A computational method for considering the contribution of biological activity to cochlear amplification mechanisms

Abstract

The present application relates to the field of biophysics technology, especially to a kind of calculation method for considering the contribution of biological activity to human sensory function.It includes a new type of calculation analysis model for considering the motion of cochlear acoustic function key support structure of biological activity based on physical mechanics principle.The present application deduces the periodic variation of the stiffness of basilar membrane in space and time while coupled with lymphatic fluid motion equation, and is solved.I.e.develop a kind of calculation method for considering the contribution of biological activity to human sensory function, and the correctness of the analytical method is verified by computer numerical simulation.The method established by the present application is easy to operate, feasible, efficient and accurate.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of biophysics technology, and particularly relates to a calculation method for considering the contribution of biological activity to cochlea sound amplification mechanism. BACKGROUND

[0002] Deafness is the most common human sensory system disorder, and 360 million people (5% of the world's population) worldwide suffer from deafness. Sensorineural hearing loss is the most challenging medical problem, and the cochlea active sound amplification mechanism is a major problem in otology. The basilar membrane is a key macroscopic structure in cochlear sound function, and Nobel laureate von Bekesy proposed a traveling wave vibration model of the basilar membrane. The previously reported cochlea calculation analysis model is based on the traveling wave theory, and so far, the understanding of the cochlea active amplification mechanism is limited to the interaction of the various tissue structures in the cochlea and the energy conversion to make the movement of the basilar membrane and microstructure produce amplification effect, but the effect of the material itself as a biological active structure changing over time is not considered. That is, the biological activity of the basilar membrane is not considered. SUMMARY

[0003] The purpose of the present application is to solve the defects proposed in the background art by proposing a calculation method for considering the contribution of biological activity to cochlea sound amplification mechanism and a battery grouping architecture.

[0004] Based on the physical mechanics theory, the control equation of the coupling motion of the cochlea endolymph and the basilar membrane is established, and the motion behavior of the basilar membrane is introduced into the Navier-Stokes equation through the body force term and coupled with the fluid motion.

[0005] The periodic function of the stiffness of the basilar membrane changing with space and time is comprehensively considered to describe the biological activity of the basilar membrane, and the coupling vibration behavior of the basilar membrane with the endolymph through the periodic change of the material itself under the condition of no external excitation is studied.

[0006] The technical scheme adopted by the present application is as follows:

[0007] On the one hand, a calculation method for considering the contribution of biological activity to cochlea sound amplification mechanism is provided, which includes.

[0008] An analytical model is established, and system stability analysis is performed, followed by non-periodic solution and periodic solution, and the system resonance characteristics are obtained.

[0009] As a preferred technical scheme of the present application: the analytical model establishment includes the calculation of the body force f:

[0010]

[0011] where δ(x) is a two-dimensional Dirac delta function, X(s, t) is the position parameter of the basement membrane in the Lagrangian coordinate system, and X0(s) = (s, 0) is the position at the equilibrium state;

[0012] The stiffness parameter of the basement membrane is assumed to vary with time and space, and thus can be expressed as a function:

[0013] K(s, t) = σe -λs (1 + 2τsin(ωt))

[0014] where σ is the average time-history elastic stiffness constant, and λ describes the stiffness variation along the basement membrane space. It is found from the previous experimental data that the stiffness of the basement membrane along the length presents an exponential variation rule, and thus an exponential function is used to describe the spatial variation of the stiffness. In addition, the amplitude parameter τ and the frequency ω are used to describe the periodic variation rule of the stiffness in the periodic vibration process of the basement membrane;

[0015] According to the coupling vibration interface condition of the fluid and the basement membrane, the following is obtained:

[0016]

[0017] The non-dimensionalization processing is used, and the non-dimensional quantities are as follows:

[0018]

[0019] where the non-dimensional quantities with the wavy upper mark are obtained by substituting the non-dimensional quantities into the following equation:

[0020]

[0021]

[0022]

[0023]

[0024]

[0025] The characteristic scales of the velocity and the pressure are expressed as:

[0026]

[0027] The parameters in the equation can be expressed as:

[0028]

[0029] The system equation is:

[0030]

[0031]

[0032] And the following conditions:

[0033] p = -k e -αx (1 + 2τsint)h(x,t)

[0034] u(x,0,t) = 0

[0035]

[0036] Wherein, h(x,t) represents the vertical displacement of the basement membrane, u(x,y,t) and v(x,y,t) are longitudinal and vertical velocities respectively.

