Virtual release method of weaving type intracranial intervention device based on curvature driving

Abstract

The invention discloses a virtual release method of a weaving type intracranial intervention device based on curvature driving, and relates to the technical field of medical instrument intervention simulation, the method comprises the following steps: step 1, carrying out strain energy analysis on the weaving type intracranial intervention device, and determining assumed conditions; 2, initial configuration parameterized representation of the woven intracranial intervention device is established; 3, inputting parameters of the aneurysm wall to obtain a final configuration; 4, establishing an energy functional expressed by the average curvature and the Gaussian curvature; step 5, solving of energy functional minimization; and step 6, calculating stress and strain. Based on the mechanical characteristics of the woven silk threads and the geometric configuration of the woven intervention device, the device deformation and stress-strain calculation can be completed within tens of seconds, the mechanical behaviors of the device under different clinical situations can be quickly and accurately simulated, and the device has important significance for optimizing the device design and improving the clinical treatment effect.

Description

Technical Field

[0001] The present invention relates to the technical field of medical device interventional simulation, and particularly to a virtual release method for a braided intracranial interventional device based on curvature driving. Background Art

[0002] The braided intracranial interventional device (such as the Woven EndoBridge, (WEB) device) is mainly made of nitinol, and makes full use of its superelasticity and shape memory characteristics to achieve self-expansion and stable fitting of the device in the aneurysm cavity. The mesh braided structure of the device can effectively slow down the blood flow impact and shear stress entering the aneurysm, promote the formation of thrombus in the aneurysm cavity, and thus achieve the occlusion and stability of the aneurysm. These characteristics enable the braided intracranial interventional device to provide continuous and effective support and occlusion in a high blood flow environment, significantly reducing the risk of aneurysm rupture. However, the mechanical performance of the braided intracranial interventional device not only depends on the material properties of nitinol, such as superelasticity, fatigue life and radial support force, but also is affected by multiple factors such as the geometric shape of the aneurysm, the lesion location and the hemodynamic conditions. Therefore, accurately simulating and evaluating the mechanical behavior of the braided intracranial interventional device in different clinical situations is of great significance for optimizing the device design and improving the treatment effect. In addition, the cost of the braided intracranial interventional device is usually high, and due to the complexity of the device design and the requirements of the production process, it is expensive, bringing a considerable economic burden to patients and the medical system. Therefore, performing virtual surgical planning in advance can simulate the effects of different treatment plans and device parameters in a digital environment, thereby helping doctors accurately select the appropriate interventional device and release position before surgery. This virtual surgical planning can not only improve the accuracy of treatment, ensure that the device can achieve the best effect in the aneurysm cavity, but also reduce unnecessary clinical experiments and physical tests by optimizing the treatment plan, thereby reducing the treatment cost.

[0003] To improve the clinical treatment effect, the virtual release algorithm is particularly necessary. In such mechanical simulations, the traditional method is to perform finite element analysis (FEM) on the entire process of the device from being constrained in the catheter to self-expansion after release. This requires the hyperelastic constitutive model based on nitinol to accurately describe the stress-strain relationship of the device and, combined with the collision contact algorithm, to simulate the complex contact process between the device and the aneurysm wall. At the same time, the fluid-structure interaction (FSI) effect of blood flow must also be taken into account to accurately evaluate the shear force distribution after implantation, the velocity distribution within the aneurysm sac, the coverage of the aneurysm neck, and the overall stability of the device. However, the finite element method relies on the discretization of local elements, requires huge computing resources, usually takes dozens of hours, and is complex to operate, making it difficult to be directly applied clinically. Therefore, the clinical demand for timeliness poses an urgent requirement for the development of a fast virtual release algorithm.

[0004] Most of the existing fast virtual release methods are based on centerline extraction techniques, which simplify and map the aneurysm geometry, such as a series of methods based on simplex mesh. These methods use internal and external forces to control a single-layer simple mesh to fit the aneurysm surface, where the external force is responsible for the out-of-plane deformation of the mesh, and the internal force controls the in-plane deformation to maintain the smoothness and geometric coordination of the mesh. In essence, these methods belong to the mapping of geometric configurations and do not consider mechanical properties, so they cannot simulate the behavior of devices with different stiffnesses. The construction of the initial mesh depends on the extraction of the centerline. For example, when using commercial or open-source software such as Mimics and VMTK, these software can only generate a single centerline for each geometry, making it difficult to flexibly adapt to the diverse deployment methods under different release directions, which limits their applicability and accuracy in complex clinical scenarios. More importantly, the existing fast algorithms do not include mechanical properties and cannot complete the calculation of mechanical properties such as stress and strain.

