Twisting simulation method for umbilical based on bicubic hermite and cosserat rod

Abstract

This invention discloses a method for umbilical cord torsion simulation based on bicubic Hermitian and Cosserat rods, belonging to the field of virtual surgical simulation technology. The method includes: establishing a three-dimensional geometric model of the umbilical cord's centerline and simulating spiral winding, discretizing the centerline into Cosserat rod elements; coupling the Cosserat rods with a bicubic Hermitian surface, and simulating the nonlinear mechanical behavior of umbilical cord tension, bending, and torsion through synchronous updates of rod mechanics and high-order surface interpolation; combining implicit Euler integration, constrained projection, and tree-accelerated collision detection to perform stable simulation of umbilical cord spiral winding under high UCI conditions, and supporting real-time operation of surgical instruments and tactile feedback. This method, through comprehensive optimization of mechanical, geometric, and tactile errors, can maintain biomechanical realism and training applicability under different individual umbilical cord conditions, achieving high-precision, real-time, and interactive umbilical cord simulation in a virtual surgical environment.

Description

Technical Field

[0001] This invention relates to the field of virtual surgical simulation technology, and in particular to a method for simulating umbilical cord torsion based on bicubic Hermite and Cosserat rods. Background Technology

[0002] Excessive umbilical cord torsion poses significant risks and demands extremely high precision from surgeons. However, traditional training methods are limited by ethical constraints and a scarcity of case studies, making it difficult for doctors to gain experience in real-world scenarios. Against this backdrop, virtual surgical simulation technology provides doctors with a safe and controllable training environment, effectively improving their emergency response and decision-making abilities. Therefore, developing umbilical cord torsion simulation models that combine accuracy, real-time performance, and interactivity has become crucial for improving obstetric surgical training.

[0003] As a flexible soft tissue, the umbilical cord requires simulation that accurately describes its nonlinear elasticity and complex mechanical behavior. Currently, simulation models for umbilical cord torsion mainly fall into two categories: high-precision physical modeling based on the finite element method (FEM) and rapid physical modeling based on real-time physics engines. FEM-based modeling, grounded in the constitutive mechanical relationship of the umbilical cord, simulates its deformation during tension, bending, and torsion by solving nonlinear elastic equations. It can accurately reflect the stress distribution and geometric changes of the umbilical cord; for example, studies have shown that the spiral structure of the umbilical artery can minimize the variability of wall shear stress, exhibiting high accuracy and interpretability, making it suitable for mechanical property studies and pathological analysis. However, this method is complex and computationally intensive, especially during large deformations, self-collisions, and cutting reconstruction, requiring extensive preprocessing and mesh updates, making it difficult to meet the computational demands of real-time simulation. In contrast, real-time physics engine-based modeling simplifies mechanical calculations and collision detection mechanisms, utilizing constraint solving to achieve the dynamic response of the umbilical cord. It can provide good tactile feedback and smooth operation while maintaining a certain level of deformation accuracy; for example, the physics engine can simulate the dynamic interaction between umbilical blood flow and the coiling index. However, such methods mostly remain at the level of geometric appearance or simple collisions, making it difficult to realistically depict the nonlinear elasticity, viscoelasticity and complex mechanical behavior of the umbilical cord. Furthermore, they lack dedicated mechanical solution modules, resulting in the umbilical cord often existing only as a visual accessory in simulations, which is insufficient to meet the requirements of realism and precision for high-risk obstetric surgery training.

[0004] These limitations collectively restrict the application of virtual simulation in high-risk obstetric surgeries, and there is currently no effective way to address the insufficient modeling of umbilical cord torsion mechanics and the limitations of interactivity. Summary of the Invention

[0005] To address the problems existing in the prior art, this invention provides a simulation method for umbilical cord torsion based on bicubic Hermite and Cosserat rods. It organically combines the bicubic Hermite element method with Cosserat rod theory, utilizing its high-order continuity and mechanical coupling mechanism to circumvent the defects of existing methods and improve the simulation accuracy and interactivity of umbilical cord torsion.

[0006] This invention adopts the following technical solution: a simulation method for umbilical cord torsion based on bicubic Hermite and Cosserat rods, comprising the following steps:

[0007] Step 1: Construct the initial morphology of the umbilical vein, establish a three-dimensional geometric model of the umbilical cord centerline and simulate spiral winding, discretize the centerline into Cosserat bar elements, and perform axial elongation, bending and torsion processing;

[0008] Step 2: Introduce Neo-Hookean nonlinear mechanics, set the mechanical properties of the Cosserat rod element to Neo-Hookean nonlinear elastic material, and set the initial bending stiffness of the rod... Initial elongation stiffness of the rod It dynamically adjusts with strain to achieve nonlinear mechanical response under large deformation;

[0009] Step 3: Construct the umbilical cord surface mesh, use the bicubic Hermite element method to perform high-order interpolation on the surface deformation, and simultaneously couple the surface curvature with the strain of the central rod to update the surface deformation and rod mechanics synchronously.

