A method for modeling a multi-layer discrete element biological tissue

Abstract

The application relates to the field of discrete element modeling, and discloses a modeling method of a multilayer discrete element biological tissue, which comprises the following steps: S1, basic mechanical parameter acquisition; S2, single tissue unit model construction; S3, single tissue bonding parameter calibration; S4, multilayer tissue model assembly and interface definition; S5, interlayer bonding parameter calibration; and S6, complete function model integration. According to the application, the bonding parameters in a single tissue are accurately calibrated by combining a physical damage test with simulation optimization in step 3; and then, the closed-loop process is repeated to accurately calibrate the interface bonding parameters between different tissues for a multilayer structure in step 5. The systematic method of calibration from inside to outside and layer by layer ensures that each component part of the model and the interaction thereof are verified through experiments, so that the finally constructed model can highly reproduce the complex mechanical response of the multilayer biological tissue under a real load.

Description

Technical Field

[0001] This invention relates to the field of discrete element modeling technology, specifically to a method for modeling multilayer discrete element biological tissues. Background Technology

[0002] Discrete element method (DEM) simulation is a numerical simulation method based on the discrete characteristics of particles. It can accurately reproduce the macroscopic and microscopic behavior of particle systems during motion, collision, and compression by establishing a mechanical model of inter-particle interactions, providing reliable simulation data support for related equipment development and process optimization. This technology has been widely applied in multiple fields: in agriculture, it can simulate the flow patterns of particles during grain harvesting and transportation, optimizing the structure of agricultural machinery; in the mining industry, it can simulate ore crushing and sorting processes, guiding the design and production of mining machinery; furthermore, it plays an important role in building material preparation, chemical particle reactions, and food processing, helping various industries improve production efficiency and product quality.

[0003] However, in the field of biomass harmless treatment technology, discrete element method (DEM) simulation technology has not yet been introduced, and within the scope of DEM modeling research, no technical solution has emerged capable of constructing multi-layered biological tissue structures. This makes DEM technology unable to serve the simulation of the treatment process of target biological objects in this specific scenario, and also difficult to support the construction of multi-layered biomechanical models. Therefore, exploring a modeling method for multi-layered DEM biological tissues is key to overcoming current technological limitations and constructing the core biomechanical models required in this field. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a modeling method for multilayer discrete biological tissues, aiming to solve the problems mentioned in the background section.

[0005] To achieve the above objectives, the present invention provides the following technical solution: a modeling method for multilayer discrete biological tissues based on the discrete element method, comprising the following steps:

[0006] Step 1: Conduct single biological tissue compression tests, inclined plate tests, and bounce tests to obtain basic mechanical parameters; the compression test measures the elastic modulus and Poisson's ratio, the inclined plate test calibrates the interparticle friction coefficient, and the bounce test assists in calibrating the recovery coefficient to ensure that the parameters match the actual mechanical properties of the tissue.

[0007] Step 2: Construct a discrete element geometric model of a single biological tissue and fill it with discrete element particles. Finally, construct and assign a bond-type bonding model to the discrete element particle system corresponding to the tissue. The parameters characterizing the mechanical properties of the discrete element particles (such as elastic modulus, Poisson's ratio, and coefficient of friction) are determined based on the measured data obtained in Step 1. For the parameters of the bond bonding model, to ensure the reliability and accuracy of subsequent model simulation results, their initial values ​​must first be defined within a scientifically reasonable parameter range, taking into account the microscopic characteristics of the biological tissue interface.

[0008] Step 3: Conduct tissue destruction experiments on single biological tissue samples, and set up a simulation scenario that matches reality to run the single biological tissue model simulation; simulate the destruction mode of the actual experiment and collect destruction simulation data. Then, screen key bonding parameters through PB and optimal steep slope tests, and optimize them in combination with BB tests to finally determine the bonding parameters of single biological tissue.

[0009] Step 4: Having obtained the discrete element parameters of individual tissues such as pork and pork bones, the coefficient of restitution and coefficient of friction between individual tissues are experimentally measured according to the method in Step 1. Based on this, multi-layer biological tissue models such as pig trotters and pork belly with skin are constructed: the individual tissue models are combined according to the anatomical structure, bonding models are set at different tissue interfaces, and the value range of the bonding parameters at each interface is initially defined.

