Apparatus and method for estimating a velocity field

Abstract

The present invention relates to an apparatus for estimating the velocity of at least one scatterer in a medium, the apparatus comprising: - a generator for generating an excitation signal; - a virtual transducer (T1 to T2) that converts the excitation signal into an Archimedes spiral wave; n ) a curved array of Sound wave radiation angle (α i ), and the curvature of the curved array of virtual transducers is determined by a reference center (O) and a radius of curvature (r n ) and a curved array for receiving, from the at least one scatterer, scattered signals generated by scattering of Archimedes spiral waves emitted from the curved array of virtual transducers; and a drive and processing unit (U) for estimating the velocity of said at least one scatterer; c ) The axial and lateral velocity components are determined by the wave radiation angle (α i ), the geometry of the curved array of transducers, and the set of local wavefront directions (α) of the Archimedean spiral waves as a function of the distance (r) to the reference center (O). eq,i ), and each local wavefront direction satisfies the following equation: [Equation 1] TIFF2023538764000056.tif15170

Description

[Technical Field]

[0001] The present invention relates to a method and apparatus for estimating the velocity vector of at least one scatterer (a remotely sensed object or group of objects) in a medium using either sound (particularly ultrasound) or electromagnetic radiation.

[0002] More particularly, the present invention relates to a vector flow imaging (VFI) method and apparatus that is a useful diagnostic tool that performs angle-independent flow estimation and provides the clinician with axial and lateral velocity components.

[0003] The motion of the scatterer is determined by emitting and receiving a pulsed wave field using an array of transducers. By using multiple pulse emissions, the motion of the intermediate pulses can be estimated, and the estimated motion and the time between pulses provide the velocity. [Background technology]

[0004] Non-invasive visualization and measurement of flow dynamics using ultrasound (US) is considered to be primarily clinically important, for example, to highlight abnormal vascular conditions.

[0005] Standard techniques, such as color flow imaging, continuous wave Doppler, and pulsed wave Doppler, provide one-dimensional views and measurements of flow along the direction of the ultrasound beam, but have inherent methodological drawbacks due to their dependence on the angle between the direction of flow and the direction of the US beam.

[0006] This can be problematic, for example, when tortuous vasculature can occur at the carotid bifurcation. It can also lead to a polar field of view, e.g., a disturbing intuitive velocity field in the case of a convex probe geometry for abdominal clinical applications.

[0007] Vector flow imaging (VFI) methods solve this problem by providing both the axial and transverse components of velocity flow. Various techniques, such as multi-beam Doppler, frame-to-frame speckle tracking, or transverse vibration, have been described in the literature.

[0008] With the widespread adoption of ultrafast US imaging in the general public, the multi-beam method has attracted great interest in recent years. Indeed, this idea takes advantage of both the high directivity and omnidirectional aspects of plane waves to derive vector flow information from the projection along the direction of the transmit beam at high frame rates, thus reducing the possibility of aliasing.

[0009] Although VFI techniques have been extensively studied due to their ability to outline detailed depictions and visual quantification of complex flow behavior within a patient's vascular system, new VFI methods are needed that are more suitable for deep vascular imaging, e.g., portal vein imaging, where imaging is typically performed with a curved array of transducers.

[0010] It is an object of the present invention to provide an apparatus and method suitable for sector imaging. Summary of the Invention

[0011] For this purpose, the invention proposes a device for estimating the velocity of at least one scatterer in a medium, said device comprising: - a generator for generating an excitation signal; - a curved array of virtual transducers that converts the excitation signal into an Archimedean spiral wave, Sound wave radiation angle α i and the curvature of the curved array of virtual transducers is defined by a reference center O and a radius of curvature r n and a curved array for receiving, from the at least one scatterer, scattered signals generated by scattering of the Archimedean spiral wave emitted from the curved array of virtual transducers; and - a driving and processing unit for driving the curved array of generators and virtual transducers and estimating the velocity of at least one scatterer; The axial and transverse velocity components (of the beam) are determined by the sound radiation angle α i , the geometry of the curved array of virtual transducers, and the set of local wavefront directions α of the Archimedean spiral wave as a function of the distance r to the reference center O. eq,i and each local wavefront direction satisfies the following equation:

number

[0012] In the context of the present invention, the term "virtual transducer array" is understood to mean a set of points defining a geometry selected as a function of the delay law applied to a real array of transducers, such that the points of said set radiate a helical wavefront.

[0013] A virtual array of transducers is a set of points in the medium arranged along a circular arc. The properties of the helical wavefront (in particular the initial emission angle) are selected for this array of virtual transducers. A delay law is then derived that applies to the real transducer array. In the framework of the wavefront approximation, everything happens as if the waves were emitted by the virtual array of transducers.

