Quantization method, device and medium for brain tissue damage degree under different strain rates

Abstract

The invention discloses a quantification method and device for brain tissue damage degrees under different strain rates and a medium. The quantification method comprises the steps that a constitutive model is constructed; fitting a brain tissue loading and unloading curve under different strain rate conditions based on the constitutive model to obtain a super-elastic-viscoelastic parameter, a Mullins effect parameter and a residual deformation parameter of the brain tissue, so as to evaluate the damage state of the brain tissue; the area defined by the brain tissue loading curve and the brain tissue unloading curve serves as total dissipated energy, the area defined by the unloading curve only considering viscoelasticity and the brain tissue unloading curve serves as damage dissipated energy, the ratio of the damage dissipated energy to the total dissipated energy is calculated, and therefore the damage degree of the brain tissue is evaluated; and fitting the ratio of the damage dissipated energy to the total dissipated energy and the maximum engineering strain so as to analyze the change relation of the brain tissue tensile damage degree along with the strain.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of soft material mechanics testing and damage assessment, and particularly relates to a method, device and medium for quantifying brain tissue damage degree under different strain rates. BACKGROUND

[0002] Traumatic brain injury (TBI) is a common type of nervous system injury in clinical practice. Diffuse axonal injury (DAI) is a typical pathological manifestation of TBI, which is mainly characterized by the microscopic structural damage of axons in the white matter and often accompanied by focal injury in brain regions such as the corpus callosum and brainstem. DAI often occurs in sudden external loading situations such as traffic accidents, falls, and explosions, and its formation mechanism is closely related to the strain level at the tissue level.

[0003] Related research has made some progress in exploring the brain tissue strain threshold. For example, Margulies et al. pointed out through experiments that the occurrence of DAI is usually related to macroscopic shear strain of 10% to 50%; Bain and Mean predicted the strain threshold for white matter morphological damage to be 0.13 to 0.34 in an in vivo experiment on the optic nerve of guinea pigs through logistic regression; Hardy et al. measured the maximum principal strain of brain tissue to be in the range of 0.07-0.22 in loading experiments close to the trauma level; Giordano and Kleiven pointed out that the strain threshold of the corpus callosum is 0.07 and that of the brainstem is 0.15; in addition, Rooij and Kuhl predicted that the threshold of the key tensile strain of axons may be distributed between 0.01 and 0.3 based on biophysical modeling.

[0004] Although the above research provides important theoretical basis for the mechanical mechanism of TBI and the prediction of brain tissue damage threshold, most of them only focus on the qualitative relationship between strain level and damage, and lack quantitative description methods for damage degree. In addition, current methods are mostly based on the judgment of a single strain threshold, and have not considered the influence factors such as viscoelastic response, residual deformation and stress softening effect of brain tissue in the loading and unloading process.

[0005] In particular, under the condition of medium and low strain rate, the damage behavior of brain tissue is more complex due to its significant viscoelastic-superelastic characteristics. Traditional constitutive models are difficult to fully characterize the damage evolution process, and cannot effectively separate the energy dissipation caused by material internal friction and damage evolution, thereby hindering the systematic and quantitative assessment of brain tissue damage degree.

[0006] Therefore, it is urgent to establish a quantitative method for brain tissue damage degree under different strain rates to provide theoretical and methodological support for the diagnosis, prediction and protection design related to traumatic brain injury TBI. SUMMARY

[0007] In view of the deficiencies in the prior art, the present application provides a method, device and medium for quantifying the damage degree of brain tissue under different strain rates.

[0008] In a first aspect, the present application provides a method for quantifying the damage degree of brain tissue under different strain rates, the method comprising:

[0009] constructing a constitutive model;

[0010] fitting the loading and unloading curves of brain tissue under different strain rates based on the constitutive model to obtain the hyperelastic-viscoelastic parameters, Mullins effect parameters and residual deformation parameters of brain tissue, thereby evaluating the damage state of brain tissue;

[0011] taking the area enclosed by the loading curve and the unloading curve of brain tissue as the total dissipated energy and taking the area enclosed by the unloading curve considering only viscoelasticity and the unloading curve of brain tissue as the damage dissipated energy, calculating the ratio of the damage dissipated energy to the total dissipated energy, thereby evaluating the damage degree of brain tissue;

[0012] fitting the ratio of the damage dissipated energy to the total dissipated energy and the maximum engineering strain, thereby analyzing the relationship between the tensile damage degree of brain tissue and strain.

[0013] In a second aspect, the present application provides a system for quantifying the damage degree of brain tissue under different strain rates, the system comprising:

[0014] a constitutive model construction module configured to construct a constitutive model;

[0015] a brain tissue damage state evaluation module configured to fit the loading and unloading curves of brain tissue under different strain rates based on the constitutive model to obtain the hyperelastic-viscoelastic parameters, Mullins effect parameters and residual deformation parameters of brain tissue, thereby evaluating the damage state of brain tissue;

[0016] a brain tissue damage degree evaluation module configured to take the area enclosed by the loading curve and the unloading curve of brain tissue as the total dissipated energy and take the area enclosed by the unloading curve considering only viscoelasticity and the unloading curve of brain tissue as the damage dissipated energy, calculate the ratio of the damage dissipated energy to the total dissipated energy, thereby evaluate the damage degree of brain tissue;

[0017] a brain tissue damage degree analysis module configured to fit the ratio of the damage dissipated energy to the total dissipated energy and the maximum engineering strain, thereby analyze the relationship between the tensile damage degree of brain tissue and strain.

[0018] In a third aspect, the present application provides an electronic device comprising:

[0019] at least one processor; and

[0020] a memory in communication with the at least one processor; wherein,

[0021] The memory stores one or more computer programs executable by the at least one processor, and the one or more computer programs are executed by the at least one processor to enable the at least one processor to perform the method for quantifying the extent of brain tissue injury at different strain rates.

