Integral modeling method and system based on nonlinear elastic potential energy model
Through the unified mechanical system modeling framework of the nonlinear elastic potential energy model, the problem of trajectory prediction of flexible needles in multi-layer heterogeneous tissues was solved, and the control accuracy and safety of flexible needles in complex environments were improved.
Patent Information
- Application Number
- CN202510802121.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-06-16
- Publication Date
- 2025-10-17
AI Technical Summary
Existing flexible needle kinematic models are generally based on the assumption of homogeneous tissue, which makes it difficult to accurately describe the mechanical behavior of the needle in multi-layer heterogeneous tissues. In particular, unexpected deflections are prone to occur in low-constraint environments such as cavities, and the friction hysteresis effect and viscoelastic energy dissipation between the needle and tissue are ignored.
Based on the nonlinear elastic potential energy model, the puncture needle and biological tissue are defined as a coupled system. The hyperelastic properties of the tissue are described by the exponential hardening model, and the tangent stiffness matrix is established. The axial-lateral decoupling modeling method is introduced to quantify the energy distribution of the axial propulsion force and the lateral bending force of the needle body. The contact boundary conditions are processed using the large number method to form a unified mechanical system modeling framework.
It significantly improves the accuracy of needle trajectory prediction in heterogeneous tissues, reduces unexpected deflections, improves the stability and accuracy of the model, adapts to the differences in mechanical properties of different tissue layers, and reduces the risk of tissue damage.
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Figure CN120809254A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the technical field of rehabilitation training, and particularly relates to a whole modeling method and system based on a nonlinear elastic potential energy model. BACKGROUND
[0002] Minimally invasive surgery has become an important direction of modern medical development due to its small trauma, fast recovery, and few complications. In this context, flexible puncture needle technology, as a key tool for realizing precise intervention of complex anatomical paths, has received widespread attention from the academic and clinical fields in recent years. Unlike traditional rigid needles, which can only puncture along a straight line, flexible needles can achieve a curved trajectory through active or passive deformation, thereby bypassing key structures such as bones, blood vessels, and nerves, and directly reaching the lesion target, significantly expanding the scope of minimally invasive surgery. Flexible needle technology, as a core innovation direction in the field of minimally invasive surgery, aims to achieve complex path puncture through a bendable needle body structure, breaking through the limitations of traditional rigid needle straight-line motion.
[0003] Current technology development presents the following characteristics: active and passive driving technologies are parallel: (a) Passive technology relies on the interaction between the needle body and the tissue, achieving trajectory control through external adjustment (such as rotation, feed) or structural optimization (such as programmable slope, inner core adjustment). (b) Active technology directly controls the deformation of the needle body through built-in driving (such as shape memory alloy, tendon driving, piezoelectric ceramic), reducing the dependence on tissue characteristics. These two technology routes have their own advantages and disadvantages. Passive flexible needles are generally simple in structure and small in diameter, but the control accuracy is greatly affected by tissue characteristics; active flexible needles have more direct and accurate control, but often require more complex driving mechanisms, increasing system complexity and diameter.
[0004] Clinical application requirements are the core driving force for the development of flexible needle technology. In neurosurgery, tumor ablation, prostate biopsy, and other scenarios, doctors often need to bypass key anatomical structures to reach deep target points. For example, in deep brain stimulation (DBS), electrodes need to be precisely implanted in specific nuclei without damaging the blood vessels and functional areas along the way; in prostate cancer brachytherapy, radioactive particles need to avoid the urethra and rectum to precisely distribute sources. These application scenarios have strict requirements for flexible needles, such as high-precision trajectory control, real-time deformation sensing, and minimal tissue damage, which directly guide the research direction of kinematic modeling methods.
[0005] From the perspective of technological development, the research of flexible needle has experienced an evolution from empirical operation to model-based control. Early research mainly relied on the experience of doctors' hands, lacking systematic theoretical guidance. With the rise of robotic-assisted surgery, model-based precise control algorithms have become the focus of research. This shift has made flexible needle technology move from "art" to "science", laying the foundation for automated and intelligent puncture. At the same time, advances in materials science have also opened up new possibilities for flexible needle design, such as the application of shape memory alloys, super-elastic materials, and intelligent polymers, greatly expanding the performance boundaries of flexible needles. In this macro context, the kinematic modeling of flexible needles serves as a bridge connecting mechanical design and clinical application, and is the theoretical basis for precise control. A good kinematic model can accurately predict needle deformation and trajectory, providing a mathematical framework for control algorithms.