[0010] Step 4: Simulate the operating force of surgical instruments on the umbilical cord using Neumann boundary conditions and external force application modules, update the rod and surface deformation, and use the constraint projection method combined with the axial bounding box tree to handle self-collision and coiling situations, and perform local position correction.

[0011] Step 5: Perform a unified simulation loop, rendering and haptic feedback. In each simulation time step, solve the rod mechanics, perform collision constraint correction, update the surface mesh in the order of implicit Euler integrator, and pass the results to the rendering and haptic feedback modules to realize real-time interaction and visualization operation.

[0012] Step 6: Construct a calibration model, calibrate the rod stiffness and surface elastic parameters based on umbilical cord biophysical data, and verify the helical shape, torsion angle and elastic response under different operating scenarios. Iterate and adjust the parameters to verify the simulation fidelity.

[0013] Step 7: Integrate steps 1 to 6 to form a unified simulation cycle and training verification closed loop, and record and output the simulation data for visualization and evaluation of umbilical cord torsion simulation.

[0014] Preferably, the method for establishing the three-dimensional centerline geometric model of the umbilical cord and simulating spiral winding in step 1 is as follows:

[0015] Step 1.1: Discretize the central line of the umbilical vein into... There are equidistant nodes, and the coordinates of the umbilical vein centerline node are: subscript Represents the umbilical vein, with a node spacing of [missing information]. ;in, Indicates the node index. ;

[0016] Step 1.2: Discretize the central lines of the two umbilical arteries into nodes corresponding to the vein nodes. There are 10 nodes, and the coordinates of the first umbilical artery centerline node are: The coordinates of the centerline node of the second umbilical artery are subscript , These represent the first and second umbilical arteries, respectively. Assume the central line of the umbilical vein runs along... Axis straight line extension, generated through helical parameterization and The three-axis coordinates;

[0017] Step 1.3: Combine the umbilical vein with the two umbilical arteries to form an array of rod node positions for three Cosserat rods. , subscript Represents a rod node and defines the initial bending stiffness of the rod. Initial elongation stiffness of the rod Initial torsional stiffness of the rod ;

[0018] Step 1.4: Input the rod node position array into the Cosserat rod solver to generate the initial position array of the helically wound rod nodes. .

[0019] Preferably, step 2 introduces Neo-Hookean nonlinear mechanics, as follows:

[0020] Step 2.1: Discretize the three Cosserat bars generated in Step 1 according to the centerline nodes. Two adjacent nodes form a bar element. Array of rod unit positions Two rod node position arrays and Composition, where subscript Indicates the rod element, Indicates the bar element index. ;

[0021] Neo-Hookean nonlinear material properties are set for each bar element, and the initial bending stiffness of the bar element is set accordingly. Initial elongation stiffness of the bar element Set as a linear function of the current axial strain, and dynamically adjust to simulate the nonlinear response of Neo-Hookean materials;

[0022] Step 2.2: Based on the Cosserat bar theory, calculate the first... Axial stress of each rod element With the Curvature of each link element ;

[0023] Step 2.3, and The information is transferred to the surface coupling module, providing curvature information, with a simulation time step of [value missing]. , Indicates the time step index;

[0024] Step 2.4: Perform preliminary nonlinear mechanical solutions for each link element to generate the dynamic displacement increments of the link nodes. ,renew Array of pole node positions at time points .

[0025] Preferably, step 3 involves constructing the umbilical cord surface mesh and coupling the surface curvature with the strain of the central rod, as follows:

[0026] Step 3.1: Initialize the position array of the link nodes of the three generated Cosserat links. Input the surface generation module to construct the initial mesh of the umbilical surface along the centerline pole nodes, and generate BHEM patches for each pole segment;

[0027] Step 3.2: Perform bicubic Hermitian interpolation on each BHEM patch to obtain the BHEM surface node position function. ;

[0028] Step 3.3: Map the bending, torsion, and elongation information of the centerline rod element to the surface nodes to obtain... Surface node position array at time step This enables the surface to update synchronously with the deformation of the rod;

[0029] Step 3.4, As the initial morphology output of the umbilical surface, while retaining BHEM patch information and rod node indexes, the surface morphology and rendered mesh are updated in each simulation time step.

