BR112019027296B1 - DEVICE AND METHOD FOR DETERMINING THE ELASTICITY OF SOFT SOLIDS - Google Patents

Abstract

The invention comprises a device and method for estimating the elasticity of elastic soft solids from surface wave measurements. The method is non-destructive, reliable and repeatable. The final device is low-cost and portable. It is based on audio frequency shear wave propagation in elastic soft solids. Within this frequency range, the shear wavelength is scaled in centimeters. Thus, experimental data are commonly collected in the field close to the source. Therefore, an inversion algorithm that takes near-field effects into account was developed for use with the device. Example applications are presented in beef samples, materials that imitate in vivo skeletal tissue and muscle from healthy volunteers.

Description

REFERENCES MENTIONED

[001] North American Patents

[002] US 6619423 B2, 9/2003, Courage

[003] US 9044192 B2, 6/2015, Geenleaf et al.

[004] International Patents

[005] EP 0329817 B1, 08/1992, Sarvazyan et al.

[006] UY 36047, 03/2015, Benech et al.

[007] Other references

[008] F. Carduza, G. Sánchez, G. Grigioni and M Irureta, “Manual of procedures for determining the physical and sensorial quality of beef”, National Institute of Agricultural Technology (INTA), INTA Ediciones, Argentina, 2012.

[009] V.V. Kazarov, B.N. Klochkov, “Low frequency mechanical properties of the soft tissue of the human arm,” Biophysics, vol. 34(4), pp. 742-747, 1989.

[010] X. Zhang, B. Qiang, J. Greenleaf, “Comparison of the surface wave method and the indentation method for measuring the elasticity of gelatin phantoms of different concentrations,” Ultrasonics, vol. 51(2), pp. 157-164, 2011.

[011] K. G. Sabra, S. Conti, P. Roux, and W. A. Kuperman, “Passive in vivo elastography from skeletal muscle noise,” Applied Physics Letters, vol. 90, pp. 194101-1941013, 2007.

[012] M. Salman, K. G. Sabra, “Surface wave measurements using a single continuously scanning laser Doppler vibrometer: Application to elastography,” Journal of Acoustical Society of America, vol. 133 (3), pp 1245-1254, 2013.

[013] N. Benech, S. Aguiar, G.A. Grinspan, J. Brum, C. Negreira, “In vivo Assessment of Muscle Mechanical Properties Using a Low-cost Surface Wave Method,” Proceedings of the IEEE Ultrasonics Symposium, vol. 2012, pp. 2571-2574, 2012.

[014] L. Landau and E. Lifshitz, Theory of elasticity, Pergamon Press, New York, 1970.

[015] E. Diuelesaint and D. Royer, “Elastic waves in solids”, Wiley, New York, 1980.

[016] G. Miller and H. Pursey, “The field and radiation impedance of mechanical radiators on the free surface of a semi-infinite isotropic solid”, Porc. R. Soc. London Ser A, vol. 223, pp. 521-541, 1954.

[017] J. Brum, J-L. Gennisson, T-M. Nguyen, N. Benech, M. Fink, M. Tanter and C. Negreira, “Application of 1D transient elastography for the shear modulus assessment of thin layered soft tissues: Comparison with supersonic shear imaging,” IEEE Trans. Ultras. Ferroelec. Freq. Control, vol. 59(4), pp. 703-713, 2012.

[018] N. Benech, C. Negreira and G. Brito, “Ultrasonic elastography for evaluating the tenderness of beef” in Technological herramientas applied to the quality and differentiation of meat, 29-44, G. Grigione and F. Paschetta , coordinators, PROCISUR publications, Montevideo, 2012.

[019] N. Benech, J. Brum, G. Grinspan, S. Aguiar and C. Negreira, “Analysis of the transient surface wave propagation in soft solids elastic plates”, J. Acoust. Soc. Am. Vol. 142, 2919-2932, 2017.

FIELD OF INVENTION

[020] The present invention refers to the fields of elastodynamics and elastography. More specifically, the present invention provides a method and device for estimating the elastic properties of non-compressible elastic solids. The present invention has application, among others, to the food industry, polymer industry, biomechanics, bioengineering and medicine.

HISTORY OF THE INVENTION

[021] Non-compressible elastic solids are sometimes also referred to as soft solids, as they are easy to deform. Elastic properties of soft solids are of great interest in the food industry (meat, beef, cheese, fruits), polymer industry (rubber, soft polymers) and medicine (muscles and soft tissues in general). Some of the existing methods for determining the elasticity of soft solids are destructive (Tensile tests, Warner-Bratzler shear force, WBSF, test). Non-destructive methods include ultrasound elastography and surface wave elastography.

[022] Ultrasound elastography is capable of locally mapping elasticity in soft tissues. Another advantage is that the method estimates tissue elasticity directly, without needing inversion algorithms. Ultrasound elastography needs a dedicated ultrasound scanner which is expensive. Furthermore, ultrasound elastography has some limitations. For example, it will not work on materials without internal sound disseminators (called non-stain materials). Furthermore, it is not useful in materials in which ultrasound frequencies are highly attenuated (food industry in general, such as cheese, yogurt and fruit). Thus, ultrasound elastography is limited to a few applications in medicine.

[023] Surface wave methods have been proposed as an alternative to ultrasound elastography. These methods have the advantage that they are low cost compared to ultrasound. However, surface waves do not have a direct relationship with elasticity and thus inversion algorithms are necessary to properly estimate elasticity. Most authors assume Rayleigh surface wave propagation. In this case, the inversion algorithm is simple. However, in most practical cases, the conditions for Rayleigh wave propagation are not achieved. Thus, the elasticity estimate is biased due to the inversion algorithm. Other authors assume oriented wave propagation in thin plaques, such as skin or arteries. However, oriented waves are affected by near-field effects that are not insignificant in soft solids. Most surface wave methods are based on laser vibrometry to scan the displacement field across the surface. An important disadvantage is that elasticity estimation is not performed in real time. These methods use a single measuring device, which scans the surface of the sample. Therefore, they cannot track rapid changes in elasticity, such as muscle activation.

