Methods, systems, and computer readable media for applying acoustic radiation force to non-destructively characterize materials based on longitudinal elasticity metrics

Abstract

A method for applying acoustic radiation force ultrasound to non-destructively characterize materials based on longitudinal elasticity metrics includes applying, using an ultrasound transducer, acoustic radiation force at a plurality of different angles of incidence relative to an axis of symmetry of a material sample. The method further includes measuring, at each of the different angles of incidence, displacements of the material sample caused by the applying of the acoustic radiation force. The method further includes determining, from the displacements, a metric of longitudinal elasticity of the material sample.

Description

[0001] METHODS, SYSTEMS, AND COMPUTER READABLE MEDIA FOR APPLYING ACOUSTIC RADIATION FORCE TO NON-DESTRUCTIVELY CHARACTERIZE MATERIALS BASED ON LONGITUDINAL ELASTICITY METRICS GOVERNMENT INTEREST This invention was made with support under Grant Numbers CA281150 and DK107740 awarded by the National Institutes of Health. The Government has certain rights in the invention. PRIORITY CLAIM This application claims the priority benefit of U.S. Provisional Patent Application Serial No. 63 / 689,680 filed August 31, 2024, the disclosure of which is incorporated herein by reference in its entirety. TECHNICAL FIELD The subject matter described herein relates to interrogating materials using ultrasound excitation at different angles of incidence relative to an axis of symmetry of the materials, measuring resulting displacements, and using the displacement measurements to determine qualitative or semi-quantitative estimates of longitudinal elasticity metrics of the materials. BACKGROUND The axis of symmetry in a material is an axis in the material about which the material is substantially structurally symmetric. A plane that extends parallel to the axis of symmetry and about which the material is substantially structurally symmetric is the plane of symmetry. The plane of isotropy in a material is a plane in which a material is substantially isotropic. Examples of the plane of symmetry and the plane of isotropy are described below with respect to Figures 1 and 2. It is desirable to qualitatively or semi-quantitatively characterize the longitudinal Young’s modulus of materials, such as tissue, for example to detect abnormalities which will cause the longitudinal Young’s modulus to differ from that of normal tissue. Tissues and other materials can be characterized by exciting the tissue or other material with ultrasound energy and measuring the response. If the angle of incidence of the ultrasound excitation used to interrogate a material is fixed at 90 ° with respect to axis of symmetry of a material, the elasticity estimates that can be obtained at this fixed angle only indicate the longitudinal shear elastic modulus, which often does not convey enough information to differentiate between materials. Because ultrasound excitation at a fixed angle of incidence of 90 ° relative to the axis of symmetry of a material can fail to provide longitudinal Young’s elasticity estimates usable to differentiate between materials, there exists a need for improved methods, systems and computer readable media for applying acoustic radiation force to non-destructively evaluate materials based on longitudinal Young’s elasticity metrics, such as the longitudinal Young’s modulus or a ratio of the longitudinal Young’s modulus and the longitudinal shear modulus. SUMMARY The subject matter described herein includes methods for characterizing the longitudinal Young’s modulus of anisotropic materials, specifically targeting soft tissues such as skeletal muscle, kidney, and breast. It is demonstrated that by leveraging Viscoelastic Response (VisR) or Double Profile Intersection (DoPIo) ultrasound, both on-axis Acoustic Radiation Force (ARF)-based elastography methods, and varying the angle of ARF incidence relative to the axis of symmetry (AoS) of transversely isotropic (TI) materials, the underlying Young’s elastic modulus (^^) or the ratio of Young’s elastic modulus to shear elastic modulus can be evaluated by measuring the change in VisR or DoPIo-measured elasticity compared to the elasticity measured at normal (90°) ARF-AoS incidence. In particular, the data described herein illustrates that for VisR ultrasound, the percent change in relative elasticity with varying incidence angles (∆^^) is proportional to the ratio of the shear longitudinal elastic modulus and compressive longitudinal elastic modulus ^ఓ^ா^^. In addition, the results discussed herein show that the that when materials are interrogated using DoPIo