Method for analysing a medium allowing the effects of artifacts due to static deformation in the medium to be reduced

Abstract

The present invention relates to a method for analysing a region of interest of a viscoelastic medium, the method including a step (200) of acquiring signals representative of the movement of at least one shear-propagation component and of a static-deformation component, and a processing step (300) for determining at least one property of the medium, the processing step comprising the following sub-steps:  determining images of the region of interest;  estimating images of movement by comparing images of the region of interest;  filtering the images of movement to attenuate the static-deformation component;  determining a property of the medium from the filtered images of movement.

Description

[0001]METHOD FOR ANALYZING A MEDIUM FOR REDUCING THE EFFECTS OF ARTIFACTS DUE TO STATIC DEFORMATIONS IN THE MEDIUM FIELD OF THE INVENTION The present invention relates to the general technical field of imaging a target object, or a diffuse medium such as human or animal biological tissue. More specifically, the present invention relates to a device and a method for measuring viscoelastic properties of a biological tissue of interest. It applies in particular, but not exclusively, to the measurement of viscoelasticity parameters of the liver of a human or animal, this measurement being correlated with the amount of fibrosis present in the liver. BACKGROUND OF THE INVENTION 1. General In order to measure tissue viscoelastic properties, it is known to use shear wave elastography.This technique involves observing the displacement of a shear wave through a region of interest (ROI) of a medium to determine parameters of the shear wave in the ROI, such as the propagation velocity of the shear wave, these parameters being directly related to the properties of the analyzed medium (e.g. the shear modulus of the analyzed medium). To do this, shear waves are generated in an ROI, for example by implementing mechanical loading, or acoustic loading. The generated shear waves cause time-varying displacements while moving from a generation point to multiple locations in the analyzed medium.Various imaging techniques such as magnetic resonance imaging (or magnetic resonance elastography), optical coherence elastography or ultrasound elastography can detect these displacements. In the particular case of ultrasound imaging, an imaging probe is used. Such an imaging probe comprises a housing and a transducer array, mechanically secured to the housing, for the emission of high-frequency ultrasound waves and the reception of acoustic echoes allowing the tracking of the shear wave displacement. In particular, the tracking of the shear wave-induced displacements as a function of time at multiple locations allows an estimation of the shear velocity, which in turn allows the estimation of one (or more) properties of the analyzed medium.The characterization of viscoelastic properties of the medium such as shear stiffness using shear rate estimation has important medical applications because these properties are closely related to the state of the medium with respect to a pathology. Typically, at least a part of a tissue may become stiffer than the surrounding tissues indicating the onset or presence of a disease or condition such as cancer, tumor, fibrosis. However, conventional shear rate imaging techniques suffer from artifacts due to the presence of static deformations – generated by probe movement and / or by movement of a patient's organ etc. – and which degrade the quality of the signals acquired by the probe, making it difficult to accurately measure the viscoelastic properties of the medium.An aim of the present invention is to propose a method for analyzing a region of interest (ROI) of a viscoelastic medium making it possible to reduce the effects associated with artifacts (due to the presence of static deformations) in the determination of one (or more) property(ies) of the viscoelastic medium. Before presenting the invention, a description of the fundamental principles associated with shear wave elastography will be detailed in order to better understand the concepts relating to the static deformation problem mentioned above. 2. Theory relating to shear wave elastography 2.1. Wave propagation in an elastic medium Fundamental principles of wave propagation in an elastic medium will now be recalled. For this, consider a homogeneous and isotropic elastic solid medium. The wave equation in the absence of force is written as follows:. where: - the vector denotes the displacement at any point, - the symbol denotes the vector differential operator, - the symbol denotes the Laplacian operator, - is the density of the medium, and - and are the first Lamé coefficient and the shear modulus of the solid, respectively. The wave equation imposes the propagation of two types of propagative components in the medium: - the propagative compression component (P waves) and - the propagative shear component (S waves). These propagative components, in a monochromatic approximation (plane wave) have distinct behaviors. The propagative compression component is zero divergence, longitudinally polarized and propagates at a speed cp such that: The shear propagative component is rotationally neutral, transversely polarized and propagates at a speed cs such that: . Thus, these two propagative components can propagate at different speeds, depending on the relative values ​​of the two Lamé coefficients. In a biological tissue, which is quasi-incompressible ( ), the speeds c and c of the compression and shear propagative components have very different values, typically around 1500 m / s for the compression wave and around 1 to 5 m / s for the shear wave. Moreover, since biological tissues are quasi-incompressible, the compression propagative component is of negligible amplitude compared to the shear propagative component and we can consider that the displacements observed in the context of elastography techniques are solely related to shear effects.It is therefore understood that the propagative compression component is that used by conventional ultrasound imaging (making it possible to achieve an acceptable spatial resolution with frequencies of the order of MHz) used to image the displacements in the context of the invention, and the propagative shear component is that on which the estimation of tissue viscoelastic parameters is based in elastography methods. 2.2. Harmonic, transient and passive elastography With reference to Figure 1, the principle of harmonic elastography is based on the use of a mechanical source to generate – in a medium – a mechanical wave including a propagative shear component CIS, CIS' (and a propagative compression component CMP, CMP' whose amplitude is negligible in biological tissues) at low frequency, the propagation of which is followed by ultrafast ultrasound imaging.In particular, Figure 1 illustrates the generation of a propagative shear component CIS and a propagative compression component CMP during compression of the medium by an S probe. Monitoring the propagation of the propagative shear component over time allows us to find its propagation speed and the Young's modulus of the medium. The underlying idea is based on a simple rheological model. Indeed, if we assume that the medium is quasi-incompressible (approximation valid in the case of biological tissues), then the shear modulus (and therefore the speed of the shear wave) is proportional to the Young's modulus of the medium as follows: Thus, measuring the speed of the propagative shear component allows us to estimate the Young's modulus of the medium.Ultrasound tissue Doppler, combined with ultrafast ultrasound to avoid any aliasing problem, makes it possible to follow the propagative shear component and thus