Method and device for locally estimating the speed of sound in a region of interest of a medium

Abstract

The present invention relates to a method for analysing a medium using an array of transducers (T1-Tn), the method comprising: - acquiring (100) two reception signals each associated with a respective pair of waves transmitted and received according to transmission and reception directions; - deforming (200) the two reception signals to obtain two deformed signals, the deformation step comprising, for each reception signal, composition of the reception signal with an affine function dependent on half the angular difference between the transmission and reception directions of the pair associated with the reception signal; - locally estimating (300) the speed of sound in a region of interest of the medium based on the comparison of the two deformed signals.

Description

[0001] METHOD AND DEVICE FOR LOCAL ESTIMATION OF THE SPEED OF SOUND IN A REGION OF INTEREST IN A MEDIUM

[0002] FIELD OF THE INVENTION

[0003] The present invention relates to the general technical field of the analysis of a medium by wave propagation, and in particular sound or ultrasonic waves, or electromagnetic waves.

[0004] More specifically, the present invention relates to a method and a device for the local estimation of the speed of sound in a region of interest of a target object, or of a diffuse medium such as biological, human or animal tissue.

[0005] In the following, the present invention will be described with reference to medical ultrasound imaging, it being understood that the teachings described here can be used in other types of applications (non-medical ultrasound, SONAR, RADAR, etc.) using waves whose amplitude, frequency and phase are controllable (i.e. coherent waves).

[0006] BACKGROUND OF THE INVENTION

[0007] Fatty liver disease is a disease characterized by excessive accumulation of hepatic fat (i.e., fat inside the liver). It can develop into fibrosis and then liver cirrhosis.

[0008] A magnetic resonance imaging (MRI)-based technique can be used to detect steatosis in a patient. Indeed, 1MR measures the fat fraction in proton density as a biomarker of hepatic fat content. However, 1MR is not widely available and is expensive.

[0009] Therefore, ultrasound-based techniques have been developed to quantify liver fat. Specifically, an imaging probe adapted to emit ultrasound waves and detect backscattered waves is used to acquire signals corresponding to said backscattered waves. These signals are then transmitted to a processing unit to evaluate the speed of sound in the liver in order to determine the accumulation of fat inside the liver.

[0010] Indeed, the speed of sound within a tissue varies depending on the amount of fat it contains. In particular, a fatty liver has a slightly lower speed of sound (typically 1460 m / s) than a healthy liver (typically 1580 m / s).

[0011] However, since this decrease in the speed of sound is small (5 to 10% variation in the speed of sound between a healthy liver and a liver in steatosis), it can be difficult to identify a speed of sound characteristic of hepatic steatosis.

[0012] Therefore, the speed of sound must be estimated as accurately as possible to detect fatty liver disease.

[0013] However, the liver is located inside the body. It is therefore covered by skin, fat, and muscle. These different tissues—located between the probe and the liver—can interfere with the estimation of the speed of sound in the liver.

[0014] Currently, most ultrasound-based techniques do not allow for local measurement of the sound speed in the liver. Thus, the sound speed estimated with such techniques corresponds to the sound speed between the upper surface of the skin and the liver. The diagnosis made by the practitioner is then highly dependent on his or her experience with the device used, since the sound speed estimated by the device does not correspond to the local sound speed in the liver.

[0015] This is why other ultrasound-based solutions have been developed to estimate the local sound speed in the liver. WO 2020 / 070104, for example, describes a method for estimating the local sound speed in the liver comprising the following steps:

[0016] • determine on a morphological image a position of at least one interface in the medium, the interface dividing the medium into an intermediate region and a target region - namely the patient's liver - in the depth direction,

[0017] • determine a first speed of sound of the intermediate region on the basis of signals detected by the probe, and

[0018] • determine the target sound speed within the target region – namely the patient's liver – based on at least some of the detected signals and taking into account the position of the interface and the first determined sound speed.

[0019] Thus in these solutions, the speed of sound in the tissues located between the probe and the liver (i.e. skin, fat and muscle) is calculated to deduce the local speed of sound in the liver.

[0020] Another solution is described in WO 2015 / 091519, which relates to a method for determining a local speed of sound in an object. This method comprises the following steps:

[0021] • transmit: o a first ultrasound pulse in a first direction, o a second ultrasound pulse in a second direction different from the first direction,

[0022] • detect: o first echoes corresponding to the backscattering of the first ultrasound pulse in the object, o second echoes corresponding to the backscattering of the second ultrasound pulse in the object,

[0023] • reconstruct: o from the first detected echoes, a first associated image of first local echoes, o from the second detected echoes, a second associated image of second local echoes, said images being located in an image plane extending in the first and second directions,

[0024] • determine, from the first and second images, a local echo phase shift corresponding to a difference in an echo duration between a first local echo and a corresponding second local echo, compared to the case of a constant sound speed assumed in the object,

[0025] • determine the local speed of sound in the object for at least one region of the image plane in the object from the local echo phase shift determined in the previous step.

[0026] Such a solution, while allowing a precise estimation of the local sound speed in the liver, requires the acquisition of numerous signals as well as the implementation of numerous calculations which are costly in terms of hardware and software resources.

[0027] These solutions are not direct, in the sense that they require obtaining information representative of the integrated sound speed (or average sound speed across all tissues traversed by the ultrasound wave), then applying an algorithm to find the local sound speed in the region of interest, such as the patient's liver.

[0028] An aim of the present invention is to provide a method and an analysis device making it possible to directly estimate the local sound speed of a region of interest such as the liver of a patient.

[0029] More specifically, an aim of the present invention is to propose a method and an analysis device which do not require calculating the speed of sound in the intermediate tissues located between an acquisition probe and a region of interest in order to estimate the speed of sound in this region of interest. BRIEF DESCRIPTION OF THE INVENTION

[0030] To this end, the invention proposes a method for analyzing a medium using a network of transducers, said method comprising:

[0031] - the acquisition of at least two reception signals each associated with a respective pair of transmitted and received waves, said at least two reception signals comprising: o a first reception signal associated with a first pair of transmitted and received waves according to first transmission and reception directions, o a second reception signal associated with a second pair of transmitted and received waves according to second transmission and reception directions, the first transmission and reception directions being different from the second transmission and reception directions, the acquisition step including, for each reception signal, the following sub-steps: o the generation in a scattering medium, by transducers of the network, of an transmitted wave having a desired transmission direction, o the reception, by transducers of the network,of reverberated signals and their combinations to obtain a temporal reception signal representative of a received wave reflected by the diffusing medium in a desired reception direction,

[0032] - the deformation of said at least two reception signals by composition with a respective affine function: o the first reception signal being deformed by composition with a first affine function to obtain a first deformed signal, the first affine function depending on the first directions of emission and reception, o the second reception signal being deformed by composition with a second affine function, different from the first affine function, to obtain a second deformed signal, the second affine function depending on the second directions of emission and reception,

[0033] - the local estimation of the speed of sound in a region of interest of the medium from the comparison of the first and second distorted signals. Thus, the method according to the invention differs from the prior art in that it makes it possible to obtain a map and / or a local measurement of the speed of sound in a region of interest directly and with the following advantages:

[0034] • the method provides a local measurement in a region of interest (map or value),

[0035] • it requires very few ultrasonic emissions (typically between two and sixteen) compared to other local measurement techniques (typically more than one hundred),

[0036] • it requires a very limited amount of computation unlike other non-direct local measurement techniques which require inverting matrices or storing large pre-inverted matrices and applying them,

[0037] • it requires a very limited amount of data from the ultrasound probe (works from two signals where other methods generally use 100 * 128 signals).