[0037] As a preferred technical solution of the present application: the solution of the system satisfies the following form:

[0038] u(x,t) = e γt P(x,t)

[0039] In the formula, the function P(x,t) represents a periodic function with a period of 2π, and the index coefficient determines the stability of the solution in the interval [-π,π] when t->∞. By representing P(x,t) in series, we can get:

[0040]

[0041]

[0042]

[0043]

[0044] In the formula, P(x,t) is expanded in space and time Fourier series. The parameters to be solved in the above equation are the Fourier coefficients u k n ,v k n ,p k n along the y-axis; by substitution, we can get the pressure equation as:

[0045]

[0046] In the formula, Because of the linear independence characteristics, we have:

[0047]

[0048] Solving the above equation, we get:​

[0049]

[0050]

[0051] Further derivation can be made to the ordinary differential equation as follows:

[0052]

[0053] In the formula,

[0054] Assuming γ+in≠0 and k≠0, the solution of the above formula is:

[0055]

[0056] According to continuity, the equation is:

[0057]

[0058] The solution is:

[0059]

[0060] According to continuity, the interface boundary condition can be derived as:

[0061]

[0062]

[0063] Further derivation can be made as follows:

[0064]

[0065]

[0066] Substituting the above formula can be obtained:

[0067]

[0068] When γ+in=0 and k=0, the above formula can be simplified as:

[0069]

[0070] The exponential function and the sine function in the above formula are Fourier expanded, and there is 1+2τsint=1-iτe it +iτe -it

[0071] The exponential function is expanded by even function period, and when γ+in≠0 and k≠0, there is:

[0072]

[0073] For γ+in= 0 and k = 0, we have:

[0074]

[0075] where,

[0076] are the Fourier coefficients of the exponential function; for ε k n The coefficients of the terms are arranged, and we have:

[0077]

[0078] For γ+in= 0 and k = 0, we have:

[0079]

[0080] To ensure the solution of the even function space symmetry, we have:

[0081]

[0082]

[0083] For the solution u(x, t) = e γt P(x, t), there are the following periodic conditions:

[0084] u(x, t + 2πn) = e γ(t+2πn) P(x, t) = ξ n u(x, t)

[0085] If γ = 0, then ξ = 1, and we have:

[0086] u(x, t + 2π) = u(x, t)

[0087] The above formula is a harmonic solution with a period of 2π. If γ = 1 / 2*i, then ξ = -1, and we have:

[0088] u(x, t + 2π) = -u(x, t), u(x, t + 4π) = u(x, t)

[0089] By reducing the system equation, another n = 0, 1,..., N, and k = 1, 2,..., M, we have:

[0090]

[0091] where,

[0092] The above equation has 2*M*(N+1) unknown coefficients to be solved, A and B are diagonal matrices; diagonal matrix A can be expressed as A=diag(A 0 , A 1 ,..., A N ), and has the following form:

[0093]

[0094] Wherein,

[0095]

[0096]

[0097] The triangular diagonal matrix B has the following form:

[0098]

[0099] Wherein,

[0100]

[0101] The matrices A and B are known, that is:

[0102]

[0103] Wherein, the eigenvalue of the stability solution in the above equation is 1 / τ.

[0104] As a preferred technical scheme of the application: the non-periodic solution includes:

[0105] When τ=0 in the stiffness function of the basement membrane, the stiffness function is a non-periodic function, the solution of the equation is stable, and the Fourier coefficient of the solution satisfies:

[0106]

[0107] When k=0, we have:

[0108]

[0109] In the above formula, φ=ν 2 / κ=π 3 μ 2 / (ρσL 3 ), which represents the ratio of the viscous resistance of the fluid to the elastic force of the basement membrane; the above equation can be expressed as Wherein, the matrix T depends on the parameters φ, γ and α. The condition for the system to have a non-singular solution is to satisfy det(T)=0, when φ and α are given, γ can be obtained by solving.

