Method for estimating force on the distal end of a continuous catheter for interventional surgery and force feedback system

Abstract

The present invention discloses a method for estimating the force on the end of a continuous catheter during interventional surgery and a force feedback system, which aims to solve the problem of delayed or low accuracy of force feedback on the end of the catheter during interventional surgery. The method for estimating the force on the end of a continuous catheter comprises the following steps: applying beam theory to the elastic mechanics modeling of the catheter, performing force / torque balance analysis on the model while considering the external force on the end, thereby establishing an elastic mechanics model of the catheter; obtaining multiple data sets of external force, internal force and joint configuration through the elastic mechanics model to form a training set and a test set of a BP neural network model, training the BP neural network model to obtain constant parameters of a nonlinear mapping function with internal force and instantaneous joint configuration as variables and external force as the dependent variable, thereby realizing the estimation of the external force on the catheter. Simulation test results show that the method for estimating the force on the end of a continuous catheter has good reliability and feasibility.

Description

Technical Field

[0001] The present invention relates to the technical field of interventional surgery control, and more particularly to a method for estimating the force applied to the distal end of a continuous catheter in interventional surgery and a force feedback system. Background Art

[0002] With the advancement of medical technology, interventional therapies and minimally invasive surgeries are becoming increasingly common. These procedures utilize specialized catheters, guidewires, and other instruments to guide through blood vessels to the site of vascular lesions for diagnosis and treatment. They offer the advantages of minimal trauma, rapid recovery, and few complications. However, these procedures require extremely high precision and stability, making force feedback at the catheter tip a crucial factor in ensuring surgical safety and effectiveness.

[0003] Catheters operate in a complex environment within the human body. Faced with varying vascular pathways, tissue structures, and lesion locations, physicians must precisely control the movement and force applied by the catheter. Lack of effective force feedback can lead to the following problems: 1. Excessive force can damage blood vessels or surrounding tissue, causing serious complications such as bleeding and perforation. 2. Lack of accurate force feedback can prevent the catheter from reaching its target location, compromising surgical outcomes.

[0004] Force feedback systems provide real-time force information, helping doctors more precisely control catheters during procedures, avoiding tissue damage and improving surgical safety and effectiveness. Current catheter tip force feedback methods rely on estimation methods based on sensor data from the mechanical end. This suffers from issues such as sensor noise, insufficient accuracy, and response lag (particularly during rapid procedures, where feedback lag can affect overall effectiveness). Therefore, a new catheter tip force estimation method is needed to overcome these issues. Summary of the Invention

[0005] Due to the problems existing in the prior art, the present invention proposes a method for estimating the force on the end of a continuous catheter during interventional surgery and a force feedback system, aiming to solve the problems of lack of force feedback and accuracy at the end of the catheter during interventional surgery.

[0006] To achieve the above objectives, in a first aspect, the present invention provides a method for estimating the force applied to the distal end of a continuous catheter during interventional surgery, comprising:

[0007] Step S1, establishing a mechanical model of the continuum catheter: assuming that a known external force is applied to the end portion of the continuum catheter, a mechanical model of the continuum catheter is established based on the Correrat beam theory to represent the joint configuration, internal forces, and internal torque relationships of the end portion of the continuum catheter;

[0008] Step S2, solving the mechanical model, that is, solving the ordinary differential equation under the boundary conditions;

[0009] Step S3: Calculate the elastic potential energy of the continuum catheter using the mechanical model, and obtain the elastic mechanical model of the coupling of the internal force, instantaneous joint configuration, and catheter external force based on the principle of virtual work. The expression is:

[0010]

[0011] Where, is the external force applied to the end of the continuum catheter, is the gradient of the elastic potential energy with respect to the perturbation in the configuration space, which is related to the material properties of the continuum conduit and the instantaneous joint configuration related, and is the velocity Jacobian matrix, which is included in the built-in Parameters; is the internal force of the continuum catheter;

[0012] Step S4: Use an internal force and instantaneous joint configuration Nonlinear mapping function as independent variable To describe external forces , expressed as: ; Constructing a BP neural network model; using joint configuration data and internal force as input features of the BP neural network model, and the corresponding end external force as output features;

[0013] Step S5: inputting the randomly generated external and internal forces into the elastic mechanics model of step S3, calculating and obtaining the instantaneous joint configuration of the catheter corresponding to each input value, and obtaining a training set and a test set for the BP neural network model; training the BP neural network model to obtain constant parameters of the nonlinear mapping function;

[0014] Step S6: using the nonlinear mapping function constant parameters obtained from the trained BP neural network model to estimate the external force on the end of the continuum catheter.

