Skeletal muscle deformation modeling method fusing biomechanical characteristics

Abstract

The invention relates to the technical field of skeletal muscle deformation modeling, in particular to a skeletal muscle deformation modeling method fusing biomechanical characteristics, and the method comprises the steps: calculating the variable elastic coefficient of a spring according to the initial length of the spring in a spring mass point model and the current length after deformation; updating the spring mass point model according to the nonlinear spring force; constructing a total potential energy function of the target skeletal muscle based on the volume constraint penalty term and the elastic potential energy term; updating the first improved model according to the volume constraint additional force and the spring stiffness function; adjusting an external force value acting on each vertex in the second improved model according to the force propagation attenuation coefficient; discretization processing and numerical solution are carried out on the motion equation corresponding to each mass point; and testing the fourth improved model, and outputting a skeletal muscle deformation model meeting a preset verification condition. According to the method, the nonlinear biomechanical characteristics and the dynamic deformation process of the skeletal muscle can be effectively processed, and the skeletal muscle deformation modeling efficiency is improved.

Description

Technical Field

[0001] This invention relates to the field of skeletal muscle deformation modeling technology, and in particular to a method for skeletal muscle deformation modeling that integrates biomechanical properties. Background Technology

[0002] Skeletal muscle, as a core component of the human musculoskeletal system, possesses complex nonlinear biomechanical properties such as hyperviscoelasticity, strain dependence, and anisotropy. The dynamic deformation process of skeletal muscle directly affects the accuracy of fields such as motor function simulation, clinical surgical planning, and rehabilitation device design. Therefore, skeletal muscle deformation modeling has become a research hotspot in interdisciplinary fields such as biomechanical simulation and medical image analysis. Currently, skeletal muscle deformation modeling methods are mainly divided into two categories: geometric modeling and physical modeling. Geometric modeling methods are mostly based on fitting and reconstructing muscle surface morphology data, focusing on restoring the external contour but neglecting the internal biomechanical properties of skeletal muscle, and failing to reflect the influence of muscle fiber stretching, contraction, shearing, and other mechanical behaviors on the deformation process. While physical modeling methods introduce simple mechanical models, they generally employ linear assumptions for simplification, ignoring the nonlinear mechanical characteristics inherent in skeletal muscle itself, as well as the real-time changes in mechanical parameters during dynamic movement. In practical applications, skeletal muscle deformation is a complex dynamic process significantly influenced by its own nonlinear biomechanical properties. Existing technologies cannot effectively integrate this nonlinear characteristic with dynamic deformation mechanism. When simulating complex deformation scenarios such as muscle stretching, contraction, and torsion, they are unable to accurately reflect the local mechanical response of skeletal muscles, such as the local strain distribution and deformation gradient after being subjected to force. This results in model deformation distortion and a large deviation from the actual deformation state of human skeletal muscles.

[0003] Chinese Patent Publication No. CN116364291A discloses a numerical simulation method for self-activated deformation of skeletal muscle based on computational fluid dynamics. This method involves first obtaining the distribution of the internal flow field of skeletal muscle through numerical simulation analysis using computational fluid dynamics, then approximating the distribution of skeletal muscle fibers using this internal flow field, and finally inputting the flow field information into Gaussian points in the finite element numerical model of the skeletal muscle using program code for subsequent mechanical deformation simulation analysis. However, this approach only combines computational fluid dynamics-based fiber distribution analysis with a finite element solid constitutive model of skeletal muscle. It cannot effectively handle the nonlinear biomechanical characteristics and dynamic deformation processes of skeletal muscle, resulting in the model failing to accurately reflect the local mechanical response of the skeletal muscle when simulating complex deformations, thus reducing the efficiency of skeletal muscle deformation modeling. Summary of the Invention

[0004] To address this, the present invention provides a skeletal muscle deformation modeling method that integrates biomechanical characteristics, thereby overcoming the problem that existing technologies cannot effectively handle the nonlinear biomechanical characteristics and dynamic deformation processes of skeletal muscles, resulting in the model failing to accurately reflect the local mechanical response of skeletal muscles when simulating complex deformations, thus reducing the efficiency of skeletal muscle deformation modeling.

[0005] To achieve the above objectives, this invention provides a method for modeling skeletal muscle deformation by incorporating biomechanical properties, comprising the following steps: S1. Based on the geometry of the target skeletal muscle, establish a spring-mass model containing mass points and springs connecting the mass points, and calculate the variable elastic coefficient of the spring based on the initial length and the current length after deformation in the spring-mass model. S2. Calculate the nonlinear spring force corresponding to the spring using the variable elastic coefficient and the change in the current length relative to the initial length, and update the spring mass model based on the nonlinear spring force to obtain a first improved model containing the nonlinear spring force. S3. Construct a volume constraint penalty term based on the deformation gradient of the spring in the first improved spring mass model, and construct an elastic potential energy term based on the integral of the preset elastic energy density function in the volume domain. Construct the total potential energy function of the target skeletal muscle based on the volume constraint penalty term and the elastic potential energy term. S4. Perform variational operation on the total potential energy function to obtain the volume constraint additional force corresponding to the target skeletal muscle, and construct a direction-dependent spring stiffness function based on the direction angle between the preset biomaterial principal direction and the spring axis. Update the first improved model based on the volume constraint additional force and the spring stiffness function to obtain a second improved model containing volume constraints. S5. Calculate the force propagation attenuation coefficient from each vertex in the second improved model to the external force point, and adjust the external force value acting on each vertex in the second improved model according to the force propagation attenuation coefficient to obtain the third improved model. S6. Based on the motion state of each particle in the third improved model, construct the motion equation corresponding to each particle, and discretize and numerically solve the motion equation corresponding to each particle based on the Euler method to obtain the fourth improved model. S7. Input the fourth improved model into the preset test software, test the fourth improved model based on the preset test plan, and output the skeletal muscle deformation model when the test results output by the fourth improved model meet the preset verification conditions.