measure its speed to find the Young's modulus. Different techniques for generating the propagative shear component have been explored in the prior art. A first technique uses a harmonic source external to the transducer array to generate the propagative shear component. The main problem with this technique lies in the use of an external vibration source which significantly increases the complexity of implementing the measurement.A second technique – called transient elastography – popularized by the “Vibration Controlled Transient Elastography” (VCTE™) method implemented in the Fibroscan system (Echosens, Paris, France), solves this problem by generating the propagative shear component using the vibration of a piezoelectric element, which is then used to track the propagation of the propagative shear component. The strength of the device is that, by symmetry effects, the longitudinally polarized propagative shear component, i.e. the near-field term, is isolated from the others and captured by Doppler processing along the line recorded by the piezoelectric element. Thus, by simple Doppler processing operated along the line recorded by the piezoelectric element, the velocity of the propagative shear component is measured.However, this second elastography technique developed in the Fibroscan does not allow two-dimensional elastography and is not suitable for capturing changes in hardness within the medium. A third technique, called ARFI or Supersonic Shear Wave depending on the implementation, consists of generating a shear wave inside the tissue itself using a high-intensity focused ultrasound beam which generates a mechanical force called 'radiation' by non-linear effect. The same ultrasound transducer is used to generate the shear wave and to measure its displacement subsequently by ultrafast acquisition. This technique has the advantage of not generating static deformation of the medium by itself, but does not prevent the static deformations of passive elastography (for example those resulting from heartbeats) described below from interfering with the generated wave.A fourth technique – called passive natural wave elastography – consists of exploiting shear waves naturally induced by the body, for example by the heart on the liver during a cardiac cycle. The original technique is based on a diffuse displacement field hypothesis: the propagating shear components propagate in all directions. Under this hypothesis, the time derivative of the spatial cross-correlation of the displacement field at a point is related to causal and anti-causal Green's functions at that point. The spatio-temporal properties of these Green's functions can be used to estimate the Young's modulus of the medium. In this context, the presence of static deformations induces a bias in the cross-correlation measurement and therefore in that of the hardness.No solution for reducing the effects associated with static deformations has been developed for this third technique, although such a solution is necessary for passive elastography applications of the liver where the heart induces strong static deformations. 2.3. Problem of static deformations Tissue Doppler allows the displacement to be measured at each point in the medium, as a function of time. In the case of passive and transient elastography, this displacement is a sum of three components: - the two propagative components of compression and shear described in 2.1; - a static deformation component described below. The static deformation component is induced by a stress on the medium caused: - either by the probe, - or by an external generator of the shear wave such as an external vibrator, - or by an organ.In the context of the present invention, the term "static deformation component" or "quasi-static deformation component" means a deformation of the medium induced by the application of a stress - for example from the surface of the medium - and revealing non-propagative shear phenomena. This static deformation component being different at each instant, it is added to the propagative components in the measured displacement. It is therefore problematic for all methods based on the measurement of propagative components, e.g. passive or transient elastography techniques. In biological tissues, this component is strong near the source of the stress, and zero infinitely far from the source of the stress. Such a static deformation component may be due to the movements of the probe, and / or to the movements of an organ - such as the heart with each heartbeat or the lungs - etc.In the following, the problem of static deformation will be presented with reference to a probe including: - a housing, - a network of transducers housed in the housing and configured to o emit ultrasonic excitation waves towards the medium to be analyzed (organ, biological tissue, etc.), and o receive acoustic echoes (i.e. ultrasonic waves reflected by the different interfaces of the medium to be analyzed), and - an exciter housed in the housing and configured to: o generate vibrations, and o transmit them to the probe in order to mechanically produce a shear wave, the observation of which allows the measurement of properties of the medium to be analyzed. Figure 2a illustrates a probe S at rest placed on the medium M to be analyzed.When the exciter is activated to generate and transmit vibrations to the probe S (to generate the propagative shear component), these vibrations cause successive support (figure 2b) and release (figure 2c) constraints of the probe S on the medium, generating local movements and static deformations. As shown in figures 2b and 2c, in the frame of reference of the probe S, the relative movement to the probe of a point (such as point A) located on the surface of the medium is zero (by continuity), while the amplitude of the relative movement to the probe of a point (such as point B, or point C) located below the surface of the medium increases with depth, and tends towards an asymptote corresponding to the amplitude of the movement of the probe for the deepest points (such as point D).In order to better understand this phenomenon, it is possible to use a physical model of the medium as illustrated in Figure 3 and which consists of a stack of springs whose stiffness coefficients CR1, CR2, CR3 are increasing as a function of depth, due to the boundary conditions of the problem. In an incompressible medium, the stiffness coefficient of these springs is linked to the shear stresses and depends on the Young's modulus of the medium, as well as on the geometry of the problem. From the physical model illustrated in Figure 3, a study of the displacement of points B, C, located at different depths in the medium can be carried out, when a force F applied by the probe induces a displacement of a point A on the surface of the medium. By a force balance, it is possible to deduce that the compressions and at points b and c are expressed by the following formulas:. So we have Thus, the displacement – ​​due to the application of the force close to point A – measured at each point A, B, C of the medium varies as a function of depth. As an illustration, Figure 4a shows a profile of the static deformation component (i.e. displacement of the medium due to the movements of the probe and relative to the probe) as a function of depth. Such a profile generally has a logarithmic shape tending towards an asymptote. As illustrated in Figure 4b, this static deformation component DS (i.e. displacement of the medium due to the movements of the probe) is superimposed on the propagative components CP (i.e. displacement of the medium due in particular to the propagative shear component of Figure 4c, the propagative compression component being negligible), which makes it difficult to observe the propagative shear component alone, and therefore to measure the properties of the medium to be analyzed. Indeed, the artifact of Figure 4a (due to thestatic deformation component generated by the movements of the probe and / or by the movements of a patient's organ etc.) is particularly troublesome because: - the temporal frequency of the displacements induced by this static deformation component DS is similar to that of the displacements induced by the propagative shear component, which makes its suppression by purely temporal filtering difficult; - the amplitude of the displacements induced by this static deformation component DS: o is significantly higher than that of the displacements induced by the underlying propagative shear component (one to two orders of magnitude), and o increases with depth, which is problematic because the amplitude of the displacements induced by the propagative shear component decreases with depth (by scattering and absorption effects). 