[0015] The continuum catheter end force estimation method applies Correrat beam theory to the catheter's mechanical modeling, thereby solving for the catheter's internal forces and joint configuration parameters under known external force conditions. Combining the catheter's mechanical model with the principle of virtual work, an elastic mechanical model equation is derived, coupling the catheter's internal forces, instantaneous joint configuration, and external forces. This equation is used to obtain multiple data sets of external forces, internal forces, and joint configurations. The calculated data sets are then used to form training and test sets for a BP neural network model. Ultimately, the internal forces and instantaneous joint configurations are obtained as variables, and by training the constant parameters of the nonlinear mapping function, an estimate of the external forces acting on the output catheter is achieved.

[0016] Furthermore, in step S2, the mechanical model is solved by using a shooting method: first, the unknown variable Set a random guess value , where k represents the number of guess cycles; then, after determining the guess value, perform integration operations on the formulas in the positive elastic mechanics model in turn to solve the internal force at the end of the central rod of the catheter, and then obtain the current error vector according to the boundary function , and obtain the residual Jacobian matrix ; Set threshold , when satisfied When the current catheter end position information is output, otherwise, the unknown variables are updated again. , repeat the integral calculation in the positive elasticity model again until the vector Until the conditions are met.

[0017] Furthermore, the BP neural network model constructed in step S5 includes 8 input neurons, 2 output neurons and 2 hidden layers, each hidden layer includes 80 neurons, and the Sigmoid function is selected as the activation function.

[0018] Furthermore, in step S5, minimum and maximum normalization is performed on each input feature of the BP neural network model, which is conducive to obtaining faster convergence speed and training effect.

[0019] Furthermore, in step S7, the trained BP neural network model is used to estimate the external force sequences that change in a sinusoidal curve and a triangular shape.

[0020] In a second aspect, the present invention provides an interventional surgery continuum catheter end force feedback system, which includes estimating the force on the interventional surgery continuum catheter end and feeding back the estimated catheter end force to the catheter controller; the interventional surgery continuum catheter end force estimation method as described above is used to estimate the interventional surgery continuum catheter end force.

[0021] Compared with the prior art, the present invention has the following technical effects:

[0022] (1) Based on the Correrat beam theory, the present invention establishes a mechanical model of the catheter, takes the external force into consideration in the mechanical model, and derives the mapping relationship between the internal force of the continuum catheter and the catheter shape (represented by the joint configuration). Then, combined with the principle of virtual work, an elastic mechanical model of the coupling of internal force, instantaneous joint configuration and external force of the catheter is obtained. The simulation results in MATLAB are numerically close to the position error under the load positioning experiment, which verifies the reliability of the mechanical modeling.

[0023] (2) The present invention estimates the external force on the end of the continuum catheter through the BP neural network model, which solves the difficulty of solving the nonlinear problem and effectively estimates the end force feedback.

[0024] (3) The present invention uses the trained BP neural network model to estimate the external force sequences with sinusoidal and triangular changes, respectively, and obtains good estimation results. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 Flowchart of a method for estimating force on the distal end of a continuum catheter according to one embodiment of the present invention.

[0026] Figure 2 Schematic diagram of beam forces in one embodiment of the present invention.

[0027] Figure 3 Schematic diagram of a continuous conduit being bent by external force in one embodiment of the present invention.

[0028] Figure 4 Schematic diagram of the BP neural network model architecture in one embodiment of the present invention.

[0029] Figure 5 This is a test flow chart of the BP neural network model predicting external force in one embodiment of the present invention.

[0030] Figure 6 This is a graph showing the test results of a sinusoidal external force sequence prediction in one embodiment of the present invention.