[0010] Step 5: Following the method in Step 3, tissue destruction experiments were conducted on the multilayer biological tissue model, and a simulation scenario matching reality was set up to collect destruction simulation data. Then, key bonding parameters were screened using the PB and optimal steep slope tests, and optimized using the BB test to finally determine the bonding parameters of the multilayer biological tissue.

[0011] Step 6: Assign the basic mechanical parameters obtained in Step 1, the single biological tissue bonding parameters optimized in Step 3, and the multi-layer biological tissue interface bonding parameters optimized in Step 5 to the discrete element particles of the multi-layer biological tissue geometric model, respectively. After completing the association configuration between the parameters and the model, the multi-layer biological tissue discrete element model based on the discrete element method can be obtained. This model can accurately reproduce the geometric morphology and mechanical response characteristics of multi-layer biological tissue.

[0012] This invention provides a method for modeling multilayer discrete-time biological tissues. It has the following beneficial effects:

[0013] 1. This invention first combines physical destruction testing with simulation optimization in step 3 to accurately calibrate the bonding parameters within a single tissue. Then, in step 5, this closed-loop process is repeated for multi-layered structures to accurately calibrate the interfacial bonding parameters between different tissues. This systematic approach, calibrating layer by layer from the inside out, ensures that every component of the model and its interactions have been experimentally verified, enabling the final model to highly reproduce the complex mechanical responses of multi-layered biological tissues under real loads. Attached Figure Description

[0014] Figure 1 This is a simplified diagram of the Bonding model of the present invention;

[0015] Figure 2 This is a simulation damage test diagram of the present invention;

[0016] Figure 3 This is a flowchart of the method of the present invention. Detailed Implementation

[0017] The technical solutions in 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.

[0018] Please see the appendix Figure 1 -Appendix Figure 3 This invention provides a method for modeling multilayer discrete-time biological tissues. S1. Acquisition of basic mechanical parameters: Conducting physical and mechanical tests on a single biological tissue to obtain its basic mechanical parameters. These tests include compression tests, inclined plane tests, and bounce tests. The compression test measures the elastic modulus and Poisson's ratio; the inclined plane test calibrates the interparticle friction coefficient; and the bounce test assists in calibrating the coefficient of restitution to ensure that the parameters match the actual mechanical properties of the tissue. The specific steps of step 1 are as follows:

[0019] First, standard specimens of single biological tissues were prepared according to the basic requirements of mechanical testing. Compression tests were then conducted on pork, pork bones, and pork fat using a universal testing machine, and stress-strain curves were collected from the compression tests. The elastic modulus of each single biological tissue was then calculated using the following formula:

[0020]

[0021] in For elastic modulus, For stress, In response to the situation;

[0022] The axial and transverse strains of each individual biological tissue were recorded during compression, and the Poisson's ratio of each individual biological tissue was calculated using the following formula:

[0023]

[0024] in Poisson's ratio, In response to the situation;

[0025] Next, a steel plate was prepared as the contact material for contacting biological tissues. It was placed and fixed on an inclined plate whose tilt angle could be adjusted. Square and cylindrical biological tissue specimens (square specimens for testing the static friction coefficient and cylindrical specimens for testing the sliding friction coefficient) were placed on the inclined plate, and the tilt angle of the inclined plate was slowly increased. This continued until the specimens could overcome the frictional limitations and move downwards at a uniform speed. The tilt angle of the inclined plate was recorded using an angle meter, and the static and sliding friction coefficients of each individual biological tissue were calculated using the following formulas:

[0026]

[0027] in The coefficient of friction, The tilt angle;

[0028] Finally, a bounce test was used to collect the coefficient of recovery between individual biological tissues and the contact material plate. First, individual biological tissue samples were fixed at the same initial height using a restraint device. Then, the restraint device was released, allowing the individual biological tissue samples to fall freely onto the contact material plate and bounce freely. The bounce height was recorded by a high-speed camera. The coefficient of recovery for each individual biological tissue was calculated using the following formula:

[0029]