[024] Document US5588440A discloses a method and apparatus for locating and evaluating soft tissue injuries that includes a probe for contacting an area of the skin.

[025] The present invention provides a non-destructive device and a reliable method for estimating the elasticity of soft solid samples using surface waves. The proposed method overcomes some disadvantages found in previous works, as described above. Thus, the present invention provides an alternative elastographic device and method, which is non-destructive, low-cost, real-time, quantitative and repeatable.

BRIEF DESCRIPTION OF THE INVENTION

[026] These and other objectives of the invention are met by means of a device and method for determining the elasticity of soft solids. The present invention is disclosed in the attached set of claims. According to a first aspect, the invention relates to a device for determining the elasticity of soft solids which comprises a wave source, a rod coupled at one of its ends to the wave source and which has a top piece at its end. opposite end, a plurality of vibration sensors equally spaced and arranged linearly relative to each other, and an analog to digital converter connected to the vibration sensors and a processor. In the device of the invention, the face of the top piece opposite the rod and the plurality of vibration sensors are in substantially the same plane on the same side of the device, and the axis of the rod is normal to the plane containing the sensors and top of the rod. and the distance between the rod and the nearest vibration sensor is the same as the distance between the vibration sensors.

[027] In a particular embodiment of the invention, the vibration sensors are piezoelectric sensors. In another particular embodiment of the invention, alone or in combination with any of the above or below embodiments, the sensors are four.

[028] In another particular embodiment of the invention, alone or in combination with any of the embodiments above or below, the face of the top piece opposite the rod (wave source) has the shape of a rectangle with its extended side perpendicular to the line that connects the rod and sensors and its short side parallel to said line.

[029] In another particular embodiment of the invention, alone or in combination with any of the above or below embodiments, the device further comprises a temperature sensor.

[030] In another particular embodiment of the invention, alone or in combination with any of the embodiments above or below, the device further comprises a pressure sensor. In a more particular embodiment of the invention, the pressure sensor consists of a load cell connected to a voltage divider circuit with comparator. The pressure sensor can be connected to LED indicators to indicate to the user whether the correct amount of pressure is being applied to the sample being measured.

[031] In another particular embodiment of the invention, alone or in combination with any of the embodiments above or below, the device further comprises a distance sensor. In a more particular embodiment of the invention, the distance sensor is an infrared sensor.

[032] According to a second aspect, the invention relates to a method for determining the elasticity of a soft solid, the method comprising the steps of: a) using a wave source to excite low amplitude audible frequency waves at a selected location of a free surface of the soft solid, the elasticity of which is to be determined, b) recording time traces of the surface displacement with a plurality of contact vibration sensors that are arranged in a linear manner and equally spaced apart, where the distance between the point at which the waves are being excited and the nearest sensor is the same as the distance between the sensors, c) computing the phase velocity of the surface wave by estimating the phase shift between sensors and a reference signal sent to the source, d) converting the phase velocity computed in step c to an elasticity value when using an inversion algorithm.

[033] In one embodiment of the method of the invention, alone or in combination with any of the embodiments above or below, an analog to digital converter receives analog information from sensors, transforms it into digital information, and transmits this digital information to a processor.

[034] In another particular embodiment of the method of the invention, alone or in combination with any of the embodiments above or below, the calculated elasticity value is displayed on a screen.

PREVIOUS TECHNIQUE 1) EP0329817B1 - date of deposit: March 3, 1988.

[035] This patent claims a non-invasive, acoustic elasticity test of soft biological tissues. In its preferred embodiment, it measures wave speed by means of a probe with a transmission and two reception piezotransducers, the reception transducers being placed symmetrically in relation to the transmitter, which allows differential amplification of the received acoustic signals. These piezotransducers are mounted to the probe via acoustic delay lines in the form of hollow, thin-walled metal rods long enough to delay the acoustic signal passing from transmitter to receiver through the body of the probe. There is also a needle contact (not a line source like on ours), a spring and a tubular contact. The conversion of the elapsed time value of the surface wave between the irradiation and reception points is indicative of the elasticity of the tissue in the direction of wave propagation. All of this is completely different - in principle and in physical construction - from our invention, which is based on surface waves and their phase change, in addition to having an analog/digital conversion system and pressure sensor that are fundamentally different from this invention. . Taking into consideration that shear waves travel through soft tissue approximately 1000 times slower and attenuate approximately 10000 times faster than conventional longitudinal ultrasound waves, both inventions are almost in different fields (radiographics.rsna.org, May - June 2017).

2) US9044192 - filing date: April 3, 2009.

[036] This patent, which could be considered alive, not for soft solids, in general, like the current invention; is based on a viscoelastic model, and must therefore determine two factors, one elastic and one viscous, while the current invention is a purely elastic model and, therefore, only one elastic parameter is determined; includes multi-layer fabrics, whereas the current invention does not; phase velocity is measured using linear regression or phase vs. distance, while in the current invention, this hypothesis is not present; is based on far-field equations (although this is not said explicitly) since normal propagation modes are used, while the current invention only accounts for the near-field; applies only to isotropic tissues - although, in Claim 13, anisotropic tissues are considered, nothing in the Memorandum justifies this claim and there is no mention of how to quantify parameters in this case - while, in the current invention, the device is used in isotropic soft solids and anisotropic (transversely isotropic), in addition, in the current invention, a method of how to quantitatively obtain the parameters is described for both cases (isotropic and anisotropic); does not include temperature corrections (since measurements are always considered at the same temperature), while the current invention does; uses remote sensors (ultrasound or laser vibrometry), while the current invention uses contact sensors. The use of far-field equations causes a deviation in the measurement results, a deviation that depends on frequency. When high frequencies are used, they are useful - using far-field equations - only for the superficial layers of tissue. This does not apply to the current invention since, when using near-field equations, the entire tissue and not just the superficial layers are precisely measured. Given all these substantial differences, patent US9044192 is only useful for medical purposes of internal organs, a completely different field from what we target in the current invention.

