Dynamic simulation and isometric analysis system based on ligament

Abstract

The invention relates to the technical field of ligament simulation analysis, and discloses a ligament dynamic simulation and isometric analysis system. A dynamic data acquisition module of the system obtains three-dimensional deformation data and real-time stress data of a ligament in the movement process, and a ligament dynamic response database is established; the finite element grid division module generates a self-adaptive variable density grid according to ligament anatomical structure features, and maps dynamic response data to grid nodes; the real-time solving module performs time domain iterative calculation based on an explicit dynamics algorithm, and outputs stress field distribution and strain energy density under different motion phases; the isometric analysis module extracts a length change sequence and calculates a length change rate and a tension balance coefficient; the damage risk assessment module generates a micro-damage probability map according to the strain energy density peak value and the tension balance coefficient deviation threshold value, and can accurately analyze the dynamic mechanical behavior of the ligament and assess the damage risk.

Description

Technical Field

[0001] This invention relates to the field of ligament simulation analysis technology, specifically to a system based on ligament dynamic simulation and isometric analysis. Background Technology

[0002] In the fields of biomedical engineering and sports science, ligaments, as key soft tissues for maintaining joint stability, have always been a focus of research, particularly regarding their dynamic biomechanical behavior and injury risk assessment during exercise. Currently, most analytical methods for ligaments rely on static experimental measurements or simplified dynamic models, which struggle to fully reproduce the true stress and deformation characteristics of ligaments during exercise.

[0003] Traditional static measurement methods are typically performed on ex vivo specimens, obtaining ligament mechanical parameters by applying a fixed load. However, these methods cannot simulate the dynamic physiological environment of ligaments during human movement, neglecting the influence of motion phase changes on the stress state of the ligaments. This leads to significant deviations between the measurement results and the actual ligament mechanical response under physiological conditions. Furthermore, static measurements cannot capture the instantaneous deformation and stress fluctuations of ligaments at different stages of movement, making it difficult to reflect the cumulative process of dynamic ligament damage.

[0004] While existing dynamic analysis models attempt to incorporate dynamic factors, they often employ uniform mesh generation to handle ligament structures, failing to consider the heterogeneity of fiber orientation and collagen bundle distribution within the ligament's anatomy. This results in mesh nodes that cannot accurately match the mechanical properties of different ligament regions, thus affecting the accuracy of stress field distribution and strain energy density calculations. Furthermore, some models use fixed time-domain iteration steps during the solution process, failing to dynamically adjust calculation parameters based on changes in mesh node data, which can easily lead to slow iteration convergence or distorted calculation results.

[0005] In ligament isometry analysis and injury risk assessment, existing techniques often analyze length changes and stress distribution separately, failing to establish a correlation mechanism between the two. This makes it impossible to accurately calculate the coupling relationship between the rate of length change and the tension balance coefficient, resulting in an incomplete assessment of ligament stability. Furthermore, injury risk assessments often rely solely on a single strain energy density threshold, ignoring the impact of tension balance coefficient deviations on cumulative damage. This makes it difficult to generate a comprehensive probability map reflecting the state of ligament micro-injuries, thus limiting the effectiveness of ligament injury early warning and rehabilitation guidance. Summary of the Invention

[0006] The purpose of this invention is to provide a system based on ligament dynamic simulation and isometric analysis to solve the problems mentioned in the background art.

[0007] To achieve the above objectives, the present invention provides a system based on ligament dynamic simulation and isometric analysis, the system comprising: The dynamic data acquisition module is used to acquire three-dimensional deformation data and real-time force data of ligaments during exercise, and to establish a dynamic response database of ligaments. The finite element mesh generation module is used to generate an adaptive variable density mesh based on the ligament anatomical structure characteristics and to map the ligament dynamic response data to the mesh nodes. The real-time solution module is used to perform time-domain iterative calculations on mesh node data based on explicit dynamic algorithms, and output the ligament stress field distribution and strain energy density under different motion phases. The isochronism analysis module is used to extract the length change sequence of ligaments during the motion cycle and calculate the length change rate and tension balance coefficient by combining stress field distribution data. The damage risk assessment module is used to generate a probability map of ligament micro-damage based on the peak strain energy density and the deviation of the tension balance coefficient from the threshold.

[0008] Preferably, the dynamic data acquisition module performs the following process: Displacement trajectory data of ligament attachment points are collected using a high-speed optical marking system, and multi-dimensional load data of implanted force sensors are acquired simultaneously. After aligning the displacement trajectory data and multidimensional load data with timestamps, a ligament dynamic response database indexed by motion phase is established.

[0009] Preferably, the finite element mesh generation module execution process includes: Identify the orientation of ligament fibers and the distribution characteristics of collagen bundles, and configure high-density grid nodes along the main fiber direction; The mesh node density is dynamically adjusted based on the deformation gradient data in the ligament dynamic response database to generate a variable density mesh with deformation adaptability.

[0010] Preferably, the execution process of the real-time solving module includes: The central difference method is used to calculate the grid node acceleration, and the time-domain iteration step size is controlled by a dynamic relaxation factor. After each motion phase iteration, the stress field distribution and strain energy density spatial gradient data of the entire ligament are output.

[0011] Preferably, the execution process of the length equality analysis module includes: The attachment point spacing sequence was extracted from the ligament dynamic response database, and the length change rate between adjacent motion phases was calculated. By combining the stress field distribution data output by the real-time solver module, the tension balance coefficients of each ligament region are generated through the tension balancing algorithm.

[0012] Preferably, the tension equalization algorithm execution process includes: The ligament is divided into multiple functional zones, and the stress vector of each zone is calculated and its angle with the overall average stress is calculated. The zone-level tension balance coefficient is generated based on the degree of deviation of the included angle and the rate of change of length.

