm is used: and the physical model is utilized to model the scattering, and the scattering correction is carried out through numerical calculation or iterative algorithm, so that the influence of scattering effect on the image is reduced.
Noise suppression: in CT scanning, the image may be affected by various factors to generate noise, such as measurement errors of X-ray attenuation coefficients, noise of the detector, and the like. The purpose of noise suppression is to reduce noise interference in an image and improve the image quality and the accuracy of a bone structure by filtering and other methods. In this embodiment, wavelet denoising is adopted: the signal is decomposed into subbands of different frequencies using wavelet transforms, and noise is suppressed by thresholding the subband coefficients.
Based on the preprocessed actual projection data, the bones are initially reconstructed by using a back projection algorithm, and initial three-dimensional model data are obtained. The actual projection data after preprocessing is expressed as:
Where P (θ, s) represents projection data at an angle θ and a distance s, f (x, y) is an absorption coefficient of a bone site, μ (x, y) is an absorption coefficient distribution, λ 1||f(x,y)||p is an Lp norm regularization term for controlling the overall smoothness of the absorption coefficient f (x, y) to avoid excessively sharp changes; Is a gradient regularization term used to control the local smoothness of the absorption coefficient f (x, y) to help preserve detailed information of the image.
This formula describes the relationship between the projection intensity P (θ, s) at the angle θ and the distance s, and the object absorption coefficient f (x, y) and the absorption coefficient distribution μ (x, y). By introducing regularization items such as Lp regularization, gradient regularization and the like, the optimization process can be guided better, the accuracy of reconstruction is improved, and the characteristics of actual projection data are matched better.
The specific steps of the initial reconstruction are as follows:
And carrying out back projection operation according to the preprocessed actual projection data P (theta, s) and the scanning geometric parameters, and carrying out back projection on the projection data on a two-dimensional plane to obtain an initial two-dimensional reconstruction image.
Repeating the steps, and carrying out back projection operation on each angle theta to obtain a series of two-dimensional reconstructed images.
After a series of two-dimensional reconstructed images are obtained, these images need to be filtered, superimposed and interpolated to obtain the initial three-dimensional model data. The method comprises the following specific steps:
and filtering each two-dimensional reconstructed image to reduce the influence of artifacts and noise and improve the image quality.
And superposing the filtered two-dimensional reconstruction images to obtain more accurate three-dimensional model data. This can be achieved by weighted superposition of each two-dimensional image to obtain more accurate three-dimensional model data.
And carrying out interpolation operation on the superimposed data to obtain complete three-dimensional model data. The interpolation operation can adopt methods such as linear interpolation, cubic spline interpolation and the like, and the embodiment adopts a bilinear interpolation mode to interpolate two-dimensional data into three-dimensional data.
And estimating the absorption coefficient distribution of each position of the skeleton according to the initial reconstructed image, and obtaining the simulated projection data according to the absorption coefficient distribution.
The initial reconstructed image may provide general information about the bone absorption coefficient distribution. In the embodiment, a simulated annealing mode is adopted, and the absorption coefficient distribution is solved reversely according to the initial reconstructed image and the actual projection data. This method can estimate the absorption coefficient distribution by minimizing the difference between the reconstructed image and the actual projection data.
By estimating the obtained absorption coefficient distribution, the simulated projection data can be calculated using the projection principle of CT reconstruction.
Modeling the reconstruction problem as an optimization problem, setting an objective function, and optimizing the objective to minimize the difference between the actual projection data and the simulated projection data.
The objective function is:
F＝min||W×(P-AX)||2+γR(μ)+εS(μ)
In the formula, P is actual projection data, A is a system matrix, X is a model parameter of an optimization model, mu is absorption coefficient distribution corresponding to X, W is a weight matrix, R is a regularization matrix, S is a regularization matrix of introduced prior information, gamma is a regularization parameter of a data fitting term, and epsilon is a regularization parameter of the introduced prior information.
The objective function comprises a weighted sum of a data fitting term for measuring how well the model fits the actual projection data and a regularization term for introducing a priori information or controlling the smoothness of the model parameters. While introducing new a priori information. The difference between the actual projection data and the simulated projection data can be better described.
Taking the simulated projection data of the initial reconstructed image as an initialization model parameter X of an optimization model, setting an initial learning rate alpha, two super parameters beta 1 and beta 2, and initializing first-order and second-order moment estimation variables m and v as zero vectors. These initialized parameters and variables will serve as the starting point for the optimization algorithm and are updated continuously with iterations to progressively optimize the model parameters.
