Systems and methods for directivity-based ultrasound imaging using multiaxial ultrasound transducers

Abstract

Systems and methods are provided for performing ultrasound imaging using directional information obtained by beamforming signals received from electrode pairs of one or more multiaxial ultrasound transducers. Multiaxial ultrasound transducers include an electro- acoustically active material or substrate having disposed on, or contacted with, at least two pairs of electrodes arranged along different axes. Signals received from the multiple electrode pairs may be beamformed to determine direction of arrival information associated with incident ultrasound energy, and the direction of arrival information may be employed, optionally with time-of-flight information, for active or passive imaging applications. An ultrasound computed tomography system may be adapted to include multiaxial ultrasound transducers, from which receive signals may be directionally beamformed to determine a direction of arrival associated with each receive event during ultrasound computed tomography data acquisition. The direction of arrival information may be employed, optionally in conjunction with time-of-flight information, when performing image reconstruction.

Description

SYSTEMS AND METHODS FOR DIRECTIVITY-BASED ULTRASOUND IMAGING USING MULTIAXIAL ULTRASOUND TRANSDUCERSCROSS-REFERENCE TO RELATED APPLICATION

[0001] This application claims priority to U.S. Provisional Patent Application No.63 / 752,483, titled “SYSTEMS AND METHODS FOR DIRECTIVITY-BASED ULTRASOUND IMAGING USING MULTIAXIAL ULTRASOUND TRANSDUCERS” and filed on January 31, 2025, the entire contents of which is incorporated herein by reference.BACKGROUND

[0002] Ultrasound transducers are made using piezoelectric materials, which are materials that can directly convert electrical to mechanical energy and vice-versa. The direct piezoelectric effect refers to the generation of an electric field within (or the accumulation of an electrical charge on) a material in response to an applied stress. The indirect piezoelectric effect refers to the analogous effect in the opposite direction: the application of an electric field to a material generates a stress and can be used to generate an ultrasound pulse. As illustrated in FIG. 1A, conventional (uniaxial) ultrasound transducers 100 have only one set of electrodes 110 applied to opposing faces. This enables such transducers to either measure the magnitude the electric field between the two uniaxial electrodes, or to employ the uniaxial electrodes to apply an electric field along the electrode axis (the uniaxial axis passing through the electrodes).

[0003] Some ultrasound imaging systems that employ an array of ultrasound elements enable the focusing of energy directed to, or coming from, a particular direction or location, via a process known as beamforming (transmit and / or receive beamforming). Conventional receive beamforming relies on delaying the signal collected by each element in an array by an amount corresponding to its time-of-flight (time-of-flight) from a particular location. These delays act as an artificial lens, and summing these signals together creates constructive interference such that any signal coming from that location is amplified and signals coming from other locations are cancelled out. However, due to reflections, noise, or variations in the speed of sound in different materials, this artificial lens may produce various artifacts such as mirroring. This is especially true for small arrays with few elements. Further, identifying time of arrival of a signal when the Signal-to-noise Ratio (SNR) is low can be difficult, resulting in time-of-flight measurement errors.SUMMARY

[0004] Systems and methods are provided for performing ultrasound imaging using directional information obtained by beamforming signals received from electrode pairs of one or more multiaxial ultrasound transducers. Multiaxial ultrasound transducers include an electro-acoustically active material or substrate having disposed on, or contacted with, at least two pairs of electrodes arranged along different axes. Signals received from the multiple electrode pairs may be beamformed to determine direction of arrival information associated with incident ultrasound energy, and the direction of arrival information may be employed, optionally with time-of-flight information, for active or passive imaging applications. An ultrasound computed tomography system may be adapted to include multiaxial ultrasound transducers, from which receive signals may be directionally beamformed to determine a direction of arrival associated with each receive event during ultrasound computed tomography data acquisition. The direction of arrival information may be employed, optionally in conjunction with time-of-flight information, when performing image reconstruction.

[0005] Accordingly, in a first aspect, there is provided a method of performing ultrasound computed tomography, the method comprising:employing a multiaxial ultrasound coherence tomography apparatus to acoustically interrogate an imaging target and obtain an ultrasound coherence tomography dataset, the multiaxial ultrasound coherence tomography apparatus comprising a plurality of multiaxial ultrasound transducers, each multiaxial ultrasound transducer comprising an acoustically active element having a plurality of electrode pairs disposed thereon, each electrode pair being suitable for electrically driving the acoustically active element along a different axis, the ultrasound coherence tomography dataset comprising, for each receive event of a plurality of receive events, a respective set of multiaxial receive signals received by a given multiaxial ultrasound transducer, each multiaxial receive signal of a given set of multiaxial receive signals being associated with a different electrode pair;performing multiaxial beamforming on each set of multiaxial receive signals to determine a respective direction of arrival corresponding to each receive event; and employing each direction of arrival when processing the ultrasound computed tomography dataset to generate, via image reconstruction, an ultrasound computed tomography image characterizing the imaging target;wherein image reconstruction is performed employing a ray tracing algorithm dependent on (i) the direction of arrival of each ray, and (ii) a vector quantity based on an accumulated gradient of slowness along a path of each ray.

[0006] In some example implementations of the method, the ray tracing algorithm employs minimization of a cost computed over a set of rays, each ray being associated with a respective receive event of the ultrasound computed tomography dataset, wherein a perray contribution to the cost is generated, for a given ray, based on a difference between: (i) a difference between a source slowness vector and a detection slowness vector, each slowness vector having a magnitude equal to a local slowness value and a direction equal to a direction of the given ray, the source slowness vector having a direction characterizing an emission direction associated with ultrasound emission by a given multiaxial ultrasound transducer employed as a source of ultrasound emission for the given ray, and wherein the detection slowness vector is determined, for the given ray, based on multiaxial the direction of arrival computed via multiaxial beamforming, and (ii) the vector quantity based on the accumulated gradient of slowness along the path of the given ray, wherein a slowness field within the imaging target is refined as the cost function is minimized.

[0007] In some example implementations of the method, the plurality of multiaxial ultrasound transducers are spatially distributed at least partially around a scanning region, the scanning region including the imaging target and a coupling medium configured to acoustically couple ultrasound energy into and out of the imaging target;wherein acoustically interrogating the imaging target and obtaining the ultrasound coherence tomography dataset comprises:a) selecting a multiaxial ultrasound transducer from the plurality of multiaxial ultrasound transducers;b) sending drive signals to at least one electrode pair of the selected multiaxial ultrasound transducer such that ultrasound energy is emitted from the selected multiaxial ultrasound transducer;c) for each multiaxial ultrasound transducer other than the selected multiaxial ultrasound transducer, employing at least two electrode pairs of the multiaxial ultrasound transducer to detect a set of multiaxial receive signals, each detected set of signals corresponding to a different receive event;d) repeating steps a) to c) a plurality of times, each time selecting a different multiaxial ultrasound transducer, thereby obtaining the ultrasound computed tomography dataset.

[0008] The drive signals may be provided to at least one selected multiaxial ultrasound transducer are provided to at least two electrode pairs to control an emission direction of ultrasound energy emitted by the at least one selected multiaxial transducer.

[0009] In some example implementations of the method, for a given multiaxial ultrasound transducer, a pre-determined mathematical relationship is known thatcharacterizes a dependence, on direction of arrival, of an amplitude ratio and a phase difference between multiaxial receive signals associated with a first electrode pair and a second electrode pair of the given multiaxial ultrasound transducer; and wherein multiaxial beamforming of multiaxial receive signals detected by the first electrode pair and the second electrode pair during a receive event are employed to determine an associated direction of arrival angle by: employing the pre-determined mathematical relationship to determine a direction of arrival having an amplitude ratio and a phase difference that best approximates an amplitude ratio and phase difference associated with the detected multiaxial receive signals.

[0010] The pre-determined mathematical relationship may comprise a first function characterizing a known direction of arrival angle dependence of a ratio of signal amplitudes from a first electrode pair and a second electrode pair, and a second function characterizing a known direction of arrival angle dependence of a phase difference in signals from the first electrode pair and the second electrode pair.

[0011] The direction of arrival angle associated with the set of multiaxial receive signals detected by the given multiaxial ultrasound transducer may be determined by: applying the first function and the second function as amplitude and phase corrections when evaluating a difference between a first receive signal obtained from the first electrode pair and a second receive signal obtained from the second electrode pair, each of the first function and the second function being applied such that the terms in the difference are expected to be equal when the first function and the second function are evaluated at an angle corresponding to the direction of arrival; and identifying the angle that minimizes the difference.

[0012] In some example implementations of the method, time of flight information associated with each receive event is employed, in addition to the direction of arrival associated with each receive event, when performing image reconstruction.

[0013] In another aspect, there is provided an ultrasound computed tomography system comprising:a plurality of multiaxial ultrasound transducers, each multiaxial ultrasound transducer comprising an acoustically active element having a plurality of electrode pairs disposed thereon, each electrode pair being suitable for electrically driving the acoustically active element along a different axis; andcontrol and processing circuitry operatively coupled to said plurality of multiaxial ultrasound transducers, said control and processing circuitry comprising at least one processor and associated memory, the memory comprising instructions executable by the at least one processor for performing operations comprising:controlling the plurality of multiaxial ultrasound transducers to acoustically interrogate an imaging target and obtain an ultrasound coherence tomography dataset, the ultrasound coherence tomography dataset comprising, for each receive event of a plurality of receive events, a respective set of multiaxial receive signals received by a given multiaxial ultrasound transducer, each multiaxial receive signal of a given set of multiaxial receive signals being associated with a different electrode pair;performing multiaxial beamforming on each set of multiaxial receive signals to determine a respective direction of arrival corresponding to each receive event; and employing each direction of arrival when processing the ultrasound computed tomography dataset to generate, via image reconstruction, an ultrasound computed tomography image characterizing the imaging target;wherein image reconstruction is performed employing a ray tracing algorithm dependent on (i) the direction of arrival of each ray, and (ii) a vector quantity based on an accumulated gradient of slowness along a path of each ray.

[0014] In another aspect, there is provided a method of performing multiaxial beamforming to determine direction of arrival angle information associated with detection of a set of multiaxial receive signals by a multiaxial ultrasound transducer, the method comprising:obtaining a pre-determined mathematical relationship characterizing a dependence, on direction of arrival, of an amplitude ratio and a phase difference between multiaxial receive signals associated with a first electrode pair and a second electrode pair of the multiaxial ultrasound transducer, the pre-determined mathematical relationship comprises a first function characterizing a known direction of arrival angle dependence of a ratio of signal amplitudes from the first electrode pair and the second electrode pair, and a second function characterizing a known direction of arrival angle dependence of a phase difference in signals from the first electrode pair and the second electrode pair; andwherein the direction of arrival angle information associated with the set of multiaxial receive signals detected by the given multiaxial ultrasound transducer is determined by:applying the first function and the second function as amplitude and phase corrections when evaluating a difference between a first receive signal obtained from the first electrode pair and a second receive signal obtained from the second electrode pair, each of the first function and the second function being applied such that the terms in the difference are expected to be equal when the first function and the second function are evaluated at an angle corresponding to a direction of arrival; andassociating one or more minima in the difference, when evaluated a function of angle, with respective direction of arrival angles of detected ultrasound energy

[0015] In some example implementations of the method, the multiaxial ultrasound transducer is a component of an ultrasound coherence tomography apparatus.

[0016] In some example implementations of the method, the direction of arrival angle is employed when generating an ultrasound coherence tomography image.

[0017] In another aspect, there is provided a method of performing ultrasound computed tomography, the method comprising:employing a multiaxial ultrasound coherence tomography apparatus to acoustically interrogate an imaging target and obtain an ultrasound coherence tomography dataset, the multiaxial ultrasound coherence tomography apparatus comprising a plurality of multiaxial ultrasound transducers, each multiaxial ultrasound transducer comprising an acoustically active element having a plurality of electrode pairs disposed thereon, each electrode pair being suitable for electrically driving the acoustically active element along a different axis, the ultrasound coherence tomography dataset comprising, for each receive event of a plurality of receive events, a respective set of multiaxial receive signals received by a given multiaxial ultrasound transducer, each multiaxial receive signal of a given set of multiaxial receive signals being associated with a different electrode pair;performing multiaxial beamforming on each set of multiaxial receive signals to determine a respective direction of arrival corresponding to each receive event; and employing each direction of arrival and time of flight information when processing the ultrasound computed tomography dataset to generate, via image reconstruction, an ultrasound computed tomography image characterizing the imaging target.

