CN110960263A - Viscoelasticity measurement method and viscoelasticity measurement system applied to viscoelastic sheet containing hard substrate - Google Patents

Viscoelasticity measurement method and viscoelasticity measurement system applied to viscoelastic sheet containing hard substrate Download PDF

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CN110960263A
CN110960263A CN201911140235.XA CN201911140235A CN110960263A CN 110960263 A CN110960263 A CN 110960263A CN 201911140235 A CN201911140235 A CN 201911140235A CN 110960263 A CN110960263 A CN 110960263A
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徐浩
罗宗平
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Abstract

The invention relates to a viscoelasticity measurement method and a viscoelasticity measurement system applied to a viscoelasticity sheet containing a hard substrate, wherein the method comprises the following steps: exciting guided waves in the material to be tested by using external excitation with different frequencies; recording the propagation information of guided waves by using a preset imaging method, determining a short-distance range and obtaining an average measurement distance; calculating the relation between the wave speed and the frequency in the short-distance area according to the propagation information of the guided wave in the short-distance range to give a dispersion curve; and determining the critical frequency according to the frequency dispersion curve and the measurement range, and fitting and calculating the viscoelasticity of the material to be measured according to the surface wave model. The invention is applied to a viscoelasticity measurement method of a viscoelasticity sheet with a hard substrate, and obtains the viscoelasticity of the sheet by utilizing a viscoelasticity surface wave model in a close range. Compared with a lamb wave method, the method has the advantages that the requirement on the measurement frequency is reduced; and because the surface wave model is simple, the requirement on post-processing of the measured data is reduced.