[0030] Preferably, the operative force of the simulated surgical instruments on the umbilical cord described in step 4 is the force exerted by the surgical instruments. Input the Cosserat link node, with the point of action being the [number]th link node. 1 node, get node Total force The force is distributed to the rod nodes according to the location of the applied force or to the surface nodes through rod-surface mapping to ensure synchronous force updates at the surface nodes.

[0031] Preferably, in step 4, the constraint projection method combined with the axial bounding box tree is used to handle self-collision and coiling situations, as follows:

[0032] Step 4.1: Establish a constraint projection method combined with an axial bounding box tree (AABB tree) for the BHEM surface mesh nodes and rod elements to detect collisions. For each pair of potentially colliding nodes... and Calculate the shortest distance :

[0033] Step 4.2, if Less than the minimum allowable spacing If the elongation between nodes exceeds the allowable range of the material, it is determined to be a collision; if the elongation between nodes exceeds the allowable range of the material, it is determined to be overstretching.

[0034] Step 4.3: For nodes identified as colliding or overstretched, iteratively perform position correction until all colliding nodes satisfy the spacing constraint, thus obtaining... Array of pole node positions at time points ;

[0035] Preferably, the unified simulation loop, rendering, and haptic feedback described in step 5 are performed as follows:

[0036] Step 5.1: Update within each time step Array of pole node positions at time points and Surface node position array at time step compute nodes Internal forces and self-weight of the rod transmitted from adjacent rod elements The node position and velocity are updated using implicit Euler integrals;

[0037] Step 5.2: Apply the method described in Step 4 to perform collision correction on the rod and surface; Array of pole node positions at time points Mapping to BHEM surface nodes and recalculating Hermitian interpolation yields... Surface node position array at time step The data is fed into the rendering engine to generate each frame of the image. ;

[0038] Step 5.3, based on nodes Internal forces and self-weight of the rod transmitted from adjacent rod elements It outputs tactile information to the force feedback device, converting the simulated force into the force feedback of the handle;

[0039] Step 5.4: Update the time step. Repeat steps 5.1 to 5.3 until the set training duration is reached. Record key quantitative indicators in each loop for training evaluation and parameter optimization.

[0040] Preferably, step 6, which involves calibrating the rod stiffness and surface elastic parameters based on umbilical cord biophysical data, is performed as follows:

[0041] Collect experimental data, including: stretching curves Bending response Morphological comparison data ,in, This indicates the material measured in the experiment over time. Axial strain at time t; This indicates the material measured in the experiment over time. Axial tensile force at time; This represents the material's bending curvature as measured experimentally. This represents the bending moment of the material as measured in the experiment;

[0042] Define the parameter vector used for calibrating the model as follows: p Structured composite objective function The optimization process employs a global search and local fine-tuning algorithm to minimize... Output the final calibration parameter set Accuracy is evaluated through multi-scenario simulation, and parameter scaling strategies are provided to ensure diversity.

[0043] Preferably, the method for forming a unified simulation cycle and training verification closed loop in step 7 is as follows:

[0044] The calibration model is integrated into the main loop, with simulation time steps. Iteratively update the solution, collision correction, surface deformation, and rendering, and record physical quantities;

[0045] The response is compared with the data to calculate the change in error. Determine if convergence is achieved;

[0046] Establish cross-scenario verification, calculate RMSE and consistency. If the expected results are not achieved, return to step 6 for iterative optimization to form a closed-loop process and output the result file.

[0047] Compared with the prior art, the present invention, employing the above technical solution, has the following technical effects:

[0048] This invention proposes a Cosserat rod coupled with a bicubic Hermitian surface, which synchronously updates rod mechanics and high-order surface interpolation to accurately simulate the nonlinear mechanical behavior of umbilical cord stretching, bending, and torsion. Combined with implicit Euler integration, constrained projection, and AABB tree-accelerated collision detection, it achieves stable simulation of umbilical cord spiral coiling under high UCI conditions and supports real-time operation of surgical instruments and tactile feedback. Furthermore, through comprehensive optimization of mechanical, geometric, and tactile errors, it ensures that the model maintains biomechanical realism and training applicability under different individual umbilical cord conditions, enabling high-precision, real-time, and interactive umbilical cord simulation in a virtual surgical environment. Attached Figure Description

[0049] Figure 1 This is a flowchart illustrating the overall process of the umbilical cord torsion simulation method of the present invention.