[0018] In another aspect, there is provided an ultrasound computed tomography system comprising:a plurality of multiaxial ultrasound transducers, each multiaxial ultrasound transducer comprising an acoustically active element having a plurality of electrode pairs disposed thereon, each electrode pair being suitable for electrically driving the acoustically active element along a different axis; andcontrol and processing circuitry operatively coupled to said plurality of multiaxial ultrasound transducers, said control and processing circuitry comprising at least one processor and associated memory, the memory comprising instructions executable by the at least one processor for performing operations comprising:controlling the plurality of multiaxial ultrasound transducers to acoustically interrogate an imaging target and obtain an ultrasound coherence tomography dataset, the ultrasound coherence tomography dataset comprising, for each receive event of a plurality of receive events, a respective set of multiaxial receive signals received by a given multiaxialultrasound transducer, each multiaxial receive signal of a given set of multiaxial receive signals being associated with a different electrode pair;performing multiaxial beamforming on each set of multiaxial receive signals to determine a respective direction of arrival corresponding to each receive event; and employing each direction of arrival and time of flight information when processing the ultrasound computed tomography dataset to generate, via image reconstruction, an ultrasound computed tomography image characterizing the imaging target.

[0019] In another aspect, there is provided a method of performing image reconstruction from an ultrasound computed tomography dataset, the ultrasound coherence tomography dataset having been acquired by a multiaxial ultrasound coherence tomography apparatus comprising a plurality of multiaxial ultrasound transducers, each multiaxial ultrasound transducer comprising an acoustically active element having a plurality of electrode pairs disposed thereon, each electrode pair being suitable for electrically driving the acoustically active element along a different axis, the ultrasound coherence tomography dataset comprising, for each receive event of a plurality of receive events, a respective set of multiaxial receive signals received by a given multiaxial ultrasound transducer, each multiaxial receive signal of a given set of multiaxial receive signals being associated with a different electrode pair;the method comprising:performing multiaxial beamforming on each set of multiaxial receive signals to determine a respective direction of arrival corresponding to each receive event; and employing each direction of arrival when processing the ultrasound computed tomography dataset to generate, via image reconstruction, an ultrasound computed tomography image characterizing an imaging target;wherein image reconstruction is performed employing a ray tracing algorithm dependent on (i) the direction of arrival of each ray, and (ii) a vector quantity based on an accumulated gradient of slowness along a path of each ray.

[0020] In another aspect, there is provided a method of performing passive multiaxial ultrasound imaging using a multiaxial ultrasound transducer, the method comprising:obtaining a pre-determined mathematical relationship characterizing a dependence, on direction of arrival, of an amplitude ratio and a phase difference between multiaxial receive signals associated with a first electrode pair and a second electrode pair of the multiaxial ultrasound transducer, the pre-determined mathematical relationship comprising a first function characterizing a known direction of arrival angle dependence of a ratio of signal amplitudes from the first electrode pair and the second electrode pair, and a second function characterizing a known direction of arrival angle dependence of a phase difference in signals from the first electrode pair and the second electrode pair; andapplying the first function and the second function as amplitude and phase corrections to generate a difference measure between a first receive signal obtained from the first electrode pair and a second receive signal obtained from the second electrode pair, each of the first function and the second function being applied such that the terms in the difference measure are expected to be equal when the first function and the second function are evaluated at an angle corresponding to the direction of arrival;generating an angle-resolved passive ultrasound image by evaluating a quantity having: (i) a numerator characterizing a measure of total acoustic power associated with the multiaxial receive signals; and (ii) a denominator including the difference measure.

[0021] A further understanding of the functional and advantageous aspects of the disclosure can be realized by reference to the following detailed description and drawings.BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Embodiments are described with reference to the accompanying drawings. In the drawings, like reference numbers can indicate identical or functionally similar elements.

[0023] FIG. 1A illustrates electrode placement for a conventional piezoelectric sensor and the electric field component measured by the electrodes.

[0024] FIG. 1B illustrates electrode placement for an example biaxial sensor and the two electric field components measured by the electrodes.

[0025] FIG. 1C shows an example of the drive and control circuitry that can be employed to control the emission of ultrasound from a multiaxial ultrasound transducer and / or to process the multiaxial receive signals detected by a multiaxial ultrasound transducer.

[0026] FIG. 2 shows a set of graphs characterizing biaxial metrics for two example biaxial transducers in a two-element array. Each transducer was characterized over a range of 110 degrees. Depth is measured from the front face of the array.

[0027] FIG. 3A is a flowchart illustrating an example multiaxial beamforming method.

[0028] FIG. 3B shows a graphical illustration of Eqn. 4 and the identification of a direction of arrival of ultrasound energy via an angle corresponding to minimum of the difference measure.

[0029] FIG. 4 is a flowchart illustrating a known multiaxial beamforming method.

[0030] FIGS. 5A and 5B illustrate the quantities used in the known and presently disclosed beamforming methods derived from the frequency domain phasors for the forward electrodes (SF(ω)) and lateral electrodes (SL(ω)). The methods use different diagonals of the parallelogram formed by SF(ω) and SL(ω). FIG. 5A shows known beamforming methods using constructive interference and methods, which only accounts for phase alignment. FIG.5B illustrates the multiaxial beamforming method using the difference between forward and lateral beamforming, accounting for phase and amplitude alignment.

[0031] FIG. 6A schematically illustrates an example geometry of a multiaxial ultrasound coherence tomography demonstration array. A circular array of transducer surrounds a phantom with regions with various acoustic impedances. The orange arrow indicates a ray path through the phantom from an emitter to a receiver.

[0032] FIG. 6B schematically illustrates an example multiaxial ultrasound coherence tomography system.

[0033] FIG. 7 illustrates an example setup for ultrasound coherence tomography reconstruction with Shepp-Logan phantom (left) at 350 kHz and breast phantom (center) at 600 kHz. Ultrasound array elements are shown in yellow. An example of wavefront ray tracing (right) with the Shepp-Logan phantom is also shown. The rays are shown in cyan and the wavefronts at different time points are shown in red.

[0034] FIG. 8 shows direction-of-arrival-based reconstructed ultrasound coherence tomography images for the Shepp-Logan phantom test using direction of arrival captured at different time points (in terms of periods) relative to the onset detection. Units are in m / s.

[0035] FIG. 9 shows direction-of-arrival-based reconstructed ultrasound coherence tomography images for the breast phantom test using direction of arrival captured at different time points (in terms of periods) relative to the onset detection. Units are in m / s.

[0036] FIG. 10 shows the root mean square error (RMSE) of tests with phantoms as a function of the number of iterations and time point, for Shepp-Logan (left) and breast (right) phantoms.

[0037] FIG. 11 shows (left) a scanning tank configuration used to collect biaxial voltage measurements and for passive imaging, (middle) a view of a biaxial transducer positioned in its top plate, and (right) a view of the assembled two-element array.

[0038] FIG. 12 shows acoustic power plots formed with biaxial beamforming across a range of angles, for a point source located at < x, z >=< -0.0180,7.03 > cm, or at the center of the characterization range, for two different multiaxial ultrasound transducers. Plots for each transducer were produced independently from each other.

[0039] FIG. 13 shows a snapshot from an animation demonstrating one-dimensional biaxial beamforming (Eq. 23) as the time window moves across the signals on the bottom. Direction of arrival based beamforming is stable throughout the entire signal. Point source was located at < x,z >=< -0.0180,7.03 > cm, or at the center of the characterization range. The time window (gray rectangle) indicates what data is being used to create the instantaneous image in the top left.

[0040] FIG. 14 is a table showing median (± IQR) aggregate results for onedimensional biaxial beamforming.

[0041] FIG. 15 presents two-dimensional passive acoustic images for a point source located at < x,z >=< -0.0180,7.03 > cm, relative to the center of the array.

[0042] FIG. 16 is a table showing median (± IQR) aggregate results for two-dimensional direction of arrival only biaxial beamforming.

[0043] FIG. 17 is a table showing median (± IQR) aggregate results for two-dimensional direction of arrival and time-of-flight biaxial beamforming.

[0044] FIG. 18 shows a snapshot from an animation demonstrating two-dimensional direction of arrival only beamforming (Eq. 24) as the time window moves across the signals on the bottom. A point source was located at < x,z >=< -0.0180,7.03 > cm, or at the center of the characterization range. The time window (gray rectangle) indicates what data is being used to create the instantaneous image in the top left.

[0045] FIG. 19 is a snapshot from an animation demonstrating two-dimensional direction of arrival and time-of-flight beamforming (Eq. 24) as the time window moves across the signals on the bottom. A point source was located at < x,z >=< -0.0180,7.03 > cm, or at the center of the characterization range. The time window (gray rectangle) indicates what data is being used to create the instantaneous image in the top left.DETAILED DESCRIPTION

[0046] Various embodiments and aspects of the disclosure will be described with reference to details discussed below. The following description and drawings are illustrative of the disclosure and are not to be construed as limiting the disclosure. Numerous specific details are described to provide a thorough understanding of various embodiments of the present disclosure. However, in certain instances, well-known or conventional details are not described in order to provide a concise discussion of embodiments of the present disclosure.

[0047] As used herein, the terms “comprises” and “comprising” are to be construed as being inclusive and open ended, and not exclusive. Specifically, when used in the specification and claims, the terms “comprises” and “comprising” and variations thereof mean the specified features, steps or components are included. These terms are not to be interpreted to exclude the presence of other features, steps or components.

[0048] As used herein, the term “exemplary” means “serving as an example, instance, or illustration,” and should not be construed as preferred or advantageous over other configurations disclosed herein.

[0049] As used herein, the terms “about” and “approximately” are meant to cover variations that may exist in the upper and lower limits of the ranges of values, such asvariations in properties, parameters, and dimensions. Unless otherwise specified, the terms “about” and “approximately” mean plus or minus 25 percent or less.

[0050] It is to be understood that unless otherwise specified, any specified range or group is as a shorthand way of referring to each and every member of a range or group individually, as well as each and every possible sub-range or sub-group encompassed therein and similarly with respect to any sub-ranges or sub-groups therein. Unless otherwise specified, the present disclosure relates to and explicitly incorporates each and every specific member and combination of sub-ranges or sub-groups.

[0051] As used herein, the term "on the order of', when used in conjunction with a quantity or parameter, refers to a range spanning approximately one tenth to ten times the stated quantity or parameter.

[0052] Unless defined otherwise, all technical and scientific terms used herein are intended to have the same meaning as commonly understood to one of ordinary skill in the art. Unless otherwise indicated, such as through context, as used herein, the following terms are intended to have the following meanings:Multiaxial Ultrasound Transducers

[0053] Although conventional ultrasound transducers employed for ultrasound imaging employ a single uniaxial electrode pair for excitation and / or signal reception, piezoelectric materials generally vibrate in three dimensions, and these additional vibrations represent additional channels of information and / or means of excitation control that can be advantageously employed to glean additional information about a detected ultrasound signal, and / or to provide additional control over emitted ultrasound energy. An ultrasound transducer element can thus be provided with at least two pairs of electrodes, with each pair of electrodes oriented in a different direction, in order to be able to measure such additional vibrations, and / or to facilitate excitation along additional spatial directions in which the underlying acoustically active material is electromechanically responsive.

[0054] Such a multi-electrode-pair ultrasound transducer, which includes at least two pairs of electrodes, is henceforth referred to as a multiaxial ultrasound transducer. It has been shown that the information simultaneously recorded from multiple pairs of electrodes of a multiaxial ultrasound transducer allows for the estimation of direction of arrival (direction of arrival) [2] and / or to steer the direction of emitted ultrasound energy generated [3, 4], For example, as illustrated in FIG. 1B, in the case of a biaxial transducer 150 having two pairs of electrodes (110, 120), signals received by the two pairs of electrodes can be employed to estimate the polar angle 9 associated with the arrival of ultrasound energy. Alternatively or additionally, signals delivered to the two pairs of electrodes can be employed to control thedirection of emission of ultrasound along a desired polar angle 9. For a multiaxial transducer with three or more electrode pairs, one can estimate the polar angle 9 and azimuthal angle associated with the arrival of ultrasound energy, and / or control the direction of emission of ultrasound along a desired polar angle 9 and azimuthal angle.