[0005] Therefore, those skilled in the art are committed to developing a virtual release method for a braided intracranial interventional device based on curvature driving. When a single wire of a braided intracranial interventional device undergoes bending deformation, it can be regarded as an Euler-Bernoulli pure bending beam, that is, the length of the wire does not change during the deformation process, and there is no shear deformation of the midline section. Therefore, the deformation energy of the beam all comes from the bending strain energy, and there is no strain energy caused by axial forces (such as tensile or compressive forces). When woven into the umbrella cage structure of the interventional device, it can be regarded as a single-layer thin film. Since the length of the wire does not change and there is no axial force, the equivalent thin film does not generate film force, only bending strain energy. Thus, the deformation of the equivalent thin film-like of the braided intracranial interventional device can be regarded as isometric deformation, that is, the length of any curve in the film is conserved before and after deformation. Gauss's Theorema Egregium points out that the Gaussian curvature of a surface is an intrinsic quantity, that is to say, the Gaussian curvature can be obtained by "internal" measurements such as distances, angles, and their rates of change on the surface, regardless of how the surface is "embedded" in three-dimensional space. When isometric deformation occurs, the Gaussian curvature is conserved before and after deformation. Based on isometric deformation, the present invention establishes a control method driven by Gaussian curvature, which can quickly obtain the deformed device configuration, and by the curvatures in different principal directions, inversely deduce the stress and strain results after deformation. Based on the mechanical properties of the braided wires and the geometric configuration of the braided interventional device, the calculation of device deformation and stress and strain can be completed within dozens of seconds, and the mechanical behavior of the device in different clinical situations can be quickly and accurately simulated, which is of great significance for optimizing device design and improving clinical treatment effects. Summary of the Invention

[0006] In view of the above-mentioned defects of the prior art, the technical problem to be solved by the present invention is how to design a virtual release algorithm to quickly and accurately simulate the mechanical behavior of a braided intracranial interventional device in different clinical situations.

[0007] To achieve the above object, the present invention provides a virtual release method for a braided intracranial interventional device based on curvature driving, characterized in that the method comprises the following steps:

[0008] Step 1, perform strain energy analysis on the braided intracranial interventional device to determine the assumed conditions for establishing the initial configuration;

[0009] Step 2, establish a parametric representation of the initial configuration of the braided intracranial interventional device;

[0010] Step 3, input the parameters of the aneurysm wall to obtain the final configuration of the braided intracranial interventional device;

[0011] Step 4: Calculate the mean curvature and Gaussian curvature of the instrument surface of the braided intracranial interventional device, and establish an energy functional represented by the mean curvature and Gaussian curvature;

[0012] Step 5: Introduce the curvature alignment energy, merge it with the energy functional for iteration, set the convergence condition, and obtain the surface expression of the optimized configuration of the braided intracranial interventional device;

[0013] Step 6: Calculate the stress and strain of the braided intracranial interventional device during the process of conforming to the aneurysm wall according to the surface expression.

[0014] Further, the braided intracranial interventional device is made of silk threads. In Step 1, the assumed conditions of the silk threads include: the axial tensile effect is ignored during the bending of the silk threads; the length of the silk threads does not change during deformation; the cross-section of the silk threads remains perpendicular to the central axis during deformation.

[0015] Further, in Step 1, the braided intracranial interventional device is regarded as a surface similar to a thin film. The assumed conditions of the surface similar to a thin film include: the membrane force of the surface is ignored; the shear stress outside the surface is ignored; the length of the curve inside the surface does not change during deformation.

[0016] Further, the braided intracranial interventional device is woven from nitinol wires or metal wires or polymer wires.

[0017] Further, in Step 2, the initial configuration of the braided intracranial interventional device in the stress-free state is a surface of revolution.

