Method and system for the ultrasonic characterisation of a medium for medical analysis

Abstract

The invention relates to a method for the ultrasonic characterisation of a medium, the method comprising the steps of generating a series of incident ultrasonic waves, measuring a canonical reflection matrix Rui(t) defined between the transmitting basis (i) at the input and a receiving basis (u) at the output, determining a focused reflection matrix Rxx(z) of the medium by focusing the canonical reflection matrix, wherein virtual transducers are at the same depth. The method then comprises filtering the focused reflection matrix xx(z) to obtain a single reflection matrix Rs(z) or a multiple reflection matrix RM(z), then determining a single scattering rate ρs(rp,z) or a multiple scattering rate ρs(rp,z) local to a spatial position point rp. The single or multiple scattering rate is a local physical characteristic representative of the local nature of the medium.

Description

[0001] METHOD AND SYSTEM FOR ULTRASOUND CHARACTERIZATION OF A MEDIUM FOR MEDICAL ANALYSIS TECHNICAL FIELD The present disclosure relates to methods and systems for the ultrasonic characterization of a medium, intended to be applied to medical imaging. These methods and systems implement a network of transducers placed in contact with, for example, a living being, an animal or a patient, to emit ultrasonic waves into its body and to measure the reflection of the diffusing medium following this emission. STATE OF THE ART In ultrasound medical imaging, certain physical parameters characterizing the propagation of the wave in the medium are measured in order to detect or monitor the development of a pathology. This is particularly the case for attenuation, the characteristic length of which is noted l ext. The extinction length refers to the characteristic distance of decay of the wave as it propagates in the medium, and depends in particular on two factors: absorption and scattering. Wave scattering is the phenomenon used in ultrasound imaging to probe the medium studied. Each scattering event by a heterogeneity of the medium produces an echo which can be used under certain conditions to construct an image of the reflectivity of the medium. In doing so, each scattering event also induces an attenuation of the incident wave whose characteristic distance is the scattering mean free path ls, the average distance between two successive scattering events. Absorption also leads to an attenuation of the incident wave whose characteristic distance is the absorption length l a . These two phenomena contribute to the overall attenuation of waves in the medium, such that ^ ^ ^^ ^ ^ = ^ ^ ^^ + ^ ^ ^^. Attenuation differs depending on the nature of the tissues probed, and induces contrast differences observable on a conventional ultrasound image. These contrast differences can be globally and approximately corrected by applying a depth gain correction on the constructed ultrasound image. Generally, in medical imaging, only attenuation is measured or estimated globally throughout the insonified medium, by the extinction length. Absorption losses and losses due to scattering have different physical origins. The characteristic lengths associated with these losses are more or less sensitive to the nature of the medium studied, impacting the highlighting of certain symptoms of a patient. The document “Multiple scattering of ultrasound in weakly inhomogeneous media: application to human soft tissue”, A. Aubry and A. Derode, J. Acoust. Soc. Am.129, 225-233 (2011), proposes a method for characterizing a medium by ultrasound in which the characteristic lengths l are measured independently. s and l aThis process is based on the discrimination of single scattering and multiple scattering components. The first component includes echoes that have been scattered only once by the scatterers in the medium. This contribution is used in ultrasound to construct an image of the reflectivity of the medium, using the relationship between echo times and the position of the scatterers in the medium under study. The multiple scattering component corresponds to waves that have undergone several scattering events before returning to the probe. Multiple scattering can pose problems in imaging because it complicates the link between echo time and the position of the scatterers. Multiple scattering has a strong impact on the construction of an image representative of the reality of the medium.The approach proposed by the previous document is based on the measurement of the reflection matrix containing all the impulse responses between each transducer of an ultrasonic probe placed opposite the medium studied. This approach exploits the differences in statistical properties between the single and multiple scattering contributions to separate these two components and measure l independently. s and l a. However, this measurement is global and does not measure the local variations of these two parameters. Patent application publication WO 2021 / 023933 illustrates the determination of a focused reflection matrix making it possible to locally probe the respective weight of the single and multiple scattering contributions, by considering the response between virtual transducers, which makes it possible to probe the propagation of the ultrasonic wave locally around said virtual transducers. However, these analyses do not make it possible to obtain information on the absorption length, and / or the attenuation length and / or the mean free path of scattering of the medium. SUMMARY The object of the present disclosure is to improve known ultrasonic probing methods, in particular in order to determine a mean free path characteristic locally around one or more points of the medium.The present disclosure relates, according to a first aspect, to an ultrasonic characterization method for medical analysis of a medium, the method comprising the steps of: - generating a series of incident ultrasonic waves in an area of ​​said medium, by means of an array of transducers, said series of incident ultrasonic waves being an emission base (i); and - measuring a canonical reflection matrix Rui(t) defined between the emission base (i) at the input and a reception base (u) at the output, the coefficients of this canonical reflection matrix corresponding to the signals received by the transducers and induced by the ultrasonic waves reflected in the medium; - determining a focused reflection matrix R. xx(z) comprising responses of the medium calculated by focusing from the canonical reflection matrix Rui(t) between a virtual input transducer of spatial position rin= (xin, z) and a virtual output transducer of spatial position rout = (xout, z), the two virtual transducers being located at the same depth z for a sound speed model c0, the coefficients of said focused reflection matrix Rxx(z) being written as follows, Rxx(z) = [R(^ ^^ , ^ ^^^ , ^)] x in , x out being included in a region around a point ^ ^ = ^^ ^ , ^ ^ ^ the set of transverse positions x in and x out virtual transducers rin and rout forming a focused base (x) at each depth z, The method further comprises the steps of: - filtering the focused reflection matrix ^ ^^ ^^^ to obtain a simple diffusion matrix ^ ^^^^ characteristic of single scattering of focused reflection matrix or multiple reflection matrix ^ ^ ^^^ characteristic of multiple scattering of the focused reflection matrix, - determination of a simple scattering rate ^ ^ ^^ ^ , ^^ as a function of the depth z in the region around point ^ ^ by calculating the ratio of the norm of the simple scattering matrix Rs(z) to the norm of the focused reflection matrix Rxx(z), or determining a multiple scattering rate ^ ^ ^^ ^ , ^^ as a function of the depth z in the region around point ^ ^ by calculating the ratio of the norm of the multiple scattering matrix R M (z) by the norm of the focused reflection matrix R xx(z). Thanks to these provisions, the method advantageously makes it possible to locally probe the medium to obtain a local estimate of the simple scattering rate and / or the multiple scattering rate. This estimate is representative of the quality of the measurements collected, and therefore of the quality of the images that can be produced from these measurements. These estimates are made by calculation from measurements made and recorded in a canonical reflection matrix. These estimates can thus be recalculated independently of the measurement acquisition phase, in particular by modifying various calculation parameters, which makes it possible to carry out various ultrasonic characterization analyses either in real time or a posteriori. These calculations can be carried out in the time domain or in the frequency domain.These calculation methods give substantially equivalent results, with a lower calculation cost in the time domain, but with better precision in frequency mode. According to various embodiments of the method, one and / or the other of the following arrangements may optionally be used. According to a variant, the filtering is carried out by: - ​​determining a set of digital focused reflection matrices ^^^. ^ , ^^ characteristics of simple diffusion in the medium, and calculated by acoustic propagation between the transducer network and a point diffuser of spatial position (^ ^ , z) in a model medium of sound speed c0, xin, xout, ^ ^ , and z being included in the region around point ^ ^ = ^^ ^ , ^ ^ ^ the coefficients of the digital focused reflection matrices are written as follows: ^ ^ ^ ^ , ^ ^ = S^^^^ , ^ ^^^ , ^ ^ , ^^ " - determination of a confocal base of several confocal matrices ^ # ^ ^ ^ calculated by ortho-normalization of at least part of the digital focused reflection matrices ^ ^ ^ ^ , ^ ^ , for depths z, k being an index between 1 and Nk ^ ^ ^ , Nk ^ ^ ^ being a positive integer, representing the number of matrices of the confocal base for depths ^, - projection of the focused reflection matrix ^ ^^ ^^^ on the confocal basis of confocal matrices ^ # ^ ^ ^ to obtain the simple reflection matrix ^ ^ ^ ^ ^ characteristic of the single scattering of the focused reflection matrix or to obtain the multiple reflection matrix ^ ^^^^ characteristic of the multiple scattering of the focused reflection matrix. According to a variant: during the determination of the confocal base, the digital reflection matrices ^^ expressed in the form ^ ^ ^ ^ , ^ = ^ $^^ ^^ , ^ ^^^ , ^ ^ , ^^" are put in the form of a two-dimensional matrix ^ % ^^^ = $^&^ ^^ , ^ ^^^ ', ^ ^ , ^^" defined for each depth z, we perform a singular value decomposition (SVD) of the two-dimensional matrix ^ %^ ^ ^ according to the following expression: in which ) * ^^^ are the singular values ​​of the two-dimensional matrix 2 ^^^^, ^ % + ^^^ = $ + ^ ̅ &^ ^^ , ^ ^^^ ', ^^" are the singular vectors of the two-dimensional matrix ^ %^ ^ ^ in the focused base (x), 4 +^^^ = 5 * ^ ^ ^ , ^^" are the singular vectors of the two-dimensional matrix 2 ^^^^ in the base of point diffusers of spatial position (^ ^ , z) , † in superscript designating the combined operation of conjugation and transposition. According to a variant: for the projection, we calculate the simple diffusion matrix ^ ^ ^^^ by a linear combination of confocal matrices ^ # ^^^ of the confocal basis, weighted by the scalar product with the focused reflection matrix ^ ^^ ^ ^ ^ , at each depth ^, this projection being obtained by the following formula: in which denotes the scalar product between the matrices ^ # ^^^ and ^ ^^ ^^^, and ∗ in superscript is the conjugation operation. According to a variant: for the projection, we calculate the simple diffusion matrix ^ ^ ^^^ by a linear combination of confocal matrices ^# ^^^ of the confocal basis, weighted by the scalar product with the focused reflection matrix ^ ^^ ^ ^ ^ , at each depth ^, this projection being obtained by the following formula: in which denotes the scalar product between the matrices ^ # ^^^ and ^ ^^ ^^^, and ∗ in superscript is the conjugation operation. According to a variant, the method further comprises a step of: - determining S(160) a mean free path of diffusion ls in the region around the point ^ ^ by identifying the decay as a function of the depth z of a simple diffusion rate ^^, or by identifying growth as a function of the depth z of a multiple diffusion rate ^^. Thanks to this arrangement, we obtain a local estimate of the mean free path of diffusion ls at several points rp of the medium. This estimate is representative of the simple diffusion (and reciprocally of the multiple diffusion) of the medium at various points of the medium, which can make it possible to detect an anomaly, potentially revealing the presence of a pathology in an identified area of ​​the medium. This estimate of the mean free path of diffusion l s can also be periodically repeated, in order to then monitor its temporal evolution, which is also relevant for the practitioner. According to a variant, the method further comprises: - determining a mapping of the mean free diffusion path ^ ^ ^^ ^ ^ for a set of points ^ ^ of the medium. According to a variant, the method further comprises: - determining a confocal image I c(x,z) as a function of depth z, from the diagonal coefficients of the focused reflection matrix R xx (z), that is to say: B C ^^, ^^ = |; ^^ ^^, , ^, ^^| D According to a variant, the method further comprises: - determining an average confocal intensity B C̅ ^^ ^ , ^^ in the region around point ^ ^ obtained by averaging the confocal image along its lateral dimension x in the region: in which the symbol 〈 … 〉 ^ denotes an average over the index variable According to a variant, the method further comprises: - determining an extinction length l ext of the region around point ^ ^ by identification of the decrease as a function of the depth z of the confocal intensity B C̅ ^^ ^, ^^ averaged over the region. According to a variant, the method further comprises: - determining a mapping of the extinction length ^ ^^^ ^^ ^ ^ for a set of points ^ ^ of the medium According to a variant, the method further comprises: - determining an absorption length la of the region around the point ^ ^ by : According to a variant, the method further comprises: - determining a mapping of the absorption length ^ ^ ^^ ^ ^ for a set of points ^ ^of the medium. The present disclosure relates, according to a second aspect, to an ultrasonic characterization system for medical analysis of a medium, and configured for implementing methods as described above. The system according to the second aspect comprises: - an array of transducers adapted to generate a series of incident ultrasonic waves in an area of ​​the medium, and to measure as a function of time the ultrasonic waves backscattered by said area; and - a computing unit associated with the array of transducers and adapted to implement the method according to the first aspect.