[0050] Figure 2 This is a flowchart illustrating the construction process of the umbilical cord spiral structure of the present invention;

[0051] Figure 3 This is a data flow diagram of the BHEM surface mesh and rod coupling of the present invention;

[0052] Figure 4 This is a flowchart of the Cosserat link node collision correction process of the present invention. Detailed Implementation

[0053] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of the application will be further described in detail below with reference to the accompanying drawings. The described embodiments are only a part of the embodiments involved in this invention. All non-innovative embodiments based on these embodiments by other researchers in the art are within the protection scope of this invention. Furthermore, the step numbers in the embodiments of this invention are only set for ease of explanation and do not limit the order of the steps. The execution order of each step in the embodiments can be adaptively adjusted according to the understanding of those skilled in the art.

[0054] In one embodiment of the present invention, a method for simulating umbilical cord torsion based on a bicubic Hermite and Cosserat bar is described in the following process: Figure 1 As shown, it includes the following steps:

[0055] Step 1: Construct the initial morphology of the umbilical vein, establish a three-dimensional geometric model of the umbilical cord centerline and simulate spiral winding, discretize the centerline into Cosserat bar elements, and perform axial elongation, bending and torsion processing;

[0056] Step 2: Introduce Neo-Hookean nonlinear mechanics, set the mechanical properties of the Cosserat rod element to Neo-Hookean nonlinear elastic material, and set the initial bending stiffness of the rod... Initial elongation stiffness of the rod It dynamically adjusts with strain to achieve nonlinear mechanical response under large deformation;

[0057] Step 3: Construct the umbilical cord surface mesh, use the bicubic Hermite element method to perform high-order interpolation on the surface deformation, and simultaneously couple the surface curvature with the strain of the central rod to update the surface deformation and rod mechanics synchronously.

[0058] Step 4: Simulate the operating force of surgical instruments on the umbilical cord using Neumann boundary conditions and external force application modules, update the rod and surface deformation, and use the constraint projection method combined with the axial bounding box tree to handle self-collision and coiling situations, and perform local position correction.

[0059] Step 5: Perform a unified simulation loop, rendering and haptic feedback. In each simulation time step, solve the rod mechanics, perform collision constraint correction, update the surface mesh in the order of implicit Euler integrator, and pass the results to the rendering and haptic feedback modules to realize real-time interaction and visualization operation.

[0060] Step 6: Construct a calibration model, calibrate the rod stiffness and surface elastic parameters based on umbilical cord biophysical data, and verify the helical shape, torsion angle and elastic response under different operating scenarios. Iterate and adjust the parameters to verify the simulation fidelity.

[0061] Step 7: Integrate steps 1 to 6 to form a unified simulation loop and training verification closed loop, record and output simulation data for visualization and evaluation of umbilical cord torsion simulation.

[0062] Specifically, in step 1, a three-dimensional geometric model of the umbilical cord's centerline is established and its spiral winding is simulated, as follows: Figure 2 As shown, specifically:

[0063] First, discretize the umbilical vein centerline into There are equidistant nodes, and the coordinates of the umbilical vein centerline node are: subscript Represents the umbilical vein, node spacing ;in, Indicates the node index. , This indicates the total length of the umbilical cord.

[0064] Subsequently, the central lines of the two umbilical arteries were discretized into those corresponding to the venous nodes. There are 10 nodes, and the coordinates of the first umbilical artery centerline node are: The coordinates of the centerline node of the second umbilical artery are subscript , Let the first umbilical artery and the second umbilical artery be represented respectively, then:

[0065] ;

[0066] ;

[0067] ;

[0068] ;

[0069] ;

[0070] ;

[0071] in, express In cross-section Coordinate components in the direction, express In cross-section Coordinate components in the direction, express Coordinate components along the axis of the center line of the first artery. express In cross-section Coordinate components in the direction, express In cross-section Coordinate components in the direction, , express Coordinate components along the axis of the center line of the second artery. Indicates the radius of the umbilical vein. This indicates the distance between the umbilical vein and the two umbilical arteries as they intertwine. Indicates the radius of the umbilical artery. The node spacing, Indicates the helix angular frequency. , This indicates the umbilical cord coiling index.

[0072] Then, the umbilical vein and the two umbilical arteries are combined to form an array of rod node positions for three Cosserat rods. , And define the initial bending stiffness of the rod. Initial elongation stiffness of the rod and the initial torsional stiffness of the rod .

[0073] Finally, the array of rod node positions is input into the Cosserat rod solver to generate the initial array of rod node positions for the helical winding. It is used for subsequent surface construction and nonlinear mechanical coupling.