3. Presentation of the state of the art Different methods have been used in order toabstract from this artifact. a. A first method, implemented in the Fibroscan® system, consists of using broadband excitation, or equivalently, retaining the vibration of an external source for the generation of the shear wave. More precisely, the Fibroscan® system proposes to attenuate the oscillation of the external source in order to generate the shear wave over a short instant, as described in document WO 2018 / 078002. This attenuation (or "damping", according to the English terminology) makes it easier to separate the displacements of the medium due to the static deformation component (which is brought back to zero after an oscillation cycle), from the displacements of the medium due to the propagation of the propagative shear component. Thus, the propagative shear component and the static deformation component are temporally decoupled. Shear is observed when the static deformation component is very lowin the medium. The major problem with this method is its low energy efficiency since a lot of energy is wasted in generating a broadband vibration (i.e. to excite and damp the external source generating the propagative shear component). b. A second method, described in a paper – entitled “Probe Oscillation Shear Elastography (PROSE): A High Frame-Rate Method for Two-Dimensional Ultrasound Shear Wave Elastography”, by DC Mellema et al. – consists of using stroboscopy to systematically sample the same realization of the static strain component. Thus, the static strain component no longer biases the measurements of the propagative shear component. The problem with this method is that it imposes a temporal sampling frequency (less than twice the vibration frequency of the external source) that is too low to effectively analyze the propagation of the componentpropagative shear wave at low frequencies, for example at 50Hz. Moreover, this method has proven to be rather ineffective in vivo due to its inability to remove the entire static deformation component, as described in the paper entitled “Probe Oscillation Shear Wave Elastography: Initial In Vivo Results in Liver” by DC Mellema et al. c. Finally, many methods based on filtering techniques have been explored in order to reduce parasitic movements (due to propagative compression components but especially to shear components in unwanted directions) from that due to the propagative shear component of interest, particularly in magnetic resonance elastography. These methods involve in particular one-dimensional or two-dimensional filtering. An example of such methods is described in the paper entitled “Spatio-temporal directional filtering for improved inversion of MR elastography images” by Manduca et al. AThe disadvantage of these methods is that they require the use of two- or three-dimensional Fourier transforms, which can be computationally expensive and pose performance problems at the limits of films. Furthermore, some of these methods are based on non-linear directional filtering (thresholding in the frequency domain) and can generate significant artifacts, e.g., ghost wave propagation in a case where there is no propagation. d. Inspired by these methods, filtering techniques using a band-pass finite impulse response (FIR) filter have been tested without success due to their lack of robustness in separating the static deformation component and the propagative shear component. These unsuccessful tests are described in the document entitled “Probe Oscillation Shear Wave Elastography: Initial In Vivo Results in Liver” by DC Mellema et al., which teaches the skilled person thatthe use of a finite impulse response filter is not suitable for filtering the static deformation component. Filtering techniques using an infinite impulse response (IIR) filter have also been considered. However, infinite impulse response (IIR) filters generate phase distortions and have transient effects, generating significant artifacts in the measurement of the propagation speed of the propagative shear component. An aim of the present invention is to propose a method for analyzing a region of interest of a medium making it possible to overcome at least one of the aforementioned drawbacks. BRIEF DESCRIPTION OF THE INVENTION To this end, the invention proposes a method for analyzing a region of interest of a viscoelastic medium, the method including a phase of acquiring signals representative of the displacement of at least one propagative shear component and a static deformation component, the phaseacquisition comprising the following steps: o successively emitting acquisition signals in the viscoelastic medium over time, o detecting and recording reception signals received from the viscoelastic medium, each reception signal being associated with a respective acquisition signal, remarkable in that the method further comprises a processing phase for determining at least one property of the medium, said processing phase comprising the following sub-steps: o determining images of the region of interest of the medium from the reception signals, each image being determined from a respective reception signal and comprising information representative of the region of interest at different times, o estimating displacement images by comparing the images of the region of interest, each displacement image comprising information representative of the propagative shear component and a deformation componentstatic, o filtering of the displacement images to attenuate the static deformation component, o determining said and at least one property of the medium from the filtered displacement images. In the context of the present invention, the term "mechanical wave" means a wave comprising: - a propagative shear component generated either naturally (i.e. passive elastography in which the propagative shear component is generated by an organ such as the heart during a cardiac cycle), or artificially (i.e. harmonic or transient elastography in which the propagative shear component is generated by the force of ultrasonic radiation, or by an external source - such as an inertial vibration exciter of the type described in document WO 2022 / 084502, - and a propagative compression component, also generated either naturally or artificially, and whose amplitude in biological tissues is lowrelative to the shear propagative component. The amplitude of this compression propagative component being very low relative to the amplitude of the shear propagative component, the latter will be neglected in the remainder of the description. In the context of the present invention, the term "shear wave" or "shear propagative component" means a "low frequency" wave polarized transversely in the far field, that is to say a wave producing movements of the medium in a direction perpendicular to the direction of propagation of the wave and whose frequency is typically between 10 Hz and 1500 Hz. In the context of the present invention, the term "compressional wave" or "compression propagative component" means a "low frequency" wave polarized longitudinally in the far field, that is to say awave producing movements of the medium in a direction parallel to the direction of propagation of the wave and whose frequency is typically between 10Hz and 1500Hz. In the context of the present invention, the term "static deformation component" refers to the deformations induced by a stress on the medium. In biological environments, this static deformation component is linked to shear phenomena. In the context of the present invention, the term "ultrasonic wave" refers to a longitudinally polarized "high frequency" compression wave, i.e. a wave producing movements of the medium in a direction parallel to the direction of propagation of the wave and whose frequency is typically between 15kHz and 20MHz. In the context of the invention, this ultrasonic wave is used as a means of acquiring the displacement images used to monitor the propagation of the propagative shear component.in the context of the present invention, by "group velocity" of a wave, a velocity at which an overall shape of the envelope of the amplitudes of the wave, known as the envelope of the wave, propagates in space. Preferred but non-limiting aspects of the analysis method according to the invention are as follows: - the filtering step may comprise the application of a finite impulse response filter whose characteristics are defined as a function of: o an average frequency of the shear propagating component between 10Hz and 1500Hz, and o a maximum group velocity of the shear propagating component in the region of interest; - the finite impulse response filter may comprise a passband and an attenuated band: o the passband being defined at least by a lower bound K , said lower bound K being equal to a ratio between the average frequency of the shear component and the maximum group velocity ofgroup of the shear component, the attenuation in the passband being less than or equal to 6 dB, o the attenuated band being defined at least by a stop terminal K proportional to the lower terminal K , the attenuation in the attenuated band being greater than or equal to 30 dB, and the ratio between the lower terminal K and the stop terminal K defining a stiffness coefficient r of the finite impulse response filter, said stiffness coefficient being between 1 and 4.5; - the minimum and maximum speeds can be determined as a function of predefined minimum and maximum hardnesses in the region of interest; - the average frequency of the shear component can be estimated from a signal representative of a time spectrum of the displacement images; - the method can further comprise an excitation phase including a step consisting of generating the propagative shear component by applying an excitation to the viscoelastic mediumhaving the form of a low-frequency pulse which has a central frequency f between 10Hz and 1500Hz; - the finite impulse response filter can be of the high-pass type in a useful frequency range between 0 and 50 m; - said finite impulse response filter can be obtained by combining an all-pass type filter and a low-pass type filter in said useful frequency range; - the low-pass type filter can be a low-pass filter with a rectangular window or a filter whose impulse response is such that its maximum value is less than or equal to 2 times its average value. BRIEF DESCRIPTION OF THE DRAWINGS Other advantages and characteristics of the analysis method according to the invention will emerge more clearly from the following description of several variant embodiments, given as non-limiting examples, from the appended drawings in which: - Figure 1 is a schematic representation illustrating the generationof compression and shear waves during compression of a medium, - Figure 2a is a schematic representation of a probe at rest positioned on a medium to be analyzed, - Figure 2b is a schematic representation illustrating the generation of static deformations by pressing the probe on the medium to be analyzed, - Figure 2c is a schematic representation illustrating the generation of static deformations by releasing the probe on the medium to be analyzed, - Figure 3 is a schematic representation of a spring model, - Figure 4a is a schematic representation of a displacement profile induced by the static deformation component as a function of a direction of propagation of the propagative shear component, - Figure 4b is a schematic representation of a displacement profile induced by the superposition of the static deformation component and the propagative shear component, as a function of adirection of propagation of the propagative shear component, - Figure 4c is a schematic representation of a displacement profile induced by the propagative shear component as a function of a direction of propagation of the propagative shear component, once the static deformation component, indicated DS in Figure 4b, has been attenuated using the method described according to the invention, - Figure 5 is a schematic representation of an analysis device according to the invention, - Figure 6 is a schematic representation of an alternative embodiment of the analysis method according to the invention, - Figure 7 is a schematic representation of an impulse response of an example of a filter that can be used during a filtering sub-step of the analysis method. DETAILED DESCRIPTION OF THE INVENTION Different embodiments of the analysis method according to the invention will now be described in more detail with reference to the figures. InIn these different figures, equivalent elements are designated by the same reference numeral. In the following, the analysis method will be described with reference to the processing of data acquired using an ultrasonic elastography probe allowing: - to generate at least one low-frequency elastic wave – called a “shear wave” – in the medium, and - simultaneously with the generation of the low-frequency wave: o to emit high-frequency ultrasonic waves, and o to receive acoustic echoes due to the reflections of the ultrasonic waves in the medium, in order to observe the propagation of the low-frequency elastic wave in the medium. It is obvious to those skilled in the art that the analysis method can be implemented with passive elastography techniques using natural waves – in which the shear waves are generated naturally by the body. In this case, the probe only comprises an array of transducers for the emission of ultrasonic wavesaccording to a high frequency depth (15kHz - 20MHz) and the reception of acoustic echoes in order to observe the propagation of one (or more) shear wave(s) generated naturally by the body. It is also obvious to those skilled in the art that the analysis method according to the invention can be implemented with imaging techniques other than ultrasound imaging ("ultrasound elastography" in English), in particular magnetic resonance imaging ("magnetic resonance elastography" in English), or optical imaging ("optical coherence elastography" in English). 1. General information With reference to Figure 5, an example of a device is illustrated in which the method for analyzing a medium described below can be implemented. This device comprises: - a signal acquisition probe S, and - a control and processing unit Uc for: o controlling the probe S, and o processing the signals acquired by the probe S. 1.1. Elastography probeThe probe S comprises: - an array of transducers for emitting ultrasonic waves and receiving acoustic echoes, and - an exciter for generating the shear wave. The exciter may be an inertial vibration exciter of the type described in document WO 2022 / 084502. It is used to generate vibrations. A fixed part of the exciter is mechanically secured to the array of transducers to transmit the vibrations to the probe in order to mechanically produce the shear wave necessary for measuring the viscoelastic properties of the tissue to be analyzed. The use of an inertial vibration exciter makes it possible to obtain a probe whose weight and size are limited. The use of an inertial vibration exciter further allows the generation of a shear wave of sufficient power to measure tissue viscoelastic properties while consuming less energy than other solutions (such assolutions based on ultrasonic radiation pressure). The exciter can also be external to the probe, and move it in its entirety, although this solution is not optimal from the point of view of size. Such a probe being known from the state of the art, it will not be described in more detail below. 