[0002] BRIEF DESCRIPTION OF THE FIGURES Other advantages and characteristics of the technique presented above will appear upon reading the detailed description below, presented in a non-limiting manner for illustrative purposes, made with reference to the figures in which: Figures 1(a) to 1(f) illustrate transmission / reception sequences used for imaging and ultrasonic characterization of a medium; Figure 2 illustrates usual confocal imaging and matrix imaging; Figure 3 illustrates an example of an ultrasonic characterization system for implementing the method according to the present disclosure; Figure 4 presents the definitions used in the method according to the present disclosure; Figure 5 is a diagram of the ultrasonic characterization method according to the present disclosure,in which a simple scattering rate or a multiple scattering rate is determined; Figure 6 is a diagram of an embodiment for the focused reflection matrix filtering step of the method illustrated in Figure 5; Figure 7 illustrates the dimensions of the area of ​​interest and the resolution cell for the calculations of the various steps of the method; Figure 8 illustrates a result of the method of Figure 5, applied to the imaging of a phantom containing two cylindrical inclusions, each having different absorption and scattering properties; Figure 8(a) is a general diagram of the phantom presented in situation with a transducer array; Figure 8(b) is an illustration of an ultrasound image of a portion of the phantom with two measurement lines; a first line crossing the first inclusion, and a second line crossing the second inclusion; Figure 8(c) illustrates values ​​of the simple scattering rate according to the depth,for the first line and the second line of Figure 8(b); Figure 9 illustrates a result of the method of Figure 5, applied to an example of liver imaging; Figure 9(a) shows an ultrasound image of the liver with the transducer array on the external surface of a patient's body; Figure 9(b) is an illustration of an ultrasound image of a portion of the medium in which the liver is located; and Figure 9(c) shows simple diffusion rate values ​​as a function of depth in the portion of Figure 9(b). In the various embodiments described with reference to the figures, similar or identical elements bear the same references unless otherwise stated. DETAILED DESCRIPTION In the detailed description which follows,only certain embodiments are described in detail to ensure clarity of the disclosure but these examples are not intended to limit the general scope of the principles emerging from the present disclosure. The different embodiments and aspects described in the present disclosure can be combined or simplified in multiple ways. In particular, the steps of the different methods can be repeated, interchanged, and / or executed in parallel, unless otherwise specified. The present disclosure relates to methods and systems for ultrasonic characterization of a medium, and applies in particular to medical imaging of living or non-living tissues. The medium is for example a heterogeneous medium that one seeks to characterize in order for example to identify and / or characterize heterogeneities. These characterization techniques are known to be non-invasive for the medium,which is advantageously preserved in particular in its nature and integrity. Usual approach to ultrasound imaging In the field of ultrasound imaging, we often seek to construct an image of the reflectivity of a medium from the echoes backscattered by heterogeneities of the medium. This is the principle of the ultrasound scanner used in medical imaging, which allows in particular to visualize the internal anatomy of an individual or an animal. For the purposes of simplification, to allow the construction of an ultrasound image, the medium is considered homogeneous, with a constant sound propagation speed c0. Conventional ultrasound methods generally use an array of piezoelectric transducers which can emit and / or receive ultrasonic signals independently or quasi-independently, each transducer being at a position u in the bar supporting said array. The array of transducers, placed opposite a medium,allows to insonify and construct a representative image of the medium in different ways. A conventional method consists of insonifying the medium using emissions focused by a technique called beamforming. This method consists of applying to the signals emitted by each transducer a set of appropriate delays τ(uin, xin, z, c0) based on a homogeneous velocity model c0, in order to make the wavelets produced by each transducer interfere at the targeted focal point of spatial position (x, in, z). Due to the physical limits of diffraction, ultrasound is emitted through the aperture of the ultrasound probe, concentrated in an area often called a "focal spot", with a lateral width δx. In order to subsequently construct an ultrasound image illustrating the characteristics of the medium studied, a digital focusing step is also carried out at reception. The echoes captured by the transducers of the network are put back in phase by shifting them temporally. The delays τ(u out , x out, z, c0) are identical to those applied to the emission, the variable uout designating the position of each transducer. In the emission phase, all the signals interfere at the position point (xin, z) at the ballistic time t = z / c0 if the velocity model c0 used corresponds to the reality of the medium studied. In reception, the signals coming from this same point (xout = xin) interfere by summation of the signals at the echo time t = 2z / c0. This summation makes it possible to obtain the final result of the focusing in reception. This confocal method with double focusing at emission and reception makes it possible to directly image the reflectivity of the medium with a lateral resolution δx and a good contrast. However, this method is time-consuming because it requires physically focusing at emission at each of the points of the medium or at least at a given depth, on each of the lines of the constructed image representative of the medium.Matrix approach to ultrasound imaging A matrix approach to ultrasound imaging has been developed in recent years by the applicant. This approach is based on the construction of a canonical reflection matrix of the medium studied. This canonical reflection matrix is ​​generally determined by experiment. In other embodiments, this canonical reflection matrix can be determined by calculations or numerical simulation, reproducing an experiment. A first proposal for creating this canonical reflection matrix is ​​to successively emit an ultrasonic pulse from each transducer of the network whose position is identified by the coordinate u. in, as shown in Figure 1(a). This gives rise to a diverging cylindrical (or spherical) incident wave. This wave is reflected by the diffusers in the medium and the backscattered field is measured by each of the transducers as a function of time as shown in Figure 1(b). By repeating this operation with each transducer used successively as a source, we determine the canonical reflection matrix Ruu(t) = [R(uout, uin, t)] expressed in the basis of the transducers, composed of the set of impulse responses R(u out , u in, t) between each transducer. This matrix is ​​then rich in information describing the medium studied. However, the method assumes that the medium remains fixed throughout the duration of the measurements, which is difficult in particular in the case of medical examinations carried out on living patients. In addition, the recorded signals have a poor signal-to-noise ratio because the medium is insonified by a single transducer. A second way of constructing this canonical reflection matrix consists of insonifying the medium with a series of plane waves. This method overcomes most of the problems inherent in the method presented previously. Figure 1(c) illustrates the principle of this plane wave illumination. A delay law τ' is applied to each signal at the emission for the formation of a wavefront inclined at an angle θ inrelative to the transducer array. At reception, as illustrated in Figure 1(d), the field backscattered by the medium, R(uout, θin, t), is measured by all uout position sensors for each incident plane wave All of these responses form a canonical reflection matrix R uθ (t) = [R(u out , θ in, t)]. The double-focusing method described above can be realized numerically by temporally shifting the measured signals before summing them coherently. This method gave rise to ultrafast imaging and elastography, and is for example described in the document: "Coherent plane-wave compounding for very high frame rate ultrasonography and transient elastography", G. Montaldo et al. (IEEE Trans. Ultrason., Ferroelect. Freq. Control 56489-506, 2009). A third alternative to create this canonical reflection matrix is ​​to insonify the medium with a diverging wave base, as shown in Figure 1(e) and Figure 1(f), which allows illuminating the acoustic field more broadly than using plane waves.This technique, used in particular in super-resolution imaging, is explained in the document: "Ultrafast imaging of the heart using Circular Wave Synthetic Imaging with Phased Arrays", Couade et al., IEEE International Ultrasonics Symposium (2009). Conventional imaging therefore consists of double focusing at emission and reception at the same focal point for each pixel of the image (xin = xout), as shown in figure 2(a). Matrix imaging consists of dissociating the focal points at emission and reception, for the same echo time t, as shown in figure 2(b).Thus, a focused reflection matrix Rxx(N) = [R(xin, xout, z, N)] is determined, this focused reflection matrix being composed of the responses between virtual input transducers and virtual output transducers of respective spatial positions rin = (xin, z) and rout = (xout, z) corresponding to focal spots synthesized at input and output at different spatial positions, and whose expected depth z is dictated by the echo time t: z=O. P t / 2. N here represents the time in the focused basis such that N = Q − 2^ / O P. The origin of this time N corresponds to the instant when the virtual source emits the ultrasonic pulse. The focused reflection matrix is ​​obtained by focusing (for example by channel formations) from the canonical reflection matrix Rui(t). This matrix allows access to more characteristic information of the studied medium than the information obtained via the method used in confocal image mode of conventional imaging. This focused reflection matrix can be synthesized in the time domain by delay laws (channel formations) or in the frequency domain by applying appropriate phase shifts. The focused reflection matrix has been described in particular in the document: “Reflection Matrix Approach for Quantitative Imaging of Scattering Media”, William Lambert, et al., Phys. Rev.X 10, 021048, (2020), and then in the paper “Ultrasound Matrix Imaging - Part I: The Focused Reflection Matrix, the F-Factor and the Role of Multiple Scattering”, William Lambert, et al., IEEE Trans. Med. Imag. 41, 3907- 3920, (2022). In these publications, the focused reflection matrix Rxx(z, N) was considered between virtual transducers at ballistic time N = 0 (t=2z / c0) While the diagonal coefficients (x. out = x in) of the matrix Rxx(z, N ^=0) allow us to construct the synthetic confocal image at depth z, its off-diagonal coefficients provide information on the potential aberration and multiple scattering effects likely to alter the quality of this same image. In the publications of patent applications WO2020 / 016250 and WO2021 / 023933, the focused reflection matrix was studied in particular to quantify the multiple scattering rate. In these publications and patent applications, this multiple scattering rate was determined by studying the ratio between the confocal intensity |R(xin=xout,z, N = 0)| 2 which combine the contributions of simple and multiple scattering and the off-diagonal intensity |R(xin≠xout,z, N = 0)| 2which contains the single multiple scattering contribution. However, this approach is only qualitative because, due to diffraction, the focal spots have side lobes and a significant part of the simple scattering also emerges on the off-diagonal coefficients of the focused reflection matrix. Furthermore, these methods do not exploit the simple or multiple scattering rates to perform a quantitative measurement of the attenuation length, the absorption length and the diffusion mean free path of the medium. To perform a quantitative measurement of these parameters, the diffraction phenomena must be taken into account in a much more precise manner in order to probe the spatial evolution of the simple and / or multiple scattering rates.Ultrasonic characterization system Figure 3 illustrates an example of an ultrasound imaging system 1 for implementing methods for ultrasound imaging of a medium such as a heterogeneous medium M, according to the present disclosure. This system and method allow the formation of an ultrasound image of at least a portion (area of ​​interest or field of view) of the medium. The system 1 comprises: - a probing device 20 or probe 20, - a computing unit 30 for calculating an image from the signals received from the probe 20, - a control panel 40 connected to the computing unit 30, this control panel comprising for example buttons 41 and a touchpad 42, - a display device 50 for viewing an image and various elements or measurements.The probe 20 is connected to the computing unit 30 via a cable 21 or via a wireless connection, and is capable of emitting ultrasonic waves W into the medium M and receiving ultrasonic waves W from the medium M, said ultrasonic waves resulting from reflections of the emitted ultrasonic waves on scattering particles or diffusers inside the medium. The probe 20 may comprise an array 10 comprising a plurality of transducers 11. The array 10 is for example a linear or curved or two-dimensional or matrix array. The transducers 11 are capable of converting an electrical signal into a vibration and vice versa. The transducers 11 are for example ultrasonic piezoelectric transducers which may be in the form of a rigid bar placed in direct or indirect contact with an external surface of the medium M to be coupled to the medium and to vibrate and emit and receive ultrasonic waves W.The network 10 of transducers 11 of the probe 20 is then associated with the calculation unit 30. The network 10 of transducers may comprise a hundred or more transducers 11. The calculation unit 30 may comprise a housing 31 including reception devices for amplifying and / or filtering the signals received from the probe 20, and converters (analog to digital converters, and digital to analog converters) for transforming the signals into data representative of the signal. The data may be recorded in a memory of the calculation unit 30 and / or directly processed to calculate intermediate data (channel formation data or others). The calculation unit 30 may implement any known method for constructing an image from the data of the signals received from the probe 20, such as channel formation.The calculated image may be: - an image of the medium (B-mode image) usually in grayscale to visualize organs in the medium, and / or - an image showing a velocity or flow in the medium (color image) for example useful to visualize blood vessels in the medium, and / or - an image showing a mechanical characteristic of the medium (elasticity) for example useful to identify tumors inside the medium. By "connection" or "link" between the probing device 20, the calculation unit 30 and the display device 50, we mean any type of wired connection of the electrical or optical type, or any type of wireless connection using any protocol such as WiFi. TM , Bluetooth TMor others. These connections or links are one-way or two-way. The associated display device 50 can be of any type, such as a touchscreen or non-touchscreen, connected or not. The display device 50 is a screen for viewing the image calculated by the calculation unit 30. The display device 50 can also display other information such as the scales of the image, or configuration information for the calculation or processing or any measurement or assistance information. The screen 50 can be articulated on a support arm 51 for better positioning for the user. The screen 50 is usually a large screen (at least 20 inches) for better viewing for the user. The control panel 40 is for example a portion of a system box, said portion comprising a panel box having a substantially planar surface 40a inclined towards the user for one-handed operation.As shown in Figure 3, the control panel 40 may comprise a control screen 49 for displaying various configuration information. The calculation unit 30 is configured for implementing calculation and / or processing steps, in particular for implementing method steps according to the present disclosure. By convention, as shown in Figure 4 showing an array 10 of transducers 11 on a surface of a medium M, a spatial reference frame of the medium M is defined, by taking a first axis X and a second axis Z perpendicular thereto. For simplification, the first axis X corresponds to the transverse direction in which the transducers 11 are aligned in the example of a linear array, and the second axis Z corresponds to the depth of the medium M relative to this array 10 of transducers 11.This definition can be adapted to the context and thus for example extended to a three-axis spatial reference frame in the case of a two-dimensional network 10, or to a polar reference frame in the case of a curved network 10, or to any other reference frame adapted and / or dependent on the structure and shape of the network 10 of ultrasonic transducers. Thus, in the remainder of the present disclosure, we will use a Cartesian reference frame XZ, corresponding to a linear probe 20, for greater simplicity in the explanations, but a specialist in the field would easily generalize and apply the results to any type of reference frame. In the remainder of the disclosure, reference is made to an array 10 of transducers 11 for transmission and reception, it being understood that, in a more general case, several transducer arrays may be used simultaneously.The transducers 11 may be both transmitters and receivers, or only transmitters for some and only receivers for others. Similarly, an array 10 may consist of one (1) to N translators 11, of identical type or of different natures. The array 10 of transducers 11 serves for example as both transmitter and receiver, or is made up of several sub-arrays of transducers, some being dedicated to the emission, others to the reception of ultrasonic waves. By array of transducers, we mean at least one transducer, an aligned or non-aligned series of transducers, or a two-dimensional distribution of transducers (for example a matrix of transducers), or any spatial distribution of transducers.When in the present disclosure, reference is made to calculation or processing steps for the implementation in particular of method steps, it is understood that each calculation or processing step can be implemented by software, hardware, firmware, microcode or any appropriate combination of these technologies or related technologies. When software is used, each calculation or processing step can be implemented by computer program instructions or code which can be for example interpreted, or executed. These instructions can be stored or transmitted to a storage medium readable by a computer (or computing unit) and / or be executed by a computer (or computing unit) in order to implement these calculation or processing steps.