[0074] Furthermore, in step 2, the introduction of Neo-Hookean nonlinear mechanics specifically involves:

[0075] Discretize the three Cosserat rods generated in step 1 according to the centerline nodes. Two adjacent nodes form a rod element. Array of rod unit positions Two rod node position arrays and Composition, where subscript Indicates the rod element, Indicates the bar element index. .

[0076] Neo-Hookean nonlinear material properties are set for each bar element, and the initial bending stiffness of the bar element is set accordingly. Initial elongation stiffness of the bar element Set as a linear function of the current axial strain, and dynamically adjusted to approximate the nonlinear response of the Neo-Hookean material:

[0077] ;

[0078] ;

[0079] in, , They represent the first The effective elongation stiffness of the first rod element under the current deformation state and the first Effective bending stiffness of a single rod element under its current deformation state. , These represent the adjustment coefficients for controlling tension and the adjustment coefficients for controlling the degree of bending nonlinearity, respectively. Indicates the first Axial strain of a single rod element;

[0080] Based on this, and according to Cosserat's rod theory, the first... Axial stress of each rod element With the Curvature of each link element ;

[0081] Then, the calculated results and The information is transmitted to the surface coupling module to provide curvature information; the simulation time step is set to... , Indicates the time step index.

[0082] Finally, a preliminary nonlinear mechanical solution is performed on each bar element to generate the dynamic displacement increments of the bar nodes at both ends of the bar element. ,renew Array of pole node positions at time points subscript Represents a rod node, which is used by the surface building module for higher-order interpolation and coupling.

[0083] Furthermore, in step 3, the umbilical cord surface mesh is constructed and coupled with the centerline rod, as follows: Figure 3 As shown, specifically:

[0084] First, the initial position array of the rod nodes of the three Cosserat rods generated in steps 1 and 2 is used. Input surface generation module;

[0085] Then, an initial mesh for the umbilical surface is constructed along the centerline pole nodes, and a BHEM patch is generated for each pole segment;

[0086] Perform bicubic Hermitian interpolation on each BHEM patch to obtain the surface node coordinates:

[0087] ;

[0088] in, Represents the function for the location of BHEM surface nodes, subscript Represents surface nodes. This indicates the Hermite control point index along the centerline of the pole. This indicates the Hermite control point index along the direction of the bar cross section. Describe the cubic Hermitian basis functions along the direction of the rod's centerline. Describes the cubic Hermitian basis functions along the direction of the bar cross section. For patch nodes, This represents the normalized parameter at the node along the centerline of the rod. Represents the normalized parameters of the nodes along the cross section of the rod;

[0089] Subsequently, the bending, torsion, and elongation information of the centerline rod element is mapped to the surface nodes:

[0090] ;

[0091] in, express The array of surface node positions at each time step. express The array of surface node positions at each time step, and the update of surface nodes. Array of pole node positions at time points Keep in sync This represents the curvature-strain mapping function, enabling synchronous updates of the surface as the rod deforms. Indicates the first The curvature of each rod element Indicates the first Axial stress of each rod element express The first moment The displacement increment of each rod element;

[0092] Finally, Surface node position array at time step As the initial morphology output of the umbilical cord surface, it is used for subsequent surgical force application, collision constraint correction, and real-time rendering; at the same time, BHEM patch information and rod node index are retained so that the surface morphology and rendering mesh can be updated in each simulation time step.

[0093] Furthermore, in step 4, the surgical procedure is applied along with a self-collision handling method, specifically as follows:

[0094] The force of the surgical instruments Input the Cosserat lever, with the point of application being the first... 1 node, get node Total force :

[0095] ;

[0096] in, Represents a node The internal forces and self-weight of the rod transmitted from adjacent rod elements. Represents a node The force exerted by the surgical instruments; the force is distributed to the rod nodes according to the location of the force application or to the surface nodes through rod-surface mapping to ensure synchronous force updates at the surface nodes.

[0097] AABB trees are built for collision detection of BHEM surface mesh nodes and rod nodes. For each pair of potentially colliding nodes... and Calculate the shortest distance .

[0098] like This indicates the minimum allowable spacing, and If the elongation between nodes exceeds the allowable range of the material, it is determined to be a collision; if the elongation between nodes exceeds the allowable range of the material, it is determined to be overstretching.

[0099] For nodes identified as colliding or overstretched, position correction is performed iteratively.