[0055] A multiaxial ultrasound transducer, as described above, is an electro-acoustically active material or substrate having disposed on, or contacted with, at least two pairs of electrodes, with each pair of electrodes defining a respective electrode axis that passes orthogonally through each electrode, the electrode pairs being disposed such that the electrode axes are non-parallel to one another.

[0056] In some example implementations, each pair of electrodes of a multiaxial ultrasound transducer is orthogonal (perpendicular) to every other pair of electrodes of the multiaxial ultrasound transducer. In other words, each pair of electrodes may define a respective electrode axis, and the electrode axes of the multiaxial ultrasound transducer may be mutually orthogonal. It will be understood, however, that in other example implementations, each pair of electrodes of a multiaxial ultrasound transducer need not be orthogonal (perpendicular) to every other pair of electrodes of the multiaxial ultrasound transducer. In other words, each pair of electrodes may define a respective electrode axis, and the electrode axes of the multiaxial ultrasound transducer need not be mutually orthogonal.

[0057] While many of the example implementations presented in the present disclosure pertain to biaxial transducers, it will be understood that the embodiments disclosed herein are not intended to be limited to biaxial ultrasound transducers, and are generally intended to be adaptable for use with multiaxial ultrasound transducers (e.g. having three pairs of electrodes). In many examples described below, prescriptions are provided for how a given biaxial implementation can be generalized for additional electrode pairs or higher dimensions. In other cases, the skilled artisan will be able to readily extend a biaxial ultrasound transducer implementation to a multiaxial ultrasound transducer implementation.

[0058] It will be understood that the underlying acoustically active material (a material for which mechanical stress is convertible into an internal electric field and vice-versa) of a multiaxial ultrasound transducer, referred to herein as the acoustically active element, substrate, slab, crystal, resonator, or structural medium, on which the electrodes are applied (disposed, adhered, deposited, laminated, patterned, or contacted) to form a multiaxial ultrasound transducer may be provided in a variety of physical shapes and compositions, provided that the acoustically active material is a piezoelectric material that exhibits the piezoelectric effect, where mechanical stress is converted into an internal electric field and vice-versa, and where piezoelectricity is exhibited in more than one spatial direction.

[0059] Multiaxial ultrasound transducers may be manufactured using piezoelectric materials. This class of materials exhibits the piezoelectric effect, where mechanical stress is converted into an internal electric field and vice-versa. For multiaxial transducers, the material will also exhibit a piezoelectric response in multiple independent directions. Multiple sets of electrodes applied to this material can be configured such that they will measure linearly independent components of the internal electric field of that material, and these linearly independent components behave differently to each other such that they give rise to the phase difference and amplitude ratio relationships that we've defined in the disclosure.

[0060] The above parameters are fulfilled by a variety of materials, including, but not limited to, piezoceramics, which have regions within them (called domains) that exhibit spontaneous polarization. These sections can be aligned to create a bulk piezoelectric effect. A non-exhaustive list of piezoceramics includes: Lead zirconatetitanate (Pb[ZrxTii-x]O3with 0 < x < 1P) - more commonly known as PZT, Potassium niobate (KNbO3), Sodium tungstate (Na2WO3), Ba2NaNb5O5, Pb2KNb5O15, Zinc oxide (ZnO), Sodium potassium niobate ((K, Na)NbO3). This material is also known as NKN or KNN, Bismuth ferrite (BiFeO3), Sodium niobate (NaNbO3), Barium titanate (BaTiO3), Bismuth titanate (Bi4Ti3O12), and Sodium bismuth titanate (NaBi(TiO3)2).

[0061] A second example class of piezoelectric materials that have the potential to replace piezoceramics is the class of crystalline piezoelectric materials. These materials are formed by a homogenous crystal structure, rather than having multiple domains that must be aligned. Thus, for a crystal structure that exhibits a strong piezoelectric response, they would provide better sensitivity and SNR than piezoceramics. However, any of these materials could be used to make a multiaxial transducer. They are very hard to manufacture and so they are not commonly used today, but should a method of manufacturing them become available they are regarded as superior the piezoceramics in many ways. A non-exhaustive list of crystalline piezoelectric materials includes: Langasite (La3Ga5SiO14), Gallium orthophosphate (GaPO4), Lithium niobate (LiNbO3), Lithium tantalate (LiTaO3), Quartz, Berlinite (AIPO4), Rochelle salt, Topaz, Tourmaline-group minerals, and Lead titanate (PbTiO3).

[0062] A third example class of acoustically active piezoelectric materials is given by polymers. The piezoelectric response of these materials is not typically as strong as that of piezoceramics, but they can have useful properties that piezoceramis do not, such as a lower acoustical impedance. This is useful for increasing the sensitivity of ultrasound transducers. A non-exhaustive list of piezoelectric polymers includes: Polyvinylidene fluoride (PVDF) and its copolymers, polyamides, and parylene-C, Polyimide Polyvinylidene chloride (PVDC), Voided charged polymers (a separate class of materials in and of itself).

[0063] Finally, it is noted that group III–V and II–VI semiconductors and ionic liquids also exhibit the piezoelectric effect, and many benign materials, such as sucrose, also exhibit weak piezoelectric responses, which, if multiple electrodes were applied, could be used as multiaxial ultrasound transducers.

[0064] The acoustically-active element may take physical forms that accommodate multiple pairs of electrodes, including planar sheets with side walls of sufficient thickness for electrode placement, prismatic structures such as rectangular, square, or polygonal prisms, cylindrical shells, multilayered stacks, hemispherical shells, arbitrarily curved shells and other geometries that support multiaxial excitation. These configurations enable independent electrode pairs to be positioned along different axes, facilitating electronic beam steering, dynamic focusing, or controlled acoustic wave propagation. They also enable measurements along different axes to facilitate, for example, electronic beamforming. Multiple elements may also be implemented as a 1 D, 1,5D, 2D, or sparse transducer array to further enhance multiaxial detection and / or control.

[0065] Non-limiting examples of suitable electrode materials include noble metals (e.g., gold, silver, platinum, palladium), transition metals (e.g., titanium, tungsten, molybdenum), conductive oxides (e.g., indium tin oxide (ITO), aluminum-doped zinc oxide (AZO)), and conductive polymers (e.g., PEDOT). In some implementations, nanomaterial-based electrodes such as graphene, carbon nanotubes, or silver nanowires may be employed to provide flexibility or transparency.

[0066] Electrodes may be applied to the underlying acoustically active substrate using various deposition and patterning techniques, including but not limited to physical vapor deposition (PVD) methods (e.g., sputtering, thermal evaporation, electron beam evaporation), chemical vapor deposition (CVD), electroplating, electroless plating, sol-gel deposition, screen printing, inkjet printing, and spray coating. Patterning of electrodes may be achieved through photolithography, laser ablation, focused ion beam milling, or chemical etching to define specific transducer architectures and optimize acoustic performance.

[0067] In some example implementations, multiple sets of electrodes are applied to an underlying acoustically active material such that the multiple electrodes facilitate measurement of linearly independent components of the internal electric field of that material, and these linearly independent components behave differently to each other such that they give rise to the phase difference and amplitude ratio relationships.

[0068] FIG. 1C shows an example of the drive and control circuitry that can be employed to control the emission of ultrasound from a multiaxial ultrasound transducer and / or to process the multiaxial receive signals detected by a multiaxial ultrasound transducer. As shown in the figure, the electrodes (110, 120) from the multiaxial transducers 150 areconnected to switchable transmit / receive channels 200, which include analog-to-digital and digital-to-analog conversion circuits 210 to alternately transmit and receive ultrasound as desired. An example of such a system is a Vantage® Research Ultrasound System, which can be purchased with between 32 to 256 individually controllable transmit / receive channels. Other commercial systems, such as the Fujifilm Vevo F2 also have similar functionality.

[0069] A controller module (e.g. computer 220), optionally packaged with the transmit / receive system, provides control over the transmission / reception parameters for each channel, collects data during reception, and sends it to a computer. Optionally, an application-specific device can be used to focus signals in a particular direction or to a particular location before the data is sent to the controlling computer that displays the final image. Alternatively, this beamforming can be performed in software with the controlling computer itself. Software on the controlling computer also provides instructions to the transmit / receive system controller regarding the data collection scheme and parameters as well as the parameters of any transmitted signals. The transmit / receive hardware can also be custom built using amplification circuits, analog-to-digital and digital-to-analog converters, and a series of microcontrollers (such as from the Arduino brand). The controlling computer can be any general purpose personal computer.Improved Multiaxial Beamforming

[0070] In some example embodiments of the present disclosure, improved multiaxial beamforming methods are disclosed that can facilitate a determination of one or more directions of arrival (receive focus) the signal received by a single multiaxial transducer. While direction of arrival information can be estimated with an array of conventional uniaxial ultrasound elements, to the best of the knowledge of the present inventors, there have not been studies that have employed an array in which each element can individually detect direction of arrival. Further, when direction of arrival information is derived from time-of-flight information, it has limited utility as it inherently has lower spatial resolution than a multiaxial system.

[0071] As described below, various example embodiments of the present disclosure employ the use of multiaxial ultrasound transducers and multiaxial beamforming to mitigate the aforementioned limitations associated with uniaxial ultrasound transducers by obtaining and employing direction of arrival information instead of, or in addition to, time-of-flight information. In some example embodiments, the ability of a multiaxial ultrasound transducer to detect a direction of arrival associated with incident ultrasound energy is employed to improve the performance of ultrasound coherence tomography, while in other exampleapplications, the directional information can be employed to facilitate improved passive ultrasound imaging with a very low number of ultrasound transducers.

[0072] Multiaxial ultrasound directional beamforming (as referred to herein as multiaxial beamforming) involves the processing of a set of receive signals to determine directional information associated with detected ultrasound energy, where each signal is obtained from a different electrode pair of a multiaxial ultrasound transducer. The direction of arrival information encoded in these signals is independent from time-of-flight information, which can disambiguate the direction and location from where an ultrasound wave originated. Moreover, direction of arrival information can be measured stably over the duration of a signal, and therefore can sidestep the difficulty in identifying time-of-flight using time of arrival in the case of low SNR. Furthermore, sensitivity may also be improved in the case of multiaxial beamforming due to better efficiency in converting mechanical energy to electrical energy.

[0073] Multiaxial imaging methods depend on the relationship between the signals measured from a multiaxial transducer and the direction of arrival of the signal that produced them. For a biaxial transducer with one electrode pair in the forward direction (sF(t)) and one in the lateral direction (sL(t)) (FIG. 1B), these are defined as the biaxial phase difference (<> / ,) and biaxial amplitude ratio (ab). Given frequency domain representations of the forward and lateral signals (SF(a») and SL(ω)), these quantities can be calculated as

[0074] ab(a)) = |^g| andz(jig!). (i)

[0075] These quantities can also be calculated equivalently in the time domain.Equation 1 can then be measured across the imaging ranges, which can be either a range of directions of arrival or positions (x) (procedure in Ref.

[0024] ). Since these multiaxial metrics are valid only between two signals at a time, it follows that for n electrode pairs, the number of multiaxial metrics between the electrodes would be N = (n - l)n (which otherwise can be stated as (”)) for both the phase difference and amplitude ratio).

[0076] FIG. 2 depicts sample metrics for a pair of biaxial transducers. Due to the differences between these metrics from transducer-to-transducer, per-element characterization may be employed. On the other hand, if the properties of multiaxial ultrasound transducers are similar among multiple transducers, one set of metrics may be employed to characterize multiple multiaxial ultrasound transducers.

[0077] The improved multiaxial beamforming method is initially described within the context of an example biaxial transducer with frequency domain representations of the forward and lateral signals being SF(a») and SL(ω), respectively. Assuming that the forward and lateral signals have similar shape and frequency, for a wave coming from a direction 0

[0078] Sp(co)] ■ (2)

[0079] Then, for a range of directions of arrival 9' e R, -180° <' < 180°:f rP-i< / >6(w,e')if 0 = 0'

[0080] s^-s^) if0 ¥= 0' (3)

[0081] By finding the magnitude of acoustic energy in the above expression, one can estimate the likelihood of a signal coming from a particular polar direction 0' withe-i06(co,0')= |SF(co) — SL(a)) 2 (4)ab(co, 0')

[0082] where Y](O, 9') demonstrates a local minimum at the angle corresponding to the direction of arrival of the signal rather than a maximum. For ultrasound coherence tomography, this provides a direct method for estimating the direction of arrival. This formulation also preserves superposition. As a result, should there be multiple signals simultaneously incident from directions 9^92,..., a local minima is expected where 0' = 0i,02>....