[0018] Further, in Step 2, the following function is used for the parametric representation of the initial configuration:

[0019]

[0020] where, N i (u) is a cubic spline function for controlling the axial cross-section, M j (v) is a circumferential cubic closed function, P i，j (α1, α2,...) is a weighted function determined by the parameters to be solved and the deformation points, is the parameter vector to be solved, N i (v) and M j (v) are used to control the initial configuration, P i，j (α1, α2,...) is used to control the deformation. For the initial configuration without deformation,

[0021] Further, in the step 3, the aneurysm wall at the maximum deformation is regarded as the input, and it evolves along the direction of the minimum strain energy to the final configuration of the braided intracranial interventional device. The aneurysm wall is parameterized by the following function:

[0022]

[0023] where the parameter is obtained from the vertices of the aneurysm wall.

[0024] Further, in the step 4, the device surface of the braided intracranial interventional device is represented as a smooth function The first fundamental form coefficients of the device surface are:

[0025] E = w u ·w u , F = w u ·w v , G = w v ·w v

[0026] where and are the tangent vectors of the device surface in the directions u and v respectively,

[0027]

[0028] where are the second mixed partial derivatives of the surface in the directions u and v respectively, is the unit normal vector of the surface, defined as:

[0029]

[0030] The mean curvature H and the Gaussian curvature K are:

[0031]

[0032] The energy functional represented by the mean curvature H and the Gaussian curvature K is:

[0033] E Willmore = M (H 2 + λK)dA,

[0034] where λ is a regulation parameter used to balance the contributions of the mean curvature term and the Gaussian curvature term.

[0035] Further, in the step 5, the curvature alignment energy is represented by the following function:

[0036] E Alignment = μ∫ M ((H - Href ) 2 +γ(K - K rer ) 2 )dA

[0037] Among them, μ and γ are weight coefficients, which respectively regulate the weighted influence of the mean curvature alignment term and the Gaussian curvature alignment term. The comprehensive energy functional E is defined as:

[0038] E = E Willmore + E Alignment

[0039] Iterating the comprehensive energy functional E along the gradient direction, the evolution equation of the surface at each iteration step can be obtained:

[0040]

[0041] Among them, Δ represents the Laplace - Beltrami operator of the surface, which is defined as:

[0042]

[0043] Through the chain rule of differentiation, the evolution equation of the surface can be reduced to the solution of the parameter to be solved :

[0044]

[0045] Set the convergence condition. When the energy change amount is less than the preset threshold or the maximum number of iterations is reached, terminate the iteration process, obtain the final parameters, and then obtain the surface expression of the optimized intervention device configuration:

[0046]

[0047] final After finding the final surface w ref calculate the deformation gradient tensor:

[0048]

[0049] E′ = w′ u · w′ u , F′ = w′ u · w′ v , G′ = w′ v · w′ v

[0050]

[0051] Then the Green - Lagrange tensor is calculated as:

[0052]

[0053] When the braided intracranial intervention device is linearly elastic, the stress is calculated as follows:

[0054] σ = λ(E xx + E yy )I + 2μE.

[0055] The beneficial technical effects of the present invention are as follows:

[0056] 1. Existing finite element-based simulation methods consume huge computing resources and take a long time to calculate, often requiring dozens of hours, and are complex to operate, making it difficult to directly apply to clinical practice. Based on the equidistant deformation of the thin-film-like and the conservation of Gaussian curvature, the present invention establishes the connection between mechanical and geometric non-linear deformations, without the need to solve the mechanical control equations for each element; the relatively regular geometric configuration of the device is convenient for parametric representation, and only the undetermined parameters need to be solved, which can reduce the computing cost. The present invention is simple to operate, has a short computing time and has a considerable accuracy, can complete the rapid virtual release of the device in the blood vessel within dozens of seconds, and can obtain the release position and deformation degree, greatly reducing the required computing resources.

