Method for estimating a movement of particles in a bone

Abstract

The invention relates to a method for estimating a movement of particles in a bone, comprising the following steps: obtaining (201) data associated with ultrasonic waves emitted at a temporal frequency (f0); obtaining (202) ultrasonic wave phase velocities in the bone in various directions followed by the ultrasonic waves; obtaining videos showing the bone at a point, the videos issuing from the ultrasonic waves; computing (203) phase variations at the point between two images of the videos; and computing (204) a particle movement at the point based on the temporal frequency (f0), the data associated with the ultrasonic waves, the phase variations, and the phase velocities in the various directions.

Description

[0001] TITLE: Method for estimating particle displacement in a bone

[0002] FIELD OF THE INVENTION

[0003] This document relates to a method for estimating particle displacement in a bone.

[0004] STATE OF THE ART

[0005] To estimate blood movement in a body, methods using ultrasound systems have been proposed. These ultrasound systems produce videos based on echoes of ultrasound waves that have passed through the body. These videos are then processed to extract movements.

[0006] These methods known from the state of the art make the following three assumptions:

[0007] • the propagation speed of an ultrasonic wave is the same throughout the investigated region,

[0008] • the propagation speed of an ultrasonic wave does not depend on the direction of propagation of the wave, and

[0009] • in a resolution cell (the smallest volume resolved by the ultrasound system), the blood moves in only one direction.

[0010] However, these methods do not allow for a sufficiently precise estimation of blood movement inside a bone.

[0011] STATEMENT OF THE INVENTION

[0012] One aim of the invention is to accurately estimate the movement of particles in a bone.

[0013] For this purpose, according to a first aspect, the method as defined in claim 1 is proposed.

[0014] The method according to the first aspect is such that the calculation of the displacement involves not a single phase velocity (i.e. a propagation velocity of the front of the ultrasonic wave), but several phase velocities in different directions, which makes it possible to take into account the fact that the bone is an anisotropic elastic medium. The method according to the first aspect thus leads to a much more accurate estimation of displacement than a method whose calculations would be based on the assumption that the bone is an isotropic elastic medium, in other words on the assumption that the phase velocity of a wave in the bone is the same in any direction in space. The method according to the first aspect may further comprise the optional features set out in the dependent claims, taken alone or in combination where technically possible.

[0015] The video filtering mentioned in claims 2 and 3 is very advantageous. The first raw video or the second raw video may show crossing points between several superimposed blood vessels containing blood flowing in two different directions. If these vessels are finer than the resolution cell of the ultrasound system used, calculating phase variations between frames of the first raw video or the second raw video may lead to erroneous displacement calculations. Calculating phase variations between frames of videos filtered as described in claims 2 and 3 overcomes this difficulty.

[0016] Other optional but advantageous features are set forth in claims 4 to 9.

[0017] It is also proposed:

[0018] • a computer-readable memory storing computer-executable instructions for carrying out the steps of the method according to the first aspect.

[0019] • The device as defined in claim 11

[0020] • The ultrasound system as defined in claim 12.

[0021] DESCRIPTION OF FIGURES

[0022] Other characteristics, aims and advantages of the invention will emerge from the following description, which is purely illustrative and non-limiting, and which must be read in conjunction with the appended drawings in which:

[0023] Figure 1 schematically illustrates an ultrasound system according to one embodiment.

[0024] Figure 2 represents a schematic trajectory of an ultrasonic wave, a point on this trajectory and the image of this point by application of a point spread function.

[0025] Figure 3 is a flowchart of steps of an ultrasound method according to one embodiment.

[0026] Figure 4 is a flowchart of steps of a method for estimating particle displacement, according to one embodiment. Figure 5a schematically represents the trajectory of an ultrasonic wave and an echo of this wave resulting from the reflection of the ultrasonic wave at a point in a medium not containing bones and whose elasticity is isotropic.

[0027] Figure 5b schematically represents the trajectory of an ultrasonic wave and an echo of this wave resulting from the reflection of the ultrasonic wave at a point inside a bone.

[0028] Figure 6 is a flowchart of steps of a filtering method according to one embodiment, this filtering method constituting a step of the method of Figure 4.

[0029] Figure 7 schematically represents data obtained at different stages of an implementation of the filtering method of Figure 6.

[0030] Figure 8 is a schematic cross-sectional view of a blood vessel located in a bone and in which particles are moving in an oblique direction.

[0031] Figure 9a shows errors that affect the speed standard estimated via the method according to the embodiment of Figure 3, and the speed standard estimated via a traditional approach.

[0032] Figure 9b shows errors that affect the angle of speeds estimated via the method according to the embodiment of Figure 3, and the angle of speeds estimated via a traditional approach.

