A method for evaluating bone structure mechanical properties based on photoacoustic guided wave waveform inversion

Abstract

The application discloses a kind of bone structure mechanical property evaluation methods based on photoacoustic guided wave waveform inversion, comprising the following steps:S1: using full laser system obtains photoacoustic guided wave signal in bone axial two points;Step S2: determine signal effective bandwidth, using separation spectrum technology to extract each narrowband component;Step S3: waveform inversion algorithm parameter initialization;Step S4: calculate guided wave structure guided wave dispersion equation, obtain guided wave frequency wave number curve;Step S5: based on ultrasonic propagation function, calculate individual correlation guided wave mode signal;Step S6: individual correlation multi-narrowband component signal residual rate calculation and individual screening;Step S7: inversion algorithm cut-off criterion, if meet, then enter step S9;Otherwise, enter step S8;Step S8: individual update, construct new analysis population, enter step S4;Step S9: input guided wave wave number dispersion and waveguide structure mechanical property.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of laser-ultrasound medical treatment, and in particular to a method for evaluating the mechanical properties of bone structure based on photoacoustic guided wave waveform inversion. BACKGROUND

[0002] The full laser-ultrasound guided wave excitation detection technology has the advantages of non-contact and rich signal information, and has attracted widespread attention in the fields of medical ultrasound diagnosis and industrial nondestructive testing. In research or engineering applications, a laser vibration meter is used to scan and obtain guided wave spatial wave field signals, a multi-dimensional Fourier transform is used to obtain a wave field frequency wave number spectrum, and a waveguide structure mechanical property evaluation is realized by combining the guided wave dispersion theory. The scholars proposed a method for evaluating the mechanical properties of waveguide structure by inverting the waveforms of two-point detection piezoelectric sensors excited by guided wave signals, which overcomes the dependence of ultrasonic guided wave quantitative evaluation technology on wave field signal acquisition, and greatly improves the flexibility of the evaluation technology implementation (for reference, Chen HL, Ling FY, Zhu WJ, et al., Waveform inversion for wavenumber extraction and waveguide characterization using ultrasonic Lamb waves. Measurement, 2023, 207:112360).

[0003] The existing method has the following disadvantages:

[0004] (1) The wave number extraction and structural mechanical property evaluation based on narrow-band guided wave signal waveform inversion are easily affected by signal frequency;

[0005] (2) The traditional narrow-band stationary signal waveform inversion technology is not suitable for wave number extraction and structural mechanical property evaluation of wideband and non-stationary photoacoustic guided waves;

[0006] (3) The bone quality evaluation method based on guided wave spatial wave field signal analysis has poor application flexibility. SUMMARY

[0007] In order to overcome the deficiencies in the prior art, the present application provides a method for evaluating the mechanical properties of bone structure based on photoacoustic guided wave waveform inversion, which overcomes the dependence of photoacoustic guided wave quantitative evaluation technology on spatial wave field signal acquisition, and improves the flexibility and reliability of the detection method implementation.

[0008] In order to achieve the above application purposes and solve the technical problems, the technical solutions adopted are as follows:

[0009] A method for evaluating the mechanical properties of bone structure based on photoacoustic guided wave waveform inversion, comprising the following steps:

[0010] Step S1: using a full optical system to excite photoacoustic guided waves in the bone, detecting and obtaining guided wave signals at two points on the bone axis, and then entering step S2;

[0011] Step S2: evaluating and determining the effective bandwidth of the photoacoustic guided wave signal, extracting different narrow-band components of the photoacoustic guided wave signal, and then entering step S3;

[0012] Step S3: waveform inversion algorithm initialization: setting individual gene range according to guided wave dispersion theory equation and ultrasonic propagation function parameter, individual initialization, setting optimization algorithm iteration update and cutoff criterion parameter, and then entering step S4;

[0013] Step S4: calculating the guided wave dispersion equation of the waveguide structure based on the individual gene parameters, obtaining the guided wave frequency wavenumber curve, and then entering step S5;

[0014] Step S5: calculating the individual related mode guided wave signal based on the ultrasonic propagation function, and then entering step S6;

[0015] Step S6: individual related multi-narrow-band component signal residual rate evaluation, individual screening, and then entering step S7;

[0016] Step S7: analyzing whether the individual residual rate and the evolution generation number meet the cutoff criterion, if yes, entering step S9; otherwise, entering step S8;

[0017] Step S8: updating the individual gene parameters, constructing a new analysis population, and then entering step S4;

[0018] Step S9: outputting the preferred individual gene and guided wave wavenumber dispersion information, and evaluating the mechanical properties of the long bone structure.