1.2. Control and processing unit The control and processing unit U is connected to the probe S by wired or wireless communication means. It allows the transducers of the probe S to be controlled, and the data acquired by the transducers of the probe S to be processed. It also allows the inertial vibration exciter to be activated for the generation of one (or more) shear wave(s) in the medium to be analyzed, which may be a patient's organ such as the liver. More precisely, the control and processing unit U allows: - to command the inertial vibration exciter to vibrate allowing the generation of a shear waveshear in the medium to be analyzed, - to command the transducers to emit ultrasonic waves towards the medium to be analyzed, - to command the transducers to receive the echoes reflected by the medium to be analyzed and convert them into reception signals, - to process the reception signals. The control and processing unit U may be composed of one or more distinct physical entities, possibly remote from the probe S. The control and processing unit U comprises for example: - one (or more) controller(s) 11, such as a Smartphone, a personal assistant (or "PDA", acronym for the English expression "Personal Digital Assistant"), or any type of mobile terminal known to those skilled in the art; and - one (or more) calculator(s) 12, such as a computer(s), a microcomputer(s), a workstation(s), and / or other devices known to those skilled in the art including a processor(s), a microcontroller(s), aprogrammable logic controller(s), application-specific integrated circuit(s), and / or other programmable circuits, - one (or more) storage unit(s) 13 comprising one (or more) memory(ies) which may be a ROM / RAM memory, a USB key, a memory of a central server. In addition to storing data associated with the analysis of a medium, the storage unit 13 also makes it possible to store programming code instructions intended to execute the steps of the analysis method described below. 1.3. Operating principle With reference to Figures 5 and 6, the operating principle of the imaging device is as follows. The controller 11 causes vibrations to be generated in the viscoelastic medium by the exciter, during an excitation step (step 100). This makes it possible to generate a mechanical wave in the medium, including a propagative shear component and a negligible propagative compression component in the tissuesbiological. The displacements of the medium induced by the propagation of the mechanical wave in the viscoelastic medium are measured by ultrasound, during an observation step (step 200) concomitant with the excitation step (100). For this purpose, the controller 11 controls the emission of ultrasonic waves (at a frequency of, for example, between 15 kHz and 20 MHz) by the transducers of the probe S. These ultrasonic waves penetrate into the medium where they are reflected on diffusing particles contained in said medium – such as, for example, collagen particles contained in the medium if it is human tissue – which makes it possible to follow the movements of the medium. The ultrasonic waves thus emitted can be “planar” (i.e. waves whose wavefront is rectilinear in an analysis plane (D, Z)) or spiral, or divergent, or even focused. In particular, the observation step (200) comprises the following sub-steps: - the controller 11 commandsthe emission by the transducer network of a succession of ultrasonic wave shots into the medium (at a rate of between 10 and 10,000 shots per second), - the controller 11 controls the detection by the transducer network, and the recording (in real time) in the storage unit 13 of the received acoustic signals comprising the echoes generated by the ultrasonic waves by interacting with the scattering particles of the medium. The acoustic signals recorded in the storage unit 13 are then processed (generally in delayed time) by the computer during a processing step 300. More precisely, the processing step 300 comprises a sub-step of determining – by a conventional beamforming process – images of a region of interest of the medium contained in the observation field (i.e. the area insonified by the ultrasonic waves). Each image is representative of the regionof interest after a respective shot. As the shots are carried out successively in time, each image is representative of the region of interest at a different time. These successive images of the region of interest are then compared, by correlation and in particular by cross-correlation: - either two by two - or with a reference image (which may be a previously determined displacement image or an image of the region of interest obtained during a preliminary observation step), to determine displacement images of the medium. These displacement images are representative of the propagation of the mechanical wave in the medium. These displacement images also include a static deformation component, which can significantly hinder the monitoring of the propagation of the mechanical wave, used for the determination of one (or more) properties of the medium. This is why the inventors have developed a sub-step for filtering the acoustic signalsreceived – and in particular displacement images – to remove the static deformation component of the measured displacements, and thus retain only the propagative component, i.e. the mechanical wave, in the displacement images. This filtering sub-step will now be described in more detail. 2. Filtering sub-step The filtering sub-step includes the application of a finite impulse response filter whose characteristics are defined as a function of: - an average frequency of the propagative shear component typically between 10Hz and 1500Hz, and - a maximum velocity (in particular a maximum group velocity) of the propagative shear component in the region of interest. The average frequency of the propagative shear component depends on the solution chosen for the generation of this propagative shear component. However, in all cases, this average frequency is known or can be measured. ByFor example, in the case of using an exciter, the latter is configured to generate a propagating shear component at a desired average frequency (for example at an average frequency of 50 Hz). In this case, the average frequency of the propagating shear component is therefore known a priori. If the solution chosen for the generation of the shear wave is natural (generation of the shear wave by an organ of the patient), then the average frequency of the propagating shear component can be calculated from the displacement images by any technique known to those skilled in the art. Similarly, the maximum group velocity of the propagating shear component in the region of interest depends on the type of region of interest observed. However, for each type of region of interest, this maximum group velocity is known in the literature or can be measured. For example, if the region of interest consists of soft tissue (liver,spleen, prostate, breast, muscle etc.), it is known that the maximum group velocity of the propagating shear component is of the order of 6m / s. Thus, the values ​​of the average frequency and the maximum group velocity of the propagating shear component are known and allow the dimensioning of the finite impulse response filter which will now be presented below. 