[0033] Figure 10 includes three views: on the left, a schematic view of a medium in which particles move in four different directions; in the middle, a view showing velocities of these particles estimated using a traditional approach; on the right, a view showing velocities of these particles estimated using the filtering method of Figure 6.

[0034] Throughout the figures, similar elements have identical references.

[0035] DETAILED DESCRIPTION OF THE INVENTION

[0036] 1) Ultrasound system according to one embodiment

[0037] Referring to Figure 1, an ultrasound system 1 comprises a probe 2, an imaging device 4, and a displacement estimation device 6. The system may also comprise a display screen 8.

[0038] The probe 2 is conventional. The probe 2 comprises a plurality of ultrasonic wave transmitters and receivers. The transmitters and receivers are distributed such that an ultrasonic wave emitted by a transmitter can be received by a receiver after its reflection at a point located inside a body to be analyzed, in particular a bone as will be seen below.

[0039] The imaging device 4 is configured to generate raw videos showing the interior of the structure to be analyzed from ultrasonic echoes received by the probe. The imaging device is known from the prior art.

[0040] As a reminder, the impulse response of the imaging device 4 can be described by the point spread function (PSF). The name of this function illustrates the fact that the response of the imaging device 4 to a point object is a pattern visible in an image generated by the imaging device 4, this pattern having parallel fringes, as illustrated in FIG. 2.

[0041] There is a close relationship between the fringes of the pattern and the front of the ultrasonic wave from which the pattern originates (this wavefront being represented on the left of Figure 2 by three parallel lines).

[0042] On the one hand, the peak-to-peak distance between two successive fringes of the pattern is A / 2, knowing that  = ^, where c0 is the phase velocity of the ultrasonic wave, and f0 is the temporal frequency fo of the ultrasonic wave.

[0043] On the other hand, the inclination of the pattern fringes in an image produced by the imaging device is a function of the direction of propagation of the ultrasonic wave.

[0044] When a point object is static relative to the probe, the fringe pattern that constitutes its response is also static in a succession of images generated by the imaging device 4. But when the point object moves relative to the probe, the fringe pattern moves in the succession of images. Thus, a signal observed at a given pixel of such a succession of images varies. This signal notably has a phase that varies from one image of the video to another.

[0045] Returning to Figure 1, the displacement estimation device 6 comprises at least one processor 10 and a memory 12.

[0046] The memory 12 is configured to store data which will be detailed below. The memory 12 is of any type. The memory 12 may in particular comprise a volatile memory for storing data temporarily (for example of the RAM type), and a non-volatile memory for storing data persistently (for example of the flash, EEPROM, HDD, etc. type). The or each processor 10 is configured to execute a program comprising code instructions stored in the memory 12. When this program is executed by the or each processor 10, the device 6 implements a method for estimating the displacement of particles in the structure probed by the probe using ultrasonic waves. This method is described below.

[0047] The or each processor 10 is of any type (CPU, controller, microcontroller, SIC, FPG, etc.). In the following, the example of an embodiment will be taken in which the estimation device comprises a processor, it being understood that, in other embodiments, several processors 10 can be used, in particular to execute different tasks of the aforementioned program in parallel.

[0048] Process implemented by the ultrasound system

[0049] Referring to Figure 3, a method implemented by the system comprises the following steps.

[0050] 2.1) Probing using ultrasonic waves

[0051] In a probing step 100, the probe 2 is used to probe a bone using ultrasonic waves. The probe 2 emits ultrasonic waves at a frequency f0 toward the bone. These ultrasonic waves penetrate the bone.

[0052] The time frequency f0 has a value between 0.1 MHz and 10 MHz.

[0053] Ultrasonic echoes resulting from the reflection of these ultrasound waves inside the bone are then received by the probe.

[0054] It should be noted that ultrasound waves following different trajectories can reach the same point located inside the bone. The ultrasound echoes resulting from the reflection of these ultrasound waves at this point also follow different trajectories.

[0055] Let us consider in particular a fixed point located inside the bone, which we will call point P.

[0056] Probe 2 emits first ultrasonic waves with a time frequency f0 towards this point P, and receives first ultrasonic echoes obtained by reflection of the first ultrasonic waves at point P.

[0057] The first ultrasound waves and the first echoes have wavefronts oriented differently during their propagation in the bone. Thus: • the orientation of the wavefront of the first ultrasound waves can be characterized by a direction normal to this wavefront, which is conventionally called the “first emission direction” (to signify that we are on an “outward” path of the first waves leading to the point P considered).

[0058] • the orientation of the wavefront of the first ultrasonic echoes can be characterized by a direction normal to this wavefront, which is conventionally called the “first direction in reception” (to signify that we are on the “return” path followed by the first echoes before reception by probe 2, and to distinguish it from the first direction in transmission defined previously).