[0031] Figure 7 This is a graph of the prediction error of the sinusoidal external force sequence in one embodiment of the present invention.

[0032] Figure 8 This is a diagram showing the test results of a triangle external force sequence prediction in one embodiment of the present invention.

[0033] Figure 9 This is a diagram of the prediction error of the triangular external force sequence in one embodiment of the present invention. DETAILED DESCRIPTION

[0034] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but they are not intended to limit the present invention.

[0035] In the following detailed description, many specific details are set forth to provide a more thorough understanding of the present invention. However, it is obvious to those skilled in the art that well-known algorithms and models are not shown in detail to avoid obscuring the subject matter of the present invention.

[0036] In addition, the order of execution of actions, steps, etc. in the devices and methods shown in the claims, specifications and drawings can be implemented in any order as long as there is no special explicit limitation on the order and the output of the previous processing is not used in the subsequent processing.

[0037] Example 1

[0038] See also Figure 1 This embodiment provides a method for estimating the force applied to the distal end of a continuous catheter during interventional surgery, comprising:

[0039] Step S1, establishing a mechanical model of the continuum catheter: Assuming that a known external force is applied to the end portion of the continuum catheter, a mechanical model of the continuum catheter is established based on the Correrat beam theory to represent the joint configuration, internal force, and internal torque relationship of the end portion of the continuum catheter.

[0040] Taking a continuum catheter with two continuum segments as an example, the driving skeleton of the catheter is approximated as an ideal rod that can be sheared / stretched and bent / torqued. The force on a beam from point c to point s is as follows: Figure 2 As shown. Based on the existing Correrat beam theory, By integrating the mechanical equilibrium differential equation within the range, the posture, internal force, and internal torque information of the end of the proximal continuous segment are obtained as follows:

[0041] (1)

[0042] In formula (1), P(s) represents the position of the end of the conduit corresponding to point s on the beam, n(s) represents the internal force of the beam corresponding to point s on the beam, m(s) represents the moment corresponding to point s on the beam, R(s) represents the rotation matrix corresponding to point s on the beam, and I 3×3 Represents the identity matrix.

[0043] Then, in middle,

[0044] (2)

[0045] In formula (2), d represents the length of the interval between two consecutive segments.

[0046] At the same time, the internal forces and internal moments at the end of the continuum tube must satisfy the following boundary conditions:

[0047] (3)

[0048] In formula (3), Indicates internal force, represents the torque, Indicates external force, Represents the external torque.

[0049] The above equations constitute the mechanical model of this continuum catheter, that is, when the external forces and external moments are known Given two pairs of internal forces , the bending shape and terminal posture of the continuum catheter can be calculated. The bending shape and terminal posture are specifically described by the catheter joint configuration parameters. The inverse model of the mechanical model can calculate two pairs of internal forces under the given terminal posture condition. .

[0050] Step S2: solving the mechanical model, that is, solving the ordinary differential equation under the boundary conditions.

[0051] We give an example of solving the mechanical model using the existing shooting method as follows. First, give the unknown variable Set a random guess value , where k represents the number of guess cycles. Then, after determining the guess value, the formulas in the positive elastic mechanics model are integrated in turn to solve the internal force at the end of the central rod of the catheter, and then the current error vector is obtained according to the boundary function. , and obtain the residual Jacobian matrix . Set the threshold , when satisfied When , output the current catheter end position information. Otherwise, re-update the unknown variables , repeat the integral calculation in the positive elasticity model again until the vector Until the conditions are met. The pseudo code of the mechanical model solution algorithm is shown in Table 1.

[0052] Table 1 Pseudo code of the algorithm for solving the mechanical model using the shooting method

[0053]

[0054] Step S3: Calculate the elastic potential energy of the continuum catheter using the mechanical model, and perform force / torque balance analysis on the model based on the principle of virtual work:

[0055] See also Figure 3 , the elastic potential energy is:

[0056]

[0057] In the above formula,

[0058] external force and internal force Virtual work done:

[0059] (4)

[0060] in: (5) is the virtual displacement of the terminal space, the Jacobian matrix Map the end force to the generalized coordinate space. Similarly, (6) is the virtual displacement of the joint space.