[0083] FIG. 3A provide a flowchart illustrating an example implementation of algorithm, with the corrections being applied to SL( o) in the present non-limiting example. FIG. 3B shows on top, an example of the values estimated using the example implementation in FIG.3A for an acoustic source. The true direction of the acoustic source is denoted as a dotted line, while the estimated direction of the acoustic source can be estimated by finding, for example, the minimum value in the image. However, this is simply an example of how to estimate the direction of arrival and other methods, such as curve fitting and interpolation, could also be employed.

[0084] It will be understood by the skilled artisan that the functional form shown in FIG. 3 represents but one example of a difference measure that can be employed for a determination of direction of arrival via the processing of multiaxial receive signals.Difference measures other than |sF(co) - SL(co)e_i<^6(:"'e)| may be employed in thealternative, provided that the angle-dependent amplitude and phase corrections are employed to correct one or both terms (SL( o) and SF(o)) such that the difference measure tends to a minimum when the angle 0 is equal to one or more angles of incidence of detected ultrasound energy. Alternative examples of suitable difference measures include |ab(co, 0) SF(OJ) — SL(co)e-t^6("'e)|, \ab(a), 9) SF(ω)el<f>b^'G^>— SL(co)|, |sF(co) +- 2SM |. - 2SL(co)|.

[0085] While the units of Eq. 4 are still acoustic power, this does not represent the total acoustic power at a location but rather a remainder of energy that is not consistent with a signal coming from a particular direction 0'. Additional implementation details are required to produce a quantity related to the acoustic energy of the source in that location.

[0086] Generalizing the preceding biaxial workflow for multiaxial transducers with N electrode pairs, a function that finds the total remaining energy from the difference of the N(N - l) / 2 signal pairs. One possible method of extending Eq. 4 fortriaxial transducers would be to take the product of multiple factors like Eq. 4 for each signal pair. For example,T](M, 0', cj)’') SF(o)) — SLl(a>)abl(,a),0SF(M) — SL2(M)ab2(a>,0(5)ah3(w,0',( / >')

[0087] This approach would produce global minima as each factor goes to zero.Alternatively, these factors could be summed instead. This would not force the whole function to zero as one individual term goes to zero. It will be understood that the skilled artisan may employ alternative adaptations of the preceding generalized method of direction of arrival determination to multiaxial ultrasound transducers with three or more pairs of electrodes without departing from the intended scope of the present disclosure.

[0088] FIG. 4 illustrates, in the form of a flow chart, a known method of multiaxial beamforming, outlined in Refs. [16,17] for B-mode imaging. In brief, this known method employs the same logic as conventional beamforming methods: the lateral signal is time delayed or, equivalently, phase shifted in the frequency domain and summed with the forward signal to focus the signals in a particular direction. The ideal phase shift for each element in their three-element array is taken as the phase shift that produces the best snr, found using a brute-force search. However, this known method is only able to account for phase alignment and is therefore distinct from the method proposed in this document.

[0089] FIGS. 5A and 5B visualize how the improved method of the present disclosure (illustrated in FIG. 3) differs from the known multiaxial beamforming method (illustrated in FIG. 4). For a particular frequency of interest, SF(a») and SL(ω) differ by a phase difference (<> / ,) and amplitude ratio (ab).

[0090] In the case of the known method of FIG. 4, the logic follows that of constructive interference methods: the sum SF(a») + SL(ω) will produce a maximum when the phase difference between SF(a») and SL(ω) is zero. Geometrically, a phase shift will rotate thephasor SL(ω) without changing its length. The major diagonal of the parallelogram (given by the sum SF(a») + SL(ω)) becomes longer as the angle between the two phasors shrinks. Thus, SF(a») + SL(ω) is maximized when a phase correction < / )ba),d) applied to to SL(ω) minimizes the angle < / )bin FIG. 5A (where d is equal to the direction of arrival of the incident signal). However, changing the length of either SF(a») or SLJ) with an amplitude correction based on abwould simply change the length of SF(a») + SL(ω) by a factor, without a consistent relationship of that change in length to the direction of arrival.

[0091] This is contrasted with the present improved multiaxial method, illustrated in FIG.5B, where the minor diagonal of the parallelogram is employed: the difference between phasors. The difference SF(a») - SL(ω) is minimized when SF(a») = SL(ω). When the proposed biaxial metrics < / >b(a),d) and ah(a>,9) are applied as corrections to SL(ω), it will approach the value of SF(a»). Therefore, |sF(a») - - SL(ω)e_i<^6(:"'e)| will be at itsminimum when d is equal to the direction of arrival of the incident signal. As noted above, it will be clear to the skilled artisan that other difference measures may be employed in the alternative, provided that the angle-dependent amplitude and phase corrections are employed to correct one or both terms (SL(ω) and SF(a»)) such that the difference measure tends to a minimum when the angle d is equal to one or more angles of incidence of detected ultrasound energy.

[0092] It is noted that Eq. 4 facilitates a method of multiaxial beamforming, or focusing energy at a certain point or in a certain direction. While Eq. 4 is written with units of acoustic power, the intent of the equation is to deconstructively focus signals at a particular location. This lies in contrast to conventional beamforming algorithms, where the focused signals constructively interfere and the resulting acoustic energy estimate is directly related to the amount of energy that came from that point or direction. This acoustic energy of the multiaxial deconstructive interference equations can be interpreted as a residual, or the amount of energy coming from somewhere other than the point at which one is effectively focusing upon receive via selection of a given angle.

[0093] When multiple acoustic sources are present within the field of view, superposition suggests that the resulting image would behave as if we had multiple fields of view added together, each with a single acoustic source within them (e.g., FOV1 + FOV2 +...). It follows that deconstructive interference approach would produce multiple minima within an image (either at locations or directions corresponding to the locations of the acoustic sources). The depth of these minima would be proportional to the relative power of these acoustic signals, and one could identify multiple acoustic sources by using thresholding and finding all the local minima within an image. All the local minima deeper than a certain threshold from the background value could be identified as potential acoustic sources.Applications of Improved Multiaxial Beamforming Method

[0094] The improved multiaxial beamforming method described above, which provides a robust method for identifying one or more directions of arrival of ultrasound energy detected by a multiaxial ultrasound transducer, may be employed in a wide range of applications, some examples of which are described in detail below. Non-limiting example applications for the implementation of the improved multiaxial beamforming method include geophysical imaging (such as for finding resources or determining the composition of various layers of the earth), non-destructive testing (such as for evaluating the integrity of concrete and passively listening for the formation of cracks in materials, or snapping wires and reinforcements), earthquake monitoring, sonar, passive underwater imaging, medical ultrasound imaging (including b-mode ultrasound imaging, ultrasound computer tomography, doppler imaging, shear wave elastography, and passive monitoring of high-intensity ultrasound therapies), among others.Ultrasound Computer Tomography using Multiaxial Direction of Arrival Information

[0095] Ultrasound coherence tomography is a method of active ultrasound imaging that can produce cross-sectional or volumetric images analogous to X-ray CT or MRI. To do so, ultrasound transducers encircling an imaging target listen for sound waves that have been transmitted, scattered, reflected, and refracted by the intervening imaging target (or medium). Characteristics about the received ultrasound can then be used to infer the acoustic properties of that medium, such as the speed of sound or impedance. In contrast, B-mode imaging (the most common type of medical ultrasound imaging) uses only reflected waves and can be conducted with a hand-held array.

[0096] While ultrasound coherence tomography has been possible for several decades (one of the first demonstrations of ultrasound coherence tomography was published in 1978), it has not seen widespread clinical adoption for several reasons. Initially, this was due to comparatively lower spatial resolution to alternatives and the much larger required array geometry. However, ultrasound coherence tomography has recently seen renewed interest as increasingly capable computer hardware has enabled reconstruction methods that provide increased spatial resolution among other image quality improvements. Development of new ultrasound coherence tomography methods continue to address remaining challenges, including a trade-off between prohibitive computational cost and superior spatial resolution, blurred edges in images, prohibitive array geometries, and required array density.

[0097] Most modern ultrasound coherence tomography image reconstruction methods employ an iterative approach, which can broadly be summarized in the following five steps known to the skilled artisan:1. Taking measurements: Ultrasound is emitted from each transducer in the array in turn, while each other element listens.2. Making a first guess: Make an educated guess about the relevant acoustic properties of the medium being imaged.3. Simulating the propagation of ultrasound: Mimic the acquired data collection procedure process as closely as possible.4. Image reconstruction: Compare the experimental and simulated results and update the guessed parameters to minimize the difference.5. Iterate: Repeat from step 3 until the image is no longer improving significantly.

[0098] For example, step 5 can be approached using generic iterative optimization to minimize a cost function. Similarly, step 3 can make use of many different acoustic simulation methods, including ray-based or finite element-based methods.

[0099] The present inventors realized that some of the aforementioned steps could be adapted to enable multiaxial ultrasound coherence tomography (in particular, steps 1, 3, and 4), in which the conventional ultrasound transducers are replaced by a set of multiaxial ultrasound transducers, and where multiaxial beamforming is employed to determine direction of arrival information associated with each receive event in the ultrasound coherence tomography workflow, and where the direction of arrival information is employed during the image reconstruction step.

[0100] For illustrative purposes, multiaxial ultrasound coherence tomography imaging is described in the example context of two-dimensional (cross-sectional) imaging with a ring array of biaxial transducers. For example, FIG. 6A shows an example of a 2D multiaxial ultrasound coherence tomography system 300 that has been adapted to include biaxial ultrasound transducers for obtaining an ultrasound coherence tomography of an imaging target 360, with acoustic coupling between the biaxial ultrasound transducers and the imaging target being provided by an acoustic coupling medium 350 (e.g. a liquid or gel). The figure shows a path of an example ray 370 based on ultrasound energy emitted by a first biaxial ultrasound transducer 150A and received (detected) by another biaxial ultrasound transducer 150B. As noted above, it will be understood that the present multiaxial ultrasound coherence tomography methods may be generalizable to three dimensions.

[0101] In one example embodiment, an ultrasound coherence tomography system and workflow may be adapted to employ multiaxial ultrasound transducers to provide direction of arrival information that is utilized during ultrasound coherence tomography imagereconstruction as follows. The multiaxial ultrasound coherence tomography apparatus includes a plurality of multiaxial ultrasound transducers, each multiaxial ultrasound transducer having an acoustically active element with multiple electrode pairs, each electrode pair being suitable for electrically driving the acoustically active element along a different axis. The multiaxial ultrasound coherence tomography apparatus is employed to acoustically interrogate an imaging target and obtain an ultrasound coherence tomography dataset, for example, as per step 1 above.

[0102] For example, multiaxial ultrasound coherent tomography data acquisition may be performed as follows. A multiaxial ultrasound transducer is initially selected from the plurality of multiaxial ultrasound transducers and drive signals are sent to at least one electrode pair of the selected multiaxial ultrasound transducer, such that ultrasound energy is emitted from the selected multiaxial ultrasound transducer. If multiple drive signals are respectively sent to different electrode pairs of the selected multiaxial ultrasound transducer, the resulting emission of ultrasound energy may be directed (steered) along a desired direction. Each of the multiaxial ultrasound transducers of the remaining (non-selected) multiaxial ultrasound transducers are then employed to detect a respective set of multiaxial receive signals (one set per multiaxial ultrasound transducer), with each detected set of multiaxial receive signals corresponding to a different receive event. This transmit-listen step is then repeated, each time selecting a different multiaxial ultrasound transducer, with the resulting sets of receive signals forming the ultrasound computed tomography dataset. The ultrasound coherence tomography dataset thus includes, for each receive event, a respective set of multiaxial receive signals received by a given multiaxial ultrasound transducer, each multiaxial receive signal of a given set of multiaxial receive signals being associated with a different electrode pair.