[0003] Analysis of a point in the medium by focused reflection matrix The present disclosure describes methods and systems for ultrasonic characterization of a medium. In practical cases, the medium is assumed to be heterogeneous. These methods and systems are based on definitions represented in Figure 4: We define in the medium: - a first point P1 of spatial position rin in the spatial reference frame of the medium, and - a second point P2 of spatial position rout in the spatial reference frame of the medium. These spatial positions rin and rout are noted in bold, to signify that these elements are position vectors, vectors taken in the spatial reference frame of the medium (X, Z). Other representations and definitions of the positions of the points are possible and accessible to any ultrasound technician. In the present disclosure, the first point P1 has a lateral position noted, x in . The second point P2 has a lateral position noted x out. The two points P1, P2 have the same expected depth zin = zout, also noted z, which is controlled by the echo time t considered. Thus, the spatial positions of the points P1 and P2 are respectively rin = (x in , z) and rout = (x out , z). These two points P1 and P2 are chosen rather at a short distance from each other, that is to say a few millimeters from each other, and for example twenty (20) millimeters or less. As shown in figure 5, the ultrasonic characterization method S100 implemented by the calculation unit 30 of the system 40 comprises the steps of: - generation S110 of a series of incident ultrasonic waves US inin an area of ​​said medium, by means of an array 10 of transducers 11, said series of incident ultrasonic waves being an emission base i; and - measurement or construction S120 of a canonical reflection matrix Rui(t) defined between the emission base i at the input and a reception base u at the output, the coefficients of this canonical reflection matrix corresponding to the signals received by the transducers and induced by the ultrasonic waves reflected by diffusers in the medium; - determination S130 of a focused reflection matrix Rxx(z) comprising responses of the medium calculated by focusing from the canonical reflection matrix Rui(t) between a virtual input transducer TVin of spatial position rin and a virtual output transducer TV outof spatial position rout. The canonical reflection matrix Rui(t) obtained may be a “real” matrix, i.e. composed of real coefficients in the time domain, the electrical signals recorded by each of the transducers being real numbers. Alternatively, this matrix may be a “complex” matrix, i.e. composed of complex values, for example in the case of demodulation for in-phase and quadrature channel formation (known in English as “IQ beamforming”). The focused reflection matrix Rxx may be expressed in different ways. In the expressions of the present disclosure, the first point P1 of spatial position (xin, z) is taken as a reference. These expressions may also be established with respect to the second point P2 of spatial position (x out , z) or relative to a midpoint between P1 and P2, of spatial position ((x in +x out) / 2, z) or with respect to any point designated as a reference point. The domain technician can make the necessary variable changes in the expressions presented. The responses of the medium are calculated by focusing from the canonical reflection matrix Rui(t). The responses of the focused reflection matrix Rxx(z) correspond to an acoustic pressure field calculated between all points of the medium of lateral positions x in , and x out, located at the expected depth z and at an echo time t, and for an assumed sound speed c0. In other words, this focused reflection matrix Rxx(z) is defined by: Rxx(z) = [R(xin, xout, z)] The parameters that are the depth z in the medium, and the sound speed co-influence the delay laws used in the focusing process. The input emission base i is for example a base of waves each generated by a single one of the transducers 11 of the array 10 or a base of plane waves with an angular inclination θ relative to the X axis or a base of virtual sources, as previously described in the disclosure of figures 2(a) to 2(f). The reception base u is for example the base of the transducers 11. Alternatively, another reception base can be used in reception, for example a frequency or spectral base. Thus, the generation step S110 of the ultrasonic waves is understood between the emission base i and the reception base u.This ultrasonic generation step is therefore defined for any type of focused or unfocused ultrasonic waves, such as plane waves. In the measurement step S120, the canonical reflection matrix Rui(t) is defined between the emission base i at the input and a reception base u at the output. This matrix contains all the temporal responses of the medium, measured at time t by each transducer 11 of spatial coordinate uout and for each emission iin. It is understood that the elements denoted with the index "in" refer to the emission (i.e. the input) and the elements denoted with the index "out" refer to the reception (i.e. the output). This canonical matrix can also be recorded and / or stored, for example in the memory of the computing unit, or on any other medium, removable or not, allowing permanent or temporary storage.In step S130, the determination of the focused reflection matrix Rxx(z) can be obtained by: - ​​an input focusing process from the canonical reflection matrix Rui(t) which uses a time of flight on the outward journey of the waves between the emission base i and the virtual input transducer TVin and which creates a so-called input focal spot around the first point P1 of spatial position rin, said input focal spot corresponding to the virtual input transducer TV. in , - an output focusing process from the canonical reflection matrix Rui(t) which uses a return flight time of the waves between the virtual TV output transducer out) and the transducers of the reception base u and which creates a so-called output focal spot around the second point P2 of spatial position rout, said output focal spot corresponding to the virtual output transducer TVout. These input and output focusing processes form an input-output focusing process, referred to in the remainder of this disclosure as focusing process or more simply focusing. In other words, in this ultrasonic characterization method, the virtual input transducer TV incorresponds to an ultrasonic "virtual source" located at the spatial position rin in the medium and the virtual output transducer TVout corresponds to an ultrasonic "virtual sensor" located at the spatial position rout. This virtual source and sensor are spatially separated by the difference in their spatial positions Δr = rout – rin. In the present case, they are separated only along a lateral axis, by Δx = xout - xin. Their expected depth is the parameter z used in the focusing law for a sound speed model c0. Their actual depth is dictated by the axial (depth) position of the isochronous volume, i.e. by the echo time t and by the sound speed distribution c(r) in the medium. The lateral dimension of the virtual transducers is dictated by the focal spot produced by focusing at this actual depth. In addition, the focused reflection matrix R xx(z) can be determined or calculated: - either in the time domain, in which case it can be explicitly noted with the time parameter N, i.e. noted Rxx(z, N), and in practice the data of the focused reflection matrix Rxx(z, t) are calculated between two predetermined time instants; - or in the frequency domain, in which case it can be explicitly noted with the pulsation parameter V which corresponds to a frequency f by V = 2W / X, i.e. notée R xx (z, V ), et in practice the data of the focused reflection matrix R xx (z, V ) are calculated between two pulsations V, of a frequency bandwidth, for example between a lower pulsation V − and a higher pulsation V + , and a central pulsation V C . Thus, the rest of the calculations of the process can be carried out in the time domain or in the frequency domain.