[0013] Preferably, the damage risk assessment module execution process includes: Identify grid nodes whose strain energy density exceeds the material yield threshold and calculate their spatial clustering. By combining the number of phases in which the tension balance coefficient continuously deviates, a spatial distribution map of the micro-damage probability is generated.

[0014] Preferably, the dynamic relaxation factor determination process includes: Monitor the rate of change of strain energy density in adjacent iterations, and trigger the relaxation factor decay when the rate of change exceeds a critical value; The time-domain iteration step size is recalculated based on the maximum acceleration of the grid nodes until the strain energy density change rate recovers to the stable range.

[0015] Preferably, the functional partitioning process includes: Based on the location of the ligament insertion point in anatomical structure, the ligament is divided into three basic sections: proximal, middle, and distal. Within each basic zone, it is further subdivided into anterior, middle, and posterior sub-zones based on the direction of the collagen bundles.

[0016] Preferably, the micro-damage probability map generation process includes: Establish a nonlinear mapping relationship between peak strain energy density and micro-damage probability; By superimposing the duration of the deviation of the tension balance coefficient as a probability weighting factor, a damage risk map with a time-cumulative effect is generated.

[0017] Compared with the prior art, the beneficial effects of the present invention are: This ligament dynamic simulation and isometric analysis system, through the collaborative work of its various modules, achieves precise analysis of ligament dynamic mechanical behavior and comprehensive assessment of injury risk. The dynamic data acquisition module can simultaneously acquire three-dimensional deformation data and real-time stress data of the ligament during movement, and establish a ligament dynamic response database indexed by the movement phase. Compared to traditional static measurement methods, it can completely capture the dynamic mechanical characteristics of the ligament at different stages of movement, reconstructing the true stress and deformation state of the ligament under physiological movement conditions, and providing more realistic basic data for subsequent analysis.

[0018] The finite element meshing module identifies the ligament fiber orientation and collagen bundle distribution characteristics based on the ligament's anatomical structure. High-density mesh nodes are configured along the main fiber direction, and the mesh node density is dynamically adjusted using deformation gradient data from the ligament dynamic response database, generating a variable-density mesh with deformation adaptability. This meshing method fully considers the heterogeneity of the ligament's anatomical structure, avoiding the problem of traditional uniform meshes failing to match the mechanical properties of different ligament regions. This allows the mesh nodes to accurately reflect the structural characteristics and deformation requirements of various ligament parts, providing a more accurate mesh model for subsequent real-time solutions and improving the accuracy of stress field distribution and strain energy density calculations.

[0019] The real-time solution module is based on an explicit dynamic algorithm and uses the central difference method to calculate the acceleration of the grid nodes. It controls the time-domain iteration step size through a dynamic relaxation factor, which can dynamically adjust the calculation parameters according to the rate of change of strain energy density in adjacent iteration steps. This avoids iteration convergence problems or result distortion caused by a fixed step size, and ensures that after each motion phase iteration, the stress field distribution and strain energy density spatial gradient data of the entire ligament can be output. This accurately presents the mechanical state of the ligament under different motion phases and provides detailed mechanical data support for isochronism analysis and damage risk assessment.

[0020] The isochronism analysis module extracts the attachment point spacing sequence from the ligament dynamic response database, calculates the length change rate between adjacent motion phases, and combines it with the stress field distribution data output by the real-time solution module. Using a tension equalization algorithm, the ligament is divided into multiple functional zones, and the stress vector sum of each zone and its angle with the overall average stress are calculated. Based on the degree of angle deviation and the length change rate, zone-level tension balance coefficients are generated. This process establishes a correlation mechanism between ligament length change and stress distribution, achieving coupled analysis of the ligament length change rate and tension balance coefficients. Compared to existing fragmented analysis methods, this provides a more comprehensive reflection of the ligament's stability state during the motion cycle.

[0021] The damage risk assessment module identifies grid nodes where strain energy density exceeds the material's yield threshold and calculates their spatial clustering. Simultaneously, it establishes a nonlinear mapping relationship between peak strain energy density and micro-damage probability by combining the number of phases with sustained deviations in the tension balance coefficient. The duration of tension balance coefficient deviation is then superimposed as a probability weighting factor to generate a spatial distribution map of micro-damage probability with a time-cumulative effect. This module overcomes the limitations of traditional damage assessments based solely on a single strain energy density threshold, fully considering the impact of tension balance coefficient deviation on damage accumulation. It can more comprehensively and accurately reflect the spatial distribution and temporal accumulation characteristics of ligament micro-damage, providing a more comprehensive analytical basis for ligament injury early warning and rehabilitation program development. Attached Figure Description

[0022] Figure 1This is a timing diagram of the ligament dynamic simulation and isometric analysis system described in this invention; Figure 2 This is a flowchart of the execution process of the dynamic data acquisition module; Figure 3 This is a flowchart of the execution process of the real-time solution module. Detailed Implementation

[0023] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0024] Please see Figure 1 This invention provides a system based on ligament dynamic simulation and isometric analysis. The system comprises a dynamic data acquisition module, a finite element mesh generation module, a real-time solution module, an isometric analysis module, and a damage risk assessment module. The modules work together to complete the dynamic simulation and isometric analysis of ligaments.

