Non-invasive method for measuring a physical quantity representative of skin elasticity

Abstract

A non-invasive method for measuring a physical quantity representative of skin elasticity, comprising: - the determination (86) of the phase velocities of the fundamental mode of the different components of a shear wave generated at the skin surface, along a measurement axis, the set of pairs, each formed by a frequency fi and the phase velocity Vi of the fundamental mode determined for that frequency fi, forming a dispersion curve of the fundamental mode in a measurement direction parallel to the measurement axis, where the index "i" is an order number of the frequency fi and the phase velocity Vi, and - the transformation (100) of this dispersion curve into a phase velocity profile as a function of depth, the phase velocity at a given depth being a physical quantity representative of skin elasticity at that depth. Fig. 3

Description

Title of the invention: Non-invasive method for measuring a physical quantity representative of the elasticity of the skin

[0001] The invention relates to a non-invasive method and apparatus for measuring a physical quantity representative of the elasticity of the skin.

[0002] The measurement of the mechanical properties of the skin such as elasticity is useful, for example, to aid in the diagnosis of certain skin diseases or, to measure the effectiveness and consequences of certain cosmetic treatments on the skin, or to measure the elasticity of skin in vitro reconstructed by tissue engineering (bio-printing), or to measure the effect of mechanical stimulation of skin in vitro reconstructed by tissue engineering (bio-printing).

[0003] Such a known method is for example described in the following article: M. Ayadh et Al: "Methods for characterizing the anisotropic behavior of the human skin's relief and its mechanical properties in vivo linked to age effects", IOP Publishing, Surf. Topogr.: Metrol. Prop. 8 (2020) 014002, 19 / 03 / 2020. Hereinafter, this article is referred to as "Ayadh2020".

[0004] This known method is advantageous in that it is non-invasive. It is therefore simple to implement on a patient's skin. This known method makes it possible to measure the Rayleigh velocity at the surface of the skin in different directions. The Rayleigh velocity is proportional to a phase velocity representative of the elasticity of the skin.

[0005] The skin resembles, in some respects, a multi-layer substrate. The method described in Ayadh2020 only makes it possible to obtain information on the mechanical properties of the superficial layer of the skin and in particular the epidermis. On the other hand, no information on the mechanical properties of the layers of the skin located beneath this superficial layer can be obtained using this known method. In particular, this known method does not make it possible to measure the mechanical properties of sub-layers such as the dermis and the hypodermis.

[0006] The invention therefore aims to propose a method for measuring a quantity representative of the elasticity of the skin which also makes it possible to measure a physical quantity representative of the elasticity of the sub-layers of the skin.

[0007] Its subject is therefore such a non-invasive method for measuring a physical quantity representative of the elasticity of the skin, this method comprising the following steps: a) the deformation of the skin at a point of impact using a stimulator to generate a shear wave comprising components at different frequencies, these different components propagating on the surface of the skin and causing a displacement of the skin surface, (b) the measurement, using a measuring device, of the displacement of the skin surface over time at at least three measuring points aligned one behind the other along a measuring axis, wherein the method also comprises the following steps: (c) the determination of the phase velocities of the fundamental mode of the different components of the shear ground generated, along the measurement axis, from the measurements of the measuring device, the set of pairs, each formed by a frequency f; and the phase velocity V; of the fundamental mode determined for this frequency fi5 forming a dispersion curve of the fundamental mode in a measurement direction parallel to the measurement axis, where the index "i" is an order number of the frequency f; and of the phase velocity V;, and d) the transformation of this dispersion curve into a profile of phase speeds as a function of depth, the phase speed at a given depth being a physical quantity representative of the elasticity of the skin at this depth.

[0008] Embodiments of this method may include one or more of the following features: 1) the transformation of the dispersion curve into a phase velocity profile in the measurement direction involves the following operations: ol) convert each frequency £ of the dispersion curve into a corresponding wavelength Å; using the following relationship: X; = V / f;, then o2) calculate the value of a coefficient a for this measurement direction using the following relation: a = Zmax / Xmax, where: - Zmax is equal to half the distance between the two measurement points furthest from each other along the measurement axis, and - Xmax is the largest of the wavelengths X; obtained after performing operation ol) for this measurement direction, o3) convert each wavelength X; obtained at the end of operation ol) into a corresponding depth p; using the following relation: p; = aX;, where a is the coefficient calculated during operation o2). 2) the method comprises carrying out steps a), b), c) and d) for at least a first and a second measuring axis angularly offset from each other, these first and second measuring axes passing through the same point of impact. 3) step c) of determining the phase speeds of the fundamental mode involves repeating the following operations for several different frequencies f: - for each measuring point: - filtering, using a band-pass filter centered on the frequency f and whose bandwidth at -3dB is between the frequencies fn and fi+i, of the signal u(x,t), measured at level of the measuring point of coordinate x along the measuring axis by the measuring device, to obtain a filtered signal u;(x,t), - the identification of an instant ti>m(x) at which the filtered signal u;(x,t) passes through its absolute minimum, then - the calculation of the propagation speed V; of this minimum along the measurement axis from the instants ti>m(x) and the positions x at which this minimum occurs, the speed Vi thus calculated being the phase speed of the fundamental mode at this frequency f;. 4) step c) comprises: - an automatic identification operation, among the set of frequencies fi5 of a minimum frequency fmin below which the frequencies f; no longer verify the following condition (1): [Math.l] St i . ro (x p )-|t u x p -n j>0 ) 2 <err wœï P=1 Or : - pu and pi o are the coefficients of the line, determined by the least squares method, best approaching the points with coordinates (x; ti>m(x)), - xp is equal to the position x of the p-th measurement point counted from the first measurement point closest to the point of impact, - Pmax is equal to the number of measurement points distributed along the measurement axis, - errmax is a predetermined constant, - then only the frequencies f; greater than or equal to this frequency fmin are retained to form the dispersion curve. 5) step c) includes: - an automatic identification operation, among the set of frequencies fi5 of a maximum frequency fmax above which the frequencies f; no longer verify condition (1), this automatic identification operation of the frequency fmax being carried out by testing this condition (1) for several frequencies fi5 then - only frequencies f; less than or equal to this frequency fmax are retained to form the dispersion curve. 6) all frequencies f; are between 1 Hz and 3000 Hz.