[0006] The kinematic modeling of passive flexible needles has been the core of early research in this field, and its theoretical basis lies in describing the complex mechanical interaction between the needle body and the tissue. Since the steering ability of passive flexible needles completely depends on the interaction between the needle body and the tissue, accurately modeling this interaction is crucial for predicting the puncture trajectory. This research direction has developed various modeling frameworks, from early geometric simplification methods to later nonholonomic constraint theories.
[0007] The Jacobian matrix method represents an early attempt at modeling passive flexible needles. By defining the needle tip operation Jacobian matrix, it establishes a direct relationship between the 3 degrees of freedom of the needle base and the 3 degrees of freedom of the needle tip. This method treats the needle body as a series of rigid links, describing the motion transmission between each link through differential geometry. Although the Jacobian matrix method is theoretically simple, its assumption of ignoring tissue constraints leads to significant shortcomings in practical applications. When the needle body interacts with dense tissue, the reaction force generated by the tissue will significantly change the needle deformation behavior, making the pure kinematic-based method have large prediction errors. In addition, this method causes significant damage to the tissue, limiting its application in sensitive areas such as brain tissue.
[0008] In response to the limitations of the Jacobian matrix method, researchers based on the nonholonomic constraint kinematics theory and Lie group theory of single-slope needle puncture proposed the "bicycle model" and "monocycle model". This theory incorporates the asymmetric mechanical properties of the needle tip slope into the model, analogous to the steering mechanism of a bicycle front wheel, describing the bending motion of the needle body as a combination of feed along the tangent direction and rotation around the axis. The core idea of the bicycle model is that when the slope is forward punctured, the tissue generates a lateral force on the needle tip, causing the needle body to bend; when the needle body rotates, the slope direction changes, thereby adjusting the bending direction. This modeling method first combines the geometric properties of the needle tip with the mechanical response of the tissue, greatly improving the accuracy of trajectory prediction.
[0009] On the basis of the bicycle model, the researchers further proposed a bicycle model with a return journey, which was verified by experiments to be adaptable in complex organizational environments. The return mechanism takes into account the trajectory changes when the needle is withdrawn, expanding the model's clinical application scenarios, such as multiple puncture adjustments and path corrections. At the same time, a rotation feed strategy based on duty cycle was proposed, which controls the time ratio of needle rotation and feeding to achieve flexible steering within the maximum curvature range. Although the duty cycle method can achieve precise trajectory control in theory, its frequent rotation operation mode can cause tissue damage in practice, especially in fragile organs such as the liver and prostate, which may cause bleeding and inflammation.
[0010] The core feature of active flexible needles is to directly control the deformation of the needle body through built-in driving mechanisms, breaking free from the dependence on tissue interaction. This technical route provides a new approach to solving the control problems of passive flexible needles in cavities and complex heterogeneous tissues, while also bringing more complex mechatronic system design and kinematics modeling challenges. The modeling of active flexible needles needs to consider multiple factors such as the motion transmission of the driving mechanism, the mechanical properties of the needle material, and environmental constraints, forming a theoretical framework different from passive methods.
[0011] The tendon-driven scheme provides active flexible needles with faster response capabilities, and its working principle is similar to the antagonistic action of the human muscle-skeleton system. This design usually distributes multiple tendons along the circumference of the needle, and by adjusting the tension ratio of each tendon, it can achieve controllable bending in three-dimensional space. From a kinematics perspective, tendon-driven needles can be modeled as continuum robots, using Cosserat rod theory or piecewise constant curvature assumptions to describe their deformation behavior. The main challenges of tendon-driven technology are motion coupling and friction loss. The tension distribution in the multi-tendon system is complexly coupled, making inverse kinematics difficult to solve; the sliding friction of tendons in narrow channels can cause control accuracy to decline. To solve these problems, researchers have developed simplified methods based on pseudo-rigid body models and static models that take into account friction effects.
[0012] Modular design is another important direction to improve the performance of tendon-driven systems. A research team proposed a flexible arm with three-dimensional motion using modular design, each module having three separate chambers to achieve multi-degree-of-freedom motion. This design idea can be transplanted to the field of flexible needles, combining modules with different functions (such as bending modules, twisting modules) to build a puncture system that adapts to specific clinical needs
[0013] Magnetic navigation technology represents another path of active control. By guiding the magnetized needle body through external magnetic field, contactless and precise control can be achieved. By optimizing the distribution of magnetic materials and the configuration of external field strength, the expected deformation mode can be achieved. The advantage of magnetic navigation is that it does not need physical connection driving mechanism, but it needs to solve the key problems of magnetic field focusing, real-time imaging and safety.