3) UY36047 - filing date: March 27, 2015.

[037] This patent and what is filed with it are based on surface waves, but there are significant differences, as follows: - In patent UY36047 only isotropic solids were considered, while in the current one, anisotropic solids are also included. - In patent UY36047, only surface waves of the Raleygh type were considered, while in the current one, near-field effects that include several surface waves are included. - The UY36047 patent was focused on correcting the effects of diffraction and oriented waves, while in the current one, both the source and the sensors were modified in such a way as to make it unnecessary to correct said effects. - Patent UY36047 does not take temperature changes into account, while the current one does. - Patent UY36047 did not take into account changes in the reported elasticity value due to the pressure exerted by the device. In the current order, this effect is in fact taken into account by means of a pressure sensor. - Patent UY36047 did not establish or specify useful frequency limits, while the current one did. It is our conclusion that, due to these significant differences, none of these patents is a useful predecessor to question the innovative character of the inventive step of the current invention.

DETAILED DESCRIPTION OF THE INVENTION

[038] The elements that make up the equipment of the present invention are described below, with the numbers with which they appear in the figures. 1 - Wave source with an attached rod 2 - Vibration sensors 3 - Outputs to the analog to digital signal converter (A/D) 4 - Audio amplifier 5 - Start button 6 - Temperature sensor 7 - Stick affixed to the cell load (pressure sensor) 8 - Indicator with LED lights 9 - Spirit level 10 - Distance sensor 11 - Retaining strap 12 - Damping sponge 13 - Retaining arch 14 - Trigger 15 - Computer

[039] The method is based on the following steps: 1) using a wave source (1), excitation of low-amplitude audible frequency waves at a selected location of a free surface of the sample. The excitation frequency, as well as the number of excited cycles, is controlled by the user. They can be selected to optimize results for the particular application. 2) Recording time traces of surface displacement using contact vibration sensors (2) arranged in a linear arrangement along the free surface of the sample. 3) Computation of surface wave phase velocity by estimating phase shift between sensors (2) and source (1). 4) Use of an inversion algorithm to convert the phase velocity computed in the previous step into a meaningful elasticity value (Block diagram, figure 10). 5) Reporting the result on a screen.

[040] The device also comprises an A/D converter (3) for digitizing the analog signals from the linear array of surface vibration sensors (2) and a processor (15) for computing time changes between sensors and performing processing. of data. Detailed aspects of the present invention will be described in the following paragraphs.

[041] The processing algorithm estimates a phase shift between the signals recorded by the linear array of vibration sensors and the reference signal sent to the source. Thus, the first step is to apply a bandpass filter centered on the source frequency with a range amplitude between 30% and 50%. This allows the elimination of unwanted frequencies that could affect the estimates. Then, the phase shift between the recorded signals and the reference signal is computed at a frequency selected within the range amplitude by the Fourier transform. The phase shift is converted to time delay by dividing the phase shift between the corresponding angular frequency. This procedure allows the estimation of surface wave speed, since the distance between source and sensor is known (distances d and d' in figure 1).

[042] The operation of the method has no limitations regarding the functional frequency. However, depending on the frequency, it may be necessary to correct the computer value, taking into account oriented wave propagation. Therefore, the main objective of this invention is to apply correction algorithms designed to automatically correct the incidence of guided waves. Thus, the invention provides a quantitative and reliable tool for estimating the shear wave velocity of tested samples. Shear wave speed is related to elastic modulus depending on the type of solid being tested.

[043] The equipment comprising the present invention consists of an external wave source having an coupled line source (1). The operating frequency variation, as well as the number of cycles, is selected by the application for which the invention is intended to be used. This source must vibrate normally to a free surface of the sample in order to excite mainly the vertical component of the surface waves. The waves thus generated will be recorded by a linear arrangement of vibration sensors (2) (for example, piezoelectric sensors, accelerometers, resistive sensors, microphones, etc.), which are placed along the free surface of the sample. These sensors record the vertical component of vibrations (figure 1). Figure 1 presents a non-limiting example of a piezoelectric sensor, consisting of a flexible PVDF piezoelectric film, having a mass at the end and a small extension attached to it. The affixed mass gives these sensors great sensitivity to record surface vibrations while maintaining their effective area (and thus signal-to-noise ratio) but with a minimal contact area. Therefore, the sensors are point type and diffraction effects on surface wave velocity estimation are avoided. The analog signal from each sensor is digitized by an analog-to-digital (A/D) signal converter (3) and subsequently transferred to a computer (15 for processing.

[044] In order for the device of the present invention to function properly, the source must be aligned with the sensor array, which must be equally spaced at a distance that avoids contact with each other (FIGURE 1). An audio amplifier (4) is employed to excite the vibrator. The set in which the sensors are arranged can cover different alternatives. As non-exclusive examples of the above, the sensors can be arranged on a plate that holds them in the correct configuration (figure 3A). The plate is positioned on the sample surface by a holding arc (Figure 3D) or by affixing it to a retainer with a holding strap (Figure 3A-3C). On the other hand, in different embodiments or embodiments of the invention, there is the possibility of including other sensors, which allow controlling and standardizing the measurement depending on external variables that can influence the results. Thus, the equipment may include a temperature sensor (6), which allows the method to estimate the elastic modulus as a function of temperature (figure 11). The equipment may also include a pressure sensor (7), consisting of a load cell connected to a voltage divider circuit with comparator and LED indicator lights (8). This allows the user to control the pressure exerted on the medium during measurements, as well as quickly adjust the pressure when it is above or below the established ideal variation. Also, a bubble level (9) affixed next to the LED indicator lights allows the user to level the pressure exerted on the medium so that it is uniform in the anterior-posterior direction. Furthermore, the equipment may also include a distance sensor (10), typically infrared, but not limiting, for measuring the thickness of the medium. Knowing the thickness of the samples allows the correction of the surface wave velocity by the guided wave effect, as described in the theoretical section.