[0009] The invention also relates to a non-invasive device for measuring a physical quantity representative of the elasticity of the skin, for implementing the above method, this device comprising: - a stimulator capable of deforming the skin at a point of impact to generate a shear wave comprising components at different frequencies, these different components spreading on the surface of the skin and causing a displacement of the skin surface, - a measuring device capable of measuring the displacement of the skin surface over time at at least three measuring points aligned one behind the other along a measuring axis, in which the device comprises a processing unit capable of: - to determine the phase velocities of the fundamental mode of the different components of the generated shear ground, along the measurement axis, from the measurements of the measuring device, the set of pairs, each formed by a frequency f; and the phase velocity V; of the fundamental mode determined for this frequency fi5 forming a dispersion curve of the fundamental mode in a measurement direction parallel to the measurement axis, where the index "i" is an order number of the frequency f; and of the phase velocity V;, and - to transform this dispersion curve into a profile of phase speeds as a function of depth, the phase speed at a given depth being a physical quantity representative of the elasticity of the skin at this depth.

[0010] Embodiments of this apparatus may include one or more of the following features: 1) - the measuring device comprises a network of sensors each capable of measuring the amplitude of the deformation of the surface of the skin at a respective measuring point, this network comprising at least three sensors which each measure the displacement of the surface of the skin at three respective measuring points aligned one behind the other along a measuring axis, and - the device comprises an articulated arm on which the sensor network is mounted, this articulated arm being capable of rotating the sensor network by a predetermined angle around an axis of rotation, to align the measurement axis of the sensor network on a first measurement axis and, alternately, on a second measurement axis angularly offset relative to the first measurement axis. 2) - the sensor network includes: - a line of optical sensors that capture the light reflected by each measuring point, and - a microprocessor configured to determine the displacement of the skin surface at each illuminated measurement point from the reflected light captured by the line of optical sensors, - the measuring device comprises an emitter of a light beam which illuminates each measuring point aligned along the measuring axis. 3) the stimulator is capable of projecting a jet of fluid onto the surface of the skin which causes deformation of the skin at the point of impact.

[0011] The invention will be better understood on reading the description which follows, given solely by way of non-limiting example and made with reference to the drawings in which: - [Fig.l] is a schematic illustration of the architecture of a device for measuring a physical quantity representative of the elasticity of the skin; - [Fig.2] is a schematic illustration of a stimulator and a measuring device of the apparatus of [Fig.l]; - [Fig.3] is a flowchart of a method for measuring a physical quantity representative of the elasticity of the skin using the device of [Fig.l]; - [Fig.4] is a three-dimensional graph illustrating displacement measurements acquired by the device of [Fig.2]: - [Fig.5] is a graph illustrating the calculation of the speed of movement of a shear wave; - [Fig.6] is a three-dimensional graph illustrating, for a frequency component, displacement measurements acquired by the device of [Fig.2]; - [Fig.7] is a graph illustrating the determination of a phase velocity of the frequency component of [Fig.6]; - [Fig.8] is a graph illustrating the damping of the frequency component of [Fig.6]; - [Fig.9] is a graph representing a dispersion curve determined using the apparatus of [Fig.l]; - [Fig. 10] is a graph illustrating a phase velocity profile determined using the apparatus of [Fig.l]; - [Fig.l 1] is a graph illustrating a tomography constructed by the device of [Fig.2]; - [Fig. 12] is a graph illustrating the damping of the frequency component of [Fig.6] as a function of depth; - [Fig. 13] is a graph illustrating, on the same graphic representation, the phase velocities measured using the method of [Fig. 3] and those determined using another known method for determining phase velocities.

[0012] In these figures, the same references are used to designate the same elements. In the remainder of this description, the characteristics and functions well known to those skilled in the art are not described in detail.

[0013] In this description, a detailed example of an embodiment is first described in a chapter I with reference to the figures. Then, in a chapter II, variants of this embodiment are presented. Finally, the advantages of the different embodiments realization are presented in chapter III.

[0014] Chapter I: Example of embodiment

[0015] [Fig.l] represents a non-invasive apparatus 2 for measuring a large physical re presentation of skin elasticity. Device 2 includes: - an articulated arm 4, - a stimulator 8 and a measuring device 10, fixed on a distal end of the arm 4, and - a computer processing unit 12 connected to the stimulator 8 and to the measuring device 10.

[0016] A proximal end of the arm 4 is fixed without any degree of freedom on a fixed support 14. The arm 4 comprises several joints 20 which make it possible to move both the stimulator 8 and the measuring device 10 simultaneously in rotation around a projection axis 22. In [Fig.l], the axis 22 is vertical. Here, the joints 20 make it possible to move the stimulator 8 and the measuring device 10 relative to the support 14 with six degrees of freedom.

[0017] Once the arm 4 has been deformed to place the stimulator 8 and the measuring device 10 in the desired position, the arm 4 holds this stimulator 8 and this device 10 stationary in this position. The joints 20 are, for example, manually actuated by a user or actuated by electric motors. The arm 4 also serves as a support for electrical conductors which connect the stimulator 8 and the measuring device 10 to the processing unit 12.

[0018] The stimulator 8 deforms the skin of a human being at a point of impact when actuated. The point of impact is located at the intersection of the projection axis 22 and the surface of the skin. The deformation of the skin produced by the stimulator 8 is such that it generates a shear wave which then propagates along the surface of the skin. This shear wave comprises frequency components at several different frequencies. Typically, in the case of human skin, the frequencies of these components are between 1 Hz and 3000 Hz and, usually, between 1 Hz and 1000 Hz.