And (3) carrying out iterative optimization by adopting an adaptive learning rate optimization algorithm, updating a model parameter X by using a parameter updating formula in each iteration, and updating simulation projection data according to the new model parameter X so as to optimize an objective function.
The parameter updating formula is as follows:
Where m t and v t are estimated variables of the first moment and the second moment, respectively, m hat and v hat are estimated values after correcting the deviation, X is a model parameter of the optimization model, g t is a gradient of the current iteration, α is a learning rate, β 1 and β 2 are super parameters, and ζ is a constant.
The parameter updating formula comprises updating of estimated variables m and v of the first moment and the second moment and calculation of estimated values m hat and v hat after correction of deviation. The model parameter X is updated by successive iterations so that the objective function gradually converges to an optimal value.
In this embodiment, iterative optimization is performed by adopting a gradient descent method, the gradient of the objective function is continuously calculated, and the model parameter X is updated according to the gradient. Meanwhile, absorption coefficient distribution and simulated projection data are required to be calculated according to the updated model parameters, and comprehensive optimization is performed by combining regularization terms. Through the optimization algorithm, the reconstruction problem can be effectively optimized, and the accuracy and stability of reconstruction are improved.
And when the iteration stop condition is reached, outputting the optimized three-dimensional model data.
In this embodiment, the iteration stop condition is that the objective function converges or reaches the maximum number of iterations.
And carrying out post-processing and visualization on the optimized three-dimensional model data to obtain a three-dimensional bone model.
Post-processing and visualization: the optimized three-dimensional model data can be subjected to operations such as smoothing, segmentation, surface reconstruction and the like, and a three-dimensional bone model is finally obtained and displayed through a three-dimensional visualization technology.
Specifically, in an embodiment of the present invention, step S2 includes:
acquiring an osteotomy range in an osteotomy requirement, wherein the osteotomy range corresponds to a rough osteotomy region of an osteotomy part, setting a dangerous region in the osteotomy range according to the osteotomy range in the requirement and combining data such as bone tissue and skin tissue of a patient, and continuously limiting the maximum range of a target region according to the dangerous region in consideration of the factor of operation safety, so that the target region is irregularly shaped in the embodiment.
After the target area is defined, three-dimensional point cloud data corresponding to the target area are extracted according to the three-dimensional skeleton model, the three-dimensional point cloud data comprise position information, namely coordinate information, and the position of the skull surface in the three-dimensional space is described. Normal vector information, reflected intensity information, etc. are also included.
Specifically, in an embodiment of the present invention, step S3 includes:
S31, randomly selecting a point from the three-dimensional point cloud data as a root node of a first state tree, and finding a point closest to the root node of the first state tree as a root node of a second state tree, wherein the first state tree is in a starting state, and the second state tree is in a target state;
s32, randomly sampling a point in the three-dimensional point cloud data as a target node, and then respectively finding a first node and a second node which are closest to the target node in a first state tree and a second state tree;
s33, expanding from the first node and the second node to the target node according to the constraint condition to obtain a new first node and a new second node; wherein the constraint conditions comprise osteotomy depth constraint, osteotomy direction constraint and osteotomy length constraint;
s34, if no collision exists between the new first node and the new second node and the constraint condition is met, connecting the new first node and the new second node; otherwise, exchanging the states of the first state tree and the second state tree, and returning to the step S32;
s35, repeating the steps S32-S35 until the first state tree and the second state tree are connected;
s36, when the first state tree and the second state tree are connected, a path is extracted from the initial state to the target state, and the path is the osteotomy line;
s37, extracting position information of the osteotomy line according to the three-dimensional bone model.
Wherein, the mathematical expression of the osteotomy depth constraint is as follows:
Wherein A is an amplitude parameter, sigma is a control parameter, For the position vector of the new node,As a position vector of the initial node,D max represents the maximum osteotomy depth, which is the normal vector in the depth direction.
The mathematical expression of the osteotomy direction constraint is as follows:
In the method, in the process of the invention, As the normal vector of the new node,In order to cut the bone direction vector,Is the maximum allowable direction deviation angle.
The mathematical expression of the osteotomy length constraint is as follows:
In the method, in the process of the invention, Representing the Euclidean distance between the new node and the nearest node, N is the number of blended components in the Gaussian mixture model, ω i is the weight of each blended component, κ i 2 is the standard deviation of each blended component, and L max is the maximum osteotomy length.