[045] Based on the above, the operation of the equipment described in the present invention has the advantage of being based on few basic directions. In a preferred embodiment or embodiment, the equipment comprises four vibration sensors arranged in a linear arrangement. They must be separated by a distance d, and it is very important that it remains constant between all the sensors in the array. Likewise, the vibrator must be placed on the surface of the soft solid, whose elasticity must be measured, being placed on the external side of the arrangement immediately before the first sensor at a distance d' (figure 1). The vibration must be normal to the surface in order to excite the vertical component of surface waves. In this way, the signals will be received and processed by the equipment, which will provide the corresponding elasticity value in real time through a monitor or screen.

DESCRIPTION OF FIGURES

[046] FIGURE 1: shows a linear arrangement of vibration sensors and a line source affixed to a vibrator by means of a rod. This is a non-limiting example of a piezoelectric vibration sensor, consisting of a flexible PVDF piezoelectric film, with a mass at the end with a small extension attached to it. Dimensions in millimeters are shown below on the left. The distance d between the sensors as well as the distance d' between the source and the first sensor are also displayed.

[047] FIGURE 2: is a flowchart for obtaining data with the present invention. Dotted lines indicate that the pressure sensor, temperature sensor and distance sensor are optional elements.

[048] FIGURES 3A to 3D: present two alternative assemblies for arranging the vibration sensors in the medium of interest. 3A-3C correspond to the bottom, top and side views, respectively. Scale bar = 12mm. Figure 3D is a strap for attaching sensors to living muscles.

[049] FIGURE 4: shows the orientation of the coordinate system for the transversely isotropic solid. The axis of symmetry is oriented along the direction parallel to the fibers (either muscle fibers or extended molecule chains). The line source oriented at an angle and relative to the direction is also displayed.

[050] FIGURE 5: Displays the directivity diagram of shear waves created by a line source in a semi-infinite isotropic elastic solid. Maximum amplitude is reached at 34°. Below this angle, the amplitude quickly decreases to 0.

[051] FIGURE 6: is a schematic representation

[052] FIGURE 7: presents the phase speed of the surface wave measured in an isotropic solid, as a function of frequency for a position 1 ■'1 ■'-. Points, experimental values. Solid line: Inversion method #1.

[053] FIGURE 8: presents the surface wave phase velocity measured in an isotropic solid as a function of frequency for a position. Points: experimental values. Solid line: Inversion method #3.

[054] FIGURE 9: presents the surface wave phase velocity measured in an isotropic solid as a function of frequency for a position <i. Points: Experimental values. Solid line: Inversion method #4.

[055] FIGURE 10: is a block diagram representing the inversion algorithm for an isotropic solid.

[056] FIGURES 11A to 11B: show an example of experimental data showing the dependence of 1" on temperature in beef samples.

[057] FIGURES 12A to 12E show the relative elastic changes during the aging maturation process in different samples of beef. All curves were normalized with respect to the r' value in the first measurement. Error bars represent one standard deviation per 10 measurements.

[058] FIGURES 13A to 13C present a comparison of the performance of the present invention with the results obtained by the standard Warner-Bratzler shear force test (WBSF).

[059] FIGURE 14 shows an example of using the present invention to classify different cuts of beef, according to their elasticity value.

[060] FIGURES 15A to 15C present examples of using the present invention to monitor musculoskeletal elasticity in vivo in dynamic situations.

THEORY OF OPERATION

[061] In linear elasticity theory, tension and force within an elastic solid are related by generalized Hooke's law:

[062] where Einstein's convention on repeated indices applies. In this equation is the stress tensor, is the force tensor defined as is the k = 1,2,3 component of the displacement field and is the hardness tensor. It has 81(34) elements representing the elastic constants. However, since and ∈kl = ∈lk, this number reduces to 36 independent coefficients. Furthermore, given the symmetry of the derivative of the force energy with respect to the force tensor, this number is further reduced to 21 independent coefficients. Thus, the 21 independent elastic coefficients define the overall anisotropic elastic solid. In order to avoid working with a fourth classification tensor, it is common to represent the constants independent of the hardness tensor in two indices α and β with values 1 to 6 corresponding to a 6x6 arrangement with the following convention:

[063] Thus, with α related to and β related to

[064] The fundamental relationship of the dynamics applied to this system grants:

[065] where is the density of the material. When using Hooke's law (1) to express the stress tensor, this equation reads:

[066] which is a system of three second-order differential equations that describes wave propagation in three three-dimensional anisotropic bodies. The plane wave solutions to this equation are expressed as:

[067] where is a unit vector in the direction of particle displacement and is referred to as the wave polarization and is a unit vector in the direction of wave propagation. Inserting equation (4) into equation (3) grants:

[068] Introducing the second classification tensor , the second rank tensor becomes the Christoffel equation:

[069] Thus, the polarization and phase velocity of a plane wave propagating in the direction are the eigenvector and eigenvalue of the Christoffel tensor respectively. Since this tensor is symmetric, its eigenvalues are real and its eigenvectors are orthogonal to each other.

Isotropic solid

[070] For an isotropic solid, the hardness matrix has the form:

[071] where . Thus, an isotropic solid has only two independent elastic constants mentioned as Lamé constants. In mechanical engineering literature, two other constants are employed, Young's modulus and Poisson's ratio . They are related to Lamé constants by:

[072] A non-compressible elastic solid is defined as a solid with Poisson's ratio . In terms of Lamé constants, this means and therefore, . The objective of the present invention, when applied to isotropic soft solids, is to estimate the value of of surface waves.