[0022] In a fourth aspect, an embodiment of the present application provides a computer readable storage medium, which stores a computer program, and the computer program, when executed by a processor, implements the method for quantifying the extent of brain tissue injury at different strain rates.

[0023] In a fifth aspect, an embodiment of the present application provides a computer program product, which includes computer programs / instructions, and the computer programs / instructions, when executed by a processor, implement the method for quantifying the extent of brain tissue injury at different strain rates.

[0024] Compared with the prior art, the present application has the following beneficial effects:

[0025] The present application provides a method for quantifying the extent of brain tissue injury at different strain rates, and by improving the constitutive model, a first damage parameter and a second damage parameter are introduced on the spring in parallel with the Maxwell unit, so that the constitutive model can represent the viscoelasticity, Mullins effect and residual deformation of the brain tissue at the same time; the present application fits the loading and unloading curves of the brain tissue under different strain rates based on the constitutive model, obtains the hyperelastic-viscoelastic parameters, Mullins effect parameters and residual deformation parameters of the brain tissue, and thus the damage state of the brain tissue can be evaluated; at the same time, the area surrounded by the loading curve of the brain tissue and the unloading curve of the brain tissue is taken as the total dissipation energy, and the area surrounded by the unloading curve considering only the viscoelasticity and the unloading curve of the brain tissue is taken as the damage dissipation energy, and the ratio of the damage dissipation energy to the total dissipation energy is calculated, and thus the extent of damage of the brain tissue can be evaluated; and the present application fits the ratio of the damage dissipation energy to the total dissipation energy and the maximum engineering strain, and thus the change relationship of the extent of brain tissue tensile damage with strain can be analyzed. The method of the present application provides a theoretical basis for quantifying the extent of brain tissue injury at different strain rates. BRIEF DESCRIPTION OF DRAWINGS

[0026] Figure 1 is a schematic diagram of an extended Zener model: spring A introduces a damage coefficient, wherein and are used to represent the Mullins effect and the residual deformation, respectively;

[0027] Figure 2are the tensile test curves of porcine brain tissue under three strain rates (left column); the loading-unloading test curves of porcine brain tissue under three maximum deformations at 0.005

[0028] Figure 3 are the experimental data and fitted curves of the tensile test of brain tissue under three strain rates;

[0029] Figure 4 are the experimental data and fitted curves of the loading-unloading tensile test of brain tissue under three maximum deformations at 0.005

[0030] Figure 5 are the theoretical predictions of the tensile engineering stress-strain curves under different maximum deformations at strain rate ; the yellow curve represents the undamaged state, and the green curve represents the damaged state;

[0031] Figure 6 is the schematic diagram of the dissipated energy related to viscoelasticity and damage;

[0032] Figure 7 are the bar charts representing the total dissipated energy, the viscoelastic dissipated energy, and the damage-related dissipated energy under different maximum deformations, respectively; the fitted curve depicts the trend of the proportion of damage-related dissipated energy in the total dissipated energy as the maximum strain changes;

[0033] Figure 8 (a) in is the schematic diagram of a split Hopkinson pressure bar (SHPB), Figure 8 (b) in is the schematic diagram of a long split Hopkinson pressure bar (LSHPB);

[0034] Figure 9 is the schematic diagram of the attenuation coefficient measurement device;

[0035] Figure 10 is the distribution diagram of the incident rod strain gauges;

[0036] Figure 11 is the schematic diagram of the strain signals recorded by the three groups of strain gauges on the incident rod;

[0037] Figure 12 is the signal of the third strain gauge 3: Figure 12 (a) in is the comparison between the prediction based on strain gauge 1 and the experiment, Figure 12 (b) in is the comparison between the prediction based on strain gauge 2 and the experiment;

[0038] Figure 13 is the schematic diagram of the wave separation strain gauge paste;

[0039] Figure 14 is the 130s​​-1 a schematic diagram of a loading and unloading curve of the material;

[0040] Figure 15 a schematic diagram of an electronic device. DETAILED DESCRIPTION

[0041] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by a person of ordinary skill in the art without creative work fall within the protection scope of the present application.

[0042] It should be noted that the features in the following embodiments and implementation manners can be combined with each other without conflict.

[0043] The method for quantifying the brain tissue injury degree under different strain rates provided by the embodiments of the present application comprises the following steps:

[0044] Step S1, constructing a constitutive model.

[0045] Specifically, first, an improved constitutive model is proposed, which can represent the viscoelasticity, Mullins effect and residual deformation characteristics of brain tissue at the same time. Based on the Zener model, a first damage parameter and a second damage parameter are introduced on the spring in parallel with the Maxwell unit, which represent the Mullins effect and the residual deformation, respectively. Wherein, the first spring A and the second spring B both adopt a hyperelastic model, as shown in Figure 1 It should be noted that the upper right corner marks A, B and D appearing in the present example respectively represent the first spring A, the second spring B and the damper D, rather than the exponential symbol.

[0046] First, the constitutive relationship of the first spring with the introduced damage parameter is analyzed.

[0047] For the first spring , the incompressibility condition is considered: wherein, , and respectively represent the principal elongation ratio, so ; therefore, the strain energy density of the first spring without considering damage can be expressed as:

[0048] (1)

[0049] In the formula,​ represents the Ogden modulus coefficient of the first spring in the first principal direction, represents the Ogden modulus coefficient of the first spring in the second principal direction, represents the exponent coefficient of the first spring in the first principal direction, represents the exponent coefficient of the first spring in the second principal direction.

[0050] After introducing the Mullins effect and the residual deformation, the strain energy density of the first spring can be expressed as:

[0051] (2)

[0052] where the function characterizes the residual strain; the function and refer to the dissipation functions, the first dissipation function measures the energy dissipated in the solid due to the Mullins effect, and the second dissipation function represents the energy dissipation due to the residual strain.