[0006] Compared with the prior art, the beneficial effects of this application are as follows: By constructing a spring-mass model containing point masses and connecting springs, the variable elastic coefficient is calculated. The nonlinear spring force is obtained by combining the change between the current length and the initial length, and the model is updated to include the nonlinear spring force. Then, a volume constraint penalty term is constructed based on the deformation gradient, and an elastic potential energy term is constructed by combining the integral of the preset elastic energy density function over the volume domain. The volume constraint additional force is obtained through variational operation, and the model is updated by combining the direction-dependent spring stiffness function to obtain the second improved model. This model accurately adapts to the nonlinear biomechanical characteristics of skeletal muscle. The nonlinear response of the spring under stress and deformation can be obtained based on the variable elastic coefficient and the nonlinear spring force. The volume constraint penalty term avoids abnormal volume changes, and the direction-dependent stiffness function fits the main directional characteristics of biological materials. This overcomes the shortcomings of existing technologies in handling nonlinear characteristics. At the same time, the spring-mass model does not require complex mesh transformation and multi-segment data transfer, which greatly improves the modeling efficiency and makes the local mechanical response more consistent with the real situation.

[0007] By calculating the force propagation attenuation coefficient from each vertex to the external force point, and adjusting the external force value at the vertex, a third improved model is obtained. Then, based on the motion state of each mass point, the motion equation is constructed, and the fourth improved model is obtained by discretization using the Euler method. The effectiveness of the model is verified by combining a preset test plan. The force propagation attenuation coefficient accurately simulates the local propagation law of external force in skeletal muscle. The Euler method efficiently realizes the solution of dynamic motion equations, effectively adapts to the dynamic deformation process, and overcomes the problems of insufficient dynamic deformation simulation and local response distortion in existing technologies. The test verification steps ensure the accuracy of the model, eliminating the need for repeated adjustment of mesh parameters, simplifying the modeling process, further improving modeling efficiency, and making the simulation of complex deformation more consistent with the real mechanical behavior of skeletal muscle.

[0008] Furthermore, S1 includes the following steps: S11. Perform three-dimensional spatial discretization on the target skeletal muscle to obtain multiple mass points and springs connecting each mass point, and construct a spring-mass point model based on the spatial topological relationship of each mass point and the springs connecting each mass point. S12. Perform initial state calibration on each spring in the spring mass model to obtain the initial length of the spring, and obtain the current length of the spring during the simulation. Calculate the difference between the current length and the initial length to obtain the instantaneous length deformation of the spring. S13. Calculate the elastic coefficient adjustment for the instantaneous length deformation to obtain the variable elastic coefficient corresponding to each spring. The variable elastic coefficient corresponding to each spring is... The mathematical expression is: In the formula, Represents the initial elastic coefficient. Represents the nonlinear strength coefficient. Indicates the current length of the spring. Indicates the initial length of the spring. This represents the nonlinear shape control coefficient.

[0009] In this scheme, the target skeletal muscle is discretized in three-dimensional space and a spring-mass model is constructed. The topological relationship of the mass points is combined to ensure the fit between the model and the spatial structure of the skeletal muscle. The initial state of the spring is calibrated and the instantaneous length deformation is calculated to accurately capture the deformation of the spring. The elastic coefficient is dynamically adjusted based on the deformation to make the elastic coefficient adapt to the nonlinear mechanical characteristics of the skeletal muscle, thereby improving the accuracy and reliability of the simulation of the mechanical behavior of the skeletal muscle.

[0010] Furthermore, S2 includes the following steps: S21. Calculate the nonlinear spring force of each spring based on the variable elastic coefficient and the instantaneous length deformation, wherein the mathematical expression for the nonlinear spring force of each spring is: In the formula, In the spring-mass model, the connecting mass points With point mass The nonlinear spring force generated by the spring; S22. Based on the nonlinear spring force of each spring, the force state of each particle in the spring-mass model is adjusted to obtain the real-time force data of each particle. Based on the real-time force data of each particle, the spatial position of the particles in the spring-mass model and the connection state of the spring are updated to obtain the first improved model containing nonlinear spring force.

[0011] In this scheme, the nonlinear spring force is calculated by combining the variable elastic coefficient and the instantaneous length deformation. The force state of the mass is adjusted according to the spring force, real-time force data is obtained, and the spatial position of the mass and the connection state of the spring are updated synchronously. An improved model containing the nonlinear spring force is constructed to enhance the ability to represent the nonlinear mechanical behavior of skeletal muscle.

[0012] Furthermore, in S3, the total potential function of the target skeletal muscle The mathematical expression is: In the formula, Represents the volume field. Indicates the deformation gradient. The elastic potential energy density function representing the deformation gradient, Represents a volume element. This represents the penalty factor used to control the strength of volumetric constraints. This represents the rate of change in volume.

[0013] In this scheme, the total potential energy function of the target skeletal muscle is constructed, and the volume domain integral calculation related to elastic potential energy density and the constraint calculation related to volume change rate are incorporated. The volume constraint strength is adjusted according to the penalty factor to effectively constrain the volume change of skeletal muscle and improve the accuracy of skeletal muscle deformation state analysis.