[0019] The device 10 measures the deformation of the skin surface, caused by the shear wave, at several measurement points aligned one behind the other along a measurement axis. This measurement axis extends parallel to a direction called "measurement direction" in this text. Typically, the device 10 comprises more than three, ten or one hundred measurement points. Here, the device 10 comprises 400 measurement points. Subsequently, the position of a measurement point along the measurement axis is identified by its abscissa x, for example expressed in mm or pm, measured from an origin O. Here, the measurement axis and the projection axis 22 intersect substantially at right angles. The origin O is taken equal to the point of intersection of these two axes.

[0020] The distance between the measuring point closest to the point of impact and the measuring point furthest from the point of impact is denoted Lmax. Here, for illustration purposes, the distance Lmax is equal to 7 mm. In this embodiment, the measuring points are uniformly distributed along the measuring axis. The distance between two consecutive measuring points is therefore equal to 17.5 μm here.

[0021] The processing unit 12 is connected to the device 10 to acquire the measurements from this device. More precisely, the unit 12 acquires over time, with a sampling frequency fe, the displacement measured at each of the measurement points. Subsequently, the displacement measured at a measurement point of abscissa x at time t is noted u(x, t). For example, here, the frequency fe is equal to 8 kHz.

[0022] The unit 12 is capable of processing the signals u(x, t) thus acquired to extract therefrom a physical quantity representative of the elasticity of the skin at different depths. For this purpose, the unit 12 comprises a central unit 30 and a machine interface 32. The central unit 30 comprises: - a memory 34 comprising instructions for executing the method of [Fig.3], and - a programmable microprocessor 36 capable of executing the instructions recorded in the memory 34.

[0023] The interface 32 makes it possible to display the measured physical quantity representative of the elasticity of the skin. Typically, for this purpose, the interface 32 comprises a screen 38. Here, the interface 32 also comprises a keyboard 40 for, for example, acquiring a command to trigger the execution of the measurement method of [Fig.3].

[0024] [Fig. 2] shows the stimulator 8 and the measuring device 10 in more detail. [Fig. 2], the skin is schematically represented under the reference 46 and the surface of the skin 46 bears the reference 48. In this figure, the surface 48 is represented in a deformed form after having undergone an impact applied by the stimulator 8. The point of impact on the surface of the skin bears the reference 49.

[0025] To create the shear wave which propagates on the surface of the skin, the stimulator 8 uses, in this embodiment, a jet of air which strikes the skin at the point of impact 49. For this purpose, the stimulator 8 comprises: - a 50 pressurized air tank, - a regulator 52 fluidically connected to the tank 50, - a controllable solenoid valve 54, and - a nozzle 56 fluidically connected to an outlet of the solenoid valve 54.

[0026] For example, the air pressure contained in the tank 50 is greater than 0.6 or 0.8 MPa. Here, the pressure reducer 52 lowers the air pressure. For example, the air pressure at the outlet of the pressure reducer 52 is between 0.1 MPa and 0.6 MPa or between 0.1 and 0.4 MPa.

[0027] The solenoid valve 56 is movable between an open position and a closed position and vice versa under the control of the unit 12. In the closed position, the solenoid valve 54 prevents air from escaping from the reservoir 50. In the open position, on the contrary, the solenoid valve 54 allows air to escape from the reservoir 50. The air escaping from the reservoir 50 is then guided by the nozzle 56 to form a jet of air along the axis 22 which strikes the surface 48 of the skin 46 at the point of impact 49.

[0028] The solenoid valve 54 makes it possible to adjust the duration of the air jet projected onto the surface 48. Typically, the duration of the air jet is less than 20 ms or 10 ms. Here, the duration of the air jet is between 5 ms and 10 ms.

[0029] At least a portion of the nozzle 56 extends along the axis 22 to direct the air jet along this axis. The end of the nozzle 56, facing the surface 48, is mechanically separated from this surface, so that there is no direct mechanical contact between the apparatus 2 and the surface 48 during its use.

[0030] The measuring device 10 is an optical measuring device. In this embodiment, it comprises for this purpose: - a 60 emitter of a light beam which illuminates each measuring point, - a line 62 of optical sensors which capture the light reflected by each of the measuring points, and - a microprocessor 64 programmed to determine the displacement of the surface 48 at each of the measuring points from the reflected light captured by each of the optical sensors.

[0031] Here, the device 10 is positioned relative to the stimulator 8 so that the measurement point closest to the point of impact 49 is separated from this point of impact by a distance greater than 0.5 mm or 0.8 mm and, typically, less than 5 mm. Preferably, the distance between the measurement point closest to the point of impact and this point of impact is between 0.7 mm and 1.3 mm or between 0.9 mm and 1.1 mm. Here, this distance is equal to 1 mm.

[0032] Such measuring devices are known and commercially available. For example, in this embodiment, the device 10 is the one marketed by the company KEYENCE® under the reference LJ-V 7020. In this case, the emitter 60 is a laser source which emits a monochromatic and collimated light beam. Thus, the device 10 is not described in more detail below.

[0033] The operation of the apparatus 2 will now be described with the aid of [Fig. 3] and with reference to the graphs of figures 4 to 13.

[0034] In an initial step 68, the arm 4 is deformed to place the stimulator 8 and the measuring device 10 close to a part of the human body covered with the skin to be studied. The apparatus 2 makes it possible to study any part of the human body. For example, the experimental results shown in Figures 4 to 13 were obtained on the forearm of a human being. Typically, the stimulator 8 and the device 10 are placed relative to the surface 48 of the skin so that the projection axis 22 makes an angle of between 75° and 110°, and preferably between 80° and 100°, relative to the direction normal to the skin at the point of impact 49.

[0035] The lower end of the nozzle 56, facing the surface 48, is separated from the point of impact 49 by a distance greater than 1 mm or 2 mm or 5 mm, and generally less than 20 mm.

[0036] Once the device 2 is correctly positioned relative to the skin 46, a phase 70 of acquiring the signals u(x, t) is carried out.