[0061] The change in elastic potential energy is expressed as:

[0062] (7)

[0063] According to the principle of virtual work, combined with the equilibrium conditions (4)-(7):

[0064]

[0065] Due to virtual displacement Any, which can be expressed as:

[0066] (8)

[0067] In formula (8), is the external force applied to the end of the continuum catheter, is the gradient of the elastic potential energy with respect to the perturbation in the configuration space, which is related to the material properties of the continuum conduit and the instantaneous joint configuration related, and is the velocity Jacobian matrix, which is included in the built-in Parameters; is the internal force of the continuum catheter.

[0068] Step S4: When the catheter tip is subjected to external force, the internal force of the catheter will change according to the external force, and there is a nonlinear relationship between the external force, the internal force and the joint configuration that is difficult to describe. and instantaneous joint configuration Nonlinear mapping function as independent variable To describe external forces , expressed as: , and then build a BP neural network model to obtain the nonlinear mapping function The constant parameters in .

[0069] Construct a BP neural network model; use joint configuration data and internal force as input features of the BP neural network model, and use the corresponding end external force as output feature.

[0070] As an example, see Figure 4 ,The BP neural network model contains 8 input neurons, 2 output neurons and 2 hidden layers, each hidden layer contains 80 neurons, and the Sigmoid function is selected as the activation function.

[0071] Step S5: The randomly generated external and internal forces are input into the elastic mechanics model of step S3, and the instantaneous joint configuration of the catheter corresponding to each input quantity is calculated to obtain the training set and test set of the BP neural network model; the BP neural network model is trained to obtain the constant parameters of the nonlinear mapping function.

[0072] As a preferred example, based on actual operating conditions, the external forces acting on the end of a continuum catheter are typically two-dimensional vectors, so we assume that the end force vectors lie in the xy plane. We randomly generate 20,000 sets of end external and internal force vectors to drive the continuum catheter to exhibit random bending angles and directions. These generated external and internal force values ​​are all within the continuum catheter's tolerance range. Next, the generated external and internal forces are input into the elasticity model, and the current joint configuration of the catheter corresponding to each input is collected. These 20,000 sets of end external and internal force vectors and their corresponding joint configuration data constitute the training dataset for the BP neural network model. To achieve faster convergence and better training results, each input feature is subjected to minimum and maximum normalization. 90% of the dataset is used as the training set, and the remainder is used as the test set. The network model was implemented in MATLAB 2019, with a batch size of 32 and 100 iterations used for training. During training, the learning rate is gradually reduced from 0.01 with the number of iterations. Once the performance on the test set begins to deteriorate, training will stop and the network parameters at that time will be saved as the optimal parameters.

[0073] The trained BP neural network model was validated. A continuum catheter elastic mechanics model built in MATLAB 2019 was used to test the reliability and feasibility of the network model.

[0074] In order to study the performance of the network model in estimating the external force of the continuum catheter under different external force sequences, two sets of test experiments were conducted as follows: Figure 5 As shown in the figure, we first input a random driving rope tension into the elasticity model. Simultaneously, a sequence of external forces, located in the xy plane, is applied to the end of the catheter. Due to the changing external forces at the end, the end position and joint configuration of the continuum catheter also change accordingly. Finally, the driving rope tension (i.e., internal force) and joint configuration at each moment are input into the trained BP neural network model to output the corresponding external force estimation sequence.

[0075] During the experiment, we recorded the prediction results of the BP neural network model for each external force sequence and compared them with the actual external force. In the simulation, the external force estimation error is used to represent the network prediction effect, which can be expressed by the following formula:

[0076] (9)

[0077] In formula (9), and are the external forces in the x-axis and y-axis directions estimated by the BP neural network model, and are given reference external force sequences respectively.