[0014] Preferred, but non-limiting aspects of the device according to the present invention are as follows. - The drive and processing unit a first set of excitation signals that enable acquisition of a first set of scattering signals; and a second set of excitation signals that allows for the acquisition of a second set of scattering signals; A series of at least two excitation signals with a fixed repetition interval T P and a controller for driving a curved array of virtual transducers that converts the at least two series of excitation signals into Archimedes spiral waves. - The drive and processing unit receiving the first and second sets of scattered signals generated by scattering of the Archimedean spiral wave; Each group of receiving beams has an acoustic radiation angle α i and the reception angle β j delaying and summing the first set of scattered signals to generate a first group of receive beams each having a Each group of receiving beams has an acoustic radiation angle α i and the reception angle β j The receiver may further comprise a beamformer that delays and sums the second set of scattered signals to generate a second group of receive beams, each having a respective Each of the first and second groups of receive beams may include a plurality of images, each image having an acoustic emission angle α i and reception angle β j and the driving and processing unit adjusts the acoustic radiation angle α so that the velocity field is estimated for each pair of different spiral directions and receive beam directions. i and reception angle β j For any given pair of images of the first and second groups of receive beams having the same pair of Doppler signals, the processor further comprises a processor for Doppler processing the first and second groups of receive beams. - The processor measures the sound wave radiation angle α i and reception angle β j for each pair of images of the first and second groups of receive beams having the same pair of: estimating a displacement field for each corresponding pixel between images of a given pair of images; estimating a Doppler frequency shift for each pixel for said given pair of images from the displacement field; The method may be configured to perform the following steps: The processor may be adapted to perform an algebraic inversion step in which several projections of the velocity field and known directions of the several projections are used to estimate radial and azimuthal components of the velocity field. The processor may be adapted to estimate axial and lateral velocity components from radial and azimuthal components of the velocity field.

[0015] The present invention further relates to a method for estimating the velocity of at least one scatterer in a medium, the method comprising: - generating an excitation signal; - converting said excitation signal into an Archimedes spiral wave; - Sound wave radiation angle (α i radiating the Archimedes spiral waves in a plurality of predetermined propagation directions defined by a set of radii of curvature (r n ) to be determined, - receiving a scattered signal generated by scattering of the Archimedean spiral wave emitted from the curved array of virtual transducers; and - estimating the velocity of at least one scatterer; During the estimation process, the axial and transverse velocity components (of the beam) are calculated based on the sound emission angle (α i ), the geometry of the curved array of transducers, and the set of local wavefront directions (α) of the Archimedean spiral waves as a function of the distance (r) to the reference center (O). eq,i ), and each local wavefront direction satisfies the following equation:

number

[0016] A preferred, but non-limiting embodiment of the method according to the present invention is as follows. - Advantageously, generating an excitation signal; a first set of excitation signals that enables acquisition of a first set of scattered signals (by emitting said first set of excitation signals and receiving said first set of scattered signals); and a second set of excitation signals that enables acquisition of a second set of scattered signals (by emitting said second set of excitation signals and receiving said second set of scattered signals); A series of at least two excitation signals with a fixed repetition interval T P generating the compound with The converting step may include converting the at least two series of excitation signals into Archimedes spiral waves. - estimating the velocity of at least one scatterer receiving the first and second sets of scattered signals generated by scattering of the Archimedean spiral wave; Each group of receiving beams has an acoustic radiation angle α i and the reception angle β j delaying and summing the first set of scattered signals to generate a first group of receive beams each having a respective Each group of receiving beams has an acoustic radiation angle α i and the reception angle β j delaying and summing the second set of scattered signals to generate a second group of receive beams each having a Each of the first and second groups of receive beams may include a plurality of images, each image having an acoustic emission angle α i and reception angle β j and estimating the velocity of at least one scatterer, each associated with a pair of The acoustic radiation angle α is used so that the velocity field is estimated for each pair of different spiral and receive beam directions. i and reception angle β j For any given pair of images of the first and second groups of receive beams having the same pair of Doppler processing, the method further includes Doppler processing the first and second groups of receive beams. The step of estimating the velocity of at least one scatterer includes estimating the velocity of the at least one scatterer by an acoustic radiation angle α. iand reception angle β j the following sub-steps for each pair of images of the first and second groups of receive beams having the same pair of: a sub-step of estimating a displacement field for each corresponding pixel between images of a given pair of images; a substep of estimating, from the displacement field, a Doppler frequency shift for each pixel for said given pair of images; It may further include: The step of estimating the velocity of the at least one scatterer may further comprise an algebraic inversion sub-step in which several projections of the velocity field and known directions of the several projections are used to estimate radial and azimuthal components of the velocity field. The step of estimating the velocity of the at least one scatterer may further comprise a calculation sub-step consisting of calculating axial and lateral velocity components from the radial and azimuthal components of the velocity field.

[0017] The present invention may be more fully understood upon consideration of the following detailed description of various embodiments in conjunction with the accompanying drawings. [Brief explanation of the drawings]

[0018] [Figure 1] 1 is a schematic diagram of an apparatus for estimating a velocity vector of at least one scatterer in a medium; [Figure 2] 1 is a schematic diagram of steps performed in a method for estimating the velocity vector of at least one scatterer in a medium; [Figure 3] FIG. 1 is a schematic diagram illustrating the acquisition of a Doppler ultrasound sequence. [Figure 4] FIG. 1 is a schematic diagram illustrating the processing of a sample of a Doppler ultrasound sequence. [Figure 5] FIG. 1 is a schematic diagram illustrating a convex array imaging configuration. [Figure 6] FIG. 1 is a schematic diagram showing a wavefront of an Archimedes spiral. [Figure 7] FIG. 1 is a schematic diagram of a convex array configuration. [Figure 8]Diagrams of Archimedes' spiral waves in various spaces. DETAILED DESCRIPTION OF THE INVENTION

[0019] Various examples of methods and apparatus according to the present invention will now be described with reference to the figures, in which like elements are designated with the same reference numerals.