[0025] The dynamic data acquisition module is responsible for acquiring three-dimensional deformation data and real-time stress data of the ligaments during motion, and establishing a ligament dynamic response database through data processing. This database stores all acquired data indexed by the motion phase. The finite element mesh generation module generates an adaptive variable density mesh based on the anatomical characteristics of the ligaments, mapping the deformation and stress data in the ligament dynamic response database to the mesh nodes, ensuring the spatial continuity of the physical field data. The real-time solution module performs time-domain iterative calculations on the mesh node data based on an explicit dynamic algorithm, outputting the stress field distribution and strain energy density of the ligaments under different motion phases, thereby reflecting the mechanical state of the ligaments. The isometric analysis module extracts the ligament length change sequence during the motion cycle from the database, and calculates the length change rate and tension balance coefficient in combination with the stress field distribution data to evaluate the isometric properties of the ligaments. The damage risk assessment module generates a ligament micro-damage probability map based on the peak strain energy density and the deviation of the tension balance coefficient from the threshold, providing a basis for damage early warning. All modules are seamlessly connected through data interfaces to ensure the continuity and real-time performance of the simulation process.

[0026] Example 1: See Figure 2The dynamic data acquisition module is a multi-stage data capture and processing process, the core of which lies in simultaneously acquiring the geometric morphology and mechanical load information of ligaments under real-world motion conditions. A high-speed optical marking system forms the basis of this module's spatial data acquisition. This system typically consists of multiple high-frequency cameras positioned around the subject, installed in a spatial configuration to ensure unobstructed 3D reconstruction of the marker points. The markers are made of highly reflective material and are precisely adhered to the skin surface at the bone attachment points at both ends of the ligament under test, or fixed to bony landmarks via minimally invasive surgery. The cameras capture two-dimensional image sequences of the marker points at extremely high sampling frequencies, and the coordinates of each marker point in 3D space are calculated in real time using triangulation principles, thus forming displacement trajectory data of the ligament attachment points. This trajectory data accurately reflects the relative motion between the origin and insertion points of the ligament during walking, running, or specific joint flexion and extension movements, and is the basis for subsequent calculations of ligament length changes. Working in parallel with the optical marking system is an implanted force sensing unit, which is responsible for directly measuring the mechanical loads borne by the ligament tissue. The sensor employs a biocompatible miniaturized design, containing sensitive elements capable of sensing multidimensional mechanical signals (such as tensile and shear forces). The sensor is surgically implanted within the ligament parenchyma or near its attachment point, and its signals are transmitted to an external data receiving device via a built-in miniature transmitter or percutaneous suture. The acquired multidimensional load data includes information on the magnitude, direction, and point of application of the force, providing direct evidence for understanding the mechanical response of the ligament under dynamic loads. To ensure data temporal consistency, the system uses a high-precision synchronization signal generator to provide a unified time reference clock for the optical camera and force sensor data acquisition card, ensuring that each frame of image data and each mechanical data sample has a timestamp accurate to the millisecond level.

[0027] Timestamp alignment is a crucial step in data fusion. The acquisition software identifies and matches data points with the same timestamp from different data sources. For data asynchrony caused by transmission delays or minor differences in sampling times, timestamp-based interpolation algorithms are used for alignment correction. For example, using the time series of mechanical data, spline interpolation is used to calculate the mechanical load value precisely corresponding to each image frame moment. The aligned data, namely the three-dimensional coordinates of the attachment point and the corresponding multidimensional load, is segmented and organized according to the motion cycle. A complete motion cycle (such as a gait cycle) is divided into several consecutive motion phases, each phase representing a moment of action (such as heel strike, mid-stance, toe lift, etc.). All displacement trajectory data and mechanical load data related to this phase are categorized and stored, collectively forming a ligament dynamic response database indexed by motion phase. This database adopts a hierarchical data model, with the top layer being the motion cycle index, followed by the motion phases. Each phase entry stores the original and preprocessed displacement, force, and time information. The implementation of the finite element mesh generation module begins with an in-depth interpretation of the microscopic anatomy of the ligaments. This module needs to process ligament geometric model data from medical images (such as micro-CT or high-field MRI). Image processing algorithms are used to identify the orientation patterns of collagen fibers within the ligaments and the distribution density of collagen bundles. The algorithms trace the principal orientation field of the fibers by analyzing the grayscale gradients and texture features of image pixels. Based on the identified fiber orientations, the mesh generation engine begins to construct the computational mesh. Its core principle is to configure higher-density mesh nodes along the principal direction of the collagen fibers. This is because the main mechanical function of the ligament is borne by collagen fibers, and stress gradient changes along the fiber direction are usually more significant; higher node density helps to accurately capture the mechanical behavior of these areas. The choice of mesh element type depends on the geometric complexity of the ligament and the computational accuracy requirements; typically, tetrahedral or hexahedral elements, which can better simulate large deformation behavior, are used.

[0028] The adaptive nature of the mesh is reflected in its ability to dynamically adjust the node distribution based on deformation data fed back during simulation. The mesh generation engine reads the overall deformation gradient data of the ligament under different motion phases stored in the ligament dynamic response database. The deformation gradient tensor describes the degree of stretching and rotation in a local region. In regions with large deformation gradients, such as areas where stress concentrates during severe stretching of the ligament, the module automatically triggers a mesh refinement operation, increasing the number of nodes in that region to improve computational resolution. Conversely, in regions with relatively gentle deformation, mesh nodes are maintained or appropriately merged to reduce computational load. This variable density mesh strategy ensures the optimal spatial allocation of computational resources. The final generated mesh file contains not only node coordinates and element connectivity information, but also the material properties associated with each node (such as Young's modulus and Poisson's ratio) and the initial boundary conditions (such as initial displacement and prestress) mapped from the ligament dynamic response database.