[0014] Active bending of needle body can be achieved by laser heating shape memory alloy (SMA). By using the phase change characteristics of SMA, the preset shape can be restored when heated. This method can theoretically achieve precise curvature control and large bending angle, but has inherent defects such as long heating and cooling period and slow response speed. In terms of kinematic modeling, SMA driven needle needs to consider the coupling effect of temperature field distribution, phase change dynamics and mechanical deformation, which makes the model highly nonlinear and difficult to identify parameters. In addition, the risk of heat damage to surrounding tissues caused by high temperature also limits its application in sensitive areas.
[0015] Although significant progress has been made in flexible needle puncture technology, it still faces multiple challenges in the process of clinical transformation. From the perspective of kinematic modeling, existing methods have obvious shortcomings in prediction accuracy, real-time performance and tissue adaptability. Tissue heterogeneity is one of the main factors affecting the accuracy of kinematic model. Most existing modeling methods are based on the assumption of homogeneous tissue, while the actual human tissue has a complex layered structure and mechanical property distribution. Gray matter and white matter in brain tissue, blood vessel network in liver, gland and stroma in prostate, etc. will produce different resistance and deformation response to the needle body, and it is extremely challenging to establish a general model that can accurately describe the behavior of the needle body in multiple heterogeneous tissues.
[0016] Therefore, the existing technology has the problem that the existing kinematic model (such as bicycle model, Jacobian matrix method) is generally based on the assumption of homogeneous tissue, and it is difficult to accurately describe the mechanical behavior of the needle body in multiple heterogeneous tissues (such as elastic tissue-cavity-skeleton alternating structure). The sudden change of tissue stiffness leads to significant deviation between the predicted trajectory and the actual puncture path, especially in low constraint environments such as cavities, flexible needles are prone to unintended deflection. And the current flexible needle model relies too much on idealized contact assumptions, ignoring the friction hysteresis effect and viscoelastic energy dissipation between the needle body and the tissue. SUMMARY
[0017] The purpose of the present application is to provide a whole modeling method based on a nonlinear elastic potential energy model, aiming at solving the technical problems existing in the traditional method.
[0018] To solve the above problems, the present application provides a whole modeling method for the interaction between cannula type flexible needle and biological tissue based on a nonlinear elastic potential energy model, and the corresponding technical solution comprises:
[0019] Step 1, define the puncture needle and biological tissue as a coupling system, the interaction between the puncture needle and the biological tissue is defined as the internal force inside the coupling system, based on the overall mechanical analysis framework of the system, obtain the equation corresponding to the internal elastic potential energy;
[0020] Step 2, based on the classical plane Euler-Bernoulli elastic beam theory, the finite element method is used to model the mechanics of the puncture needle, to obtain the elastic potential energy equation and the basic stiffness matrix of the puncture needle due to deformation.
[0021] Step 3, define the potential energy of the exponential hardening model, and create the equation corresponding to the elastic potential energy stored due to the deformation of the biological tissue according to the potential energy of the aforementioned exponential hardening model;
[0022] Step 4, assume that the axial of the puncture needle remains linear response during the puncture process, only the lateral and rotation will introduce nonlinear response, and create the corresponding decoupling equation and tangential stiffness matrix according to the equation of step 3;
[0023] Step 5, combine the basic stiffness matrix and the tangential stiffness matrix to create the total potential energy equation of the coupling system, and combine the feed freedom of the linear motorized slide to obtain the final kinematic model of the operable puncture needle system.
[0024] Further, the equation corresponding to the aforementioned internal elastic potential energy is:
[0025]
[0026] In the formula: U e represents the potential energy of the puncture needle-biological tissue system unit; represents the elastic potential energy stored by the manipulable flexible needle unit, i.e. the puncture needle due to deformation; represents the elastic potential energy stored due to the deformation of the biological tissue.
[0027] Further, the elastic potential energy equation in the aforementioned step 2 is
[0028]
[0029] q e =[u i v i θ i u j v j θ j ](3)
[0030] The corresponding basic stiffness matrix is:
[0031]
[0032] In the formula, q eNode displacement vector of the representation unit; Base stiffness matrix of the representation unit.
[0033] Further, the potential energy equation of the exponential stiffening model in the aforementioned step 3 is:
[0034] Let the node displacement be j, the node velocity be v j , and the rotation angle be θ j , then the potential energy of the exponential stiffening model is defined as:
[0035]
[0036] where k y0 is the initial transverse stiffness of the biological tissue, k θ0 is the initial rotational stiffness of the biological tissue, α is the transverse stiffness exponential coefficient, and β is the rotational stiffness exponential coefficient.