ultrasound, the change in relative elasticity correlates directly with the compressive longitudinal elastic modulus (Young’s modulus), rather than ratio of shear longitudinal elastic modulus and compressive longitudinal elastic modulus. The change in relative elasticity measurements that correlate directly with compressive longitudinal elastic modulus can be used to differentiate between normal tissue and inflamed, fibrotic, fatty, necrotic, fragmented, or otherwise pathologic tissue in humans. The change in relative elasticity measurements that correlate with the ratio of the shear longitudinal elastic modulus and compressive longitudinal elastic modulus can be used to different between normal tissue and inflamed, fibrotic, fatty, necrotic, fragmented, or otherwise pathologic tissue in humans. The findings have been validated in silico using VisR and DoPIo simulations on TI materials with mechanical properties representative of anisotropic soft tissues, ensuring the technique’s reliability and applicability to real-world biological tissues. These evaluations of Young’s modulus have the potential to yield novel, semi-quantitative biomarkers for the evaluation of anisotropic tissues such as kidney, skeletal muscle, and breast. In addition, the results discussed in the section described below entitled, “VisR Ultrasound with Non-Normal ARF-AoS Incidence Interrogates Both Shear and Young’s Elastic Moduli in Transversely Isotropic Materials,” demonstrates the results of interrogating ex vivo tissue samples using VisR ultrasound to determine qualitative or semi-quantitative measurements of a ratio of longitudinal Young’s modulus to longitudinal shear modulus. According to one aspect of the subject matter described herein, a method for applying acoustic radiation force ultrasound to non-destructively characterize materials based on longitudinal elasticity metrics includes applying, using an ultrasound transducer, acoustic radiation force at a plurality of different angles of incidence relative to an axis of symmetry of a material sample. As used herein, “axis of symmetry” is intended to refer an axis that is oriented parallel to a plane of symmetry in a material the, where the plane symmetry in the material sample is a plane in which the sample is substantially structurally symmetric or more symmetric than in other planes. The term “plane of symmetry” is not intended to be limited to a plane in which the material sample is completely structurally symmetric. For example, the plane of symmetry in a muscle tissue sample may be a plane oriented in the longitudinal direction of the muscle fibers. The method further includes measuring, at each of the different angles of incidence, displacements of the material sample caused by the applying of the acoustic radiation force. The method further includes determining, from the displacements, a qualitative or semi-quantitative metric of longitudinal elasticity of the material sample. The metrics of longitudinal elasticity obtained using the methodologies described herein are qualitative because they are relative to the unknown magnitude of the applied acoustic radiation force and, in the case where the measurements represent a ratio of longitudinal Young’s modulus and longitudinal shear modulus, semi-quantitative because the measurements represent a ratio of two numbers. It is believed that these qualitative or semi-quantitative metrics can be used to distinguish between material samples, such as tissue samples, with and without abnormalities that will affect the values of the qualitative or semi-quantitative metrics. The measurements of change in relative elasticity obtained using DoPIo ultrasound that correlate directly with Young’s modulus are quantitative in that they correlate with a single metric of elasticity, rather than a ratio. According to another aspect of the subject matter described herein, applying the acoustic radiation force at different angles of incidence relative to the axis of symmetry of the material sample includes tilting the ultrasound transducer and / or the material sample to vary the angle of incidence of a beam of ultrasound energy generated by the ultrasound transducer relative to the axis of symmetry of the material sample. According to another aspect of the subject matter described herein, the ultrasound transducer includes an array of transducer elements and applying the acoustic radiation force at different angles of incidence relative to the axis of symmetry of the material sample includes using transducer elements in the array oriented in different directions or activated with different time delays to generate beams of ultrasound energy that impact the material sample at different angles relative to the axis of symmetry