[0059] The probe 2 furthermore emits second ultrasonic waves at the same time frequency f0 towards the same point P, and receives second ultrasonic echoes obtained by reflection of the second ultrasonic waves at point P.

[0060] The second ultrasound waves and the second echoes have differently oriented wavefronts as they propagate through the bone. Thus:

[0061] • the orientation of the wavefront of the second ultrasonic waves can be characterized by a direction normal to this wavefront, which is conventionally called the “second direction in emission” (to signify that we are on an “outward” path of the second waves leading to the point P considered).

[0062] • the orientation of the wavefront of the second ultrasonic echoes can be characterized by a direction normal to this wavefront, which is conventionally called the “second direction in reception” (to signify that we are on the “return” path followed by the second echoes before reception by the probe 2, and to distinguish it from the second direction in transmission defined previously).

[0063] The second ultrasonic waves and the second echoes have the same temporal frequency and are distinguished from the first ultrasonic waves and their echoes in particular by their propagation trajectory, and by the orientation of their wave fronts during their propagation. In other words, at least one of the following two conditions is satisfied:

[0064] • the second direction in emission is different from the first normal direction in emission, and

[0065] • the second direction in reception is different from the first normal direction in reception.

[0066] Thus, at least two pairs of wavefront directions are formally associated with the same point P located inside the bone, these pairs of different directions characterizing different trajectories of emitted ultrasonic waves and of received ultrasonic echoes passing through this point P. As will be seen below, the probe can use more than two pairs of wavefront directions at step 100.

[0067] As will be seen in more detail later, the directions normal to the wavefronts discussed above may be directions in two-dimensional space or three-dimensional space. Furthermore, these directions may be indicated by data in various forms, including angular data or vectors. For example, when considering directions in a plane, the first direction in transmission may be indicated by a first phase angle in transmission, and the first direction in reception may be indicated by a first phase angle in reception.

[0068] 2.2) Reconstruction of bone videos from ultrasound echoes

[0069] In a reconstruction step 102 known from the state of the art, the imaging device 4 uses the ultrasound echoes received by the probe to reconstruct raw videos showing the interior of the bone.

[0070] Each raw video generated by the imaging device includes a succession of images showing the interior of the bone at different times. When particles move inside the observed bone, for example red blood cells, these particles can be represented at different locations in different frames of the same video.

[0071] Each image represents a layer of bone extending in a plane defined by two axes X and Z (indicated in Figure 2).

[0072] In particular, the imaging device 4 generates a first raw video showing the interior of the bone at point P, from the first ultrasound echoes.

[0073] Additionally, the imaging device generates a second raw video showing the interior of the bone at point P, from the second ultrasound echoes.

[0074] Each raw video generated in the reconstruction step 102 is stored in the memory 12 (in particular the first raw video and the second raw video).

[0075] Likewise, each pair of angles used by the probe in the probing step 100 is stored in the memory 12 (in particular the first pair of angles and the second pair of angles). This storage can be carried out before or after the probing step 100 implemented by the probe 2. The determination of these pairs of angles is known to those skilled in the art.

[0076] 2.3) Estimation of particle displacement in the bone The estimation device 6 implements a method for estimating particle displacement in the bone. This method comprises the following steps, relating to Figure 4.

[0077] In a step 201, the estimation device obtains data associated with different ultrasonic waves, and this data reveals the orientation of the wavefronts of the associated waves and their echoes.

[0078] In particular, in step 201, the estimation device obtains first data associated with the first ultrasonic waves, the first data indicating the first direction in transmission and the first direction in reception. The estimation device further obtains second data, the second data indicating the second direction in transmission, and the second direction in reception. The second data are at least partly different from the first data.

[0079] In a step 202, the processor 10 obtains at least one ultrasonic wave phase velocity in the bone. It will be seen below that the number of velocities obtained during this step can vary, depending on the embodiment considered.

[0080] In a step 203, the processor 10 calculates phase variations at point P, between two images coming from different videos.

[0081] In particular, the processor 10 calculates in step 203 a first phase variation at point P between two first images taken directly or indirectly from the first raw video. This calculation is a step known in the state of the art.

[0082] Furthermore, the processor calculates a second phase variation at point P, between two second images separated by the same time gap as the first two images discussed previously. The second two images are taken directly or indirectly from the second raw video.

[0083] In reality, several phase variations (including the first phase variation A and the second phase variation are calculated by the processor for a pixel of fixed coordinates in images (including the first two images and the second two images), this pixel imaging the point P discussed previously. We can therefore say that the first phase variation and the second phase variation are calculated at point P.

[0084] In a step 204, the processor 10 calculates a particle displacement U at point P. This displacement U is a vector U with several components. The displacement U is calculated by the processor from the following data:

[0085] • the time frequency f0, • the first data and the second data obtained in step 201,

[0086] • the first phase variation and the second phase variation A^n calculated in step 203, and

[0087] • each ultrasonic wave phase velocity in the bone, obtained in step 202.