2.1 Filter characteristics With reference to Figure 7, the frequency response (i.e. variation of the filter gain as a function of the frequency of the signal applied to it as input) of an example of a filter that can be used during the filtering sub-step has been illustrated. This frequency response is a curve representing an attenuation (in dB) as a function of a frequency (in Hz). In this embodiment, the finite impulse response filter is a "high-pass" filter. As illustrated in Figure 7, this frequency response (or gain plot of a diagramBode frequency) is composed of: - an attenuated band BA, - a passband BP, and - a transition band BT between the attenuated and passbands BA, BP. 2.1.1. Attenuated band The attenuated band BA corresponds to a frequency range in which a signal applied to the filter input appears strongly reduced at the filter output: in this frequency range, the amplitude of the signal applied to the filter input is attenuated (to a value close to zero) at the filter output. In the case of a high-pass filter, the attenuated band BA can be defined by a stop limit. The stop limit – or stop wave number – corresponds to a ratio between a frequency and a group velocity (representative of the propagation speed of the shear propagating component) expressed in cycles per meter. This stop limit is used to express at which frequency the filter ceases to produce its “attenuated” effect. In the context of the present invention, this “attenuated effect” isconsidered produced when the amplitude of a signal applied to the filter input is divided by 32 (or more) at the filter output (-30dB). We will therefore use the term K in the rest of the text to characterize the upper part of the attenuated band. Thus, the stop terminal K (or stop wave number K ) of the attenuated band BA is representative of the frequency at which the amplitude of a signal applied to the filter input is divided by 32 at the filter output (-30dB). In this attenuated band BA, the amplitude of a signal applied to the filter input is therefore attenuated by an attenuation factor FA greater than or equal to 30dB. 2.1.2. Bandwidth The bandwidth BP corresponds to a frequency range in which a signal applied to the filter input appears little or not attenuated at the filter output: in this frequency range, the amplitude of the signal applied to the filter input is substantially unchanged (or slightly attenuated) at the filter output. In the case of a filterhigh-pass, the BP bandwidth can be defined by a lower bound. This lower bound – or wave number – corresponds to a ratio between a frequency and a group velocity (representative of the propagation speed of the shear propagating component) expressed in cycles per meter. This lower bound makes it possible to express at which frequency the filter ceases to produce its “passing” effect. In the context of the present invention, this “passing effect” is considered to be produced when the amplitude of a signal applied to the filter input is divided by 2 (or less) at the filter output (-6dB). We will therefore use the term K in the rest of the text to characterize the lower part of the bandwidth. Thus, the lower bound K of the BP bandwidth is representative of the frequency at which the amplitude of a signal applied to the filter input is divided by 2 at the filter output (-6dB). In this BP bandwidth, the amplitude of a signal applied inThe input of the filter is therefore attenuated by an attenuation factor FA less than or equal to 6 dB. The lower limit K corresponds to the ratio between: - the average frequency of the propagative shear component, and - the maximum group velocity of the propagative shear component. As indicated previously, the average frequency of the propagative shear component is known. Similarly, the maximum group velocity of the propagative shear component is known (of the order of 6 m / s in the case of soft tissue). It is therefore possible to define the lower limit K of the bandwidth BP according to the type of tissue analyzed and the type of excitation envisaged for the generation of the propagative shear component. 2.1.3. Transition band The transition band BT corresponds to a frequency range in which a signal applied at the input is neither strongly attenuated (attenuated band BA) nor substantially kept unchanged (passband BP). Thistransition band BT characterizes the filter's ability to retain or reject frequencies more or less abruptly. It is therefore representative of the "reactivity" of the filter. In this transition band, we characterize the filter by a stiffness coefficient (or "stiffness constant") corresponding to the ratio between: - the lower limit K of the passband BP, and - the stop limit K of the attenuated band BA. Thus, the stiffness coefficient is defined as the following ratio: This stiffness coefficient illustrates the slope of the amplitude response of the filter in the transition band between a regime where the filter strongly attenuates and a regime where the filter no longer attenuates. The inventors have determined that it is preferable for the stiffness coefficient to be less than or equal to 4.5 so that the filter allows significant attenuation of the static deformation component in the received acoustic signals without unacceptably impacting the frequencieslow shear waves corresponding to high shear wave speeds, and therefore high hardnesses. The efficiency of the filter depends on two criteria of the transition band: - a cut-off frequency, - the stiffness coefficient. The cut-off frequency of the filter corresponds to the useful operating limit frequency of the filter. More precisely, the cut-off frequency makes it possible to express towards which frequency the filter begins to produce its "passing" effect. Thus, the lower limit K of the bandwidth BP is representative of the cut-off frequency of the filter. 2.2. Filter variants Other types of filters can be used to attenuate the static deformation component contained in the signals received by the probe. For example, a band-pass filter can be used instead of the high-pass filter illustrated in Figure 7. In the case of a band-pass filter, the bandwidth BP is further defined by an upper limit K equal to aratio between the average frequency of the shear propagating component and a minimum group velocity of the shear propagating component. The values ​​of the average frequency and the minimum group velocity being known (measurable or known from the literature depending on the tissue to be imaged), this upper bound K is easily determinable. In all cases, the chosen filter exhibits the behavior of a high-pass type filter in a useful frequency range, for example between 0 and 50 m . Advantageously, this finite impulse response filter can be obtained by combining an “all-pass” type filter and a “low-pass” type filter in said useful frequency range. This makes it easier to obtain an effective filter for: - attenuation of the static deformation component, and - conservation of the shear propagating component. 2.3. Theory relating to the invention A filtering technique alongof the direction of the static strain component is proposed, in order to drastically reduce the impact of the static strain component. This technique is based on the idea that the static strain component and the propagative shear component have very different spatial characteristics: - short wavelengths (a few cms at most at 50Hz) for the propagative shear component with group velocities varying between 0.5 m / s and 6 m / s in soft tissues such as the spleen and liver. - long wavelengths (tens of m at 50Hz) for the static strain component. 