[0078] (1) Sine force sequence test

[0079] In the first set of experiments, we applied a sinusoidal external force sequence to the continuum catheter with a sequence length of 500. These external force sequences are divided into two components: the component amplitude in the x-axis direction is 0.3, and the component amplitude in the y-axis direction is also 0.4. The amplitude and change speed of these external force sequences are different, aiming to test the response ability of the BP neural network model to complex external force conditions. The estimated results of the external force components along the x-axis and y-axis are shown in Figure 2. Figure 6 Figure 7 depicts the prediction error diagram for the sinusoidal external force sequence. Calculations show that the maximum and average estimation errors for the external force are 0.035 N and 0.017 N, respectively. Through this set of simulation tests, we verified the accuracy and stability of the BP neural network model when processing sinusoidal external force sequences.

[0080] (2) Triangular external force sequence test

[0081] In the second set of experiments, we applied a sequence of alternating increasing and decreasing external forces to the continuum robot arm, also known as a triangle sequence, with a sequence length of 500. This external force sequence has sudden changes and is intended to test the network model's ability to accurately predict external forces in specific working scenarios. The estimated results of the external force components along the x-axis and y-axis are shown in Figure 2. Figure 8 shown. Figure 9 The prediction error graph for the triangular external force sequence is depicted. The maximum and average estimation errors of the external force are calculated to be 0.03 N and 0.015 N, respectively. Through this set of experiments, we verified the performance of the network model in handling abruptly changing external force sequences.

[0082] Step S6: using the nonlinear mapping function constant parameters obtained from the trained BP neural network model to estimate the external force on the end of the continuum catheter.

[0083] As can be seen from the above method steps and test results, this embodiment applies beam theory to catheter elasticity modeling. By approximating the catheter's driving framework as an ideal rod capable of shear / stretching, bending / torque, and considering external forces at the distal end, a force / torque balance analysis is performed on the model, thereby establishing an elasticity model of the catheter. Furthermore, a BP neural network model is proposed to solve the nonlinear model problem, thereby obtaining parameters for estimating the magnitude of the external forces acting on the catheter. Simulation test results demonstrate the reliability and feasibility of this method.

[0084] Example 2

[0085] See also Figure 5 This embodiment provides an interventional surgery continuum catheter end force feedback system, including estimating the interventional surgery continuum catheter end force and feeding back the estimated catheter end force to the catheter controller; the interventional surgery continuum catheter end force estimation method as described in Example 1 is used to estimate the interventional surgery continuum catheter end force.

[0086] This interventional surgery continuum catheter end force feedback system can effectively accelerate the catheter end force feedback speed during the interventional surgery and provide more accurate catheter force feedback.

[0087] The aforementioned method for estimating the force applied to the distal end of a continuous catheter during interventional surgery can be embodied in the form of a computer program product or a software functional unit. If the aforementioned method for estimating the force applied to the distal end of a continuous catheter during interventional surgery is implemented as a software functional unit and sold or used as a standalone product, it can be stored in a computer-readable storage medium. Therefore, the essence of this technical solution, or the portion that contributes to the prior art, or the portion of this technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions for enabling an electronic system (which can be a personal computer, server, or network system, etc.) to perform all or part of the steps of the method described in various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as a USB flash drive, a mobile hard drive, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk.

[0088] Those skilled in the art will appreciate that the units, i.e., algorithm steps, of the various examples described in conjunction with this embodiment can be implemented using electronic hardware or a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professionals and technicians may use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0089] In summary, the present invention provides a method for estimating the force on the end of a continuous catheter during interventional surgery and a force feedback system, which aims to solve the problem of delayed or low accuracy of force feedback on the end of the catheter during interventional surgery. The method for estimating the force on the end of a continuous catheter includes the following steps: applying beam theory to the elastic mechanics modeling of the catheter, performing force / torque balance analysis on the model while considering the external force on the end, thereby establishing an elastic mechanics model of the catheter; obtaining multiple data groups of external force, internal force and joint configuration through the elastic mechanics model to form a training set and a test set of a BP neural network model, training the BP neural network model to obtain constant parameters of a nonlinear mapping function with internal force and instantaneous joint configuration as variables and external force as the dependent variable, thereby realizing the estimation of the external force on the catheter. Simulation test results show that the method for estimating the force on the end of a continuous catheter has good reliability and feasibility.

[0090] Those skilled in the art should understand that they can implement variations by combining the prior art with the above embodiments, which will not be described in detail here. Such variations do not affect the essence of the present invention and will not be described in detail here.