[0038] Preferred but non-limiting aspects of the invention are as follows:

[0039] - the estimation step may comprise the following sub-steps: o determination of a transformation coefficient between the first and second distorted signals, said transformation coefficient being representative of a difference in time scale between the first and second distorted signals, o obtaining the speed of sound in the region of interest of the medium from the transformation coefficient;

[0040] - the estimation step may comprise a sub-step of calculating a resulting signal representative of an average correlation between the first and second distorted signals;

[0041] - the average correlation can be obtained by at least one of the following methods: o averaging over different depths in the region of interest, o averaging over different media of the same sound speed, o averaging over signals obtained with different transmission or reception strategies, o averaging over different signals obtained by disturbing delay laws applied to the network of transducers in transmission or reception; - the transformation coefficient can be determined by deriving a phase of the resulting signal representative of the average correlation between the first and second distorted signals;

[0042] - the transformation coefficient D can be determined from the following formula: where: o corresponds to the average correlation of the first and second distorted signals s and s', where is the time derivative operator of the phase;

[0043] - the sub-step of obtaining the speed of sound in the region of interest may include solving the following formula: where: o « c r » is the speed of sound in the region of interest, o « Cth » is a theoretical speed of sound used to calculate the first and second affine functions during the deformation step, o « D » is the transformation coefficient, o « a>c » is a central pulsation of the signals s and s' at the depth considered, o « <5 » is a half-angular difference between the first emission and reception directions of the first pair of waves emitted and received, o « ô' » is a half-angular difference between the second emission and reception directions of the second pair of waves emitted and received;

[0044] - each affine function can be of the type: f(t) = At ​​+ B, where: o “A” is a direction coefficient depending on the half-angular difference between the direction of emission and the direction of reception of the pair of waves emitted and received associated with the reception signal, and o “B” is a factor for aligning the reception signals at a desired depth corresponding to the depth of the region of interest;

[0045] - the method may comprise a step of determining the alignment factor “B”, said determining step comprising the sub-steps consisting of: o acquiring two primary signals each associated with a respective pair of waves transmitted and received according to transmission and reception directions, each primary signal representing an amplitude as a function of a time variable, o temporally widening each primary signal by applying a factor to the time variable to obtain an enlarged primary signal, the factor depending on the angular half-difference between the transmission direction and the reception direction of the pair associated with the primary signal, o correlating the enlarged primary signals, o deducing from the phase of the correlation an optimal shift index B;

[0046] - for each reception signal, the sub-step of combining the reverberated signals may comprise the summation of the reverberated signals according to a respective delay law, said respective delay laws being defined so that the bisectors of the directions of the emission and reception waves of each pair of emitted and received waves are merged;

[0047] - the method may further comprise a step of estimating the central pulsation of the signals s and s' at the depth considered, said estimation step comprising the following sub-steps: o estimation of the central pulsation of the first reception signal s from its autocorrelation, o estimation of the central pulsation of the second reception signal from its autocorrelation, o estimation of a final central pulsation from the average of the central pulsations of each of the reception signals.

[0048] BRIEF DESCRIPTION OF THE DRAWINGS Other advantages and characteristics of the method and the analysis device according to the invention will emerge more clearly from the following description of several variant embodiments, given as non-limiting examples, from the attached drawings in which:

[0049] • Figure 1 is a schematic representation of an analysis method for estimating a sound speed,

[0050] • Figure 2 is a schematic representation of an ultrasound imaging device including an acquisition probe and one (or more) computing unit(s),

[0051] • Figure 3 is a schematic representation of plane, spiral and divergent waves emitted by plane and curved transducer arrays,

[0052] • Figure 4 is a schematic representation illustrating the principle of emission of a plane wave from a network of transducers,

[0053] • Figure 5 is a schematic representation of waves emitted and reverberated by a medium for three different times,

[0054] • Figure 6 is a schematic representation illustrating two pairs of emission and reception angles,

[0055] • Figures 7a to 7f illustrate examples of transmission and reception of pairs of transmission and reception waves,

[0056] • figure 8 is a schematic cross-sectional representation of a medium to be imaged,

[0057] • Figure 9 is a graph illustrating a phase of a correlation between two reception signals associated with different pairs of transmitting and receiving ultrasonic waves (pair (10°, -10°) and pair (0°, 0°)) as a function of time,

[0058] • Figure 10 is a graph illustrating an expansion factor as a function of time,

[0059] • Figure 11 is a graph illustrating the speed of sound as a function of time,

[0060] • Figure 12 schematically illustrates the propagation of a non-zero angle emission wave at an interface between two layers of a medium to be imaged.

[0061] DETAILED DESCRIPTION OF THE INVENTION

[0062] We will now describe in more detail different embodiments of the method and device for analyzing a medium according to the invention with reference to the figures. In these different figures, equivalent elements are designated by the same numerical reference.

[0063] In the following, the invention will be described with reference to the field of imaging of the human body by ultrasound. It is obvious to those skilled in the art that the method and device for analyzing a medium according to the invention can be used for other applications, such as SONAR, RADAR applications, or other non-medical applications (seismography, study of materials such as concrete or polycrystalline materials, etc.).

[0064] 1. Presentation

[0065] The method and analysis device described below allow direct estimation of the local sound speed of a region of interest of a scattering medium, such as a patient's liver, by ultrasound imaging.

[0066] Referring to Figure 1, the analysis method comprises the following steps:

[0067] - the acquisition 100 of at least the first and second reception signals, said step of acquiring the first (respectively the second) reception signal comprising the following sub-steps: o emission in the medium of a first (respectively second) emitted ultrasonic wave in a first (respectively second) emission direction of angle a (respectively a different from angle a), and o reception of signals reverberated by the medium, and their combination to obtain the first (respectively second) reception signal according to a first (respectively second) reception direction of angle β (respectively β' different from 0),

[0068] - the deformation 200 of each of said first and second reception signals, by composition with a respective affine function (first affine function for the first reception signal, and second affine function for the second reception signal), to obtain first and second deformed signals, the direct estimation 300 of a local speed of sound by comparison of the first and second deformed signals.

[0069] Advantageously, in addition to combining the signals reverberated by the medium, the reception sub-step may comprise a windowing of the reverberated signals. More precisely, each reverberated signal is multiplied by a function (i.e. observation window function), such as a rectangular function h(t) defined such that: (t) = { 1 if t ∈ [T1; T2] 0 otherwise .

[0070] Thus, the reverberated signals can be truncated (i.e. windowed) over a time window of duration Δt centered around a time t (which can for example correspond to a flight time of the ultrasonic wave to reach a depth of interest in the medium). The first and second reception signals resulting from the combination of the truncated reverberated signals are representative of the medium over a period of time (of a duration between T1-T2) desired for the observation of said medium.

[0071] Furthermore, the first and second directions of reception of angles β and β' can advantageously be chosen so that the bisector of the first directions of emission and reception coincides with the bisector of the second directions of emission and reception (i.e. the angles (α+ ) / 2 and (α'+ ) / 2 are equal), as will become clear below.