[0029] The mapping process is a necessary step to assign the acquired physical field data from measurement points (markers, sensor locations) to grid nodes. Since measurement points and grid nodes typically do not coincide spatially, spatial interpolation algorithms are required. For displacement data, methods such as inverse distance weighted interpolation or radial basis function interpolation can be used to smoothly distribute the displacement trajectory data of the marker points to the nodes of the entire grid, based on the spatial distance between the measurement points and grid nodes. For mechanical data, the point loads measured by the implanted sensors need to be equivalently distributed to multiple grid nodes around the sensor according to Saint-Venant's principle, or applied as force boundary conditions in the corresponding regions. The entire process ensures that the continuum mechanics model can carry the real experimental observation data in a discretized form, laying the geometric and load foundation for subsequent numerical simulations. The quality of the grid, including the shape regularity of the elements and aspect ratio, is automatically checked and optimized after generation to avoid singular elements in the calculation that could lead to non-convergence.

[0030] Example 2: See Figure 3 The real-time solution module performs time-domain integration on the ligament finite element model with given initial and boundary conditions using an explicit dynamic algorithm, thereby solving for the model's dynamic response throughout the entire motion cycle. This module reads the mesh file generated by the finite element mesh generation module and the initial data mapped onto it, treating each motion phase as an independent transient dynamic problem for analysis. The explicit dynamic algorithm uses the central difference method for time recursion. This method is characterized by not requiring the assembly and inversion of the overall stiffness matrix; instead, it directly uses the nodal displacements and velocities of the current time step to calculate the acceleration, velocity, and displacement of the next time step. At the start of the calculation, based on the initial displacements and velocities of the mesh nodes and the applied load boundary conditions, the module obtains the internal and external force vectors of the nodes through nodal force calculation (involving element stress-strain relationships and constitutive model integration), and then calculates the instantaneous acceleration of each node according to Newton's second law.

[0031] After obtaining the nodal accelerations, the time integration process officially begins. The central difference method uses the acceleration and velocity of the current time step to explicitly update the velocity and displacement of the next time step. The entire time-domain iteration process advances step by step with a fixed time step size controlled by a dynamic relaxation factor. The dynamic relaxation factor, a scalar coefficient between 0 and 1, adjusts the actual computational step size to balance computational efficiency and numerical stability. The module monitors the response of the entire model system in real time, especially calculating the sum of strain energy densities of all elements and tracking its rate of change between adjacent iterations. The rate of change of strain energy density is an important indicator of the stability of the system's computational state. A rapid increase or increased oscillation may indicate that the calculation is deviating from the actual physical process or is facing the risk of numerical instability. The determination process of the dynamic relaxation factor is a typical closed-loop feedback control process. This factor is not fixed but dynamically adjusted based on real-time feedback during the calculation process. At the beginning of the iteration, the dynamic relaxation factor is set to a relatively conservative initial value to ensure stability during the initial computation phase. After each iterative calculation, the module immediately calculates the total strain energy density of the model in the current iteration and compares it with the total strain energy density of the previous iteration to obtain the absolute value of its rate of change. This rate of change is compared with a critical value pre-set based on experience or theoretical analysis, which defines the boundary of numerical stability. When the rate of change of strain energy density is detected to exceed this critical value, the control logic determines that the current calculation may face the risk of instability and then triggers the relaxation factor decay mechanism.

[0032] Relaxation factor decay is typically achieved by multiplying by a decay coefficient less than 1, such as multiplying the current factor value by 0.8, thereby immediately reducing the effective computational step size. The decayed dynamic relaxation factor is applied to the calculation of the next time step; a smaller step size means stricter constraints on time integration, helping to suppress numerical oscillations and divergences. While adjusting the relaxation factor, the module re-evaluates the motion state of all nodes in the mesh, paying particular attention to the maximum node acceleration. This is because the stable step size condition of the explicit algorithm is related to the system's highest natural frequency, and the maximum node acceleration indirectly reflects the severity of the system response. Based on the new, decayed dynamic relaxation factor and the maximum node acceleration in the current computational domain, the module recalculates the next permissible time-domain iteration step size, which is typically smaller than the previous step size. The computation continues with this new, smaller step size, and the module continuously monitors the rate of change of strain energy density. If the rate of change begins to fall and gradually enters a preset stable range (a relatively narrow numerical range indicating a stable system response), it indicates that the adjustment is effective and the computation has returned to a stable trajectory. The dynamic relaxation factor can remain constant, or, to improve computational efficiency while ensuring stability, it can be slowly increased until an optimal value balancing efficiency and stability is found. If the rate of change of strain energy density does not return to the stable range after step size adjustment, further attenuation may be necessary, or even pausing the calculation to check the rationality of model parameters or boundary condition settings. This process gives the solver a certain degree of adaptability, enabling it to cope with the numerical challenges posed by the drastic deformation or complex contact interactions that may occur in ligaments during motion.

[0033] After all iterative calculations for each motion phase are completed, the module outputs the complete mechanical state field data of the ligament model for that phase. This includes the stress tensor at each mesh node, which can be further processed to obtain the magnitude and direction of principal stresses, von Mises equivalent stresses, etc. Simultaneously, based on the calculated stress field and elastic constitutive relation, the module calculates the strain energy density element by element, i.e., the elastic deformation energy stored per unit volume. To more precisely describe the spatial distribution differences of the strain energy density, the module also calculates its spatial gradient data, reflecting the rate of change of strain energy density between different regions within the ligament, which is particularly important for identifying stress concentration areas. All these output data, including nodal stresses, element strain energy densities, and their gradients, are stored in a standard data format with corresponding motion phase identifiers, providing direct mechanical input for subsequent isochronism analysis and damage risk assessment.