[0014] Furthermore, S4 includes the following steps: S41. Perform variational operations on the total potential energy function to obtain the variational derivative of the total potential energy, and analyze the gradient of the penalty function corresponding to the volume constraint based on the variational derivative to generate the additional force of the volume constraint acting on the target skeletal muscle. The mathematical expression for the variational operation on the total potential energy function is: , The variation representing the total potential energy. The variational expression representing the deformation gradient, This represents the inverse transpose of the deformation gradient. Elastic potential energy density function representing the deformation gradient For deformation gradient Partial differential operations, volume constraint additional force The mathematical expression is: ; S42. Obtain the axial vector of the spring from the first improved model, and calculate the angle between the axial vector and the preset principal direction vector of the biomaterial. Based on a preset smooth transition function, map the angle to a spring stiffness value to construct a direction-dependent spring stiffness function, wherein the mathematical expression of the spring stiffness function is: , , , This represents the angle between the axial vector and the preset principal direction vector of the biomaterial. The spring stiffness value represents the angle between the axial vector and the preset principal direction vector of the biomaterial. This indicates the preset minimum spring stiffness value. This indicates the preset maximum spring stiffness value. This indicates that in each spring, from the point mass... To the point mass directional vector, Indicates the presupposed biomaterial at the mass point The principal direction vector, Represents a point mass The position vector, Represents a point mass The position vector; S43. Update the spring stiffness parameters and mass force state in the first improved model according to the volume constraint additional force and the spring stiffness function to obtain a second improved model containing volume constraints.

[0015] In this scheme, variational operations are performed on the total potential energy function to analyze the gradient of the penalty function corresponding to the volume constraint in order to generate the additional force of the volume constraint. At the same time, the spring axial vector is obtained and the angle between it and the principal direction vector of the biological material is calculated. The direction-dependent spring stiffness function is obtained by mapping. The model parameters and the force state of the mass point are updated by combining the additional force and the stiffness function, and a second improved model containing volume constraints is obtained, which effectively improves the fit and accuracy of the second improved model in simulating skeletal muscle deformation and mechanical properties.

[0016] Furthermore, in S5, the mathematical expression for the force propagation attenuation coefficient from each vertex to the point of external force application is: In the formula, This represents the actual magnitude of the force exerted on each vertex by the external force point after force propagation and attenuation in the second improved model. Indicates the initial magnitude of the external force. Indicates the force propagation attenuation coefficient. This represents the spatial distance between each vertex and the point of external force in the second improved model.

[0017] In this scheme, by determining the force propagation attenuation coefficient from each vertex to the point of external force application, the degree of attenuation of external force with spatial distance is quantified, accurately reflecting the propagation law of force in the second improved model, and improving the accuracy of mechanical response analysis of target skeletal muscle under external force.

[0018] Furthermore, in S6, the mathematical expression for the equation of motion corresponding to each particle is: In the formula, Indicates the first The mass of a point mass Indicates the first The position vector of a particle. Indicates time, Indicates the first The acceleration of a point mass Indicates the first The internal force vector acting on a particle. Indicates the first The vector of external forces acting on a particle.

[0019] In this scheme, by constructing the motion equations corresponding to each particle, the changes in the particle's mass and position are associated with the internal and external forces acting on it, thus clarifying the mechanical driving relationship of the particle's motion and improving the reliability of the model in simulating the dynamic motion process of skeletal muscle particles.

[0020] Furthermore, S7 includes the following steps: S71. Generate a corresponding test data sequence based on a preset test plan. The test data sequence includes multiple boundary conditions and multiple external force loading modes. S72. Import the fourth improved model into the preset test software, and apply the boundary conditions and external force loading modes in the test data sequence to the corresponding vertices of the fourth improved model in sequence, record the dynamic deformation response data of the fourth improved model under each test data, and obtain the test response dataset corresponding to each test data. S73. Automatically compare the test response dataset corresponding to each type of test data with the preset verification conditions. When the test response dataset corresponding to all test data meets the preset verification conditions, output the skeletal muscle deformation model. The preset verification conditions are used to verify and judge the dynamic deformation response data output by the fourth improved model. The preset verification conditions include the quasi-incompressibility error threshold, the deviation threshold between the displacement response and the preset displacement response, and the model deformation time threshold.

[0021] In this scheme, by generating test data sequences containing multiple boundary conditions and external force loading modes, the fourth improved model is systematically tested and dynamic deformation response data is recorded. Combined with preset verification conditions, automatic comparison and verification are performed, which can accurately control the model performance and finally output a skeletal muscle deformation model that meets the requirements of quasi-incompressibility, displacement response deviation and deformation time, effectively ensuring the accuracy of skeletal muscle deformation modeling. Attached Figure Description

[0022] Figure 1 This is a flowchart illustrating a method for modeling skeletal muscle deformation that incorporates biomechanical properties, according to an embodiment of the present invention. Figure 2 This is a schematic diagram showing the positions of points A and B on the surface of the trapezius muscle model. Figure 3 This is a comparison diagram of volume changes in an embodiment of the present invention; Figure 4 This is a schematic diagram showing the force situation at points A and B in an embodiment of the present invention. Detailed Implementation