[0020] 1. Apparatus for estimating the radial and azimuthal velocity of at least one scatterer in a medium - Patent Application 20070122997 An example of an apparatus according to the present invention is shown in FIG.

[0021] The apparatus is adapted to estimate the radial and azimuthal velocity of at least one scatterer in a medium, and in particular is configured with a program to perform one or more of the steps of the method described below.

[0022] The device comprises: - a generator for generating an excitation signal; - Virtual transducers T1 to T n a curved array of The excitation signal is converted into an Archimedes spiral wave, and each direction has its own sound wave radiation angle (α i radiating the Archimedes spiral wave in a plurality of predetermined propagation directions defined by a curved array configured to receive echoes resulting from scattering of the Archimedean spiral wave at at least one scatterer and convert the echoes into a set of scattered signals; a drive and processing unit, A controller that drives the generator and the curved array of virtual transducers; A beamformer that beamforms the set of scattered signals; a drive and processing unit including a processor that processes the set of beamformed scattered signals to determine the radial and azimuthal velocities of each scatterer;

[0023] 1.1. Curved array of virtual transducers Virtual transducers T1 to T n The curved array of <n>A set of ultrasonic transducers ( <n>(where > is an integer equal to or greater than 1). Each ultrasonic transducer may be made of a piezoelectric material (e.g., ceramic, silicon, ...) which is further covered on both sides by electrodes and on one side by some auxiliary layers such as a matching layer and a lens. The ultrasonic transducers may be linear or curved in configuration.

[0024] When arranged linearly, delay laws are applied to the transducers to enable the generation of ultrasound waves that follow a desired contour. In the following, the desired contour is referred to as "virtual transducers T1 to T2." n It is defined as a "curved array of

[0025] Virtual transducers T1 to T n The curved array is adapted to emit Archimedes spiral waves (defined in more detail below) that pass through the medium to be analyzed (such as the vascular system) and to receive acoustic echoes (i.e., ultrasound waves reflected by scatterers contained within the medium).

[0026] 1.2. Drive and Processing Unit Drive and processing unit U c communicates (wired or wirelessly) with the transducer. The driving and processing unit - Generators and virtual transducers T1 to T n driving a curved array of - Virtual transducers T1 to T n and processing the data acquired by the curved array of the .

[0027] Drive and processing unit U c may be comprised of one physical entity (or various physical entities) that may be integrated into the housing containing the curved array of virtual transducers, or may be located remotely from the curved array of virtual transducers.

[0028] For example, the drive and processing unit U c teeth, one (or several) controllers 11, which may be a smartphone and / or an electronic tablet (such as an IPAD) and / or a personal digital assistant (PDA), or of any other type known to those skilled in the art; - one (or several) computers 12 (beamformers, processors, etc.), such as personal computers and / or workstations; - one (or several) storage units 13 containing at least one memory such as random access memory (RAM) and / or read-only memory (ROM) and / or USB key It can be composed of:

[0029] In addition to storing acquired / processed data, the storage unit makes it possible to store programming code instructions intended to execute the steps of the method for estimating radial and azimuthal velocities described below.

[0030] 2. Method for estimating the radial and azimuthal velocities of at least one scatterer in a medium - Patent Application 20070122997 As shown in FIG. 2, a method for estimating the velocity of at least one scatterer in a medium includes the following steps. - at least two pulse-echo blocks are generated, said at least two pulse-echo blocks having a fixed repetition interval T P A Doppler ultrasound sequence generation process 10 operates as follows: where the sequence generation process comprises the following sub-processes for each pulse-echo block: Each direction has its own sound wave radiation angle (α i applying an excitation signal to a curved array of virtual transducers that converts the excitation signal into Archimedes spiral waves radiated in a plurality of predetermined propagation directions defined by a substep 120 of receiving echoes generated by scattering of said Archimedean spiral wave by at least one scatterer back to a curved array of virtual transducers, said curved array of virtual transducers converting said echoes into a set of backscattered signals; Reception angle (β j a substep 130 of beamforming the set of backscattered signals to generate a group of receive beams each having an acoustic emission angle (α i ) and reception angle (β j a sub-step 130, comprising: At least two pulse-echo blocks are used to extract the Doppler frequency shift. i ) and reception angle (β j a Doppler processing step 20, which is processed for any given pair of images of a group of receive beams having the same pair of A calculation step 30 in which the radial and azimuthal velocity fields are calculated from the entire set of pairs of different spiral directions and receive beam directions by using the entire set of Doppler frequency shifts.

[0031] 2.1. General Description 2.1.1. Doppler ultrasound sequence generation process: slow time / scan time / fast time samples The first step of the method consists of generating a Doppler sequence.

[0032] In the context of vector Doppler sequences, there are three relevant time scales that can be considered formally: - Fast time is the front-end sampling time scale adapted to the bandwidth of the pulse and the recording of the composite wavefront and echo propagation time, also known as time of flight, for a given field of view. - scan time is the time scale used to complete a set of projections of a given field of view; in the context of focused imaging, scan time is also the time scale when a left-right sweep of the imaging beam is performed; in the context of synthetic imaging, scan time corresponds to the acquisition of the entire synthetic aperture data set; in the context of vector Doppler, scan time also corresponds to the acquisition time scale of additional directional samples. - slow time is the time scale of pulse repetition at a selected pulse repetition frequency (PRF), and the slow time samples may constitute the statistical ensemble required to enable phase (or equivalent frequency) shift calculations and achieve Doppler velocity field estimation for each of the directional beams, and the total number of slow time samples used for Doppler estimation typically scales with the ensemble length (N EL ), and typically a minimum of two late time samples are required.