[0110] As a preferred technical solution of the present application, the periodic solution includes solving the equation

[0111]

[0112] and

[0113]

[0114] τ and the corresponding eigenvector can be obtained, and on this basis, the periodic solution h(x, t) is solved by the equation

[0115]

[0116] BRIEF DESCRIPTION OF DRAWINGS

[0117] Figure 1 is a two-dimensional cochlea model diagram of the preferred embodiment of the present application;

[0118] Figure 2 is a real part and imaginary part solution diagram of γ satisfying det(T) = 0 in the preferred embodiment of the present application;

[0119] Figure 3 is a non-dimensionalized basilar membrane displacement amplitude curve in the preferred embodiment of the present application;

[0120] Figure 4 is a peak position of basilar membrane vibration changing with frequency diagram in the preferred embodiment of the present application;

[0121] Figure 5 is a basilar membrane displacement changing with time curve diagram in the preferred embodiment of the present application;

[0122] Figure 6 is a basilar membrane displacement changing with time curve diagram in the preferred embodiment of the present application (wherein ω = 400 s -1 , τ = 0.05, 0.08 and 0.1 respectively correspond to upper, middle and lower);

[0123] Figure 7 is a basilar membrane displacement changing with time curve diagram in the preferred embodiment of the present application (wherein ω = 600 s -1 , τ = 0.05, 0.08 and 0.1 respectively correspond to upper, middle and lower);

[0124] Figure 8 is a basilar membrane displacement changing with time curve diagram in the preferred embodiment of the present application (wherein ω = 800 s -1 , τ = 0.05, 0.08 and 0.1 respectively correspond to upper, middle and lower);

[0125] Figure 9 ​Figures of displacement of the basilar membrane with respect to position at different frequencies in preferred embodiments of the present application. DETAILED DESCRIPTION

[0126] It should be noted that the embodiments in the present embodiment and the features in the embodiments can be combined with each other without conflict, and the technical solutions in the embodiments of the present application will be described clearly and completely in combination with the drawings of 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. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the protection scope of the present application.

[0127] Reference Figures 1-9 The preferred embodiments of the present application provide a calculation method for considering the contribution of biological activity to the cochlea sound amplification mechanism.

[0128] The present application mainly analyzes the vibration characteristics of the basilar membrane in the cochlea system, and therefore the cochlea model is reasonably simplified, and a simplified 2D cochlea model is considered, as shown in FIG. 1. The cochlea channel is a two-cavity rectangular structure with a length of L and a half-cavity height of H, and the basilar membrane is located at the center of the cavity. The influence of the essential characteristics of the basilar membrane on vibration is studied. Figure 1 The solid line in FIG. 2 represents the vibration of the basilar membrane away from the equilibrium position, and the dashed line represents the equilibrium position of the basilar membrane. The X-axis is defined along the length direction of the cochlea, and the Y-axis is defined along the thickness direction. Figure 1

[0129] Based on the incompressible N-S equation, there are:

[0130]

[0131]

[0132] In the formula, u(x, t) is the fluid velocity, p(x, t) is the pressure, ρ is the density, and μ represents the viscosity coefficient. The present application mainly studies the change of stiffness in space and time, and therefore the volume force f is:

[0133]

[0134] In the formula, δ(x) represents a two-dimensional Dirac delta function, X(s, t) represents the position parameter of the basilar membrane in the Lagrangian coordinate system, and X0(s) = (s, 0) represents the equilibrium position. The volume force f of the equation is determined by the intrinsic property stiffness K(s, t) of the basilar membrane, and the vibration characteristics under the adjustment of the intrinsic property of the basilar membrane can be described by the change of the parameter of the basilar membrane stiffness. The stiffness parameter of the basilar membrane is assumed to change with time and space, and therefore can be represented by a function as: ​

[0135] K(s,t) = σe -λs (1+2τsin(ωt)) (3)

[0136] In the formula, σ is the average time-history elastic stiffness constant, λ describes the stiffness variation along the spatial direction of the basilar membrane. From the previous experimental data, it is found that the stiffness of the basilar membrane presents an exponential variation rule along the length, and therefore an exponential function is used to describe the spatial variation of the stiffness. In addition, the amplitude parameter τ and the frequency ω are used to describe the periodic variation rule of the stiffness in the periodic vibration process of the basilar membrane.

[0137] According to the coupling vibration interface condition of the fluid and the basilar membrane, the following can be derived:

[0138]

[0139] In order to have commonality of the present application, dimensionless processing is adopted, and the dimensionless quantities are as follows:

[0140]

[0141] In the formula, the upper mark with the wavy line is a dimensionless quantity. Uc and Pc represent the characteristic scales of the velocity and the pressure respectively. The above dimensionless quantity is substituted into formula (4) to obtain:

[0142]

[0143]

[0144]

[0145]

[0146]

[0147] The characteristic scales of the velocity and the pressure are represented as:

[0148]

[0149] Therefore, the parameters in equations (6) and (9) can be represented as:

[0150]

[0151] For the above established equation, further processing is needed in order to solve and analyze. Since the amplitude of the basilar membrane is generally in the nanometer scale, which is very small compared with the size of the cochlear channel, it means that the Reynolds number of the fluid is very small, and therefore the nonlinear effect of the fluid can be ignored. In addition, the vibration of the basilar membrane is mainly in the transverse Y direction, and the present model only considers the vibration in the Y direction. In summary, the system equation can be:

[0152]

[0153]

[0154] and the following conditions:

[0155] p = -k e -αx (1 + 2τsint)h(x,t)

[0156] u(x,0,t) = 0

[0157]

[0158] where h(x,t) represents the vertical displacement of the basement membrane, and u(x,y,t) and v(x,y,t) are the longitudinal and vertical velocities, respectively.