[0037] The equation corresponding to the elastic potential energy (i.e., the direction-dependent elastic potential energy) stored due to the deformation of the biological tissue is defined as:
[0038]
[0039] Further, the decoupling equation in the aforementioned step 4 is:
[0040]
[0041] The corresponding transverse force and rotational moment are obtained by taking the first-order derivative of the potential energy function with respect to displacement and rotation angle, i.e.:
[0042]
[0043] Taking the derivative of f y and τ θ , the tangent stiffness term is obtained:
[0044]
[0045] Since the axial displacement is ignored, the stiffness matrix only includes transverse and rotational degrees of freedom, so the tangent stiffness matrix is:
[0046]
[0047] Further, the total potential energy equation of the coupled system in the aforementioned step 5 is
[0048]
[0049] where P e is the unit node load array, and ∑ represents the stiffness equation set. When Π takes the stationary value, the equilibrium state of the coupled system can be calculated, i.e.:
[0050] (∑k needle +∑k tissue )q=Kq=P (15)
[0051] P=[P1 P2 P30τ e ] (16)
[0052] q=[0000 q x q y q θ ] (17)
[0053] The boundary condition (17) is introduced into the aforementioned tangential stiffness matrix by using the large number method, and an approximate relationship formula is obtained as follows:
[0054] ζK 1,1 q1+…+K 1,n q n ≈ζK 1,1 q1(18)
[0055] Further, the node displacement is obtained by the following formula:
[0056]
[0057] wherein is the modified stiffness matrix;
[0058] Finally, combined with the feeding degree of freedom of the linear motorized slide, the final kinematic model of the operable puncture needle system is obtained:
[0059]
[0060] wherein L is the feeding displacement of the linear motorized slide.
[0061] Under the guidance of the same inventive concept, the application further provides a whole modeling system of a nonlinear elastic potential energy model based on the foregoing method, which is characterized by comprising:
[0062] an internal elastic potential energy analysis unit, which is used for defining the puncture needle and the biological tissue as a coupled system, defining the interaction between the puncture needle and the biological tissue as an internal force inside the coupled system, and obtaining an equation corresponding to the internal elastic potential energy based on a whole mechanical analysis framework of the system;
[0063] a first elastic potential energy analysis unit, which is used for performing mechanical modeling on the puncture needle by using the finite element method based on the classical plane Euler-Bernoulli elastic beam theory, so as to obtain an elastic potential energy equation and a basic stiffness matrix of the puncture needle due to deformation;
[0064] a second elastic potential energy analysis unit for defining a potential energy of an exponential hardening model and creating an equation corresponding to an elastic potential energy stored due to deformation of the biological tissue according to the potential energy of the exponential hardening model;
[0065] a decoupling analysis unit for assuming that, in the puncture process of the puncture needle, the axial direction keeps a linear response, only the lateral direction and the rotation direction introduce a nonlinear response, and creating a corresponding decoupling equation and a tangent stiffness matrix according to the equation of the second elastic potential energy analysis unit;
[0066] a kinematic model analysis unit for combining the basic stiffness matrix and the tangent stiffness matrix, creating a total potential energy equation of the coupled system, and combining the feed freedom of the linear motorized slide to obtain a final kinematic model of the operable puncture needle system.
[0067] Implementing the embodiments of the present application will have the following beneficial effects:
[0068] Firstly, the present application proposes a unified mechanical system modeling framework, which regards the needle body and the biological tissue (including elastic tissue, cavity, bone, etc.) as a coupled system, describes the hyperelasticity characteristics of the tissue through an exponential hardening model, establishes a tangent stiffness matrix to adapt to the differences in mechanical properties of different tissue layers, and effectively solves the trajectory prediction problem of heterogeneous tissue puncture; secondly, the present application introduces a nonlinear elastic potential energy model, quantifies the energy distribution of the axial pushing force and the lateral bending force of the needle body respectively through an axial-lateral decoupling modeling method, and effectively constrains the contact boundary conditions of the needle body and the tissue by using the law of large numbers to accurately process, which significantly improves the modeling accuracy of the interaction force. BRIEF DESCRIPTION OF DRAWINGS
[0069] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, brief descriptions will be given to the drawings needed to be used in the embodiments or prior art descriptions. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.
[0070] Among them:
[0071] Figure 1 is the overall step flowchart of the present application;
[0072] Figure 2 is the simulation effect comparison of the method and the finite element simulation method described in the present application Figure 1 ;
[0073] Figure 3 is the simulation effect comparison of the method and the finite element simulation method described in the present application Figure 2 . DETAILED DESCRIPTION
[0074] With reference to the drawings of the embodiments of the present application, the technical solutions in the embodiments of the present application will be clearly and completely described, obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments of the present application, all other embodiments obtained by a person of ordinary skill in the art without creative labor fall within the protection scope of the present application.