[0053] The first damage parameter related to the Mullins effect and the second damage parameter related to the residual deformation satisfy the following relation:

[0054]

[0055] (3)

[0056] Substituting equation (2) into equation (3) gives:

[0057] (4)

[0058] Therefore, equation (4) implicitly defines the first damage parameter and the second damage parameter in terms of the principal stretch ratio.

[0059] The first damage parameter related to the Mullins is expressed as:

[0060] (5)

[0061] where , and are parameters related to the degree of damage; the parameter r controls the amount of damage, and as r increases, the amount of damage decreases, which behavior is due to the fact that the larger the value of r, the first damage parameter The smaller the deviation from 1; the parameter m controls whether damage occurs at low strain levels, if m = 0, then a large amount of damage occurs at low strain levels; , respectively the principal stretch ratios, is the maximum strain energy reached on the initial loading path, denotes the first spring The strain energy density without damage is considered.

[0062] The second damage parameter is a parameter related to the residual deformation, which can be expressed as:

[0063] (6)

[0064] where, is an exponential parameter related to the maximum strain energy density during loading, which has the following relation to :

[0065] (7)

[0066] where the parameters and are material parameters to be fitted.

[0067] Considering the incompressibility condition, the function for the residual strain can be expressed as:

[0068] (8)

[0069] where, denotes the material parameters, and j denotes the material parameter.

[0070] and the material parameter depends on the maximum stretch ratio , which has the following relation:

[0071] (9)

[0072] where, , , and are material parameters to be fitted.

[0073] It is worth noting that the function for the residual strain and the first spring the strain energy density without damage The superscript tilde indicates the state after damage.

[0074] At this time, the first spring The Cauchy stress in the principal direction can be expressed as:

[0075] (10)

[0076] Under the loading condition of uniaxial tension, the principal elongation ratio satisfies where is the principal elongation ratio of the material in the loading direction. According to formula (2) and (10), the first spring The Cauchy stress in the loading direction can be expressed as:

[0077] (11)

[0078] where represents the Ogden modulus coefficient of the first spring A in the first principal direction, represents the Ogden modulus coefficient of the first spring A in the second principal direction, represents the exponential coefficient of the first spring A in the first principal direction, represents the exponential coefficient of the first spring A in the second principal direction.

[0079] If the first damage parameter , the uniaxial Cauchy stress under the undamaged condition can be obtained. Similarly, the second spring under the undamaged condition The Cauchy stress in the loading direction can be expressed as:

[0080] (12)

[0081] where is the elongation ratio of the second spring in the loading direction; the material parameters and are the Ogden modulus coefficient and the exponential coefficient of the spring , respectively.

[0082] According to the stress relationship of the parallel spring, the external Cauchy stress can be expressed as:

[0083] (13)

[0084] For the damper, the evolution formula of viscous deformation is:

[0085] (14)

[0086] where the viscous elongation ratio is given by formula (15):

[0087] (15)

[0088] Where, is the deviatoric stress of the damper, represents the viscosity constant of the damper. All superscript Both refer to the damper. Deviatoric stress in the loading direction It can be expressed as:

[0089] (16)

[0090] in, represents the hydrostatic pressure. Substituting formulas (12), (14) and (15) into formula (16), we can get the elongation ratio of the damper , deviatoric stress With the second spring Elongation ratio The relationship can be expressed as:

[0091] (17)

[0092] For the Zener model, the extension ratio of the second spring B is , the elongation ratio of the damper Elongation ratio to the material itself There are the following relationships:

[0093] (18)

[0094] Differentiating both sides of equation (18) yields:

[0095] (19)

[0096] Substituting into formulas (17) and (18), we can obtain:

[0097] (20)

[0098] Therefore, the second spring can be solved from formula (20) Elongation ratio in the loading direction and the second spring Elongation ratio in the loading direction Substituting into formula (13), we can get the stress Therefore, the engineering stress can be expressed as:

[0099] (twenty one)

[0100] Elongation ratio and engineering strain Correlation:

[0101] (22)

[0102] By simultaneously solving equations (13), (20), (21) and (22), the mathematical relationship between the engineering stress and the engineering strain of the material can be derived. The curve obtained from the experimental test is the relationship curve between the engineering strain and the engineering stress. Based on the above constitutive theory, the experimental curve can be fitted to determine the corresponding parameters of the brain tissue. In this example, all curve fitting is based on the lsqcurvefit.m function of MATLAB.

[0103] Step S2, based on the constitutive model, the loading and unloading curves of the brain tissue under different strain rates are fitted to obtain the hyperelastic-viscoelastic parameters, Mullins effect parameters and residual deformation parameters of the brain tissue, so as to evaluate the damage state of the brain tissue.

[0104] Next, the process of obtaining the loading and unloading curve of the brain tissue under low strain rate is taken as an example to be described in detail.

[0105] Specifically, under low strain rate, the loading and unloading test of the brain tissue is carried out. In the experiment, the cylindrical sample with a diameter of 15 mm and a thickness of 10 mm to 15 mm is used for tensile test, which can effectively ensure the realization of uniaxial tension state.

[0106] The experimental sample is a fresh pig brain slice purchased from a market. During the experiment, the sample is soaked in a 0.9% sodium chloride solution and stored in a 4°C refrigerator to ensure that the test is completed within 8 hours. The INSTRON 5965 testing machine is used to carry out low-speed tensile test under quasi-static strain rate. The sensor on the testing machine can measure the maximum axial force of 10 N with a resolution of 0.001 mN. In the tensile test, the sample is taken from the mixed area of the pig brain gray matter and white matter, and cut into a cylindrical sample with a diameter of 15 ± 0.3 mm and a height of 10 mm to 15 mm. This sample size ensures the effective maintenance of the uniaxial stress condition.