of the material sample. According to another aspect of the subject matter described herein, applying the acoustic radiation force at different angles of incidence includes varying an angle of incidence of the acoustic radiation force through angles ranging from about -45° to about 45° relative to a normal to the axis of symmetry of the material sample. According to another aspect of the subject matter described herein, applying the acoustic radiation force and measuring the displacements includes utilizing Viscoelastic Response (VisR) ultrasound in which, at each of the angles of incidence, applying the acoustic radiation force includes applying a plurality of pulses of ultrasound energy to the material sample and measuring the displacements includes measuring on-axis displacements of the material sample caused by each of the pulses. According to another aspect of the subject matter described herein, determining the metric of longitudinal Young’s elasticity includes determining a relative elasticity of the material sample from the displacements, determining a rate of change in the relative elasticity relative to the angle of incidence, and correlating the rate of change in the relative elasticity to a ratio of longitudinal Young’s modulus and longitudinal shear modulus of the material sample. According to another aspect of the subject matter described herein, applying the acoustic radiation force and measuring the displacements includes using Double Profile Intersection (DoPIo) ultrasound in which, at each of the angles of incidence, applying the acoustic radiation force includes applying a pulse of ultrasound energy and measuring the displacements includes measuring on-axis displacements using first and second tracking beams of different focal configurations and obtaining first and second displacement profiles of the material sample from the first and second tracking beams. According to another aspect of the subject matter described herein, determining the metric of longitudinal elasticity includes using a time intersection of the first and second displacement profiles to determine an elasticity metric at each of the angles of incidence, determining a rate of change in the elasticity metric relative to the angle of incidence, and correlating the rate of change in the elasticity metric to a longitudinal Young’s modulus. According to another aspect of the subject matter described herein, the material sample comprises a tissue sample, such as an in vivo or ex vivo human tissue sample or a preclinical subject tissue sample, such as an in vivo or ex vivo preclinical mammalian tissue sample. According to another aspect of the subject matter described herein, the method for applying acoustic radiation force ultrasound to non- destructively characterize materials based on longitudinal elasticity metrics includes using the metric of longitudinal elasticity to detect an abnormality in the tissue sample. According to another aspect of the subject matter described herein, a system for applying acoustic radiation force ultrasound to non-destructively characterize materials based on longitudinal elasticity metrics. The system includes an ultrasound transducer. The system further includes a computing platform including at least one processor and a memory. The system further includes a controller executable by the at least one processor for controlling the ultrasound transducer to apply acoustic radiation force at a plurality of different angles of incidence relative to an axis of symmetry of a material sample. The system further includes a longitudinal elasticity metric determiner executable by the at least one processor for measuring, at each of the different angles of incidence, displacements of the material sample caused by the applying of the acoustic radiation force and determining, from the displacements, a metric of longitudinal elasticity of the material sample. According to another aspect of the subject matter described herein, a non-transitory computer readable medium having stored thereon executable instructions that when executed by a processor of a computer control the computer to perform steps is provided. The steps include controlling an ultrasound transducer to apply acoustic radiation force at a plurality of different angles of incidence relative to an axis of symmetry of a material sample. The steps further include measuring, at each of the different angles of incidence, displacements of the material sample caused by the applying of the acoustic radiation force. The steps further include determining, from the displacements, a metric of longitudinal elasticity of the material sample. The subject matter described herein can be implemented in software in combination with hardware