Method for positioning the end of a minimally invasive surgery actuator based on the current field

Abstract

The present application relates to a kind of minimally invasive surgery executor end coordinate positioning method based on current field navigation, belong to surgical navigation positioning technical field, comprising the following steps: S1: assume an initial current source vector, obtain the distribution of rough conductivity, obtain the potential distribution at this time by positive problem calculation process, and judge whether residual is less than the set exit threshold value;S2: calculate Jacobian matrix;S3: calculate the current source vector of next time;S4: obtain the potential distribution at this time by positive problem calculation process, and compare the measured potential distribution and calculate residual;S5: after changing current electrode pair, repeat steps S1-S4 until all current electrode pairs are traversed, calculate whether total residual is less than the set exit threshold value;If not less than exit threshold value, repeat steps S2-S5;If greater than exit threshold value, stop calculation, the current source vector at this time is the current source vector approximate solution that meets the condition.

Description

Technical Field

[0001] This invention belongs to the field of surgical navigation and positioning technology, and relates to a method for end-effector coordinate positioning of a minimally invasive surgical actuator based on current field navigation. Background Technology

[0002] Minimally invasive surgery is a technique that uses minimally invasive incisions or natural body cavities to enter the body and, with the help of imaging equipment, precisely treats diseases. Its core advantages include minimal trauma, rapid recovery, and fewer complications. It is applicable to the diagnosis and treatment of cardiovascular, tumor, and nervous system diseases and has become an important direction for the development of modern medicine.

[0003] In minimally invasive interventional surgery, the accuracy of the positioning and navigation of the probe at the front end greatly affects the treatment effect. However, conventional medical image guidance methods cannot meet the real-time requirements of intraoperative guidance. Multiple corrections from multiple angles are needed to determine the position of the interventional probe, catheter, or scalpel inside the body and its relative position to the lesion. Prolonged use can cause radiation damage to the human body. It is also difficult to determine the end coordinates of surgical instruments inside the body in real time, which has significant limitations. Summary of the Invention

[0004] In view of this, the purpose of the present invention is to provide a method for end-effector coordinate positioning of a minimally invasive surgical actuator based on current field navigation.

[0005] To achieve the above objectives, the present invention provides the following technical solution: A method for end-effector coordinate positioning in minimally invasive surgery based on current field navigation includes the following steps: S1: First, assume an initial current source vector, obtain a rough conductivity distribution through prior knowledge, obtain the potential distribution at this time through the forward problem calculation process, and determine whether the residual is less than the set exit threshold. S2: Calculate the Jacobian matrix; S3: Calculate the current source vector for the next iteration based on the iterative formula; S4: Obtain the potential distribution at this time through the forward problem calculation process, and compare it with the measured potential distribution to calculate the residual.

[0006] S5: After changing the current electrode pair, repeat steps S1~S4 until all current electrode pairs have been traversed. At this point, calculate whether the total residual is less than the set exit threshold. S6: If the current source vector is not less than the exit threshold, repeat steps S2-S5; if it is greater than the exit threshold, stop the calculation. The current source vector at this time is the approximate solution of the current source vector that satisfies the conditions.

[0007] Furthermore, the forward problem calculation process specifically includes: The finite element method is used for partitioning and solving. The governing equations for the surgical area are:

[0008] In the formula, Represents the distribution of spatial conductivity. This indicates the electrical potential distribution within the surgical area. Indicates the injected current. This represents the coordinates of a point in the surgical area. Indicates the coordinates of the current injection point. It is a three-dimensional Dirac function, indicating that the current only exists in the three-dimensional Dirac function. Inject at the location; First, we construct an equivalent variational problem, derive the derivation using the weighted residual method, and introduce appropriate trial functions. Multiply both sides of the control equation by Later in the surgical area By integrating, we obtain:

[0009] Based on the sieving property of the Dirac function, combined with the divergence theorem, and by incorporating boundary conditions into the equation, we can simplify to obtain:

[0010] In the formula, The coordinates representing the current flowing out of the electrode; Finite element discretization is performed, dividing the surgical area into a finite number of elements. Tetrahedral elements are used in three-dimensional space, and an approximate solution of the finite element method is represented by a set of basis functions. :

[0011] in It involves substituting coefficients; the basis functions are coordinate interpolation functions. , The number of bases is used to select trial functions using Galerkin's method. , The discrete equations are obtained by exchanging the summation and integration, and can be written as:

[0012] Define the stiffness matrix A and the load vector f as follows:

[0013] The load vector is:

[0014] The discretized linear system is obtained:

[0015] in It is the potential distribution matrix, that is:

[0016] Solve for the stiffness matrix and finally the potential distribution: .