[0107] To prevent the sample from dehydrating, physiological saline solution is applied to the surface of the sample periodically during the cutting and testing process. The cutting of the sample is divided into two stages. First, the sample is extracted from one brain hemisphere, and then the sample is cut from the other hemisphere after testing. This operation helps to maintain the stability of the tissue stiffness and prevent dehydration, thereby improving the repeatability of the experiment.

[0108] To begin the experiment, apply cloth tape to the upper and lower discs holding the sample in the INSTRON tester and evenly apply cyanoacrylate glue. Next, place the cylindrical sample on the lower disc and gradually lower the upper disc until it lightly touches the top surface of the cylindrical sample. Allow the sample to sit for two minutes after contact to ensure a secure bond between the sample and the discs. Due to the height of the cylindrical sample, it is important to ensure that the sample remains upright when lowering the upper disc to maintain its original shape and minimize potential errors during testing.

[0109] At quasi-static strain rates of 0.3 , 0.003 and 0.0003 Under the loading conditions of 0.005, the pig brain samples were tensile tested with a maximum engineering strain of 0.6, and more than 8 samples were tested under each strain rate condition. Under the conditions of , loading and unloading tests were carried out with maximum tensile engineering strains of 0.1, 0.3 and 0.5, and more than 9 samples were tested under each working condition. Figure 2 As shown, Figure 2 The left column is the tensile test curve of pig brain tissue samples at three strain rates. Figure 2 The right column in the middle pair is the pig brain tissue under the quasi-static strain rate of 0.005 The loading and unloading test curves of the three maximum deformations are shown in the figure. The average curve of the samples is shown, and the shaded area represents the standard deviation.

[0110] The constitutive model provided in this example can characterize the viscoelasticity, Mullins effect, and residual deformation characteristics of pig brain samples. First, the hyperelastic-viscoelastic parameters are determined by fitting the loading curves at three strain rates. Then, based on the fixed viscoelastic parameters, the unloading curves are further fitted to obtain the Mullins effect parameters and residual deformation parameters. The fitting results of the loading curves at three strain rates and the 0.005 The loading and unloading curve fitting results of the three maximum deformation conditions are as follows: Figure 3 and Figure 4 The experimental data are presented as discrete points, the solid line represents the theoretical fitting curve, and the shaded area reflects the standard deviation of the experimental data.

[0111] from Figure 3 It can be observed that the mechanical response of pig brain tissue under three loading strain rates shows significant rate dependence. Increased to 0.3 Under the same engineering strain conditions, the engineering stress of the porcine brain tissue samples increased significantly, indicating that it is sensitive to loading rate and exhibits typical viscoelastic characteristics. At higher strain rates, the relative movement of the fluid within the tissue and the stretching effect of the molecular chains may lead to a higher stress response, thereby enhancing the overall deformation resistance.

[0112] In addition, from Figure 4 Analysis of the loading and unloading experimental data can further reveal the deformation characteristics of pig brain tissue during the loading and unloading process. When the external loading force gradually decreased and was eventually removed, although the engineering stress dropped to zero, the sample did not completely recover to its initial state, but still maintained a certain residual strain. This indicates that the pig brain tissue underwent irreversible deformation during the tensile process, causing it to still have permanent deformation in the absence of external force. Further analysis found that as the maximum engineering strain increased, the degree of residual strain also increased, indicating that at larger strain levels, the tissue may have experienced more significant microstructural damage or irreversible molecular rearrangement, resulting in a further reduction in its resilience.

[0113] The experimental data also clearly demonstrated a significant damage effect, that is, after undergoing the loading process, the subsequent unloading stage showed a significant softening effect, which is consistent with the Mullins effect. Specifically, at the same strain level, the engineering stress corresponding to the unloading process was significantly lower than the stress generated during the loading process. This phenomenon may be attributed to the reorganization of the microstructure within the tissue, the destruction of molecular bonds, or energy dissipation, which causes the unloading path to deviate from the loading path, forming a significant softening curve. This stress-softening effect is particularly prominent under large deformation conditions, indicating that pig brain tissue may have experienced a certain degree of structural damage or irreversible internal evolution mechanism under repeated stress.

[0114] By combining theoretical analysis of viscoelasticity, the Mullins effect, and residual deformation with tensile test results, this example not only successfully fitted loading curves at three strain rates and loading and unloading curves at three maximum deformations, but also derived a set of parameters describing the viscoelastic effect, Mullins effect, and residual deformation of brain tissue using a constitutive model. These parameters, summarized in Table 1, accurately reflect the mechanical behavior and nonlinear characteristics of brain tissue under different loading conditions.

[0115] These fitted parameters are of great significance for predicting the extent of tensile damage to brain tissue. First, the viscoelastic effect-related parameters reveal the time-dependent mechanical response of brain tissue during loading and unloading, providing a basis for quantifying the damage accumulation process at different strain rates. Second, the Mullins effect parameters reflect the stress softening and energy dissipation characteristics of brain tissue during unloading, which can be used to characterize the microscopic damage evolution of tissue during tension and help establish more accurate damage criteria. Finally, the residual deformation parameters can reveal the irreversible deformation of brain tissue after large deformation or injury, providing key quantitative data for determining the critical threshold of tensile damage.

[0116] Table 1: Key parameters of hyperviscoelasticity, Mullins effect, and residual deformation characterizing the tensile behavior of porcine brain tissue from theoretical fitting

[0117]

[0118] In step S3, the area enclosed by the brain tissue loading curve and the brain tissue unloading curve is taken as the total dissipated energy, and the area enclosed by the unloading curve considering only viscoelasticity and the brain tissue unloading curve is taken as the damage dissipated energy. The ratio of the damage dissipated energy to the total dissipated energy is calculated to assess the degree of brain tissue damage.