[0023] The following detailed description illustrates the specific implementation method: like Figure 1 As shown, it is a flowchart illustrating a skeletal muscle deformation modeling method incorporating biomechanical properties according to an embodiment of the present invention, including the following steps: S1. Based on the geometry of the target skeletal muscle, establish a spring-mass model containing mass points and springs connecting the mass points, and calculate the variable elastic coefficient of the spring based on the initial length and the current length after deformation in the spring-mass model. S2. Calculate the nonlinear spring force corresponding to the spring using the variable elastic coefficient and the change in the current length relative to the initial length, and update the spring mass model based on the nonlinear spring force to obtain a first improved model containing the nonlinear spring force. S3. Construct a volume constraint penalty term based on the deformation gradient of the spring in the first improved spring mass model, and construct an elastic potential energy term based on the integral of the preset elastic energy density function in the volume domain. Construct the total potential energy function of the target skeletal muscle based on the volume constraint penalty term and the elastic potential energy term. S4. Perform variational operation on the total potential energy function to obtain the volume constraint additional force corresponding to the target skeletal muscle, and construct a direction-dependent spring stiffness function based on the direction angle between the preset biomaterial principal direction and the spring axis. Update the first improved model based on the volume constraint additional force and the spring stiffness function to obtain a second improved model containing volume constraints. S5. Calculate the force propagation attenuation coefficient from each vertex in the second improved model to the external force point, and adjust the external force value acting on each vertex in the second improved model according to the force propagation attenuation coefficient to obtain the third improved model. S6. Based on the motion state of each particle in the third improved model, construct the motion equation corresponding to each particle, and discretize and numerically solve the motion equation corresponding to each particle based on the Euler method to obtain the fourth improved model. S7. Input the fourth improved model into the preset test software, test the fourth improved model based on the preset test plan, and output the skeletal muscle deformation model when the test results output by the fourth improved model meet the preset verification conditions.

[0024] Specifically, S1 includes the following steps: S11. Perform three-dimensional spatial discretization on the target skeletal muscle to obtain multiple mass points and springs connecting each mass point, and construct a spring-mass point model based on the spatial topological relationship of each mass point and the springs connecting each mass point. S12. Perform initial state calibration on each spring in the spring mass model to obtain the initial length of the spring, and obtain the current length of the spring during the simulation. Calculate the difference between the current length and the initial length to obtain the instantaneous length deformation of the spring. S13. Calculate the elastic coefficient adjustment for the instantaneous length deformation to obtain the variable elastic coefficient corresponding to each spring. The variable elastic coefficient corresponding to each spring is... The mathematical expression is: In the formula, Represents the initial elastic coefficient. Represents the nonlinear strength coefficient. Indicates the current length of the spring. Indicates the initial length of the spring. This represents the nonlinear shape control coefficient.

[0025] In this embodiment, when performing three-dimensional spatial discretization on the target skeletal muscle, firstly, three-dimensional spatial morphological data of the target skeletal muscle is acquired using medical imaging scanning technology. Based on the three-dimensional spatial morphological data, a three-dimensional solid model of the target skeletal muscle is constructed. Subsequently, a uniform grid discretization algorithm is used to divide the three-dimensional solid model of the target skeletal muscle into several continuous discrete units in three-dimensional space according to a preset particle density threshold. The geometric center of each discrete unit is a particle, ensuring that all particles uniformly cover the three-dimensional spatial range of the target skeletal muscle. For the particles corresponding to adjacent discrete units, a spring is connected according to the spatial position correlation. The two ends of the spring are fixed to two adjacent particles, ensuring that the spring can simulate the mechanical connection relationship between adjacent tissues of the target skeletal muscle, thereby obtaining multiple particles and the spring connecting each particle. Further, the preset particle density threshold is determined based on the distribution density of skeletal muscle fibers and the accuracy requirements of mechanical analysis, while also taking into account computational efficiency. Values ​​are taken in different mechanical characteristic regions such as the muscle belly and tendon; for example, 5 particles are taken in the high mechanical analysis region of the muscle belly. Two tendon deformity areas were taken. It is suitable for simulation requirements of uniform grid discretization and mechanical connection.

[0026] The construction of a spring-mass model based on the spatial topological relationships of each mass point and the springs connecting them involves: first, calibrating the spatial coordinates of all acquired mass points, establishing a three-dimensional coordinate system, and recording the unique spatial coordinates of each mass point. This process clarifies the spatial topological relationships of the mass points, identifying their adjacency, hierarchy, and relative positional connections. Based on this spatial topological relationship, the two mass points corresponding to each spring are determined, ensuring that the connection relationship of the springs perfectly matches the spatial topological relationship of the mass points; that is, only adjacent mass points with mechanical connections are connected by springs. Subsequently, all mass points and their corresponding springs are integrated into the same three-dimensional model framework. The mass attributes of the mass points and the initial connection state of the springs are defined, and the spatial coordinate information of each spring and its two ends is associated, enabling the model to accurately reflect the spatial structure of the target skeletal muscle, ultimately constructing a complete spring-mass model.

[0027] The initial state calibration of each spring in the spring-mass model is performed to obtain its initial length. This involves first placing the spring-mass model in a naturally relaxed state without external force, where the spring is in its undeformed initial state. Using a three-dimensional spatial measurement tool, the three-dimensional spatial coordinates of the two ends of each spring in this relaxed state are read. The straight-line distance between the two ends is calculated using the formula for the distance between two points in space; this straight-line distance is the initial length of the spring. During calibration, each spring must be individually checked, and the coordinates of the mass points at both ends of each spring and the calculated initial length must be recorded. Simultaneously, it must be ensured that all springs are under the same natural relaxation condition to avoid external force interference that could lead to errors in the initial length measurement. After completing the initial length measurement of all springs, the initial lengths of all springs are stored in the parameter library of the spring mass model.