[0057] 2. Existing rapid calculation methods are based on simple mapping of graphics, cannot simulate the mechanical properties of the instrument, cannot simulate devices with different stiffnesses and braiding methods, and cannot obtain results including mechanical properties such as stress and strain. The present invention is based on the derivation of mechanical methods, includes the complete mechanical properties of the device, has strong interpretability, and can simulate scaffolds with different stiffnesses and braiding methods. The present invention regards the braided wire as an Euler-Bernoulli pure bending beam, and there is no shear deformation in the mid-axis section during deformation, and the length does not change after deformation. Therefore, when the whole device is regarded as a thin-film-like structure, it conforms to the Gauss's Theorema Egregium and equidistant deformation of the curved surface, that is, the conservation of Gaussian curvature. The present invention keeps the minimization of the Gaussian curvature integral after deformation, and obtains the representation method of the Gaussian curvature of the device after release. It can not only obtain the position and combined shape of the instrument after release, but also obtain the stress of the device in the Cartesian coordinate system, the second Piola-Kirchhoff stress in the local coordinate system, and the strain distribution after release, as well as the contact and interaction with the aneurysm wall, which can further analyze the stability of the intervention device at the current position and facilitate further prognosis analysis. The present invention can also obtain the results under different mechanical characteristics and braiding methods, which can not only be used for timely imaging in clinical practice and preoperative virtual surgical planning, but also analyze the different mechanical performances of different mechanical characteristics and configurations, and can be used for industrial optimization design of the instrument.

[0058] 3. In existing algorithms, whether it is the finite element algorithm or the fast calculation method, it is necessary to determine the contact between the device and the blood vessel wall in each iteration. In the traditional contact determination method, the contact relationship between surfaces needs to be frequently detected and processed during the surface evolution process, increasing the computational complexity and time overhead. From the perspective of curvature evolution, the present invention directly evolves along the direction of the minimum strain energy, avoiding complex contact detection and processing in each iteration, and significantly improving the overall computational efficiency. The present invention takes the surface with the maximum curvature that completely fits the aneurysm as the input, and the configuration of the device in the stress-free state as the reference surface. By driving the surface to evolve along the direction of the minimum strain energy through the Willmore energy, the final surface can be obtained. The present invention significantly reduces the computational complexity and greatly improves the overall computational efficiency. Considering both the blood vessel and the device as surface structures ensures the smoothness and geometric consistency of the surface, making it more efficient and easier to implement. This construction method introduces a fourth-order partial differential equation, enhancing the stability of numerical calculations and avoiding numerical oscillations and surface collapse problems caused by contact determination.

[0059] 4. The existing fast calculation method is based on the generation of the centerline and can only generate one release result along the centerline. In the present invention, the generation of the initial configuration does not depend on the centerline of the geometric structure, is more flexible, and can meet the release requirements from multiple angles in real clinical situations. The present invention parameterizes the device and establishes two sets of coordinate systems, a fixed Cartesian coordinate system and a local natural coordinate system. The solution of the second Piola-Kirchhoff stress and strain is based on the natural coordinate system, and the results can be transformed into the fixed Cartesian coordinate system according to different angles of release defined by the user. The present invention can obtain the virtual release results of the interventional device at different angles defined by the user, meet the complex working conditions and requirements of real clinical practice, facilitate virtual surgical planning, explore the impact of different release positions on the prognosis, and improve the treatment success rate.

[0060] The concept, specific structure and technical effects of the present invention will be further described below in conjunction with the accompanying drawings to fully understand the purpose, features and effects of the present invention. Description of the Drawings

[0061] Figure 1 is a schematic diagram of the principle of a virtual release method for a curvature-driven braided intracranial interventional device according to a preferred embodiment of the present invention;

[0062] Figure 2 is the morphology of an umbrella cage-shaped braided intracranial interventional device in a stress-free state according to a preferred embodiment of the present invention;

[0063] Figure 3 is the morphology of an umbrella cage-shaped braided intracranial interventional device after being released into an aneurysm according to a preferred embodiment of the present invention. Detailed Embodiments

[0064] The following describes several preferred embodiments of the present invention with reference to the accompanying drawings of the specification to make its technical content clearer and easier to understand. The present invention can be embodied in many different forms of embodiments, and the protection scope of the present invention is not limited to the embodiments mentioned in the text.

[0065] In the drawings, the dimensions and thicknesses of each component shown in the drawings are arbitrarily shown, and the present invention does not limit the dimensions and thicknesses of each component. To make the illustration clearer, the thicknesses of some parts in the drawings are appropriately exaggerated.

[0066] Step 1: Establish assumptions and strain energy analysis.

[0067] The present invention first analyzes the strain energies of the device and identifies the main strain energies.

[0068] Principle: The braided intracranial intervention device is made of soft nitinol wires or other metal or polymer wires. When deformed, the strain energy required to resist stretching is much greater than the strain energy required to resist bending. Therefore, the energy change can be regarded as the change of bending strain energy dominated by bending. When analyzing a single wire, the following assumptions can be made:

[0069] a. The axial stretching effect is ignored during the bending of the wire, and the change in axial strain energy is negligible.