[0075] It should be noted that all directionality indications (such as up, down, left, right, front, back, etc.) in the embodiments of the present application are only used to explain the relative position relationship, motion condition, etc. between components in a certain specific posture (as shown in the drawings), and if the specific posture changes, the directionality indications also change accordingly.
[0076] In addition, the description of “first”, “second” and the like in the present application is only for the purpose of description, and cannot be understood as indicating or implying the relative importance of the indicated technical features or implicitly indicating the number of the indicated technical features. Therefore, the features defined as “first”, “second” can explicitly or implicitly include at least one of the features. In addition, the technical solutions of each embodiment can be combined with each other, but it must be based on the fact that a person of ordinary skill in the art can realize it, and when the combination of technical solutions appears contradictory or unachievable, it should be considered that the combination of technical solutions does not exist, and is not within the protection scope required by the present application.
[0077] For the deformation problem of the operable flexible needle under complex constraint conditions, the present application proposes a whole modeling method based on a nonlinear elastic potential energy model suitable for the interaction between the sleeve type flexible needle and the biological tissue. By regarding the needle body and the tissue (including elastic tissue, cavity, bone, etc.) as a unified mechanical system, the basic stiffness matrix and the tangential stiffness matrix of the needle body are established. The exponential hardening model is introduced to describe the hyperelasticity of the biological tissue, the axial-lateral decoupling modeling method is proposed, and the multiplication is effectively used to process the cantilever beam boundary constraint.
[0078] As Figure 1 A whole modeling method based on a nonlinear elastic potential energy model, comprising:
[0079] Step 1, define the puncture needle and the biological tissue as a coupled system, the interaction between the puncture needle and the biological tissue is defined as an internal force in the coupled system, based on the whole mechanical analysis framework of the system, the equation corresponding to the internal elastic potential energy is obtained;
[0080] Step 2, based on the classical plane Euler-Bernoulli elastic beam theory, the finite element method is used for mechanical modeling of the puncture needle, so as to obtain the elastic potential energy equation and the basic stiffness matrix stored by the puncture needle due to deformation.
[0081] Step 3, define the potential energy of the exponential reinforcement model, and create an equation corresponding to the elastic potential energy stored due to the deformation of the biological tissue according to the potential energy of the aforementioned exponential reinforcement model;
[0082] Step 4, assuming that the axial response of the puncture needle remains linear during the puncture process, only the lateral and rotational responses will introduce nonlinear responses, and the corresponding decoupling equation and tangential stiffness matrix are created according to the equation of step 3;
[0083] Step 5, combining the base stiffness matrix and the tangential stiffness matrix, creating the total potential energy equation of the coupled system and combining the feed freedom of the linear motorized slide, obtaining the final kinematic model of the operable puncture needle system.
[0084] In combination with the above, it can be seen that due to the fact that the traditional flexible needle kinematic model mainly relies on the simplified interaction assumption of the needle body and the tissue, the nonlinear mechanical properties of the biological tissue and the differences between the heterogeneous layers are ignored, resulting in a large trajectory prediction error. The specific problems include: insufficient modeling of tissue mechanics: biological tissues (such as elastic soft tissues, cavities, and bones) exhibit hyperelasticity, viscoelasticity, and anisotropy, and traditional linear elastic models cannot accurately describe their large deformation behavior; stiffness mismatch between heterogeneous layers: the stiffness of different tissue layers (such as skin, muscle, and blood vessels) in the puncture path can differ by several times, making it difficult for traditional homogenization models to adapt; rough handling of contact boundary conditions: the calculation of contact force between needle body and tissue does not consider nonlinear friction and dynamic contact state changes, resulting in model inaccuracy. The present invention creatively proposes a unified mechanical system modeling framework, treating the needle body and biological tissue (including elastic tissue, cavity, bone, etc.) as a coupled system, describing the hyperelasticity of the tissue through an exponential hardening model, establishing a tangential stiffness matrix to adapt to the mechanical property differences of different tissue layers, and effectively solving the trajectory prediction problem of heterogeneous tissue puncture. At the same time, the present invention introduces a nonlinear elastic potential energy model, quantifies the energy distribution of the needle advancement force and the bending force through axial-lateral decoupling, and uses the multiplication of large numbers to constrain the contact boundary conditions, i.e. through the decoupling equation to clearly distinguish the energy contribution of different motion modes, providing a theoretical basis for trajectory optimization. The multiplication of large numbers can effectively handle nonlinear contact problems, avoid numerical oscillation in iterative solution, and improve model stability. The traditional coupled model ignores the energy distribution difference, resulting in a deviation in force prediction. The simulation comparison of the two methods is shown in Figures 2-3 .