[0037] More precisely, once the stimulator 8 and the device 10 are correctly positioned relative to the surface 48, during a step 72, the unit 12 controls the stimulator 8 to cause the emission of an air jet and deform the skin. Here, the unit 12 controls the solenoid valve 54 to generate this air jet. This air jet then strikes the skin at the point of impact 49. This causes a brief deformation of the surface 48 at this point of impact 49. This deformation of the surface 48 in turn generates a shear wave which propagates along the surface 48 in all directions, and therefore in particular along the measurement axis of the device 10.

[0038] During a step 74, the device 10 measures, at each of the measurement points, the displacement of the surface 48 caused by the shear wave which propagates on the surface of the skin.

[0039] In parallel, during a step 76, at each sampling instant and for each measurement point, the unit 12 acquires the measurement of the device 10. Thus, the unit 12 acquires each of the signals u(x, t).

[0040] [Fig.4] represents on a three-dimensional graph an example of the signals u(x, t) acquired. In this graph: - the horizontal axis represents time in milliseconds, - the vertical axis represents the amplitude, in millimeters, of the displacement of the surface 48, and -the depth axis represents, in pm, the x position of the measuring point along the measuring axis.

[0041] Once the different signals u(x, t) have been acquired, the acquisition phase 70 ends and a phase 80 of processing the signals u(x, t) begins. Phase 80 is carried out by the unit 12.

[0042] During a step 82, for each signal u(x, t), the unit 12 searches for and identifies the instant tmin(x) at which the signal u(x, t) passes its absolute minimum.

[0043] Then, during a step 84, the unit 12 determines the equation of the line D which best approximates the cloud of points formed by the points with coordinates (x; tmin(x)). The equation of the line is as follows: t = pix + po. The coefficients pi and po are those obtained by implementing the least squares method.

[0044] [Fig.5] represents the cloud of points formed by the points with coordinates (x; tmin (x)) and the line D obtained by the least squares method.

[0045] The shear wave which propagates in the skin 46 is a dispersive wave, that is to say that its phase velocity depends on the frequency. The phase velocity is therefore not the same for each frequency component of this shear wave. By phase velocity, we mean here, in the absence of any indication to the contrary, the phase velocity of the fundamental mode of the shear wave. The fundamental mode corresponds to the mode for which the amplitude of the displacement of the surface 48 is maximum. This phase velocity is denoted V; for the frequency fi5 where the index i is an order number identifying the frequency f;. Here, the frequencies are classified from the smallest frequency, denoted fb to the largest frequency denoted fPmax.

[0046] In the case of the skin, it has been observed that the different frequency components which propagate in the skin 46 are typically between 1 Hz and 3000 Hz and, most often, between 1 Hz and 1000 Hz or between 1 Hz and 500 Hz or between 1 Hz and 400 Hz. By way of illustration, here, the frequencies £ are chosen in this interval going from 1 Hz to 1000 Hz.

[0047] The smallest frequency, denoted fmin, for which there is a phase velocity is of particular importance. It has been observed that this smallest frequency fmin is generally between 1 Hz and 10 Hz. Thus, in this method, the sampling step of the frequencies f; in the interval [1 Hz; 10 Hz] is chosen to be small, i.e. here less than 2 Hz or 1 Hz. Conversely, in the interval [10 Hz, 1000 Hz], the sampling step of the frequencies f; is chosen to be larger. For example, in this interval [10 Hz; 1000 Hz], the sampling step is greater than 5 Hz or 10 Hz or 20 Hz. Thus, the frequencies f; are separated from each other by a step of 1 Hz in the interval [1 Hz; 10 Hz] while they are separated from each other by a step greater than 5 Hz or 10 Hz in the interval [10 Hz; 1000 Hz].

[0048] During a step 86, the unit 12 determines, for each frequency f; chosen, if it exists, the corresponding phase speed V;.

[0049] For this, during an operation 88, the unit 12 filters, using a band-pass filter centered on the frequency fi5, each signal u(x, t). The signal u(x, t) filtered at the frequency f; is subsequently denoted u;(x, t). The -3 dB bandwidth of this band-pass filter is between the frequencies f^ and fi+b. Typically, this bandwidth is less than 20 Hz or 10 Hz for the frequencies £ included in the interval [10 Hz; 1000 Hz] and less than 2 Hz for the frequencies f included in the interval [1 Hz; 10 Hz],

[0050] [Fig.6] represents different signals u;(x, t) obtained by filtering, at the frequency of 20 Hz, the signals u(x, t) of [Fig.4]. This graph is identical to the graph of [Fig.4] except that it represents the signals u;(x, t) and not the signals u(x, t).

[0051] During an operation 90, the unit 12 searches for and identifies, for each signal u;(x, t), the instant ti>m(x) where this signal passes through its absolute minimum. For this, if the instant Li,m(x) or ti+i,m(x) has already been identified for, respectively, the frequency f^ or the frequency fi+i, the unit 12 searches for the instant t;,m(x), as a priority, in a time interval centered on this instant Li,m(x) or ti+i>m(x).

[0052] If no instant Li>m(x) or ti+i>m(x) has previously been identified, then the instant ti>m (x) is searched for in a time interval centered on the instant tmin(x) identified during step 82.

[0053] During an operation 92, the unit 12 calculates the phase velocity V; for the frequency f; from the signals u;(x, t). For this, the unit 12 determines the equation of the line D; which best approximates the cloud of points formed by the points with coordinates (x; ti>m (x)). The equation of the line D; is as follows: ti>e(x) = pux + pi>0. The coefficients pu and pij0 are obtained by implementing the least squares method as described for step 84.

[0054] [Fig.7] represents the cloud of points with coordinates (x, ti>m(x)) as well as the line Di.

[0055] Once the equation of the line D; is determined, the unit 12 also estimates the approximation error, that is to say the difference which exists between the points of coordinates (x; ti>m (x)) and the points of coordinates (x; ti e(x)) which have the same abscissas and which are on the line D;.