Description

Viscoelasticity measurement method and viscoelasticity measurement system applied to viscoelastic sheet containing hard substrate
Technical Field
The invention relates to a viscoelasticity measurement method and a viscoelasticity measurement system applied to a viscoelasticity sheet with a hard substrate.
Background
Tissue pathologies typically result in changes in the mechanical properties of biological tissues. Therefore, the elastography method is used for measuring the mechanical properties of biological tissues in vivo, and has great significance for diagnosis and monitoring of certain serious diseases and evaluation of drug efficacy.
For articular cartilage structures, noninvasive quantitative mechanical property diagnosis techniques are clinically desirable. Summarizing the conventional cartilage elasticity measurement methods, there are roughly two types in principle:
1) elasticity measurement based on stress-strain method
The principle is to measure the stress σ and strain ε on cartilage and then calculate the elastic modulus E from the stress-strain relationship E ═ σ/ε. The difficulty with this approach is that it is difficult to measure cartilage stress non-invasively. In the concrete implementation, a tiny window is opened on the articular cartilage, so that the stress of the articular cartilage is measured in a invasive (or minimally invasive) way, such as cartilage elasticity measurement based on the imprinting principle; or only measuring the strain, and realizing qualitative measurement of the cartilage elasticity, such as articular cartilage strain elasticity imaging based on nuclear magnetism. Therefore, the elasticity of articular cartilage cannot be quantitatively and non-invasively measured based on the stress-strain method.
2) Elastic measurement based on wave velocity method
The principle is to measure the wave velocity in the tissue and then calculate the tissue elasticity according to the corresponding relation between the wave velocity and the tissue elasticity (i.e. the wave propagation law). At present, an ultrasonic elastic instrument based on a wave velocity method can quantitatively and non-invasively measure the elasticity of biological tissues such as liver, mammary gland, blood vessels and the like. The sizes of liver and mammary tissues are large, the liver and mammary tissues can be similar to a three-dimensional structure, and the wave propagation rule meets a shear wave model; the vascular wall is thinner, the elasticity of peripheral tissues is lower, the vascular wall can be similar to a thin-wall structure, and the wave propagation rule meets the lamb wave model in the single-layer plate. Articular cartilage is a special structure that is distinguished from the liver and blood vessels. The thickness of cartilage is relatively thin, and the elastic modulus of bones connected with cartilage is much higher than that of cartilage. Therefore, from the mechanical point of view, the articular cartilage is a double-layer viscoelastic plate structure and has a hard substrate. Cartilage viscoelasticity on ex vivo bovine articular cartilage has been measured based on the lamb wave model in a double-layer plate. However, the viscoelastic wave propagation rule in the double-layer structure is very complex, the wave velocity is related to the thickness of the cartilage, and the difficulty in measuring and calculating the viscoelastic property of the cartilage is high.
Disclosure of Invention
The invention aims to provide a viscoelasticity measurement method applied to a viscoelasticity sheet containing a hard substrate, which reduces the requirement on measurement frequency and the requirement on post-processing of measurement data
In order to achieve the purpose, the invention provides the following technical scheme: a method of measuring viscoelasticity applied to a viscoelastic sheet comprising a hard substrate, the method comprising:
s1, exciting guided waves in the material to be tested by using external excitation with different frequencies;
s2, recording the propagation information of the guided wave by using a preset imaging method, calculating a close range and obtaining an average measurement distance;
s3, calculating the relation between the wave speed and the frequency in the close range according to the propagation information of the guided wave in the close range to give a dispersion curve;
s4, determining a critical frequency according to the dispersion curve and the average measurement distance;
and S5, fitting and calculating the viscoelasticity of the material to be measured by using the frequency dispersion curve according to the surface wave model and the critical frequency.
Further, the material to be tested comprises articular cartilage or a viscoelastic sheet with a hard substrate.
Further, the external excitation is a mechanical excitation or an ultrasonic radiation excitation.
Further, the preset imaging includes one of ultrasound imaging, magnetic imaging, and optical imaging.
Further, the surface wave model is:
Figure BDA0002280714360000021
wherein ρ is density, ω is angular frequency, and ρ is poisson ratio.
Further, in the step S4, the critical frequency f is utilizedcriticalCan be expressed as:
Figure BDA0002280714360000022
further, the near area is an area close to a driving point of an external excitation acting on the material to be measured.
Further, the step S2 further includes: the thickness h of the thin plate is measured, and the short distance value range technical method comprises the following steps: x is the number ofcritical1.35 h, where h is the sheet thickness.
The invention also provides a viscoelastic measuring system which adopts the viscoelastic measuring method applied to the viscoelastic sheet with the hard substrate.
The invention has the beneficial effects that: the viscoelastic measuring method applied to the viscoelastic sheet containing the hard substrate utilizes the critical frequency in a close range and obtains the viscoelasticity of the viscoelastic sheet according to a surface wave model. Compared with a lamb wave method, the method has the advantages that the requirement on the measurement frequency is reduced; and because the surface wave model is simple, the requirement on post-processing of the measured data is reduced.
The foregoing description is only an overview of the technical solutions of the present invention, and in order to make the technical solutions of the present invention more clearly understood and to implement them in accordance with the contents of the description, the following detailed description is given with reference to the preferred embodiments of the present invention and the accompanying drawings.
Drawings
FIG. 1 is a flow chart of a viscoelasticity measurement method applied to a viscoelastic sheet containing a hard substrate;
FIG. 2 is a schematic representation of a model of articular cartilage;
FIG. 3 is a cloud of dimensionless velocities measured after external stimulation of articular cartilage;
FIG. 4a is a close-up dimensionless velocity cloud;
FIG. 4b is a two-dimensional FFT result calculated from the velocity cloud plot (FIG. 4 a);
FIG. 5a is a graph of wave velocity versus frequency;
FIG. 5b is a graph showing the relationship between the frequency and the wavelength calculated according to FIG. 5 (a).
Detailed Description
The following detailed description of embodiments of the present invention is provided in connection with the accompanying drawings and examples. The following examples are intended to illustrate the invention but are not intended to limit the scope of the invention.
Referring to fig. 1, the method for measuring viscoelasticity of a viscoelastic sheet comprising a rigid substrate according to the present invention comprises:
and S1, exciting guided waves in the material to be tested by using external excitation with different frequencies, wherein the material to be tested comprises articular cartilage or a viscoelastic sheet with a hard substrate, and the external excitation is mechanical excitation or ultrasonic radiation excitation.
S2, recording the propagation information of the guided wave by using a preset imaging method, measuring the thickness h of the thin plate, calculating the close range and obtaining the average measurement distance, wherein the preset imaging comprises one of ultrasonic imaging, nuclear magnetic imaging and optical imaging;
s3, calculating the relation between the wave speed and the frequency in the close range according to the propagation information of the guided wave in the close range to give a dispersion curve;
s4, determining a critical frequency according to the dispersion curve and the average measurement distance;