[0034] Example 3: The implementation of the isometry analysis module focuses on quantifying the length stability of ligaments and the uniformity of their internal tension distribution during dynamic motion. This module relies on the data foundation processed by the preceding modules. The module first accesses the ligament dynamic response database, extracting a time-sequential sequence of ligament attachment point distances throughout the entire motion cycle. Each data point in this sequence represents the straight-line distance between the ligament's origin and insertion points, measured at a specific moment using a high-speed optical marking system. Since the motion cycle is pre-divided into several consecutive motion phases, the extracted distance sequence naturally corresponds to these phases, with each phase corresponding to an average distance value or an instantaneous distance value at a specific moment. The completeness of the sequence is crucial for subsequent analysis, as it fully records the length change trajectory of the ligament throughout a complete cycle from its initial state, through stretching and relaxation, to its final return to its initial state.

[0035] After acquiring the length sequence, the module calculates the rate of length change between adjacent motion phases. This calculation aims to quantify the severity or smoothness of ligament length changes. The calculation involves taking the distance between attachment points corresponding to two adjacent phases, calculating the absolute value of the difference, and then dividing this difference by the time interval between the two phases. The time interval is determined by a high-precision timestamp from the data acquisition system, providing high temporal resolution. The result is a sequence that changes over time (or with the motion phase), with positive values ​​indicating the ligament is in a stretching phase and negative values ​​indicating a retraction phase. The absolute value directly reflects the rate of length change. This rate of length change parameter is an important dynamic indicator for assessing ligament isometric properties; excessively rapid length changes may suggest joint kinematic abnormalities or weakened ligament restraint function.

[0036] After calculating the rate of change of length, the module needs to perform a more in-depth analysis of tension equalization by combining the stress field distribution data output by the real-time solver. The stress field distribution data provides spatial distribution information of the internal stress vectors of the ligament in each phase of motion. The core task of the tension equalization algorithm is to generate an index that can quantify the uniformity of tension distribution within the ligament, namely the tension balance coefficient. The algorithm first requires functional partitioning of the ligament, dividing the entire ligament geometric model into several anatomically or functionally significant sub-regions. Each sub-region contains a certain number of finite element mesh nodes, and the partitioning may be based on factors such as the anatomical insertion point of the ligament, the orientation characteristics of collagen fibers, or clinically relevant functional areas.

[0037] For each partition, the algorithm calculates its partition stress vector sum, a process involving vector summation of the stress tensors of all mesh nodes within that partition. The stress tensor is a second-order tensor, but when calculating the vector sum, its principal stress directions are typically considered, or it is decomposed and synthesized according to the coordinate system. Simultaneously, the algorithm calculates the average stress vector across all mesh nodes of the entire ligament; this overall average stress represents the overall stress state of the ligament during that motion phase. Next, the algorithm calculates the spatial angle between the stress vector sum of each partition and the overall average stress vector; the magnitude of this angle reflects the degree of deviation of the stress direction of that partition from the overall average stress direction.

[0038] To quantify this deviation and combine it with the effect of length variation, the tension balance coefficient for each zone is calculated using the following formula: ; in: This represents the calculated zone-level tension balance coefficient; the smaller the value, the more balanced the tension state of that zone is with the whole. The angle between the aforementioned zoned stress vector and the overall average stress vector is expressed in radians. This indicates taking the absolute value of the included angle; This represents the rate of change of length calculated in the current phase of motion. This is an adjustment function based on the rate of change of length. The function is designed so that its value increases accordingly when the rate of change of length is large, thereby reducing the weight of the angle deviation on the balance coefficient. This means that during the phase of rapid ligament length change, the algorithm's sensitivity to uneven tension distribution is moderately reduced to avoid misjudging normal dynamic mechanical responses as abnormal. The introduction of this adjustment function reflects the algorithm's understanding of ligament dynamic function; that is, during rapid expansion and contraction, temporary tension imbalances may be physiological.

[0039] The calculation process is repeated for each functional zone in each motion phase, ultimately outputting a zone-level tension balance coefficient sequence that varies over time (motion phase). This coefficient sequence, together with the length change rate sequence, constitutes the core result of the isometric analysis. They describe the functional state of the ligament during motion from different dimensions: the length change rate reflects the ligament's stretching and contraction at the macroscopic kinematic level, while the tension balance coefficient reveals the uniformity of load transmission at the internal mechanical distribution level. All of this generated data is structured and stored, and correlated with the corresponding motion phase information, providing key input parameters regarding the ligament's isometric characteristics and mechanical state for the final injury risk assessment module. The entire analysis process achieves a multi-faceted assessment of the ligament's dynamic mechanical behavior from macroscopic to microscopic levels, and from geometric to mechanical perspectives.

[0040] Example 4: Fine functional zoning of ligaments and execution of tension balancing algorithms based on this, illustrated below with a specific example. Consider dynamic isolength analysis of the anterior cruciate ligament (ACL) of the knee joint, which connects the femur and tibia; its isolength characteristics are crucial for knee joint stability. The functional zoning process strictly follows anatomical features. First, based on the two bony insertion points of the ligament, it is divided into three basic zones: the proximal zone is the area near the femoral attachment point, defined as approximately one-third of the ligament's total length extending from the femoral attachment point into the ligament parenchyma; the distal zone is the area near the tibial attachment point, similarly defined as approximately one-third of the ligament's total length extending from the tibial attachment point into the ligament parenchyma; the mid-section zone is the middle part connecting the proximal and distal sections, occupying approximately one-third of the remaining length. This zoning method reflects the differences in the mechanical functions that the ligament may bear in different segments. The proximal and distal sections usually directly bear the mechanical transmission from the bony insertion points, while the mid-section reflects more the mechanical behavior of the ligament parenchyma itself.