[0028] The instantaneous length deformation of the spring is calculated by subtracting the current length from the initial length. This includes: during the simulation, the dynamic three-dimensional spatial coordinates of each end mass point in the spring mass model are collected in real time. These coordinates change in real time with the simulated motion of the target skeletal muscle. Based on the real-time collected coordinates of the end mass points, the actual length of the spring at that moment is calculated again using the distance formula between two points in space; this is the current length of the spring. Then, the pre-stored initial length of the spring is invoked. According to the difference calculation rules, the current length of the spring is used. Subtract the initial length The obtained value is the instantaneous length deformation of the spring. If the calculation result is positive, it means that the spring is in a stretched state; if it is negative, it means that the spring is in a compressed state. During the calculation process, it is necessary to ensure that the coordinate measurement standards of the current length and the initial length are consistent to ensure the accuracy of the instantaneous length deformation calculation, and at the same time, the deformation data of each spring is updated in real time.

[0029] Specifically, S2 includes the following steps: S21. Calculate the nonlinear spring force of each spring based on the variable elastic coefficient and the instantaneous length deformation, wherein the mathematical expression for the nonlinear spring force of each spring is: In the formula, In the spring-mass model, the connecting mass points With point mass The nonlinear spring force generated by the spring; S22. Based on the nonlinear spring force of each spring, the force state of each particle in the spring-mass model is adjusted to obtain the real-time force data of each particle. Based on the real-time force data of each particle, the spatial position of the particles in the spring-mass model and the connection state of the spring are updated to obtain the first improved model containing nonlinear spring force.

[0030] In this embodiment, the force state of each mass in the spring-mass model is adjusted based on the nonlinear spring force of each spring to obtain real-time force data for each mass. This includes: firstly, identifying the connecting springs corresponding to each mass in the spring-mass model; each mass is connected to other mass via springs, and each connecting spring generates a corresponding nonlinear spring force. For each mass, the nonlinear spring forces generated by all springs connected to that mass are collected one by one, combined with the forces of the mass connected to the springs. With point mass The positional relationship determines the direction of each nonlinear spring force, and the direction of each nonlinear spring force is always along the connecting mass point. With point mass The direction of the spring axis. All nonlinear spring forces acting on the mass point are vector-superimposed, and other additional forces that may exist in the model (such as damping force, external load, etc., if the model includes them) are also included. The resultant force on the mass point is calculated by the principle of mechanical synthesis, which is the real-time force data of the mass point. This accurately reflects the influence of each nonlinear spring force on the force state of the corresponding mass point, and finally the real-time force data of all mass points are obtained.

[0031] The spatial positions of the particles and the connection states of the spring-mass model are updated based on the real-time force data of each particle, resulting in a first improved model incorporating nonlinear spring forces. This model involves: deriving the particle's acceleration based on the real-time force data and the inherent mass of each particle using dynamic principles; then integrating the acceleration over a time step to obtain the instantaneous velocity and displacement increment of the particles. The spatial coordinates of the corresponding particles in the spring-mass model are adjusted according to the displacement increment, thus updating the particle's spatial position. Simultaneously, the connected particles are recalculated based on the updated spatial positions. With point mass The instantaneous length deformation of the spring is used to determine whether the connection relationship of the spring remains stable (e.g., whether it is within the effective connection range, without breakage or detachment). If the connection state remains unchanged, the original connection relationship is maintained; if the connection state changes, the connection relationship of the corresponding spring is adjusted synchronously. The updated spatial position of the mass point and the spring connection state are integrated to form a complete first improved model that includes nonlinear spring forces.

[0032] Specifically, in S3, the total potential energy function of the target skeletal muscle The mathematical expression is: In the formula, Represents the volume field. Indicates the deformation gradient. The elastic potential energy density function representing the deformation gradient, Represents a volume element. This represents the penalty factor used to control the strength of volumetric constraints. This represents the rate of change in volume.

[0033] Specifically, S4 includes the following steps: S41. Perform variational operations on the total potential energy function to obtain the variational derivative of the total potential energy, and analyze the gradient of the penalty function corresponding to the volume constraint based on the variational derivative to generate the additional force of the volume constraint acting on the target skeletal muscle. The mathematical expression for the variational operation on the total potential energy function is: , The variation representing the total potential energy. The variational expression representing the deformation gradient, This represents the inverse transpose of the deformation gradient. Elastic potential energy density function representing the deformation gradient For deformation gradient Partial differential operations, volume constraint additional force The mathematical expression is: ; S42. Obtain the axial vector of the spring from the first improved model, and calculate the angle between the axial vector and the preset principal direction vector of the biomaterial. Based on a preset smooth transition function, map the angle to a spring stiffness value to construct a direction-dependent spring stiffness function, wherein the mathematical expression of the spring stiffness function is: , , , This represents the angle between the axial vector and the preset principal direction vector of the biomaterial. The spring stiffness value represents the angle between the axial vector and the preset principal direction vector of the biomaterial. This indicates the preset minimum spring stiffness value. This indicates the preset maximum spring stiffness value. This indicates that in each spring, from the point mass... To the point mass directional vector, Indicates the presupposed biomaterial at the mass point The principal direction vector, Represents a point mass The position vector, Represents a point mass The position vector; S43. Update the spring stiffness parameters and mass force state in the first improved model according to the volume constraint additional force and the spring stiffness function to obtain a second improved model containing volume constraints.

[0034] In this embodiment, obtaining the axial vector of the spring from the first improved model includes: firstly, calling the first improved model containing nonlinear spring forces, extracting the connection relationships of all springs and the position information of the corresponding mass points in the first improved model, and clarifying the mass points connected to each spring. With point mass Read the particle from the first improved model. Position vector and particle The position vector is used to calculate the position vector of each spring from the mass point. To the point mass The direction vector is the axial vector of the spring.