and S5, fitting and calculating the viscoelasticity of the material to be measured by using the frequency dispersion curve according to the surface wave model and the critical frequency.
In step S5, the surface wave model is:
Figure BDA0002280714360000041
where ρ is the density, ω is the angular frequency, and upsilon is the poisson ratio. This surface wave model is based on the Voigt material model. The surface wave model can also be established based on other viscoelastic material models, such as a Maxwell material model, a Zener material model, and the like. The viscoelastic law of the material can also be calculated according to the limited window 2DFFT method without assuming a material model in advance.
The critical frequency f utilized in the "determining the critical frequency from the dispersion curve and the average measurement distancecriticalCan be expressed as:
Figure BDA0002280714360000042
in the step S2, the close range region is a region close to a driving point of the external excitation acting on the material to be measured, and specifically, the close range taking technical method is as follows: x is the number ofcritical1.35 h, where h is the sheet thickness.
The viscoelastic measurement method applied to the viscoelastic sheet containing the hard substrate can be applied to a computer or a calculation carrier to form a viscoelastic measurement system.
The viscoelasticity measurement method applied to the viscoelastic sheet with the hard substrate obtains the viscoelasticity of the viscoelastic sheet according to the surface wave model by utilizing a dispersion curve in a close range. Compared with a lamb wave method, the method has the advantages that the requirement on the measurement frequency is reduced; and because the surface wave model is simple, the requirement on post-processing of the measured data is reduced.
In order to illustrate the advantages of the embodiments of the present invention more clearly, the following comparison is made with a detailed embodiment.
The wave propagation process in the articular cartilage is numerically simulated by using commercial finite element software Abaqus, and it needs to be explained that: from a mechanical point of view, articular cartilage can be simplified into a double-layer plate (as shown in fig. 2), wherein cartilage can be regarded as a viscoelastic thin plate 1, bone can be regarded as an elastic hard substrate 2, and both cartilage and bone adopt axisymmetric units (cax4 r). Wherein the cartilage has a thickness of 2.5mm and a density of 1100kg/m3Poisson's ratio of 0.25 and viscoelastic constitutive relation of Voigt model (μ ═ μ%1+iωμ2) Shear modulus μ1Is 1MPa, viscosity coefficient mu2Was 30 Pa.s. The thickness of the bone is 150mm, and the density is 743kg/m3The Poisson's ratio is 0.25, the constitutive relation is a linear elastic model, and the Young modulus is 100 MPa. On articular cartilageSine waves of different frequencies (6000-.
Under the action of the driving force, the mechanical wave propagates from the action point of the driving force to the far field (as shown in fig. 3). As shown in fig. 3, the velocity cloud may be divided into 2 parts. The first part is viscoelastic wave propagation, in the range of about 0-5 mm; the second part is beyond 5mm, and at this time, because the wave propagation in the cartilage is already attenuated due to the influence of the high viscosity of the cartilage, the vibration of the bone pushes the surface of the cartilage to move, and therefore the wave velocity is extremely large and is close to the shear wave velocity of the bone. Thus, only the first portion can be used to measure the viscoelastic wave velocity in the cartilage. The first part is analyzed in detail below.
The first section can be divided into two sections, wherein the close-range (near the drive point) wave propagation mode is the coupling of the surface wave and the weak surface wave, and when the frequency is high enough, the close-range wave propagation approaches the surface wave CRI.e. by
Figure BDA0002280714360000051
Wherein ρ is density, ω is angular frequency, and ρ is poisson ratio. And the wave propagation mode at a long distance (far away from the driving point) is the coupling of lamb waves and weak surface waves, and when the frequency is high enough, the wave propagation model at the long distance approaches the lamb wave model in the double-layer plate, namely:
Figure BDA0002280714360000052
Figure BDA0002280714360000061
wherein the coefficient matrix g is:
Figure BDA0002280714360000062
Figure BDA0002280714360000063
Figure BDA0002280714360000064
Figure BDA0002280714360000065
Figure BDA0002280714360000066
Figure BDA0002280714360000067
Figure BDA0002280714360000068
g24＝g13
Figure BDA0002280714360000069
Figure BDA00022807143600000610
g33＝＝g22
g34＝g12
Figure BDA00022807143600000611
g42＝g31
g43＝g21
g44＝g11.(3)
wherein k is cL/ω，cLFor the lamb wave velocity, other parameters are not described in detail here, and reference may be made to the existing literature. The near and far thresholds can be expressed as:
Xcritical≈1.35*h (4)
wherein h is the sheet thickness.
The cartilage thickness in the finite element simulation was 2.5mm, so the near and far thresholds were 3.37mm, respectively. Two-dimensional FFT calculations (fig. 4b) were performed on the velocity clouds at near (2mm-3.37mm, fig. 4a) and far (3.37mm-4.37mm) to obtain the velocity of wave propagation at that frequency. The above process is repeated to obtain wave propagation velocities at different frequencies (fig. 5). It should be noted that the method for calculating the wave propagation velocity may also adopt a finite window two-dimensional FFT algorithm, a peak method, and the like. Only when the frequency is high enough, the near wave propagation law satisfies the surface wave model, and the far wave propagation law satisfies the lamb wave model. Therefore, the critical frequency needs to be determined first. The critical frequency can be expressed as:
Figure BDA0002280714360000071
wherein xmean＝mean(xi) For measuring the distance on average, i.e. with a wavelength of about 2 ×mean. 2x for near and farmean5.37mm and 7.74mm, respectively, so that the critical frequencies for near and far distances of 8000Hz and 8500Hz, respectively, can be determined from the frequency versus wavelength (Table 5). The measured wave velocities (wave velocities above the critical frequency) are then fitted to the surface wave and lamb wave models, i.e., the viscoelastic modulus of the material can be inverted (see table 1).
TABLE 1 inversion of material viscoelasticity
Measuring range (mm) Critical frequency (Hz) Elasticity mu1(MPa) Viscosity mu2(Pa.s)
Finite element material parameters -- -- 1 30
Surface wave method 2.00-3.37 8000 0.9 28.8
Lamb wave method 3.37-4.37 8500 1.07 31
By the above comparative examples, the surface wave method and the lamb wave method were compared. The lamb wave theoretical model (formula 2) is more complex, the wave speed frequency relation (as shown in figure 5) is more complex, and the wave speed of the surface wave model is monotonically increased along with the frequency; the critical frequency of the surface wave method is lower. In conclusion, compared with the lamb wave method, the method adopted by the invention reduces the requirement on the measurement frequency; the wave speed of the surface wave method is independent of the thickness of the cartilage, and the wave speed of the lamb wave method is related to the thickness of the cartilage; and the requirement on post-processing of the measured data is reduced due to the simplicity of the surface wave model. Therefore, based on the ultrasonic elastography (or magnetic elastography, optical interference imaging) instrument (or system) of the invention, noninvasive quantitative viscoelasticity measurement of cartilage can be expected. In addition, the application range of the invention comprises biological tissues, biological materials and other non-biological materials, etc.
The technical features of the embodiments described above may be arbitrarily combined, and for the sake of brevity, all possible combinations of the technical features in the embodiments described above are not described, but should be considered as being within the scope of the present specification as long as there is no contradiction between the combinations of the technical features.
The above-mentioned embodiments only express several embodiments of the present invention, and the description thereof is more specific and detailed, but not construed as limiting the scope of the invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the inventive concept, which falls within the scope of the present invention. Therefore, the protection scope of the present patent shall be subject to the appended claims.