[0041] Within each basic zone, further subdivision is required based on the orientation of the collagen fiber bundles, determined by processing high-resolution ligament microstructure images or diffusion tensor imaging data. Within the proximal zone, based on the relative positions of the fiber bundles on the sagittal plane, it can be further subdivided into anterior, middle, and posterior sub-zones. The anterior sub-zone contains the fiber bundles located in the anterior part of the ligament that are first stretched during knee flexion; the posterior sub-zone contains the fiber bundles located in the posterior part of the ligament that play a major restraining role at specific angles; the middle sub-zone lies between the two. Similarly, the mid-section and distal zones are subdivided according to the same principle, ultimately dividing the entire anterior cruciate ligament into nine functional sub-zones (3 basic zones × 3 sub-zones). This multi-level zoning strategy allows biomechanical analysis to pinpoint the specific functional units of the ligament.

[0042] After defining the sub-regions, the tension equalization algorithm begins processing data for specific motion phases, such as the "mid-stance" phase in the gait cycle. The algorithm extracts stress tensor data from all finite element mesh nodes within each functional sub-region from the stress field results output by the real-time solver. For a given sub-region, such as the proximal-anterior deltoid sub-region, the algorithm iterates through all nodes within that sub-region, decomposing the stress tensor (a 3x3 matrix) of each node into principal stress directions or performing vector synthesis based on the global coordinate system, and then calculating the stress vector sum for that sub-region. The stress vector sum is a vector that roughly represents the direction and magnitude of the resultant internal force in space for that sub-region. Simultaneously, the algorithm calculates the average stress vector across all nodes of the entire anterior cruciate ligament (ACL), representing the overall stress trend of the ligament during that motion phase. The algorithm calculates the spatial angle between the stress vector sum of each sub-region and the overall average stress vector, obtained through vector dot product, and its magnitude reflects the degree of deviation of the force direction of that sub-region from the overall average direction. A small angle indicates that the force direction of that sub-region is consistent with the overall direction, while a large angle suggests that the force direction may deviate abnormally. For a comprehensive assessment, the dynamic stretching and contraction of the ligament in the current motion phase also needs to be considered, i.e., the rate of length change obtained from the isometric analysis module. The rate of length change serves as a moderating factor to correct the interpretation of angle deviations. For example, in phases where ligament length changes rapidly, a large angle deviation may fall within the normal physiological adaptation range; while in phases where length is relatively stable, even a small angle deviation may warrant attention.

[0043] Referring to Table 1, a hypothetical example is presented, showing some intermediate data and results obtained from the tension balancing algorithm calculation of the anterior cruciate ligament (ACL) in the "mid-stance" phase. The table lists the stress vector sums (expressed in vector form) for several representative functional sub-regions, the calculated angles with the overall average stress, the rate of length change for that phase, and the final tension balancing coefficient. Note that the data in the table are for illustrative purposes only; vector components are in megapascals (MPa), angles are in degrees, and the rate of length change is a dimensionless standardized value.

[0044] Table 1: Zone tension balance analysis data of the anterior cruciate ligament in the mid-stance phase Functional sub-division Stress vector and (X, Y, Z components) / MPa Angle with overall average stress / degrees Rate of change in length Tension balance factor Proximal - Anteversa (1.52,-0.83,0.41) 12.5 0.015 8.33 Proximal - Mesaversa (1.48,-0.91,0.38) 14.8 0.015 9.87 Proximal - Retroversa (0.95,-0.45,0.22) 25.3 0.015 16.87 Mid - Anteversa (1.61,-0.75,0.50) 8.7 0.015 5.80 Mid - Retroversa (0.88,-0.35,0.18) 28.9 0.015 19.27 Distal - Mesaversa (1.56,-0.88,0.45) 11.2 0.015 7.47 The schematic data reveals differences in the biomechanical states of different sub-regions. For example, the proximal-posterior and mid-posterior sub-regions exhibit larger angles, which may be related to their specific functions in the "mid-stance" phase. The calculation of the tension balance coefficient integrates information on angle deviation and length change rate. The magnitude of the coefficient value directly determines the degree of tension balance in that sub-region during a specific motion phase. A higher coefficient value indicates a poorer coordination between the tension state of that sub-region and the overall ligament. The algorithm repeats the above calculation process for each motion phase, thus obtaining a curve showing the change of the tension balance coefficient of each functional sub-region over time (or with the motion phase). These sub-regional coefficient data reveal subtle changes in the internal ligament mechanics more effectively than a single coefficient for the ligament as a whole, helping to accurately locate potential areas of biomechanical abnormality. For example, if the tension balance coefficient of a certain sub-region is consistently significantly higher than that of other sub-regions throughout the motion cycle, it suggests that this area may be subjected to abnormal loads and is a potential area of ​​injury risk. This fine-grained sub-regional analysis method provides detailed biomechanical evidence for a deeper understanding of ligament function.

[0045] Example 5: The damage risk assessment module transforms mechanical data into clinically interpretable risk information. This module performs a comprehensive analysis based on the strain energy density field and tension equilibrium coefficient sequence calculated by the preceding module. The module first scans the strain energy density field data output by the real-time solver, identifying mesh nodes whose values ​​exceed a preset material yield threshold. The material yield threshold is a key parameter set according to the biomechanical properties of the ligament, typically determined by the stress-strain curve obtained from ex vivo tissue tensile experiments. For each motion phase, the module traverses the entire ligament finite element model, comparing the strain energy density of all nodes with this threshold and marking all nodes that exceed it. These nodes are considered to have experienced mechanical overloads that could potentially cause microstructural damage under the corresponding motion phase.