[0035] Mapping the directional angle to a spring stiffness value based on a preset smooth transition function includes: first, calculating the directional angle between the spring's axial vector and the preset biomaterial principal direction vector; obtaining the cosine of the angle through vector dot product to ensure accurate correspondence between the values ​​of the axial vector and the preset biomaterial principal direction vector during the calculation. The preset smooth transition function is a cosine square function; the calculated cosine value of the angle is substituted into this function to obtain the result. Then, combining the preset minimum and maximum spring stiffness values, and following the calculation logic of the spring stiffness function, the difference between the preset minimum and maximum spring stiffness values ​​is multiplied by the smooth transition function result, and then added to the preset minimum spring stiffness value to map the angle to the corresponding spring stiffness value. The preset minimum spring stiffness value is determined based on the actual mechanical properties of the target skeletal muscle's non-biomaterial principal direction, and its value closely matches the minimum elastic stiffness in that direction, typically ranging from 100-500 N / m (adapting to the mechanical response of the skeletal muscle in the non-principal direction). The preset maximum spring stiffness value is determined based on the mechanical test data of the target skeletal muscle biomaterial in the principal direction. The value is matched with the highest elastic stiffness in that direction, usually 1000-5000 N / m (which matches the mechanical characteristics of the skeletal muscle in the principal direction).

[0036] When updating the spring stiffness parameters and mass force states in the first improved model based on the volume constraint additional force and the spring stiffness function, the original spring stiffness parameters in the first improved model are first replaced with the mapped spring stiffness values ​​according to the direction-dependent spring stiffness function, thus completing the spring stiffness parameter update. Then, the volume constraint additional force is superimposed on the real-time force data of the corresponding mass points in the first improved model, readjusting the force states of each mass point to obtain updated mass force data. Finally, the updated spring stiffness parameters and mass force states are integrated, and the adaptability of the spring connection state and the spatial position of the mass points is simultaneously verified to form a second improved model containing volume constraints.

[0037] Specifically, in S5, the mathematical expression for the force propagation attenuation coefficient from each vertex to the point of external force application is: In the formula, This represents the actual magnitude of the force exerted on each vertex by the external force point after force propagation and attenuation in the second improved model. Indicates the initial magnitude of the external force. Indicates the force propagation attenuation coefficient. This represents the spatial distance between each vertex and the point of external force in the second improved model.

[0038] Specifically, in S6, the mathematical expression for the motion equation corresponding to each particle is: In the formula, Indicates the first The mass of a point mass Indicates the first The position vector of a particle. Indicates time, Indicates the first The acceleration of a point mass Indicates the first The internal force vector acting on a particle. Indicates the first The vector of external forces acting on a particle.

[0039] Specifically, S7 includes the following steps: S71. Generate a corresponding test data sequence based on a preset test plan. The test data sequence includes multiple boundary conditions and multiple external force loading modes. S72. Import the fourth improved model into the preset test software, and apply the boundary conditions and external force loading modes in the test data sequence to the corresponding vertices of the fourth improved model in sequence, record the dynamic deformation response data of the fourth improved model under each test data, and obtain the test response dataset corresponding to each test data. S73. Automatically compare the test response dataset corresponding to each type of test data with the preset verification conditions. When the test response dataset corresponding to all test data meets the preset verification conditions, output the skeletal muscle deformation model. The preset verification conditions are used to verify and judge the dynamic deformation response data output by the fourth improved model. The preset verification conditions include the quasi-incompressibility error threshold, the deviation threshold between the displacement response and the preset displacement response, and the model deformation time threshold.

[0040] In this embodiment, as Figure 2 , Figure 3 and Figure 4As shown, the preset test plan is a systematic test plan pre-established to verify the biomechanical performance of the fourth improved model. It clearly defines the test types, boundary conditions, external force loading modes, test objects, and data acquisition standards. The preset test plan includes quasi-incompressibility verification (with or without volume constraints, a vertically downward external force of 5N), anisotropy verification (selecting two points A and B on the surface of the trapezius muscle model and applying external force along the surface normal vector), and real-time verification (performing compression / tension experiments on the trapezius muscle model and recording data using the Unity3D analyzer). The test object is the trapezius muscle model, and data acquisition covers deformation, displacement, and deformation time. The preset test software is a professional simulation testing tool used to import the fourth improved model, apply test conditions, collect dynamic deformation response data, and analyze test results. In this embodiment, the preset test software is Unity3D. Utilizing Unity3D's built-in model import, physical force loading, and analyzer functions, it supports the application of force and recording of deformation data at the model vertex level, can generate a visual test interface, and also has data statistical analysis capabilities for efficiency comparison in real-time verification. Furthermore, the quasi-incompressibility error threshold is 5%, the deviation threshold between the displacement response and the preset displacement response is 0.1 mm, and the model deformation time threshold is 30 ms. During the experiment with the fourth improved model, the following conditions must be met: quasi-incompressibility error ≤ 5%, in anisotropy verification, the deviation of the displacement response at points A and B from the reference standard is ≤ 0.1 mm, in real-time verification, the deformation time of the trapezius muscle model is ≤ 30 ms, meeting the 30 fps real-time rendering requirement in the Unity3D environment.

[0041] In step S71, based on a pre-defined test plan, a test data sequence containing various boundary conditions and external force loading modes is generated. First, boundary conditions are designed according to the pre-defined test plan. For quasi-incompressibility verification, two boundary conditions are set: one with volume constraints and one without. The external force loading mode is set to a constant downward force of 5N. For anisotropy verification, two points A and B at different locations on the surface of the trapezius muscle model are selected as test points. The loading mode is to apply a gradually varying external force (range 1-10N, gradient 1N) along the surface normal vector direction of the two test points. For real-time verification, the boundary condition is a free deformation constraint on the trapezius muscle model. The loading mode is to alternately apply compressive force (maximum 8N) and tensile force (maximum 6N). Simultaneously, the data sequence format is clearly defined to ensure that each boundary condition and loading mode corresponds to a unique identifier, providing a basis for subsequent application and data recording, and fully covering all verification scenarios in the pre-defined test plan.