[0070] b. The length of the wire does not change during deformation.

[0071] c. The shear stress on the surface of the wire is ignored, that is, the cross-section of the wire remains perpendicular to the central axis during deformation.

[0072] The intervention device can be obtained by braiding the wires in a certain direction. This method can regard the intervention device as a kind of thin film, and its curved surface can be analyzed. According to the mechanical characteristics of the wire, it can be known that the length of the curve on the surface does not change during the deformation of the curved surface, and the force required for stretching the curved surface is much greater than the bending force. Therefore, the following assumptions can be made:

[0073] a. The film force of the curved surface of the device is ignored, and the change in tensile strain energy is negligible.

[0074] b. The shear stress outside the curved surface is ignored, that is, the cross-section of the curved surface remains perpendicular to the central plane during deformation.

[0075] c. The length of the curve in the plane does not change during deformation, which conforms to the isometric deformation and Gauss's Theorema Egregium. The curved surface bending strain energy can be represented by the Gaussian curvature.

[0076] Function and effect: Through rigorous analysis and reasonable assumptions of strain energy, this method transfers the mechanical characteristics of each silk thread to the curved surface. Therefore, only the modeling and analysis of the curved surface woven by silk threads are required. According to its mechanical properties, the connection between mechanics and geometry is established. For the main non-linear large deformation behavior, a complete representation method of its geometric internal quantities is established. For the mechanical characteristics of the device curved surface, based on the assumptions and analysis made by this method, according to the isometric deformation and the Gauss's Theorema Egregium, the bending strain energy of the device curved surface can be completely represented by the Gaussian curvature, and only the minimization of the bending strain energy represented by the Gaussian curvature after deformation needs to be solved, without the need to solve the contact and mechanical control equations, achieving the purpose of rapid calculation.

[0077] Step 2: Establishment of the reference configuration: Parametric representation of the initial configuration of the braided intracranial intervention device.

[0078] The initial configuration of the braided intracranial intervention device in the stress-free state can be regarded as a surface of revolution. In the parametric representation, to ensure the geometric compatibility condition of the out-of-plane displacement, the parametric surface should have at least second-order continuity both axially and circumferentially. Therefore, this method uses the following to parametrically represent the initial configuration:

[0079]

[0080] where N i (u) is a cubic spline function that controls the axial cross-section, M j (v) is a cubic closed function in the circumferential direction, P i，j (α1, α2,...) is a weighted function determined by the parameters to be solved and the deformation points, is the vector of parameters to be solved. N i (u) and M j (v) are used to control the initial configuration, and P i，j (α1, α2,...) is used to control the deformation. For the initial configuration that has not undergone deformation,

[0081] Function and effect: The surface parameterization adopted by this method considers the two dimensions of the axial and circumferential directions, and this approach conforms to the dimensions of the intervention device formed by silk thread weaving and its formation process. The deformation described by the Gaussian curvature requires at least second-order continuity. Given the uncertainties existing in the deformation process, this combination method can ensure that even when the continuity of is undetermined, the entire surface function still maintains at least second-order continuity. And this combination represents the deformation by the vector of parameters to be solved , and only the vector of parameters to be solved needs to be solved, achieving the purpose of rapid calculation.

[0082] Step 3. Input of the model: Parametric representation of the aneurysm wall.

[0083] When the braided wire completely conforms to the aneurysm wall, the deformation of the interventional device reaches its maximum value. Therefore, this method uses the aneurysm wall as the input of the model and takes the initial configuration of the stent in the stress-free state as a reference. By simulating the evolution of the input surface to minimize its strain energy and finally tend to the equilibrium state, the final configuration of the interventional device is obtained, as Figure 1 shown.

[0084] The aneurysm wall can be parametrically represented as:

[0085]

[0086] where N i and M j are consistent with the initial configuration, and the parameters are obtained by substituting the vertices of the aneurysm wall in STL format.