[073] For an isotropic solid, the Christoffel tensor is independent of the propagation direction. It reads:

[074] Therefore, the eigenvalues are (degenerate) and corresponding to polarizations perpendicular and parallel to the propagation direction, respectively. Thus, Vr is the velocity of transverse or shear waves and is the velocity of longitudinal or compression waves. Due to the relationship into a soft solid. If the density of the sample material is known, the value of -li- can be estimated by measuring the speed l?." of the shear waves and inverting the first eigenvalue relation written above: Thus, the task changed to estimating from the surface displacement field measurement.

[075] By inserting the hardness matrix given in equation (7) into the wave equation (3), the wave equation for isotropic solids is obtained. It can be written in vector form as:

[076] Considering the divergence in the above equation, it is granted:

[077] Thus, is a non-rotating wave that propagates with the velocity, that is, the speed of the compressible wave. Consider D to be a characteristic dimension of the sample being tested (e.g., its length or width). If the wave excitation frequency is chosen so that and, then the wavelength of the non-rotating wave lJ is much greater than D. Therefore, is approximately constant within the sample and it is possible to write Under this condition, wave equation (11) becomes:

[078] That is, low-frequency waves in soft solids propagate almost like shear waves. This last statement is true for volume wave propagation in an infinite solid. If the sample is bounded by a free surface, surface waves also propagate.

[079] Without loss of generality, consider a surface wave that propagates along the X1 direction. The displacement field is given by:

[080] where Inserting (14) into the wave equation (3) and using the hardness matrix for an isotropic solid (7), we grant:

[081] where is is the speed of the surface wave and the starters on the functions indicate the derivative with respect to its increase. The solution to this system is given by:

[082] in which the coefficients are determined by the mechanical boundary conditions and

[083] For a free surface, the relevant boundary conditions in Using (1) and (7), the boundary conditions are read:

[084] In order to avoid the trivial solution, the determined coefficient matrix must be zero. This gives rise to the secular equation for surface waves:

[085] Substituting, in this equation, the values of and in terms of velocities, the secular equation becomes the well-known Rayleigh equation:

[086] It is known that if , this equation has one real root and two complex conjugate roots. The real root corresponds to the speed of a propagating surface wave (Rayleigh wave). The complex roots correspond to a physical surface wave called the vanishing surface with propagation velocity. When using the relationship in equation (23), it was found that:

[087] Therefore, Rayleigh speed has a simple relationship with shear speed: Therefore, many authors use, as an inversion algorithm to estimate Í;+T from surface wave measurements, the following expression:

[088] However, this relationship only holds in a semi-infinite medium and in the distant filled, where the escape wave is insignificant due to its complex speed. Real samples are, in fact, finite. Thus, in order to meet the conditions for equation (25) to be valid, many authors employ high-frequency wave propagation. Thus, the wavelength of the Rayleigh wave is much smaller than the height of the sample and the medium is considered semi-infinite. However, the use of high frequencies is not desirable for many reasons. Firstly, because the surface wave only detects a small part of the entire sample (its penetration depth is limited to one wavelength). Furthermore, real samples are mitigating. The attenuation coefficient grows as a frequency energy. Thus, the higher the frequency, the shorter the wave propagation distance. Finally, for high frequencies, the compressible wave is not negligible and guided wave propagation cannot be avoided.

[089] If the wavelength of the shear wave is comparable to the height of the sample being tested, the inversion algorithm used in equation (25) is no longer valid. In this case, many authors resort to the RayleighLamb model of guided wave propagation in plates. Since low frequencies are employed, inversion algorithms based on zero-order modes are used, as they are the only modes without a limiting frequency. However, data are commonly collected in the field close to the source and for brief periods. Under these conditions, Rayleigh-Lamb modes are not yet developed. This fact leads to deviations in the estimation of Therefore, in the present invention, a different inversion algorithm is used to recover the shear wave velocity surface displacement.

[090] Consider an isotropic elastic homogeneous soft solid plate of height 2h, which is excited by a source located on the free surface at = 0, as shown in figure 6. The source vibrates normally to the free surface of the plate, that is, at direction ^. If the vibration frequency is chosen appropriately, only shear waves propagate to the plate volume, as expressed in equation (13). The directivity diagram H(θ) of the shear wave for a source acting normally to the free surface is given by:

[091] and shown in figure 5. The angle for the maximum value in the lobe is 34° in relation to the source axis. The wave displacement amplitude decreases rapidly for angles below 34°. Thus, only waves propagating above this direction will produce appreciable reflected waves. This wave reaches the opposite surface at and reflects back to the middle at the same angle. Reaches the free surface at a distance from the source given by: 2.7h. Since the compressible wave is negligible, the surface displacement field in it has no contributions from the opposite surface. Thus, within this region, only surface waves propagate. This includes the Rayleigh wave, but also the trailing surface wave. The trailing surface wave attenuates as it propagates along the vi direction. Using the values of K.- from equation (24), it was found that this phase velocity is twice the speed of the shear wave and its characteristic attenuation distance is given by:

[092] in which is the shear wavelength. Thus, the attenuation distance of the trailing surface wave along the -v direction is comparable to the shear wavelength in soft solids. Therefore, the inversion algorithm expressed in equation (25) is valid only if . However, the value of is not insignificant at low frequencies. For example, typical values of the velocities involved in soft tissue are . Therefore, the shear wavelength can vary from 10 to 1 cm for excitation frequencies in the range of 100 - 1000 Hz. Therefore, the leakage wave is not insignificant in the near field. Therefore, interference between the surface Rayleigh and escape wave is possible. This fact has consequences for the phase velocity of the surface field, as shown below.