[0033] The above mentioned time scales are chosen according to the typical velocity of the scatterers so that the scatterers do not move between the successive acquisitions of two scanning time samples and of course two fast time samples.

[0034] The last two aforementioned time scales can be considered in a more continuous manner when using an interpolation scheme or a sliding window (eg, in the case of a uniform repartition of the scanning time samples).

[0035] With reference to FIG. 3, the vector Doppler sequence is P The signal consists of a plurality (at least two) of slow time samples 101, 102, 103 (i.e., pulse-echo blocks) generated periodically at

[0036] More specifically, the vector Doppler sequence is P N time intervals EL (The subscript "EL" stands for "ensemble length") late time samples 101, 102, 103.

[0037] Each of the slow time samples 101, 102, and 103 has a sound wave radiation angle α i The scan time samples 101, 102, 103 include a set of scan time samples (i.e., a collection of scattered signals) corresponding to the element raw data recorded sequentially by the transducer elements, corresponding to the tilted Archimedean spiral waves at (i=1, ..., N). In particular, each slow time sample 101, 102, 103 includes a set of images, each image corresponding to a given acoustic emission angle α i is obtained for (i=1, ..., N).

[0038] As mentioned above, the Doppler ultrasound sequence generation process is performed with a pulse repetition interval T P The method includes the following sub-steps, which are repeated periodically: - Each direction has its own sound wave radiation angle (α i a sub-step 110 of emitting Archimedes spiral waves in a plurality of predetermined propagation directions defined by - receiving and recording a set of N scan time samples (i.e., a collection of scattering signals); - Scanning time radio frequency or beamformed in-phase orthogonal data sets (i.e., a group of receive beams each having a receive angle) by using a receive angle (β j ) and beamforming each scan time sample.

[0039] As shown in Figure 4, the reception angle β j (j=1~M) (each, sound wave radiation angle α i The beamforming of N scanning time samples 101 (each associated with i=1 to N) is performed for each emission and reception angle pair (α i , β j ) to obtain M×N sets of beamformed IQ data 101a, 101b, 101c.

[0040] 2.1.2. Doppler Processing The second step of the method consists of Doppler processing of the late time samples 101, 102, 103 (ie pulse-echo blocks).

[0041] In particular, the at least one scatterer is moving between the acquisition of two successive slow time samples.

[0042] During the Doppler processing step, the pixel-by-pixel displacement of each moving scatterer is calculated by the same angular pair of emission / reception angles (α i , β j ) over slow time samples. This extraction can be performed using any state-of-the-art method and is described in point 2.2.4. This makes it possible to obtain the displacement field of each moving scatterer during the Doppler ultrasound sequence.

[0043] Emission and reception angles (α i , β j The pixel-by-pixel Doppler frequency shift for each pair of θ is estimated from the displacement field.

[0044] 2.1.3. calculation process The third step of the method is to use the Doppler frequency shift to determine the difference between the emission and reception angles (α i , β j ) pairs) to calculate the radial and azimuthal velocity fields of each scatterer.

[0045] More specifically, the calculation step includes the following substeps: - forming, for each radial coordinate, a Doppler linear operator relating the Doppler frequency shift to the radial and azimuthal velocity fields, such that the operator depends on the local wavefront angle of each transmitted Archimedean spiral wave; and - For each radial coordinate, a sub-step of solving the corresponding system of linear equations using standard linear algebraic methods to extract the radial and azimuthal velocity components.

[0046] 2.1.4. Advantages of the proposed method The main contribution of the proposed method is the use of Archimedes spiral waves to ensure the directionality of the radiation.

[0047] Indeed, it will be shown below that an Archimedean spiral wave emitted at a particular emission angle defines a wavefront whose local angle can be expressed as a function of the radial coordinate of the pixel of interest. In other words, the Archimedean spiral is highly directional in polar coordinates, similar to a plane wave in Cartesian coordinates, and this directivity can be exploited in VFI to estimate the radial and azimuthal velocity components.

[0048] The radial and azimuthal components are expressed in a polar coordinate system.

[0049] In a final step, a polar to Cartesian conversion can be performed to obtain the lateral and axial velocity components, which can then be expressed in a Cartesian coordinate system by polar to Cartesian scan conversion.

[0050] Essentially, another advantage is the use of Archimedes spiral acoustic radiation compared to other diverging acoustic radiation (including plane waves) in a convex probe configuration. For a virtual array of transducers that matches a real array of transducers, the Archimedes spiral is the best choice in terms of single transducer element directivity across the entire transducer array. As a result, the entire convex field of view can be utilized.

[0051] 2.2. Detailed Description Different aspects of the method according to the invention will now be described in more detail.

[0052] In the following, a curved array of virtual transducers T1 to Tn is defined as a probe with radius r (usually expressed as the convex radius of the probe). n The space between two adjacent virtual transducers is denoted as p, which is called the pitch.

[0053] 2.2.1. Radiation of Archimedean spiral wavefronts The radiation of an Archimedean spiral wavefront by a curved array of virtual transducers T1 to Tn is performed by applying a linear delay law profile to the virtual transducers.