[0159] Since there is a time-varying stiffness parameter in the system, the solution of the system satisfies the following form:

[0160] u(x,t) = e γt P(x,t) (16)

[0161] where the function P(x,t) represents a periodic function with a period of 2π, and the coefficient of the exponential term determines the stability of the solution as t->∞. By representing P(x,t) as a series in the interval [-π,π], we obtain:

[0162]

[0163]

[0164]

[0165]

[0166] where P(x,t) is expanded in space and time Fourier series. The parameters to be solved in the above equations are the Fourier coefficients u k n ,v k n ,p k n along the y-axis. Substituting equations (17-19) into equations (13) and (14) gives the Poisson equation for pressure, which is expressed as:

[0167]

[0168] where Due to the linear independence property, we have:

[0169] ​

[0170] By solving equation (22), we have:

[0171]

[0172] Substituting equation (18) into equation (13), we have:

[0173]

[0174] Further derivation can be made to the ordinary differential equation as:

[0175]

[0176] In which,

[0177] Assuming γ+in≠0 and k≠0, the solution of equation (25) is:

[0178]

[0179] According to continuity, we have equation:

[0180]

[0181] Solving it, we have:

[0182]

[0183] According to continuity, the interface boundary condition can be derived as:

[0184]

[0185]

[0186] Further derivation can be made to:

[0187]

[0188]

[0189] Substituting equations (32) and (33) into equation (23), and further substituting into equation (13), we have:

[0190]

[0191] When γ+in=0 and k=0, equation (34) can be simplified as:

[0192]

[0193] The Fourier expansion of the exponential function and the sine function in the above formula is 1+2τsint=1-iτe it +iτe -it

[0194] Since e -ax It is not a periodic function in [0, π], so its Fourier series cannot converge in [0, π], so the function is extended to the interval [-π, π] for expansion, and only the interval x≥0 is concerned. Therefore, the exponential function is expanded as an even function, and when γ+in≠0 and k≠0, there is:

[0195]

[0196] For γ+in=0 and k=0, there is:

[0197]

[0198] where,

[0199]

[0200] is the Fourier coefficient of the exponential function. The coefficients of the εkn terms are arranged to obtain:

[0201]

[0202] For γ+in=0 and k=0, there is:

[0203]

[0204] For α≠0, the above equations (39) and (40) form a linear system, hjn in which is a spatially varying stiffness parameter, and the coupling effect between various spatial modes is considered.

[0205] Because the present application mainly studies the stability of the cochlear mechanical system, we mainly solve the periodic solution in equations (39) and (40), i.e. when Re{γ}=0. In addition, for the solution of the stability boundary, the parameter γ has two types of values, the first type is γ=0, which corresponds to the harmonic solution of the system; the second type is γ=1 / 2*i, which corresponds to the subharmonic solution of the system. In order to ensure that h(x, t) takes a value in the range of real numbers, the condition is introduced, where the h with a horizontal line above the head represents the conjugate complex of h. In order to ensure the even function space symmetry of the solution, there is:

[0206]

[0207]

[0208] For the solution (16), there are the following periodic conditions:

[0209] u(x, t + 2πn) = e γ(t+2πn) P(x, t) = ξ n u(x, t) (43)

[0210] For any positive integer n, when ξ = e γ2π and t takes a fixed value, the above conditions are satisfied. When n -> ∞, if |ξ| < 1, the solution is stable, and if |ξ| > 1, the solution is unstable. When ξ = ±1, it corresponds to the boundary condition of the periodic solution from stable to unstable state. If γ = 0, then ξ = 1, and there is:

[0211] u(x, t + 2π) = u(x, t) (44)

[0212] The above formula is a harmonic solution with a period of 2π. If γ = 1 / 2*i, then ξ = -1, and there is:

[0213] u(x, t + 2π) = -u(x, t), u(x, t + 4π) = u(x, t) (45)