[093] Note that, depending on the frequency, the value of may be greater than . A crucial frequency can be defined as . The value of It is given by:

[094] From the above considerations, the surface displacement component for frequencies below A it can be written as:

[095] corresponding to the sum of the Rayleigh surface and escape waves, where is the real part of the wavenumber of the vanishing surface wave. For low frequencies, and therefore:

[096] where is defined as Defining

[097] the phase This wave can be expressed as:

[098] Thus, the phase velocity V of the surface wave for a given frequency is expressed as:

[099] where the starters on the function indicate the derivative with respect to X1. Note that this expression grants a different dispersion curve for each value of X1. Thus, this is not the dispersion curve for Rayleigh-Lamb modes. At this stage, two inversion methods are envisaged to recover VT from the experimental values of V. - First inversion method. If, for a given position , an experimental dispersion curve for frequencies is available, then equation (32) can be fitted in a least squares sense to the experimental data. The value that minimizes the sum of quadratic differences is the best estimate for the shear wave velocity. This was the inversion method used in figure 7. - Second inversion method. If, for a given position a single value of V is available, corresponding to a single frequency then equation (32) can be used to construct the curve . The abscissa corresponding to the intersection between the experimental and theoretical values provides the estimate for the shear wave velocity V.

[0100] To date, the inversion methods proposed above only consider the surface displacement field to If the reflected shear waves are not insignificant and must be taken into account in the inversion method. To this end, the effects of a colliding shear wave on the free surface must be considered first.

[0101] Consider a collision shear wave on the free surface X3= θ. This wave produces a reflected shear wave and, due to mode conversion, a reflected compressible wave. If o are the amplitude and angle of the incident shear wave, the amplitude and angle of the reflected compressible wave are given by:

[0102] Since the angle is complex even if Consider where where it is real and positive. Now consider the components of the wave vector of the compressible wave reflected along :

[0103] Thus, whatever the incident angle, the collision shear wave produces an evanescent compressible wave confined to the free surface of the soft solid. Thus, it is a surface wave that we call an SP wave (figure 6). The VSP phase velocity of this wave along the X1 direction can be computed as:

[0104] Therefore, the phase speed of the SP wave varies from almost infinite to for After some computation, the amplitude of the SP wave is given by:

[0105] where the approximation is valid if . . This is always the case since . Thus, due to the complex denominator, the SP wave is out of phase with the reflected shear wave. The phase difference depends on the incident angle of the shear wave. We expect to observe the SP wave whenever the amplitude of the shear wave is maximum. According to the shear wave directivity pattern, it has a maximum for . At this angle, the phase velocity of the SP wave is Thus, the surface displacement field in the vicinity of -5 is a complicated superposition of the different wave types, each with its own phase velocity. If , the surface field component can be expressed as the superposition of the Rayleigh wave, the reflected shear wave and the SP wave as:

[0106] where is the component of the shear wave vector along is the phase angle of the SP wave with respect to the shear wave and is the amplitude of the shear wave reflected in . Taking into account directivity and geometric attenuation, it is given by:

[0107] Now, for low frequencies, equation (35) can be expressed as:

[0108] Defining , the phase velocity is expressed as:

[0109] Thus, a third inversion method is possible: Third inversion method. If, for a given position an experimental dispersion curve for frequencies is available, then equation (37) can be fitted in a least squares sense to the experimental data. The value that minimizes the sum of quadratic differences is the best estimate for the shear wave velocity. This was the inversion method used in figure 8.

[0110] A third possibility regarding the position (1 at which the surface displacement is measured should be considered. If few back and forth reflections at the sample interfaces occur. Thus, in this zone, Rayleigh-Lamb modes developed. Due to the type of source and polarization used in this invention, it favors antisymmetric modes. Furthermore, since low frequencies are employed, only the zero-order mode propagates. Thus, two other inversion methods are possible, in the same spirit as methods 1 and 2: - Fourth inversion method. If, for a given position an experimental dispersion curve available, then the zero-order antisymmetric Rayleigh-Lamb mode can be fitted in a least-squares sense to the experimental data. The value that minimizes the sum of quadratic differences is the best estimate for the shear wave velocity. This was the inversion method used in figure 9. - Fifth inversion method. If, for a given position a single value of V is available, corresponding to a single frequency , then the zero-order asymmetric Rayleigh-Lamb mode can be used to construct the curve The abs scissa corresponding to the intersection between the experimental and theoretical values provides the estimate for the shear wave speed.

[0111] As a final observation for isotropic solids, here, we note that due to the interference of different types, the amplitude of the surface displacement is a complicated function of position x and frequency a. Thus, an estimate of the attenuation coefficient by fitting the amplitude of the displacement field to the common exponential slope is meaningless, at least in the near field. If far-field measurements are available, then the amplitude must be diffraction corrected before attempting to estimate the attenuation coefficient.

Transversely isotropic solid

[0112] Possible applications of the present invention include estimation of the elastic properties of semitendinosus skeletal muscles, for example, meat samples or in vivo application to external human muscles, such as biceps, triceps, quadriceps, etc. Due to the parallel fiber orientation of this type of muscles, they can be modeled as transversely isotropic materials. Furthermore, some long-chain polymers with chains aligned to a preferred direction are also modeled as transversely isotropic models.

[0113] The hardness matrix has five independent elastic moduli for this type of materials. Consider À- the axis of symmetry, that is, the axis of orientation of muscle fibers or long molecule chains. Thus, the X2 and X3 axes are perpendicular to the fibers as shown in figure 4. For this choice of axis orientation, the hardness matrix reads:

[0114] The constants are related to compressible wave propagation along and perpendicular to the symmetry axis respectively: It is . In many non-compressible transversely isotropic solids (such as musculoskeletal, for example), these two values of compressible wave velocities are almost equal to each other. Like this, , that is, the solid is isotropic with respect to compression waves. The constant Li-i is related to a shear wave that propagates perpendicular to the axis of symmetry with perpendicular polarization The constant is related to a shear wave that propagates parallel to the axis of symmetry with polarization perpendicular As in the case of isotropic solid whenever polarization. Like this, Finally, the constant is related to wave propagation (compressible or shear waves) in directions outside the main axes.