2.3.1. High-pass FIR filter In one embodiment, the filtering technique is based on a high-pass finite impulse response (FIR) filter (not necessarily with a linear phase response). Its frequency characteristics are defined as a function of the average frequency of the shear waves studied as well as the group velocitiesminimum and maximum The average frequency of the shear wave can be estimated using the formula below: Where: - is a signal representative of the time spectrum of the shear wave (e.g. the time Fourier transform of the displacement images). Typical values ​​of the mean frequency of shear waves are between 10Hz and 500Hz. The mean frequency value is most often assumed to be known. For example, in the case where the shear wave is generated naturally (passive elastography), the mean frequency value can be measured. In the case where the shear wave is generated artificially (transient elastography), the mean frequency value is deduced from the characteristics of the mechanical source used. The group velocity of a shear wave whose frequencies lie in the interval is estimated as follows: Typical values ​​of shear wave group velocity are between 0.5 m / s and 5.5 m / s for soft tissues such as the liver. We are particularly interested in two values ​​of wavenumber: ^ which corresponds to the wavenumber value (in number of cycles per meter) for which the filter attenuation is equal to 6 dB, ^ which corresponds to the wavenumber value (in number of cycles per meter) for which the filter attenuation is equal to 30 dB. For information, we recall that the "wavenumber" (also known as "repetition") is a quantity proportional to the inverse of the wavelength. The "wavenumber" is the spatial analog of the temporal frequency and characterizes the propagation of a wave in space, as the temporal frequency does in time.The above mentioned attenuation is calculated based on the filter gain value in the passband as follows:. where: - is the amplitude of the frequency response of the filter of interest and - is a quantity representative of the filter gain in the passband. This quantity can be, for example, the maximum of the absolute value of the frequency response in the passband or the average value of the absolute value of the frequency response in the passband. Associated with these two values, we define the stiffness coefficient of the high-pass filter response as follows: This stiffness coefficient characterizes the average slope of the frequency response of the filter between these two values ​​since we have: At a higher level, it can be seen as a quantifier of the efficiency of the high-pass filter. This filter is very generic and can be produced by a person skilled in the art using finite impulse response filter synthesis tools, such as the "firwin" and "firwin2" functions of the "scipy signal processing" library of the Python programming language. Advantageously, the stiffness coefficient of the filter is chosen in order to obtain sufficient efficiency of the filter. For example, the value of the stiffness coefficient can be chosen to be less than 4.5. A high-pass filter of this type can be produced by a person skilled in the art by building a phase-distorting FIR filter. A code example is given below for the case of a shear wave whose group frequency is assumed to be 50Hz.We define a finite impulse response filter of 2.5 cm length. # Sampling frequency Dz = 0.6523e-3 # Shear wave frequency f = 50 # Hz # High pass filter definition probe_fir_len = 2.5e-2 probe_half_fir = int(np.round(probe_fir_len / Dz - 1) / 2) probe_fir = -np.ones((2 * probe_half_fir +1, )) / (2 * probe_half_fir + 1) probe_fir[probe_half_fir] = 0 probe_fir[probe_half_fir] = 1 - 1. / len(probe_fir) # Frequency response of the filter w, h_probe_fir = sig.freqz(probe_fir, fs=1 / Dz, worN=8192) # Cutoff frequency and coefficient of associated stiffness cutoff_0 = np.argmin(np.abs(20*np.log10(np.abs(h_probe_fir) / np.abs(h_probe_fir[-1])) + 30)) cutoff_1 = np.argmin(np.abs(20*np.log10(np.abs(h_probe_fir) / np.abs(h_probe_fir[-1])) + 6)) k_6 = w[cutoff_1] k_30 = w[cutoff_0] c_max = f / k_30 c_min = f / k_6 r = k_6 / k_30 In this case, the characteristic quantities of the filter are: , and .The reader will appreciate that a stiffness constraint lower than 4.5 is difficult to achieve using the "firwin2" function since the "firwin2" function imposes a phase linearity constraint (or equivalently filter antisymmetry) to ensure that the filter does not exhibit phase distortion. An example below illustrates this difficulty in a case similar to above: probe_fir_len = 2.5e-2 probe_half_fir = int(np.round(probe_fir_len / Dz - 1) / 2) numtaps = 2 * probe_half_fir cutoff_1 = k_min cutoff_0 = k_min / 16 hp = sig.firwin2(numtaps, [0.0, cutoff_0, cutoff_1, 1.0 / 2 / Dz], [0, 10**(-30 / 20), 1.0, 1.0], fs = 1 / Dz, antisymmetric=True, window='rect') w, h = sig.freqz(hp, fs=1 / Dz, worN=2048*4) cutoff_0_meas = np.argmin(np.abs(20*np.log10(np.abs(h) / np.abs(h[-1])) + 30)) cutoff_1_meas = np.argmin(np.abs(20*np.log10(np.abs(h) / np.abs(h[-1])) + 6)) k_6 = w[cutoff_1_meas] k_30 = w[cutoff_0_meas] c_max = f / k_30 c_min = f / k_6 r = k_6 / k_30 slope = 1. / alpha In this case, the associated stiffness coefficient is 16.7. To reduce the stiffness coefficient, it is possible to vary the filter length or other parameters. Thus, the example below allows to achieve a stiffness lower than 4.5 using “firwin” and a filter of size 3.2 cm. # Sampling frequency Dz = 0.6523e-3 # Shear wave characteristics f = 50 # Hz c_min = np.sqrt(12 / 3) # m / s c_max = np.sqrt(500 / 3) # m / s k_max = f / c_min # m^-1 k_min = f / c_max # m^-1 # Definition of high pass filter probe_fir_len = 3.2e-2 probe_half_fir = int(np.round(probe_fir_len / Dz - 1) / 2) numtaps = 2 * probe_half_fir hp = sig.firwin(numtaps+1, k_max, width=2*(k_max-k_min), fs = 1 / Dz, pass_zero='highpass') # Answer filter frequency w, h = sig.freqz(hp, fs=1 / Dz, worN=2048*4) # Wave numbers k_6 and k_30 and associated stiffness coefficient cutoff_0_meas = np.argmin(np.abs(20*np.log10(np.abs(h) / np.abs(h[-1])) cutoff_1_meas = np.argmin(np.abs(20*np.log10(np.abs(h) / np.abs(h[-1])) + 6)) k_6 = w[cutoff_1_meas] k_30 = w[cutoff_0_meas] c_max = f / k_30 c_min = f / k_6 r = k_6 / k_30 In this case, the characteristic quantities of the filter are as follows:. , and . We can thus generate a filter according to the stiffness specification, but the length necessary to create the filter: 3.2 cm, will be lost for the visualization of the shear wave velocities (shortening the depth of the area of ​​interest). Of course, other Matlab or python functions (than the "fiwin2" function) can be used. 2.3.2. Bandpass FIR filter In one embodiment of the invention, the filtering technique is based on a one-dimensional bandpass filter applied along the deformation. Similar to the high-pass filter defined in point 2.4.1, we are interested in the following quantities: ^ which corresponds to the value of the wave number (in number of cycles per meter) for which the attenuation of the filter is equal to 6 dB in the lower transition band, ^ the stiffness coefficient of the filter.It should be noted that the corresponding stiffness coefficient on which we impose a constraint similar to that of the high-pass filter (i.e. stiffness coefficient less than or equal to 4.5) is defined in this case on the lower transition band of the band-pass filter. No constraint is imposed on the stiffness coefficient in the upper transition band. The length of its impulse response should not exceed a few cm, a typical size being between 1 cm and 3 cm, in order to limit boundary effects while maintaining a sufficiently large region in the medium of interest. The reader will have understood that many modifications can be made to the invention described above without materially departing from the new teachings and advantages described herein. Therefore, all such modifications are intended to be incorporated within the scope of the appended claims.