[0017] Furthermore, after the forward problem is calculated, the calculated potential of the body surface electrodes is obtained, thus providing a computational basis for solving the inverse problem. The inverse problem uses least squares solutions to approximate the exact solution, expressed as:

[0018] in Let represent the least-squares solution of a set of current electrode pairs corresponding to the local current source vectors. This represents the operator for solving positive problems. This represents the potential matrix measured by a set of current electrode pairs; the overall current source vector is:

[0019] in Indicates the first The least-squares solution for the local current source vector corresponding to the current electrode pair. It measures the number of electrodes; The corresponding local residual is defined as follows: : .

[0020] Furthermore, in step S1, an initial current source vector is first assumed. By obtaining a rough distribution of conductivity through prior knowledge, the potential distribution at this point is obtained through a forward problem calculation process. And determine whether the residual is less than the set exit threshold. Specifically, it includes: .

[0021] Furthermore, the calculation of the Jacobian matrix in step S2 specifically includes: Calculate the local Jacobian matrix of the current source vector relative to the potential. :

[0022] in yes No. One portion, yes No. One portion, yes The length of the vector yes The length of the vector; The final assembled Jacobian matrix is:

[0023] in Indicates the first The local Jacobian matrix corresponding to the group of current electrode pairs.

[0024] Furthermore, step S3, which involves calculating the next current source vector according to the iterative formula, specifically includes: The least squares solution is obtained using Newton's iterative method, expressed as: .

[0025] Furthermore, in step S4, the potential distribution at this point is obtained through a forward problem calculation process. The residuals are calculated by comparing them with the measured potential distribution. .

[0026] Furthermore, in step S5, the total residual .

[0027] Furthermore, the measurement potential matrix corresponding to each current electrode pair is assembled into a total measurement potential matrix. :

[0028] Similarly, the calculated potential matrix is ​​processed to obtain the total calculated potential matrix. : .

[0029] Furthermore, in step S6, the current vector is finally obtained through iteration. Then, the current vector represents the current at each finite element node. The component with the largest value in the current vector is the node corresponding to the internal source electrode. Let the node be numbered as follows: Then the source coordinates are the node coordinates. 3D coordinates This allows for the reconstruction of the source coordinates.

[0030] The beneficial effects of this invention are as follows: In the process of iterating the inverse problem, this method updates the current source vector, while the conductivity distribution remains unchanged throughout the process. This ensures that the finite element stiffness matrix, which is only related to the conductivity distribution, is updated. The stiffness matrix remains unchanged throughout the iteration process, so the inverse of the stiffness matrix only needs to be solved once in the first step. It doesn't require repeated updates during the iterations, which is precisely the most computationally intensive step in the iterative process of the finite element forward and inverse problems. Subsequent iterations can reuse this indefinitely. Direct calculation using the inverse matrix can reduce computational load and increase calculation speed. Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0031] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein: Figure 1 This is a schematic diagram of the coordinate positioning method of the present invention; Figure 2 This is a flowchart of the method for locating the three-dimensional coordinates of an in vivo electrode based on body surface potential measurement according to the present invention. Detailed Implementation

[0032] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0033] It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Therefore, the drawings only show the components related to the present invention and are not drawn according to the actual number, shape and size of the components in the actual implementation. In the actual implementation, the form, quantity and proportion of each component can be arbitrarily changed, and the layout of the components may also be more complex.

[0034] In the following description, numerous details are explored to provide a more thorough explanation of embodiments of the invention. However, it will be apparent to those skilled in the art that embodiments of the invention may be practiced without these specific details. In other embodiments, well-known structures and devices are shown in block diagram form rather than in detail to avoid obscuring embodiments of the invention.

[0035] Example 1: like Figure 1 As shown, this invention provides a method for intraoperative positioning of the end-effector coordinates of a surgical actuator based on current field navigation. The surgical actuator in the surgical area is regarded as the in vivo source electrode. By alternately switching each body surface measuring electrode as the current outflow electrode, the potential distribution on the body surface is measured, and the coordinates of the in vivo source electrode are reconstructed, thereby realizing real-time three-dimensional positioning of the in vivo electrode.