[0088] In a subsequent step, the processor can calculate a particle velocity vector at point P, by dividing the displacement vector U by the time difference between the two frames of the first video (corresponding to the time difference between the two frames of the second video).

[0089] This velocity vector can then be displayed superimposed on an image of the interior of the bone by the display screen 8 (the point of origin of this vector being located at the pixel of this image which shows the point P discussed previously).

[0090] All the preceding steps are repeated for several points located inside the bone, imaged in different pixels of the videos considered.

[0091] In the following, we will begin by describing a traditional approach for estimating particle movements in a medium, before detailing different embodiments of the method 104, which differ from this traditional approach.

[0092] 2.3.1) Traditional approach: isotropic elastic medium, 2D displacement, processing based on raw videos

[0093] A known method consists of implementing steps 201 to 204 on images showing soft tissue only (i.e. no bones). In this known method:

[0094] • the first two frames belong to the first raw video;

[0095] • the second two images belong to the second raw video;

[0096] • the displacement U is a 2D displacement vector, i.e. with two components: a displacement component U z parallel to the Z axis, and a displacement component U xparallel to the X axis.

[0097] Furthermore, in this first embodiment, the processor assumes in the calculation step 204 that the medium observed in the videos is isotropic, as illustrated in FIG. 5a. For this, an ultrasonic wave phase velocity c0 in the medium crossed is stored in the memory 12, assumed to be the same for any direction of wave propagation. This velocity is determined beforehand using a method known to those skilled in the art.

[0098] In the first embodiment, the first data comprises: • a phase angle fa of the first ultrasonic waves during their propagation in the medium crossed, before reaching point P. This phase angle fa indicates the first direction in emission.

[0099] • a phase angle of the first ultrasonic echoes, during their propagation in the medium crossed. This phase angle indicates the first direction in reception.

[0100] Furthermore, the second data includes:

[0101] • a phase angle η2 of the second ultrasonic waves during their propagation in the medium, before reaching point P. This phase angle fa indicates the second direction in emission.

[0102] • a phase angle μ2 of the first ultrasonic echoes, during their propagation in the medium. This phase angle μ2 indicates the second direction in reception.

[0103] In this embodiment, each of these phase angles is considered to be equal to the group angle of the corresponding wave or echo. In other words, we have: Or :

[0104] • θ1 is the group angle of the first ultrasonic waves,

[0105] • φ1 is the group angle of the first ultrasonic echoes,

[0106] • θ2 is the group angle of the second ultrasonic waves, and

[0107] • φ2 is the group angle of the second ultrasonic echoes.

[0108] These equalities between group angle and phase angle come from the fact that the medium crossed by the waves has isotropic elasticity.

[0109] In this known method, the calculation carried out in step 204 comprises a resolution of the following matrix equation by the processor 10, in which these two components are U z and U x are unknowns:

[0110] Thus, only one phase velocity is involved in this calculation. 2.3.2) Implementation 1: bone assumed to be an anisotropic elastic medium, 2D displacement, processing based on raw videos

[0111] In a first embodiment of the estimation method 104:

[0112] • the first two frames belong to the first raw video;

[0113] • the second two images belong to the second raw video;

[0114] • the displacement U is a 2D displacement vector, i.e. with two components: a displacement component U z parallel to the Z axis, and a displacement component U x parallel to the X axis.

[0115] The first embodiment differs from the known method discussed previously in that the medium traversed contains a bone, and the processor assumes that the bone is an elastically anisotropic medium, as illustrated in Figure 5b.

[0116] In the presence of a bone, the image reconstruction must correct the refraction effect appearing at the interface between the bone and the surrounding soft tissue. An ultrasound beam changes its direction when it enters or leaves a bone, as illustrated in Figure 5b. Such an image reconstruction is known to those skilled in the art; it involves tracing ultrasound rays. The result of this image reconstruction provides in particular the group angles in emission and reception at each point of the image. These group angles correspond to the angle of the last portion of the ultrasound beam which reaches a point P in emission and to the angle of the first portion of the ultrasound beam reflected by a point P in reception.

[0117] In the first embodiment, the first data and the second data comprise the same phase angles than in the first embodiment.

[0118] On the other hand, as we assume in the first embodiment that the bone is an elastically anisotropic medium, there is no longer equality of phase angles et the group angles respectively.

[0119] For example, phase angles aforementioned can be determined from the group angles of the corresponding waves or echoes, and from a bone anisotropy model known to those skilled in the art.

[0120] The equation below is a model illustrating the relationship between the group angle θ of a wave, and the phase angle η of that wave, and the phase velocity v of that wave. In this equation, v depends on the phase angle η, hence its partial derivation.