[0054] More precisely, a curved array of virtual transducers T1 to Tn is formed with a radius r, a pitch (inter-element distance) p, and a sound speed c. n If the system is assumed to consist of n virtual transducers spaced along an arc of a circle, the linear delay profile is defined as:

number

[0055] The angle α is made the steering angle, so that each virtual transducer of the curved array emits a short ultrasonic wave after a delay given by the above equation.

[0056] 2.2.2. Archimedes spiral-based beamforming Once emitted, the wavefront propagates through the medium and becomes reflected when it experiences local changes in acoustic impedance, i.e., density and sound speed (scatterers), which are modeled through the tissue reflectivity function γ(r) at the considered target location r=[r,θ] in the tissue.

[0057] The scattered wave propagates back to the virtual transducer and thus the corresponding echo is recorded. The signal recorded by the i-th virtual transducer is denoted by m i(t) It is expressed as:

[0058] The beamforming process is performed by dividing the recorded signal m i is equivalent to reconstructing the estimated reflectivity of the medium γ(^)(r) from

[0059] The usual delay-and-sum (DAS) estimate is constructed as follows:

number

[0060] A polar coordinate system is adopted, where the origin O is located at the center of the curved array of virtual transducers T1 to Tn, so that the virtual transducers are i =[r n ,θ i ]. Here, as shown in Figure 5, r n represents the convex radius of the curved array of virtual transducers T1 to Tn. Using this coordinate system, the delay profile can be expressed as a function of transducer element coordinates:

number

[0061] The reception delay corresponds to a simple time-of-flight calculation, as follows, r j and the target position r considered:

number

[0062] The global transmit delay is defined to be the instant when the considered target location is first hit by the pulse wave emitted by any of the emitting transducer elements of the array, in other words, it is derived from minimizing both the transmit delay and the transmit flight time to the considered target location in the medium.

number

[0063] By expanding the terms and offsetting the constant delay with the new time origin, the minimization equation can be rewritten as:

number

[0064] The solution to the latter minimization is left to those skilled in the art. Additional details on the method are presented in the theory section (3.2.1). As a result, the global transmission delay to a point located at r = [r, θ] can be expressed as:

number

[0065] In the wavefront approximation, this equation can be viewed as a parametric equation for the transmitted wavefront.

[0066] To derive a method for performing vector flow imaging in polar coordinates, our idea is to identify a wave that is highly directional in polar space, similar to a plane wave in Cartesian space. The following proof shows that Archimedean spiral waves have this property of well-defined direction in polar space.

[0067] The direction of the wavefront is the direction in which the global transmit delay increases at its maximum (i.e., perpendicular to the direction in which it is constant). This direction can be determined unambiguously by calculating the transmit delay gradient with respect to polar coordinates. The global transmit delay gradient is calculated using the polar gradient formula:

number

[0068] The resulting gradient formula after simplification is:

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[0069] Formally, the concept of equivalent steering angle can be introduced using the following equation:

number

number

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[0070] Therefore, the formula for the global transmit delay gradient is given by: eq Shows.

[0071] As shown in FIG. 6, the Archimedean spiral wavefront W is highly directional in polar coordinates, similar to a plane wave in Cartesian coordinates.

[0072] Our idea is to exploit this directivity to extract the radial and azimuthal velocity components from their projections along the wavefront, as explained below.

[0073] 2.2.3. Archimedes spiral-based beamforming at a given receive angle The previous section shows that transmit directivity is achieved by tilted Archimedean spiral waves.

[0074] To achieve directionality in reception, we rely on techniques known in the literature and developed for vector flow imaging with linear arrays.

[0075] In one embodiment, the inventors propose the use of separate sub-apertures with desired angles of reception as described in the document by M. Tanter, J. Bercoff, L. Sandrin and M. Fink, October 2002, entitled "Ultrafast compound imaging for 2-D motion vector estimation: application to transient elastography", IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 49, no. 10, pp. 1363-1374.

[0076] In another embodiment, the data may be beamformed as described in the previous section and then the 2D spectrum of the beamformed data may be filtered according to a desired angle as proposed by Stahli et al. (See the document entitled "Improved forward model for quantitative pulse-echo speed-of-sound imaging," by P. Stahli, M. Kuriakose, M. Frenz, and M. Jaeger, December 2020, Ultrasonics, vol. 108, p. 106168).

[0077] where γ(^)(r,α) with β being the reception angle eq , β), the beamforming method allows for an increase in the size of the beamforming data cube.

[0078] 2.2.4. Displacement extraction and Doppler frequency shift estimation In US imaging, displacement extraction is performed by analyzing changes in the IQ or RF images along slow time.

[0079] Therefore, all techniques begin with the transmission / reception and beamforming of a set of IQ images, represented as slow time samples, typically acquired at a constant rate, represented as a pulse repetition frequency, called the slow time samples.

[0080] The slow time samples (γ i ) i∈NEL Many techniques have been developed in the literature to extract the Doppler frequency shift from the backscattered signal. Nevertheless, the various techniques all share the common idea of ​​tracking the translation of the recorded backscattered signal between successive pulses.

[0081] The different methods depend primarily on the nature of the received backscattered echoes (RF or IQ, narrowband or broadband).