[0100] Note: Step 4 completes the single-step force application and collision correction method, and the final update of the rod node position array and surface morphology is handled uniformly in the simulation loop of step 5.

[0101] Furthermore, in step 5, the simulation loop, rendering, and haptic feedback are unified, such as... Figure 4 As shown, specifically:

[0102] First, let the simulation time step be... The time step is consistent with that in step 2, and updates are performed within each time step. Array of pole node positions at time points and Surface node position array at time step ;

[0103] Then, compute the nodes. Internal forces and self-weight of the rod transmitted from adjacent rod elements The node position and velocity are updated using implicit Euler integrals;

[0104] Then, using the method described in step 4, collision detection and position correction are performed on the rod and surface; Array of pole node positions at time points Mapping to BHEM surface nodes and recalculating Hermitian interpolation yields... Surface node position array at time step The data is fed into the rendering engine to generate each frame of the image. ; and according to the nodes Internal forces and self-weight of the rod transmitted from adjacent rod elements Output tactile information to the force feedback device;

[0105] Finally, the simulated force is converted into a handle feedback force; the time step is updated, and the above operations are repeated until the set training duration is reached; key quantitative indicators are recorded in each loop for training evaluation and parameter optimization.

[0106] Furthermore, in step 6, parameters are calibrated based on umbilical cord biophysical data, and the simulation fidelity is verified, specifically as follows:

[0107] Collect experimental data, including: stretching curves Bending response Morphological comparison data ,in, This indicates the material measured in the experiment over time. Axial strain at time t; This indicates the material measured in the experiment over time. Axial tensile force at time; This represents the material's bending curvature as measured experimentally. This represents the bending moment of the material as measured in the experiment.

[0108] Define the parameter vector used to calibrate the model. p Structured composite objective function :

[0109] ;

[0110] in, The weighting coefficients representing mechanical errors. Indicates mechanical error. The weighting coefficients representing geometric errors, Indicates geometric error, Represents the regularization weight coefficient. This represents the regularization function.

[0111] During the optimization process, a global search and local fine-tuning algorithm is used to minimize the minimum value. Output the final calibration parameter set Accuracy is evaluated through multi-scenario simulation, and parameter scaling strategies are provided to ensure diversity.

[0112] Furthermore, in step 7, a unified simulation cycle and training-verification closed loop are formed, specifically as follows:

[0113] Integrate the calibration model into the main loop to Iterative updates are performed on the solution, collision correction, surface deformation, and rendering, while recording physical quantities. The response is compared with the data to calculate the change in error. Determine convergence. Establish cross-scenario validation, calculate RMSE and consistency. If the expected results are not achieved, return to step 6 for iterative optimization, forming a closed-loop process. Output the results file for visualization and evaluation.

[0114] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A simulation method for umbilical cord torsion based on bicubic Hermite and Cosserat rods, characterized in that, Includes the following steps: Step 1: Construct the initial morphology of the umbilical vein, establish a three-dimensional geometric model of the umbilical cord centerline and simulate spiral winding, discretize the centerline into Cosserat bar elements, and perform axial elongation, bending and torsion processing; Step 2: Introduce Neo-Hookean nonlinear mechanics, set the mechanical properties of the Cosserat rod element to Neo-Hookean nonlinear elastic material, and set the initial bending stiffness of the rod... Initial elongation stiffness of the rod It dynamically adjusts with strain to achieve nonlinear mechanical response under large deformation; Step 3: Construct the umbilical cord surface mesh, use the bicubic Hermite element method to perform high-order interpolation on the surface deformation, and simultaneously couple the surface curvature with the strain of the central rod to update the surface deformation and rod mechanics synchronously. Step 4: Simulate the operating force of surgical instruments on the umbilical cord using Neumann boundary conditions and external force application modules, update the rod and surface deformation, and use the constraint projection method combined with the axial bounding box tree to handle self-collision and coiling situations, and perform local position correction. Step 5: Perform a unified simulation loop, rendering and haptic feedback. In each simulation time step, solve the rod mechanics, perform collision constraint correction, update the surface mesh in the order of implicit Euler integrator, and pass the results to the rendering and haptic feedback modules to realize real-time interaction and visualization operation. Step 6: Construct a calibration model, calibrate the rod stiffness and surface elastic parameters based on umbilical cord biophysical data, and verify the helical shape, torsion angle and elastic response under different operating scenarios. Iterate and adjust the parameters to verify the simulation fidelity. Step 7: Integrate steps 1 to 6 to form a unified simulation loop and training verification closed loop, record and output simulation data for visualization and evaluation of umbilical cord torsion simulation. Step 3 involves constructing the umbilical cord surface mesh and coupling the surface curvature with the strain of the central rod, as follows: Step 3.1: Initialize the position array of the link nodes of the three generated Cosserat links. Input the surface generation module to construct the initial mesh of the umbilical surface along the centerline pole nodes, and generate BHEM patches for each pole segment; Step 3.2: Perform bicubic Hermitian interpolation on each BHEM patch to obtain the surface node coordinates: ； in, Represents the function for the location of BHEM surface nodes, subscript Represents surface nodes. This indicates the Hermite control point index along the centerline of the pole. This indicates the Hermite control point index along the direction of the bar cross section. Describe the cubic Hermitian basis functions along the direction of the rod's centerline. Describes the cubic Hermitian basis functions along the direction of the bar cross section. For patch nodes, This represents the normalized parameter at the node along the centerline of the rod. Represents the normalized parameters of the nodes along the cross section of the rod; Step 3.3: Map the bending, torsion, and elongation information of the centerline rod element to the surface nodes: ； in, express The array of surface node positions at each time step. express The array of surface node positions at each time step, and the update of surface nodes. Array of pole node positions at time points Keep in sync This represents the curvature-strain mapping function, enabling synchronous updates of the surface as the rod deforms. Indicates the first The curvature of each rod element Indicates the first Axial strain of each rod element express The first moment The displacement increment of each rod element; Step 3.4, As the initial morphology output of the umbilical surface, while retaining BHEM patch information and rod node indexes, the surface morphology and rendered mesh are updated in each simulation time step.