[0019] Further, in step S1, a pulsed laser is used to excite photoacoustic guided waves in the long bone, and optical means is used to collect and obtain guided wave signals at two detection points on the bone axis. The photoacoustic guided wave wavenumber extraction and bone structure mechanical property evaluation are realized through two-point detection signals.

[0020] Further, in step S2, the effective bandwidth of the photoacoustic guided wave signal is determined based on Fourier spectrum analysis, and each narrow-band component in the two detection photoacoustic guided wave signals is extracted using a Gaussian filter box-based separation spectrum technology, converting the wideband non-stationary signal into multiple narrow-band stationary signals.

[0021] Further, step S2 includes the following contents:

[0022] Step S21: analyzing the Fourier spectrum of the photoacoustic guided wave signal to obtain the signal effective bandwidth interval [ω d ,ω u ];

[0023] Step S22: Extracting each narrowband component of the photoacoustic guided wave signal by using a Gaussian window band-pass filter box, specifically as formula (1) and (2):

[0024]

[0025] In the formula, G m is a band-pass Gaussian filter box, ω u and ω d are the upper and lower cut-off frequencies of the filter, m and M are the filter window number and the number of windows, respectively, and u and u m are the detection signal and the extracted narrowband component, respectively.

[0026] Further, in the step S2, each narrowband component in the two detection photoacoustic guided wave signals is extracted by using continuous wavelet transform, and the wideband non-stationary signal is converted into multiple narrowband stationary signals.

[0027] Further, in the step S3, individual genes are set according to the long bone guided wave dispersion theory equation and the ultrasonic propagation function, and the individual population is initialized; the individual gene update control parameters are set according to the inversion optimization algorithm type.

[0028] Further, in the step S4, the guided wave frequency-wave number curve in the long bone within the effective bandwidth range of the photoacoustic signal is calculated by using the dichotomy or the Legendre polynomial expansion method.

[0029] Further, in the step S5, based on the ultrasonic propagation function, the narrowband frequency component of the guided wave signal of the first detection point is extracted as a virtual excitation source, the wave number dispersion curve is calculated by using the step S4, and the forward simulation signal of the individual related mode guided wave at the second detection point is calculated according to the distance between the two detection points.

[0030] Further, the step S6 includes the following contents:

[0031] Step S61: Calculating the residual rate of different narrowband components for individual screening and gene parameter updating;

[0032] Step S62: Arranging the residual rates of each signal in ascending order, and combining the related mode signals in turn to obtain a new simulation signal;

[0033] Step S63: Recalculating the residual rate based on the new simulation signal; when the residual rate is reduced, the two mode signals are retained as the individual related signals; otherwise, only the guided wave mode signal with the minimum residual rate is retained as the individual related signal;

[0034] Step S64: Retaining the individual with the minimum residual rate of the individual related mode signal in the analysis of different narrowband components and the guided wave mode signal as the elite individual and the optimized signal in multiple narrowband frequency sections.

[0035] Further, in the step S8, the gene parameter is updated according to the optimization algorithm type and the individual residual rate to generate a new child population 1; the parent individual gene crossover and the mean value are taken to generate a new child population 2; and the parent individual, the child population 1 and the child population 2 are combined to form a new generation analysis population.