[0004] In the first case of calculation in the time domain, the focused reflection matrix Rxx(z, N) of the medium between the virtual input transducer TVin and the virtual output transducer TV out is obtained by focusing by a calculation of channel formation at the inputs and outputs. The coefficients of this focused reflection matrix Rxx(z, N) can be determined by: in which: Nin is the number of elements of the emission base (i) Nout is the number of elements of the reception base (u), Rui(t) is the confocal reflection matrix, of which R(uout, iin, t) is the element of the confocal reflection matrix Rui(t) recorded by the spatial position transducer uout following the emission of index iin in the emission base (i) and at time t, to which the delay times τin and τout have been applied; ^^ ^ ] ^^ , ^ ^^ ^ ^ And \ ^^^ ^ ^ ^^^ , ^^^^ , ^ ^ are apodization coefficients which are predefined, for example to keep a constant numerical aperture both in transmission and in reception; N ^^ ′^] ^^ , ^ ^^ , ^^ is the expected flight time for each incident wave ] ^^ to reach the first focal point of spatial position ^^ ^^ , ^^ in a model medium of sound speed c0N ^^^ ^^ ^^^ , ^ ^^^ , ^^ is the expected time of flight for a reflected wave from the second focal point of spatial position ^^ ^^^ , ^^ to the position transducer ^ ^^^ . These delay times τ in and τ outare usually calculated by a person skilled in the art from an established model of sound speed. A relatively simplifying assumption is to assume a homogeneous medium with a constant sound speed c0 in the medium. In this case, the flight times are directly obtained from the distances between the probe transducers and the virtual transducers. Thus, these delay time calculations are a function of the wave type, the assumed sound speed, and the geometry of the transducer array. The number of elements in the transmission base Nin is, for example, greater than or equal to one (1), and advantageously greater than or equal to two (2). The number of elements in the reception base N outis for example greater than or equal to two (2). The previous path formation formula is therefore a double sum of the temporal responses recorded in the canonical reflection matrix Rui, a first sum according to the emission basis i translating a focusing at emission and a second sum according to the reception basis u linked to a focusing at reception, this calculation being carried out for the spatial coordinates of the two points P1 and P2, that is to say the respective points of expected spatial positions rin = (x in , z) and rout = (x out , z). The result of this path-forming formula is therefore a time signal for these two spatial coordinates (rin, rout) or for these two lateral positions xin, xout. Finally, the focused reflection matrix Rxx(z, N) expressed in the time domain, can be transformed in the frequency domain into a focused reflection matrix Rxx(z, V) by a Fourier transform, that is to say by: This Fourier transform can be implemented by any type of discrete Fourier transform, normalized or not. In the second case of calculation in the frequency domain, the canonical reflection matrix Rui(t) expressed in the time domain, since it is made up of the signals received by the transducers, can be transformed in the frequency domain into a canonical reflection matrix Rui(V) by a Fourier transform, that is to say by: This Fourier transform can be implemented by any type of discrete Fourier transform, normalized or not. Thus, the focused reflection matrix Rxx(z) or Rxx(z, V) of the medium can be obtained by focusing by the matrix calculation below, substantially equivalent to the focusing by the time channel formation explained previously, that is to say by the following matrix product: in which the matrix ^ hi ^ V ^is the Fourier transform of the canonical reflection matrix ^ hi ^ Q ^ , the matrix j h^ ^ ^, V ^ is the transition matrix from the receiving base (u) to the focused base (x) at depth z and pulsation V, the matrix k i^ ^^, V^ is the transition matrix from the emission basis (i) "i" to the focused basis (x) at depth z and pulsation V, The symbols ∗ and † respectively denote the conjugation and transposition-conjugation matrix operations. Local determination of the single scattering rate / multiple scattering rate The method S100 according to the present disclosure further comprises the steps of: - filtering S140 of the focused reflection matrix ^ ^^ ^^^ to obtain a simple diffusion matrix ^ ^ ^^^ characteristic of single scattering of focused reflection matrix or multiple scattering matrix ^ ^^^^ characteristic of multiple scattering of the focused reflection matrix, - determination S150 of a simple scattering rate as a function of the depth z in the region around point ^ ^ by calculating the ratio of the norm of the simple diffusion matrix R s (z) by the norm of the focused reflection matrix R xx (z), or determination of a multiple diffusion rate ^ ^ ^^ ^ , ^^ as a function of the depth z in the region around point ^ ^by calculating the ratio of the norm of the multiple scattering matrix RM(z) to the norm of the focused reflection matrix Rxx(z). The simple scattering matrices and multiple scattering matrices are complementary to each other, as can be seen from relations (14) and (14'). The simple scattering rate and the multiple scattering rate are also complementary to each other, as explained by relations (5') and (8'). It is therefore possible to carry out the calculations according to any one of the two alternatives of the filtering step S140 and the determination step S150. These different possible calculations are detailed below. Thanks to these provisions, the method advantageously makes it possible to locally probe the medium to obtain a local estimate of the simple scattering rate and / or the multiple scattering rate. These quantities are representative of the level of multiple scattering on the ultimately constructed ultrasound image and therefore of its reliability.Typically, a multiple scattering ratio greater than 0.5 shows that the simple scattering hypothesis on which the principle of ultrasound is based is false and that the image produced is therefore not a correct estimator of the reflectivity of the medium. Conversely, a multiple scattering ratio less than 0.5 (a simple scattering ratio greater than 0.5) shows that the simple scattering hypothesis of conventional ultrasound is correct. Furthermore, these estimates are performed by calculation from the measurements performed and recorded in the canonical reflection matrix. These estimates can be recalculated at any time by modifying certain calculation parameters, which makes it possible to renew ultrasound characterization analyses either in real time or a posteriori, for example in an unconnected manner. In particular, in step S150, the simple scattering ratio ^. ^ ^^ ^ , ^^ can be calculated by the following ratio: in which: ‖q ‖ r = sTr & MM ' is the Frobenius norm of a matrix q, Tr&4' is the trace of the matrix X, q- is the conjugate transpose matrix of the matrix M. Thus, the simple diffusion rate ^ ^ ^^ ^ , ^^ can be obtained by the simple reflection matrix ^ ^ ^^^ and the focused reflection matrix ^ ^^ ^^^. This simple diffusion rate ^ ^ ^^ ^ , ^^ can be calculated: - either from the simple reflection matrix ^ ^ ^^^ and the focused reflection matrix R xx (z) calculated in the time domain, and the previous formula can be expressed as: - either from the simple reflection matrix ^ ^ ^ ^ ^ and the focused reflection matrix Rxx(z) calculated in the frequency domain, and the previous formula can be expressed as: This simple diffusion rate is then determined in a frequency bandwidth of interest, for example between a lower pulsation V − and a higher pulsation V + . Conversely, in step S150, the simple diffusion rate ^ | ^^ ^ , ^^ can be calculated by the following ratio: (5') in which: ‖q ‖ r = sTr & MM ' is the Frobenius norm of a matrix q, Tr&4' is the trace of the matrix X, q- is the conjugate transpose matrix of the matrix M. Thus, the simple diffusion rate ^ ^ ^^ ^ , ^^ can also be obtained by the multiple reflection matrix ^ ^ ^ ^ ^ and the focused reflection matrix ^ ^^ ^ ^ ^ . This calculation can also be performed either in the time domain or in the frequency domain, as in the previous simple diffusion rate calculation ^ ^ ^^ ^, ^^ passing through the multiple reflection matrix. Thus, the simple scattering rate ^ ^ ^^ ^ , ^^ can be obtained by the simple reflection matrix ^ ^ ^^^ and the focused reflection matrix ^ ^^ ^^^. At step S150, the multiple diffusion rate: in which: is the Frobenius norm of a matrix q, Tr & 4 ' is the trace of the matrix X, q- is the conjugate transpose matrix of the matrix M. Thus, the multiple diffusion rate ^ ^ ^^ ^ , ^^ can be obtained by the multiple reflection matrix ^ ^ ^^^ and the focused reflection matrix ^ ^^ ^^^. This calculation can be performed either in the time domain or in the frequency domain as previously explained. Conversely, in step S150, the multiple diffusion rate ^ ^ ^^ ^ , ^^ can be calculated by the following ratio: (8') in which: is the Frobenius norm of a matrix q, Tr&4' is the trace of the matrix X, q- is the conjugate transpose matrix of the matrix M. Thus, the multiple diffusion rate ^ ^ ^^ ^ , ^^ can be obtained by the simple reflection matrix ^ } ^^^ and the focused reflection matrix ^ ^^ ^^^. These calculations can be performed either in the time domain or in the frequency domain, as previously explained. Therefore, one can determine the simple diffusion rate ^ | ^^ ^ , ^^ by calculating the simple scattering matrix or the multiple scattering matrix. Similarly, one can determine the multiple scattering rate ^ | ^^ ^, ^^ by calculating the simple scattering matrix or the multiple scattering matrix. Thus, the method according to the present disclosure determines a simple scattering rate or a multiple scattering rate, locally, around a point of spatial position ^ ^ at depth z, in the medium M. However, before calculating the single / multiple scattering rate, a filtering of the focused reflection matrix must be performed. The following passages of the present disclosure will explain ways of performing such filtering.