2. The umbilical cord torsion simulation method based on bicubic Hermite and Cosserat rods according to claim 1, characterized in that, Step 1 involves establishing a three-dimensional geometric model of the umbilical cord's centerline and simulating its spiral winding. The method is as follows: Step 1.1: Discretize the central line of the umbilical vein into... There are equidistant nodes, and the coordinates of the umbilical vein centerline node are: subscript Represents the umbilical vein, node spacing ;in, Indicates the node index. , Indicates the total length of the umbilical cord; Step 1.2: Discretize the central lines of the two umbilical arteries into nodes corresponding to the vein nodes. There are 10 nodes, and the coordinates of the first umbilical artery centerline node are: The coordinates of the centerline node of the second umbilical artery are subscript , These represent the first and second umbilical arteries, respectively. Assume the central line of the umbilical vein runs along... Axis straight line extension, generated through helical parameterization and The three-axis coordinates; Step 1.3: Combine the umbilical vein with the two umbilical arteries to form an array of rod node positions for three Cosserat rods. , subscript Represents a rod node and defines the initial bending stiffness of the rod. Initial elongation stiffness of the rod Initial torsional stiffness of the rod ; Step 1.4: Input the rod node position array into the Cosserat rod solver to generate the initial position array of the helically wound rod nodes. .

3. The umbilical cord torsion simulation method based on bicubic Hermite and Cosserat rods according to claim 2, characterized in that, The coordinates of the first umbilical artery centerline node are generated using spiral parameterization. Coordinates of the centerline node of the second umbilical artery The formula is as follows: ； ； ； ； ； ； in, express In cross-section Coordinate components in the direction, express In cross-section Coordinate components in the direction, express Coordinate components along the axis of the center line of the first artery. express In cross-section Coordinate components in the direction, express In cross-section Coordinate components in the direction, express Coordinate components along the axis of the center line of the second artery. Indicates the radius of the umbilical vein. This indicates the distance between the umbilical vein and the two umbilical arteries as they intertwine. Indicates the radius of the umbilical artery. The node spacing, Indicates the helix angular frequency. , This indicates the umbilical cord coiling index.

4. The umbilical cord torsion simulation method based on bicubic Hermite and Cosserat rods according to claim 2, characterized in that, Step 2 introduces Neo-Hookean nonlinear mechanics, and the method is as follows: Step 2.1: Discretize the three Cosserat bars generated in Step 1 according to the centerline nodes. Two adjacent nodes form a bar element. Array of rod unit positions Two rod node position arrays and Composition, where subscript Indicates the rod element, Indicates the bar element index. ; Neo-Hookean nonlinear material properties are set for each bar element, and the initial bending stiffness of the bar element is set accordingly. Initial elongation stiffness of the bar element Set as a linear function of the current axial strain, and dynamically adjust to simulate the nonlinear response of Neo-Hookean materials: ； ； in, , They represent the first The effective elongation stiffness of the first rod element under the current deformation state and the first Effective bending stiffness of a single rod element under its current deformation state. , These represent the adjustment coefficients for controlling the degree of tensile nonlinearity and the adjustment coefficients for controlling the degree of bending nonlinearity, respectively. Indicates the first Axial strain of each rod element; Step 2.2: Based on the Cosserat bar theory, calculate the first... Axial stress of each rod element With the Curvature of each link element : Step 2.3, and The information is transferred to the surface coupling module, providing curvature information, with a simulation time step of [value missing]. , Indicates the time step index; Step 2.4: Perform preliminary nonlinear mechanical solutions for each link element to generate the dynamic displacement increments of the link nodes at both ends of the link element. ,renew Array of pole node positions at time points .