[0036] Compared with the prior art, the present application has the following advantages and positive effects:

[0037] According to the bone structure mechanical property evaluation method based on photoacoustic guided wave waveform inversion, the wave number dispersion curve of the guided wave in the bone structure in a wide frequency range can be obtained through two-point detection of the photoacoustic guided wave signal, acoustic characterization of the structural mechanical properties such as bone thickness, elastic modulus, density and Poisson's ratio is realized, and the flexibility and stability of the long bone bone quality quantitative evaluation and detection technology are enhanced. BRIEF DESCRIPTION OF DRAWINGS

[0038] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings needed in the embodiment description will be briefly introduced. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor. In the drawings:

[0039] Figure 1 is a schematic diagram of the photoacoustic guided wave detection experiment in the full laser ultrasonic system board in the embodiment of the present application;

[0040] Figure 2 is a schematic diagram of the photoacoustic guided wave waveform inversion waveguide structure mechanical property evaluation method in the embodiment of the present application. DETAILED DESCRIPTION

[0041] The technical solutions of the present application will be described in detail below with reference to the drawings. Obviously, the described embodiments are only some embodiments of the present application, not all 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 scope of protection of the present application.

[0042] The embodiment discloses a bone structure mechanical property evaluation method based on photoacoustic guided wave waveform inversion, comprising the following steps:

[0043] Step S1: a full optical system is used to excite photoacoustic guided waves in the bone, and a laser vibration detector is used to detect guided wave signals at two points on the bone axis, and then the step S2 is entered;

[0044] Specifically, in step S1, a pulse laser is used to excite photoacoustic guided waves in a long bone, and an optical method is used to collect guided wave signals at two detection points on the bone axis, and the photoacoustic guided wave wavenumber extraction and bone structure mechanical property evaluation are realized through two-point detection signals.

[0045] Step S2: Evaluate the effective bandwidth of the photoacoustic guided wave signal, separate the spectrum technology to extract the different narrowband components of the photoacoustic guided wave signal, and then enter step S3;

[0046] Further, in step S2, the effective bandwidth of the photoacoustic guided wave signal is determined based on Fourier spectrum analysis, and the separation spectrum technology based on the Gaussian filter box is used to extract each narrowband component in the two detection photoacoustic guided wave signals, and the wideband non-stationary signal is converted into multiple narrowband stationary signals. Alternatively, continuous wavelet transform is used to extract each narrowband component in the two detection photoacoustic guided wave signals, and the wideband non-stationary signal is converted into multiple narrowband stationary signals.

[0047] Specifically, step S2 includes the following contents:

[0048] Step S21: Analyze the Fourier spectrum of the photoacoustic guided wave signal to obtain the signal effective bandwidth interval [ω d ,ω u ];

[0049] Step S22: Extract each narrowband component of the photoacoustic guided wave signal using a Gaussian window bandpass filter box, specifically as formulas (1) and (2):

[0050]

[0051] In the formula, G m is a bandpass Gaussian filter box, ω u and ω d are the upper and lower cutoff frequencies of the filter, m and M are the filter window number and number, respectively, and u and u m are the detection signal and the extracted narrowband component.

[0052] Step S3: Waveform inversion algorithm initialization: according to the long bone guided wave dispersion theory equation and the ultrasonic propagation function parameter, set the individual gene range, perform individual initialization, set the optimization algorithm iteration update and cutoff criterion parameters, and then enter step S4;

[0053] Specifically, in step S3, the individual gene is set according to the long bone guided wave dispersion theory equation and the ultrasonic propagation function, and the individual population is initialized; the individual gene update control parameter is set according to the type of inversion optimization algorithm (genetic algorithm, firework algorithm, evolutionary algorithm, etc.).

[0054] Step S4: Calculate the waveguide structure guided wave dispersion equation based on the individual gene parameters, obtain the guided wave frequency wavenumber curve, and then enter step S5;

[0055] Specifically, in the step S4, the bisection method or the Legendre polynomial expansion method is used to calculate the guided wave frequency-wave number curve in the long bone in the effective bandwidth range of the photoacoustic signal.

[0056] Step S5: Calculate the individual-related mode guided wave signals based on the ultrasonic propagation function, and then enter step S6;

[0057] Specifically, in the step S5, based on the ultrasonic propagation function (3), the first detection point signal is calculated as the first detection point signal 1,m And the distance x in step S1 is calculated as the second detection point signal

[0058]

[0059] In the formula, H(ω,x) is the acoustic wave propagation function, A is the signal amplitude, n and N are the mode number and the number of guided waves respectively.