and / or firmware. For example, the subject matter described herein can be implemented in software executed by a processor. In one exemplary implementation, the subject matter described herein can be implemented using a non-transitory computer readable medium having stored thereon computer executable instructions that when executed by the processor of a computer control the computer to perform steps. Exemplary computer readable media suitable for implementing the subject matter described herein include non-transitory computer-readable media, such as disk memory devices, chip memory devices, programmable logic devices, and application specific integrated circuits. In addition, a computer readable medium that implements the subject matter described herein may be located on a single device or computing platform or may be distributed across multiple devices or computing platforms. BRIEF DESCRIPTION OF THE DRAWINGS Exemplary implementations of the subject matter described herein will now be explained with reference to the accompanying drawings, of which: Figure 1A illustrates a three-dimensional representation of a transversely isotropic (TI) material, with an axis of symmetry (AoS) (shown by the arrow), Figure 1B illustrates the plane of symmetry, and, Figure 1C illustrates the plane of isotropy; Figure 2A illustrates non-normal ARF-AoS incidence angles in the plane of symmetry and underlying material composition as seen by an ultrasound transducer. It is hypothesized that VisR and DoPIo elasticity measurements will reflect a combination of longitudinal shear and Young’s elastic moduli (^^and ^^) as the angle of ARF-AoS incidence deviates from 90°, and Figure 2B illustrates non-normal ARF-AoS incidence angles in the plane of isotropy and underlying material composition as seen by an ultrasound transducer. As mechanical properties do not vary with direction, it is hypothesized that VisR and DoPIo elasticity measurements will remain unaffected by ARF-AoS incidence angle or transverse Young's modulus (^்), providing a reflection solely of the transverse shear elastic modulus (^்); Figure 3A illustrates the 9 ARF-AoS incidence angles analyzed in the plane of symmetry, achieved using a combination of beam tilting and material tilting, and Figure 3B illustrates the same combinations of ARF-AoS incidence angles were also analyzed in the plane of isotropy; Figure 4A illustrates relative elasticity (RE) versus ARF-AoS incidence angle in simulated TI materials clustered by the same ^^, with the transducer aligned to interrogate the plane of symmetry (longitudinal orientation), and Figure 4B illustrates percent change in RE (∆^^) compared to the RE measured at 90° versus ARF-AoS incidence angle; Figure 5 illustrates slopes of ∆^^ versus ARF-AoS incidence angle for each material from Figure 4B, plotted against the corresponding materials’ ^^ / ^^ratios. Statistical difference between the slopes of materials with adjacent ^^ / ^^values, as assessed by Wilcoxon rank sum tests (with 95% confidence interval), is indicated by ‘*’; Figure 6Aillustrates RE versus ARF-AoS incidence angle in simulated TI materials clustered by the same ^், with the transducer aligned to interrogate the plane of isotropy (transverse orientation), and Figure 6B illustrates percent change in RE (∆^^) compared to the RE measured at90°^versus^ARF െ AoS^incidence^angle;Figure 7A illustrates DoPIo-measured elasticity versus ARF-AoS incidence angle in simulated TI materials clustered by the same ^^, with the transducer aligned to interrogate the plane of symmetry (longitudinal orientation), Figure 7B illustrates change in DoPIo-derived elasticity (∆^^^^^^^^^^) compared to the elasticity measured at 90° versus ARF-AoS incidence angle, and Figure 7B illustrates linear regression lines fitted to ∆^^^^^^^^^^ versus ARF-AoS incidence angle data for each material from Figure 7B; Figure 8A illustrates DoPIo-measured elasticity versus ARF-AoS incidence angle in simulated TI materials clustered by the same ^், with the transducer aligned to interrogate the plane of isotropy (transverse orientation), Figure 8B illustrates change in DoPIo-derived elasticity (∆^^^^^^^^^^) compared to the elasticity measured at 90° versus ARF-AoS incidence angle; and Figure 8C illustrates linear regression lines fitted to ∆^^^^^^^^^^ versus ARF-AoS incidence angle data for each material from Figure 8B; Figure 9 is a block diagram illustrating an exemplary system for applying acoustic radiation force ultrasound to non-destructively characterize materials based on longitudinal elasticity metrics; Figure 10 is a flow chart illustrating an exemplary process for applying acoustic radiation force ultrasound to non-destructively characterize materials based on