[0085] Further embodiments, the aforementioned step 1: the puncture needle and the biological tissue (including elastic soft tissue, cavity structure, bone, etc.) are regarded as a coupled system, based on the overall mechanical analysis framework of the system, the external load is only composed of the root reaction force and the torque equivalent to the tip; the interaction between the puncture needle and the biological tissue is modeled as an internal force within the system, and the corresponding equation for the internal elastic potential energy is:
[0086]
[0087] In the formula: U e represents the potential energy of the puncture needle-biological tissue system unit; represents the elastic potential energy stored by the steerable flexible needle unit due to deformation; represents the elastic potential energy stored due to the deformation of the biological tissue.
[0088] Further embodiments, the aforementioned step 2: based on the classical plane Euler-Bernoulli elastic beam theory, the finite element method is used to model the mechanics of the puncture needle, to obtain the elastic potential energy equation and the basic stiffness matrix of the puncture needle due to deformation, and the corresponding equations are respectively:
[0089]
[0090] q e = [u i v i θ i u j v j θ j ](3)
[0091]
[0092] In the formula, q e represents the node displacement vector of the unit; u i , v i , θ i respectively represent the displacement of the unit in the x direction, the displacement in the y direction and the rotation angle; represents the basic stiffness matrix of the unit.
[0093] Further embodiments, the aforementioned step 3: research shows that human soft tissue has the characteristics of nonlinearity, non-uniformity, viscoelasticity, etc., and generally has structured and hierarchical nature. In the medical puncture process, the movement of the puncture needle, i.e. the soft needle, can be divided into the following stages: the soft needle just contacts the skin layer, the skin tissue deforms biologically, and in this stage the soft needle is only subjected to the elastic force generated by the elastic properties of the soft tissue; The soft needle pierces the skin layer, at this time the needle body is subjected to the cutting force of the needle tip bevel in addition to the resistance of the skin layer; penetrate into multiple layers of tissue, the soft needle successively pierces the muscle layer, the fat layer, the organ tissue layer, and finally reaches the lesion target, in the process, the needle body is subjected to the friction force from the skin layer, the fat layer, the muscle layer, and the organ tissue layer. At the same time, due to the extrusion of the tissue on the needle tip bevel of the soft needle, the needle body will bend and thus also be subjected to the resistance of each layer of tissue.
[0094] The interaction between the needle and the tissue during the puncture process can involve various mechanisms, such as elastic deformation, viscous dissipation, and possibly plastic deformation or damage. Considering the response of biological tissue under compression or shear, they initially exhibit a softer response, with the stiffness gradually increasing as the deformation progresses, a phenomenon known as strain hardening. This hardening behavior is more consistent with an exponential growth, as the exponential function exhibits a slower initial growth followed by a rapid increase, which is closer to the hyperelastic properties of biological tissue.
[0095] In combination with the foregoing analysis, the following settings are made:
[0096] Let the node displacement be j, the node velocity be v j , and the rotation angle be θ j The potential energy of the exponential hardening model can be defined as:
[0097]
[0098] where k y0 is the initial lateral stiffness of the tissue, k θ0 is the initial rotational stiffness of the tissue, α is the lateral stiffness exponential coefficient, and β is the rotational stiffness exponential coefficient. The direction-dependent elastic potential energy is defined as:
[0099]
[0100] where x is the position coordinate along the axial direction of the puncture needle, and h is the rotational coordinate of the puncture needle.