[0087] Function and effect: The first two terms N anu in w i and M j are consistent with the initial configuration w ref , ensuring that the deformation is referenced to the initial configuration. The deformation is completely determined by the function term , ensuring the formal consistency of the representation method. This method does not adopt the traditional contact determination method, does not require contact determination in each iteration step, nor does it require setting a penalty function separately in the Lagrangian action. Instead, from the perspective of curvature evolution, the aneurysm wall at the maximum deformation is regarded as the input and evolves along the direction of the minimum strain energy to the final configuration.

[0088] Step 4. Energy functional represented by Gaussian curvature

[0089] In the present invention, the parametric representation method is adopted to represent the surface of the instrument as a smooth function To achieve the curvature diffusion smoothing of the input model surface and make it gradually approach the reference configuration, thereby minimizing the strain energy, it is necessary to accurately calculate the mean curvature H and Gaussian curvature K of the surface.

[0090] First, the coefficients of the First Fundamental Form of the surface are:

[0091] E = w u ·w u , F = w u ·w v , G = w v ·w v

[0092] where, and are the tangent vectors of the surface in the directions of u and v, respectively.

[0093]

[0094] Among them, are the second-order mixed partial derivatives of the surface in the directions of u and v, respectively. is the unit normal vector of the surface, defined as:

[0095]

[0096] The mean curvature H and the Gaussian curvature K are:

[0097]

[0098] Among them, the denominator 2(EG - F 2 ) is the determinant of the first fundamental form, ensuring that the parameterization at this point remains non-degenerate during the deformation process. The mean curvature H measures the local bending degree of the surface at this point and is a combination of the first fundamental form and the second fundamental form, while the Gaussian curvature K reflects the intrinsic geometric properties of the surface at this point, representing the product of the curvatures at this point.

[0099] In the construction of the energy functional, the energy E represented by the mean curvature and the Gaussian curvature Willmore is defined as:

[0100] E Willmore = ∫ M (H 2 + λK)dA,

[0101] where λ is a tuning parameter used to balance the contributions of the mean curvature term and the Gaussian curvature term. This energy functional aims to achieve the smoothing and optimization of the surface by minimizing the line integral of the squared curvature and the Gaussian curvature.

[0102] Function and effect: This method takes the aneurysm wall as the input of the model and uses the initial configuration of the stent in the stress-free state as a reference. Through the energy minimization of the Willmore flow, it ensures that the deformation process is guided by the reference configuration. This mechanism ensures that the final obtained configuration of the interventional device not only has good smoothness but also can accurately fit the geometric shape of the aneurysm wall, achieving the minimization of strain energy and the best structural matching.

[0103] This method does not require the use of traditional contact determination methods or the setting of penalty functions in the Lagrangian action, which simplifies the numerical calculation process to a certain extent. Traditional contact determination methods require complex contact detection and processing in each iteration, while the introduction of penalty functions increases the complexity of the energy functional and the computational burden. By starting from the perspective of curvature evolution and using the Willmore energy to drive the surface to evolve along the direction of minimum strain energy, the efficiency and operability of the algorithm are improved.

[0104] Step 5: Solving the minimization of the energy functional

[0105] The Gaussian curvature is an intrinsic geometric property of the surface and is independent of the choice of coordinate system. In actual calculations, both the input surface and the reference surface use the natural coordinate system. To align the curvature of the input surface with that of the reference configuration, the curvature alignment energy E Alignment :

[0106] E Alignment = μ ∫ M ((H - H ref ) 2 + γ(K - K ref ) 2 ) dA

[0107] where H ref and K ref are the mean curvature and Gaussian curvature in the initial configuration respectively, and μ and γ are weight coefficients that regulate the weighted influence of the mean curvature alignment term and the Gaussian curvature alignment term respectively. Therefore, the comprehensive energy functional E is defined as:

[0108] E = E Willmore + E Alignment

[0109] By iterating the comprehensive energy functional E along the gradient direction, the evolution equation of the surface at each iteration step can be obtained:

[0110]

[0111] where Δ represents the Laplace - Beltrami operator of the surface, which is defined as:

[0112]

[0113] Through the chain rule of differentiation, the evolution equation of the surface can be reduced to the solution of the parameter to be determined :

[0114]

[0115] Set the convergence conditions, such as the energy change being less than a preset threshold or reaching the maximum number of iterations, terminate the iterative process, obtain the final parameters, and then obtain the surface expression of the optimized intervention device configuration:

[0116]