[0119] Specifically, after fitting the hyperelastic-viscoelastic parameters, Mullins effect parameters and residual deformation parameters, the parameters can be set to = , substituted into formula (5) to obtain =1, in order to eliminate the damage effect in stress; and then characterize the sample at 0.005 The loading and unloading prediction curves with and without damage effects at different maximum tensile strains are shown below. Figure 5 As shown, the green curve represents the undamaged state, and the yellow curve represents the damaged state.

[0120] from Figure 5It can be observed that the influence of damage on the unloading curve is almost negligible when the maximum engineering strain is 0.1, and the damage and non-damage unloading curves are almost completely coincident. This indicates that the damage effect does not have a significant influence on the mechanical response of the sample at this strain level. However, when the maximum engineering strain increases to 0.2 and 0.3, although the loading curves remain substantially consistent, the unloading curves have shown significant differences. Further increasing the maximum tensile strain, the loading curves still maintain a high consistency, but the deviation of the unloading curves gradually increases. This indicates that the damage effect gradually emerges and has an increasingly significant influence on the unloading process as the strain increases. Specifically, under the same strain conditions, the unloading curve without considering the damage effect corresponds to a higher engineering stress and a smaller residual deformation, while the unloading curve considering the damage effect exhibits a lower stress value and a larger residual deformation. This trend indicates that the damage effect gradually influences the mechanical behavior of the sample during the unloading process.

[0121] Further, the present example takes the area enclosed by the brain tissue loading curve and the brain tissue unloading curve as the total dissipated energy in the loading process; when considering viscoelasticity and damage effect, it takes the area enclosed by the unloading curve considering only viscoelasticity (i.e., the first damage parameter equals 1) and the brain tissue unloading curve as the damage dissipated energy (i.e., the additional energy dissipation caused by damage), calculates the ratio of the damage dissipated energy to the total dissipated energy, and thereby evaluates the damage degree of the brain tissue.

[0122] As shown in Figure 6 , the purple area represents the energy dissipation caused by viscoelastic effect, and the yellow area represents the energy dissipation caused by damage effect, and the sum of the two is the total dissipated energy. Therefore, in order to further quantify the damage degree of the pig brain tissue under the strain rate of 0.005 , the unit volume energy dissipation values caused by viscoelasticity and damage respectively and the total dissipation values under different maximum engineering strains are calculated, and the results are shown in Figure 7 .

[0123] The data show that with the increase of the maximum engineering strain, the three types of dissipated energy all show an increasing trend. Among them, the damage-related dissipated energy grows particularly significantly: at a strain of 0.1, this energy can be almost negligible; however, when the strain increases to 0.5, its value is close to the viscoelastic dissipated energy. This phenomenon indicates that under smaller tensile deformation, the viscoelastic effect dominates the energy dissipation, while under larger strain conditions, the damage effect becomes a key factor and significantly improves the contribution to the overall dissipated energy.

[0124] In order to quantitatively evaluate the variation of the damage degree of the pig brain sample with strain, the present example calculates the proportion of the damage-related dissipated energy to the total dissipated energy, and takes Figure 7The data points in the figure represent the damage dissipation energy. The results show that the damage-induced energy dissipation per unit volume gradually increases with the increase of tensile strain. When the strain is 0.1, the damage dissipation energy accounts for only 0.99%, indicating that the damage effect can be ignored. This conclusion is verified in Figure 5 the loading-unloading curve, which is almost completely coincident when considering damage and not considering damage. However, with the increase of strain, the damage effect gradually appears. When the strain rises to 0.2, the damage dissipation energy accounts for 6.6%; at 0.3 strain, it further rises to 14.4%; when the strain reaches 0.4, the damage dissipation energy accounts for 27.9%; finally, at 0.5 strain, the damage dissipation energy accounts for 46.5%. Although the damage-related dissipation energy has not yet exceeded half of the total dissipation energy, it has shown a significant growth trend. These results clearly reveal the evolution law of damage-related dissipation energy with the increase of strain, providing quantitative basis for in-depth understanding of the damage mechanism.

[0125] Step S4, fitting the ratio of damage dissipation energy to total dissipation energy and the maximum engineering strain, so as to analyze the change relationship of brain tissue tensile damage degree with strain.

[0126] In addition, under the condition that the strain rate is 0.005 , the relationship between the damage dissipation energy ratio and the maximum engineering strain can be effectively fitted by a power function, and the fitting equation is as follows:

[0127] (23)

[0128] The equation quantitatively describes the relationship between the maximum engineering strain and the damage-related dissipation energy ratio, thereby characterizing the evolution trend of brain tissue tensile damage degree with strain. This constitutive model not only helps to reveal the damage evolution mechanism of brain tissue under tensile load, but also provides quantitative basis for the determination of damage threshold, which has important reference value for the biomechanical evaluation of brain injury.

[0129] Embodiment 1

[0130] Next, the process of obtaining the brain tissue loading-unloading curve at medium-high strain rate in the present example is described in detail.

[0131] The test of brain tissue at medium-high strain rate needs to use a split Hopkinson pressure bar (SHPB) device; only the loading-unloading curve of pig brain sample at medium-high strain rate is obtained, and the damage coefficient of pig brain at the corresponding strain rate can be fitted by damage constitutive, and the damage degree can be quantified.

[0132] Figure 8(a) and Figure 8 (b) in the figure shows the overall structure of the split Hopkinson pressure bar system (SHPB) and the extra-long split Hopkinson pressure bar system (LSHPB). Both systems are composed of three parts: an impact rod (impact bullet), an incident rod and a transmission rod. All rod materials are made of polycarbonate to reduce the system impedance and slow down the wave speed, so as to better adapt to the dynamic loading characteristics of biological soft tissues. Specifically, in the conventional SHPB system, the lengths of the impact rod, incident rod and transmission rod are 0.6 m, 1.52 m and 0.7 m respectively; while the LSHPB system further extends the rod length to 4 m, 5 m and 5 m respectively, to obtain a longer loading pulse duration, thereby meeting the experimental requirements in the medium strain rate range. It should be noted that the SHPB system can achieve 500s -1 Above strain rate, while LSHPB can achieve 200–300s -1 strain rate.