[0056] If this error exceeds a predetermined threshold errmax, then it is considered that there is no phase velocity for the frequency f; because the energy of the frequency component of frequency f; of the shear stress is negligible. Here, for example, the approximation error is estimated using the following relation (1): [Math.2] Hî,0 ) " — ? max p = l Or : - pu and pi>0 are the coefficients of the line D;, - xp is equal to the position x of the p-th measurement point counted from the first measurement point closest to the point of impact, - Pmax is equal to the number of measurement points distributed along the measurement axis, - errmax is a predetermined constant.

[0057] If this approximation error is less than or equal to the threshold errmax, then the phase speed V; is taken equal to 1 / pii. The phase speed V; thus obtained is the speed of phase of the fundamental mode at frequency f;. In fact, it is only obtained from the minima of the signals u;(x, t), that is to say from the points where the amplitude of the displacement is maximum.

[0058] During an operation 94, the unit 12 also determines the attenuation A;(x) of the frequency component at the frequency f;. Here, the attenuation A;(x) is taken equal to the amplitude of the minimum of the signal u;(x, t) identified during the operation 90. Thus, in this embodiment, the attenuation A;(x) is equal to u;(x; t;,m(x)).

[0059] [Fig.8] represents the evolution of the attenuation A;(x) as a function of the position x for the signals u;(x,t) of [Fig.4].

[0060] Operations 88 to 94 are repeated for each of the frequencies f;. Subsequently, we denote by fmin and fmax, respectively, the smallest and the largest of the frequencies f; for which a phase velocity V; has been determined. The curve formed by the set of points with coordinates (V; ; fi) is called the dispersion curve. [Fig.9] represents the dispersion curve obtained from the signals u(x,t) of [Fig.4].

[0061] The greater the wavelength Xi of a frequency component of the shear wave, the deeper this frequency component propagates under the surface 48 of the skin 46. Thus, the speed V; of a frequency component of wavelength Xi represents the mechanical properties of the skin at a depth p;. At this stage, it is recalled that the phase speed V; is linked to the mechanical properties of the skin 46 by the following relationship: V; =(Ei / (2pi(l+Vi)))0'5, where: - Ei is the Young's modulus of the skin at depth p,, - pi is the volume density of the skin at depth p,, and - V; is the Poisson's ratio of the skin at depth p;.

[0062] Thus, if we consider that the volume density p; and the coefficient v; are known constants, the speed V; is directly representative of the Young's modulus E; at the depth p;. Thus, the speed V; is representative of the elasticity of the skin at the depth p;.

[0063] Therefore, the profile of the speeds V; as a function of the depth p; corresponds to a sectional view, along the measurement axis, of the mechanical properties of the skin.

[0064] During a step 100, the unit 12 transforms the dispersion curve into a velocity profile as a function of the depth p;.

[0065] For this, during an operation 102, the unit 12 converts each frequency f; into a corresponding wavelength X;. For this purpose, the unit 12 uses the following relation (2): X; = Vi / f.

[0066] Then, during an operation 104, the unit 12 calculates the value of a coefficient a which makes it possible to convert each wavelength X; into a corresponding depth p;. Here, the depth p; is the distance which separates a point, buried under the skin, from the surface 48 of the skin. This coefficient a links each wavelength X; to the depth Pi corresponding according to the following relation (3): p; = aX;.

[0067] This coefficient a is a constant for a given measurement axis. On the other hand, in the case of anisotropic viscoelastic materials such as skin, the coefficient a varies depending on the measurement direction. In other words, the coefficient a depends on the direction in which the measurements are made.

[0068] Here, the coefficient a is calculated by unit 12 using the following relation (4): Q Zmax / Xmax, OR . - Zmax is equal to half the distance Lmax, and - Xmax is the largest of the wavelengths Xj obtained at the end of operation 102.

[0069] Once the value of the coefficient a has been calculated, during an operation 106, the unit 12 converts each wavelength Xj into a depth p; using relation (3) above. Thus, a frequency f; corresponds to a wavelength Xj which itself corresponds to a depth p;. By replacing in each point of coordinates (V; ; fi), the frequency f by the corresponding depth p;, the velocity profile measured by the device 2 is obtained. An example of such a speed profile is shown in [Fig.10],

[0070] Here, step 68 and phases 70 and 80 are repeated several times, each time rotating the measuring axis by a predetermined angle around the axis 22. For this, during each new iteration of step 68, the arm 4 is deformed so as to rotate the stimulator 8 and the measuring device 10 on themselves.This rotation does not modify the position of the projection axis 22, and therefore the position of the point of impact 49. For example, during each new iteration of step 68, the measurement axis is angularly offset relative to its previous position by at least 1° or 5°, and for example by 10° or 20°.

[0071] During each new iteration of phase 80 of processing the acquired data, step 100 is executed again. Indeed, as explained previously, the value of the coefficient a depends strongly on the direction of the measurement axis in the case of human skin.

[0072] Finally, during a step 110, the mechanical properties of the skin as a function of the depth p; are displayed on the screen 38. Different graphical representations are possible. For example, the velocity profile, such as that shown in [Fig. 10], is displayed on the screen 38. However, preferably, the different velocity profiles obtained for different measurement directions are simultaneously displayed on the same graph to form a tomography of the skin 46 at the point of impact 49. Such a tomography is shown in [Fig. 11]. In this tomography, the ordinate axis represents the depth p;. The axis 22 corresponds to the projection axis of the apparatus 2. Different measurement planes PU to Pl6 are shown. These planes PU to Pl6 are angularly offset from each other. Here, each of These measuring planes contain the axis 22 and extend parallel to a respective measuring direction. Each measuring plane contains the velocity profile measured along the measuring axis parallel to this respective measuring direction. The abscissa axes therefore represent the coordinates Vix and Viy of the measured velocity V;.