[0060] Step S6: Individual-related multi-narrow-band component signal residual rate evaluation, individual screening, and then enter step S7;

[0061] Specifically, the step S6 includes the following contents:

[0062] Step S61: Calculate the residual rate of different narrow-band components based on formula (4) for individual screening and gene parameter θ update;

[0063]

[0064] In the formula, ε m is the individual residual rate calculated by the narrow-band component extracted by the mth filter window, θ=[ρ,E,υ,h,a] is the individual gene vector, ρ is the density, E is the Young's modulus, υ is the Poisson's ratio, h is the thickness, and a is the amplitude vector of each guided wave mode;

[0065] Step S62: Arrange the signal residual rates in ascending order, and combine the related mode signals in turn to obtain new simulation signals;

[0066] Step S63: Recalculate the residual rate based on the new simulation signals; when the residual rate decreases, retain the two mode signals as the individual-related signals; otherwise, only retain the guided wave mode signal with the minimum residual rate as the individual-related signal;

[0067] Step S64: Retain the individual with the minimum individual-related mode signal residual rate in the different narrow-band component analysis and the guided wave mode signal as the elite individual and the optimized signal in the multiple narrow-band frequency sections.

[0068] Step S7: analyze whether the individual residual rate and the evolution number meet the cut-off criterion, if yes, go to step S9, otherwise, go to step S8;

[0069] Step S8: update the individual genetic parameters, construct a new analysis population, and then go to step S4;

[0070] Specifically, in step S8, the genetic parameter update is performed according to the optimization algorithm type and the individual residual rate to generate a new offspring population 1; the new offspring population 2 is generated by crossing and averaging the parent individual genes of different narrowband component analysis; the parent individual, the offspring population 1 and the offspring population 2 are combined to form a new generation analysis population, thereby ensuring the convergence of the algorithm.

[0071] Step S9: output the preferred individual gene and the guided wave wavenumber dispersion information, and evaluate the mechanical properties of the long bone structure.

[0072] Embodiment:

[0073] Figure 1 is the schematic diagram of the photoacoustic guided wave detection experiment in the full laser ultrasonic system plate in the embodiment of the application. In this embodiment, a pulsed laser is first used to excite photoacoustic guided waves in the bone plate, and a laser vibration meter is used to scan and obtain photoacoustic guided wave signals at two positions in the axial direction of the bone plate.

[0074] Figure 2 is the schematic diagram of the method flow for evaluating the mechanical properties of the waveguide structure by photoacoustic guided wave waveform inversion in the embodiment of the application, which includes the following steps:

[0075] Step S1: a full laser ultrasonic detection system is used to excite and detect photoacoustic guided wave signals u0 and u in the long bone, and then go to step S2.

[0076] Step S2: Fourier spectrum analysis is used to determine the effective bandwidth of the signal, and a separate spectrum technique is used to extract different narrowband components of the photoacoustic guided wave signal, and then go to step S3.

[0077] Step S21: analyze the Fourier spectrum of the photoacoustic guided wave signal to obtain the effective bandwidth [ω d ,ω u ] of the photoacoustic guided wave signal;

[0078] Step S22: a Gaussian window bandpass filter box is used to extract each narrowband component of the photoacoustic guided wave signal, specifically as shown in equations (1) and (2):

[0079]

[0080] In the formula, G m is a bandpass Gaussian filter box, ω u and ω dare the upper and lower cutoff frequencies of the filter, m and M are the filter window number and the filter window number respectively, u and u m are the collected signal and the extracted narrowband component respectively.

[0081] Step S3: Waveform inversion algorithm initialization: Set the evaluation range of individual genes based on parameters such as long bone structure density, thickness, elastic modulus and Poisson's ratio, perform individual initialization, set adaptive genetic algorithm crossover, mutation and cutoff judgment parameters, and then enter step S4.

[0082] Step S4: Calculate the waveguide dispersion equation based on the individual gene parameters to obtain the frequency-wave number curve: that is, based on the evaluation bandwidth of step S21 and the bisection method to calculate the Lamb wave dispersion equation (5) in the isotropic plate, the frequency-wave number curve within the effective bandwidth of the photoacoustic signal is obtained, and then step S5 is entered.