[0030] in The coefficient of recovery, This is the starting height. This is the rebound height;

[0031] S2. Single Tissue Unit Model Construction: Based on the single biological tissue in step S1, a discrete element geometric model of the single biological tissue is constructed, and the discrete element particles are filled. Finally, for the discrete element particle system corresponding to the tissue, a bond-type bonding model is constructed and assigned. The parameters characterizing the mechanical properties of the discrete element filling particles are determined based on the measured data obtained in step S1. For the parameters of the bond bonding model, to ensure the reliability and accuracy of the subsequent model simulation results, the initial values ​​need to be defined within a scientifically reasonable parameter range, taking into account the microscopic characteristics of the biological tissue interface. The specific steps of step 2 are as follows:

[0032] First, based on the size of the single biological tissue sample used in Step 1, a model of the same size as the actual biological tissue sample is created in 3D modeling software and exported as an STL file. Then, the STL file is imported into Discrete Element Method (DEM) software to generate a 3D DEM model and fill it with DEM particles. The mechanical parameters obtained in Step 1 are input into the DEM particles. A Bonding model is then set up to simulate the bonding behavior between particles. The Bonding model is a bonded particle model based on Hertz-Mindlin contact theory and further improved, used to simulate the nonlinear evolution process of interparticle bonding behavior. In this model, when the center distance between two particles is less than the sum of their contact radii, the model triggers the bond formation mechanism. When the external force exceeds the critical stress of the bond, the bond breaks, leading to bonding failure between particles. The schematic diagram is shown below. Figure 1 As shown in the figure. The relationships between the relevant parameters are as follows:

[0033] ;

[0034] ;

[0035] ;

[0036] ;

[0037] ;

[0038] ;

[0039] ;

[0040] ;

[0041] In the formula: The area of ​​the particle; Let be the polar moment of inertia of the particle; and These are the normal stiffness and the tangential stiffness, respectively. For time step ; and These are the normal velocity and tangential velocity of the particle, respectively. and These are the normal acceleration and tangential acceleration of the particle, respectively. This represents the increment of the normal force; This represents the increment of the tangential force. This represents the increment of the normal torque; This represents the increment of the tangential torque; Normal torque; Tangential torque; Normal force; Tangential force; Normal stress per unit area; Tangential stress per unit area; The particle bonding radius;

[0042] To ensure the accuracy of the model, the initial values ​​of the bonding parameters in the bond model need to be set to a reasonable range.

[0043] S3. Single Tissue Bonding Parameter Calibration: Physical destructive tests are performed on the single biological tissue standard specimens prepared in step S1, and a simulation scenario matching the actual situation is set up. The single biological tissue model constructed in step S2 is run for simulation; the actual test destructive mode is simulated, and the destructive simulation data is collected. Then, key bonding parameters are screened through PB and optimal steep slope tests, and optimized by combining BB tests. Finally, the bonding parameters of the single biological tissue are determined. The specific steps of step 3 are as follows:

[0044] First, a standardized shear failure experiment (not limited to shear testing) was designed for single biological tissue samples. An experimental system was built using a universal testing machine, equipped with a dedicated shearing blade. Before the experiment, the samples were pre-treated, transforming the original shape of the single biological tissue into standard specimens of uniform size according to experimental specifications. Three to five parallel specimens were prepared for each group to reduce random errors. During the experiment, the specimens were fixed in the fixture, and the loading parameters were set using the universal testing machine. Loading was initiated until the shearing blade pressed the sample from the middle to both ends. The force-displacement curves throughout the entire process were recorded using a data acquisition system. The maximum destructive force of each group of specimens was extracted, and the average value was taken as the experimental baseline. At the same time, the failure morphology, crack initiation location, and tissue separation method are recorded for subsequent simulation comparison.