[0103] Multiaxial directional beamforming may then be employed on each set of multiaxial receive signals to determine a respective direction of arrival corresponding to each receive event. Any suitable method of multiaxial beamforming may be used, such as, for example, the improved multiaxial beamforming method described above, or adaptations thereof, or other methods of multiaxial beamforming. For example, in some example implementations, a pre-determined mathematical relationship may be known that characterizes a dependence, on direction of arrival, of an amplitude ratio and a phase difference between multiaxial receive signals associated with a first electrode pair and a second electrode pair of the given multiaxial ultrasound transducer, and multiaxial beamforming to determine an associated direction of arrival angle by: employing the predetermined mathematical relationship to determine a direction of arrival having an amplitude ratio and a phase difference that best approximates an amplitude ratio and phase difference associated with the detected multiaxial receive signals.

[0104] The direction of arrival information is then employed when processing the ultrasound computed tomography dataset to generate, via image reconstruction, an ultrasound computed tomography image characterizing the imaging target. The ultrasound coherence tomography dataset may also include time-of-flight information, which is available from the signals received by each multiaxial ultrasound transducer.

[0105] It will be understood that a wide range of image reconstruction methods may be adapted to employ the direction of arrival information (and optionally also time-of-flight information) when generating the ultrasound computed tomography image. One example method described herein employs a variation of a ray-based wavefront tracing method provided in Ref.

[0026] to simulate the propagation of ultrasound.

[0106] Ray-based methods typically employ an initial estimate (first guess) of the properties of the medium in the form of a speed of sound field. For mathematical convenience, this is often transformed into a slowness field (s(T), the reciprocal of speed of sound). One then finds the ray path through s(x) that takes the least time to connect the emitting and receiving ultrasound transducers (called an eigenray). This eigenray is allowed to refract and bend as it travels through the slowness field. For direction of arrival based methods, one may keep track of additional information about the ray beyond its time of arrival, primarily in the form of a vectorized ray path and a unit vector representing the direction of arrival at the receiving transducer.

[0107] There are many different trade-offs to consider when selecting a simulation method to be employed during image reconstruction. For example, ray-based methods may be computationally efficient but traditionally have had poorer resolution than alternatives such as full-waveform algorithms. In the present example embodiment, image quality of raybased methods is improved with the incorporation of direction of arrival information. The systems of equations derived below indicate that direction of arrival information may improve accuracy of these methods, mitigating some of the disadvantages of ray-based methods compared to full-waveform methods.

[0108] During image reconstruction, estimates the parameters of the unknown medium are employed. One can do so by solving an inverse problem where, for some function (<medium>) = <measurements> that takes the parameters of a medium and outputs a measurement, one may seek to find medium parameters that produces a particular set of measurements. In the present case, the function f is some method of propagating ultrasound. As mentioned in the previous section, one may use raytracing methods fortheir computational efficiency.

[0109] In ray acoustics, ultrasound propagation is described using rays that travel along wavefronts. A wavefront is a surface along which a waveform feature is beingsimultaneously received. For example, for a pulse of ultrasound whose leading edge arrives at a location x at a time T(X), the wavefront is described by the set of all points satisfying t = T( ) for a time t. A ray is then defined as the line traced by a point that travels in time with the wavefront. The path a ray takes is constrained and, in most cases, can be described as the path with the shortest travel time between two points.

[0110] Conventional time-of-flight based methods of performing ray-based ultrasound coherence tomography find this travel time (d) by integrating along the ray path. Intuitively, the time it takes a ray to travel from a source to a detector is inversely proportional to the speed of sound along the path the ray took. Formally, one can express this as the line integral

[0111] d = ∫_Γ (1 / c(x̄)) dl = ∫_Γ s(x̄)dl, (6)

[0112] where s(i) is the isotropic slowness at a particular location x, r is the ray path, and dl is an infinitesimal along the ray path. Equation 6 forms the basis of conventional raybased ultrasound coherence tomography techniques, where s(i) is the medium’s property that one is attempting to recover.

[0113] For direction of arrival based methods, once can derive a corresponding equation for the direction of arrival of a wave, starting from the ray equations given by Ref.

[0036] , A simplifying assumption is initially made that is relevant to the present example application: since patients are assumed to be sitting still, one can assume that the medium has no ambient fluid velocity and that the medium’s properties are independent of time. Then, the paths along which acoustic rays travel can be described using the set of ordinary differential equations given by

[0114] dx̄ / dt = -(c(x̄))²s̄

[0115] and

[0116] (7)

[0117] where s is the wave slowness vector (pointing in the direction of propagation of the ray) and the scalar field c( ) is the speed of sound at location x. The wave slowness vector is a derived quantity: at a specific point in space the wave slowness vector is given by

[0118] s̄ = s(x̄)n̄ = n̄ / c(x̄), (8)where n̄ is a unit vector representing the direction of propagation of the ray and s(x̄) = 1 / c(x̄) is the scalar slowness. Note that n̄ encodes the direction of arrival of a ray, provided relevant coordinate transformations are used such that the direction of arrival is expressed relative to the surface normal of each transducer. Also note that the direction of arrival is related to the change in the speed of sound ∇c(x̄).

[0119] Because a key property of the medium that affects the propagation of these acoustic rays is the speed of sound, it is the speed of sound (or equivalently, the slowness) of the medium for which recovery is attempted. Various other methods of describing ultrasound propagation, as well as extensions of these ray equations, can be employed to solve for other parameters such as density or the anisotropic speed of sound of a medium.

[0120] Continuing by rearranging Eq. 7, which is a separable differential equation,

[0121] ds̄ = -(∇c(x̄) / c(x̄))dt = -(s(x̄))²∇(1 / s(x̄))dl, (9)

[0122] where dl = dt / s(x̄) is an infinitesimal distance along the ray path Γ. By the chain rule,rule, (s(x))²(∂ / ∂x)(1 / s(x)) ≈ -(∂ / ∂x)s(x) (at all points except where s(x) = 0, which in practical applications is not a concern). The differential equation then simplifies to:

[0123] ds̄ = -∇s(x̄)dl. (10)

[0124] Integrating along the ray path, one finds that:

[0125] ∫_Γ ds̄ = -∫_Γ ∇s(x̄)dl, (11)

[0126] s̄_d - s̄_s = -∫_Γ ∇s(x̄)dl, (12)

[0127] where ssis the ray slowness vector at the source (the transducer that emitted the pulse of ultrasound) and sdis the ray slowness vector at the detector (the transducer that received the pulse of ultrasound).

[0128] This leaves four variables to account for:• s(x): The slowness field is what is sought to recover in this inversion process.• dl: The ray path is calculated at each iteration of the ultrasound coherence tomography inverse problem because it changes with every update to the slowness field s(x). It is calculated with the ultrasound propagation method described in section.• sd: The ray direction at each detector is measured by multiaxial transducers.• ss: The ray direction at each source depends on the ray path, and therefore is also dependent on the slowness field s(x) and can be calculated at each iteration of the ultrasound coherence tomography inverse problem.

[0129] For s(x) and ss, one can assume initial values to start the iterative improvement process. For s(x), one can start, for example, with a flat water background (s = 1 / 1500 s / m everywhere) by convention. This avoids any real or perceived bias from using an initial guess optimized for the particular test case. Within each step of the ultrasound coherence tomography iterative image reconstruction process, the speed of sound field is assumed to be stationary.

[0130] For ss, one can assume that the starting position of each ray is at the center of the transducer that produced it and its starting direction to be going straight from the source to the detector. This gives a correct solution tor the initial uniform speed of sound field selected above. However, once s(x) has been updated, the ray will interact with the new speed of sound field and once can calculate a new ray path. Using the ultrasound propagation method described in section, one finds the fastest ray to reach a detector by modelling the full wavefront and then back-propagating along the path that wavefront took to find ss.

[0131] It should be noted, however, it has been assumed conventional operation of transducers for emission (this tacitly assumes that each transducer is a spherical emitter when observed more than a few wavelengths away from the transducer). Recalling that one can steer the ultrasound emitted by a multiaxial transducer, one can devise novel ways collect experimental data. For example, at each iteration of the ultrasound coherence tomography inversion problem, one could steer the ultrasound from each transducer in the direction of ssthat was found through back-propagation and collect new data. This may increase the signal-to-noise ratio of images by focusing ultrasound only in the direction relevant to the ray being studied. By steering ultrasound in a range of directions, one may also be able to increase ray coverage of the imaging target which typically increases image quality. These types of data collection schemes will be further investigated with the creation of an experimental ultrasound coherence tomography system.

[0132] Finally, one may rearrange Eq. 12 to find the direction of the ray at the detector, s̄_d = s̄_s - ∫_Γ ∇s(x̄)dl. (13)Jr

[0133] This equation is intuitively similar to Eq. 6 and provides an equation in the form (<medium>) = <measurements>, which is what is sought. Unfortunately, this function does not have a direct inverse because a set of measurements can correspond to many potential mediums. However, as one solution to this equation is sought, and one can provide bounds on what the solution might look like, such as maximum / minimum values for the speed of sound.

[0134] Therefore, by assuming that there is only one reasonable solution within these bounds, one can attempt to find the medium’s properties by looking in the neighbourhood of a first guess. One can assess the “goodness” of any particular guess by comparing the resulting sdvalues to those experimentally measured. The guess is then updated to minimize the error between the experimental and simulated results. Accordingly, the image reconstruction step may be performed via the processing of a measure dependent on (i) thedirection of arrival of each ray, and (ii) a vector quantity based on an accumulated gradient of slowness along a path of each ray.

[0135] To implement this process via a computer (e.g. processing circuitry), one may first discretize Eq. 13 (and the same can be done for Eq. 6 in parallel to demonstrate how the present example method differs and how it can be combined for direction of arrival + time of flight ultrasound coherence tomography).

[0136] Numerical implementations (for processing by a computer) may seek to find the properties of a medium by discretizing those properties into a grid (or image) of N pixels. For time-of-flight based methods, Eq. 6 is approximated as:

[0137] d = L(s) • s (14)

[0138] where s is a vector of size N containing the medium’s slowness at each pixel, and d is a vector of size M containing the time-of-flight for each ray M that links a source and a detector. L(s) is then the ray-length matrix of size M x N which contains the distance each ray travelled through each pixel.

[0139] For direction of arrival based methods, once can instead discretize Eq. 13. Fora single ray, the slowness vector sdat the detector is given by

[0140] s̄_d = n̄_d s_0 = s̄_s - l(s) · G(s) and G(s) = ∇s (15)

[0141] where 1 is a vector of size N (the number of pixels) containing the distance travelled by the ray through each pixel and G is a matrix of size N x K containing the gradient of the slowness at each pixel. For this proof-of-concept, the two-dimensional problem is studied and so K = 2. However, this can be easily generalized to three dimensions for triaxial transducer by using K = 3. l(s) is written as a function of the slowness distribution because, due to refraction, the path of the rays will change depending on the slowness gradient that they encounter. This causes the ray to “bend” differently every time the guess is updated and is the source of the name “bent-ray inversion”.

[0142] To generalize this for a number of projected rays M, one may write

[0143] Sd= Ss- L(s) • g(s) (16)

[0144] where Sdand Ssare now matrices of size KM, L(s) is now a matrix of size KM x N, and g(s) is a vector of size KN (a flattened version of G(s)). The spatial dimension K is flattened to keep L(s) two-dimensional and remaining variables as vectors. This is primarily for convenience during implementation as many matrix solvers prefer these conventions.

[0145] To assess the “goodness” of a particular guess, one can use least squares criteria to quantify the accuracy of a guess s at each iteration. This is also called a cost function or error, and the cost function for time-of-flight based methods is given by as

[0146] C(s) = ||L(s) ’s^measured Hi (17)

[0147] During the ultrasound coherence tomography inversion process, one can seek to minimize this cost function. As image reconstruction progresses, improvements in the cost function generally diminish at an accelerating rate. Therefore, the stopping condition is often defined as a threshold for the change in the cost function. The form of the cost function above is justified when the errors have the same variance and are independent. Prior information can also be incorporated using regularization during the inversion process.