[0121] This equation can be solved to determine:

[0122] • the phase angle η1 from the group angle θ1,

[0123] • the phase angle η2 from the group angle θ2,

[0124] • the phase angle μ1 from the group angle φ1, and

[0125] • the phase angle μ2 from the group angle φ2.

[0126] This determination of the phase angles from group angles can be implemented by the processor 10 during step 201. Alternatively, the phase angles are determined by another piece of equipment, then supplied to the estimation device 6. In the first embodiment, the processor 10 also obtains different phase speeds of ultrasonic waves in the bone. These phase speeds are no longer equal to a single speed c0 as was the case in the first embodiment. Thus, the phase speeds in the following directions are obtained by the processor 10:

[0127] • the first direction in emission,

[0128] • the first direction in reception,

[0129] • the second direction in emission,

[0130] • the second direction in reception.

[0131] In this embodiment, we will consider that the waves arriving at point P are compression waves; their phase velocity is noted v p .

[0132] To determine these phase speeds, the processor 10 or other equipment can use a bone anisotropy model known to those skilled in the art, formed by a mathematical function, for example for a compression wave whose phase speed is noted v p This mathematical function allows to calculate, from a phase angle, an ultrasonic wave phase velocity in the bone in a direction indicated by this phase angle.

[0133] The ultrasonic wave phase velocities can therefore be as follows, when such a bone anisotropy model is used

[0134] An anisotropy model that can be used by those skilled in the art to determine these phase velocities is described in the document “Measuring anisotropy of elastic wave velocity with ultrasound imaging and an autofocus method: application to cortical bone.”, Guillaume Renaud, Pierre Clouzet, Didier Cassereau, Maryline Talmant, published in November 2020. This anisotropy model is as follows: Or :

[0135] • α0 denotes a propagation speed of a compression wave in the bone in the direction in which the propagation speed is maximum.

[0136] • β0 designated a propagation speed of a so-called vertically polarized shear wave in the bone in the direction of maximum propagation speed of a compression wave, or a direction normal to it.

[0137] • δ* denotes an elastic anisotropy parameter of the bone.

[0138] • e denotes another elastic anisotropy parameter of the bone, representative of a difference between the maximum propagation speed in the bone of a compression wave and the minimum propagation speed in the bone of a compression wave, typically observed in a direction normal to the direction of maximum propagation speed of a compression wave.

[0139] The four parameters listed above are called Thomsen parameters, because they were proposed by L. Thomsen in the paper entitled “Weak elastic anisotropy”, published in 1986.

[0140] Another anisotropy model that can be used by those skilled in the art to determine these phase velocities, also proposed by L. Thomsen in 1986, is the following: Or

[0141] • V os1 is the propagation speed of compression waves in the bone in the direction for which the propagation speed is maximum,

[0142] • vos2 is the propagation speed of compression waves in the bone in the direction for which the propagation speed is minimal,

[0143] • ξ is the anisotropy parameter of the bone,

[0144] • η is a phase angle, defined with respect to the direction for which the propagation speed is minimal, is a phase speed of compression waves in the bone corresponding to the phase angle fa

[0145] In the first embodiment, the calculation performed in step 204 involves the phase velocities of ultrasonic waves in the bone , and not a single speed c0 as is the case in the first embodiment.

[0146] The calculation 204 comprises in the first embodiment a resolution of the following matrix equation by the processor 10, in which the two components U z and U x are unknowns:

[0147] Assuming here that bone is an anisotropic medium is more faithful to reality. Consequently, the estimation of particle displacement is more accurate in the first embodiment than in the known method, the principles of which are recalled in section 2.3.1.

[0148] 2.3.3) Displacement calculation based on a larger number of transmit-receive angle pairs / 3D displacement

[0149] In the embodiments described above, a displacement at point P is calculated from only two phase variations respectively associated with first and second data in the form of pairs of phase angles This is sufficient to determine the two unknowns which are the two U components z and U x .

[0150] However, in other embodiments, additional data may be obtained by the estimation device in step 201, resulting in the calculation of variation of additional phases in step 203, which are then used to calculate a particle displacement in the bone in step 204.

[0151] Generally, the probe can emit ultrasonic waves according to M different phase angles in transmission and according to N different phase angles in reception. which gives rise to NM pairs of angles NM phase variations at point P are then calculated.

[0152] The calculation of the first embodiment can therefore be generalized to the following equation:

[0153] Similarly, the calculation of the first embodiment can therefore be generalized to the following equation, involving NM different phase speeds:

[0154] These embodiments involve the prior determination of NM ultrasonic wave phase velocities (one velocity per angle and per angle fa).