[0036] This problem is highly nonlinear and ill-posed. The inverse problem is solved by iteratively solving the forward problem in two major steps: first, by assuming a current source vector and then iteratively optimizing it step by step to approximate the real current source vector, thereby improving the accuracy and stability of the solution.

[0037] For the forward problem, the finite element method is used for partitioning and solving. The governing equations for the surgical region are: (1) In the formula, Represents the distribution of spatial conductivity. This indicates the electrical potential distribution within the surgical area. Indicates the injected current. This represents the coordinates of a point in the surgical area. Indicates the coordinates of the current injection point. It is a three-dimensional Dirac function, indicating that the current only exists in the three-dimensional Dirac function. Inject at the location.

[0038] ① First, construct an equivalent variational problem, use the weighted residual method for derivation, and introduce appropriate trial functions. Multiply both sides of the control equation (1) by Later in the surgical area By integrating, we obtain: (2) Based on the sieving property of the Dirac function, combined with the divergence theorem, and by introducing the boundary conditions into equation (2), we can simplify to obtain: (3) In the formula, This indicates the coordinates where the current flows out of the electrode.

[0039] ② Finite element discretization is performed, dividing the surgical area into a finite number of elements. Tetrahedral elements are used in three-dimensional space, and an approximate solution of the finite element method is represented by a set of basis functions. .

[0040] (4) in It involves substituting coefficients; the basis functions are coordinate interpolation functions. , The number of bases is used to select trial functions using Galerkin's method. , The discrete equations are obtained. By exchanging the summation and integration, they can be written as: (5) Define the stiffness matrix A and the load vector f as follows: (6) Observing the above formula, it can be seen that the stiffness matrix A is only related to the conductivity distribution and is independent of the size and location of the current source.

[0041] The load vector (right-hand term) is: (7) The discretized linear system is obtained: (8) in It is the potential distribution matrix, that is: (9) ③ Solve for the stiffness matrix and finally solve for the potential distribution. Multiplying both sides of equation (8) by the inverse of a stiffness matrix on the left, we obtain the potential distribution at this point: (10) The purpose of the forward problem is to solve for the boundary potential of the surgical region, i.e., to calculate the potential of the surface electrodes, given the magnitude and coordinates of the injected current. This provides a computational basis for solving the inverse problem (finding the coordinates of the current source given the boundary potential).

[0042] Solving the inverse problem is highly nonlinear and ill-posed, making it difficult to obtain an exact analytical solution. Therefore, the least squares method is used to find an approximate solution to approximate the exact solution, which can be expressed as: (11) in Let represent the least-squares solution of a set of current electrode pairs corresponding to the local current source vectors. This represents the operator for solving positive problems. This represents the potential matrix measured by a set of current electrode pairs. Therefore, the overall current source vector is: (12) in Indicates the first The least-squares solution for the local current source vector corresponding to the current electrode pair. This refers to the number of measuring electrodes. The corresponding local residual is defined as follows: : (13) The total residual is defined as , The least squares solution is obtained using Newton's iterative method, expressed as: (14) in The local Jacobian matrix of the current source vector relative to the potential can be calculated using the following formula: (15) in yes No. One portion, yes No. One portion, yes The length of the vector yes The length of the vector. The final assembled Jacobian matrix is: (16) in Indicates the first The local Jacobian matrix corresponding to the group of current electrode pairs.

[0043] To facilitate calculation and retrieval, the measurement potential matrix corresponding to each current electrode pair is assembled into a total measurement potential matrix. : (17) Similarly, the calculated potential matrix is ​​processed to obtain the total calculated potential matrix. : (18) like Figure 2 As shown, the overall calculation process can be represented by the following steps: ① First, assume an initial current source vector. By obtaining a rough distribution of conductivity through prior knowledge, the potential distribution at this point is obtained through a forward problem calculation process. And determine whether the residual is less than the set exit threshold. ; (19) ② Calculate the Jacobian matrix according to equation (16) ; ③ Calculate the next current source vector according to the iterative formula; (20) ④ Obtain the potential distribution at this time through the forward problem calculation process. The residuals are calculated by comparing them with the measured potential distribution.

[0044] (twenty one) ⑤ After changing the current electrode pair, repeat steps ①-④ until all current electrode pairs have been traversed. At this point, calculate whether the total residual is less than the set exit threshold. That is, the total residual ; ⑥ If the value is not less than the exit threshold, repeat steps ②-⑤; if the value is greater than the exit threshold, stop the calculation. It is then considered to be an approximate solution of the current source vector that satisfies the conditions.