[0148] Similarly, the cost function for direction of arrival based methods can be written as

[0149] C(s) = ||S_s - L · g(s) - S_d,measured||²₂ (18)

[0150] We can also write a cost function that takes into account multiple types of measurements (e.g., both direction of arrival and time-of-flight), for example:2

[0151] C(s) = ||L(s) · s - d_measured||²₂ + ξ||S_s - L(s) · g(s) - S_d,measured||²₂ (19)

[0152] where is a weighting factor that converts the units of the direction of arrival based cost function to be consistent with those of the time-of-flight based cost function (e.g., could be the size length of a pixel). Different weightings can also be employed as regularization parameters to emphasize one variable over the other. Various forms of regularization can be applied to any of these cost functions to assist with convergence, such as total variation and Laplacian regularization.

[0153] Accordingly, in some example implementations, a raytracing algorithm may employs minimization of a cost computed over a set of rays, each ray being associated with a respective receive event of the ultrasound computed tomography dataset, wherein a perray contribution to the cost is generated, for a given ray, based on a difference between: (i) a difference between a source slowness vector and a detection slowness vector, each slowness vector having a magnitude equal to a local slowness value and a direction equal to a direction of the given ray, the source slowness vector having a direction characterizing an emission direction associated with ultrasound emission by a given multiaxial ultrasound transducer employed as a source of ultrasound emission for the given ray, and where the detection slowness vector is determined, for the given ray, based on multiaxial the direction of arrival computed via multiaxial beamforming, and (ii) a vector quantity based on the accumulated gradient of slowness along the path of the given ray, where a slowness field within the imaging target is refined as the cost function is minimized.

[0154] The above cost functions are simply examples of one possible implementation method, and cost functions for direction of arrival or time-of-flight based methods could be formulated in many different ways. In general, one can expect that, since direction of arrival measurements demonstrate a direct relationship with the gradient of the slowness distribution, integration of this information with traditional image reconstruction methodswould increase edge definition in heterogeneous media. Once can also hypothesize that the overall signal-to-noise ratio will improve since information directly related to the spatial derivative of the slowness will lead to second-order error rather than first-order error. Finally, it is expected that multiaxial steering will provide greater target coverage and better snrthan a conventional array with a similar number of transducers.

[0155] The present multiaxial ultrasound coherence tomography imaging methods provides a novel and improved ultrasound imaging modality. Unlike conventional ultrasound imaging methods, the present example multiaxial ultrasound coherence tomography imaging methods perform image reconstruction using the measured direction of arrival of a ray, and optionally also the time-of-flight information, rather than the time-of-flight information alone. The aforementioned example image reconstruction method, advantageously employed a relationship between the direction of arrival of a ray and the gradient of the speed of sound field that it travelled through. Consequently, in stratified media, direction of arrival information is affected more by the boundaries between regions rather than the speed of sound within a region. This lies in contrast to the time-of-flight of a ray, which is related directly to the speed of sound field. Accordingly, the present example ultrasound coherence tomography image reconstruction scheme using the gradient of the speed of sound field rather than the speed of sound field directly may find new and beneficial clinical utility.

[0156] Preliminary simulation results contrasting multiaxial and conventional ultrasound coherence tomography arrays with the same hardware (including driving, beamforming, array geometry, transducer element size, transducer element properties, number of transducer elements, and transducer element positions) demonstrate several benefits over conventional methods, including, for example, significantly sharper edges between regions, proportional speed of sound differences between different regions, and (due to the stability of direction of arrival based measurements across a signal) image reconstruction using an arbitrary wavefront, not just the initial wavefront. This can further enable reconstruction with more pronounced wavefronts in attenuating media, and time-averaged image reconstruction schemes.

[0157] For application such as tumor detection and / or surgical planning, reconstruction using the gradient of the speed of sound field can demonstrate even greater benefits because one of the primary goals in these cases is the segmentation of different regions of tissues. Forthat reason, direction of arrival based ultrasound coherence tomography methods provide significantly better qualitative image quality (sharper edge definition, reduced noise, and fewer artifacts) with the same number of sensors. This is ideal for cases in which the relative positions of regions and their boundaries is important. For quantitative imaging (recovering the absolute value of the sound speed for a particular location and usingthe quantitative value to make decisions), time-of-flight based methods may have the advantage in retrieving the true values of the speed of sound field. However, because direction of arrival based methods are entirely compatible with time-of-flight based methods, direction of arrival and time-of-flight can be used to produce quantitative images with better edge definition between tissues.

[0158] As noted above in the discussion regarding multiaxial beamforming, in some cases, multiple directions of arrival may be identified. This may occur in the context of ultrasound coherence tomography when multiple wavefronts from a single source are incident on a single detector at the same time due to refraction. This could hold valuable information about the image and could potentially be integrated into the aforementioned image reconstruction scheme with few modifications. Examples of modifications include: a more advanced method of simulating the propagation of ultrasound (as described in section lll-B) and further analysis to identify multiple ray paths that correspond to multiple detected directions of arrival at a detector. It may also be helpful to extend the present example methods to estimate the received amplitude of a wavefront as well because the acoustic power of later arrivals may be substantially lower.

[0159] FIG. 6B illustrates an example system for performing ultrasound coherence tomography. The example system includes an ultrasound coherence tomography apparatus 300 having a set of multiaxial ultrasound transducers arranged, at least in part, around a scanning region. The electrodes of the multiaxial ultrasound transducers are interfaced with a Tx / Rx switch 520, which is operably connected to an optional transmit beamformer 500 (e.g. for direction of arrival beamforming) and a receive beamformer 510. For example, for each multiaxial ultrasound transducer may be a biaxial ultrasound transducer having associated first and electrode pairs, and separate electrode connections 540 and 550 may be provided for receiving signals from each electrode pair (while the figure shows a single set of electrode connections, one set would be provided for each multiaxial ultrasound transducer, e.g. unless signal multiplexing is employed).

[0160] Control and processing circuitry 400 is employed to control the transmit beamformer 500 and the receive beamformer 510, and to process the beamformed signals for the acquisition of ultrasound coherence image data and the generation of ultrasound coherence images. As shown in FIG. 6B, in one embodiment, control and processing unit 400 may include a processor 410, a memory 420, a system bus 405, one or more input / output devices 430, and a plurality of optional additional devices such as communications interface 460, data acquisition interface 470, display 440, and external storage 450. It is to be understood that the example system shown in the figure is notintended to be limited to the components that may be employed in a given implementation. For example, the system may include one or more additional processors.

[0161] The present example methods the acquisition, and subsequent processing, of ultrasound coherence tomography image data, can be implemented via processor 410 and / or memory 420. For example, multiaxial directional beamforming to determine a direction of arrival associated with each receive event may be implemented by control and processing hardware 400, via executable instructions or hardware logic represented as multiaxial directional beamforming module 480, and the use of direction of arrival (and optionally time-of-flight information) during image reconstruction may be implemented by control and processing hardware 400, via executable instructions or hardware logic represented as image reconstruction module 485. The modules may be implemented, for example, as any combination of software, hardware, and firmware.

[0162] The functionalities described herein can be partially implemented via hardware logic in processor 410 and partially using the instructions stored in memory 420. Some embodiments may be implemented using processor 410 without additional instructions stored in memory 420. Some embodiments are implemented using the instructions stored in memory 420 for execution by one or more general purpose microprocessors. In some example embodiments, customized processors, such as application specific integrated circuits (ASIC) or field programmable gate array (FPGA), may be employed. Thus, the disclosure is not limited to a specific configuration of hardware and / or software.

[0163] Embodiments of the present disclosure can be implemented via processor 410 and / or memory 420. For example, the functionalities described below can be partially implemented via hardware logic in processor 410 and partially using the instructions stored in memory 420. Some embodiments are implemented using processor 410 without additional instructions stored in memory 420. Some embodiments are implemented using the instructions stored in memory 420 for execution by one or more general purpose microprocessors. Thus, the disclosure is not limited to a specific configuration of hardware and / or software.

[0164] It is to be understood that the example system shown in FIG. 6B is not intended to be limited to the components that may be employed in a given implementation. For example, the system may include one or more additional processors. Furthermore, one or more components of control and processing hardware 400 may be provided as an external component that is interfaced to a processing device. For example, as shown in the figure, the transmit beamformer 500 and the receive beamformer 510 may be included as a component of the control and processing unit 400 (as shown within the dashed line), or may be provided as one or more external devices. The transmit beamformer 500, receivebeamformer 510, or another imaging processing module may be configured or programmed to execute algorithms for performing the methods described herein.

[0165] While some embodiments can be implemented in fully functioning computers and computer systems, various embodiments are capable of being distributed as a computing product in a variety of forms and are capable of being applied regardless of the particular type of machine or computer readable media used to actually effect the distribution.

[0166] At least some aspects disclosed herein can be embodied, at least in part, in software. That is, the techniques may be carried out in a computer system or other data processing system in response to its processor, such as a microprocessor, executing sequences of instructions contained in a memory, such as ROM, volatile RAM, non-volatile memory, cache or a remote storage device.

[0167] A computer readable storage medium can be used to store software and data which when executed by a data processing system causes the system to perform various methods. The executable software and data may be stored in various places including for example ROM, volatile RAM, nonvolatile memory and / or cache. Portions of this software and / or data may be stored in any one of these storage devices. As used herein, the phrases “computer readable material” and “computer readable storage medium” refers to all computer-readable media, except for a transitory propagating signal perse.Passive Ultrasound Imaging

[0168] Passive ultrasound imaging can be employed in a wide variety of applications, including, for example, monitoring the progression of cavitation-mediated high-intensity focused ultrasound (HIFU) therapies, monitoring seismic activity, and performing nondestructive acoustic emission testing. Existing single-element systems can provide quantitative information about the progression of these activities, but currently lack the ability to localize said activity. Localization instead requires an array of several transducers, where the estimated time-of-flight (TOF) of the signal to each sensor is used to reconstruct an image. This family of algorithms relies on constructive interference, such as with delay, sum, and integrate (DSAI) style algorithms. However, methods dependent on time-of-flight can fail to identify a singular location for the ultrasound’s origin when using arrays with few elements.

[0169] The present example embodiment employs the use of biaxial ultrasound sensors, or more generally, multiaxial ultrasound sensors, for creating passive imaging arrays capable of accurately localizing acoustic activity with only one or two sensors. A single-element system that can map acoustic intensity in one dimension, as well as a two-element system that can map acoustic energy in two dimensions using only direction of arrival, are experimentally demonstrated without time-of-flight information. A combineddirection of arrival and time-of-flight algorithm is also described for further improving image performance metrics. The example embodiments may be employed in space-constrained applications, such as, for example, monitoring of HIFU therapies.

[0170] The goal of passive ultrasound imaging is to produce a spatial map of acoustic energy. This can be at an instantaneous time or integrated across a period of time. As mentioned above, Eq. 4, or variations thereof described above, produces a spatial map intuitively corresponding to the likelihood that received acoustic energy came from a certain direction. In other words, one is focusing the signals measured from a multiaxial transducer such that they deconstructively interfere at the location or direction in which they originated. Conventional passive ultrasound imaging and, in fact, most conventional ultrasound imaging modalities do the opposite: they focus signals such that they constructively interfere at the location or direction in which they were produced. The advantage of conventional methods is that they can directly estimate how much acoustic energy originated from a particular location.

[0171] This advantage can be mimicked by restating the focusing algorithms such that they also estimate how much acoustic energy originated from a particular location (or direction). In its most basic form, an equation of the following form may be employed:

[0172] / (o7,0') = ^(S) / i (77(07,0')), (20)

[0173] where / (a*, 0') is the estimated acoustic power in a direction d' and measured at the frequency co, and g(S) is a function of any signals collected by a transducer (e.g., SFand SL) that gives the total acoustic power received by the transducer held within those signals. Finally, / I(T7(O7, 0')) is a function which transforms 77(07,0') such that it behaves more like a conventional focusing algorithm: it produces a peak (not necessarily related to the power received by the transducer) in the direction d' where the ultrasound most likely originated from. For example, / I(T7(O7, 0')) could be defined as:[01741 '■(’>«“■«')) = ^7). CD

[0175] where 0 < e < 1 is a user-selected parameter to mitigate the effect of division by zero. In practice, once may chose, for example, e = 0.1 leading to a factor of 10 increase of the acoustic power when 77(07,0') = 0 and suppressing any region where 77(07, 0') > 0.9. The present inventors found that this formulation produced the best image quality, but it will be understood that the preceding example method is not intending to be limiting. For example,h(j](w, is a Gaussian-like function that also would also produce a peak when 77(07,0') goes to zero. There are many possible variations on these two equations and likely completely different formulations that would give a similarly shaped function, but these are two examples that I have tested and determined to work.