[0214] The above formula is a bi-periodic sub-harmonic solution. In order to solve equations (39)-(42), we reduce the system equation, and n = 0, 1,..., N, and k = 1, 2,..., M, and by matrix representation, we have:

[0215]

[0216] where,

[0217] The above equation has a total of 2*M*(N+1) unknown coefficients to be solved, and A and B are diagonal matrices. The diagonal matrix A can be expressed as A = diag(A 0 , A 1 ,..., A N ), and has the following form:

[0218]

[0219] where,

[0220]

[0221] The triangular diagonal matrix B has the following form:

[0222]

[0223] where,

[0224]

[0225] Both matrices A and B are known, the solution of equation (46) can be seen as an eigenvalue problem, i.e.

[0226]

[0227] The eigenvalue of the stability solution in the above equation is 1 / τ. For the physical problem discussed in this paper, we only focus on those values of τ which are real numbers and less than 1 / 2, so as to ensure that the stiffness function K(s, t) is real and non-negative.

[0228] When τ = 0 in the stiffness function of the basement membrane, the stiffness function is aperiodic, the solution of the equation is stable, and the Fourier coefficients of the solution satisfy:

[0229]

[0230] When k = 0, we have:

[0231] In equation (54), φ = v 2 / κ = π 3 μ 2 / (ρσL 3 ), which represents the ratio of the viscous resistance of the fluid to the elastic force of the basement membrane. The above equation can be simply expressed as where the T matrix depends on the parameters φ, γ and α. The condition for the existence of a non-singular solution of the system is to satisfy det(T) = 0, when given φ and α, γ can be obtained by solving.

[0232] Let α = 1, M = 20, and calculate γ under two conditions φ = 1*10 -8 , 1*10 -4 , respectively. The calculation results are shown in Figure 2 . Among them, the thick line represents the real part of the solution, and the thin line represents the imaginary part of the solution. The intersection point of the real part and the imaginary part corresponds to the resonance mode of the system.

[0233] As can be seen from Figure 2 , the intersection point of the real part and the imaginary part is always negative, which indicates that the solution is stable. For a relatively small φ, the Im{γ} of the main mode is non-zero, so the solution is oscillatory. When φ increases to 1*10 -4 , the effect of fluid viscosity increases, the main mode presents decay, and there is no oscillation. In the above two cases, the system mode gradually decays with the increase of time, therefore, when τ = 0, the periodic solution or the unstable solution does not exist, and the non-zero τ parameter considering the time-varying effect in the stiffness function must exist, and the periodic solution exists.

[0234] When considering tau≠0, the stiffness function of the basilar membrane is equivalent to introducing an intrinsic accommodation mechanism varying with time, which has the same effect as considering the biological activity of the basilar membrane, that is, the material of the basilar membrane changes with time and has self-repairing property. By solving equations (39) and (40), tau and the corresponding characteristic vector can be obtained, and on this basis, the periodic solution h(x, t) is solved by equation (20). The parameters selected in the calculation are shown in Table 1.

[0235] Table 1 Parameters for calculating the human cochlea system

[0236]

[0237]

[0238] According to the parameters in Table 1, the vertical displacement curves of the basilar membrane when the frequency ω=400, 1000, 2000, 5000 are calculated respectively peak , wherein t peak represents the time corresponding to the maximum vertical displacement, and the calculation results are shown in Figure 3 . The curve results in the figure are dimensionless results, and the envelope curve is determined by calculating the complex function of the basilar membrane, wherein the real part of the complex function is the vibration amplitude of the basilar membrane, and the imaginary part is the Hilber transform. Among them, the internal wavy solid line represents the harmonic vibration of the basilar membrane, the dashed line represents the subharmonic vibration of the basilar membrane, and the external wavy solid line represents the envelope curve of the basilar membrane vibration

[0239] The COMSOL software is used for simulation in the application.

[0240] Since the perilymph fluid has low viscosity and is incompressible, and the Reynolds number is low, the fluid is selected as a laminar flow model, and is assumed to be an incompressible viscous fluid. The N-S equation of the fluid is:

[0241]

[0242]

[0243] In the formula, ρ and μ are the density and viscosity coefficient of the fluid respectively, u fluid and p represent the velocity and pressure of the fluid respectively, and F represents the volume force density acting on the fluid.

[0244] The interface between the basilar membrane and the perilymph fluid is a fluid-structure coupling interface, and has

[0245] u fluid = u solid

[0246]

[0247] That is, the displacement of the solid and the displacement of the fluid on the interface are equal, the pressure generated by the fluid motion acts on the solid, at the same time, the stress generated by the solid deformation acts on the fluid, and the solid unit nodes and the fluid unit nodes on the interface keep corresponding and consistent, and are distinguished from each other.