5. The umbilical cord torsion simulation method based on bicubic Hermite and Cosserat rods according to claim 4, characterized in that, The method for simulating the operating force of surgical instruments on the umbilical cord in step 4 is as follows: The force of the surgical instruments Input the Cosserat lever, with the point of application being the first... 1 node, get node Total force : ； in, Represents a node The internal forces and self-weight of the rod transmitted from adjacent rod elements. Represents a node The force exerted by the surgical instruments; the force is distributed to the rod nodes according to the position of the force application or to the surface nodes through rod-surface mapping to ensure synchronous force updates of the surface nodes.

6. The umbilical cord torsion simulation method based on bicubic Hermite and Cosserat rods according to claim 5, characterized in that, Step 4 describes using the constraint projection method combined with the axial bounding box tree to handle self-collision and coiling situations. The method is as follows: Step 4.1: Establish a constraint projection method combined with axial bounding box tree to detect collisions for the BHEM surface mesh nodes and rod nodes. For each pair of colliding nodes... and Calculate the shortest distance ; Step 4.2, if Less than the minimum allowable spacing If the elongation between nodes exceeds the allowable range of the material, it is determined to be a collision; if the elongation between nodes exceeds the allowable range of the material, it is determined to be overstretching. Step 4.3: For nodes determined to be in collision or overstretched, perform position correction iteratively.

7. The umbilical cord torsion simulation method based on bicubic Hermite and Cosserat rods according to claim 6, characterized in that, The unified simulation loop, rendering, and haptic feedback described in step 5 are as follows: Step 5.1: Update within each time step Array of pole node positions at time points and Surface node position array at time step compute nodes Internal forces and self-weight of the rod transmitted from adjacent rod elements The node position and velocity are updated using implicit Euler integrals; Step 5.2: Apply the constraint projection method described in Step 4 to perform collision correction on the rod and surface; Array of pole node positions at time points Mapping to BHEM surface nodes and recalculating Hermitian interpolation yields... Surface node position array at time step The data is fed into the rendering engine to generate each frame of the image. ; Step 5.3, based on nodes Internal forces and self-weight of the rod transmitted from adjacent rod elements It outputs tactile information to the force feedback device, converting the simulated force into the force feedback of the handle; Step 5.4: Update the time step. Repeat steps 5.1 to 5.3 until the set training duration is reached. Record key quantitative indicators in each loop.

8. The umbilical cord torsion simulation method based on bicubic Hermite and Cosserat rods according to claim 7, characterized in that, Step 6 involves calibrating the rod stiffness and surface elastic parameters based on umbilical cord biophysical data, and the method is as follows: Collect experimental data, including: stretching curves Bending response Morphological comparison data ,in, This indicates that the material measured in the experiment... Axial strain at time t; This indicates that the material measured in the experiment... Axial tensile force at time; This represents the material's bending curvature as measured experimentally. This represents the bending moment of the material as measured in the experiment; Define the parameter vector used to calibrate the model. p Structured composite objective function : ； in, The weighting coefficients representing mechanical errors. Indicates mechanical error. The weighting coefficients representing geometric errors, Indicates geometric error, Represents the regularization weight coefficient. Represents the regularization function; The optimization process employs a global search and local fine-tuning algorithm to minimize... Output the final calibration parameter set .

9. The umbilical cord torsion simulation method based on bicubic Hermite and Cosserat rods according to claim 8, characterized in that, Step 7 describes the formation of a unified simulation cycle and training / verification closed loop, which is achieved as follows: The calibration model is integrated into the main loop, with simulation time steps. Iteratively update the solution, collision correction, surface deformation, and rendering, and record physical quantities; The response is compared with the data to calculate the change in error. Determine if convergence is achieved; Establish cross-scenario verification, calculate RMSE and consistency. If the expected results are not achieved, return to step 6 for iterative optimization to form a closed-loop process and output the result file.

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