Claims

CLAIMS 1. Method for analyzing a region of interest of a viscoelastic medium, the method including a phase of acquisition (200) of signals representative of the displacement of at least one propagative shear component and one static deformation component, the acquisition phase (200) comprising the following steps: o successively emitting acquisition signals in the viscoelastic medium over time, o detecting and recording reception signals received from the viscoelastic medium, each reception signal being associated with a respective acquisition signal, characterized in that the method further comprises a processing phase (300) for determining at least one property of the medium, said processing phase comprising the following sub-steps: o determining images of the region of interest of the medium from the reception signals,each image being determined from a respective reception signal and comprising information representative of the region of interest at different times, o estimation of displacement images by comparing the images of the region of interest, each displacement image comprising information representative of the propagative shear component and a static deformation component, o filtering the displacement images to attenuate the static deformation component, o determination of said and at least one property of the medium from the filtered displacement images.

2. Analysis method according to claim 1, wherein the filtering step comprises the application of a finite impulse response filter whose characteristics are defined as a function of: o an average frequency of the propagative shear component between 10Hz and 1500Hz, and, o of a maximum group velocity of the propagating shear component in the region of interest.

3. Analysis method according to claim 2, wherein the finite impulse response filter comprises a passband (BP) and an attenuated band (BA): o the passband (BP) being defined at least by a lower bound K , said lower bound K being equal to a ratio between the average frequency of the shear component and the maximum group velocity of the shear component, the attenuation in the passband being less than or equal to 6 dB, o the attenuated band (BA) being defined at least by a stop bound K proportional to the lower bound K , the attenuation in the attenuated band being greater than or equal to 30 dB, and the ratio between the lower bound K and the stop bound K defining a stiffness coefficient r of the finite impulse response filter, said stiffness coefficient being between 1 and 4.

5. 4.Analysis method according to any one of claims 2 or 3, wherein the minimum and maximum speeds are determined as a function of predefined minimum and maximum hardnesses in the region of interest.

5. Method according to any one of claims 2 to 4, wherein the average frequency of the shear component is estimated from a signal representative of a time spectrum of the displacement images.

6. Method according to one of claims 2 to 4, which further comprises an excitation phase (100) including a step of generating the propagative shear component by applying to the viscoelastic medium an excitation having the form of a low-frequency pulse which has a central frequency f between 10Hz and 1500Hz.

7. Method according to any one of claims 2 to 6, wherein the finite impulse response filter is of the high-pass type in a useful frequency range between 0 and 50 m.

8. Method according to claim 7, wherein said finite impulse response filter is obtained by combining an all-pass type filter and a low-pass type filter in said useful frequency range.

9. Method according to claim 8, wherein the low-pass type filter is a rectangular window low-pass filter or a filter whose impulse response is such that its maximum value is less than or equal to 2 times its average value.

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