[0155] These embodiments use excess data to determine two unknowns. This excess data nevertheless has the advantage of providing a displacement estimate that is more robust to noise.

[0156] The method can be generalized to allow the calculation at step 204 of a displacement in a three-dimensional space where the displacement to be estimated has three unknown components Ux, Uy and Uz. It then becomes easier to describe the orientation of the wavefront by the unit vector normal to the surface of the ultrasonic wavefront, E(Ex,Ey,Ez) in emission and R(Rx,Ry,Rz) in reception, rather than with a phase angle. To estimate the three components of the displacement in the three spatial dimensions called x,y and z, it is then necessary to use at least three pairs of emission and reception directions. These three pairs of emission and reception directions would then be defined by the pairs of unit vectors (E1,R1), (E2,R2) and (E3,R3).

[0157] As for a two-dimensional space, this system of three linear equations with three unknowns can be extended to an overdetermined system of equations using M directions in transmission and N directions in reception, in order to obtain a more noise-robust estimate of the displacement.

[0158] 2.3.4) Pre-filtering of videos by direction of movement In other embodiments, for all m and for all n, the two images leading to the phase variation do not belong to the raw video associated with the angle pair but belong to a filtered video generated during an additional step of decomposition 200 implemented by the processor 10. This decomposition step 200, optional but very advantageous, is represented in dotted lines in figure 4.

[0159] Referring to Figure 6n in decomposition step 300, the processor decomposes the raw video associated with the angle pair into K first filtered videos, and this for all m and for all n.

[0160] The 300 decomposition of the raw video associated with the angle pair ( includes the following sub-steps.

[0161] The processor applies to the raw video associated with the pair of angles a transformation, so as to generate a transform (step 300). The transform has the particular property of including information relating to movements of particles in the bone in K different directions, and which can be distinguished from each other.

[0162] The processor applies filtering to the transform, so as to produce K filtered transforms. Each filtered transform selectively includes particle displacement information in the bone in one of the K directions, to the exclusion of all other particle displacement directions.

[0163] The processor then applies an inverse transform to each filtered transform, so as to obtain the first K filtered videos. The first K filtered videos contain different and complementary movement information.

[0164] In particular, the transformation applied in step 300 is a Fourier transform, and the transformation applied in step 304 is an inverse Fourier transform.

[0165] As an illustration, consider an example of the implementation of decomposition 200 in which K=2 is chosen. The transform then comprises:

[0166] • information on particle movement in the bone in a first direction (for example upwards), and

[0167] • information on particle movement in the bone in a second direction opposite to the first direction (for example downwards).

[0168] In this embodiment, the processor can produce at step 302: a filtered transform comprising the displacement information in the first direction, but not the displacement information in the second direction; and • a first complementary filtered transform, comprising the displacement information in the second direction, but not the displacement information in the first direction.

[0169] Then, two first filtered videos are obtained by applying the inverse transformation to these two filtered transforms.

[0170] Alternatively, K=4 can be chosen. The first transform then includes:

[0171] • information on particle movement in the bone in a first direction, and

[0172] • information on particle movement in the bone in a second direction opposite to the first direction.

[0173] • information on particle movement in the bone in a third direction perpendicular to the first direction.

[0174] • information on particle movement in the bone in a fourth direction opposite to the third direction.

[0175] Figure 7 represents an embodiment of the decomposition with K=4, and using a Fourier transform. On the left of Figure 7, a raw video is represented in the form of a succession of images associated with different times. The four directions of movement considered are movements in two mutually perpendicular diagonal directions (top left direction, top right direction, bottom left direction, bottom right direction). With such a division, the Fourier transform obtained in step 300 comprises, for a given temporal frequency, four quadrants respectively containing the movement information in the four aforementioned directions. In step 302, a mask is applied to the Fourier transform, making it possible to select one quadrant out of the four, for example the quadrant corresponding to the top right direction of movement. On the right of Figure 7 is represented the filtered video resulting from this filtering and the subsequent inverse transformation.

[0176] As previously indicated, the decomposition step 200 is implemented for all m and for all n, that is to say for each raw video associated with a pair of angles so as to produce K associated filtered videos for a pair of angles In total, MNK filtered videos are therefore produced.

[0177] Then, for all m and for all n, the processor selects a filtered video among the K filtered videos associated with the pair of angles MN filtered videos are therefore selected. The video MNs filtered and then selected by the processor all result from filtering in the same direction of particle movement (for example the first direction of movement mentioned above).

[0178] Each filtered and then selected video then gives rise to the calculation of a phase variation as indicated previously.

[0179] Filtered videos are much more readable images than the raw videos originally generated by the imaging device. Thus, applying steps 203 and 204 to images belonging to these filtered videos improves the accuracy of the estimated displacement.