[0082] Known techniques are generally based on the methods described by Angelsen (see the document by B.A. J. Angelsen, 1981, entitled "Instantaneous Frequency, Mean Frequency, and Variance of Mean Frequency Estimators for Ultrasonic Blood Velocity Doppler Signals," IEEE Transactions on Biomedical Engineering, vol. BME-28, no. 11, pp. 733-741, doi:10.1109 / tbme.1981.324853) and Kasai et al. (C. Kasai and K. Namekawa, 1985, entitled "Real-Time Two-Dimensional Blood Flow Imaging Using an Autocorrelation Technique," IEEE Transactions on Biomedical Engineering, vol. BME-28, no. 11, pp. 733-741, doi:10.1109 / tbme.1981.324853). This consists of calculating the phase shift using the lag-1 temporal autocorrelation R1 expressed as the Kasai autocorrelation (or 1D autocorrelation) as described by [Ultra-Speed ​​Symposium, doi:10.1109 / ultsym.1985.198654].However, other Doppler estimators known to those skilled in the art may equally be considered, such as, for example, 2D autocorrelators or crosscorrelators (now commonly known as Loupas estimators) (see the document by T. Loupas, J.T. Powers and R.W. Gill, 1995, entitled "An axial velocity estimator for ultrasound blood flow imaging, based on a full evaluation of the Doppler equation by means of a two-dimensional autocorrelation approach", IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, vol. 42, no. 4, pp. 672-688, doi:10.1109 / 58.393110).

[0083] In the following, we will detail the phase-based estimation method described by Kasai et al.

[0084] Formally, T P =1 / f P and time interval T P , N obtained during the pulse repetition period EL Consider that (ensemble length) consecutive late time samples are used, where f P is the pulse repetition frequency (PRF) and the Doppler phase shift ΔΦ∈R Nr×Nθ is estimated from the following formula:

number

[0085] Note that the ensemble length can be two consecutive frames. The estimated phase shift and Doppler frequency shift δf p are related by the following equation:

number

[0086] In addition, the velocity module projected along the propagation of the ultrasound beam can be related to the Doppler frequency shift as follows:

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[0087] Thus, there is a maximum velocity associated with a given PRF that corresponds to a maximum phase shift of ±π between successive signals that can be derived from the above equation as follows:

number

[0088] Those skilled in the art will find that the highest possible v max The importance of having a high PRF can be subtracted from the above formula so that

[0089] 2.2.5. Radial and azimuthal velocity estimation Using simple geometric projection, the same relationship as in plane wave imaging can be expressed pixel by pixel in polar coordinates as follows:

number

[0090] Radiation alpha i , i=1,...,N, and the received β j , j=1,...,M, we can construct the following system of linear equations:

number

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[0091] For NM≧2, the linear system may be well-posed and standard least squares may be used to extract the velocity components:

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[0092] matrix A k It can be noticed that {right arrow over (x)} is defined for all depths and is therefore not unique as in plane wave imaging. Therefore, more inversions are required, which makes the algorithm more computationally expensive.

[0093] The axial and lateral velocities are then derived from the radial and angular velocities using standard conversion formulas given below:

number

[0094] Those skilled in the art will recognize that x ∈R Nr×Nθ and v z ∈R Nr×Nθ You will notice that is still represented on a polar grid.

[0095] The final step of the method may consist of performing a scan conversion from a uniform polar grid to a uniform Cartesian grid.

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[0096] Standard techniques use 2D interpolation methods, such as bilinear or bicubic interpolation, to estimate values ​​on a regular grid from values ​​on an irregular grid.

[0097] 2.3. conclusion The vector flow imaging method described above is adapted for sector imaging. The proposed method exploits the directivity of steered Archimedean spiral wavefronts in polar space to extract the radial and azimuthal velocity components from their projections along the transmit and receive beam directions.

[0098] The medium is sequentially insonified with various steered Archimedean spiral wavefronts. The angular displacement field is calculated and a system of linear equations is constructed that relates the field to the radial and azimuthal components of the velocity flow. By solving this system, the two-dimensional flow can be extracted.

[0099] The proposed method leads to ultrafast vector flow imaging in a convex array configuration, which may be of great interest for several clinical applications where tortuous flows occur in deep abdominal organs, e.g., portal venous flow imaging in cirrhotic patients or characterization of abdominal aortic aneurysms.

[0100] 3. Theory of the Invention 3.1. introduction Non-invasive visualization and measurement of flow dynamics using ultrasound (US) is considered to be primarily clinically important, for example, to highlight abnormal vascular conditions.

[0101] Standard techniques, such as color flow imaging, continuous wave Doppler, and pulsed wave Doppler, provide one-dimensional views and measurements of flow along the axial dimension. These methods have inherent drawbacks due to their dependence on the angle between the direction of flow and the direction of the US beam. This can be problematic, for example, when tortuous vasculature can occur at the carotid bifurcation.

[0102] Vector flow imaging (VFI) methods solve this problem by providing both the axial and transverse components of velocity flow.

[0103] Various techniques, such as multibeam Doppler [1], frame-to-frame speckle tracking [2] or transverse vibration [3], have been described in the literature. For a comprehensive review, see [4], [5]. With the widespread adoption of ultrafast US imaging in the general public, multibeam methods have attracted great interest in recent years. Indeed, this idea takes advantage of both the high directivity and the omnidirectional aspect of plane waves to derive vector flow information from the projection along the direction of the transmit beam at high frame rates, thus reducing the possibility of aliasing [6].