[0117] Function and effect: By aligning the parametric representation with the curvature, this method can effectively control the deformation direction of the intervention device, enabling it to evolve along a physically reasonable and computationally efficient path to the final configuration. By minimizing this energy functional, the surface tends to reduce local curvature fluctuations during the evolution process, thereby achieving overall smoothness. Compared with the traditional Mean Curvature Flow (MCF), due to the Laplace operator and in this method, which involves higher-order derivative terms, the final solution form is a fourth-order partial differential equation (PDE), making the flow process have a stronger inhibitory ability for sharp and unrealistic kinks and deformations, thus generating a smoother surface. When appropriate time steps and numerical integration methods are adopted, the fourth-order PDE theoretically has better stability characteristics and can effectively avoid problems such as numerical oscillations and surface collapse. And due to the sparsity of the Laplace operator matrix, sparse matrix operation libraries and parallel computing technologies can be used to further improve the calculation speed. This method uses the chain rule of differentiation to return the final solution object to the parameters that control the surface shape, with a simpler form and easier to construct a stable numerical solution format.

[0118] Step 6: Calculation of stress and strain

[0119] After obtaining the final surface w final , the deformation gradient tensor can be calculated according to the reference surface w ref :

[0120]

[0121] E′ = w′ u ·w′ u , F′ = w′ u ·w′ v , G′ = w′ v ·w′ v

[0122]

[0123] Then the Green-Lagrange tensor can be calculated as:

[0124]

[0125] For intervention devices with different materials and configurations, substituting the constitutive equation can obtain the strain, as Figure 1 shown. Taking the linear elastic constitutive equation as an example here, the calculation of stress is:

[0126] σ = λ(E xx + E yy )I + 2μE

[0127] where λ and μ are the Lame constants of the material, related to the elastic modulus and Poisson's ratio. I is the unit tensor, representing the contribution of volume expansion. E is the strain tensor, and its components include the normal strains Exx and Eyy in the x and y directions and the shear strain Exy.

[0128] Function and effect: The calculation of strain and stress can reveal the internal forces borne by the intervention device during the process of conforming to the aneurysm wall. This is crucial for ensuring the mechanical stability of the stent in the body. Currently, there is no calculation method based on mechanical principles that can quickly obtain stress and strain. This method starts from curvature driving and can complete the calculation of device stress and strain within dozens of seconds, analyze the stress distribution, and identify potential stress concentration areas, which may become weak points for device fracture or deformation. By optimizing the device configuration and material distribution, these problems can be effectively avoided, ensuring the reliability and durability of the device during long-term use. Stress and strain analysis provides a scientific basis for the selection of device materials and structural design. The differences in mechanical properties of different materials directly affect the stress distribution and deformation characteristics of the stent. Through simulation and optimization, the most suitable material combination and design parameters can be selected to meet clinical requirements and improve the overall performance and service life of the stent.

[0129] This method combines the Willmore flow energy and curvature alignment methods, and through efficient numerical solution and optimization algorithms, can quickly calculate the strain and stress distributions. This efficient calculation process greatly shortens the design cycle, making the stent design and optimization process more rapid and flexible.

[0130] The preferred specific embodiments of the present invention have been described in detail above. It should be understood that those of ordinary skill in the art can make many modifications and variations based on the concept of the present invention without creative labor. Therefore, all technical solutions that can be obtained by those skilled in the art in the technical field based on the concept of the present invention through logical analysis, reasoning, or limited experiments on the basis of the prior art should be within the protection scope determined by the claims.

Claims

1. A virtual release method for a curvature-driven braided intracranial interventional device, characterized in that: The method comprises the following steps: Step 1, performing strain energy analysis on the braided intracranial intervention device to determine the assumptions for establishing the initial configuration; Step 2, establishing a parameterized representation of the initial configuration of the braided intracranial intervention device; Step 3, inputting the parameters of the aneurysm wall to obtain the final configuration of the braided intracranial intervention device; Step 4, calculating the average curvature and Gaussian curvature of the instrument surface of the braided intracranial intervention device, and establishing an energy functional represented by the average curvature and Gaussian curvature; Step 5, introducing curvature alignment energy, merging it with the energy functional, iterating, setting convergence conditions, and obtaining a surface expression of the optimized braided intracranial intervention device configuration; Step 6: Calculate the stress and strain of the braided intracranial intervention device in the process of fitting to the aneurysm wall according to the surface expression.