[0248] By Figure 3 It can be seen that the envelope curve of the substrate membrane vibration presents an asymmetric distribution characteristic, and the curve amplitude increases slowly from the base to the top, reaches a peak point, and then decreases rapidly. The peak position is different under different frequencies. As can be seen, the traveling wave vibration of the substrate membrane does not necessarily need external active force to realize, because the stiffness of the substrate membrane itself changes with time and space, and the same calculation results as the previous pure tone excitation model can be obtained.

[0249] Figure 4 The Figure 3 Peak position of the curve shown in the figure changes with frequency, which is displayed in the logarithmic coordinate system. The solid square is the analytical solution obtained in the above, the hollow circle is the finite element simulation result, and the hollow triangle is the test result. As can be seen from the figure, the peak position of the vibration presents a nearly piecewise linear decreasing trend with the increase of frequency, and the frequency of 2000s -1 The point is the piecewise point, and the analytical result is consistent with the numerical simulation result and the test result, so the analytical model developed by the application is reasonable and accurate.

[0250] In order to solve formula (53), a simple special case α=0 is considered first, that is, the stiffness function of the substrate membrane does not depend on the position of the substrate membrane, so the Fourier series can be decoupled in space, and for each spatial wave number k, there is:

[0251]

[0252] Formula (56) can be simply expressed as:

[0253]

[0254] Wherein, for each k, there is:

[0255]

[0256]

[0257] Wherein, D k N Determined by formula (50). Select parameters ω=900, 1000, 1100s -1 , and τ=0.1, 0.2, other parameters refer to table 1, the amplitude of the substrate membrane under different parameters is calculated, as shown in Figure 4 .

[0258] From Figure 5 it can be known that (wherein α=0, k=1), when τ=0.1, for ω equal to 900s -1 and 1100s -1 , the vibration of the basement membrane is stable, that is, with the increase of time, the basement membrane finds nearly equal amplitude vibration, and a slight attenuation occurs at the end time; and for ω equal to 1000s -1 , with the increase of time, the amplitude of the basement membrane gradually increases, and resonance occurs at the end time. When τ=0.2, only for ω equal to 900s -1 , the vibration of the basement membrane is stable, and resonance occurs in the basement membrane at other frequencies. By comparison, for ω equal to 1000s -1 , the basement membrane all appears resonance, and the amplitude is the largest, and the amplitude at other frequencies is relatively small.

[0259] The finite element numerical simulation results established by the application are consistent with the analytical model results (see Figure 3 , 4 and Figure 9 ), and due to the consideration of the effect of the change of the material of the basement membrane with time, the non-stable resonance motion characteristics of the basement membrane are found. The difference is that the analytical model does not consider the external excitation, and only the periodic change of the stiffness parameter of the basement membrane is modulated to cause the non-stable global resonance phenomenon of the basement membrane, while the finite element model not only considers the change of the nature of the material itself with time, but also considers the time variation factor of the external excitation, which means that only through the change of the biological activity of the basement membrane itself, the basement membrane can perceive different frequency sounds, so as to produce different vibration amplitudes and vibration forms.

[0260] Continue to analyze the case of α≠0, that is, the stiffness of the basement membrane is coupled in the spatial position, and presents an exponential change with the length. For the selected different parameters ω (400, 600, 800s -1 ) and τ (0.05, 0.08, 0.1), the vibration amplitude curve of the basement membrane changing with time is calculated, as shown in Figures 6-8 .

[0261] It can be known from the figure that when τ=0.05, the vibration of the basement membrane gradually attenuates with the increase of time, but the internal force change caused by the stiffness cannot significantly cause the instability of the vibration of the basement membrane. When τ increases to 0.08, the instability of the vibration of the basement membrane is obviously strengthened, and periodic fluctuation is maintained. When τ increases to 0.1, the unstable vibration of the basement membrane is very violent.

[0262] Based on the above analysis, the time-varying effect of the stiffness parameter is reflected in the frequency ω and the amplitude parameter τ of the periodicity. With the change of the frequency and the amplitude parameter, the basilar membrane will produce a sharp resonance, which can trigger the sensitive active hearing process and the sound amplification process of the cochlea. The resonance phenomenon of the basilar membrane becomes more intense with the increase of the amplitude parameter τ of the periodicity, and the resonance phenomenon at low frequency is more significant than that at medium and high frequencies. The spatial and temporal parameter variation of the basilar membrane stiffness is derived from the spatial distribution and biological activity of the material of the basilar membrane structure itself, rather than from the external feedback force, that is, the vibration sound amplification process of the basilar membrane is realized through the inherent property of the basilar membrane material, i.e. biological activity.