[0083]

[0084] In the formula, h is the plate thickness, E is the elastic modulus, υ is the Poisson's ratio, ρ is the density, n is the waveguide mode number, v l and v t are the longitudinal wave and transverse wave velocities respectively, f is the frequency; v p is the phase velocity, which is related to the wave number as k = 2πf / v p .

[0085] Step S5: Calculate the individual related waveguide mode signals based on the ultrasonic propagation function, that is: based on the ultrasonic propagation equation (3), the narrowband signal u 1,m extracted from the first detection point and the distance x between the two detection points in step S1 is used to simulate the waveguide mode signal of the second detection point Then enter step S6.

[0086]

[0087] In the formula, H(ω,x) is the acoustic wave propagation function, A is the signal amplitude, n and N are the waveguide mode number and number respectively.

[0088] Step S6: Individual related narrowband component signal residual rate comprehensive evaluation, individual screening, etc., and then enter step S7.

[0089] Step S61: Calculate the residual rate of different narrowband components based on formula (4) for individual screening and gene parameter θ update.

[0090]

[0091] In the formula, ε mThe individual residual rate calculated for the narrow-band component extracted for the mth filter window, θ = [p, E, v, h, a] is the individual gene vector, p is the density, E is the Young's modulus, v is the Poisson's ratio, h is the thickness, and a is the amplitude vector of each guided wave mode.

[0092] Step S62: arranging the individual signal residual rates in ascending order, combining the relevant mode signals in sequence to obtain a new analog signal;

[0093] Step S63: bringing the new analog signal into formula (4) to recalculate the residual rate; when the residual rate is reduced, retaining two mode signals as individual relevant signals; otherwise, retaining only the guided wave mode signal with the minimum residual rate as the individual relevant signal;

[0094] Step S64: retaining the individual with the minimum residual rate of the individual relevant mode signals in the analysis of different narrow-band components and the guided wave mode signal as the elite individual and the optimized signal of the frequency section;

[0095] Step S7: stopping criterion: when the residual rate of the retained elite individual is less than the preset residual rate value or the evolution generation number of the optimization algorithm reaches the maximum generation number, step S9 is entered; otherwise, step S8 is entered;

[0096] Step S8: updating all individual genes based on the adaptive crossover and mutation strategy to obtain offspring population 1, ; crossing the genes of the retained elite individuals in different narrow-band component analyses and taking the average to generate new offspring individual population 2; combining all the retained elite individuals, offspring population 1 and offspring population 2 to form a new generation of analysis population; then, step S4 is entered;

[0097] Step S9: outputting the preferred elite individual gene and guided wave wavenumber dispersion information and evaluating the mechanical properties of the long bone structure.

[0098] The above describes only the preferred specific embodiments of the present application, but the protection scope of the present application is not limited thereto, and any person skilled in the art can easily think of changes or replacements within the technical scope disclosed by the present application, which should be covered within the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A method for evaluating mechanical properties of a bone structure based on photoacoustic guided wave waveform inversion, characterized by, The method comprises the following steps: Step S1: a full optical system is used to excite photoacoustic guided waves in the bone, and guided wave signals of two points on the bone axis are detected, and then step S2 is entered; Step S2: the effective bandwidth of the photoacoustic guided wave signal is evaluated and determined, and different narrow-band components of the photoacoustic guided wave signal are extracted, and then step S3 is entered; Step S3: waveform inversion algorithm initialization: according to the guided wave dispersion theory equation and the ultrasonic propagation function parameter, the individual gene range is set, the individual initialization is performed, the optimization algorithm iteration update and the stop criterion parameter are set, and then step S4 is entered; Step S4: the guided wave frequency wave number curve in the waveguide structure is calculated based on the individual gene parameter, and then step S5 is entered; Step S5: the individual related mode guided wave signal is calculated based on the ultrasonic propagation function, and then step S6 is entered; Step S6: individual related multi-narrow-band component signal residual rate evaluation, individual screening, and then step S7 is entered; Step S7: whether the individual residual rate and the evolution generation number meet the stop criterion is analyzed, if yes, step S9 is entered; Otherwise, step S8 is entered; Step S8: the individual gene parameter is updated, a new analysis population is constructed, and then step S4 is entered; Step S9: the optimal individual gene and the guided wave wave number dispersion information are output, and the long bone structure mechanical property is evaluated.