The following description is given by way of a specific example:
The trajectory planning algorithm adopted in this embodiment is based on the idea of bidirectional search, and searches from the initial state and the target state at the same time to find the shortest path or the optimal solution. In this algorithm, a method of alternately expanding the connection of the initial state and the target state and the first state tree and the second state tree are used to improve the searching efficiency and accuracy.
First, the reason for using two state trees is to search from the start state and the target state at the same time in order to find the shortest path or optimal solution faster. By searching from two directions at the same time, the search space can be reduced and the search efficiency can be improved.
Second, the method of using the alternate expansion of the start state and target state connections is to continuously update the connection path between the start state and the target state during the search. By alternating the expansion, the path information can be updated continuously during the search process in order to find the optimal solution faster. In addition, the method can avoid trapping in a local optimal solution and improve the global property of searching.
The specific implementation process of the track planning algorithm is as follows:
Randomly selecting a point from the three-dimensional point cloud data as a root node of a first state tree, and finding a point closest to the root node of the first state tree as a root node of a second state tree, wherein the first state tree is in a starting state, and the second state tree is in a target state. In the three-dimensional point cloud data, one point may be selected as a root node of the first state tree by random sampling or according to a specific rule. Then, a point closest to the root node of the first state tree is found by nearest neighbor search or the like as the root node of the second state tree. For example, a nearest neighbor algorithm may be used to find the closest point as the root node of the second state tree.
Randomly sampling a point in the three-dimensional point cloud data as a target node, and then respectively finding a first node and a second node which are closest to the target node in a first state tree and a second state tree. A point may be selected as the target node by random sampling or according to a specific rule. Then, in the first state tree and the second state tree, the first node and the second node closest to the target node may be found using a nearest neighbor search or the like. For example, a nearest neighbor algorithm may be used to find the node closest to the target node.
According to the constraint condition, expanding from the first node and the second node to the target node to obtain a new first node and a new second node; wherein the constraint conditions comprise osteotomy depth constraint, osteotomy direction constraint and osteotomy length constraint.
According to the constraint condition, expanding from the first node and the second node to the target node to obtain a new first node and a new second node; wherein the constraint conditions comprise osteotomy depth constraint, osteotomy direction constraint and osteotomy length constraint. The osteotomy depth constraint, the osteotomy direction constraint, and the osteotomy length constraint may be considered when expanding from the first node and the second node to the target node. For example, the depth of the new node may be limited according to specific osteotomy depth requirements; limiting the direction of the new node according to the osteotomy direction requirement; and limiting the moving distance of the new node according to the length requirement of the osteotomy.
Wherein, the mathematical expression of the osteotomy depth constraint is as follows:
Wherein A is an amplitude parameter, sigma is a control parameter, For the position vector of the new node,As a position vector of the initial node,D max represents the maximum osteotomy depth, which is the normal vector in the depth direction.
The osteotomy depth constraint condition is depth constraint based on a Gaussian function, and the range of the depth constraint is adjusted through a control parameter sigma, so that the depth between a new node and an initial node is within a certain range. This constraint can ensure that the generated path does not deviate too far in the depth direction, thereby ensuring the safety and rationality of path planning.
The mathematical expression of the osteotomy direction constraint is as follows:
In the method, in the process of the invention, As the normal vector of the new node,In order to cut the bone direction vector,Is the maximum allowable direction deviation angle.
The osteotomy direction constraint condition limits the relation between the normal vector of the new node and the osteotomy direction vector based on the cosine value of the vector included angle, and ensures that the deviation of the path in the specific direction is not excessive. The constraint condition can ensure that the deviation of the generated path in a specific direction is controlled within a certain range, so that the path planning is more in line with the actual requirement.
The mathematical expression of the osteotomy length constraint is as follows:
In the method, in the process of the invention, Representing the Euclidean distance between the new node and the nearest node, N is the number of blended components in the Gaussian mixture model, ω i is the weight of each blended component, κ i 2 is the standard deviation of each blended component, and L max is the maximum osteotomy length.
The osteotomy length constraint condition is based on the length constraint of a Gaussian mixture model, and the influence range of different mixed components is adjusted through weights and standard deviations, so that the length of a path is limited. The constraint condition can ensure that the generated path length is not overlong, and meanwhile, the shape and the length of the path can be flexibly adjusted according to the quantity and the parameters of the mixed components, so that the path planning is more flexible and has stronger adaptability.