[0045] Subsequently, a model matching the actual scenario and a single biological tissue standard specimen model (such as...) were constructed in discrete element simulation software. Figure 2 As shown): In the geometric modeling stage, based on the actual dimensions of the experimental specimen, a 3D modeling software was used to create the specimen, which was then imported into the discrete element method (DEM) software. When assigning material properties, the parameters determined in the previous mechanical experiments—elastic modulus, Poisson's ratio, and particle friction coefficient—were substituted into the particle property column of the DEM. The bond parameters—normal stiffness per unit area, tangential stiffness per unit area, critical normal strength, and critical tangential strength—were temporarily set as variables to be optimized and not assigned fixed values. Simulation boundary conditions and load replication must strictly match the experiment: Constraints consistent with the actual fixture were set in the simulation, with the top moving synchronously with the shear blade holder, and the loading rate and direction being exactly the same as in the experiment. Simultaneously, in key areas of the specimen, the loading points were monitored, and force changes during the simulation were collected in real time to ultimately extract the maximum destructive force from the simulation. This serves as a benchmark for subsequent parameter optimization.

[0046] Next, key parameters were selected from the candidate bonding parameters using Plackett-Burman (PB) experiments: the initial range of the candidate bonding parameters was determined, and two levels were set for each parameter, with the level difference covering the potential influence range of the parameter on the failure response. PB test schemes were generated using experimental design software based on the number of candidate parameters. Typically, n candidate parameters correspond to n+1 tests, including a blank test to eliminate systematic errors. The parameters of each test scheme were substituted into the discrete element model, failure simulation was run, and the relative error between the simulated maximum failure force and the experimental baseline value was calculated. The error calculation formula is as follows:

[0047]

[0048] Using this error as an evaluation index, the significance of each parameter's influence on the error was analyzed through analysis of variance (ANOVA): a significance level of P<0.05 was set, parameters with P<0.05 and large absolute values ​​of influence coefficients were retained as key bonding parameters, and minor parameters with P≥0.05 were eliminated. This reduced the variable dimensions for subsequent optimization and improved optimization efficiency.

[0049] After identifying key significant factors through the PB experiment, the optimal steep slope experiment should begin with the parameter combination that minimizes error from the PB experiment. This combination, due to its good data repeatability and weak interference, effectively reduces initial bias and prevents subsequent climbing directions from deviating from the optimal region. Subsequently, the climbing direction is determined based on the effect values ​​of each significant factor obtained from the PB experiment, exploring along the path with the fastest change in response value. The step size is adjusted appropriately to balance parameter coverage with experimental efficiency and accuracy, ensuring no potential optimal regions are overlooked while avoiding unnecessary experiments due to inappropriate step sizes. Simultaneously, non-significant factors identified in the PB experiment are controlled at fixed levels to reduce their interference with the experimental results. Ultimately, the range of significant factor values ​​is narrowed from the wide range of the PB experiment, laying the foundation for subsequent BB experiment optimization.

[0050] Finally, parameter optimization was completed using Box-Behnken experiments: For the selected key adhesion parameters, three levels (upper, middle, and lower) were set within the optimal search interval, with the center point as the midpoint of the interval to verify model stability. Experimental design software was used to generate a Box-Behnken experimental plan containing 15-20 sets of experiments, with the center point repeated three times to evaluate repeatability. The parameters of each set of experiments were substituted into the discrete element model, and a failure simulation was run, recording the corresponding error values. A quadratic response surface model was constructed based on the experimental data, and the coefficient of determination was used to determine the optimal performance. The model fit is assessed; a good fit accurately reflects the relationship between parameters and error. Using error minimization as the objective function, the software's multi-objective optimization module is used to solve for the theoretically optimal parameter combination, with the constraint that the parameters must be within the optimal search interval. The solved theoretically optimal parameters are substituted into the discrete element model, and the failure simulation is repeated three times to obtain the average maximum failure force. The deviation from the experimental baseline value is calculated: if the deviation is less than 5%, the parameter combination is the final single biological tissue adhesion parameter; if the deviation is greater than or equal to 5%, the parameter level settings of the PB experiment need to be checked back for rationality, and whether the search interval of the optimal steep slope experiment has missed key areas. Adjustments are made, and the optimization process is repeated until the error meets the requirements, ensuring that the final parameters accurately match the actual failure characteristics of a single biological tissue.