longitudinal elasticity metrics; Figure 11 illustrates an experimental setup for acquiring ex vivo data from bovine longissimus dorsi and chicken pectoralis major samples labelled as follows: (1) ex vivo sample (chicken sample demonstrated), (2) 6-DoF serial robotic arm (Meca500, Mecademic, Montreal, Quebec, Canada), (3) 9- L4 transducer (Siemens Healthineers, Ultrasound Division, Issaquah, WA, USA) attached to robotic arm with custom transducer holder, and (4) S3000 Helix imaging system (Siemens Healthineers, Ultrasound Division, Issaquah, WA, USA). Data were acquired at normal (90°) ARF-AoS incidence followed by 10°, 20°, 30°, and 40° tilting of the transducer about a fixed center axis using the robotic arm; Figures 12A-12I illustrate transducer positioning for ARF-AoS incidence angles of (Figure 12A) 90°, (Figure 12B) 70°, and (Figure 12C) 50° degrees in longitudinal orientation in a TI material; B-mode images of chicken pectoralis major at ARF-AoS incidence angles of (Figure 12D) 90°, (Figure 12E) 70°, and (Figure 12F) 50° in longitudinal orientation; and parametric RE images of chicken pectoralis major at ARF-AoS incidence angles (Figure 12G) 90°, (Figure 12H) 70°, and (Figure 12I) 50° in longitudinal orientation. These RE images were generated from the regions marked by the rectangles in the corresponding B-mode images; Figures 13A-13I illustrates transducer positioning for ARF-AoS incidence angles of (Figure 13A) 90°, (Figure 13B) 70°, and (Figure 13C) 50° degrees in transverse orientation in a TI material; B-mode images of chicken pectoralis major at ARF-AoS incidence angles of (Figure 13D) 90°, (Figure 13E) 70°, and (Figure 13F) 50° in transverse orientation; and parametric RE images of chicken pectoralis major at ARF-AoS incidence angles (Figure 13G) 90°, (Figure 13H) 70°, and (Figure 13I) 50° in transverse orientation. These RE images were generated from the regions marked by the rectangles in the corresponding B-mode images; Figure 14A illustrates VisR RE versus ARF-AoS incidence angle in ex vivo chicken pectoralis major and bovine longissimus dorsi samples, with the transducer oriented to interrogate the plane of symmetry (longitudinal orientation), and, Figure 14B illustrates corresponding percent change in RE versus ARF-AoS incidence angle (∆^^^ for both samples; Figure 15A illustrates VisR RE versus ARF-AoS incidence angle in ex- vivo chicken pectoralis major and bovine longissimus dorsi samples, with the transducer oriented to interrogate the plane of isotropy (transverse orientation), and Figure 15B illustrates corresponding percent change in RE versus ARF AoS incidence angle ^∆^^^^for both samples; and Figure 16 illustrates slopes of linear regression lines fit to ∆^^ versus ARF-AoS incidence angle for chicken pectoralis major and bovine longissimus dorsi in longitudinal orientation. Statistical difference (Wilcoxon rank sum tests with 95% confidence interval) indicated by ‘*’. DETAILED DESCRIPTION Introduction Ultrasound Elastography (UE) techniques provide a noninvasive means to assess tissue stiffness [1], which is valuable for characterizing soft tissues that have undergone changed elasticity due to pathological or physiological processes [2]. Several of these techniques utilize acoustic radiation forces (ARF) generated by focused ultrasound beams to induce localized mechanical perturbations within tissues. The average axial displacements induced in these tissues in response to these perturbations are tracked over time, and subsequently leveraged to evaluate underlying mechanical properties [3]. However, in the majority of such applications, the evaluated soft tissue are assumed to be locally homogenous and isotropic, such that their inherent mechanical properties do not vary with direction [4]. While this assumption may hold for organs such as liver [5], it is important to note that most biological tissues including skeletal muscle, kidney, and breast are mechanically anisotropic [6], [7], [8]. The structure and composition of such tissues results in a higher elasticity longitudinally along the direction of the fibers than across them in the transverse plane. In the simplest form, this corresponds to the definition of a transversely isotropic (TI) medium [9], in which the shear and Young’s elastic moduli vary along versus across a material axis of symmetry (AoS). A representative TI material is illustrated in Figure 1A. The AoS is oriented along the direction of the fibers, and two separate distinct planes can be identified: the plane of symmetry (Figure 1B) and the plane of isotropy (Figure 1C). Considering both rotational and reflective symmetries, as well as the condition of incompressibility, a TI material can be characterized by four material constants