[0042] In step S72, the fourth improved model is imported into the preset test scenario through the model import function of Unity3D software. After the import, the vertices of the fourth improved model are calibrated one by one to ensure that the vertex positions of the fourth improved model are consistent with the preset test scheme. Subsequently, according to the generated test data sequence, the boundary conditions and the external force loading mode are applied to the corresponding vertices of the fourth improved model in turn. During the application process, the loading status is monitored in real time through the Unity3D test interface. In the nearly incompressibility verification, a 5N vertical downward external force is applied to the fourth improved model with / without volume constraints respectively, and the volume change data is recorded synchronously; in the anisotropy verification, an external force is applied along the surface normal vector directions of points A and B on the trapezius muscle model surface, and the displacement responses of the two points are recorded in real time; in the real-time verification, a compression and stretching experiment is carried out on the trapezius muscle model, and the trapezius muscle deformation information and deformation time are recorded by using the analyzer built in Unity3D. The dynamic deformation response data under all test data are stored in a unified format and summarized to form a test response data set.

[0043] In step S73, the data comparison function of Unity3D is called to automatically compare the test response data set with the preset verification conditions, and the performance of the fourth improved model is verified item by item. In terms of nearly incompressibility, the volume change data with / without volume constraints is compared with the reference standard of the classical spring-mass system, and the volume change error is calculated. If the volume change error ≤ 5%, this item meets the standard; in terms of anisotropy, the deviation between the displacement responses of points A and B and the preset displacement responses is compared, and the deviation ≤ 0.1mm is qualified; in terms of real-time, the trapezius muscle deformation time recorded by the Unity3D analyzer is statistically analyzed, and the efficiency comparison results calculated by the two methods are shown in Table 1.

[0044] Table 1 Comparison table of calculation efficiency between this application and the classical spring-mass system

[0045] As shown in Table 1, the fourth improved model has an average deformation time of 10.47 ms and an average deformation frame rate of 95.51 fps, while the classic spring-mass system has an average deformation time of 9.31 ms and an average deformation frame rate of 107.41 fps. Although the fourth improved model has a slightly longer average deformation time and a slightly lower frame rate, it still meets the preset requirements of an average deformation time ≤ 30 ms and a frame rate ≥ 30 fps. Furthermore, the fourth improved model has better biomechanical rationality in terms of quasi-incompressibility and anisotropy, achieving a performance balance. When all three verifications are met, the dynamic deformation response data output by the fourth improved model is deemed to meet the preset verification conditions, and the skeletal muscle deformation model is output. If any verification item does not meet the preset verification conditions, the previous steps are returned to adjust the parameters of the fourth improved model, and steps S71 to S73 are re-executed for testing and verification. Experimental verification shows that the improved skeletal muscle deformation model can meet the real-time requirements while ensuring biomechanical rationality, providing an effective simulation model for massage training systems and biomechanical research.

[0046] The above are merely embodiments of the present invention. Commonly known structures and characteristics are not described in detail here. Those skilled in the art are aware of all common technical knowledge in the field prior to the application date or priority date, are aware of all existing technologies in that field, and have the ability to apply conventional experimental methods prior to that date. Those skilled in the art can, under the guidance of this application, improve and implement this solution in combination with their own capabilities. Some typical known structures or methods should not be obstacles for those skilled in the art to implement this application. It should be noted that those skilled in the art can make several modifications and improvements without departing from the structure of the present invention. These should also be considered within the scope of protection of the present invention, and will not affect the effectiveness of the implementation of the present invention or the practicality of the patent. The scope of protection claimed in this application should be determined by the content of its claims, and the specific embodiments described in the specification can be used to interpret the content of the claims.

Claims

1. A method for modeling skeletal muscle deformation by incorporating biomechanical properties, characterized in that: Includes the following steps: S1. Based on the geometry of the target skeletal muscle, establish a spring-mass model containing mass points and springs connecting the mass points, and calculate the variable elastic coefficient of the spring based on the initial length and the current length after deformation in the spring-mass model. S2. Calculate the nonlinear spring force corresponding to the spring using the variable elastic coefficient and the change in the current length relative to the initial length, and update the spring mass model based on the nonlinear spring force to obtain a first improved model containing the nonlinear spring force. S3. Construct a volume constraint penalty term based on the deformation gradient of the spring in the first improved spring mass model, and construct an elastic potential energy term based on the integral of the preset elastic energy density function in the volume domain. Construct the total potential energy function of the target skeletal muscle based on the volume constraint penalty term and the elastic potential energy term. S4. Perform variational operation on the total potential energy function to obtain the volume constraint additional force corresponding to the target skeletal muscle, and construct a direction-dependent spring stiffness function based on the direction angle between the preset biomaterial principal direction and the spring axis. Update the first improved model based on the volume constraint additional force and the spring stiffness function to obtain a second improved model containing volume constraints. S5. Calculate the force propagation attenuation coefficient from each vertex in the second improved model to the external force point, and adjust the external force value acting on each vertex in the second improved model according to the force propagation attenuation coefficient to obtain the third improved model. S6. Based on the motion state of each particle in the third improved model, construct the motion equation corresponding to each particle, and discretize and numerically solve the motion equation corresponding to each particle based on the Euler method to obtain the fourth improved model. S7. Input the fourth improved model into the preset test software, test the fourth improved model based on the preset test plan, and output the skeletal muscle deformation model when the test results output by the fourth improved model meet the preset verification conditions.