If there is no collision between the new first node and the new second node and the constraint condition is satisfied, connecting the new first node and the new second node; otherwise, the states of the first state tree and the second state tree are exchanged, and the step S32 is returned. In determining whether there is a collision between the new first node and the new second node and whether the constraint condition is satisfied, the use of a collision detection algorithm and a constraint condition determination algorithm may be considered. For example, collision detection algorithms (e.g., bounding box collision detection or geometric collision detection) may be utilized to determine whether there is a collision between nodes; meanwhile, whether the new node meets the requirement is judged according to the constraint condition. If the condition is satisfied, connecting the new first node with the new second node; otherwise, the state is exchanged and the search is resumed.
Repeating the connecting and expanding steps until the first state tree and the second state tree are connected. The node and path information of the state tree may be updated continuously until the first state tree and the second state tree are connected. This process may be performed using a loop iteration until the connection condition is satisfied.
When the first state tree and the second state tree are connected, a path is extracted from the initial state to the target state, and the path is the osteotomy line. According to the three-dimensional bone model, the position information of the osteotomy line can be extracted. This may be accomplished by correlating the osteotomy line with a three-dimensional bone model to determine the specific location of the osteotomy line in three-dimensional space.
Specifically, in an embodiment of the present invention, step S4 includes:
Position information of the osteotomy line, namely coordinates of a series of key points, is extracted according to the steps.
Establishing a mechanical arm coordinate system:
the position and attitude of the end effector of the robotic arm, i.e., the extreme end of the robotic arm, such as a hand, clamp, etc., is determined. And performing positive kinematic calculation according to the structure and joint parameters of the mechanical arm to obtain the positions and the postures of all joints of the mechanical arm and the positions and the postures of the end effector. And determining the origin and coordinate axis direction of the mechanical arm coordinate system according to the position and the gesture of the mechanical arm end effector. The position of the end effector is selected as the origin of the coordinate system, and the direction of the coordinate axes can be determined according to the structure and the motion rule of the mechanical arm. The robot arm coordinate system is generally represented by using euler angles, quaternions or transformation matrices, and in this embodiment, the transformation matrices are represented, assuming that the robot arm coordinate system is O-XYZ, the coordinates of the robot arm end effector are (x end,yend,zend), the pose is represented by a rotation matrix R, and the mathematical expression of the robot arm coordinate system can be represented as:
Where R is 3*3, the rotation matrix represents the pose of the robot arm, and the position of the end effector (x end,yend,zend)) represents the position of the origin of the robot arm coordinate system in the world coordinate system.
Coordinate transformation: the position information of the osteotomy is transformed from the world coordinate system or other reference coordinate system to the robot arm coordinate system so that the robot arm can plan and execute according to the position information.
The coordinate transformation is implemented by a mapping formula, and assuming that coordinates in the robot arm coordinate system are (x arm,yarm,zarm) and world coordinates of points in the osteotomy line are (x world,yworld,zworld), the position information of the osteotomy line can be mapped into the robot arm coordinate system by the following formula:
Wherein R is a rotation matrix, O is a translation vector, and the rotation matrix R and the translation vector O can be obtained through the positive kinematics of the mechanical arm.
Track planning: and (3) performing track planning in a mechanical arm coordinate system, and determining the path of the mechanical arm end effector so that the mechanical arm end effector can move according to the position information of the osteotomy line.
According to the above, the track planning of the osteotomy robot is obtained.
According to the method, the target area is determined in the three-dimensional model in advance and the track planning is carried out, so that the operation time in the operation can be reduced; the accurate track planning and robot assisted surgery can realize the minimally invasive surgery, reduce the damage to surrounding tissues and accelerate the postoperative rehabilitation of patients; through accurate three-dimensional model reconstruction and track planning, the accuracy and controllability of operation can be improved.
The foregoing description of the preferred embodiments of the invention is not intended to be limiting, but rather is intended to cover all modifications, equivalents, alternatives, and improvements that fall within the spirit and scope of the invention.