[0072] 2. Device for analyzing an environment

[0073] With reference to Figure 2, an example of a device is illustrated in which the method for analyzing a medium described below can be implemented.

[0074] This device includes:

[0075] - a T1-T transducer network n for signal acquisition, and

[0076] - a control and processing unit U c for: o the control of the T1-T transducer network n and o the processing of signals acquired by the Ti-Tn transducer network.

[0077] 2. 1. Transducer network

[0078] The T1-T transducer array n comprises a set of “n” ultrasonic transducers (“n” being an integer greater than or equal to one) arranged linearly. Alternatively, the transducers T1-T n of the network can be arranged in a curve, or in concentric circles, or in a matrix.

[0079] The T1-T transducer array nallows the emission of exciting ultrasonic waves towards a medium to be analyzed (organ, biological tissue, etc.), and the reception of acoustic echoes (i.e. ultrasonic waves reflected by the medium to be analyzed).

[0080] Each T1-T transducer n consists for example of a rectangular plate of piezoelectric material coated on its front and rear faces with electrodes and covered on the front face with lenses and acoustic impedance matching layers. Such transducers are known to those skilled in the art and will not be described in more detail below.

[0081] In the embodiment illustrated in Figure 2, all T1-T transducers n of the network are used for both transmission and reception. In other embodiments, separate transducers may be used for transmission and reception.

[0082] 2.2. Control and processing unit

[0083] The control and processing unit U c is connected to the T1-T transducer network n .

[0084] It allows you to control the T1-T transducers n of the network, and to process the data acquired by the T1-T transducers n of the network.

[0085] More specifically, the control and processing unit U c allows: - to control the Ti-Tn transducers to emit ultrasonic waves towards the medium to be analyzed,

[0086] - to order the T1-T transducers n the reception of echoes reflected by the medium to be analyzed and their conversion into reception signals,

[0087] - to process reception signals.

[0088] The control and processing unit U c may be composed of one or more distinct physical entities, possibly distant from the T1-T transducer network n .

[0089] The LL control and processing unit includes, for example:

[0090] - one (or more) controller(s) 11, such as a Smartphone, a personal assistant (or “PDA”, acronym for the Anglo-Saxon expression “Personal Digital Assistant”), or any type of mobile terminal known to those skilled in the art; and

[0091] - 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), a programmable automaton(s), an application-specific integrated circuit(s), and / or other programmable circuits,

[0092] - 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.

[0093] 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.

[0094] 3. Analysis process

[0095] 3. 1. General information

[0096] One of the advantageous aspects of the analysis method according to the invention concerns the use of highly angular waves in transmission and reception, such as plane, spiral, divergent, or weakly focused waves. In addition, these waves can be two-dimensional or three-dimensional.

[0097] Such waves are illustrated in Figure 3. More precisely, Figure 3 illustrates:

[0098] - a plane wave Op emitted by a network of plane transducers Tp,

[0099] - a spiral wave Os emitted by a network of curved transducers Tc,

[0100] - a divergent wave OD emitted by a network of curved transducers Tc.

[0101] It is obvious to those skilled in the art that the type of wave is independent of the shape of the transducer array. In particular, a planar transducer array can be configured to emit a spiral wave or a divergent wave (using a suitable delay law). Similarly, a curved transducer array can be configured to emit a plane wave (using a suitable delay law).

[0102] The direction of such a wave is defined as its direction of propagation in a region of interest. This direction can be characterized by an angle defined with respect to a reference direction. For a pair of transmitted and received waves, the bisector of the directions can thus be defined as the average between the direction of the transmitted wave and that of the received wave. The half-angular difference between the directions of transmission and reception can also be defined as half the angle formed by the directions of transmission and reception.

[0103] We will now describe in more detail the different stages of the analysis process, and in particular the stages:

[0104] - emission in a diffusing medium of at least: o a first emitted ultrasonic wave propagating in a first direction of emission angle α, and o a second emitted ultrasonic wave propagating in a second direction of emission angle α',

[0105] - acquisition of at least: o a first reception signal representative of a first received wave propagating in a first reception direction having a first reception angle, o a second reception signal representative of a second received wave propagating in a second reception direction having a second reception angle different from the first reception angle,

[0106] - deforming each of the first and second reception signals, by composition with an affine function, to obtain first and second deformed signals, and

[0107] - direct estimation of a local sound speed from the first and second distorted signals.

[0108] For the sake of simplicity, these steps will be described in the case of plane waves, with a set of "n" ultrasonic transducers arranged linearly. This process can, however, be generalized to other transducer geometries and other types of waves (notably spiral or divergent).

[0109] 3.2. Issue

[0110] In a first step, the analysis method comprises emitting a plurality (two or more) of ultrasonic emitted waves each having a respective emission angle different from the emission angles of the other emitted waves of the plurality of ultrasonic emitted waves.

[0111] More precisely, for each emitted ultrasonic wave, the transducers (T1-T n ) of the network are activated in transmission according to a respective activation delay law, so that each transducer (T1-T n) emits an elementary ultrasonic wave (Eh-EIn) at a respective instant according to said activation delay law. The elementary ultrasonic waves (Eh-EIn) combine to form the emitted wave propagating in a direction having the desired emission angle, the emission angle of the emitted wave depending on the activation delay law used.

[0112] More precisely, depending on the phase and amplitude of the excitation voltages applied to the transducers T1-T n by the control and processing unit U c , it is possible to control the T1-T transducers n so that they produce elementary ultrasonic waves Eh-EIn combining to form an emitted ultrasonic wave 14 which propagates through the medium to be analyzed in a desired direction 15 (see figure 4).

[0113] This resulting emitted ultrasonic wave 14 can be emitted according to different emission angles (i.e. different directions) by varying the activation times (t, t+At, t+2At, ... t+nAt) of each transducer T1-T n of the network.

[0114] For example, for the generation of an emitted plane wave, all T1-T transducers n can be activated:

[0115] - simultaneously to obtain an emitted plane wave propagating at a zero emission angle relative to the T1-T transducer array n , Or

[0116] - successively (according to an activation delay law) to obtain an emitted plane wave propagating according to a non-zero emission angle relative to the T1-T transducer network n .

[0117] 3.3. Acquisition

[0118] After each emission of an emitted wave of desired emission angle, the transducers (T1-T n) of the network are activated in reception for the acquisition of a time-dependent reception signal.

[0119] Each reception signal is representative of a received wave propagating in a direction with a desired reception angle. For the acquisition of a reception signal, one solution is to activate (in reception) simultaneously the transducers T1-T n of the network. In this case, the T1-T transducers n simultaneously acquire the reverberated signals, independently of the orientation of the received waves (i.e. independently of the directions of movement of their wavefronts).

[0120] Thus, after the emission of an emitted wave presenting a given emission angle, each transducer is activated simultaneously in reception to record reverberated signals representative of the reverberation by the medium of the emitted wave.

[0121] For each Ti-Tn transducer, a reverberated signal function of time t, {Si(t)} 0≤i≤n-1 is recorded.

[0122] The reverberated signals recorded by the T1-T transducers n are then summed according to a time delay law depending on the desired reception angle for the received wave.