[0263] Based on the established finite element model, the relationship between the displacement of the basilar membrane along the Y direction and the space under different excitation frequencies is calculated, as shown in FIG. A-3. In the figure, high frequency 15000s -1 , medium frequency 5000s -1 , 1000s -1 , and low frequency 500s -1 and 200s -1 are selected. As can be seen from the figure, when the excitation frequency gradually decreases from high frequency to low frequency, the maximum displacement of the basilar membrane generally extends from the base to the top. However, when the frequency decreases to 500s -1 , the vibration form of the basilar membrane is different from the previous traveling wave vibration (only local intense vibration is produced). The basilar membrane not only has a peak value in the local part, but also has a resonance phenomenon along the whole space. When the frequency continues to decrease to 200s -1 , the whole basilar membrane produces a relatively intense resonance phenomenon, which explains the experimental phenomenon that the basilar membrane produces a resonance phenomenon different from the traveling wave vibration at low frequency, which cannot be described by the previous traveling wave theory.

[0264] Based on the established finite element model, the relationship between the displacement of the basilar membrane along the Y direction and the space under different excitation frequencies is calculated, as shown in FIG. A-3. In the figure, high frequency 15000s -1 , medium frequency 5000s -1 , 1000s -1 , and low frequency 500s -1 and 200s -1 . As can be seen from the figure, when the excitation frequency gradually decreases from high frequency to low frequency, the maximum displacement of the basilar membrane generally extends from the base to the top. However, when the frequency decreases to 500s -1 , the vibration form of the basilar membrane is different from the previous traveling wave vibration (only local intense vibration is produced). The basilar membrane not only has a peak value in the local part, but also has a resonance phenomenon along the whole space. When the frequency continues to decrease to 200s -1When the frequency is less than 400s -1 , the vibration of the basilar membrane is different from the previous traveling wave vibration (only local intense vibration is produced), the basilar membrane not only appears peak value in local, but also along the whole space resonance phenomenon, when the frequency is 200s -1 , the basilar membrane produces relatively intense resonance phenomenon, which also explains the experimental phenomenon that the previous traveling wave theory cannot describe, that is, the basilar membrane produces different resonance phenomenon from traveling wave vibration at low frequency.

[0265] The present application establishes a biomechanical model considering the characteristics (biological activity) of the periodic variation of the stiffness parameter of the basilar membrane with space and time, not only reproduces the basilar membrane traveling wave vibration behavior of the previous experiment, verifies the correctness of the model, but also finds that the basilar membrane exists unstable resonance phenomenon, through the calculation and analysis of analysis and numerical simulation, the following conclusions are obtained:

[0266] (1) When the stiffness of the basilar membrane does not exist time variation effect, that is, when τ=0, the vibration of the basilar membrane is stable, due to the consideration of the viscosity of the fluid, the vibration of the basilar membrane is gradually attenuated with the increase of time. When the basilar membrane has biological activity, that is, when τ≠0, the vibration of the basilar membrane becomes unstable, and presents periodic vibration characteristics.

[0267] (2) When the frequency is greater than or equal to 400s -1 , the vibration of the basilar membrane presents the vibration characteristics of traveling wave, with the increase of the frequency parameter of the stiffness, the maximum amplitude of the basilar membrane gradually deviates from the base top to the base, due to the viscosity of the fluid and the damping of the basilar membrane itself, the amplitude gradually decreases. When the frequency is less than 400s -1 , the vibration form of the basilar membrane is different from the previous traveling wave vibration (only local intense vibration is produced), the basilar membrane not only appears peak value in local, but also along the whole space resonance phenomenon, when the frequency is 200s -1 , the basilar membrane produces relatively intense resonance phenomenon, which also explains the experimental phenomenon that the previous traveling wave theory cannot describe, that is, the basilar membrane produces different resonance phenomenon from traveling wave vibration at low frequency. [10,39-40] .

[0268] (3) When the spatial position variation parameter α of the stiffness of the basilar membrane is described as 0, that is, the coupling of the time variation parameter and the spatial variation parameter is not considered, when ω is equal to 1000s -1 , no matter the time parameter τ=0.1 or 0.2, the basilar membrane all occurs unstable resonance phenomenon, the amplitude at other frequencies is small. Only when the time parameter τ gradually increases, the basilar membrane will occur stable resonance motion at other frequencies.