[0176] Similarly, g(S) can be defined as

[0177] 5(S) = |SF(6)) + SL(6))e-^(e')|2(22)

[0178] which was proposed in Refs. [16, 17], This equation has another benefit: it is actually a beamformer itself. By applying a phase shift to the lateral signal, the signals are focused to constructively interfere at the location or direction in which they were produced. Anecdotally, while it was a good beamformer for b-mode imaging as outlined in Refs. [16, 17], it is not a particularly good beamformer for passive ultrasound imaging with at best around 1-2 dB of SNR and a full-width half-max so large that it was not captured within the imaging window of about 100 degrees. For multiaxial transducers with N electrode pairs, this approach can be generalized such that all lateral signals are appropriately phase corrected and then summed with the forward signal to produce constructive interference.

[0179] Alternatives include more traditional methods of finding the signal power. For example, g(S) = |SF(to)|2, g(S) = |SF(to)|2+ |SL(to)|2, or g(s) = sF(t) + H(sF(t)') (where W(s) is the Hilbert transform and sF(t) + W(sF(t)) gives the upper envelope of the signal sF(t) at a particular time). All of these would likely provide passable results and there are too many variations to outline here. However, these are some of the most common methods of finding acoustic power.

[0180] For the present experimental demonstration, the following delay-and-sum style algorithm has been implemented based on Eq. 22:|sF(w)+SL(w)e“i"<;’6(e')|2

[0181] = -L’

[0182] Equation 23 is then summed over the desired frequency bins, giving / (£') =!■$>(") + SL(ω)e-i"^6(e,)| / (e +?7(a»,0')). In the present example implementations, the adjacent two frequency bins were summed over to the frequency of the point source to find the energy across three bins total.

[0183] To generate a two-dimensional image estimating acoustic power over a range of imaging locations x using both transducers, one can use:ro«4i(25)

[0185] where the primary difference is thatn(x) and ab n(x) are now characterized per-element and in two-dimensions. This approach can be intuitively thought of as the projection of the one-dimensional maps given by Eq. 23 out from each transducer. When using two biaxial transducers, this produces a characteristic “x” shape where the onedimensional profiles overlap.

[0186] Recognizing that traditional techniques employ time-of-flight for constructive interference, time-of-flight information was also incorporated for two-dimensional images using the alternative formulation

[0187] 1< M = I ^=1I2’ (26)

[0188] where rn(x) = |xn- x| / c is the expected time taken for the sound to travel from an imaging point to the sensor, and c = 1488 m / s is the speed of sound in the medium (in this case, water).

[0189] While the present example methods of passive multiaxial beamforming employ the difference measure of Eqn. 4 in the denominator, it will be understood that other functional forms of the difference measure may be employed in the alternative, such as, for example, include|ai,(a»,0)SF(a») - and |ai,(a»,0)SF(a»)e“i^6(:"'e)-SL(ω)|.EXAMPLES

[0190] The following examples are presented to enable those skilled in the art to understand and to practice embodiments of the present disclosure. They should not be considered as a limitation on the scope of the disclosure, but merely as being illustrative and representative thereof.Example 1: Numerical Demonstration of Multiaxial Ultrasound Coherence Tomography

[0191] FIG. 7 shows the setup for tests with Shepp-Logan and breast tissue phantoms using direction of arrival information. The phantoms include speeds of sound ranging from 1460 to 1580 m / s. The ultrasound coherence tomography array for the Shepp-Logan phantom is a 128-element ring with a diameter of 38.5 cm operating at 350 kHz and an element length of 5 mm. For the breast tissue, the device is a 128-element ring with a diameter of 21 cm operating at 600 kHz and an element length of 3 mm. To generate experimental data for this numerical demonstration, an open-source tool for solving the viscoelastic wave propagation with a finite-difference time-difference (FDTD) solver was used to calculate the two-dimensional forward pressure fields for each transducer element using a 10-pulse sinusoidal burst modulated with a cosine ramp function. Resolution was set to 0.71 mm and 0.41 mm for Shepp-Logan and breast phantoms, respectively, matching 6 points per wavelength in water conditions.

[0192] The direction of arrival was calculated using the phase map of the incident pressure field at the detectors, which simulations with a spherical source indicated that it correlates linearly with direction of arrival (R2> 0.99, p < 10-6). The experimental directionof arrival calculated with the FDTD method was calculated at different time points relative to the onset detection of the signal. Calculations of experimental direction of arrival were done at 0.0, 1.0, 2.0, 3.0, 4.0 and 5.0 periods of the fundamental frequency relative to the onset detection.

[0193] As also shown in FIG. 7, a full wavefront ray tracer was used as the forward model during the inversion procedure. The wavefront ray tracer ensures that all detectors are reached with a maximal distance of 1 pixel to the center of each detector. The average of total variation and Laplacian minimization methods were used to solve the inverse problem with a loop of 20 iterations. The initial map before inversion was set to a value of 1500 m / s.

[0194] FIG. 8 shows the reconstruction obtained using direction of arrival input data for the Shepp-Logan phantom at different time points. The regions at low values of speed of sound are well reconstructed and overall the interfaces are well recovered. While a strong contrast of the interfaces can be reconstructed, the whole range of speed of sound values, especially in the high speed of sound region at the rim of the phantom, is not completely recovered. Images can be reconstructed at different time points providing similar contrast at 0, 1 and 2 periods, while for latter time points an inversion of the contrast, with some blurriness, can be observed at the interfaces.

[0195] FIG. 6B shows the reconstruction of the breast phantom using direction of arrival based ultrasound coherence tomography. Compared to the Shepp-Logan test, more variability was observed in the reconstructed images at different time points. The reconstruction at the time of onset (0 periods) produced the most contrasted interfaces of the breast tissue, with the highest speed of sound at the rim of the phantom, which is aligned with the ground truth. However, some streaking artifacts were observed at the water-tissue interface. Reconstruction at 2 and 3 periods showed comparable images, with a similar observation as for the Shepp-Logan phantom where the high speed of sound of the edges is not fully recovered. Blurriness started to appear on tests at 4 and 5 periods. FIG. 10 shows the root mean square error (RMSE) for the two phantom tests. Overall, reconstruction converged to a steady state between 7 and 10 iterations.

[0196] As observed in the reconstructed images in FIG. 8, for the Shepp-Logan test, the error reduced when choosing direction of arrival calculated from 0 to 2 periods and started to increase for 4 and 5 periods. For the breast phantom, the test at 0 periods showed the lowest error and increased with the number of periods. While image reconstruction using late time points degraded the image, results indicated that it is possible to obtain reconstructed images without needing to account for the exact detection of the time of arrival.

[0197] To the best of the knowledge of the present inventors, this disclosure provides the first numerical demonstration that ultrasound coherence tomography image reconstruction is entirely possible using exclusively direction of arrival information.Experimental Demonstration of Passive Multiaxial Imaging

[0198] A two-element biaxial array was manufactured which, along with a hemispherical acoustic source, were used to experimentally demonstrate biaxial passive ultrasound imaging (FIG. 11). A grid of 341 positions for the spherical source (-50.41 mm < x < 50.05 mm, 30.00 mm < y < 110.57 mm, resolution 5 mm, positions relative to the center of the array) was used to collect data. Grid positions were calculated in post using time-of-flight to triangulate 7 points throughout the grid.

[0199] FIG. 12 depicts sample one-dimensional images, one each for both transducers, when the acoustic source was at the center-most point in the characterized range. FIG. 14 summarizes the aggregate one-dimensional beamforming results across 117 different point source positions. Transducer 1 demonstrates superior performance to transducer 2 in terms of localization error, although transducer 2 demonstrates a smaller FWHP. These differences are attributed to manufacturing differences between the two transducers. FIG. 13 is a snapshot from a video animation depicting the frame-by-frame reconstruction of an image using Eq. 23. The full animation shows how transducer 1 can stably identify the direction of arrival of the incident ultrasound energy even in instantaneous images.

[0200] FIG. 15 depicts sample two-dimensional images for when the point source was located at the center of the characterization range. The failure of time-of-flight based methods to identify a unique location where cavitation is likely is contrasted with direction of arrival only and direction of arrival / time-of-flight fusion methods, where a single point is much more obvious. In general, two elements were insufficient for time-of-flight only methods.

[0201] FIG. 16, which is a table showing median (± IQR) aggregate results for two-dimensional direction of arrival only biaxial beamforming, includes aggregate results across the 117 most central points of the characterization range for direction of arrival only image reconstruction. Overall error for this array configuration was 12.20 mm or, for a wavelength of approximately 4.18 mm in the present case, 2.92 wavelengths of overall error. The lateral localization error is much smaller, representing a median error value of 0.34 wavelengths. This is contrasted with the axial error at 2.73 wavelengths, indicating that most of the overall localization error is due to errors in the axial direction. This is expected based on the geometry of the array and the increased triangulation error as the point source gets further away from the array. The variance in all three cases indicates that the error can vary on the order of several wavelengths in both the lateral and axial directions. Finally, there is a smallbias to the localization errors, with results favouring the left side of the array and closer to the array.

[0202] FIG. 17, which is a table showing median (± IQR) aggregate results for two-dimensional direction of arrival and time-of-flight biaxial beamforming, shows similar aggregate results for direction of arrival and time-of-flight reconstruction. In general, these results demonstrate improved SNR and reduced A50area but similar localization errors.

[0203] FIG. 18 shows a snapshot from an animation demonstrating two-dimensional direction of arrival only beamforming (Eq. 24) as the time window moves across the signals on the bottom. A point source was located at < x,z >=< -0.0180,7.03 > cm, or at the center of the characterization range. The time window (gray rectangle) indicates the data that is being used to create the instantaneous image in the top left. FIG. 19 shows a snapshot from an animation demonstrating two-dimensional direction of arrival and time-of-flight beamforming, with the images showing a pattern distinct from that of direction of arrival only beamforming, with banding like that in the time-of-flight only reconstructed images. However, this algorithm is computationally more expensive.

[0204] The specific embodiments described above have been shown by way of example, and it should be understood that these embodiments may be susceptible to various modifications and alternative forms. It should be further understood that the claims are not intended to be limited to the particular forms disclosed, but rather to cover all modifications, equivalents, and alternatives falling within the spirit and scope of this disclosure.REFERENCES[1] N. Meulenbroek, S. Delgado, L. Curiel, and S. Pichardo, “Multi-axial transducers for passive point source localization,” in 2021 IEEE International Ultrasonics Symposium (IUS), pp. 1–4, IEEE, 9 2021.[2] N. E. Meulenbroek, S. Delgado, L. Curiel, A. C. Waspe, and S. Pichardo, “Passive directivity detection using individual biaxial ultrasound transducers,” IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, pp. 1-1, 2022.[3] S. Delgado, L. Curiel, and S. Pichardo, “Application of the biaxial driving method to focus ultrasound using only two electric signals,” in 2020 IEEE International Ultrasonics Symposium (IUS), vol. 2020September, pp. 1–3, IEEE, 9 2020.[4] S. Delgado, L. Curiel, and S. Pichardo, “Steering single-element lead zirconate titanate ultrasound transducers using biaxial driving,” Ultrasonics, vol. 110, p. 106241, 2 2021.[5] S. Delgado, L. Curiel, and S. Pichardo, “Focal size reduction and displacement in a single-element biaxial ring transducer at 510 khz and 1.66 mhz,” in 2021 IEEE UFFC Latin America Ultrasonics Symposium (LAUS), pp. 1–3, IEEE, 10 2021.[6] F. Aulanier, B. Nicolas, P. Roux, and J. I. Mars, “Time-angle sensitivity kernels for soundspeed perturbations in a shallow ocean,” The Journal of the Acoustical Society of America, vol. 134, p. 88, 7 2013.[7] F. Aulanier, B. Nicolas, P. Roux, and J. I. Mars, “Time-angle sensitivity kernels for soundspeed perturbations in a shallow ocean,” The Journal of the Acoustical Society of America, vol. 134, pp. 88–96, 7 2013.[8] S. Pichardo, L. Curiel, S. Delgado, and N. Meulenbroek, “Systems and Methods for the Operation of Multiaxial Ultrasound Transducers.” Provisional Patent, United States of America, Apr. 2021.[9] J. Cole, S. J. Ahmed, L. Curiel, S. Pichardo, and O. Rubel, “Marble game with optimal ferroelectric switching,” Journal of Physics: Condensed Matter, vol. 26, p. 135901, 3 2014.