[0104] While VFI methods have been extensively studied in linear array configurations, the literature is lacking for convex array geometries. VFI methods in convex array configurations may be of great interest for various applications, such as portal vein imaging. In this paper, a new VFI method for convex array configurations is proposed based on the transmission of a steered Archimedean spiral wavefront. It is demonstrated that the Archimedean spiral is highly directional in pseudopolar space, which makes it possible to extract radial and azimuthal velocity components from the projection of the wavefront along the propagation direction. In addition, it is shown that the use of such a wavefront allows for a clear similarity to VFI methods developed in plane wave imaging. Therefore, the proposed algorithm, which is primarily derived from that derived in [6], is based on the sequential transmission of several steered Archimedean spiral wavefronts. The displacement field associated with each steering angle is derived, and a linear system of equations is constructed that relates the field to the corresponding projections of the radial and azimuthal velocity components.

[0105] Solving the system using simple linear algebra allows one to obtain pixel-by-pixel estimates of both radial and azimuthal velocity components which can be easily converted to these components if required.

[0106] 3.2. Theoretical Examination 3.2.1. Archimedes' spiral-based imaging Consider the imaging configuration shown in Figure 7, where a convex probe is defined in polar coordinates with its convex radius r n and its angular pitch θ p and the number of transducer elements N t = 2N+1 are used to sonicate the medium Ω. Each transducer element π i is the sum of i between -N and N (r n ;i θ p ) and the angular span of the probe is Δθ=N t θ p The medium of interest Ω, assumed to be homogeneous with a constant sound speed c, is characterized by:

number

[0107] Archimedes spiral-based imaging is performed as described in the detailed description (Section 2.2). The medium is insonified with an Archimedes spiral wavefront characterized by a steering angle α. The global transmit delay for this wavefront is derived by minimizing the following equation:

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[0108] Solving this minimization problem is a matter of θ i This involves solving a second order polynomial, which involves zeroing out the derivative for each, leading to the following identity:

number

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[0109] The radius r within the field of view is the probe radius r n Since the equivalent angle α eq Note that the absolute value of is always smaller than the initial delay angle α, and the following holds:

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[0110] Looking at the configuration shown in Figure 5, θ i It can be noted that when is greater than θ, then α is negative and the following holds:

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[0111] By substituting the identity into the minimization equation, after simplification, the following expression for the global transmission delay can be obtained:

number

[0112] In that formula, α eq By substituting, we obtain the global send delay formula given in the detailed description (Section 2.2).

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[0113] A first order Taylor expansion of α in the global transmit delay equation gives:

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[0114] Fixing the global transmission delay yields a parametric equation for the wavefront that corresponds to the Archimedes spiral equation of the shape r=a+bθ.

number

[0115] 1 and N a Steering angle α for k between k (Assuming they are all different) a Consider radiating Archimedes spirals. For each steering angle, we obtain a delay-and-sum (DAS) estimate of the media tissue reflectance function, Γ k ∈C NrXNθ Reconstruct N r ∈lN and N θ ∈lN corresponds to the number of pixels in the radial and azimuthal directions, respectively.

[0116] DAS estimated Γ klu is given by

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[0117] 3.2.2. Vector Flow Imaging Physically speaking, the direction of the wavefront is defined as the normal to the isophase surface, or equivalently as the direction of the wavefield phase gradient, also known as the wavevector. Because the transmit time-of-flight is known unambiguously, the transmit phase gradient can be derived unambiguously at any given point. The transmit phase gradient is calculated using the polar gradient formula:

number

number

[0118] The resulting gradient equation after simplification is:

number

[0119] Formally, the concept of equivalent steering angle can be introduced using the following equation:

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number

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[0120] Therefore, the equation for the wave vector is given by the specific steering direction α relative to the local polar coordinates: eq Shows.

[0121] The pressure field (6) is at an angle α eq This corresponds to that of a wavefront steered by . The wavefront is flattened at the depth shown in FIG.

[0122] An Archimedean spiral wavefront is highly directional in polar coordinates, similar to a plane wave in Cartesian coordinates, so the idea is to exploit this directivity to extract the radial and azimuthal components from their projections along the wavefront, as explained below.

[0123] Pulse repetition period T PR N a Corner N e Get a consecutive set of , from which 1 and N a k between 1 and N e DAS estimates Γ for e between ek Consider computing the displacement using the Kasai autocorrelation algorithm [9] as follows:

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number

number

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[0124] Equation (11) allows us to express the following system of linear equations:

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number

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[0125] N a For ≧2, the linear system (12) is well-posed and can be solved using standard linear algebra methods, for example by computing the Moore pseudoinverse.