[0269] (4) When α≠0, that is, the stiffness of the basilar membrane is coupled in the spatial position, the basilar membrane all occurs unstable vibration at different frequencies, and with the increase of τ, the unstable vibration of the basilar membrane becomes intense, resonance phenomenon occurs.

[0270] Through the research of the application, an important conclusion is obtained: without considering the external excitation, only through the periodic change modulation of the stiffness parameter of the basilar membrane in time and space, the non-stable overall resonance phenomenon of the basilar membrane can be caused, so as to trigger the sensitive perception and amplification process of the cochlea to sound, which implies that without the additional force action, only through the change of the biological activity of the basilar membrane itself, the basilar membrane and the surrounding lymph fluid can produce violent coupling vibration, (that is, a part of the amplification mechanism of the cochlea to sound is derived from the biological activity of the basilar membrane and its microstructure itself, which has not been reported in the previous research.) The calculation model can help humans to comprehensively reveal the amplification mechanism of the cochlea to sound.

[0271] From the research results of the application, an important conclusion can be drawn: when modeling and analyzing living beings by applying physical mechanics principles, the classical theoretical method for studying objects in the past should be broken through, and the change of biological activity of living beings should be supplemented, which is the essential difference between biological mechanics and general mechanics.

[0272] The application provides an accurate, feasible and efficient calculation method for modeling and analyzing living beings by applying physical mechanics principles.

[0273] It is apparent to those skilled in the art that the application is not limited to the details of the foregoing exemplary embodiments, and the application can be implemented in other specific forms without departing from the spirit or essential characteristics of the application. Therefore, the embodiments should be regarded as exemplary and non-limiting, and the scope of the application is defined by the appended claims rather than the foregoing description, and all changes falling within the meaning and range of equivalent elements of the claims are intended to be included in the application. Any reference signs in the claims should not be regarded as limiting the claims involved.

[0274] In addition, it should be understood that although the present specification is described in terms of embodiments, not every embodiment contains only one independent technical solution, and the description manner of the specification is only for the sake of clarity, and those skilled in the art should regard the specification as a whole, and the technical solutions in each embodiment can also be properly combined to form other embodiments that those skilled in the art can understand.

Claims

1. A calculation method for considering the contribution of biological activity to the cochlear acoustic amplification mechanism, characterized in that, include: An analytical model is established, and system stability analysis is performed. Then, non-periodic and periodic solutions are obtained to determine the system's resonance characteristics. The analytical model establishment includes the calculation of volume force f: In the formula, δ(x) represents the two-dimensional Dirac delta function; The stiffness parameters of the basement membrane are assumed to vary with time and space, and therefore can be expressed as a function: K(s,t)=σe -λs (1+2τsin(ωt)) In the formula, σ is the average time history elastic stiffness constant, and λ describes the stiffness variation along the space of the basement membrane. According to the analysis of previous experimental data, the stiffness of the basement membrane exhibits an exponential variation along its length. Therefore, an exponential function is used to describe the spatial variation of stiffness. In addition, the periodic variation of stiffness during the periodic vibration process of the basement membrane is described by the amplitude parameter τ and the frequency ω. Based on the coupling vibration interface conditions between the fluid and the basement membrane, it is deduced that: The dimensionless quantities are as follows: In the formula, quantities marked with a wavy line are dimensionless quantities, U c and P c Representing the characteristic scales of velocity and pressure respectively, substituting the dimensionless quantities, we get: The characteristic scales of velocity and pressure are expressed as follows: The parameters in the equation can be expressed as: The system equations are: And the following conditions must be met: p=-κe -αx (1+2τsint)h(x,t) u(x,0,t)=0 Where h(x,t) represents the vertical displacement of the basement membrane, and u(x,y,t) and v(x,y,t) are the longitudinal and vertical velocities, respectively; The aperiodic solution includes: When τ = 0 in the stiffness function of the basement membrane, the stiffness function is a non-periodic function, the solution of the equation is stable, and the Fourier coefficients of the solution satisfy: When k = 0, we have: In the above formula, φ=ν 2 / κ=π 3 μ 2 / (ρσL 3 This represents the ratio of fluid viscous resistance to the elastic force of the basement membrane; The periodic solution includes solving the formula. and We can obtain τ and its corresponding eigenvectors. Based on this, we can use the formula... Solve for the periodic solution h(x,t).

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