[0073] [Fig. 12] represents the attenuation A;(x) as a function of depth. More precisely, the abscissa axis represents the position x of the measurement point. The ordinate axis represents the depth p; in millimeters. The color of each point with coordinates (x; p) codes the attenuation of the speed V; for this depth p and this abscissa x. For this, the depth is transformed into a corresponding wavelength X; using relation (3), then the wavelength X; thus obtained is transformed into a corresponding frequency f; using relation (2). During step 94, the attenuation A;(x) as a function of position x was recorded for all frequencies fi5 and therefore for the particular frequency f; corresponding to this depth p. This has been illustrated on the graph of [Fig.8]. On the graph of [Fig.8], the attenuation A;(x) corresponding to the abscissa x is noted.It is the value of this attenuation Ai(x) noted which is coded by a particular color at the level of the point of coordinates (x; p) in the graph of [Fig. 12].

[0074] The different phase speeds V; can be determined, from the signals u(x, t), by other methods, such as for example the method known by the acronym MASW (Multichannel Analysis of Surface Waves). The MASW method makes it possible to determine, for each frequency fi5, the speed V; of the fundamental mode as well as the phase speeds of the modes of order higher than the order of the fundamental mode.

[0075] [Fig. 13] represents on the same graph the phase velocity V; determined by the method of [Fig.3] and the different phase velocities determined by the MASW method. The abscissa axis represents the frequency fi5 the ordinate axis represents the amplitude of the determined phase velocity. The velocities V; determined by the method of [Fig.3] are represented by a dotted curve 120.

[0076] The phase velocities for a given frequency f; as determined by the MASW method are coded by a color that is darker the larger the amplitude of this phase velocity. For the same frequency fi5 the MASW method determines several phase velocities corresponding, respectively, to the fundamental mode and to the other higher order modes. Among these different phase velocities determined, the one with the largest amplitude corresponds to the phase velocity of the fundamental mode. As this graph shows, in most cases, the velocity V; determined by the method of [Fig.3] passes to the darkest location of the graph of [Fig.13]. This indicates that the phase velocities of the fundamental mode determined by the two different methods coincide.

[0077] On the other hand, there are areas, surrounded by ellipses on the graph of [Fig. 13] where this is not the case. This situation is found in particular for high frequencies, i.e. here frequencies above 240 Hz, but also for some lower frequencies. In these areas, the phase velocity of the fundamental mode, as determined by the MASW method, drops sharply before rising just as sharply. Subsequently, these sharp drops in the phase velocity of the fundamental mode are called "phase jumps". Such a phase jump is surrounded by a circle near 90 Hz in [Fig. 13]. Conversely, the method of [Fig. 13] does not produce such phase jumps. Moreover, the method of [Fig. 13] allows the phase velocity of the fundamental mode to be determined for much higher frequencies than is possible using the MASW method. Because of this, the method of [Fig.13] is considered to be more accurate than known methods.

[0078] Chapter II: Variants

[0079] Variants of the measuring device:

[0080] In a particular variant, the device is capable of measuring, simultaneously and along several measurement axes angularly offset from each other, the displacement of the surface of the skin. Thus, with such a measuring device, it is not necessary to rotate it around the projection axis 22 or the number of rotations to be carried out is smaller. For example, for this, such a measuring device comprises a network of optical sensors for each measurement axis.

[0081] In another embodiment, the measuring axis does not pass through the point of impact 49 but next to this point of impact.

[0082] The device 10 can also be produced using a camera which acquires images of the surface 48 at a high frequency.

[0083] Other embodiments of the stimulator 8 are possible. For example, in one variant, the air jet is replaced by a jet of another gas, such as carbon dioxide, or by a jet of liquid such as water.

[0084] The stimulator does not necessarily emit a jet of fluid to generate the ci wave protrusion on the surface of the skin. Such a shear wave can also be generated by a stimulator that directly contacts the skin using a utensil. For example, the stimulator can be a hammer that strikes the skin at the point of impact 49. It can also be a projectile such as a rubber ball or the like that is projected along the axis 22 to strike the skin at the point of impact 49.

[0085] The measuring device is not necessarily an optical measuring device. This is particularly true when the apparatus 2 is applied to a large surface substrate where the space constraints are relaxed. For example, the signals u(x, t) can also be measured by placing a displacement sensor directly on each of the measurement points. There are many known displacement sensors that could be suitable for such an application. For example, this displacement sensor could be an accelerometer.

[0086] In another embodiment, an element radiating electromagnetic waves or reflecting electromagnetic waves at a particular wavelength is arranged at each of the measuring points. The sensors of the measuring device measure the displacement of the surface at each of these measuring points from the electromagnetic radiation emitted or reflected at the measuring point.

[0087] Variants of the process:

[0088] Other methods are possible for constructing the phase velocity of the fundamental mode as a function of depth. For example, as indicated with respect to [Fig. 13], the method known by the acronym MASW can be applied even if it is today considered to be less precise. In another embodiment, a variant of the MASW method is applied, this variant having been modified to reduce the problem of phase jumps observed in [Fig. 13]. Finally, methods other than the MASW method have been developed in other technical fields such as for example the field of geophysics and can be transposed here from the moment when these methods determine the phase velocity of the fundamental mode.

[0089] Alternatively, the sampling step of the frequencies f; is the same over the entire analysis interval. For example, in the previous exemplary embodiment, the sampling step is the same over the entire interval from 1 Hz to 1000 Hz.

[0090] Other methods for searching and identifying the instant tim(x) are possible. For example, the instants ti>m(x) are searched without limiting the search to a predetermined time interval. In this case, the search is carried out without taking into account the instants Li n^x) or ti+i>m(x) or tmin(x). Thus, steps 82 and 84 can be omitted.

[0091] The approximation error can be estimated differently. In particular, many other relations are possible to calculate this approximation error. For example, the following relation (5) can be used instead of relation (1): [Math.3] p ■L E t- ( x )—u- ( x — it- a <err p="l"

[0092] In another embodiment, the coefficient a is not determined as a function of the signals u(x, t) measured by the device 10. For example, in a mode of realization simplified lization, the coefficient a, used for a given measurement direction, is provided by the user of the device 12.