[0010] ,

[0011] : ^ Young’s modulus along the longitudinal direction (^^): describes the stiffness of the material in the direction parallel to the fibers. ^ Young’s modulus along the transverse direction (^்): describes the stiffness of the material in the direction perpendicular to the fibers. ^ Shear modulus along the longitudinal direction (^^): describes the material's ability to resist shear deformation along the direction parallel to the fibers. ^ Shear modulus along the transverse direction (^்): describes the material's ability to resist shear deformation along the direction perpendicular to the fibers. TI material properties have been evaluated extensively using Viscoelastic Response (VisR) ultrasound, an on-axis ARF-based elastography technique

[0012] ,

[0013] . Previous research has demonstrated that VisR-derived elasticity measurements vary as the lateral-elevational long-axis of an ARF point spread function (PSF) is rotated from being aligned across (longitudinal orientation) to along (transverse orientation) the AoS of TI media, and that the degree of this variation is proportional to the ratio of the underlying shear elastic anisotropy (^^ / ^்). This effect has been demonstrated in-silico

[0014] ,

[0015] , as well as in-vivo, where the variation in VisR elasticity measurements taken along versus across tissue fibers was able to differentiate between patients with and without lower limb dystrophic skeletal muscle

[0016] , and patients with benign vs. malignant breast tumors

[0017] ,

[0018] . It is important to note that previous studies investigating the relationship between VisR-derived elasticity measurements and shear elastic anisotropy typically assumed the ARF excitation to be incident normal to the underlying material AoS. This assumption meant that the observed displacements were mainly indicative of the shear elastic modulus within the examined plane. We herein present a technique to characterize the longitudinal shear-to-Young’s modulus ratio ^^ / ^^of TI materials. We demonstrate that by varying the angle of ARF incidence relative to the AoS in the plane of symmetry and assessing the percent change in VisR-measured elasticity compared to the elasticity measured at a normal (90°) incidence, we can evaluate the underlying ^^ / ^^of a TI material. We further show that Double Profile Intersection (DoPIo) ultrasound

[0019] ,

[0020] , can also be used to interrogate Young’s modulus by varying the ARF-AoS incidence angle in the plane of symmetry and evaluating the rate of change in DoPIo elasticity estimates with tilt angle. General Description Prior research has shown that when the incident angle of an applied force varied between 0° and 90° relative to the AoS of glass fiber reinforced polymer (GFRP) — a TI material — the resulting stiffness measurements reflected a combination of Young's and shear elastic moduli

[0021] . We propose that this relationship extends to VisR and DoPIo interrogations in the plane of symmetry (longitudinal orientation). More specifically, elasticity measurements taken as the angle of ARF incidence deviates from 90° will reflect both longitudinal shear and Young’s moduli (^^and ^^), rather than just the shear modulus. Hence, we hypothesize that by obtaining VisR and DoPIo elasticity measurements across a range of ARF-AoS incidence angles (as illustrated in Figure 2A), we can achieve two goals: I. Identify the angle at which the ARF is perpendicular to the underlying AoS. II. Simultaneously assess both longitudinal shear and Young’s moduli (^^and ^^). In contrast, mechanical properties are known to be directionally invariant in the plane of isotropy

[0011] . Therefore, we hypothesize that in the transverse orientation (Figure 2B) VisR and DoPIo elasticity measurements will remain unaffected by the ARF-AoS incidence angle or the transverse Young’s modulus (^்), providing a reflection solely of the transverse shear elastic modulus (^்). Experimental Methods The methods for demonstrating the innovation are first described for VisR ultrasound. The in-silico simulation framework was adapted from the methods developed by Palmeri et al.

[0022] and later implemented by Hossain et al.

[0014] ,

[0015] ,

[0023] . Using the finite-element modelling (FEM) software LS-DYNA3D (Livermore Software Technology Corporation, Livermore, CA, USA), MATLAB (Mathworks Inc., Natick, MA, USA) and an acoustic intensity map generated by the linear ultrasound simulator Field-II

[0024] , simulations were conducted where a VisR ARF push was incident on 12 different TI materials. The materials were defined to have mechanical properties representative of fibrous tissue such as skeletal muscle, kidney and breast as found in literature

[0025] –

[0032] . Each material was assessed in two different orientations: (i) with the long axis of the lateral-elevational ARF PSF aligned across the material AoS (i.e., interrogating the plane of symmetry in longitudinal orientation), and (ii) with the long axis of the lateral-elevational ARF PSF aligned along the material AoS (i.e., interrogating the plane of isotropy in transverse orientation). In each orientation, variations in the ARF-AoS incidence angle were achieved by tilting the VisR push to -20°, 0°, and 20° and by tilting the material by 0°, 12°, and 24°, for a total of nine incidence angles as shown in Figure 3A, for the plane of symmetry and Figure 3B, for the plane of isotropy. The simulations were allowed to run for a total of 4.35ms, and displacement data were sampled every 0.1ms to represent a conventional ultrasound imaging ensemble with 10^^^ pulse repetition frequency (PRF). Next, using Field-II, 3D volumes were defined consisting of sub-resolution-cell particles made of acoustically scattering media, or “scatterers” at each nodal position consistent with the LS-DYNA3D calculations, with a density of 15 scatterers per resolutional cell. The LS-DYNA3D-derived displacements were used to linearly interpolate the scatterer positions for every time step in the acquisition ensemble using MATLAB. After generating the scatterer position matrices for each time step, the corresponding ultrasound radio-frequency (RF) lines were simulated using Field II. White gaussian noise was added to each RF line using the awgn function in MATLAB in order to simulate a system SNR of 40^^^, which is typical of commercially available clinical ultrasound imaging systems. Motion tracking was performed using normalized cross-correlation with respect to a pre-displacement reference RF line according to procedures described in