[0180] Furthermore, it is possible to calculate up to K-1 additional displacements at point P by repeating the calculation steps for frames from the filtered videos that have not been selected so far.

[0181] 3) Results and benefits

[0182] 3.1. Advantages conferred by the first embodiment, compared to the traditional approach

[0183] Figure 8 shows an example of a blood vessel in a bone in which particles are moving in an oblique direction at an angle of 8.13 degrees to its outer surface of the bone. The true speed of these particles is 7.07 centimeters per second.

[0184] The implementation of the method according to the first embodiment detailed in section 2.3.2 and according to the traditional approach set out in section 2.3.1 makes it possible to produce particle displacements, from which particle velocity vectors can be deduced, as indicated previously.

[0185] As shown in Figures 9a and 9b, the norm and direction of these estimated velocity vectors are affected by errors compared to the "true" velocity vector of the particles. However, it can be seen that the first embodiment makes it possible to obtain displacements affected by smaller norm and direction errors than with the traditional approach.

[0186] 3.1. Advantages of filtering compared to the traditional approach

[0187] On the left of Figure 10 is shown a section of a fictitious bone comprising particles moving in four directions, in two directions forming an X. These particles intersect at a central intersection (center of the X).

[0188] In the middle of Figure 10 is shown a simulated raw image of this section that would be reconstructed by the imaging device 4, based on ultrasound echoes reflected by the fictitious bone at this section. The arrows shown on the simulated raw image represent particle velocity vectors calculated at different points, without filtering.

[0189] On the right of Figure 10 is shown a filtered image of this same section which is obtained by applying the filtering according to step 200 to the simulated raw image (the direction of movement retained in the filtered image is a direction of upward particle movement). The arrows shown on this filtered image represent particle velocity vectors calculated at different points, with prior filtering in the upward direction of movement). Then the estimation of the velocity vectors is repeated by selecting the downward direction of movement. In other words, in this embodiment, we have K=2. It can be seen that the simulated raw image contains a certain number of vectors having aberrant orientations, in particular at the central intersection. This is due to the fact that the spatial resolution of the ultrasound system is not sufficient to spatially distinguish the different vessels.Thanks to the directional filtering in the "up" direction then in the "down" direction, the velocity vectors that could be determined are much less aberrant.

Claims

DEMANDS 1. A method for estimating particle displacement in bone, the method comprising the steps of: • obtaining (201) first data associated with first ultrasonic waves emitted at a time frequency (f0), the first data indicating: o a first direction of emission, the first direction of emission being normal to a wavefront of the first ultrasonic waves towards a point located inside the bone, during their propagation in the bone, and o a first direction of reception, the first direction of reception being normal to a wavefront of first ultrasonic echoes obtained by reflection of the first ultrasonic waves at the point, during their propagation in the bone, • obtaining (201) second data associated with second ultrasonic waves emitted at the time frequency (f0), the second data being at least partly different from the first data, the second data indicating: o a second direction in emission, the second direction in emission being normal to a wavefront of the second ultrasonic waves towards the point, during their propagation in the bone, and o a second direction in reception, the second direction in reception being normal to a wavefront of second ultrasonic echoes obtained by reflection of the second ultrasonic waves at the point, during their propagation in the bone, • obtaining (202) ultrasonic wave phase velocities in bone in the following directions: o the first direction in emission, o the first direction in reception, o the second direction in emission, o the second direction in reception, • Obtaining a first video showing the bone in focus, the first video being derived from the first ultrasound echoes, and obtaining a second video showing the bone in focus, the second video being derived from the second ultrasound echoes, • calculation (203) of a first phase variation at the point between two images of the first video, and a second phase variation at the point between two images from the second video, • calculation (204) of a particle displacement at the point from: o the time frequency (f0), o the first and second data points, o the first and second phase changes o the phase velocities of ultrasound waves in bone.

2. A method according to the preceding claim, further comprising the following steps: • transformation of a first raw video from the first ultrasonic echoes into a first transformed video, the first transformed video including o first information on particle movement in the bone in a first direction, and o second information on particle movement in the bone in a second direction opposite to the first direction, • filtering the first transform to obtain a first filtered transform including the first pieces of information but not including the second pieces of information, • the first video being generated by applying an inverse transformation to the first filtered transformation.

3. A method according to the preceding claim, further comprising the following steps: • transformation of a second raw video from the second ultrasonic echoes into a second transformed video, the second transformed video including o third pieces of information on particle movement in the bone in the first direction, and o fourth pieces of information on particle movement in the bone in the second direction, • Filtering the second transform to obtain a second filtered transform that includes the third pieces of information but excludes the fourth pieces of information. • the second video being generated by applying an inverse transformation to the second filtered transformation.