[0133] The sample is 2 mm thick and is clamped between the incident rod and the transmission rod. The incident rod and the transmission rod are respectively attached with ordinary strain gauges and semiconductor strain gauges ( Figure 8 (Indicated by a cross in the figure), the arrow on the impact rod indicates the direction of impact. The entire experimental setup is precisely mounted on a 16-meter-long optical platform. The platform design effectively ensures the reliability of the experimental data and the reproducibility of the experimental process.

[0134] The operating principles of both Hopkinson pressure bar systems are essentially the same. During the experiment, the sample is placed between the incident bar and the transmission bar. When the driving bullet strikes the end of the incident bar, an incident compression wave is generated, which propagates along the incident bar to the sample. Due to the difference in wave impedance between the sample and the bar material, the incident wave is partially reflected at the sample interface, forming a reflected wave that returns to the incident bar. The remaining wave energy passes through the sample as a transmitted wave and enters the transmission bar. When the transmitted wave reaches the end of the transmission bar, the transmission bar effectively dissipates the remaining momentum through collision with a buffer device or through a connected absorption bar, thus avoiding data interference caused by the transmitted wave reflecting back to the sample.

[0135] To accurately measure stress waves, conventional resistance strain gauges are attached to the incident rod to record the strain signals of the incident and reflected waves. Given that the signal amplitude of the transmitted wave is typically much lower than that of the incident wave, a highly sensitive semiconductor strain gauge is installed on the transmission rod to improve detection sensitivity and accurately capture changes in the transmitted wave. Furthermore, the combination of conventional strain gauges, semiconductor strain gauges, and an ultra-dynamic resistance strain measurement system installed on the incident and transmission rods enables dynamic response acquisition of the entire stress wave process, providing a reliable basis for subsequent data processing and damage assessment.

[0136] The SHPB experimental technique is based on two basic assumptions: (1) the wave propagation in the rod is one-dimensional stress wave; (2) the stress and strain on the short specimen are uniformly distributed along the length. Under the condition that the one-dimensional stress wave assumption is met and the rod material is in an elastic state, the strain, stress, and strain rate of the specimen can be calculated by the following equations:

[0137] (24)

[0138] wherein, and represent the incident and reflected strain histories at the interface between the incident rod and the specimen, respectively, represents the transmitted strain history at the interface between the transmitted rod and the specimen. , are the elastic wave velocity and the elastic modulus of the polycarbonate rod, respectively; is the thickness of the specimen, which is uniform at 2 mm in the present example; and are the cross-sectional area of the polycarbonate rod and the initial cross-sectional area of the specimen before compression, respectively.

[0139] According to the assumption that the stress and strain are uniformly distributed along the length of the short specimen, when the stress and strain in the specimen reach uniformity, the relationship that the sum of the incident wave and the reflected wave is equal to the transmitted wave can be met:

[0140] (25)

[0141] Thus, the calculation formulas of the strain , stress , and strain rate of the specimen can be simplified as:

[0142]

[0143]

[0144] (26)

[0145] After eliminating the time parameter, the stress-strain curve of the specimen under the test conditions can be obtained. The common three-wave method is to analyze the mutual relationship of the incident wave, the reflected wave, and the transmitted wave to calculate the stress-strain curve of the specimen. The two-wave method is based on the principle that the sum of the incident wave and the reflected wave is equal to the transmitted wave, and uses any two of the incident wave, the reflected wave, and the transmitted wave for analysis, thereby deducing the stress-strain relationship of the specimen in the loading process.

[0146] In the actual experiment, the transverse motion of the particles in the bar and the stress wave dispersion phenomenon caused by the viscoelastic wave propagation cannot be ignored. In the split Hopkinson pressure bar (SHPB) system, the influence of the dispersion effect on the experimental results is small due to the short length of the bar; however, when the long split Hopkinson pressure bar (LSHPB) system is used, the length of the incident bar can reach 5 meters, so the influence of the dispersion effect must be considered and corrected.

[0147] If the minimum wavelength of the loading pulse is much larger than the transverse size of the bar, the transverse motion of the bar can be ignored. At this time, the engineering stress and the longitudinal strain between the cross section at time and the axial displacement of the cross section at time have the following relationship:

[0148] (27)

[0149] Under the premise of one-dimensional assumption, the wave equation of the stress wave propagation problem in the cylindrical bar in the frequency domain can be expressed as:

[0150] (28)

[0151] where and respectively represent the Fourier transform of the stress and strain history in the frequency domain. The relationship between the angular frequency and the frequency is . The bar as a linear viscoelastic material, the constitutive equation in the frequency domain can be expressed as:

[0152] (29)

[0153] where is the complex elastic modulus of the bar. The propagation coefficient can be expressed as:

[0154] (30)

[0155] Combining equations (28), (29) and (30), the one-dimensional equation of the axial motion of the viscoelastic bar can be expressed as:

[0156] (31)

[0157] The general solution of equation (31) can be expressed as:

[0158] (32)

[0159] where the function and are defined at due to the strain caused by the wave propagating along axis in positive and negative directions.

[0160] Consider a rod of length with its left end subjected to an impact by a bullet of the same material as the rod, resulting in a strain wave pulse propagating from left to right (as shown in Figure 9 . A strain gage is installed at on the rod to record the wave signal at this location. The right end of the rod is free and is labeled as location .