2. A virtual release method for a curvature-driven braided intracranial interventional device as claimed in claim 1, characterized in that: The braided intracranial interventional device is made of braided silk threads. In step 1, the assumed conditions of the silk threads include: axial tensile effect of the silk threads is ignored during bending; the length of the silk threads does not change during deformation; and the cross section of the silk threads remains perpendicular to the central axis during deformation.

3. A virtual release method for a curvature-driven braided intracranial interventional device as claimed in claim 2, characterized in that: In step 1, the braided intracranial intervention device is regarded as a film-like surface, and the assumptions of the film-like surface include: ignoring the film force of the surface; ignoring the shear stress outside the surface; and the length of the curve inside the surface does not change during deformation.

4. The virtual release method of the curvature-driven braided intracranial interventional device according to claim 1, characterized in that: The braided intracranial intervention device is braided from nickel-titanium alloy wires or metal wires or polymer wires.

5. The virtual release method of the curvature-driven braided intracranial interventional device according to claim 1, characterized in that: In step 2, the initial configuration of the braided intracranial intervention device in a stress-free state is a rotating body.

6. A virtual release method for a curvature-driven braided intracranial interventional device as claimed in claim 5, characterized in that: In step 2, the following function is used to perform parameterized representation of the initial configuration: Among them, N i (u) is the cubic spline function controlling the axial section, M j (v) is a cubic closed function in the circumferential direction, P i，j (α1, α2, ...) are the weighted functions determined by the parameters to be determined and the deformation points, is the parameter vector to be determined, N i (u) and M j (v) is used to control the initial configuration, P i，j (α1, α2, ...) is used to control the deformation. For the initial configuration without deformation, 7. A virtual release method for a curvature-driven braided intracranial interventional device as claimed in claim 6, characterized in that: In step 3, the aneurysm wall at the time of maximum deformation is regarded as input, and evolves along the direction of minimum strain energy to the final configuration of the braided intracranial intervention device, and the aneurysm wall is parameterized by the following function: Among them, the parameters Derived from the apex of the aneurysm wall.

8. The virtual release method of the curvature-driven braided intracranial interventional device according to claim 7, characterized in that: In step 4, the device surface of the braided intracranial intervention device is represented as a smooth function The first basic form coefficient of the instrument surface is: E=w u ·w u ,F=w u ·w v ,G=w v ·w v in, and are the tangent vectors of the instrument surface in directions u and v, respectively, in, are the second-order mixed partial derivatives of the surface in directions u and v, is the unit normal vector of the surface, defined as: The mean curvature H and Gaussian curvature K are: The energy functional represented by the mean curvature H and Gaussian curvature K is: Yes willmore =∫ M (H 2 +λK)dA, Among them, λ is an adjustment parameter used to balance the contribution of the mean curvature term and the Gaussian curvature term.

9. A virtual release method for a curvature-driven braided intracranial interventional device as claimed in claim 8, characterized in that: In step 5, the curvature alignment energy is represented by the following function: E Alignment =μ∫ M ((HH rer ) 2 +γ(KK ref ) 2 )dA Among them, μ and γ are weight coefficients, which regulate the weighted influence of the mean curvature alignment term and the Gaussian curvature alignment term respectively. The comprehensive energy functional E is defined as: E=E Willmore +E Alignment By iterating the comprehensive energy functional E along the gradient direction, the evolution equation of each iteration of the surface can be obtained: Where Δ represents the Laplace-Beltrami operator of the surface, which is defined as: By using the chain rule of derivation, the surface evolution equation can be reduced to the parameter to be determined. The solution: Set the convergence condition. When the energy change is less than the preset threshold or reaches the maximum number of iterations, terminate the iteration process, obtain the final parameters, and then obtain the surface expression of the optimized interventional device configuration:

10. The virtual release method of the curvature-driven braided intracranial intervention device according to claim 9, characterized in that: In step 6, the final surface w is obtained final After that, according to w ref Calculate the deformation gradient tensor: E′=w′ u ·w′ u ,F′=w′ u ·w′ v ,G′=w′ v ·w′ v Then the Green-Lagrange tensor is calculated as: When the braided intracranial intervention device is linear elastic, the stress is calculated as: σ=λ(E xx +E yy )I+2μE.

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