4. A method according to the preceding claim, further comprising the following steps: filtering the first transform so as to obtain a first filtered complementary transform comprising the second pieces of information but not the first pieces of information, • generation of a first complementary video showing the bone in focus, by applying an inverse transformation to the first filtered complementary transform, • calculation of a first complementary phase variation at the point between two images of the first complementary video, • filtering the second transform to obtain a second complementary filtered transform including the fourth pieces of information but not the third pieces of information, • generation of a second complementary video showing the bone in focus, by applying an inverse transformation to the second filtered complementary transform, • Calculation of a second complementary phase variation at the point between two images of the second complementary video, • Calculation of a complementary particle displacement at the point from: o the time frequency (f0), o the first and second datasets, o the first phase change and the second phase variation and o the phase velocities of ultrasound waves in bone.

5. A method according to any one of the preceding claims, comprising the following steps: • obtaining third data points associated with third ultrasonic waves emitted at the time frequency (f0), the third data points being at least partly different from the first and second data points, the third data points indicating: o a third direction in emission, the third direction in emission being normal to a wavefront of the third ultrasonic waves towards the point, during their propagation in the bone, o a third direction in reception, the third direction in reception being normal to a wavefront of third ultrasonic echoes obtained by reflection of the third ultrasonic waves at the point, during their propagation in the bone, • obtaining a third video showing the bone in focus, the third video being derived from the third ultrasound echoes, • calculation of a third phase variation at the point between two images of the third video, • obtaining additional ultrasound wave phase velocities in bone in the following directions: o the third direction in emission, o the third direction in reception, in which the displacement is also calculated from the third data, the third phase variation and the ultrasound wave phase velocities in additional bone.

6. A method according to the preceding claim, further comprising the following steps: • transformation of a third raw video from the third ultrasonic echoes into a third transformed video, the third transformed video including o fifth pieces of information on particle movement in the bone in the first direction, and o sixth pieces of information on particle movement in the bone in the second direction, • filtering the third transform to obtain a filtered third transform including the fifth pieces of information but not the sixth pieces of information, • the third video being generated by applying an inverse transformation to the third filtered transformation.

7. A method according to any one of claims 2 to 6, wherein the transformation is a Fourier transform.

8. A method according to any one of the preceding claims, wherein the time frequency (f0) has a value between 0.1 MHz and 10 MHz.

9. A method according to the preceding claims, wherein the point is a point of passage for red blood cells.

10. Computer-readable memory storing computer-executable instructions for carrying out the steps of the process according to any one of the preceding claims.

11. Device (6) for estimating particle displacement in a bone, device (6) comprising: a memory (12) configured to store: o of the first data associated with the first ultrasonic waves emitted at a temporal frequency (f0), the first data indicating: ■ a first emission direction, the first emission direction being normal to a wavefront of the first ultrasonic waves towards a point located inside the bone, during their propagation in the bone, and ■ a first direction of reception, the first direction of reception being normal to a wavefront of first ultrasonic echoes obtained by reflection of the first ultrasonic waves at the point, during their propagation in the bone, o of the second data associated with second ultrasonic waves emitted at the time frequency (f0), the second data being at least partly different from the first data, the second data indicating: ■ a second emission direction, the second emission direction being normal to a wavefront of the second ultrasonic waves towards the point, during their propagation in the bone, and ■ a second direction in reception, the second direction in reception being normal to a wavefront of second ultrasonic echoes obtained by reflection of the second ultrasonic waves at the point, during their propagation in the bone, of phase velocities of ultrasonic wave in the bone in the following directions: ■ the first direction in transmission, ■ the first direction in reception, ■ the second direction in transmission, ■ the second direction in reception, o a first video showing the bone in focus, the first video being from the first ultrasound echoes, and a second video showing the bone in focus, the second video being from the second ultrasound echoes, • at least one processor (10) configured to: o calculate a first phase change at the point between two images From the first video, calculate a second phase variation at the point between two images From the second video, calculate the displacement of a particle at point A starting point from: ■ the temporal frequency (f0), ■ the first data and the second data, ■ the first phase change (and the second change in phase and ■ the phase velocities of ultrasound waves in bone.

12. Ultrasound system (1) comprising: • a probe (2) configured to: o emit first ultrasonic waves at a reference frequency (f0) towards a point located inside a bone, o receive first ultrasonic echoes, the first ultrasonic echoes being obtained by reflection of the first ultrasonic waves at the point, o emit second ultrasonic waves at the reference frequency (f0) towards the point, o receive second ultrasonic wave echoes, the second ultrasonic echoes being obtained by reflection of the second ultrasonic waves at the point, • an imaging device (4) configured to: o generate a first video showing the bone in focus from the first ultrasound echoes, o generate a second video showing the bone in focus from the second ultrasound echoes, • a device (6) for estimating the displacement of particles in bone according to the preceding claim.

Images