[0093] Instead of rotating the stimulator 8 on itself to take measurements in different measurement directions, it is also possible to keep the measurement direction constant and move the point of impact along a straight line to progressively scan a portion of the skin.

[0094] Measurements along the same measurement axis can be repeated at different times to see the evolution over time of these measurements. For example, this can be applied to measure the evolution over time of the mechanical properties of the skin following the application of a moisturizer.

[0095] Other variants:

[0096] The apparatus 2 described herein can be applied to other viscoelastic and anisotropic materials than skin. For example, it can be applied to any similar viscoelastic materials such as artificial skin. It can also be applied to the skin of animals, including the skin of marine animals such as fish skin.

[0097] The apparatus 2 can also be applied to other viscoelastic materials such as, for example, the skin of vegetables or fruits.

[0098] When the apparatus 2 is applied to viscoelastic materials other than the skin, the interval in which the frequencies f for which the unit 12 calculates the speed V are located may be different from the interval [1 Hz; 1000 Hz]. Similarly, if the viscoelastic material to which the apparatus 2 is applied is not anisotropic, the coefficient a may be calculated for a first measurement direction and the same value of this coefficient a is then used for other measurement directions angularly offset from the first measurement direction. In this case, for these other measurement directions, the operation 104 is not repeated.

[0099] Other mechanical properties than the Young's modulus of the skin at different depths can be deduced from the phase velocity V;. For example, the viscosity can also be estimated from the velocity V;.

[0100] The method of [Fig. 3] described for constructing the dispersion curve can be implemented in all non-invasive applications for measuring a physical quantity representative of mechanical properties of a substrate. Indeed, as explained previously, this method makes it possible to obtain a more precise phase velocity of the fundamental mode. For example, the method of [Fig. 3] can also be implemented in a non-invasive device for measuring deep mechanical properties of a substrate such as a road surface or any multi-layer structure. In the case of such substrates, it is not necessary to measure the velocity profile in several different directions angularly offset from each other. It is also not necessary to determine the value of the coefficient a for each of the di measurement directions. Finally, in the case of substrates other than the skin, the stimulator 8 and the measuring device 10 are adapted to this substrate. For example, in the case of a road surface, the stimulator 8 is formed of a mass which strikes the surface of the road surface. The device 10 measures, in the case of a road surface, the shear wave over a distance typically greater than 7 mm.

[0101] The determination of the value of the coefficient a as a function of the measurements of the measuring device can also be implemented in any other device for measuring the mechanical properties of a substrate from a phase velocity profile of the fundamental mode. Indeed, the calculation of the value of the coefficient a as described previously makes it possible to increase the precision of the conversion of the dispersion curve into a velocity profile.

[0102] Chapter III: Advantages of the described embodiments

[0103] The measuring method described here makes it possible to measure the phase velocity of the fundamental shear stress mode at different depths and not only on the surface. It therefore makes it possible to reveal mechanical properties of the skin at different depths under the skin and not only on the surface. In addition, the apparatus 2 makes it possible to reveal the mechanical properties at different depths while remaining non-invasive, i.e. without the need for an incision in the skin.

[0104] Calculating the value of the coefficient a from the measured signals u(x, t) and more precisely from the dispersion curve, makes it possible to automatically adapt the value of the coefficient a to the skin on which the measurement is made and to the chosen measurement direction. Indeed, unlike other substrates, it has been observed that the value of the coefficient a varies significantly from one human being to another and also varies significantly depending on the chosen measurement direction. Thus, the automatic calculation of the value of the coefficient a therefore makes it possible to improve the accuracy of the phase velocity profile. This results in better accuracy over the observation depth.

[0105] Constructing a phase velocity profile for several directions angularly offset from each other makes it possible to generate a tomography of a mechanical property of the skin. Such a tomography makes it possible in particular to observe the anisotropy of this mechanical property as a function of the measurement direction.

[0106] Calculating the phase velocity of the fundamental mode from the instants t;,m(x) and the positions x where the minimum of the signal u;(x, t) occurs makes it possible to precisely determine the phase velocity of the fundamental mode at the frequency f;. This therefore increases the precision of the phase velocity profile constructed, and therefore the precision in measuring the mechanical properties of the skin.

[0107] Automatically identifying the frequency fmin makes it possible to increase the repro ductibility of the measurement method because this minimum frequency is not determined manually by the user. In addition, when condition (1) is used, this allows the wavelength Xmax to be determined more precisely, which also improves the accuracy of determining the value of the coefficient a, and thus ultimately the accuracy of the phase velocity profile.

[0108] Automatically identifying the frequency fmax makes it possible to avoid determining phase velocities for frequency components of the shear wave that do not exist or are negligible. This therefore improves the accuracy of the phase velocity profile constructed by the device 2.< / err>

Claims

Claims

1. A non-invasive method for measuring a physical quantity representative of the elasticity of the skin, this method comprising the following steps: a) deforming (72) the skin at a point of impact using a stimulator to generate a shear wave comprising components at different frequencies, these different components propagating on the surface of the skin and causing a displacement of the surface of the skin, b) measuring (74), using a measuring device, the displacement of the surface of the skin over time at at least three measuring points aligned one behind the other along a measuring axis, characterized in that the method also comprises the following steps: c) determining (86) the phase velocities of the fundamental mode of the different components of the generated shear wave, along the measuring axis, from the measurements of the measuring device, all of the pairs,each formed by a frequency f; and the phase velocity V i of the fundamental mode determined for this frequency fi5 forming a dispersion curve of the fundamental mode in a measurement direction parallel to the measurement axis, where the index "i" is an order number of the frequency f; and of the phase velocity V;, and d) the transformation (100) of this dispersion curve into a profile of phase velocities as a function of depth, the phase velocity at a given depth being a physical quantity representative of the elasticity of the skin at this depth, in which the method comprises the execution of steps a), b), c) and d) for at least a first and a second measurement axes angularly offset from each other, these first and second measurement axes passing through the same point of impact.,

2. Method according to claim 1, in which the transformation (100) of the dispersion curve into a phase velocity profile in the measurement direction comprises the following operations: 1) converting (102) each frequency f; of the dispersion curve, into a corresponding wavelength X; using the following relation: = V i / fi, then 2) calculating (104) the value of a coefficient a for this measurement direction using the following relation: a = Zmax / Xmax, where: - Zmax is equal to half the distance between the two measurement points furthest from each other along the measurement axis, and - Xmax is the largest of the wavelengths X; obtained after performing operation 1) for this measurement direction, 3) convert (106) each wavelength X; obtained after operation 1) into a corresponding depth p; using the following relationship: p; = aX;, where a is the coefficient calculated during operation 2).