[0161] To determine the attenuation coefficient of the strain wave, the strain gage records the initial rightward propagating wave shape excited by the impact, and the first leftward propagating wave shape after the wave is reflected at the free end. To avoid the superposition interference of the two consecutive wave signals at the strain gage, in addition to the requirement that the impact bullet be of the same material as the rod, the following conditions must also be met: the length of the impact bullet should be less than the length of the rod, and the cross-sectional areas of the two should remain consistent. Under the above conditions, the recorded wave signals and can be Fourier transformed to obtain their frequency domain expressions and :

[0162] (33)

[0163] Here, denotes the Fourier transform operator, and correspond to the frequency domain forms of the initial strain wave and the reflected strain wave recorded at the location of the rod. Since the rightmost end of the rod is free, it can be obtained from equation (24) that:

[0164] (34)

[0165] Therefore, we have:

[0166] (35)

[0167] Thus, the attenuation coefficient can be obtained.

[0168] In fact, the determination of the attenuation coefficient is not limited to the specific experimental setup. In actual tests, the Hopkinson pressure bar system usually has two or more strain gauges arranged on the incident bar. Therefore, as long as the strain signals recorded by the strain gauges at different positions can be obtained, and the propagation direction and the distance between the two strain gauges are clear , the attenuation coefficient can be accurately calculated by a similar method. For example, the following method is used: before the formal strain rate impact experiment is carried out, a very small initial speed is first given to the rod, so that the three groups of strain gauges arranged on the incident bar can record the wave form completely. The arrangement of the strain gauges is shown in Figure 10 , from right to left, they are strain gauges 1, 2 and 3. During the experiment, the strain signals recorded by the three groups of strain gauges are shown in Figure 11 .

[0169] To calculate the attenuation coefficient, first, the time-domain strain signals collected by the first strain gauge 1 and the second strain gauge 2 are subjected to Fourier transform to obtain the corresponding frequency-domain signals. Then, the obtained frequency-domain signals are substituted into formula (35) to calculate the attenuation coefficient of the rod. In order to verify the accuracy of the calculation result, further use the strain data of the strain gauge 1 and the strain gauge 2, combined with the calculated propagation coefficient, to predict the strain waveform at the third strain gauge 3, and the prediction result is shown in Figure 12 .

[0170] It should be noted that the third strain gauge 3 is attached to the incident bar near the sample side, and in theory it should record a negative strain signal. However, due to its position too close to the end of the rod, the measured signal is affected by the superposition of the incident wave and the reflected wave, so it shows a positive value, as shown in Figure 12 . In addition, when using the experimental data of the first strain gauge 1 and the second strain gauge 2 to predict the signal of the third strain gauge 3, the deviation between the predicted value and the actual measured value can also be attributed to this position effect. Despite these influencing factors, it can be observed that the peak values of the predicted waveforms have good consistency with the experimental recorded data, indicating that the calculated propagation coefficient has high reliability.

[0171] Therefore, before the formal experiment is carried out, by determining the attenuation coefficient of the polycarbonate rod, the accuracy and reliability of the subsequent medium strain rate experiment results can be effectively improved.

[0172] In order to obtain the unloading curve under the medium strain rate, the wave separation method is used. Considering a rod with a fourth strain gauge A and a fifth strain gauge B attached to the left and right ends respectively, as shown in Figure 13 ; the strain waves recorded by the two strain gauges are and . At this time, the strain waves recorded by the strain gauges are the superposition of the right-running wave and the left-running wave, which satisfies the following relationship:

[0173] (36)

[0174] The subscripts of the right-moving and left-moving waves are denoted asc and des respectively; and the two round trip times of the wave propagating in the rod are denoted as . Satisfaction: in When , the strain wave recorded by the fourth strain gauge A is equal to the right-traveling wave, that is, At this time, the right-traveling wave transmitted to the fifth strain gauge B is: . is the attenuation coefficient, is the distance between the first strain gauge 1 and the second strain gauge 2. The right-traveling and left-traveling waves of the fifth strain gauge B also satisfy the relationship (36), so the left-traveling wave of strain gauge B can be calculated, and so on. Based on this relationship, the right-traveling and left-traveling waves of the fourth strain gauge A and the fifth strain gauge B in each time period can be derived by using the attenuation correction and formula (36). -1 As an example, the impact curve under strain rate is as follows: Figure 14 This method can be used to obtain the loading and unloading curves of brain tissue under medium and high strain rates; by fitting the constitutive model, the degree of brain damage under the corresponding medium and high strain rates can be quantified.

[0175] Accordingly, the present application also provides an electronic device, comprising: one or more processors; a memory for storing one or more programs; when the one or more programs are executed by the one or more processors, the one or more processors implement the above-mentioned method for quantifying the degree of brain tissue damage under different strain rates. Figure 15 As shown in FIG, a hardware structure diagram of any device with data processing capability in which the method for quantifying the degree of brain tissue damage at different strain rates provided by the embodiment of the present invention is used, except Figure 15 In addition to the processor, memory, and network interface shown, any device with data processing capabilities in which the apparatus in the embodiment is located may also include other hardware, generally based on the actual functions of the device with data processing capabilities, which will not be described in detail.

[0176] Correspondingly, the application further provides a computer readable storage medium, which stores computer instructions, and the instructions are executed by a processor to implement the method for quantifying brain tissue injury degree under different strain rates as described above. The computer readable storage medium can be an internal storage unit of any device with data processing capability, such as a hard disk or a memory. The computer readable storage medium can also be an external storage device, such as a plug-in hard disk, a smart media card (SMC), an SD card, a flash card, etc. Further, the computer readable storage medium can include both the internal storage unit of any device with data processing capability and the external storage device. The computer readable storage medium is used to store the computer program and other programs and data required by the device with data processing capability, and can also be used to temporarily store data that has been output or will be output.