[0115] Now, consider an anisotropic soft solid in which whatever the direction of propagation of the waves. The wave equation for this case cannot be written in a simple way as for the isotropic case. However, it is still valid that the contribution of compressible waves is negligible at low frequencies. Thus, low-frequency waves propagate almost like shear waves. The object of the present invention, when applied to transversely isotropic solids, is to estimate tn.^ or both of them.

A. Estimation of c44

[0116] If wave propagation occurs in a plane perpendicular to the axis of symmetry (plane in figure 4), the speed of the shear wave is and is independent of the propagation direction within that plane. Using the relationships mentioned above between the elastic constants for the case of a soft solid, that is, , the Rayleigh wave equation has exactly the same form as in the isotropic case with Therefore, if the source does not excite the ui component of the field, the inversion method for estimation proceeds exactly as for the isotropic soft solid. To achieve this condition, the invention is equipped with a line source (item (1), figure 3). The length of the line source is much greater than the shear wavelength, the line source is “infinite”). If the source is aligned parallel to the *1 direction, it excites the u2 and u3 components of the field, but not the .

B. Estimation of

[0117] To estimate, consider the line source oriented parallel to the X2 axis. In this case, wave propagation occurs in a plane that includes the axis of symmetry (plane in figure 4). The secular equation for the Rayleigh wave under this condition is given by:

[0118] where Since the medium is considered isotropic for compressible waves, the constant r.i2 is no longer an independent constant. It is related to other constants by:

[0119] Since the secular equation (39) is expressed as:

[0120] As for the isotropic case, this equation has a real root (corresponding to the Rayleigh wave) and two complex conjugate roots corresponding to the vanishing surface wave:

[0121] Note that the attenuation distance for the leakage wave is greater than for the isotropic case , Another difference in relation to the isotropic solid refers to the directivity pattern of the shear wave. There is no simple expression for the pattern of directivity in the plane However, some authors have computed this numerically. It is shown that the main lobe is oriented at 60° to the source. Therefore, the value of is now given by . Thus, the value of the crucial frequency at which It is given by , which is smaller than the isotropic case. Therefore, if It is the inversion method to obtain í'55 proceeds as given by equation (32) for the isotropic solid, but changing the values of and by those given in equation (41).

[0122] The inversion procedures for are complicated, since analytical expressions for the directivity of shear waves are not available. Furthermore, in-plane Rayleigh-Lamb modes are difficult to compute even numerically. Therefore, the present invention does not include inversion methods for these cases.

[0123] The absence of an inversion algorithm for does not prohibit the estimation of L'-, in common applications of the invention. Consider, for example, skeletal muscles such as biceps brachii. The average value of its height in adults is 2h = 28 + 7 mm. Like this, . The average height for other skeletal muscles, such as vastus lateralis or vastus medialis, is even greater than 28 mm. Therefore, if data is collected at positions the value of can be estimated by the inversion methods proposed in the present invention.

APPLICATION EXAMPLES Temperature dependence of Css

[0124] The elasticity of soft tissues depends on temperature. In order to compare the elasticity of different beef samples, it is important that they are all collected at the same temperature. However, this is not always the case. The temperature in slaughterhouses can vary within a range between 3 and 10 °C. In this example, the temperature dependence of beef samples is shown in Figures 11A-11B. A consistent reduction in elasticity with increasing temperature in the tested samples.

Aging maturation process

[0125] Aging maturation is a fundamental process in the meat industry. It is mediated by the action of many enzyme systems. After rigor mortis, these enzymatic systems produce a progressive softening of the beef, allowing it to achieve the desired tenderness required by consumers. There is a lack of a non-destructive monitoring method for enzyme maturation. In this example, the maturation process of 5 different cuts, consisting of 5 samples of each, is monitored with the present invention. The samples were kept vacuum sealed inside a cold room between 0 and 4 °C for 21 days. All samples were measured once a day. Figures 12A to 12E show the normalized elasticity in relation to the first day for each cut. Error bars represent one standard deviation of the 5 samples for each slice. After initial oscillations, a reduction in elasticity is observed for all samples. Roughly, an asymptotic value is reached approximately 14 days of maturation for all samples.

Comparison with Warner-Bratzler Shear Strength Test (WBSF)

[0126] WBSF testing is a destructive method. It measures the force that a sharp inverted V-shaped knife needs to cut through the beef sample while moving at a constant speed. It is the standard test in the meat industry to quantify tenderness. In this example, the results of WBSF tests on two different beef samples are presented (Figure 13A). The results of the present invention applied to the same sample are shown in figure 13 B. Figure 13C shows the proportion between the elastic moduli of the two samples. This proportion is in line with the expected proportion from WBSF tests (Figure 13 A).

Classification of beef cuts according to tenderness

[0127] The tenderness of beef samples represents a variable that defines, in a high percentage, their commercial value. The standard procedure for evaluating softness is the WBSF test. In the previous example, it was shown that the shear force test and elasticity are correlated. Thus, the present invention can be used to differentiate beef samples according to their tenderness. Figure 14 shows the elasticity value of different cuts of beef and their classification according to 4 degrees of tenderness: resistant, medium resistant, tender and extremely tender.

Estimation of elasticity in skeletal muscle in vivo

[0128] Estimating the elastic properties of skeletal muscle in dynamic conditions is important in sports science to assess the health status of muscles. Thus, the present invention would be beneficial in this and related areas. In this example, the present invention is used to monitor changes in the biceps brachii of three healthy volunteers during isometric contraction. Volunteers were asked to contract the muscle to 40% of their maximum voluntary contraction (MVC, previously measured with an isokinetic dynamometer) in 20 seconds. Then, this contraction is maintained for another 5 seconds and, finally, the contraction is reduced to 0% in 20 seconds. Figures 15A-15C show the results obtained for each volunteer, in which it can be seen that the present invention is capable of monitoring changes in elasticity in dynamic situations.