Claims (4)
1. The track planning method of the osteotomy robot is characterized by comprising the following steps of:
S1, CT scanning is carried out on bones through medical imaging equipment, three-dimensional model data of the bones are obtained, and three-dimensional reconstruction is carried out on the three-dimensional model data by utilizing a reconstruction algorithm, so that a three-dimensional bone model is obtained;
S2, defining a target area in a three-dimensional skeleton model according to osteotomy requirements, extracting three-dimensional point cloud data of the target area, wherein the three-dimensional point cloud data comprise position information;
osteotomy requirements include osteotomy depth, osteotomy direction, osteotomy length, and osteotomy site;
S3, searching an osteotomy line in a target area according to osteotomy requirements and a track planning algorithm, and obtaining position information of the osteotomy line;
The step S3 comprises the following steps:
S31, randomly selecting a point from the three-dimensional point cloud data as a root node of a first state tree, and finding a point closest to the root node of the first state tree as a root node of a second state tree, wherein the first state tree is in a starting state, and the second state tree is in a target state;
s32, randomly sampling a point in the three-dimensional point cloud data as a target node, and then respectively finding a first node and a second node which are closest to the target node in a first state tree and a second state tree;
s33, expanding from the first node and the second node to the target node according to the constraint condition to obtain a new first node and a new second node; wherein the constraint conditions comprise osteotomy depth constraint, osteotomy direction constraint and osteotomy length constraint;
s34, if no collision exists between the new first node and the new second node and the constraint condition is met, connecting the new first node and the new second node; otherwise, exchanging the states of the first state tree and the second state tree, and returning to the step S32;
s35, repeating the steps S32-S34 until the first state tree and the second state tree are connected;
s36, when the first state tree and the second state tree are connected, a path is extracted from the initial state to the target state, and the path is the osteotomy line;
s37, extracting position information of an osteotomy line according to the three-dimensional bone model;
The mathematical expression of the osteotomy depth constraint is as follows:
Wherein A is an amplitude parameter, sigma is a control parameter, For the position vector of the new node,As a position vector of the initial node,As a normal vector in the depth direction, D max represents the maximum osteotomy depth;
The mathematical expression of the osteotomy direction constraint is as follows:
In the method, in the process of the invention, As the normal vector of the new node,In order to cut the bone direction vector,Is the maximum allowable direction deviation angle;
The mathematical expression of the osteotomy length constraint is as follows:
In the method, in the process of the invention, Representing Euclidean distance between the new node and the nearest node, N is the number of mixed components in the Gaussian mixture model, omega i is the weight of each mixed component, kappa i 2 is the standard deviation of each mixed component, and L max is the maximum osteotomy length;
and S4, mapping the position information of the osteotomy line into a mechanical arm coordinate system of the osteotomy robot to obtain a track plan.
2. The trajectory planning method of an osteotomy robot of claim 1, wherein step S1 includes:
S11, CT scanning is carried out on bones through medical imaging equipment to obtain actual projection data, preprocessing is carried out on the acquired actual projection data, and the preprocessing comprises scattering correction and noise suppression;
S12, based on the preprocessed actual projection data, performing initial reconstruction on bones by using a back projection algorithm to obtain initial three-dimensional model data;
S13, estimating the absorption coefficient distribution of each position of bones according to the initial reconstructed image, and obtaining the simulated projection data of the initial reconstructed image according to the absorption coefficient distribution;
S14, establishing an optimization model, setting an objective function, and taking simulated projection data of an initial reconstructed image as an initialization model parameter X of the optimization model;
S15, carrying out iterative optimization by adopting an adaptive learning rate optimization algorithm, updating a model parameter X by utilizing a parameter updating formula in each iteration, and updating simulation projection data according to the new model parameter X so as to optimize an objective function;
s16, outputting the optimized three-dimensional model data when the iteration stop condition is reached;
And S17, carrying out post-processing and visualization on the optimized three-dimensional model data to obtain a three-dimensional bone model.
3. The trajectory planning method of an osteotomy robot of claim 2, wherein step S12 includes:
the actual projection data after preprocessing is expressed as:
Where P (θ, s) represents projection data at an angle θ and a distance s, f (x, y) is an absorption coefficient of a bone site, μ (x, y) is an absorption coefficient distribution, λ 1||f(x,y)||p is an Lp norm regularization term for controlling the overall smoothness of the absorption coefficient f (x, y), Is a gradient regularization term for controlling the local smoothness of the absorption coefficient f (x, y);
performing back projection operation according to the projection data P (theta, s), and back projecting the projection data onto a two-dimensional plane;
and filtering, superposing and interpolating the data obtained by back projection to obtain initial three-dimensional model data.
4. The trajectory planning method of an osteotomy robot of claim 2, wherein the objective function is:
F＝min||W×(P-AX)||2+γR(μ)+εS(μ)
In the formula, P is actual projection data, A is a system matrix, X is a model parameter of an optimization model, mu is absorption coefficient distribution corresponding to X, W is a weight matrix, R is a regularization matrix, S is a regularization matrix of introduced prior information, gamma is a regularization parameter of a data fitting term, and epsilon is a regularization parameter of the introduced prior information.
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