[0051] S4. Assembly and Interface Definition of Multilayer Tissue Model: Based on the obtained discrete element parameters of a single tissue, the coefficient of restitution and coefficient of friction between single tissues are experimentally measured according to the method in step S1. Based on this, a corresponding multilayer biological tissue model is constructed. The specific steps of step 4 are as follows:

[0052] The recovery coefficient and friction coefficient between different biological tissues were obtained through the inclined plane and bounce tests in step 1. The spatial relationships and key interfaces of individual tissues in intact biological tissues such as pig trotters and pork belly with skin were clarified. Next, the geometric framework of the overall model was built in discrete element method (DEM) software. Each individual tissue model was imported and positioned according to its anatomical location to ensure a close fit to the actual physiological structure. Then, discrete element particles containing the parameters of each tissue were filled into each individual tissue model, and bonding models were set at different tissue interfaces. Finally, the value ranges of the bonding parameters at each interface were preliminarily defined to prepare for subsequent optimization.

[0053] S5. Calibrating interlayer bonding parameters: Following the method in step S3, tissue destruction experiments were conducted on the multilayer biological tissue model. A simulation scenario matching the actual situation was set up, destruction simulation data was collected, and key bonding parameters were screened through PB and optimal steep slope tests. Optimization was then performed using BB tests to finally determine the bonding parameters of the multilayer biological tissue. The specific steps of step 5 are as follows:

[0054] First, based on the actual anatomical structure of multilayer biological tissues (such as pig hooves and pig bones), single tissue models of pig skin, pig fat, pork, and pig bones were precisely assembled according to their actual locations. Then, actual destructive tests were designed for the destructive scenarios, and shear tests were conducted using a universal testing machine, simultaneously recording complete force-displacement curves. Next, a matching destructive simulation scenario was set in discrete element method (DEM) software to simulate the actual shear loading method and boundary constraints, collecting simulation destructive force curves and structural change data, running the simulation, and exporting the results. Then, key bonding parameters that significantly affect the destructive force response were screened through Pb tests and optimal slope tests. Finally, the optimal bonding parameters for the multilayer biological tissues were determined using BB tests with gradient adjustments (see step 3 for details). To verify the reliability of the discrete element model parameters, actual shear tests were conducted on multilayer biological tissue samples of the same type but different geometric dimensions according to the established experimental procedures. The maximum destructive force at the point of sample failure was recorded in real time using high-precision data acquisition equipment to ensure the accuracy and repeatability of the experimental data. Then, in the discrete element method (DEM) simulation software environment, a multilayer biological tissue DEM numerical model that perfectly matches the geometric dimensions of the sample used in the actual experiment is constructed based on the three-dimensional geometric parameters of the actual sample. On this basis, key experimental parameters such as boundary conditions, loading methods, and ambient temperature in the actual experiment are strictly reproduced to ensure the consistency between the simulation environment and the physical experimental scenario.

[0055] After the simulation calculation is completed, the maximum destructive force data in the simulation results is extracted and quantitatively compared with the maximum destructive force measured in the actual shear test. The relative error or absolute error between the two is calculated. If the error value is within the preset acceptable range, it indicates that the current discrete element model's material constitutive parameters, contact parameters, and other settings can accurately reflect the mechanical response characteristics of multilayer biological tissues, and the parameter settings are reasonable and effective.

[0056] S6. Integration of the complete functional model: The basic mechanical parameters obtained in step S1, the single biological tissue bonding parameters optimized in step 3, and the multi-layer biological tissue interface bonding parameters optimized in step 5 are respectively assigned to the discrete element particles of the multi-layer biological tissue geometric model. After completing the association configuration between the parameters and the model, a multi-layer biological tissue discrete element model based on the discrete element method can be obtained. This model can accurately reproduce the geometric morphology and mechanical response characteristics of multi-layer biological tissues. The specific steps of step 6 are as follows:

[0057] First, retrieve the pre-assembled multilayer biological tissue geometric model (such as a pig's trotter or pork belly model with skin) in the Discrete Element Method (DEM) software. Then, accurately assign values ​​step-by-step according to parameter type: assign the basic mechanical parameters obtained in step 1 to the respective DEM particles of pig skin, fat, pork, and pig bone; match the single biological tissue bonding parameters obtained in step 3 and the multilayer biological tissue bonding parameters obtained in step 5 to the Bonding model. After all parameters are associated and adapted with the DEM particles and the inter-particle models, a multilayer biological tissue DEM model based on the DEM method can be constructed. This model can not only accurately reproduce the layered geometry of pig skin, fat, pork, and pig bone, but also reproduce the mechanical response consistent with reality under destructive scenarios such as vibration.