2. The method of evaluating bone structure mechanical properties based on photoacoustic guided wave waveform inversion according to claim 1, characterized in that, In the step S1, a pulsed laser is used to excite photoacoustic guided waves in the long bone, and the guided wave signals of two detection points on the bone axis are collected and obtained by an optical method, and the photoacoustic guided wave wave number extraction and the long bone structure mechanical property evaluation are realized by the two-point detection signals. 3.The bone structure mechanical property evaluation method based on photoacoustic guided wave waveform inversion according to claim 1, characterized in that, In the step S2, the effective bandwidth of the photoacoustic guided wave signal is determined based on Fourier spectrum analysis, and each narrow-band component in the two detection photoacoustic guided wave signals is extracted by using the separation spectrum technology based on the Gaussian filter box, so that the wideband non-stationary signal is converted into multiple narrow-band stationary signals.

4. The method of evaluating bone structure mechanical properties based on photoacoustic guided wave waveform inversion according to claim 1, characterized in that, The step S2 comprises the following contents: Step S21: analyzing the Fourier spectrum of the photoacoustic guided wave signal to obtain the signal effective bandwidth interval [ω d ,ω u ]; d u ; Step S22: each narrow-band component of the photoacoustic guided wave signal is extracted by using the Gaussian window band-pass filter box, and the specific formulae are (1) and (2): In the formula, G m is a band-pass Gaussian filter box, ω u and ω d are the upper and lower cut-off frequencies of the filter, m and M are the filter window number and number of filters, respectively, and u and u m are the detection signal and extracted narrow-band component, respectively.

5. The method of evaluating bone structure mechanical properties based on photoacoustic guided wave waveform inversion according to claim 1, characterized in that, In the step S2, continuous wavelet transform is used to extract each narrow-band component in the two detection photoacoustic guided wave signals, and the wideband non-stationary signal is converted into multiple narrow-band stationary signals.

6. The bone structure mechanical property evaluation method based on photoacoustic guided wave waveform inversion according to claim 1, characterized in that, In the step S3, the individual gene is set according to the long bone guided wave dispersion theory equation and the ultrasonic propagation function, and the individual population initialization is performed; the individual gene update control parameter is set according to the inversion optimization algorithm type.

7. The method of evaluating bone structure mechanical properties based on photoacoustic guided-wave waveform inversion according to claim 1, characterized in that, In the step S4, the guided wave frequency wave number curve in the long bone within the effective bandwidth range of the photoacoustic signal is calculated by using the dichotomy or the Legendre polynomial expansion method. 8.The bone structure mechanical property evaluation method based on photoacoustic guided wave waveform inversion according to claim 1, characterized in that, In the step S5, based on the ultrasonic propagation function, the narrow-band frequency component of the guided wave signal of the first detection point is extracted as a virtual excitation source, the wave number dispersion curve is calculated in the step S4, and the forward simulation signal of the individual related mode guided wave at the second detection point is calculated according to the distance between the two detection points. 9.The bone structure mechanical property evaluation method based on photoacoustic guided wave waveform inversion according to claim 1, characterized in that, The step S6 comprises the following contents: Step S61: the residual rate of different narrow-band components is calculated, which is used for individual screening and gene parameter updating; Step S62: the signal residual rates are arranged in ascending order, the related mode signals are combined in sequence, and a new simulation signal is obtained; Step S63: Recalculate the residual rate based on the new simulation signal; when the residual rate is reduced, retain two mode signals as individual correlation signals; otherwise, only retain the minimum residual rate correlation guided wave mode signal as the individual correlation signal; Step S64: Retain the individual and guided wave mode signal with the minimum residual rate in different narrowband component analysis as the elite individual and optimized signal of multiple narrowband frequency sections.

10. The bone structure mechanical property evaluation method based on photoacoustic guided wave waveform inversion according to claim 1, characterized in that, In step S8, the gene parameters are updated according to the optimization algorithm type and the individual residual rate to generate a new child population 1; the retained parent individual genes in different narrowband component analysis are crossed and averaged to generate a new child population 2; the parent individual, the child population 1 and the child population 2 are combined to form a new generation of analysis population.

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