Determination of lf in simulators that imitate tissue

[0129] In this section, we present experimental results for the application of the present invention in simulants based on gelatin and agar-agar (isotropic solid). These types of simulators are widely used to simulate the mechanical properties of soft tissues. They were made with a mixture of agar-agar (1% w/w) and gelatin (3% w/w) in hot water (> 80 °C). Alcohol and antibiotics were also added for preservation purposes. Thus, we created a parallelepiped-shaped sample with height 2h = 20 mm, extension and width 100 and 120, respectively. FIGURES 7, 8 and 9 present the dispersion curve for the surface wave phase velocity, obtained for the configurations respectively. Each point on these curves was obtained by exciting the surface actuator with 6 sinusoid cycles at the corresponding frequency. Then the phase velocity for each receive channel was computed. Thus, by adjusting the experimental data to the theoretical curves provided by the appropriate inversion method, according to the configuration, the corresponding values of were obtained.

Claims (15)

1. DEVICE FOR DETERMINING THE ELASTICITY OF SOFT SOLIDS, characterized in that the device comprises: a low amplitude audible wave line source (1) which is configured to excite low amplitude audible frequency waves at a selected location of a free surface of the soft solid whose elasticity must be determined,, - a rod coupled, at one of its ends, to the wave source (1) and having a top piece at its opposite end, the rod and the top piece being configured to transmit the low amplitude audible frequency waves from the waveline source to the free surface of the soft solid, - a plurality of vibration sensors (2) equally spaced and linearly arranged relative to each other which are configured to record time traces of sound waves. surface, including Rayleigh waves and surface leakage waves, generated by low-amplitude audible frequency waves, where, when the device is in use, the top part and vibration sensors (2) come into contact with the surface free of the soft solid, - an analogue to digital converter (3) connected to the vibration sensors (2) and to a processor (15) which is configured to transform the analogue signal received from the vibration sensors (2) into digital signals and send the digital signals to the processor (15), and surface recorded by the vibration sensors (2) and a reference signal sent to the waveline source (1), and to convert the calculated phase velocity to an elasticity value of the soft solid using an inversion algorithm, the inversion algorithm considering the phase velocity of the surface Rayleigh and trailing waves, wherein the face of the top part opposite the rod and the plurality of vibration sensors (2) are substantially in the same plane on the same side of the device, wherein the axis of the rod is normal to said plane, and wherein the distance between the rod and the nearest vibration sensor (2) is the same distance as that between vibration sensors. vibration (2). 2. DEVICE, according to claim 1, characterized in that the vibration sensors (2) are piezoelectric sensors. 3. DEVICE according to any one of claims 1 or 2, characterized in that there are four vibration sensors (2). 4. DEVICE according to any one of claims 1 to 3, characterized in that the face of the top piece opposite the rod is in the shape of a rectangle with its extended side perpendicular to the line connecting the rod and the sensors (2) and its short side parallel to said line. 5. DEVICE according to any one of claims 1 to 4, characterized by additionally comprising a temperature sensor (6) configured to monitor the temperature of the free surface of the soft solid and in which the processor (15) is configured to determine the elasticity value of the soft solid based on the measured temperature. 6. DEVICE, according to any one of claims 1 to 5, characterized by additionally comprising a pressure sensor (7) configured to monitor the pressure exerted by the device at the selected location on the free surface of the soft solid. 7. DEVICE, according to claim 6, characterized in that the pressure sensor (7) consists of a load cell connected to a voltage divider circuit with comparator. 8. DEVICE according to claim 7, characterized in that the pressure sensor is connected to LED light indicators (8) to indicate to a user whether a correct amount of pressure is being applied to the free surface of the soft sole. 9. DEVICE according to any one of claims 1 to 8, characterized in that it further comprises a distance sensor (10) configured to measure a thickness of the soft solid at the selected location and in which the processor (15) is configured to correct the phase speed of the surface wave based on the measured thickness. 10. DEVICE according to claim 9, characterized in that the distance sensor (10) is an infrared sensor. 11. METHOD FOR DETERMINING THE ELASTICITY OF A SOFT SOLID, the method is characterized by comprising the steps of: a) using a low amplitude audible wave line source (1) to excite low amplitude audible frequency waves in a selected location of a free surface of the soft solid whose elasticity is to be determined, b) recording the time traces of the surface displacement of low-amplitude frequency waves, including Rayleigh waves and trailing surface waves, when transmitted on the free surface of the soft solid with a plurality of contact vibration sensors (2) that are arranged in a linear manner and equally spaced apart, wherein the distance between the point at which the waves are being excited and the nearest sensor (2) is the same as the distance between the sensors (2), c) computing by a processor (15) connected to an analog-to-digital converter that converts digital signals to the contact vibration sensors into digital signals, the phase speed of the surface when estimating a phase shift between vibration sensors and a reference signal sent to the waveline source, d) converting, by the processor, the phase velocity computed in step c) to a soft solid elasticity value when using an inversion algorithm, the inversion algorithm considering the phase velocity of the surface Rayleigh and escape waves. 12. METHOD, according to claim 11, characterized in that the soft solid is an isotropic solid, and in which the inversion algorithm takes into account near-field effects and employs: a) a dispersion curve comprising a variety of frequencies, or b) a single frequency value. 13. METHOD, according to claim 11, characterized in that the soft solid is a transversely isotropic solid, and in which the inversion algorithm takes into account near-field effects and the propagation direction of surface waves and employs: a) a dispersion curve comprising a range of frequencies, or b) a single frequency value. 14. METHOD, according to any one of claims 11 to 13, characterized in that an analogue-to-digital converter (3) receives analogue information from sensors (2), transforms it into digital information, and transmits this digital information to a processor ( 15). 15. METHOD, according to claims 11 to 14, characterized in that the calculated elasticity value is displayed on a screen.