3. Method according to any one of the preceding claims, in which step c) of determining the phase speeds of the fundamental mode comprises the repetition of the following operations for several different frequencies f;: - for each measurement point: - filtering (88), using a band-pass filter centered on the frequency f; and whose bandwidth at -3dB is between the frequencies f^ and fi+i, of the signal u(x,t), measured at the measurement point of coordinate x along the measurement axis by the measuring device, to obtain a filtered signal u;(x,t), - the identification (90) of an instant ti>m(x) at which the filtered signal u;(x,t) passes through its absolute minimum, then - the calculation (92) of the speed V; of propagation of this minimum along the measurement axis from the instants ti>m(x) and the positions x at which this minimum occurs, the speed V; thus calculated being the phase speed of the fundamental mode at this frequency f;.

4. Method according to claim 3, in which step c) comprises: - an automatic identification operation, among the set of frequencies fi5 of a minimum frequency fmin below which the frequencies f; no longer satisfy the following condition (1): [Math.5] P 'ùdX ^p Pi.o) — p = l Or : - pu and pi>0 are the coefficients of the line, determined by the least squares method, best approaching the points with coordinates (x; ti,m(x)), - xp is equal to the position x of the p-th measurement point counted from the first measurement point closest to the point of impact, - Pmax is equal to the number of measurement points distributed along the measurement axis, - errmax is a predetermined constant, - then only the frequencies f; greater than or equal to this frequency f min are retained to form the dispersion curve.

5. Method according to claim 4, in which step c) comprises: - an automatic identification operation, among the set of frequencies fi5 of a maximum frequency fmax above which the frequencies f; no longer verify the condition (1), this automatic identification operation of the frequency fmax being carried out by testing this condition (1) for several frequencies fi5 then - only the frequencies f; less than or equal to this frequency fmax are retained to form the dispersion curve.

6. A method according to any preceding claim, wherein all frequencies f; are between 1 Hz and 3000 Hz.

7. Non-invasive apparatus for measuring a physical quantity representative of the elasticity of the skin, for implementing a method according to any one of the preceding claims, this apparatus comprising: - a stimulator (8) capable of deforming the skin at a point of impact to generate a shear wave comprising components at different frequencies, these different components propagating on the surface of the skin and causing a displacement of the surface of the skin, - a measuring device (10) capable of measuring the displacement of the surface of the skin over time at at least three measuring points aligned one behind the other along a measuring axis, for at least a first and a second measuring axes angularly offset from each other, these first and second measuring axes passing through the same point of impact,characterized in that the apparatus comprises a processing unit (12) capable of: - determining the phase speeds of the fundamental mode of the different components of the generated shear ground, along the measurement axis, from the measurements of the measuring device, the set of pairs, each formed by a frequency f and the phase speed V; of the fundamental mode determined for this frequency f;, forming a dispersion curve of the fundamental mode in a direction of, measurement parallel to the measurement axis, where the index "i" is an order number of the frequency f; and the phase velocity V;, and - to transform this dispersion curve into a phase velocity profile as a function of depth, the phase velocity at a given depth being a physical quantity representative of the elasticity of the skin at this depth the processing unit (12) being capable of determining the phase velocities and transforming the dispersion curve for at least the first and second measurement axes.

8. Apparatus according to claim 7, wherein the processing unit (12) is configured to perform the following operations to transform the dispersion curve into a phase velocity profile in the measurement direction: 1) convert each frequency £ of the dispersion curve into a corresponding wavelength Xi using the following relationship: = V i / fi, then 2) calculate the value of a coefficient a for this measurement direction using the following relation: a = Zmax / Xmax, where: - Zmax is equal to half the distance between the two measurement points furthest from each other along the parallel measurement axis, and - Xmax is the largest of the X wavelengths; obtained after performing operation 1) for this measurement direction, 3) convert each wavelength X; obtained from operation 1) into a corresponding depth p; using the following relation: p; = a * Xi, where a is the coefficient calculated during operation 2).

9. Apparatus according to claim 7 or 8, wherein: - the measuring device comprises a network (62) of sensors each capable of measuring the amplitude of the deformation of the surface of the skin at a respective measuring point, this network comprising at least three sensors which each measure the displacement of the surface of the skin at three respective measuring points aligned one behind the other along a measuring axis, and - the apparatus comprises an articulated arm (4) on which the sensor network is mounted, this articulated arm being capable of rotating the sensor network by a predetermined angle around an axis of rotation, to align the measurement axis of the sensor network on a first measurement axis and, alternately, on a second measurement axis offset angularly slightly relative to the first measurement axis.

10. Apparatus according to claim 9, wherein: - the sensor array comprises: - a line (62) of optical sensors which capture the light reflected by each measurement point, and - a microprocessor (64) configured to determine the displacement of the skin surface at each illuminated measurement point from the reflected light captured by the line of optical sensors, - the measuring device comprises an emitter (60) of a light beam which illuminates each measurement point aligned along the measurement axis.

11. Apparatus according to any one of the preceding claims, wherein the stimulator (8) is capable of projecting onto the surface of the skin a jet of fluid which causes the deformation of the skin at the point of impact.

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