[0058] 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 method for modeling multilayer discrete-time biological tissues, characterized in that, Includes the following steps: S1. Acquisition of basic mechanical parameters: Conduct physical and mechanical experiments on single biological tissues to obtain their basic mechanical parameters; S2. Single tissue unit model construction: Based on the single biological tissue in step S1, construct a discrete element geometric model of the single biological tissue, complete the filling of discrete element particles, and construct a discrete element contact model. S3. Single Tissue Adhesion Parameter Calibration: Physical destruction tests are conducted on single biological tissues, and a matching simulation scenario is constructed. By comparing the results of physical tests and simulations, the key adhesion parameters of the discrete element contact model of single biological tissues are screened and optimized to determine the adhesion parameters of single biological tissues. S4. Multi-layer tissue model assembly and interface definition: Obtain the interface contact parameters between individual tissues, and construct a multi-layer biological tissue model based on the discrete element geometric model of a single biological tissue. S5: Interlayer bonding parameter calibration: Tissue destruction experiments were conducted on multilayer biological tissues, and a matching simulation scenario was constructed. By comparing the physical test results and simulation results, the interlayer bonding parameters of the multilayer biological tissue model were screened and optimized to determine the bonding parameters of multilayer biological tissues. S6: Integration of complete functional model: The basic mechanical parameters obtained in step S1, the single biological tissue bonding parameters optimized in step 3, and the multi-layer biological tissue interface bonding parameters optimized in step 5 are associated with the discrete element particles of the multi-layer biological tissue model to obtain the multi-layer biological tissue discrete element model.

2. The method for modeling multilayer discrete-element biological tissues according to claim 1, characterized in that, In step S3, the key bonding parameters of the discrete element contact model of a single biological tissue are screened and optimized. Specifically, this includes: collecting failure simulation data and using Plackett-Burman experiments to screen out key bonding parameters that have a significant impact on the failure results; using the optimal steep slope experiment to determine the optimal value range of the key bonding parameters; and using Box-Behnken experimental design to establish a response surface model, perform multi-objective optimization of the key bonding parameters, and finally determine the bonding parameters of a single biological tissue.

3. The method for modeling multilayer discrete-element biological tissues according to claim 1, characterized in that, In step S5, the screening and optimization of interlayer bonding parameters of the multilayer biological tissue model specifically includes: collecting simulation data of multilayer tissue failure, using Plackett-Burman tests to screen out key parameters that significantly affect interlayer bonding force; using the optimal steep slope test to determine the value range of key parameters; combining the Box-Behnken test to perform precise parameter optimization, and finally determining the interlayer bonding parameters of the multilayer biological tissue.

4. The method for modeling multilayer discrete biological tissues according to claim 1, characterized in that, In step S2, the discrete element contact model is a Bond-type bonding model; when constructing the model, the initial values ​​of the Bond-type bonding model parameters are set within a preset parameter range, taking into account the microscopic characteristics of the biological tissue interface.

5. The method for modeling multilayer discrete-element biological tissues according to claim 1, characterized in that, In step S1, the physical and mechanical tests include: compression test, inclined plate test and bounce test, wherein the elastic modulus and Poisson's ratio of biological tissue are obtained through the compression test; the static friction coefficient and rolling friction coefficient between particles are calibrated through the inclined plate test; and the coefficient of restitution is calibrated through the bounce test.

6. The method for modeling multilayer discrete-element biological tissues according to claim 1, characterized in that, In step S4, obtaining the interfacial contact parameters between individual tissues specifically involves measuring the coefficient of recovery and coefficient of friction between different individual tissues according to the physical and mechanical testing method in step S1.

7. The method for modeling multilayer discrete biological tissues according to claim 1, characterized in that, The filling parameters of the discrete element particles in step S2 are determined based on the measured data obtained in step S1.

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