[0126] In a final step, the axial and lateral velocity components can be derived from the radial and azimuthal velocities as follows:

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[0127] Those skilled in the art will appreciate that many modifications may be made to the invention described above without substantially departing from the novel teachings and advantages herein described, and all modifications of this type are intended to be incorporated within the scope of the appended claims.< / n> < / n>

Claims

1. 1. An apparatus for estimating a velocity of at least one scatterer in a medium, the apparatus comprising: a generator for generating an excitation signal; a virtual transducer (T) that transforms the excitation signal into an Archimedes spiral wave １ ~T ｎ ) a curved array of ・Sound wave radiation angle (α ｉ ), and the curvature of the curved array of virtual transducers is determined by a reference center (O) and a radius of curvature (r ｎ ) and a curved array that receives, from the at least one scatterer, scattered signals generated by scattering of Archimedes spiral waves emitted from the curved array of virtual transducers; and a drive and processing unit (U) for driving said generator and the curved array of virtual transducers and for estimating the velocity of said at least one scatterer; ｃ ) The axial and lateral velocity components are determined by the wave radiation angle (α ｉ ), the geometry of the curved array of virtual transducers, and a set of local wavefront directions (α ｅｑ，ｉ ), and each local wavefront direction is estimated using the following equation: [Equation 1] An apparatus characterized by satisfying the above.

2. The drive and processing unit (U ｃ )teeth, a first series of excitation signals that enable acquisition of a first set of scattering signals; and a second series of excitation signals that allows for the acquisition of a second set of scattering signals; and a series of at least two excitation signals with a fixed repetition interval T Ｐ and driving a curved array of virtual transducers that converts at least two series of excitation signals into Archimedes spiral waves.

3. The drive and processing unit (U ｃ )teeth, receiving first and second sets of scattered signals produced by scattering of the Archimedean spiral wave; Each group of receiving beams has an acoustic radiation angle (α ｉ ) and the corresponding reception angles (β ｊ delaying and summing the first set of scattered signals to generate a first group of receive beams each having a Each group of receiving beams has an acoustic radiation angle (α ｉ ) and the corresponding reception angles (β ｊ 3. The apparatus of claim 2, further comprising a beamformer that delays and sums a second set of scattered signals to generate a second group of receive beams each having a different scattering frequency.

4. Each of the first and second groups of receive beams includes a plurality of images, each image having an acoustic emission angle (α ｉ ) and reception angle (β ｊ ) pair, and ｃ ) is calculated by the acoustic emission angle (α) so that the velocity field is estimated for each pair of different spiral and receive beam directions. ｉ ) and reception angle (β ｊ 4. The apparatus of claim 3, further comprising a processor that, for any given pair of images of the first and second groups of receive beams having the same pair of (a) and (b), Doppler processes the first and second groups of receive beams.

5. The processor calculates the sound wave emission angle (α ｉ ) and reception angle (β ｊ ) for each pair of images of the first and second groups of receive beams having the same pair of - estimating a displacement field for each corresponding pixel between said images of a given pair of images; estimating a Doppler frequency shift for each pixel for said given pair of images from said displacement field; 5. The apparatus of claim 4, configured to perform:

6. 1. A method for estimating the velocity of at least one scatterer in a medium, the method comprising: generating an excitation signal; - converting said excitation signal into an Archimedes spiral wave; - sound wave radiation angle (α ｉ radiating (110) the Archimedes spiral waves in a plurality of predetermined propagation directions defined by a set of radii of curvature (r), wherein the curvature of the curved array of virtual transducers is determined by a reference center (O) and a radius of curvature (r ｎ ) and receiving (120) scattered signals generated by scattering of said Archimedes spiral waves emitted from said curved array of virtual transducers; - estimating the velocity of at least one scatterer, The axial and lateral velocity components are determined by the wave radiation angle (α ｉ ), the geometry of the curved array of transducers, and the set of local wavefront directions (α) of the Archimedes spiral wave as a function of the distance (r) to the reference center (O). ｅｑ，ｉ ), and each local wavefront direction is estimated using the following equation: [Equation 2] A method characterized by satisfying the following.

7. 7. The method of claim 6, the step of generating an excitation signal comprises: a first series of excitation signals that enable acquisition of a first set of scattering signals; and a second series of excitation signals that allows for the acquisition of a second set of scattering signals; and a series of at least two excitation signals with a fixed repetition interval T Ｐ generating a - said step of converting comprises converting said at least two series of excitation signals into Archimedes spiral waves.

8. 8. The method of claim 7, The step of estimating the velocity of the at least one scatterer comprises: receiving first and second sets of scattered signals generated by scattering of the Archimedean spiral wave; Each group of receiving beams has an acoustic radiation angle (α ｉ ) and the corresponding reception angles (β ｊ delaying and summing the first set of scattered signals to generate a first group of receive beams each having a Each group of receiving beams has an acoustic radiation angle (α ｉ ) and the corresponding reception angles (β ｊ a beamforming substep (130) comprising delaying and summing a second set of scattered signals to generate a second group of receive beams each having a different scattering frequency.

9. 9. The method of claim 8, Each of the first and second groups of receive beams includes a plurality of images, each image having an acoustic emission angle (α ｉ ) and reception angle (β ｊ ) and estimating the velocity of at least one scatterer, - The acoustic emission angle (α ｉ ) and reception angle (β ｊ For any given pair of images of the first and second groups of receive beams having the same pair of (a) and (b), Doppler processing (20) the first and second groups of receive beams.

10. 9. The method of claim 8, The step of estimating the velocity of the at least one scatterer includes estimating the velocity of the at least one scatterer based on the acoustic emission angle (α ｉ ) and reception angle (β ｊ the following sub-steps for each pair of images of the first and second groups of receive beams having the same pair of beams: a sub-step of estimating a displacement field for each corresponding pixel between said images of a given pair of images; - estimating, from said displacement field, a Doppler frequency shift for each pixel for said given pair of images; The method further comprises:

Images