[0005] Filtering the focused reflection matrix According to an embodiment of the method of the present disclosure, the filtering S140 can be carried out according to the following steps, illustrated in Figure 6: - determination S141 of a set of focused reflection matrices ^^^ ^, ^^ characteristics of simple diffusion in the medium, and calculated by acoustic propagation between the transducer network and a point diffuser of spatial position (^ ^ , z) in a model medium of sound speed c0, xin, xout, ^ ^ , and z being included in the region around point ^ ^ = ^^ ^ , ^ ^ ^ the coefficients of the digital focused reflection matrices are written for example in the following manner: ^ ^ ^ ^ , ^ ^ = S^^ ^^ , ^ ^^^ , ^ ^ , ^^ " - S142 determination of a confocal base of several confocal matrices calculated by ortho-normalization of at least part of the digital focused reflection matrices ^ ^ ^ ^ , ^ ^ , for depths z and pulsation V, k being an index between 1 and Nk ^ ^ ^ , Nk ^ ^ ^being a positive integer, representing the number of matrices of the confocal base for depths ^, - S143 projection of the focused reflection matrix ^ ^^ ^^, on the confocal basis of confocal matrices ^ # ^^, V^ to obtain the simple reflection matrix ^ ^ ^^, V^ characteristic of the single scattering of the focused reflection matrix or to obtain the multiple reflection matrix ^ ^ ^^^ characteristic of the multiple scattering of the focused reflection matrix. Steps S141, S142, S143 are also performed on time data or according to a frequency mode in a bandwidth, for example between a lower pulsation V − and an upper pulsation V + , and a central pulsation V C . At step S141, the set of digital focused reflection matrices ^^^ ^, ^^ corresponds to an ultrasonic mathematical model of the medium. At step S142, a confocal basis of several confocal matrices ^ # ^^, V^ of this model is constructed, limited to a number Nk of confocal matrices, which will allow a truncation or filtering of the focused reflection matrices ^ ^^ ^ ^ ^measured in the real medium by the projection carried out in step S143. These arrangements for filtering the reflection matrix focused by a confocal base, the method for determining the characterization of the medium, and in particular for determining the simple scattering rate or the multiple scattering rate, make it possible to obtain local characteristics located in the medium. In addition, the values ​​determined by such filtering are advantageously more precise than in the prior methods. This filtering method is also simpler to implement. According to a first embodiment of the method, the determination of the confocal base of step S142 can be carried out by a Gram-Schmidt ortho-normalization calculation. According to a second embodiment of the method, the determination of the confocal base of step S142 can be carried out as follows: the digital reflection matrices ^^^ ^ , ^^ expressed in the form ^ ^ ^ ^ , ^^ = $^^ ^^ , ^ ^^^ , ^ ^ , ^^" are put in the form of a two-dimensional matrix ^ % ^^^ = $^&^ ^^ , ^ ^^^ ', ^ ^ , ^^" defined for each depth z; a singular value decomposition (SVD) of the two-dimensional matrix ^ %^ ^ ^ is carried out according to the following expression: in which: ) * ^^^ are the singular values ​​of the two-dimensional matrix 2 ^^^^, ^ % + ^ ^ ^ = $ + ^ ̅ & ^ ^^ , ^ ^^^ ' , ^^ " are the singular vectors of the two-dimensional matrix ^ % ^^^ in the focused base (x), 4 + ^ ^ ^ = 5 * ^ ^ ^ , ^^ " are the singular vectors of the two-dimensional matrix 2 ^ ^ ^ ^in the base of point diffusers of spatial position (^ ^ , z), and † in superscript denoting the combined operation of transposition and conjugation. Thanks to these provisions for determining the confocal basis by singular value decomposition of numerical matrices in two-dimensional form, we obtain a more precise filtering of the focused reflection matrix. In addition, the rank N kallows the filtering to be dimensioned optimally. Such a calculation is also faster than the Gram-Schmidt method, and simpler to implement. Figure 7 shows an example of dimensions used in the calculations of the various steps of the method, which uses an array 10 of transducers 11 of dimension D in the lateral direction x for the reception base u, and which seeks to characterize a region around a point of spatial position rp. The lateral analysis region has a lateral dimension ∆^. Each resolution cell on the line at depth z has a lateral dimension ^^^^^ and a vertical dimension ^^. The lateral dimension ^^^^^ of the resolution cell depends on the depth z. The rank Z * ^^^ of each two-dimensional matrix ^ % ^^^ during the determination of the confocal base of step S142 is then fixed by the number of resolution cells contained in the region, that is to say by the following calculation: in which ∆^ is the lateral dimension of the region around point ^ ^ , ^^ ^ ^ ^ is the lateral dimension of a resolution cell at depth z. These quantities depend on the pulsation V, in the case of a calculation by frequency method. The lateral dimension of a resolution cell is for example estimated by a physical model of the type ^^^^, V^ = ^^V^ / 2atan^^ / ^2^^^" (11) in which ^ ^ V ^ = 2WO P / V is the wavelength at pulsation V, for the speed of sound O P , and D is the lateral dimension of the network 10 of transducers 11. Thus, the singular value decomposition (SVD) procedure makes it possible to find the singular vectors of the digital reflection matrices ^^^ ^, ^^ in the focused basis (x), these singular vectors being the majority elements for constructing a filtered matrix, comprising only single scattering components or multiple scattering components. In step S143, the projection step makes it possible to carry out this construction, and this projection is carried out according to the first alternative of the simple scattering matrix calculation, by: calculating the simple scattering matrix ^ ^ ^ ^ ^ by a linear combination of confocal matrices ^ # ^ ^ ^ of the confocal basis, weighted by the scalar product with the focused reflection matrix ^ ^^ ^ ^ ^ , at each depth ^, this projection being obtained by the following formula: in which denotes the scalar product between the matrices ^ # ^ ^ ^ and ^ ^^ ^ ^ ^, and ∗ in superscript is the conjugation operation. In step S143, the projection step makes it possible to carry out this construction, and this projection is carried out according to the second alternative of the multiple scattering matrix calculation, by: calculating the multiple scattering matrix ^ ^ ^^^ by a linear combination of confocal matrices ^ # ^^^ of the confocal basis, weighted by the scalar product with the focused reflection matrix ^ ^^ ^^^, at each depth ^, this projection being obtained by the following formula: (12') in which denotes the scalar product between the matrices ^ # ^^^ and ^ ^^ ^^^, and ∗ in superscript is the conjugation operation. Indeed, we can go from the simple scattering matrix to the multiple scattering matrix, or vice versa from the multiple scattering matrix to the simple scattering matrix. Thus, the multiple scattering matrix ^ ^^^^ can be obtained by subtraction of the simple scattering matrix ^ ^ ^^^ to the focused reflection matrix ^ ^^ ^^^; ie by: ^ ^ ^^^ = ^ ^^ ^^^ − ^ } ^^^ Thus, the simple scattering matrix ^ } ^^^ can be obtained by subtraction of the multiple scattering matrix ^ ^ ^^^ to the focused reflection matrix ^ ^^ ^^^; ie by: ^ } ^^^ = ^ ^^ ^^^ − ^ ^^^^ (14') It is thus possible: - to directly calculate the simple reflection matrix by the projection of formula (12), or - to directly calculate the multiple reflection matrix by the projection of formula (12'), or - to calculate the simple reflection matrix by the projection of formula (12) and obtain the multiple reflection matrix by the subtraction of formula (14), or - to calculate the multiple reflection matrix by the projection of formula (12') and obtain the simple reflection matrix by the subtraction of formula (14'), These different variants then make it possible to determine the simple diffusion rate ^ ^ ^^ ^ , ^^ and / or the multiple diffusion rate ^ ^ ^^ ^ , ^^, by various equivalent computational paths. Mean free path l s A link between the simple diffusion rate ^ ^ ^^ ^ , ^^ local and the local mean free path value determined at a point ^^ of the medium M was identified by the applicant. In particular, the simple diffusion rate ^ ^ ^^ ^ , ^^ is a decreasing function of depth z. For example, said decreasing function is a function of the linear type or of the exponential type, decreasing as a function of the depth z in the range of interest. Other models of decreasing functions can be applied. For a function of the linear type, we can thus for example have: For an exponential type function, we can have: With ^ a predetermined decay parameter. This decay parameter is generally between one-half (0.5) and one (1). Furthermore, it is a function of the characteristics of the probe 20, such as its geometry, or the directivity of the transducers 11 constituting said probe 20. In particular, the inventors have analyzed that, surprisingly, this decay parameter is substantially optimal for a value of two-thirds: ^ = 2 / 3. Furthermore, the mean free path can be determined conversely from the multiple scattering rate ^ ^ ^^ ^ , ^^ by applying the complementarity formula: ^ | ^^ ^ , ^^ = 1 − ^ ^ ^^ ^ , ^^, (17) in the previous relations. In this case, the multiple scattering rate ^ ^ ^^ ^, ^^ is an increasing function as a function of the depth z. Thus, the method for characterizing by ultrasound the medium M described in the present disclosure may optionally further comprise the following additional step, illustrated in Figure 5: - determination S160 of a mean free diffusion path l s in the region around point ^ ^ by identifying the depth decay of a simple diffusion rate ^ ^ ^^ ^ , ^^, or by identifying the growth in depth of a multiple diffusion rate ^ ^ ^^ ^ , ^^. This step consists of determining the simple diffusion rate ^ ^ ^^ ^ , ^^ by identification or determination of a better fit of the curve of the decreasing function to the values ​​obtained from the simple diffusion rate ^ ^ ^^ ^, ^^ as a function of depth z. The same adaptation procedure applies to the multiple scattering rate ^ ^ ^^ ^ , ^^. Examples of decreasing function curves are shown in dotted lines in Figures 8(c) and 9(c) which are described in more detail below. In these cases, the decreasing function curves are quasi-linear and best approximate the positions of the determined points of simple diffusion rate as a function of depth z. This calculation of the diffusion mean free path l s is a local estimate around a point ^ ^ . Then, the process for characterizing the medium M by ultrasound determines an image or mapping of the medium corresponding to the mean free path of diffusion ^ ^ ^^ ^ ^ for a set of points ^ ^of the medium. This mapping or image of the mean free path of diffusion in the medium gives a quantitative characterization of the physical properties of the medium, in the volume of the medium M. The mean free path of diffusion is a significant quantity of a pathology in the medium. This mapping makes it possible to locate said pathology. Confocal image and mean confocal intensity According to an embodiment of the ultrasonic characterization method of the present disclosure, the method further comprises a step of: - determining a confocal image Ic(x,z) as a function of the depth z, from the diagonal coefficients of the focused reflection matrix R xx (z), that is to say by the following calculation: B C ^^, ^^ = |; ^^ ^^, , ^, ^^| D(18) Such a confocal image corresponds to a classic ultrasound image freed from any influence of multiple diffusion. Thanks to the confocal image, it is then possible to carry out a step of: - determination of an average confocal intensity B C̅ ^^ ^ , ^^ in the region around point ^ ^ , obtained by averaging the confocal image along its lateral dimension x in the region, that is to say by the following calculation: in which the symbol 〈 … 〉 ^ denotes an average over the index variable, i.e. the lateral dimension x. Extinction length l ext and Absorption length l a According to an embodiment of the ultrasonic characterization method of the present disclosure, illustrated in Figure 5, once an average confocal intensity has been calculated, an optional step of: - determination S170 of an extinction length l can be carried out ext of the region around point ^^ by identification of the decrease as a function of the depth z of the confocal intensity B C̅ ^^ ^ , ^^ averaged over the region. According to a first variant, the extinction length is determined by identification of a linear decrease as a function of the depth z of the confocal intensity B C̅ ^^ ^ , ^^ averaged over the region of interest. According to a second variant, the extinction length lext is determined by identifying an exponential decay as a function of the depth of the confocal intensity B C̅ ^^ ^ , ^^ averaged over the region, given by: (20) with I0 a constant independent of the depth z. The identification method described for the determination of the mean free path applies in a similar way. A set of confocal intensity values ​​at different depths z allows the extinction length l to be deduced extaround point ^ ^ . Similarly, a mapping of the extinction length ^ ^^^ ^^ ^ ^ for a set of points ^ ^ of the medium M can be carried out, this mapping corresponding to an image of this quantity of characterization of the medium. As represented in figure 5, one can then carry out an optional step of: - determination S180 of an absorption length la of the region around the point ^ ^ by : A mapping of the absorption length ^ ^ ^^ ^ ^ for a set of points ^ ^of the medium M can also be carried out, this mapping corresponding to an image of this quantity of characterization of the medium. Thus, thanks to the various calculations presented above, it is possible to differentiate the losses by absorption from the losses by diffusion of the medium M during insonification. The medium M is then characterized locally and much more precisely than in the methods of the prior art which only propose global estimates of these quantities. In particular, the formulas presented in the present disclosure are valid over a large depth range, that is to say these formulas are also valid in the near field, and not only in the far field.