[0123] For example, for the acquisition of a reception signal representative of a received wave having a reception angle p from the reverberated signals {Si(t)} 0≤i≤n-1 measured by T1-T transducers n , the following summation operation is performed:

[0124] Or :

[0125] - “c” represents the speed of the wave in the medium,

[0126] - “p” represents the probe pitch (i.e. distance between the centers of two adjacent transducers in the transducer array),

[0127] - the “ai” coefficients are apodization coefficients of the elements of the transducer network.

[0128] Advantageously, it is possible to apply apodization during the reception operation, i.e. spatial windowing resulting in coefficients in front of the signals from each transducer. The processing of the reverberated signal block makes it possible to "reorient" the responses recorded by the different T1-T transducers n to obtain reception signals representative of the waves received at the different desired reception angles.

[0129] As previously stated, the delay laws used for summing the reverberated signals recorded by the array transducers to determine the receive signals depend on the desired reception angles for the received waves associated with those receive signals.

[0130] These desired reception angles are chosen so that the bisectors of the different pairs of waves emitted and received coincide.

[0131] For example, in the case of the successive emission of first, second and third emitted waves associated respectively with first, second and third emission angles (for example equal to 0°, -10° and -20° respectively), then the reverberated signals recorded by the transducers are summed according to first, second and third delay laws representative of first, second and third received waves associated respectively with first, second and third reception angles (for example 0°, 10° and 20°) chosen so that:

[0132] - the bisector of the couple formed by the first waves emitted and received (couple a = 0°, P = 0°),

[0133] - the bisector of the couple formed by the second waves emitted and received (couple a' = - 10°, β' =10°),

[0134] - the bisector of the couple formed by the third waves emitted and received (couple a” = - 20°, β” = 20°), are merged.

[0135] In other words, each pair of waves emitted and received (a, p; a', p'; a”, p”) “shares” the same average angle Thus, the delay laws used to calculate the reception signals representative of the waves received at the different reception angles are determined so that the average angles of the transmitted and received wave pairs are equal.

[0136] 3.4. Deformation

[0137] At the end of the acquisition step, a plurality of time-dependent reception signals are obtained, each reception signal being associated with a respective pair of transmitted and received waves. Typically for two transmitted waves, it is possible to determine between two and several tens of received waves, making it possible to obtain between two and several tens of reception signals associated with respective pairs of transmitted and received waves.

[0138] As the average angles of the different pairs of emitted waves and received are equal (equal to 0 in the case of a first pair a = 0° and p = 0°, of a second pair a' = -10° and p' =10°, and of a third pair a” = -20°, p” = 20°), the reception signals associated with these different pairs are theoretically equal, to within a deformation.

[0139] Indeed, each reception signal contains information representative of the same imaged area. However, since the emission and reception angles of each pair are different, this information is not received at the same time by the transducers, so that the different signals are distorted in time.

[0140] More precisely, the emitted and received waves of each pair propagate at the same speeds through the different layers of the scattering medium. However, the distance traveled by the emitted and received waves of each pair varies according to their emission and reception angles. The greater the emission and reception angles of a pair, the shorter the distance traveled by the emitted and received waves of this pair to reach a depth in the medium.Thus, the information representative of the imaged area contained in a first reception signal associated with a first pair of transmitted and received waves will be “compressed” in time relative to the information contained in a second reception signal associated with a second pair of transmitted and received waves if the transmission and reception angles of the first pair are greater than the transmission and reception angles of the second pair (later reception on the transducers in the case of the second reception signal since the transmitted and received waves of the first pair travel a distance less than the distance traveled by the transmitted and received waves of the second pair).

[0141] It follows that the reception signals associated with the different pairs of transmitted and received waves are of different durations, even if they contain the same information. This is notably illustrated in Figure 7e in which two reception signals s(t) and s'(t) each associated with a respective pair of transmitted and received waves contain the same information over a different duration: the signal s(t) (associated with a pair of transmitted and received waves having angles of emission and reception smaller than the angles of emission and reception of the pair of transmitted and received waves associated with the signal s'(t)) is temporally dilated with respect to the signal s'(t).

[0142] To compensate for this difference in duration, the reception signals are deformed by composition with an affine function allowing the reception signals to be expressed over the same duration.

[0143] In particular, a homothetic change of variable is applied to each of the reception signals. This homothetic change of variable consists, for each reception signal, of a mathematical time dilation or contraction.

[0144] The term "mathematical time dilation" (respectively "mathematical time contraction") refers to the dilation (respectively contraction) transformation when applied to a time signal. It allows the duration of the time signal to be increased or decreased without changing its overall shape. In other words, a time signal is obtained that is slowed down (respectively accelerated) compared to the original time signal. Thus, the analysis method includes a step of deformation (time stretching or time compression) of each of the reception signals, by composition with an affine function, to obtain deformed reception signals having an identical duration.

[0145] More precisely, for each reception signal, the deformation step may consist of applying to said reception signal an affine function whose direction coefficient is a function of the half-angle difference between the emission angle and the reception angle of the waves emitted and received from the pair associated with said reception signal.

[0146] As an illustration, for each reception signal, this affine function can be a cosine function of the half-angle difference between the emission angle and the reception angle of the transmitted and received wave pair associated with said reception signal. For example, in the case:

[0147] - of a first reception signal associated with a pair of transmitted and received waves having transmission and reception angles equal to 0 (pair a = 0° and p = 0°), the deformation can consist of multiplying the time base by the value 1

[0148] - of a second reception signal associated with a pair of transmitted and received waves having transmission and reception angles equal to -10 and 10 respectively (pair a' = - 10° and p' = 10°), the deformation can consist of multiplying the time base by the value cos 10

[0149] - of a third reception signal associated with a pair of transmitted and received waves having transmission and reception angles equal to -20 and 20 respectively (pair α” = - 20° and p” = 20°), the deformation can consist of multiplying the time base by the value cos 20

[0150] This allows for distorted signals (dilated or compressed) to be obtained, all theoretically having the same duration.

[0151] As previously stated, these transformed signals are theoretically identical since they contain information representative of the same imaged area. In practice, since the speed of sound is not known, the actual angles of emission and reception of each pair of transmitted and received waves are not known. Indeed, due to the laws of refraction, the directions of the transmitted and received waves are directly related to the local speed of sound of the medium. Thus, (the slope coefficient of) the affine function applied to each reception signal (which is a function of the half-difference between the emission angle and the reception angle of the pair associated with said reception signal) may be incorrect.

[0152] It is this error in the distortion applied to each reception signal that makes it possible to locally estimate the speed of sound in an area of ​​interest.

[0153] 3.5. Estimate

[0154] Once the signals are distorted, they are compared two by two to locally estimate the speed of sound in the region of interest. More precisely, the speed of sound of a region of interest in the medium is estimated from the evolution of a time shift between the distorted signals in said region of interest.

[0155] In particular, the local speed of sound is obtained using a formula using a correlation of the distorted signals in pairs (i.e. the distorted signals are correlated two by two) to obtain a resulting time signal.