[0177] The above examples are only used to illustrate the design concept and characteristics of the present application, and the purpose is to enable those skilled in the art to understand the present application and implement it, and the protection scope of the present application is not limited to the above examples. Therefore, any equivalent changes or modifications made according to the disclosed principles and design ideas of the present application are within the protection scope of the present application.

Claims

1. A method for quantifying the degree of brain tissue damage under different strain rates, characterized in that: The method comprises: Construct constitutive models; Based on the constitutive model, the loading and unloading curves of brain tissue under different strain rates were fitted to obtain the hyperelastic-viscoelastic parameters, Mullins effect parameters, and residual deformation parameters of the brain tissue, thereby evaluating the damage state of the brain tissue. The area enclosed by the brain tissue loading curve and the brain tissue unloading curve is taken as the total dissipated energy, and the area enclosed by the unloading curve considering only viscoelasticity and the brain tissue unloading curve is taken as the damage dissipated energy. The ratio of the damage dissipated energy to the total dissipated energy is calculated to assess the degree of brain tissue damage. The ratio of damage dissipated energy to total dissipated energy and the maximum engineering strain were fitted to analyze the relationship between the degree of brain tissue tensile injury and strain.

2. The method for quantifying the degree of brain tissue damage under different strain rates according to claim 1, characterized in that: The expression of the constitutive model is as follows: ； ； Where, represents the total Cauchy stress, represents the Cauchy stress of the first spring in the loading direction, represents the Cauchy stress of the second spring in the loading direction, represents the first damage parameter, represents the second damage parameter, represents the Ogden modulus coefficient of the first spring in the first principal direction, represents the Ogden modulus coefficient of the first spring in the second principal direction, represents the exponential coefficient of the first spring in the first principal direction, represents the exponential coefficient of the first spring in the second principal direction, represents the Ogden modulus coefficient of the second damaged spring in the first principal direction, represents the Ogden modulus coefficient of the second damaged spring in the second principal direction, Indicates the elongation ratio of the material, is the extension ratio of the second spring in the loading direction, represents the exponential coefficient of the second spring in the first principal direction, represents the exponential coefficient of the second spring in the second principal direction, represents the viscosity constant of the damper, and are the material parameters to be fitted.

3. The method for quantifying the degree of brain tissue damage under different strain rates according to claim 1 or 2, characterized in that: The hyperelastic-viscoelastic parameters include the exponential coefficient of the first spring in the first main direction , the exponential coefficient of the first spring in the second main direction , Ogden modulus of the first spring in the first principal direction , Ogden modulus of the first spring in the second principal direction , Viscosity constant of the damper , the exponential coefficient of the second spring in the first principal direction , the exponential coefficient of the second spring in the second main direction , Ogden modulus coefficient of the second damaged spring in the first principal direction , Ogden modulus of the second damaged spring in the second principal direction ; The Mullins effect parameters include parameters r, m, and β to be fitted; The residual deformation parameters include b, k, i, j, p, and q to be fitted.

4. The method for quantifying the degree of brain tissue damage under different strain rates according to claim 3, characterized in that: The Mullins effect parameter is based on the first damage parameter Get, including: ； In the formula, r, m, and β represent the parameters to be fitted. is the maximum strain energy reached on the initial loading path, represents the strain energy density of the first spring without considering damage, 、 Both represent the principal extension ratio of the first spring.

5. The method for quantifying the degree of brain tissue damage under different strain rates according to claim 3, characterized in that: The residual deformation parameter is obtained based on the second damage parameter and the residual strain function, including: ； Where, represents the strain energy density of the first spring without considering damage, 、 Both represent the principal extension ratio of the first spring, is the maximum value of strain energy achieved on the initial loading path; is the maximum value of strain energy density during loading The relevant index parameters are The relationship is expressed as: ； Where b and k are the parameters to be fitted; The expression of the residual strain function is as follows: ； ； Where, represents the maximum elongation ratio, and i, j, p, and q are the parameters to be fitted.

6. The method for quantifying the degree of brain tissue damage under different strain rates according to claim 1, characterized in that: The process of obtaining the unloading curve considering only viscoelasticity includes: setting the first damage parameter is equal to 1, thus obtaining the unloading curve considering only viscoelasticity.

7. A system for quantifying the degree of brain tissue damage under different strain rates, characterized in that: The system comprises: Constitutive model building module, used to build the constitutive model; The brain tissue damage state assessment module is used to fit the loading and unloading curves of brain tissue under different strain rates based on the constitutive model to obtain the hyperelastic-viscoelastic parameters, Mullins effect parameters, and residual deformation parameters of the brain tissue, thereby assessing the damage state of the brain tissue; A brain tissue damage assessment module is used to use the area enclosed by the brain tissue loading curve and the brain tissue unloading curve as the total dissipated energy, and the area enclosed by the unloading curve that only considers viscoelasticity and the brain tissue unloading curve as the damage dissipated energy. The ratio of the damage dissipated energy to the total dissipated energy is calculated to assess the degree of brain tissue damage. The brain tissue damage degree analysis module is used to fit the ratio of damage dissipated energy to total dissipated energy and the maximum engineering strain, so as to analyze the relationship between the degree of brain tissue tensile damage and strain.

8. An electronic device, characterized in that: include: at least one processor; as well as a memory communicatively connected to the at least one processor; wherein, The memory stores one or more computer programs executable by the at least one processor, and the one or more computer programs are executed by the at least one processor to enable the at least one processor to perform the method for quantifying the degree of brain tissue damage under different strain rates as described in any one of claims 1 to 7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the computer program implements the method for quantifying the degree of brain tissue damage under different strain rates according to any one of claims 1 to 7.

10. A computer program product comprising a computer program / instructions, characterized in that When the computer program / instruction is executed by a processor, the method for quantifying the degree of brain tissue damage under different strain rates as described in any one of claims 1 to 7 is implemented.

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