[0046] After identifying potential overload nodes, the module needs to assess their spatial distribution characteristics, as the damage risk implied by an isolated single node overload differs from that implying a concentrated overload over a large area. The module employs a spatial clustering algorithm to analyze the clustering degree of these overload nodes. A commonly used method is density-based clustering, which searches for node clusters within a predetermined physical distance. The number of overload nodes in each cluster, the physical size of the cluster, and the average strain energy density value of the nodes within the cluster are calculated as fundamental indicators for assessing the damage risk of the area. A cluster containing a large number of high strain energy density nodes in a concentrated spatial range is considered to have a higher damage risk than dispersed, isolated nodes. While analyzing the spatial distribution of peak strain energy density, the module calls upon historical tension balance coefficient data for each functional zone, recorded by motion phase and generated by the isochronism analysis module. The module focuses on the duration for which the tension balance coefficient deviates from its normal reference range, which can be obtained by analyzing baseline data of healthy ligaments. For each functional zone, the module examines the number of phases in which its tension balance coefficient consistently exceeds a set deviation threshold within a complete motion cycle or across multiple consecutive motion cycles. The more phases that continuously deviate, the longer that region has been in a state of mechanical imbalance. This cumulative effect is believed to increase the risk of fatigue damage to the tissue. The module records the starting phase, ending phase, and total duration of continuous deviation for each region.

[0047] The generation of the micro-damage probability map is a data fusion and mapping process. The module needs to establish a quantitative relationship between the peak strain energy density and the micro-damage probability. This relationship is usually non-linear, and can be described by an S-shaped function, which maps the strain energy density value to a probability value between 0 and 1. For each identified overload node or node cluster, a basic micro-damage probability is calculated based on its strain energy density value through this non-linear mapping relationship. This probability value reflects the instantaneous risk based solely on the current mechanical overload level. The module introduces a time dimension for probability weighting, with the weighting factor based on the duration of the tension balance coefficient deviation of the functional zone where the node is located. The weighting factor is designed such that if the zone has experienced continuous tension imbalance in the recent motion cycles, the weight is increased; conversely, if it is only an instantaneous deviation, the weight is smaller. Multiplying the basic micro-damage probability by this time-weighted factor yields the comprehensive micro-damage probability of the node, taking into account both the severity of the instantaneous overload and the adverse effects of the long-term mechanical environment.

[0048] The module needs to map the calculated comprehensive micro-damage probability values ​​of all nodes back onto the ligament's geometric model, generating a visualized probability distribution map. This process involves spatial interpolation to ensure smooth probability contour lines are generated in regions with varying node densities. The generated probability map can be two-dimensional, overlaid on the ligament's surface model, or three-dimensional, displayed within the ligament's volume model. The map typically uses color coding, for example, using a blue-to-red gradient to represent micro-damage probabilities from low to high, thus visually indicating high-risk areas within the ligament that require focused attention. This map can be dynamically updated, refreshed with new motion cycle data input, achieving near real-time biomechanical assessment and visual early warning of ligament injury risk.

[0049] Example 6: In the rehabilitation scenario of knee ligament injury, nursing staff can carry out their work based on the technical solution of a ligament dynamic simulation and isometric analysis system. During the dynamic data acquisition phase, nursing staff assist the patient in adjusting to a comfortable position that meets the data acquisition requirements, such as maintaining a neutral position with the knee naturally flexed and extended, to avoid affecting data accuracy due to improper positioning. Following the system's operating procedures, nursing staff accurately attach high-speed optical markers to the skin surface corresponding to the knee ligament attachment points. Before attachment, the skin must be cleaned to ensure the markers are secure, and the fixation of the implanted force sensor is checked to prevent displacement during patient movement. During data acquisition, nursing staff accompany the patient throughout, guiding them to complete preset knee joint movements, such as slow flexion, extension, and rotation. If the patient experiences pain or discomfort during movement, data acquisition is immediately paused, and the patient is reassured. The process is continued only after the patient's condition stabilizes, ensuring that the acquired ligament three-dimensional deformation data and real-time force data accurately reflect the patient's ligament dynamic response within a safe range of motion. The acquired data is then transmitted to the system to assist in establishing a ligament dynamic response database indexed by the movement phase.

[0050] In the finite element mesh generation stage, although nursing staff do not directly participate in the operation of the mesh generation algorithm, they need to combine their observation of the patient's knee joint ligament anatomy during daily care. For example, they can understand the general direction and shape of the ligaments through palpation. After the system generates an adaptive variable density mesh based on the ligament anatomy characteristics, nursing staff can assist technicians in checking the matching degree between the mesh and the patient's actual ligament structure. For example, they can check whether the mesh covers the key areas of the ligament. If a significant deviation is found in the mesh in a certain functional area of ​​the ligament, the nursing staff should promptly report it to the technicians so that the technicians can further adjust the mesh node density based on the deformation gradient data in the ligament dynamic response database. This ensures that the mesh nodes can accurately match the mechanical properties of different areas of the ligament and accurately map the ligament dynamic response data to the mesh nodes.

[0051] During the real-time solution module operation, nursing staff are primarily responsible for observing the correlation between the patient's condition and the system's data output. The system performs time-domain iterative calculations on the grid node data based on an explicit dynamics algorithm. Nursing staff can view the output results at different motion phases through the system interface, such as the stress field distribution of the knee ligaments at different stages of flexion and extension. When the system uses the central difference method to calculate the grid node acceleration and adjusts the time-domain iteration step size through a dynamic relaxation factor, nursing staff need to record the patient's subjective feelings at the corresponding motion phase, such as whether there is a noticeable pulling sensation at a certain flexion-extension angle. This information, along with the strain energy density data output by the system, is compiled to provide a reference for subsequent analysis. If abnormal fluctuations are found in the system output data, technical personnel should be notified promptly to check the equipment and data transmission.