[0156] Since distorted signals are complex signals containing both amplitude and phase information, the resulting time signal obtained by correlating two distorted signals considered is also a complex signal:

[0157] - the amplitude of the resulting time signal is representative of a similarity over time between the two distorted signals considered,

[0158] - the phase of the resulting time signal is representative of a phase shift over time between the two distorted signals considered. By temporally deriving the phase of the resulting time signal, a transformation coefficient between the two distorted signals considered is obtained, this transformation coefficient being representative of a difference in time scale between the two distorted signals considered.

[0159] From this transformation coefficient, it is possible to estimate the local speed of sound in the region of interest.

[0160] Thus, the step of estimating the speed of sound in the region of interest includes the sub-steps of:

[0161] - determining a transformation coefficient between the distorted signals considered in pairs, said transformation coefficient being representative of a difference in time scale between the distorted signals considered in pairs,

[0162] - obtain the speed of sound in the region of interest of the medium from the transformation coefficient.

[0163] To determine the transformation coefficient, a resulting time signal is calculated by averaged correlation between the distorted signals considered in pairs, the phase of this resulting signal being representative of the phase shift (or time difference) between the distorted signals considered. The implementation of an average correlation makes it possible to temporally smooth the resulting time signal.

[0164] The transformation coefficient is then obtained by time derivation of the phase of the resulting signal.

[0165] Considering first and second reception signals associated respectively with first and second pairs of waves transmitted and received according to first and second angles of transmission and reception, the transformation coefficient can be mathematically determined from the following formula: Or : corresponds to the average correlation of the first and second distorted signals s and s', is the time derivative operator of the phase.

[0166] The speed of sound in the region of interest can then be obtained by solving the following formula: Or :

[0167] - "c r » is the speed of sound in the region of interest,

[0168] - “Cth” is the theoretical speed of sound used to: o calculate the delay laws used during the acquisition step to determine the first emission and reception angles of the first pair of emitted and received waves associated with the first reception signal o calculate the delay laws used during the acquisition step to determine the second emission and reception angles of the second pair of emitted and received waves associated with the second reception signal, o calculate the first affine function used during the deformation step to deform the first reception signal in order to obtain the first deformed signal, o calculate the second affine function used during the deformation step to deform the second reception signal in order to obtain the second deformed signal,

[0169] - “D” is the transformation coefficient,

[0170] - "w c» is the central pulsation of the signals s and s' at the depth considered,

[0171] - “6” is the half-difference between the first emission and reception angles of the first pair of waves emitted and received associated with the first reception signal,

[0172] - "6'" is the half-difference between the second emission and reception angles of the second pair of transmitted and received waves associated with the second reception signal. In summary, the step of estimating the speed of sound of a region of interest consists of estimating a local speed of sound from a transformation coefficient between time portions of interest of first and second distorted signals by deriving the phase of the average correlation of the first and second distorted signals.

[0173] For each pair of distorted signals considered, it is thus possible to determine a resulting time signal. When several pairs are considered, several resulting time signals are obtained and can be combined to estimate a sound speed. For example, several elementary sound speeds can then be calculated from the several resulting time signals. The sound speed is then estimated as the average of these several elementary sound speeds. In another version, several transformation coefficients (unbiased by the difference of half-differences) can be calculated and averaged, in order to obtain a robust transformation coefficient used to determine the sound speed.

[0174] 4. Theory relating to the invention

[0175] We will now present various theoretical elements relating to the invention to enable those skilled in the art to better understand the advantages associated with the method and device described above.

[0176] This technique is based on an angular approach to ultrasound imaging. For the sake of simplicity, the invention will be described with reference to the use of plane waves and a linear probe in a two-dimensional medium.

[0177] However, any type of highly angular transmission and reception (such as plane, spiral, divergent, or weakly focused waves) works. Similarly, any probe geometry can be used to generate these waves, such as linear or curved, simple or two-dimensional probes. The linear probe considered is composed of N ultrasonic transducers, whose acoustoelectric and electroacoustic responses are assumed to be equal and denoted h(t). We place ourselves in a Cartesian coordinate system whose origin is located at the center of the probe and whose abscissa axis is aligned with the probe.

[0178] To begin with, we assume that the ultrasonic probe is placed in contact with a diffusing medium, characterized by its reflectivity modeling the local variations of acoustic impedance, in which ultrasonic waves propagate and are reverberated. We also place ourselves within the framework of the first-order Born approximation (that is to say, we assume that multiple scattering is negligible compared to simple scattering), and we assume that the medium has a homogeneous and known speed of sound.

[0179] 4. 1. Issuance strategy

[0180] First, at least two plane waves are emitted by the ultrasonic probe P, a first E1 in a direction a and a second in a second direction a. The direction of a plane wave designates the angle that the plane wavefront E1 makes with respect to the probe P, and therefore the abscissa axis in the reference frame considered, as illustrated in Figure 5.

[0181] To emit a plane wave in direction a (also called a plane wave of angle a) with a linear probe S, each transducer i of the probe P is electrically excited by means of a signal e(t), being delayed according to its position as follows:

[0182] Or : is the delay applied to the transducer located at position x, and

[0183] - It is the speed of sound of the medium.

[0184] A plane wave is thus transmitted in the medium, such that the pressure field in the medium is of the form: where u = e * h is the convolution between the transducer excitation function and its electroacoustic response, which we will assume to be a complex function formed by the multiplication of a Gaussian function with zero mean and standard deviation a with a complex pulsation modulation:

[0185] 4.2. Reception strategy

[0186] In a second step, the emitted plane waves are reverberated by the diffusing medium, and the corresponding echoes are captured by the probe transducers, giving rise to signals Si, i between 1 and N.

[0187] These signals are then transformed to select the signals from the β directions for the plane wave emitted in the a direction and β' for the plane wave emitted in the a direction.

[0188] To select the signals coming from the direction β, in the case of plane waves, the received signals are transformed to obtain a signal representative of the reverberated plane wave of angle β . To do this, the signal received by transducer i is delayed depending on its position, as in the case of transmission as follows:

[0189] These delayed signals are then multiplied by a windowing function ω i (potentially time dependent) and finally summed: where s is the signal obtained. 4.3. Interpretation of the angular signal and isochronous volume

[0190] The angular signal s obtained in the previous section, after the emission of a plane wave E1 of angle a and the reception of a plane wave R1 of angle β, has certain properties for the invention.

[0191] Indeed, we can express s(t) as a function of the reflectivity of the medium like this:

[0192] By designating by γ = (α + ) / 2 the bisector of the two directions, by δ = (α - β / 2) the half angular difference, and by using the change of variable , we obtains after simplifications: where is the Radon transform of the reflectivity function of the medium, evaluated at the angle γ and the depth formally defined as follows: where dir(.) denotes the Dirac distribution.

[0193] This quantity corresponds to the integral of the reflectivity function of the medium along the line of angle 7 and depth .

[0194] From the previous equation, we can deduce that if the signal is very limited in time such that we can approximate it by a Dirac distribution, we obtain directly: Thus, the signal received at time t is equal to the integral of the reflectivity function of the medium along the line of angle 7 and depth ct / (2 cos δ) (or projection), that is to say it contains the sum of all the echoes coming from this line.

[0195] In practice, since the signal is band-limited, the reflectivity is not integrated along a simple line but along a surface V of a certain axial thickness. This surface V (or volume in a three-dimensional study) corresponds to the concept of isochronous volume introduced by Mailart and Fink.