[0101] In further embodiments, the aforementioned step 4:
[0102] During the puncture process of the puncture needle, the interaction between the puncture needle and the tissue has a clear direction dependence, with the mechanical response in the axial direction (along the needle length) and the lateral direction (perpendicular to the needle length) being significantly different. The decoupled modeling method can improve the calculation efficiency and accurately describe the physical properties. Since the axial tensile / compressive stiffness (EA) of the needle material (nickel-titanium alloy) is usually 1-3 orders of magnitude higher than the lateral bending stiffness (EI), the axial stiffness is much larger than the lateral stiffness, resulting in minimal axial deformation, which can be approximated as stiffness. In turn, the lateral displacement (bending) and rotation will induce nonlinear responses in the tissue, such as compression hardening, fiber stretching, etc. More importantly, since the axial stiffness of the needle is much larger than the lateral stiffness, it is assumed that the axial response remains linear, and only the lateral and rotational responses will introduce nonlinearity: the corresponding decoupled equations are created according to the equations of step 3 as follows:
[0103]
[0104] The lateral force and the rotational moment are obtained by taking the first-order derivative of the potential energy function with respect to the displacement and the rotation angle:
[0105]
[0106] f y and τ θ Taking derivative, the tangent stiffness term can be obtained:
[0107]
[0108] Since axial displacement is neglected, the stiffness matrix only contains lateral and rotational DOFs, and the tangential stiffness matrix is:
[0109]
[0110] Further embodiments, the aforementioned step 5:
[0111] The total potential energy equation of the coupled system is created, which is
[0112]
[0113] where P e is the unit nodal load array, τ e represents the tangential load associated with the needle, and ∑ represents the stiffness equation set. When Π takes the stationary value, the equilibrium state of the coupled system can be calculated, i.e.:
[0114] (∑k needle +∑k tissue )q=Kq=P (15)
[0115] P=[P1 P2 P30τ e ] (16)
[0116] Unlike the traditional finite element modeling method, the elastic system formed by the needle and the tissue is regarded as a whole, so the external force of all nodes except the first and last nodes is 0, and therefore the structure can be represented as:
[0117] q=[0000 q x q y q θ ] (17)
[0118] The boundary conditions are introduced into the above stiffness matrix by using the large number method. Specifically, the diagonal elements of the stiffness matrix corresponding to the known node displacements are multiplied by a large number ζ, and ζK 1,1 , ζK 2,2 , ζK 3,3 are used to replace K 1,1 , K 2,2 , K 3,3 , respectively, and the corresponding node loads are modified. Obviously, when ζ is large enough, the following approximate relationship holds:
[0119] ζK 1,1 q1+…+K 1,n qn ≈ζK 1,1 q1(18)
[0120] At this point, the node displacement can be obtained by the following formula:
[0121]
[0122] In the formula is the modified stiffness matrix.
[0123] For the operable puncture needle, the planar position of the needle tip is more concerned, and in combination with the feeding freedom of the linear motorized slide, the final kinematic model of the operable puncture needle system can be obtained:
[0124]
[0125] In the formula, L is the feeding displacement of the linear motorized slide, and n is the number of model nodes.
[0126] Under the same inventive concept guidance, the application also proposes a whole modeling system of a nonlinear elastic potential energy model based on the foregoing method, characterized by comprising:
[0127] An internal elastic potential energy analysis unit is configured to define the puncture needle and the biological tissue as a coupled system, define the interaction between the puncture needle and the biological tissue as an internal force inside the coupled system, and obtain an equation corresponding to the internal elastic potential energy based on a whole mechanical analysis framework of the system.
[0128] A first elastic potential energy analysis unit is configured to perform mechanical modeling of the puncture needle based on the classical planar Euler-Bernoulli elastic beam theory and using the finite element method, so as to obtain an elastic potential energy equation and a basic stiffness matrix of the puncture needle due to deformation.
[0129] A second elastic potential energy analysis unit is configured to define the potential energy of the exponential hardening model and create an equation corresponding to the elastic potential energy stored due to deformation of the biological tissue according to the potential energy of the foregoing exponential hardening model.
[0130] A decoupling analysis unit is configured to assume that the puncture needle keeps linear response in the axial direction during the puncture process and only the lateral and rotation directions will introduce nonlinear response, and create a corresponding decoupling equation and a tangential stiffness matrix according to the equation of the second elastic potential energy analysis unit.
[0131] A kinematic model analysis unit is configured to combine the basic stiffness matrix and the tangential stiffness matrix, create a total potential energy equation of the coupled system, and obtain the final kinematic model of the operable puncture needle system in combination with the feeding freedom of the linear motorized slide.
[0132] The above merely provides the preferred embodiment of the application, and cannot allude the protection scope of the application, therefore any equivalent changes made according to the claims of the application shall be within the scope of the application.
Claims
1. An overall modeling method based on a nonlinear elastic potential energy model, characterized in that: include: Step 1: Define the puncture needle and biological tissue as a coupled system, define the interaction between the puncture needle and biological tissue as the internal force within the coupled system, and obtain the equation corresponding to the internal elastic potential energy based on the overall mechanical analysis framework of the system; Step 2: Based on the classical plane Euler-Bernoulli elastic beam theory, the finite element method is used to perform mechanical modeling of the puncture needle to obtain the elastic potential energy equation stored by the puncture needle due to deformation and the basic stiffness matrix; Step 3: defining the potential energy of the exponential strengthening model, and creating an equation corresponding to the elastic potential energy stored due to deformation of the biological tissue based on the potential energy of the exponential strengthening model; Step 4: Assume that the puncture needle maintains a linear response in the axial direction during puncture, and only the lateral and rotational directions introduce nonlinear responses. Create the corresponding decoupling equations and tangential stiffness matrix based on the equations in step 3. Step 5: Combine the basic stiffness matrix and the tangential stiffness matrix to create the total potential energy equation of the coupled system and combine it with the feed freedom of the linear electric slide to obtain the final kinematic model of the operable puncture needle system.