[0052] During the isolength analysis phase, nursing staff assist the system in extracting the ligament length change sequence within the movement cycle. After the patient completes a series of knee joint movements, the nursing staff, following system prompts, confirms the start and end points of the movement cycle to ensure the completeness of the extracted length change sequence. When the system calculates the length change rate and tension balance coefficient in conjunction with stress field distribution data, the nursing staff can observe the patient's coordination in different movement cycles, such as whether the patient's knee flexion and extension are smooth and whether there are any pauses in movement. These observations are then correlated with the coefficient data calculated by the system. If a significant deviation in the tension balance coefficient is found within a certain movement cycle, and the patient's movements are noticeably uncoordinated within that cycle, the relevant information is recorded promptly to provide actual performance data for subsequent analysis of ligament stability.

[0053] In the injury risk assessment phase, nursing staff develop targeted care plans based on the ligament micro-injury probability map generated by the system. After the system generates the map based on the peak strain energy density and the deviation of the tension balance coefficient from the threshold, nursing staff view the areas with a high probability of micro-injury in the map and correspond them to the actual location of the patient's knee joint. They then focus on these areas in daily care, such as avoiding putting additional pressure on these areas when assisting patients with rehabilitation activities. Nursing staff adjust care measures based on changes in the map. If subsequent follow-up examinations show a decrease in the probability of micro-injury in a certain area, gentle rehabilitation movements corresponding to that area can be appropriately increased; if the probability increases, related activities are reduced and close observation is strengthened. Through coordination with system data, nursing support tailored to the actual needs of patients with knee ligament injury rehabilitation is provided.

[0054] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0055] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A system based on ligament dynamic simulation and isometric analysis, characterized in that, The system includes: The dynamic data acquisition module is used to acquire three-dimensional deformation data and real-time force data of ligaments during exercise, and to establish a dynamic response database of ligaments. The finite element mesh generation module is used to generate an adaptive variable density mesh based on the ligament anatomical structure characteristics and to map the ligament dynamic response data to the mesh nodes. The real-time solution module is used to perform time-domain iterative calculations on mesh node data based on explicit dynamic algorithms, and output the ligament stress field distribution and strain energy density under different motion phases. The isochronism analysis module is used to extract the length change sequence of ligaments during the motion cycle and calculate the length change rate and tension balance coefficient by combining stress field distribution data. The damage risk assessment module is used to generate a probability map of ligament micro-damage based on the peak strain energy density and the deviation of the tension balance coefficient from the threshold.

2. The system based on ligament dynamic simulation and isometric analysis according to claim 1, characterized in that, The execution process of the dynamic data acquisition module includes: Displacement trajectory data of ligament attachment points are collected using a high-speed optical marking system, and multi-dimensional load data of implanted force sensors are acquired simultaneously. After aligning the displacement trajectory data and multidimensional load data with timestamps, a ligament dynamic response database indexed by motion phase is established.

3. The system based on ligament dynamic simulation and isometric analysis according to claim 1, characterized in that, The execution process of the finite element mesh generation module includes: Identify the orientation of ligament fibers and the distribution characteristics of collagen bundles, and configure high-density grid nodes along the main fiber direction; The mesh node density is dynamically adjusted based on the deformation gradient data in the ligament dynamic response database to generate a variable density mesh with deformation adaptability.

4. The system based on ligament dynamic simulation and isometric analysis according to claim 1, characterized in that, The execution process of the real-time solution module includes: The central difference method is used to calculate the grid node acceleration, and the time-domain iteration step size is controlled by a dynamic relaxation factor. After each motion phase iteration, the stress field distribution and strain energy density spatial gradient data of the entire ligament are output.

5. The system based on ligament dynamic simulation and isometric analysis according to claim 1, characterized in that, The execution process of the length equality analysis module includes: The attachment point spacing sequence was extracted from the ligament dynamic response database, and the length change rate between adjacent motion phases was calculated. By combining the stress field distribution data output by the real-time solver module, the tension balance coefficients of each ligament region are generated through the tension balancing algorithm.

6. The system based on ligament dynamic simulation and isometric analysis according to claim 5, characterized in that, The execution process of the tension equalization algorithm includes: The ligament is divided into multiple functional zones, and the stress vector of each zone is calculated and its angle with the overall average stress is calculated. The zone-level tension balance coefficient is generated based on the degree of deviation of the included angle and the rate of change of length.

7. The system based on ligament dynamic simulation and isometric analysis according to claim 1, characterized in that, The damage risk assessment module execution process includes: Identify grid nodes whose strain energy density exceeds the material yield threshold and calculate their spatial clustering. By combining the number of phases in which the tension balance coefficient continuously deviates, a spatial distribution map of the micro-damage probability is generated.

8. The system based on ligament dynamic simulation and isometric analysis according to claim 4, characterized in that, The process for determining the dynamic relaxation factor includes: Monitor the rate of change of strain energy density in adjacent iterations, and trigger the relaxation factor decay when the rate of change exceeds a critical value; The time-domain iteration step size is recalculated based on the maximum acceleration of the grid nodes until the strain energy density change rate recovers to the stable range.

9. The system based on ligament dynamic simulation and isometric analysis according to claim 6, characterized in that, The functional partitioning process includes: Based on the location of the ligament insertion point in anatomical structure, the ligament is divided into three basic sections: proximal, middle, and distal. Within each basic zone, it is further subdivided into anterior, middle, and posterior sub-zones based on the direction of the collagen bundles.

10. The system based on ligament dynamic simulation and isometric analysis according to claim 7, characterized in that, The micro-damage probability map generation process includes: Establish a nonlinear mapping relationship between peak strain energy density and micro-damage probability; By superimposing the duration of the deviation of the tension balance coefficient as a probability weighting factor, a damage risk map with a time-cumulative effect is generated.

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