[0196] 4.4. Composition by an affine function

[0197] From the preceding equations follows an important property of the angular approach.

[0198] We observe that for several pairs of emission and reception angles, for example (α,β) and (α',β'), whose bisectors γ = (α + β ) / 2 and γ' = (a'+β' ) / 2 are equal, there are instants for which the isochronous volumes are the same.

[0199] Indeed, in both cases, these are lines of angle 7 = (of a certain thickness in the case of a band-limited pulse). Such a case is represented in Figure 6 illustrating two pairs of emission and reception angles (α,β) and (a',β') sharing the same bisector y=y'. The two pairs give rise to the same isochronous volumes: the straight lines of angle y with the horizontal.

[0200] In this case, however, the two pairs of angles give rise to different half-angular deviations δ and δ', which gives a different relationship between time t and depth ζ:

[0201] The difference between these time-depth relationships creates a dilation phenomenon between the two signals, as represented in Figures 7a-7e which illustrate examples of emission and reception of two pairs E1 -R1 and E2-R2 of angles (α,β) and (α', β') sharing the same bisector y=y' in a given medium. More precisely, Figures 7a and 7b illustrate the emission and propagation of a plane wave E1 of angle a and the reception R1 at an angle β, Figures 7c and 7d illustrate the emission and propagation of a plane wave E2 of angle a and the reception R2 at an angle β'. Figure 7e illustrates the signals s and s' obtained in both cases, as a function of time. The instants corresponding to the coherent reception of the echoes coming from each isochronous volume V1, V2 are represented there. We observe that the signals s and s' are identical, except for one expansion.

[0202] To compensate for this expansion effect and realign the different angular signals, the received signal is transformed by composing it with an affine function: Or :

[0203] - a is the slope coefficient which we set to cos(5) and

[0204] - b an offset that we set to 0 for the moment.

[0205] Thus, the link between time and depth becomes for Such a link is independent of the angles emitted and received. We note that, thanks to this composition by an affine function, all the signals obtained by having emitted and received pairs of directions having the same bisector are realigned and become equal. This effect is represented in figure 7f which illustrates the signals s and s' after dilation of these by a factor cos(5).

[0206] Theoretically, by including the affine transformation in the equation defining s, we obtain:

[0207] We observe in this equation that the half-angular deviation δ only intervenes as a general factor in u. This effect is generally neglected because it no longer disturbs the link between time and depth but only has a slight frequency shift effect. It is also possible to compensate for this frequency shift by filtering the received signal. In our case, this factor is neither neglected nor compensated, but taken into account in the rest of the equations.

[0208] 4.5. Effect of an unknown heterogeneous medium

[0209] We are now considering a more complex medium, which is intended to be closer to reality. This medium is composed of several horizontal layers of varying thicknesses and sound speeds.

[0210] Suppose we are studying signals that correspond to a specific layer. In this layer, we have a homogeneous but unknown speed of sound. It is this speed of sound that we want to determine.

[0211] We denote the time interval considered (corresponding to the layer of interest) [to, ti]. We denote the corresponding depths of the isochronous volumes [ζo, ζi]. Such a configuration is represented in Figure 8.

[0212] Such a configuration is representative of different biological environments such as the liver, where layers of skin, fat and muscle cover the liver layer.

[0213] 4.6. Refraction

[0214] When an emission wave passes from a first layer having a sound speed ci to a second layer having a sound speed C2, the laws of refraction imply that the angle of the emission wave is changed.

[0215] In fact, we have: where en and CT2 correspond to the angles of the emission wave in the first and second layers. By recursion, we obtain a link between the speed of sound in any layer n and the speed of sound in this same layer with the angle and the speed of sound in the first layer:

[0216] 4.7. Transmission and reception with unknown speed of sound

[0217] As described previously, to emit or receive an ultrasonic plane wave, delays are applied to the transducers.

[0218] However, calculating these delays requires knowledge of the speed of sound in the medium.

[0219] In the case of an unknown medium, we can only assume a sound speed cth in order to emit or receive a theoretical angle α th or β th .

[0220] The form of the delay law applied to the transducers gives for transmission (reception being similar):

[0221] Thus, by choosing r(x), we choose not the angle but the quotient of the sine of the angle over the speed of sound.

[0222] The actual angle emitted therefore depends on the speed of sound in the first layer in the same way as for the laws of refraction.

[0223] The probe therefore behaves like an additional layer of infinitesimal thickness and sound speed cth. We finally obtain in layer n: These equations are valid for both transmission and reception by reciprocity.

[0224] 4.8. Shape of the signal obtained

[0225] In the following, we denote:

[0226] - the supposed quantities: “-th”, and

[0227] - the actual quantities in the layer of interest: "- r ".

[0228] Assuming a sound speed of cth, we expect to emit and receive plane waves of angle α th and β th, having an angle half yth and a half angular deviation δ th .

[0229] In practice, the actual speed of sound in the layer of interest is c r and the real angular quantities are:

[0230] We deduce the signal received before composition with the affine function, between times to and ti:

[0231] To realign the signals, we compose them with an affine function whose slope coefficient is the cosine of the assumed half-angular deviation δ th and the bias is set to zero. We obtain: Or is an unknown constant corresponding to the misalignment caused by all layers above the layer of interest.

[0232] To ensure maximum alignment, it is possible to use the composition bias with the affine function to empirically compensate for this shift. This compensation is, however, only necessary for surface layers with sound speeds very different from the assumed one and is not necessary in the general case.

[0233] We will note that in the case of an infinitely fine signal u (Dirac), we obtain:

[0234] The signal is therefore independent of the angle torque used provided that δ th = δ r and ζ c =0.

[0235] In this method the constant ζ c does not really interest us since it is linked to layers which are not the ones of interest.

[0236] This is the quantity Cr / 2 * cosδ th / cosδ r which interests us, since it is linked only to the speed of sound in the layer of interest.

[0237] To locally estimate the speed of sound in the medium of interest, the principle is to detect this factor. Indeed, this quantity informs us about the angle error made between δ th and δ r and therefore, via the laws of refraction, on the error in sound speed made between cth and Cr.

[0238] 4.9. Obtaining the transformation coefficient

[0239] To detect this transformation coefficient, a reference is needed. To do this, we use two signals s and s' generated with two pairs of angles ( α th , β th ) and ( α' th , β' th ) which share the same bisector γ th =γ' th. To compare these signals, we calculate their correlation. It is the phase of this correlation that will lead us to the transformation coefficient, as represented in Figure 9 which is a graph illustrating the phase of the correlation of two signals s and s' corresponding to the pairs (10°, -10°) and (0°, 0°) of emitted / received waves as a function of time, in a medium composed of several layers. As represented in this figure, the speed of sound in the region of interest ROI is equal to 1540m / s. The different curves correspond to several hypotheses of sound speed cth, which lead to several compositions with affine functions.

[0240] In order to study this correlation, some assumptions and simplifications are used:

[0241] - we assume that the real bisectors are the same (yr=y'r); this allows us to consider that the two signals correspond to the same integration volumes, apart from a time shift; this approximation is close to reality since the difference between these two bisectors is generally less than 0.1°,

[0242] - it is assumed that the medium is composed mainly of uniform speckle, that is to say that the Radon transform of the reflectivity function can be interpreted as a probabilistic density whose realizations are independent depending on the media or depths and whose average is uniformly equal to m in the layer of interest; this allows us to write that the average correlation on the media or on the depth of the Radon transform of the reflectivity function is: where dir(.) is a Dirac and <.> denotes the averaging operation over time or over different media with the same characteristics.