[0045] The current vector was eventually obtained through iteration. Then, the current vector represents the current at each finite element node. The current is injected from the inner positioning electrode and flows out from the outer electrode. The node number of the current flowing out of the electrode is known, so the component with the largest value in the current vector can be considered as the node corresponding to the inner source electrode. Let the node number be . Then the source coordinates are the node coordinates. 3D coordinates This enabled the reconstruction of the source coordinates.

[0046] Example 2: An electronic device, comprising a memory and a processor; The memory is used to store computer programs; The processor is configured to implement the method described in Embodiment 1 when executing the computer program.

[0047] Example 3: A computer-readable storage medium storing a computer program that, when executed by a processor, implements the method described in Embodiment 1.

[0048] Example 4: A computer program product includes a computer program that, when executed by a processor, implements the method described in Example 1.

[0049] In the above embodiments, the reference to "this embodiment" in the specification indicates that a specific feature, structure, or characteristic described in connection with the embodiment is included in at least some embodiments, but not necessarily all embodiments. Multiple appearances of "this embodiment" do not necessarily all refer to the same embodiment.

[0050] In the above embodiments, although the invention has been described in conjunction with specific embodiments thereof, many substitutions, modifications, and variations of these embodiments will be apparent to those skilled in the art from the foregoing description. For example, other memory structures (e.g., dynamic RAM (DRAM)) may be used with the embodiments discussed. The embodiments of the invention are intended to cover all such substitutions, modifications, and variations falling within the broad scope of the appended claims.

[0051] As will be understood by those skilled in the art, the computer-readable storage medium described in this embodiment allows for the implementation of all or part of the steps in the above method embodiments by computer program-related hardware. The aforementioned computer program can be stored in a computer-readable storage medium. When executed, the program performs the steps of the above method embodiments; and the aforementioned storage medium includes various media capable of storing program code, such as ROM, RAM, magnetic disks, or optical disks.

[0052] The electronic terminal provided in this embodiment includes a processor, a memory, a transceiver, and a communication interface. The memory and the communication interface are connected to the processor and the transceiver and complete communication between them. The memory is used to store computer programs, the communication interface is used to perform communication, and the processor and the transceiver are used to run the computer programs, so that the electronic terminal performs the steps of the above method.

[0053] In this embodiment, the memory may include random access memory (RAM) and may also include non-volatile memory, such as at least one disk storage device.

[0054] The processors mentioned above can be general-purpose processors, including central processing units (CPUs), network processors (NPs), etc.; they can also be digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components.

[0055] This invention can be used in a wide range of general-purpose or special-purpose computing system environments or configurations. Examples include: personal computers, server computers, handheld or portable devices, tablet devices, multiprocessor systems, microprocessor-based systems, set-top boxes, programmable consumer electronics, network PCs, minicomputers, mainframe computers, and distributed computing environments including any of the above systems or devices, etc.

[0056] This invention can be described in the general context of computer-executable instructions, such as program modules, that are executed by a computer. Generally, program modules include routines, programs, objects, components, data structures, etc., that perform a specific task or implement a specific abstract data type. This invention can also be practiced in distributed computing environments where tasks are performed by remote processing devices connected via a communication network. In distributed computing environments, program modules can reside in local and remote computer storage media, including storage devices.

[0057] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for end-effector coordinate positioning in minimally invasive surgery based on current field navigation, characterized in that: Includes the following steps: S1: First, assume an initial current source vector, obtain a rough conductivity distribution through prior knowledge, obtain the potential distribution at this time through the forward problem calculation process, and determine whether the residual is less than the set exit threshold. S2: Calculate the Jacobian matrix; S3: Calculate the current source vector for the next iteration based on the iterative formula; S4: Obtain the potential distribution at this time through the forward problem calculation process, and compare it with the measured potential distribution to calculate the residual; S5: After changing the current electrode pair, repeat steps S1~S4 until all current electrode pairs have been traversed. At this point, calculate whether the total residual is less than the set exit threshold. S6: If the current source vector is not less than the exit threshold, repeat steps S2-S5; if it is greater than the exit threshold, stop the calculation. The current source vector at this time is the approximate solution of the current source vector that satisfies the conditions.