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Claims

CLAIMS1. A method of performing ultrasound computed tomography, the method comprising:employing a multiaxial ultrasound coherence tomography apparatus to acoustically interrogate an imaging target and obtain an ultrasound coherence tomography dataset, the multiaxial ultrasound coherence tomography apparatus comprising a plurality of multiaxial ultrasound transducers, each multiaxial ultrasound transducer comprising an acoustically active element having a plurality of electrode pairs disposed thereon, each electrode pair being suitable for electrically driving the acoustically active element along a different axis, the ultrasound coherence tomography dataset comprising, for each receive event of a plurality of receive events, a respective set of multiaxial receive signals received by a given multiaxial ultrasound transducer, each multiaxial receive signal of a given set of multiaxial receive signals being associated with a different electrode pair;performing multiaxial beamforming on each set of multiaxial receive signals to determine a respective direction of arrival corresponding to each receive event; and employing each direction of arrival when processing the ultrasound computed tomography dataset to generate, via image reconstruction, an ultrasound computed tomography image characterizing the imaging target;wherein image reconstruction is performed employing a ray tracing algorithm dependent on (i) the direction of arrival of each ray, and (ii) a vector quantity based on an accumulated gradient of slowness along a path of each ray.

2. The method according to claim 1 wherein the raytracing algorithm employs minimization of a cost computed over a set of rays, each ray being associated with a respective receive event of the ultrasound computed tomography dataset, wherein a per-ray contribution to the cost is generated, for a given ray, based on a difference between: (i) a difference between a source slowness vector and a detection slowness vector, each slowness vector having a magnitude equal to a local slowness value and a direction equal to a direction of the given ray, the source slowness vector having a direction characterizing an emission direction associated with ultrasound emission by a given multiaxial ultrasound transducer employed as a source of ultrasound emission for the given ray, and wherein the detection slowness vector is determined, for the given ray, based on multiaxial the direction of arrival computed via multiaxial beamforming, and (ii) the vector quantity based on the accumulated gradient of slowness along the path of the given ray, wherein a slowness field within the imaging target is refined as the cost function is minimized.

3. The method according to claim 1 or 2 wherein the plurality of multiaxial ultrasound transducers are spatially distributed at least partially around a scanning region, the scanning region including the imaging target and a coupling medium configured to acoustically couple ultrasound energy into and out of the imaging target;wherein acoustically interrogating the imaging target and obtaining the ultrasound coherence tomography dataset comprises:a) selecting a multiaxial ultrasound transducer from the plurality of multiaxial ultrasound transducers;b) sending drive signals to at least one electrode pair of the selected multiaxial ultrasound transducer such that ultrasound energy is emitted from the selected multiaxial ultrasound transducer;c) for each multiaxial ultrasound transducer other than the selected multiaxial ultrasound transducer, employing at least two electrode pairs of the multiaxial ultrasound transducer to detect a set of multiaxial receive signals, each detected set of signals corresponding to a different receive event;d) repeating steps a) to c) a plurality of times, each time selecting a different multiaxial ultrasound transducer, thereby obtaining the ultrasound computed tomography dataset.

4. The method according to claim 3 wherein the drive signals provided to at least one selected multiaxial ultrasound transducer are provided to at least two electrode pairs to control an emission direction of ultrasound energy emitted by the at least one selected multiaxial transducer.

5. The method according to any one of claims 1 to 4 wherein, for a given multiaxial ultrasound transducer, a pre-determined mathematical relationship is known that characterizes a dependence, on direction of arrival, of an amplitude ratio and a phase difference between multiaxial receive signals associated with a first electrode pair and a second electrode pair of the given multiaxial ultrasound transducer; andwherein multiaxial beamforming of multiaxial receive signals detected by the first electrode pair and the second electrode pair during a receive event are employed to determine an associated direction of arrival angle by:employing the pre-determined mathematical relationship to determine a direction of arrival having an amplitude ratio and a phase difference that best approximates an amplitude ratio and phase difference associated with the detected multiaxial receive signals.

6. The method according to claim 5 wherein the pre-determined mathematical relationship comprises a first function characterizing a known direction of arrival angle dependence of a ratio of signal amplitudes from a first electrode pair and a second electrode pair, and a second function characterizing a known direction of arrival angle dependence of a phase difference in signals from the first electrode pair and the second electrode pair.

7. The method according to claim 6 wherein the direction of arrival angle associated with the set of multiaxial receive signals detected by the given multiaxial ultrasound transducer is determined by:applying the first function and the second function as amplitude and phase corrections when evaluating a difference between a first receive signal obtained from the first electrode pair and a second receive signal obtained from the second electrode pair, each of the first function and the second function being applied such that the terms in the difference are expected to be equal when the first function and the second function are evaluated at an angle corresponding to the direction of arrival; andidentifying the angle that minimizes the difference.

8. The method according to any one of claims 1 to 7 wherein time of flight information associated with each receive event is employed, in addition to the direction of arrival associated with each receive event, when performing image reconstruction.

9. An ultrasound computed tomography system comprising:a plurality of multiaxial ultrasound transducers, each multiaxial ultrasound transducer comprising an acoustically active element having a plurality of electrode pairs disposed thereon, each electrode pair being suitable for electrically driving the acoustically active element along a different axis; andcontrol and processing circuitry operatively coupled to said plurality of multiaxial ultrasound transducers, said control and processing circuitry being configured to perform operations comprising:controlling the plurality of multiaxial ultrasound transducers to acoustically interrogate an imaging target and obtain an ultrasound coherence tomography dataset, the ultrasound coherence tomography dataset comprising, for each receive event of a plurality of receive events, a respective set of multiaxial receive signals received by a given multiaxial ultrasound transducer, each multiaxial receive signal of a given set of multiaxial receive signals being associated with a different electrode pair;performing multiaxial beamforming on each set of multiaxial receive signals to determine a respective direction of arrival corresponding to each receive event; andemploying each direction of arrival when processing the ultrasound computed tomography dataset to generate, via image reconstruction, an ultrasound computed tomography image characterizing the imaging target;wherein image reconstruction is performed employing a raytracing algorithm dependent on (i) the direction of arrival of each ray, and (ii) a vector quantity based on an accumulated gradient of slowness along a path of each ray.

10. A method of performing multiaxial beamforming to determine direction of arrival angle information associated with detection of a set of multiaxial receive signals by a multiaxial ultrasound transducer, the method comprising:obtaining a pre-determined mathematical relationship characterizing a dependence, on direction of arrival, of an amplitude ratio and a phase difference between multiaxial receive signals associated with a first electrode pair and a second electrode pair of the multiaxial ultrasound transducer, the pre-determined mathematical relationship comprises a first function characterizing a known direction of arrival angle dependence of a ratio of signal amplitudes from the first electrode pair and the second electrode pair, and a second function characterizing a known direction of arrival angle dependence of a phase difference in signals from the first electrode pair and the second electrode pair; andwherein the direction of arrival angle information associated with the set of multiaxial receive signals detected by the given multiaxial ultrasound transducer is determined by:applying the first function and the second function as amplitude and phase corrections when evaluating a difference between a first receive signal obtained from the first electrode pair and a second receive signal obtained from the second electrode pair, each of the first function and the second function being applied such that the terms in the difference are expected to be equal when the first function and the second function are evaluated at an angle corresponding to a direction of arrival; andassociating one or more minima in the difference, when evaluated a function of angle, with respective direction of arrival angles of detected ultrasound energy.

11. The method according to claim 10 wherein the multiaxial ultrasound transducer is a component of an ultrasound coherence tomography apparatus.

12. The method according to claim 11 wherein the direction of arrival angle is employed when generating an ultrasound coherence tomography image.

13. A method of performing ultrasound computed tomography, the method comprising:employing a multiaxial ultrasound coherence tomography apparatus to acoustically interrogate an imaging target and obtain an ultrasound coherence tomography dataset, the multiaxial ultrasound coherence tomography apparatus comprising a plurality of multiaxial ultrasound transducers, each multiaxial ultrasound transducer comprising an acoustically active element having a plurality of electrode pairs disposed thereon, each electrode pair being suitable for electrically driving the acoustically active element along a different axis, the ultrasound coherence tomography dataset comprising, for each receive event of a plurality of receive events, a respective set of multiaxial receive signals received by a given multiaxial ultrasound transducer, each multiaxial receive signal of a given set of multiaxial receive signals being associated with a different electrode pair;performing multiaxial beamforming on each set of multiaxial receive signals to determine a respective direction of arrival corresponding to each receive event; and employing each direction of arrival and time of flight information when processing the ultrasound computed tomography dataset to generate, via image reconstruction, an ultrasound computed tomography image characterizing the imaging target.

14. An ultrasound computed tomography system comprising:a plurality of multiaxial ultrasound transducers, each multiaxial ultrasound transducer comprising an acoustically active element having a plurality of electrode pairs disposed thereon, each electrode pair being suitable for electrically driving the acoustically active element along a different axis; andcontrol and processing circuitry operatively coupled to said plurality of multiaxial ultrasound transducers, said control and processing circuitry being configured to perform operations comprising:controlling the plurality of multiaxial ultrasound transducers to acoustically interrogate an imaging target and obtain an ultrasound coherence tomography dataset, the ultrasound coherence tomography dataset comprising, for each receive event of a plurality of receive events, a respective set of multiaxial receive signals received by a given multiaxial ultrasound transducer, each multiaxial receive signal of a given set of multiaxial receive signals being associated with a different electrode pair;performing multiaxial beamforming on each set of multiaxial receive signals to determine a respective direction of arrival corresponding to each receive event; and employing each direction of arrival and time of flight information when processing the ultrasound computed tomography dataset to generate, via image reconstruction, an ultrasound computed tomography image characterizing the imaging target.

15. A method of performing image reconstruction from an ultrasound computed tomography dataset, the ultrasound coherence tomography dataset having been acquired by a multiaxial ultrasound coherence tomography apparatus comprising a plurality of multiaxial ultrasound transducers, each multiaxial ultrasound transducer comprising an acoustically active element having a plurality of electrode pairs disposed thereon, each electrode pair being suitable for electrically driving the acoustically active element along a different axis, the ultrasound coherence tomography dataset comprising, for each receive event of a plurality of receive events, a respective set of multiaxial receive signals received by a given multiaxial ultrasound transducer, each multiaxial receive signal of a given set of multiaxial receive signals being associated with a different electrode pair;the method comprising:performing multiaxial beamforming on each set of multiaxial receive signals to determine a respective direction of arrival corresponding to each receive event; and employing each direction of arrival when processing the ultrasound computed tomography dataset to generate, via image reconstruction, an ultrasound computed tomography image characterizing an imaging target;wherein image reconstruction is performed employing a ray tracing algorithm dependent on (i) the direction of arrival of each ray, and (ii) a vector quantity based on an accumulated gradient of slowness along a path of each ray.

16. A method of performing passive multiaxial ultrasound imaging using a multiaxial ultrasound transducer, the method comprising:obtaining a pre-determined mathematical relationship characterizing a dependence, on direction of arrival, of an amplitude ratio and a phase difference between multiaxial receive signals associated with a first electrode pair and a second electrode pair of the multiaxial ultrasound transducer, the pre-determined mathematical relationship comprising a first function characterizing a known direction of arrival angle dependence of a ratio of signal amplitudes from the first electrode pair and the second electrode pair, and a second function characterizing a known direction of arrival angle dependence of a phase difference in signals from the first electrode pair and the second electrode pair; andapplying the first function and the second function as amplitude and phase corrections to generate a difference measure between a first receive signal obtained from the first electrode pair and a second receive signal obtained from the second electrode pair, each of the first function and the second function being applied such that the terms in the difference measure are expected to be equal when the first function and the second function are evaluated at an angle corresponding to the direction of arrival;generating an angle-resolved passive ultrasound image by evaluating a quantity having: (i) a numerator characterizing a measure of total acoustic power associated with the multiaxial receive signals; and (ii) a denominator including the difference measure.

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