[0006] Results on a calibrated experimental medium (called "phantom") Figure 8 illustrates a result of the method according to the present disclosure, applied to a phantom with two cylindrical inclusions having different reflectivity and simple scattering values. Figure 8(a) is the general diagram of this phantom obtained with the network 10 of transducers 11 positioned to the left of the figure on the external surface of the phantom to emit ultrasonic waves towards the right of the figure (i.e. in the direction of depth z). A rectangular area of ​​interest surrounds the two inclusions I1, I2. The system 1 produces an ultrasound image of the area of ​​interest. This ultrasound image is shown in Figure 8(b). This image makes it possible to visualize that the first inclusion I1 is on average lighter than the second inclusion I2.Two measurement lines are then defined along the depth direction: a first line L1 crosses the first inclusion, and a second line L2 crosses the second inclusion. The method according to the present disclosure is applied to a set of points (points of spatial positions rp) along each of these lines. For each of these points, a region, for example a lateral region of points, is used to apply the method. Figure 8(c) shows the values ​​V1 of the simple diffusion rate obtained on the first line L1 as a function of depth, and the values ​​V2 of the simple diffusion rate obtained on the second line L2 as a function of depth. The method therefore makes it possible to precisely identify local values ​​of the simple diffusion rate.The method according to the present disclosure then makes it possible to identify a decreasing function F1 for the depth zone of the first inclusion and a decreasing function F2 for the depth zone of the second inclusion. These functions have different decreases which are representative of the so-called mean free path length l. s of each of the inclusions. By fitting the experimental points with the theoretical curve, ^ ^ ^ ^ ^ = exp ^ −4^ ⁄ 3^ ^ ^ the process therefore makes it possible to identify in a sufficiently differentiated manner the local mean free path measured in the bright inclusion (V1, l s ~32 mm) and in the darker inclusion (V2, l s~80 mm), the two inclusions being present in the medium. Results on a liver Figure 9 illustrates a result of the method according to the present disclosure, applied to a mammalian liver, insonified by the system 1. Figure 9(a) shows an ultrasound image of the liver with the network 10 of transducers 11 on the external surface of the body of a subject (on the left of the figure) to emit ultrasound waves towards the right of the figure (i.e. in the direction of depth z). A rectangular area of ​​interest surrounds the liver of the subject. An ultrasound image of the area of ​​interest is generated by means of the system 1. This ultrasound image, shown in Figure 9(b), makes it possible to visualize the liver. The method according to the present disclosure is applied to a set of points (points of spatial positions rp) along a line in the direction of depth z. For each of these points, a region for example lateral of points (in direction x) is used to apply the method.Figure (c) shows the simple diffusion rate values ​​V obtained on the line considered, as a function of depth. The method therefore makes it possible to precisely identify local values ​​of the simple diffusion rate. The method according to the present disclosure then makes it possible to identify a decreasing function F in the liver. This function has a decrease which is representative of the mean free path ls in this liver. By fitting the experimental points with the theoretical curve, ^. ^ ^ ^ ^ = exp ^ −4^ ⁄ 3^ ^ ^, the method therefore makes it possible to identify in a significantly differentiated manner between the two zones, the local mean free path in the liver: ls~20 mm. These differences can then be used clinically by the practitioner to give an opinion or diagnosis. Ultrasonic characterization system The system 1 for ultrasonic characterization for medical analysis of the medium M according to the present disclosure is illustrated in figure 3. It comprises: - an array 10 of transducers 11 adapted to generate a series of incident ultrasonic waves in a zone of the medium, and to measure as a function of time the ultrasonic waves backscattered by said zone;and - a calculation unit 30 connected to the network of transducers and adapted to implement a method comprising steps of: - generation S110 of a series of incident ultrasonic waves USin in the zone of the medium, by means of the network 10 of transducers 11, this series of incident ultrasonic waves being an emission base i; and - measurement S120 of a canonical reflection matrix Rui(t) defined between the emission base i at the input and a reception base u at the output, the coefficients of this canonical reflection matrix corresponding to the signals received by the transducers and induced by the ultrasonic waves reflected in the medium;- determination S130 of a focused reflection matrix Rxx(z) comprising responses of the medium calculated by focusing from the canonical reflection matrix Rui(t) between a virtual input transducer of spatial position rin= (xin, z) and a virtual output transducer of spatial position rout = (xout, z), the two virtual transducers being located at the same depth z for a sound speed model c0, the coefficients of said focused reflection matrix R; xx (z) written as follows, Rxx(z) = [R(^ ^^ , ^ ^^^ , ^)] x in , x out being included in a region around a point ^ ^ = ^^ ^ , ^ ^ ^, the set of transverse positions x in and x outvirtual transducers rin and rout forming a focused base (x) at each depth z, said method being characterized in that it further comprises steps of: - filtering S140 of the focused reflection matrix ^ ^^ ^ ^ ^ to obtain a simple diffusion matrix ^ ^ ^ ^ ^ characteristic of single scattering of focused reflection matrix or multiple scattering matrix ^ ^ ^ ^ ^ characteristic of multiple scattering of the focused reflection matrix, - determination S150 of a simple scattering rate ^ ^ ^^ ^ , ^^ as a function of the depth z in the region around point ^ ^ by calculating the ratio of the norm of the simple diffusion matrix R s (z) by the norm of the focused reflection matrix R xx (z), or determination of a multiple diffusion rate ^ ^ ^^ ^, ^^ as a function of the depth z in the region around point ^ ^ by calculating the ratio of the norm of the multiple scattering matrix R M (z) by the norm of the focused reflection matrix R xx (z).