2. The overall modeling method based on the nonlinear elastic potential energy model according to claim 1, characterized in that The equation corresponding to the aforementioned internal elastic potential energy is: Where: U e represents the potential energy of the puncture needle-biological tissue system unit; It represents the elastic potential energy stored in the maneuverable flexible needle unit, i.e., the puncture needle, due to deformation; It represents the elastic potential energy stored due to deformation of biological tissue.
3. The overall modeling method based on the nonlinear elastic potential energy model according to claim 1, characterized in that: The elastic potential energy equation in step 2 above is q e =[u i v i θ i u j v j θ j ](3) The corresponding foundation stiffness matrix is: Where q e represents the nodal displacement vector of the element; Represents the basic stiffness matrix of the element.
4. The overall modeling method based on the nonlinear elastic potential energy model according to claim 3, characterized in that: The potential energy equation of the exponential intensification model in step 3 above is: Let the node displacement be j and the node velocity be v j , the rotation angle is θ j , then the potential energy of the exponential reinforcement model is defined as: where k y0 is the initial lateral stiffness of the biological tissue, k θ0 is the initial rotational stiffness of the biological tissue, α is the lateral stiffness index coefficient, and β is the rotational stiffness index coefficient; The equation for the elastic potential energy stored due to deformation of biological tissue, i.e., the direction-dependent elastic potential energy, is defined as:
5. The overall modeling method based on the nonlinear elastic potential energy model according to claim 4, characterized in that: The decoupling equation in the above step 4 is: The corresponding lateral force and rotational torque are obtained by taking the first-order derivative of the potential energy function with respect to displacement and rotation angle, namely: f y and τ θ Taking the derivative, we get the tangent stiffness term: Since the axial displacement is neglected, the stiffness matrix only contains the lateral and rotational degrees of freedom, and the tangential stiffness matrix is:
6. The overall modeling method based on the nonlinear elastic potential energy model according to claim 5, characterized in that: The total potential energy equation of the coupled system in step 5 above is Among them, P e is the unit node load array, ∑ represents the stiffness equation group, and when π takes the stationary value, the equilibrium state of the coupled system can be calculated, that is: (∑k needle +∑k tissue )q=Kq=P (15) P=[P1 P2 P30τ e ] (16) q=[0000 q x q y q θ ] (17) The boundary condition (17) is introduced into the aforementioned tangential stiffness matrix using the method of large numbers, and the approximate relationship formula is obtained: ζK 1,1 q1+…+K 1,n q n ≈ζK 1,1 q1(18) Then the node displacement is obtained, which is specifically obtained by the following formula: In the formula is the modified stiffness matrix; Finally, combined with the linear electric slide's feed freedom, the final kinematic model of the operable puncture needle system is obtained: Where L is the feed displacement of the linear electric slide.
7. An overall modeling system of a nonlinear elastic potential energy model based on the method according to any one of claims 1 to 6, characterized in that: include: An internal elastic potential energy analysis unit is used to define the puncture needle and biological tissue as a coupled system, define the interaction between the puncture needle and biological tissue as the internal force within the coupled system, and obtain the equation corresponding to the internal elastic potential energy based on the overall mechanical analysis framework of the system; A first elastic potential energy analysis unit is used to perform mechanical modeling of the puncture needle using the finite element method based on the classical plane Euler-Bernoulli elastic beam theory to obtain the elastic potential energy equation stored in the puncture needle due to deformation and the basic stiffness matrix; a second elastic potential energy analysis unit, configured to define the potential energy of the exponential reinforcement model and create an equation corresponding to the elastic potential energy stored due to deformation of the biological tissue based on the potential energy of the exponential reinforcement model; A decoupling analysis unit is used to assume that the puncture needle maintains a linear response in the axial direction during puncture, and only the lateral and rotational directions introduce nonlinear responses, and to create corresponding decoupling equations and a tangential stiffness matrix based on the equations of the second elastic potential energy analysis unit; The kinematic model analysis unit is used to combine the basic stiffness matrix and the tangential stiffness matrix to create the total potential energy equation of the coupled system and combine it with the feed freedom of the linear electric slide to obtain the final kinematic model of the operable puncture needle system.