2. The method for modeling skeletal muscle deformation incorporating biomechanical properties according to claim 1, characterized in that: S1 includes the following steps: S11. Perform three-dimensional spatial discretization on the target skeletal muscle to obtain multiple mass points and springs connecting each mass point, and construct a spring-mass point model based on the spatial topological relationship of each mass point and the springs connecting each mass point. S12. Perform initial state calibration on each spring in the spring mass model to obtain the initial length of the spring, and obtain the current length of the spring during the simulation. Calculate the difference between the current length and the initial length to obtain the instantaneous length deformation of the spring. S13. Calculate the elastic coefficient adjustment for the instantaneous length deformation to obtain the variable elastic coefficient corresponding to each spring. The variable elastic coefficient corresponding to each spring is... The mathematical expression is: In the formula, Represents the initial elastic coefficient. Represents the nonlinear strength coefficient. Indicates the current length of the spring. Indicates the initial length of the spring. This represents the nonlinear shape control coefficient.

3. The method for modeling skeletal muscle deformation incorporating biomechanical properties according to claim 2, characterized in that: S2 includes the following steps: S21. Calculate the nonlinear spring force of each spring based on the variable elastic coefficient and the instantaneous length deformation, wherein the mathematical expression for the nonlinear spring force of each spring is: In the formula, In the spring-mass model, the connecting mass points With point mass The nonlinear spring force generated by the spring; S22. Based on the nonlinear spring force of each spring, the force state of each particle in the spring-mass model is adjusted to obtain the real-time force data of each particle. Based on the real-time force data of each particle, the spatial position of the particles in the spring-mass model and the connection state of the spring are updated to obtain the first improved model containing nonlinear spring force.

4. The method for modeling skeletal muscle deformation incorporating biomechanical properties according to claim 2, characterized in that: In S3, the total potential energy function of the target skeletal muscle The mathematical expression is: In the formula, Represents the volume field. Indicates the deformation gradient. The elastic potential energy density function representing the deformation gradient, Represents a volume element. This represents the penalty factor used to control the strength of volumetric constraints. This represents the rate of change in volume.

5. The skeletal muscle deformation modeling method incorporating biomechanical properties according to claim 4, characterized in that: S4 includes the following steps: S41. Perform variational operations on the total potential energy function to obtain the variational derivative of the total potential energy, and analyze the gradient of the penalty function corresponding to the volume constraint based on the variational derivative to generate the additional force of the volume constraint acting on the target skeletal muscle. The mathematical expression for the variational operation on the total potential energy function is: , The variation representing the total potential energy. The variational expression representing the deformation gradient, This represents the inverse transpose of the deformation gradient. Elastic potential energy density function representing the deformation gradient For deformation gradient Partial differential operations, volume constraint additional force The mathematical expression is: ; S42. Obtain the axial vector of the spring from the first improved model, and calculate the angle between the axial vector and the preset principal direction vector of the biomaterial. Based on a preset smooth transition function, map the angle to a spring stiffness value to construct a direction-dependent spring stiffness function, wherein the mathematical expression of the spring stiffness function is: , , , This represents the angle between the axial vector and the preset principal direction vector of the biomaterial. The spring stiffness value represents the angle between the axial vector and the preset principal direction vector of the biomaterial. This indicates the preset minimum spring stiffness value. This indicates the preset maximum spring stiffness value. This indicates that in each spring, from the point mass... To the point mass directional vector, Indicates the presupposed biomaterial at the mass point The principal direction vector, Represents a point mass The position vector, Represents a point mass The position vector; S43. Update the spring stiffness parameters and mass force state in the first improved model according to the volume constraint additional force and the spring stiffness function to obtain a second improved model containing volume constraints.

6. The method for modeling skeletal muscle deformation incorporating biomechanical properties according to claim 1, characterized in that: In S5, the mathematical expression for the force propagation attenuation coefficient from each vertex to the point of external force application is: In the formula, This represents the actual magnitude of the force exerted on each vertex by the external force point after force propagation and attenuation in the second improved model. Indicates the initial magnitude of the external force. Indicates the force propagation attenuation coefficient. This represents the spatial distance between each vertex and the point of external force in the second improved model.

7. The method for modeling skeletal muscle deformation incorporating biomechanical properties according to claim 1, characterized in that: In S6, the mathematical expression for the equation of motion corresponding to each particle is: In the formula, Indicates the first The mass of a point mass Indicates the first The position vector of a particle. Indicates time, Indicates the first The acceleration of a point mass Indicates the first The internal force vector acting on a particle. Indicates the first The vector of external forces acting on a particle.

8. The method for modeling skeletal muscle deformation incorporating biomechanical properties according to claim 1, characterized in that: S7 includes the following steps: S71. Generate a corresponding test data sequence based on a preset test plan. The test data sequence includes multiple boundary conditions and multiple external force loading modes. S72. Import the fourth improved model into the preset test software, and apply the boundary conditions and external force loading modes in the test data sequence to the corresponding vertices of the fourth improved model in sequence, record the dynamic deformation response data of the fourth improved model under each test data, and obtain the test response dataset corresponding to each test data. S73. Automatically compare the test response dataset corresponding to each type of test data with the preset verification conditions. When the test response dataset corresponding to all test data meets the preset verification conditions, output the skeletal muscle deformation model. The preset verification conditions are used to verify and judge the dynamic deformation response data output by the fourth improved model. The preset verification conditions include the quasi-incompressibility error threshold, the deviation threshold between the displacement response and the preset displacement response, and the model deformation time threshold.

Images