[0091] The above describes the preferred embodiments of the present invention. It should be understood that the present invention is not limited to the above-mentioned specific embodiments, and the systems and structures that are not described in detail should be understood to be implemented in a common manner in the art; any technician familiar with the art can use the above-mentioned disclosed methods and technical contents to make many possible changes and modifications to the technical solutions of the present invention without departing from the scope of the technical solutions of the present invention, or modify them into equivalent embodiments of equivalent changes, which does not affect the essential content of the present invention. Therefore, any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention that do not depart from the content of the technical solutions of the present invention are still within the scope of protection of the technical solutions of the present invention.

Claims

1. A method for estimating the force on the distal end of a continuous catheter during interventional surgery, characterized in that: include: Step S1, establishing a mechanical model of the continuum catheter: assuming that a known external force is applied to the end portion of the continuum catheter, a mechanical model of the continuum catheter is established based on the Correrat beam theory to represent the joint configuration, internal forces, and internal torque relationships of the end portion of the continuum catheter; Step S2, solving the mechanical model, that is, solving the ordinary differential equation under the boundary conditions; Step S3: Calculate the elastic potential energy of the continuum catheter using the mechanical model, and obtain the elastic mechanical model of the coupling of the internal force, instantaneous joint configuration, and catheter external force based on the principle of virtual work. The expression is: Where, is the external force applied to the end of the continuum catheter, is the gradient of the elastic potential energy with respect to the perturbation in the configuration space, which is related to the material properties of the continuum conduit and the instantaneous joint configuration related, and is the velocity Jacobian matrix, which is included in the built-in Parameters; is the internal force of the continuum catheter; Step S4: Use an internal force and instantaneous joint configuration Nonlinear mapping function as independent variable To describe external forces , expressed as: ; Constructing a BP neural network model; using joint configuration data and internal force as input features of the BP neural network model, and the corresponding end external force as output features; Step S5: inputting the randomly generated external and internal forces into the elastic mechanics model of step S3, calculating and obtaining the instantaneous joint configuration of the catheter corresponding to each input value, and obtaining a training set and a test set of the BP neural network model; Training the BP neural network model to obtain constant parameters of the nonlinear mapping function; Step S6: using the nonlinear mapping function constant parameters obtained from the trained BP neural network model to estimate the external force on the end of the continuum catheter.

2. The method for estimating the force on the distal end of a continuous catheter in interventional surgery according to claim 1, characterized in that: In step S2, the shooting method is used to solve the mechanical model: first, the unknown variable Set a random guess value , where k represents the number of guess cycles; then, after determining the guess value, perform integration operations on the formulas in the positive elastic mechanics model in turn to solve the internal force at the end of the central rod of the catheter, and then obtain the current error vector according to the boundary function , and obtain the residual Jacobian matrix ; Setting thresholds , when satisfied When the current catheter end position information is output, otherwise, the unknown variables are updated again. , repeat the integral calculation in the positive elasticity model again until the vector Until the conditions are met.

3. The method for estimating the force on the distal end of a continuous catheter in interventional surgery according to claim 1, characterized in that: The BP neural network model constructed in step S5 includes 8 input neurons, 2 output neurons and 2 hidden layers, each hidden layer includes 80 neurons, and the Sigmoid function is selected as the activation function.

4. The method for estimating the force on the distal end of a continuous catheter for interventional surgery according to claim 1 or 3, characterized in that: In step S5, minimum and maximum normalization is performed on each input feature of the BP neural network model.

5. The method for estimating the force on the distal end of a continuous catheter in interventional surgery according to claim 1, characterized in that: In step S7, the trained BP neural network model is used to estimate the external force sequences that vary in a sinusoidal curve and a triangular shape.

6. A force feedback system for the distal end of a continuous catheter for interventional surgery, comprising estimating the force applied to the distal end of a continuous catheter for interventional surgery and feeding back the estimated force applied to the distal end of the catheter to a catheter controller; characterized in that: The force on the end of a continuous catheter for interventional surgery is estimated using the method for estimating the force on the end of a continuous catheter for interventional surgery as described in any one of claims 1 to 5.

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