[0243] To simplify the calculations to come, we define the intermediate functions: in order to obtain: And

[0244] It is possible to calculate the form of the correlation between these two signals averaged over time (i.e. the depth). After a few calculations, we obtain:

[0245] Using the assumptions described above, this expression simplifies to:

[0246] In order to understand the influence of the expansion factor on this correlation, we develop the function u using its expression defined at the beginning:

[0247] Here we see that the phase of the integrated expression is representative of the difference of the intermediate functions. By definition of intermediate functions, we see that it informs us about this expansion factor. It will therefore be the phase of this expression that interests us.

[0248] To calculate it, we start by studying the two functions g(f(t, .)) and g(f'(t, .)). The function g being a Gaussian with law N(0, σ 2 ) and f(t, .) and f'(t, .) being affine functions, we deduce that the two composite functions are themselves Gaussian functions according to the laws: Now, the product of two Gaussians is itself a Gaussian function, whose average is: where μ1, 2 are the means of the two multiplied Gaussian functions and σ 1, 2 their variances.

[0249] In our case, after simplifications we obtain:

[0250] Noting G(ζ) the equivalent Gaussian with mean μ tot and noting that f(t, ζ) - f'(t, ζ) is an affine function in ζ which we will note f(t, ζ) - f'(t, ζ) = aζ + b, we obtain:

[0251] Now, it is possible to prove by Hilbertian symmetry around μ tot that the phase of such an expression is simply:

[0252] By replacing μ tot , a and b, we obtain the formula after simplifications: where C is a constant that does not depend on time.

[0253] In this equation, C represents the offset caused by all layers between the probe and the layer of interest, while the coefficient in front of w ct is representative of the expansion factor and depends only on the layer of interest. This is represented in Figure 9, where we see that the quantity of interest is in fact the derivative of this phase. We note for example that in the case where cth=1540m / s, the derivative of this phase is zero because the assumed angle difference δ th is equal to the actual angle deviation δ r . For assumed speeds cthtoo high, the derivative will be negative because the assumed angle deviation δ th is too large, and for speeds that are too low, the derivative will be positive.

[0254] Thus, to obtain only the information on the layer of interest, we note D the local transformation coefficient calculated as follows:

[0255] Such a measured transformation coefficient, in the case of the medium corresponding to Figure 8, is represented in Figure 10 which illustrates a measured expansion factor for a multi-layer medium and for several sound speed hypotheses. To use the properties of the "speckle", a sliding averaging of approximately 20μS was used on the latter, degrading the axial resolution.

[0256] We note once again that in the case where cth=1540m / s, the estimated transformation coefficient is zero. For speeds assumed to be too high, this transformation coefficient will be negative, and for speeds that are too low, it will be positive.

[0257] All that remains is to find an explicit formula that links the actual speed of sound to this expansion factor.

[0258] 4. 10. Obtaining the local speed of sound

[0259] To obtain the local speed of sound from the local transformation coefficient D, we study the expression for D by carrying out a development limited to order 2 on the angles. We obtain that 5r~δ th (c r / cth), and in the same way δ' r ~d' th (c r / cth), which gives: We therefore obtain for the speed of sound:

[0260] Such a measured speed of sound, in the case of the medium corresponding to Figure 8, is represented in Figure 11 which illustrates a speed of sound estimated from an expansion factor for a multi-layer medium as a function of time.

[0261] We observe here that the speed of sound, directly obtained from the correlation between the two signals s and s', is indeed a local quantity. Moreover, all the hypotheses of the speed of sound cth assumed give very similar results (to within 10 m / s).

[0262] Note that this speed of sound is obtained here from a simulation, with only two pairs of plane waves emitted and received.

[0263] The invention presented here makes it possible to locally estimate the speed of sound with only two emissions, two signals obtained (i.e. an extremely limited number of data), and an inexpensive calculation (a composition by affine function, a correlation, a transition to the phase, a derivation and the application of a direct formula).

[0264] 4. 11. Interpretation

[0265] The speed of sound obtained by the above equation is representative of a local speed of sound, undisturbed by heterogeneities of the medium located higher than the region of interest, assuming a medium stratified in horizontal layers.

[0266] We obtain that the calculated speed of sound will be substantially equal to the average of the speeds of sound along the isochronous volume (by limited development, error of less than 5 m / s for speeds of sound ranging from 1400 to 1650 m / s).

[0267] 4.12. Central pulsation The w factor c present in the equation above corresponds to the central pulsation of the ultrasonic wave.

[0268] It can be assumed to be equal to the excitation pulsation of the transducers.

[0269] However, ultrasonic media tend to nonlinearly attenuate ultrasonic signals, causing a shift towards low frequencies of this central pulsation. To counter this effect, it is possible to measure the value of this pulsation over time using the autocorrelation of the signals.

[0270] We have in fact:

[0271] Where the average is taken over time or across different environments.

[0272] 4. 13. Sensitivity and choice of pairs of angles

[0273] The calculation of the local speed of sound from the expansion factor depends on the choice of angles. More specifically, it depends on the difference of the squares of the half-angle deviations. The smaller this difference, the more a slight variation in the expansion factor will imply a large variation in the estimated speed of sound. It is therefore advisable to choose pairs of angles whose half-angle deviations are sufficiently far apart to ensure a certain stability of the technique.

[0274] Finally, it should be noted that the stability of the method does not depend on depth, which presents an advantage over several state-of-the-art techniques, in particular for the quantification of the speed of sound in organs located several centimeters deep, such as the liver.

[0275] 4.14. Case of non-horizontal layers In practice, it is possible to want to image a medium composed of non-horizontal layers. In this case, the laws of refraction no longer apply in such a simple way.

[0276] Let us suppose that a plane wave of angle cri propagates from a layer i to a layer i+1, with sound speeds Ci and Ci+i and separated by an interface of angle 0i. Such a configuration is represented in Figure 12 which represents the propagation of an emission wave of angle cri between a first layer Ci and a second layer Ci+1 separated by an interface Int of angle 0i.

[0277] In this case, the laws of refraction indicate that: where T and 771+1 are the angles between the incident wave and the refracted wave and the normal to the interface. We obtain:

[0278] The modification of this recurrence formula, valid both in emission and in reception, will disturb the local expression of cr and β and therefore that of 5.

[0279] In practice, it is possible to carry out a limited Taylor development of order 2 on the angles, simplifying these relations and preserving the simplified recurrence relation:

[0280] In the most common case of interfaces with angles smaller than 45°, we obtain angle deviations with the simplified formula of less than 2°.

[0281] The previous theory can therefore still be applied. Of course, the larger the interface angles, the more bias there may be in the method described above. 4. 15. Value, profiles and map

[0282] The technique presented here makes it possible to easily obtain three types of results.

[0283] First, the local speed of sound in a region of interest can be obtained directly. To do this, a windowing function for transmission and / or reception will be chosen to limit the lateral extension of the waves used. On the other hand, the axial extension of the region of interest will be used to average the correlation between the two signals s and s' on the one hand and to calculate a robust derivative of the phase of the correlation on the other hand.