Claims (9)

1. A method of measuring viscoelasticity applied to a viscoelastic sheet comprising a rigid substrate, the method comprising:
s1, exciting guided waves in the material to be tested by using external excitation with different frequencies;
s2, recording the propagation information of the guided wave by using a preset imaging method, calculating a close range and obtaining an average measurement distance;
s3, calculating the relation between the wave speed and the frequency in the close range according to the propagation information of the guided wave in the close range to give a dispersion curve;
s4, determining a critical frequency according to the dispersion curve and the average measurement distance;
and S5, fitting and calculating the viscoelasticity of the material to be measured by using the frequency dispersion curve according to the surface wave model and the critical frequency.
2. The method for measuring viscoelasticity applied to a viscoelastic sheet containing a hard substrate according to claim 1, wherein the material to be measured comprises articular cartilage or a viscoelastic sheet having a hard substrate.
3. The method for measuring viscoelasticity applied to a viscoelastic sheet comprising a hard substrate according to claim 1, wherein the external excitation is mechanical excitation or ultrasonic radiation excitation.
4. The method of claim 1, wherein the predetermined imaging comprises one of ultrasonic imaging, magnetic imaging, and optical imaging.
5. The method for measuring viscoelasticity applied to a viscoelastic sheet comprising a hard substrate according to claim 1, wherein the viscoelastic surface wave model is:
Figure RE-FDA0002381365500000011
wherein ρ is density, ω is angular frequency, and ρ is poisson ratio.
6. The method for measuring viscoelasticity of a viscoelastic sheet comprising a hard substrate according to claim 1, wherein the critical frequency f used in step S4criticalCan be expressed as:
Figure RE-FDA0002381365500000012
7. the method for measuring viscoelasticity of a viscoelastic sheet comprising a hard substrate according to claim 1, wherein the close region is a region near a driving point of an external excitation acting on the material to be measured.
8. The method for measuring viscoelasticity applied to a viscoelastic sheet comprising a hard substrate according to claim 7, wherein the step S2 further comprises: the thickness h of the thin plate is measured, and the short distance value range technical method comprises the following steps: x is the number ofcritical1.35 h, where h is the sheet thickness.
9. A viscoelasticity measurement system, characterized in that the viscoelasticity measurement system employs the viscoelasticity measurement method applied to a viscoelastic sheet containing a hard substrate according to any one of claims 1 to 8.
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CN107367462A (en) * 2017-06-29 2017-11-21 华中科技大学鄂州工业技术研究院 A kind of viscoelastic quantitative detection system of biological tissue
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