Claims

CLAIMS 1. Ultrasonic characterization method (S100) for medical analysis of a medium, comprising the steps of: - generation (S110) of a series of incident ultrasonic waves (US in ) in an area of ​​said medium, by means of an array (10) of transducers (11), said series of incident ultrasonic waves being an emission base (i); and - measurement (S120) of a canonical reflection matrix Rui(t) defined between the emission base (i) at the input and a reception base (u) at the output, the coefficients of this canonical reflection matrix corresponding to the signals received by the transducers and induced by the ultrasonic waves reflected in the medium; - determination (S130) of a focused reflection matrix R xx(z) comprising responses of the medium calculated by focusing from the canonical reflection matrix Rui(t) between a virtual input transducer of spatial position rin= (xin, z) and a virtual output transducer of spatial position rout = (x out , z), the two virtual transducers being located at the same depth z for a sound speed model c0, the coefficients of said focused reflection matrix Rxx(z) being written as follows, Rxx(z) = [R(^ ^^ , ^ ^^^ , ^)] xin, xout being included in a region around a point ^ ^ = ^^ ^ , ^ ^ ^ the set of transverse positions x in and x out virtual transducers rin and rout forming a focused base (x) at each depth z, said method being characterized in that it further comprises steps of: - filtering (S140) of the focused reflection matrix ^ ^^ ^ ^ ^to obtain a simple diffusion matrix ^ ^ ^ ^ ^ characteristic of single scattering of focused reflection matrix or multiple reflection matrix ^ ^ ^ ^ ^ characteristic of the multiple scattering of the focused reflection matrix, - determination (S150) of a simple scattering rate ^ ^ ^^ ^ , ^^ as a function of the depth z in the region around point ^ ^ by calculating the ratio of the norm of the simple diffusion matrix R s (z) by the norm of the focused reflection matrix R xx (z), or determination of a multiple diffusion rate ^^ as a function of the depth z in the region around point ^ ^ by calculating the ratio of the norm of the multiple scattering matrix R M (z) by the norm of the focused reflection matrix R xx(z).

2. Method according to claim 1, in which the filtering (S140) is carried out by: - ​​determining (S141) a set of digital focused reflection matrices ^^^ ^ , ^^ characteristics of simple diffusion in the medium, and calculated by acoustic propagation between the transducer network and a point diffuser of spatial position (^ ^ , z) in a model medium of sound speed c0, x in , x out , ^ ^ , and z being included in the region around point ^ ^ = ^^ ^ , ^ ^ ^ the coefficients of the digital focused reflection matrices are written as follows: ^^^ ^ , ^^ = S^^ ^^ , ^ ^^^ , ^ ^ , ^^" - determination (S142) of a confocal base of several confocal matrices ^ # ^^^ calculated by ortho-normalization of at least part of the digital focused reflection matrices ^^^ ^, ^^, for depths z, k being an index between 1 and N k ^^^, N k ^^^ being a positive integer, representing the number of matrices of the confocal base for depths ^, - projection (S143) of the focused reflection matrix ^ ^^ ^^^ on the confocal basis of confocal matrices ^ # ^^^ to get the simple reflection matrix ^ ^ ^^^ characteristic of the single scattering of the focused reflection matrix or to obtain the multiple reflection matrix ^ ^ ^^^ characteristic of the multiple scattering of the focused reflection matrix.

3. The method of claim 2, wherein: during the determination of the confocal basis (S142), the digital reflection matrices ^^ expressed in the form ^^^ ^ , ^^ = $ ^ ^ ^^ , ^ ^^^ , ^ ^ , ^ ^" are put in the form of a two-dimensional matrix ^ %^^ ^ = $ ^& ^ ^^ , ^ ^^^ ' , ^ ^ , ^ ^" defined for each depth z, we perform a singular value decomposition (SVD) of the two-dimensional matrix ^ %^ ^ ^ according to the following expression: in which ) * ^ ^ ^ are the singular values ​​of the two-dimensional matrix 2 ^ ^ ^ ^ , ^ % + ^^^ = ^^" are the singular vectors of the two-dimensional matrix ^ %^ ^ ^ in the focused base (x), 4 + ^^^ = 5 * ^ ^ ^ , ^^" are the singular vectors of the two-dimensional matrix 2 ^^^^ in the base of point diffusers of spatial position (^ ^, z) , † in superscript designating the combined operation of conjugation and transposition.

4. Method according to claim 2, in which: for the projection (S143), the simple diffusion matrix ^ is calculated ^ ^ ^ ^ by a linear combination of confocal matrices ^ # ^ ^ ^ of the confocal basis, weighted by the scalar product with the focused reflection matrix ^ ^^ ^^^, at each depth ^, this projection being obtained by the following formula: in which denotes the scalar product between the matrices ^ # ^ ^ ^ and ^ ^^ ^ ^ ^ , and ∗ in superscript is the conjugation operation.

5. The method of claim 2, wherein: for the projection (S143), the simple diffusion matrix ^ is calculated ^ ^^^ by a linear combination of confocal matrices ^ #^^^ of the confocal basis, weighted by the scalar product with the focused reflection matrix ^ ^^ ^^^, at each depth ^, this projection being obtained by the following formula: in which denotes the scalar product between the matrices ^ # ^ ^ ^ and ^ ^^ ^ ^ ^ , and ∗ in superscript is the conjugation operation.

6. Method according to one of claims 1 to 5, further comprising a step of: - determining (S160) a mean free diffusion path l s in the region around point ^ ^ by identifying the decay as a function of the depth z of a simple diffusion rate ^^, or by identifying growth as a function of the depth z of a multiple diffusion rate ^^.

7. Method according to claim 6, further comprising: - determining a mapping of the mean free diffusion path ^ ^ ^^ ^ ^ for a set of points ^ ^ of the medium.

8. Method according to one of claims 1 to 7, further comprising: - determining a confocal image I c (x,z) as a function of depth z, from the diagonal coefficients of the focused reflection matrix Rxx(z), i.e.: B C ^ ^, ^ ^ = | ; ^^ ^^, , ^, ^^ |D 9. Method according to claim 8, further comprising: - determining an average confocal intensity B C̅ ^^ ^ , ^^ in the region around point ^ ^ obtained by averaging the confocal image along its lateral dimension x in the region: in which the symbol 〈… 〉 ^denotes an average over the variable with index 10. Method according to claim 9, further comprising: - determining (S170) an extinction length lext of the region around the point ^ ^ by identification of the decrease as a function of the depth z of the confocal intensity averaged over the region.

11. The method of claim 10, further comprising: - the determination of a mapping of the extinction length ^ ^^^ ^^ ^ ^ for a set of points ^ ^ of the medium 12. Method according to claim 6 and claim 10, further comprising: - determining (S180) an absorption length l a of the region around point ^ ^ by :

13. The method of claim 12, further comprising: - determining a mapping of the absorption length ^ ^ ^^ ^ ^ for a set of points ^ ^of the medium.

14. System (1) for ultrasonic characterization for medical analysis of a medium (M), the system comprising: - an array (10) of transducers adapted to generate a series of incident ultrasonic waves in an area of ​​the medium, and to measure as a function of time the ultrasonic waves backscattered by said area; and - a calculation unit (30) connected to the array of transducers and adapted to implement the method according to one of claims 1 to 13.

Images