[0284] It is also possible to obtain the profile of the local sound speed along the bisector y used (quasi-axial profile). To obtain such a profile, it is sufficient to measure the local sound speed at several depths.

[0285] These first two results can be consolidated by repeating the technique for different pairs of angles sharing the same bisectors y but different half angular separations 5, or even slightly different bisectors.

[0286] The results obtained with these different pairs of angles can be grouped at different stages of the calculation. For example, it is possible to average all the final velocities obtained or to directly average the correlation phases, taking care to scale them by dividing them by the difference of the squares of the half angular deviations.

[0287] Finally, by transmitting several pairs of angles with varied bisectors, we obtain enough spatial information to reconstruct a map, for example by measuring the local sound speed in a multitude of regions of interest distributed in the medium. It is also possible to reconstruct a map using an angle-based approach. Indeed, as detailed in the interpretation paragraph, the local sound speed obtained is actually close to the average sound speed along the isochronous volume (typically a line of angle y with the horizontal). Thus, Radon inversion algorithms can be used to recover a local sound speed map, such as inverse projection or other inverse problems.These algorithms can operate on the local sound speeds obtained by the technique, or directly at earlier stages in the calculation (typically on the expansion factors scaled by dividing them by the difference of the squares of the half angular deviations).

[0288] 5. Conclusions

[0289] The method described above differs from the prior art because it makes it possible to obtain a map and / or a local measurement of the speed of sound in a region of interest directly and with the following advantages:

[0290] • it provides a local measurement in a region of interest (map or value),

[0291] • it requires very few ultrasonic emissions (typically between 2 and 16) compared to other local measurement techniques (typically more than 100),

[0292] • it requires a very limited amount of computation unlike other non-direct local measurement techniques which require inverting matrices or storing large pre-inverted matrices and applying them,

[0293] • it requires a very limited amount of data from the ultrasound probe (works from 2 signals where other methods generally use 100 * 128 signals).

[0294] In the foregoing description, the invention was described in the case of the use of plane waves. The reader will appreciate that the invention can be implemented using other types of strongly directional waves, such as spiral waves and diverging waves.

[0295] Similarly in the foregoing description, the invention was described with reference to a T1-T transducer array nhaving a linear geometry. It is obvious to those skilled in the art that the Ti-Tn transducer network can have other shapes such as a curved or matrix shape.

[0296] In the case of a matrix probe, therefore two-dimensional, the previous method is generalized by defining two-dimensional plane, spiral or divergent waves.

[0297] These plane, spiral or divergent waves are nothing other than the combination of a plane, spiral or divergent wave along one axis with a plane, spiral or divergent wave along another axis, thus giving delay laws defined in Cartesian, cylindrical or polar reference frames.

Claims

DEMANDS 1. A method for analyzing a medium using a transducer array (T1-Tn), said method comprising: - the acquisition (100) of at least two reception signals, each associated with a respective pair of emitted and received waves, said at least two reception signals comprising: o a first reception signal associated with a first pair of emitted and received waves along first emission and reception directions, o a second reception signal associated with a second pair of emitted and received waves along second emission and reception directions, the first emission and reception directions being different from the second emission and reception directions, the acquisition step including, for each reception signal, the following sub-steps: o the generation in a diffusing medium, by transducers (T1 -Tn) of the network, of an emitted wave having a desired emission direction, o the reception, by transducers (T1 -Tn) of the network,of reverberated signals and their combinations to obtain a time-domain reception signal representative of a received wave reflected by the diffusing medium along a desired reception direction, - the deformation (200) of said at least two received signals by composition with a respective affine function: o the first received signal being deformed by composition with a first affine function to obtain a first deformed signal, the first affine function depending on the first directions of emission and reception, o the second received signal being deformed by composition with a second affine function, different from the first affine function, to obtain a second deformed signal, the second affine function depending on the second directions of emission and reception, - the local estimation (300) of the speed of sound in a region of interest of the medium from the comparison of the first and second distorted signals.

2. An analysis method according to claim 1, wherein the estimation step comprises the following substeps: - determination of a transformation coefficient between the first and second distorted signals, said transformation coefficient being representative of a difference in temporal scale between the first and second distorted signals, - obtaining the speed of sound in the region of interest of the medium from the transformation coefficient.

3. Analysis method according to claim 2, wherein the estimation step includes a substep of calculating a resulting signal representative of an average correlation between the first and second distorted signals.

4. An analytical method according to claim 3, wherein the average correlation is obtained by at least one of the following methods: - averaging over different depths in the region of interest, - averaging over different media with the same speed of sound, - averaging over signals obtained with different transmission or reception strategies, - averaging over different signals obtained by perturbing delay laws applied to the transducer network in transmission or reception.

5. Analytical method according to any one of claims 3 or 4, wherein the transformation coefficient is determined by derivation of a phase of the resulting signal representative of the average correlation between the first and second distorted signals.

6. Analytical method according to claim 5, wherein the transformation coefficient D is determined from the following formula: Or : corresponds to the average correlation of the first and second distorted signals s and s', is the time-dependent phase operator.

7. An analysis method according to any one of claims 2 to 6, wherein the substep of obtaining the speed of sound in the region of interest includes solving the following formula: Or : - "c r " is the speed of sound in the region of interest, - "cth" is a theoretical speed of sound used to calculate the first and second affine functions during the deformation step, - "D" is the transformation coefficient, - « o>c » is a central pulsation of signals s and s' at the considered depth, - “<5” is half the angular difference between the first directions of emission and reception of the first pair of emitted and received waves, - "ô'" is half the angular difference between the second directions of emission and reception of the second pair of emitted and received waves.

8. An analysis method according to any one of claims 1 to 7, wherein each affine function is of the form: f(t) = At ​​+ B, where: - "A" is a slope coefficient dependent on half the angular difference between the emission direction and the reception direction of the emitted and received wave pair associated with the received signal, and - "B" is a factor for aligning the received signals to a desired depth corresponding to the depth of the region of interest.

9. An analysis method according to claim 8, comprising a step for determining the alignment factor "B", said determination step comprising the substeps of: - to acquire two primary signals, each associated with a respective pair of emitted and received waves along emission and reception directions, each primary signal representing an amplitude as a function of a time variable, - to temporally expand each primary signal by applying a factor to the time variable to obtain an expanded primary signal, the factor depending on half the angular difference between the emission direction and the reception direction of the torque associated with the primary signal, - correlate the broadened primary signals, - deduce from the phase of the correlation an optimal shift index B.

10. Analysis method according to any one of the preceding claims, wherein for each received signal, the substep of combining the reverberated signals comprises the summation of the reverberated signals according to a respective delay law, and wherein said respective delay laws are defined such that the bisectors of the directions of the emitted and received waves of each pair of emitted and received waves coincide. 1.

1. A method according to claim 7, further comprising a step of estimating the central pulsation of the signals s and s' at the depth considered, said estimation step comprising the following substeps: - Estimation of the central pulse of the first received signal s from its autocorrelation, - Estimation of the central pulse of the second received signal from its autocorrelation, - Estimation of a final center pulse from the average of the center pulses of each of the received signals.

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