2. The method for end-effector coordinate positioning of a minimally invasive surgical actuator based on current field navigation according to claim 1, characterized in that: The calculation process for the positive problem specifically includes: The finite element method is used for partitioning and solving. The governing equations for the surgical area are: In the formula, Represents the distribution of spatial conductivity. This indicates the electrical potential distribution within the surgical area. Indicates the injected current. This represents the coordinates of a point in the surgical area. Indicates the coordinates of the current injection point. It is a three-dimensional Dirac function, indicating that the current only exists in the three-dimensional Dirac function. Inject at the location; First, we construct an equivalent variational problem, derive the derivation using the weighted residual method, and introduce appropriate trial functions. Multiply both sides of the control equation by Later in the surgical area By integrating, we obtain: Based on the sieving property of the Dirac function, combined with the divergence theorem, and by introducing boundary conditions into the equation, we can simplify to obtain: In the formula, The coordinates representing the current flowing out of the electrode; Finite element discretization is performed, dividing the surgical area into a finite number of elements. Tetrahedral elements are used in three-dimensional space, and an approximate solution of the finite element method is represented by a set of basis functions. : in It involves substituting coefficients; the basis functions are coordinate interpolation functions. , The number of bases is used to select trial functions using Galerkin's method. , The discrete equations are obtained by exchanging the summation and integration, and can be written as: Define the stiffness matrix A and the load vector f as follows: The load vector is: The discretized linear system is obtained: in It is the potential distribution matrix, that is: Solve for the stiffness matrix and finally the potential distribution: 。 3. The method for end-effector coordinate positioning of a minimally invasive surgical actuator based on current field navigation according to claim 2, characterized in that: After the forward problem is calculated, the calculated potential of the body surface electrodes is obtained, thus providing a computational basis for solving the inverse problem. The inverse problem uses least squares to solve for an approximate solution to approximate the exact solution, expressed as: in Let represent the least-squares solution of a set of current electrode pairs corresponding to the local current source vectors. This represents the operator for solving positive problems. This represents the potential matrix measured by a set of current electrode pairs; the overall current source vector is: in Indicates the first The least-squares solution for the local current source vector corresponding to the current electrode pair. It refers to the number of measuring electrodes; The corresponding local residual is defined as follows: : 。 4. The method for end-effector coordinate positioning of a minimally invasive surgical actuator based on current field navigation according to claim 3, characterized in that: In step S1, an initial current source vector is first assumed. By obtaining a rough distribution of conductivity through prior knowledge, the potential distribution at this point is obtained through a forward problem calculation process. And determine whether the residual is less than the set exit threshold. Specifically, it includes: 。 5. The method for end-effector coordinate positioning of a minimally invasive surgical actuator based on current field navigation according to claim 4, characterized in that: The calculation of the Jacobian matrix in step S2 specifically includes: Calculate the local Jacobian matrix of the current source vector relative to the potential. : in yes No. One portion, yes No. One portion, yes The length of the vector yes The length of the vector; The final assembled Jacobian matrix is: in Indicates the first The local Jacobian matrix corresponding to the group of current electrode pairs.

6. The method for end-effector coordinate positioning of a minimally invasive surgical actuator based on current field navigation according to claim 5, characterized in that: Step S3, which involves calculating the next current source vector according to the iterative formula, specifically includes: The least squares solution is obtained using Newton's iterative method, expressed as: 。 7. The method for end-effector coordinate positioning of a minimally invasive surgical actuator based on current field navigation according to claim 6, characterized in that: In step S4, the potential distribution at this point is obtained through a forward problem calculation process. The residuals are calculated by comparing them with the measured potential distribution. 。 8. The method for end-effector coordinate positioning of a minimally invasive surgical actuator based on current field navigation according to claim 7, characterized in that: In step S5, the total residual .

9. The method for end-effector coordinate positioning of a minimally invasive surgical actuator based on current field navigation according to claim 8, characterized in that: The measurement potential matrix corresponding to each current electrode pair is assembled into a total measurement potential matrix. : Similarly, the calculated potential matrix is ​​processed to obtain the total calculated potential matrix. : 。 10. The method for end-effector coordinate positioning of a minimally invasive surgical actuator based on current field navigation according to claim 1, characterized in that: In step S6, the current vector is finally obtained through iteration. Then, the current vector represents the current at each finite element node. The component with the largest value in the current vector is the node corresponding to the internal source electrode. Let the node be numbered as follows: Then the source coordinates are the node coordinates. 3D coordinates This allows for the reconstruction of the source coordinates.

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