[0033] , and the peak correlation at each axial depth within a 80µm search window for a 2-lambda kernel was transcribed as the displacement at each PRF timepoint. Hence, datasets describing axial displacements over time were generated for each unique TI material with specific orientation and ARF-AoS incidence angle. The displacements were fit to the VisR mass- spring-damper model via non-linear least squares minimization to derive Relative Elasticity (RE)

[0012] ,

[0013] . RE measurements were analyzed in terms of mean and standard deviation of values from the same region-of-interest (ROI) (a 2mm region about the focal depth). The methods employed for DoPIo imaging were similar to those described for VisR, except 1) one ARF push was used to induce displacement, 2) that induced displacement was tracked using two simultaneously beamformed RF lines, and 3) the time of intersection of the resulting two temporal displacement profiles was related to elastic modulus using an empirically derived formula

[0019] ,

[0020] . DoPIo elastic modulus estimates were also analyzed in terms of their mean and standard deviation of values from the same region of interest (ROI), a 2mm region centered about the focal depth. Results Figure 4A, illustrates VisR RE versus ARF-AoS incidence angle for longitudinal orientation in 4 simulated TI materials. The materials are clustered by longitudinal shear modulus values, with two materials having ^^^ൌ^16.20^kPa and two materials having ^^ ^ൌ ^4.80^kPa. Three observations arenotable. First, when the ARF- AoS incidence angle is 90°, RE varies by shear elastic modulus only. Second, as the ARF-AoS incidence angle deviates (increases or decreases) from 90°, RE increases. Finally, for a given shear elastic moduli, the degree of this RE increase is greater in the material with the larger Young’s moduli. For all simulated materials, the percentage change in RE at different ARF-AoS incidence angles compared to the RE measured at 90° was calculated and defined as ∆^^. Figure 4B shows ∆^^ versus ARF-AoS incidence angle for materials with different ratios of longitudinal shear-to- Young’s elastic moduli (^^ / ^^^. Materials with lower ^^ / ^^exhibited greater percent change in RE for a given change in ARF-AoS incidence angle. The statistical relationship between ∆^^ and ^^ / ^^was assessed using Spearman’s correlation test. The correlation coefficients, reported in Table I, indicate a strong correlation, particularly for 78oand smaller incidence angles. Table I. Spearman correlation coefficients between ^^^^^°^ and ^^ / ^^at each incidence angle in the plane of symmetry. Correlation ^^^^^°^ with ^^ / ^^^^^^86°^ -0.63^^^^78°^ -0.98^^^^70°^ -0.97^^^^66°^ -0.97^^^^58°^ -0.98^^^^46°^ -0.99To quantify the relationship between ∆^^^and ^^ / ^^, linear regression was performed on the ∆^^ versus ARF-AoS incidence angle data for each material from Figure 4B. The slopes of the fitted lines, representing the rate of change of ∆^^ with respect to ARF-AoS incidence angle, were then extracted. These slopes were plotted against the corresponding ^^ / ^^ratios of the materials, as shown in Figure 5. It can be observed that slope decreases with increasing ^^ / ^^ratio. Wilcoxon rank sum tests (with 95% confidence intervals) indicated that the slopes of materials with the same or similar ^^ / ^^values (0.26, 0.26, 0.26, and 0.27) were not statistically different, while the slopes of all other materials with adjacent ^^ / ^^values were statistically different. Figure 6A, illustrates VisR RE versus ARF-AoS incidence angle for transverse orientation in 4 simulated TI materials. The materials are clusteredby transverse shear modulus values, with two materials having ^் ^ൌ ^3.60^kPaand two materials having ^் ^ൌ ^3.20^kPa. It can be observed that RE variesby ^்but is not impacted by the ARF-AoS incidence angle. Furthermore, from Figure 6B, it is notable that ∆^^ values are negligible across all simulated materials regardless of the ARF-AoS incidence angle. The corresponding results using DoPIo ultrasound are shown in Figures 7A-7C for the plane of symmetry and Figures 8A-8C for the plane of isotropy. Figure 7A illustrates DoPIo measured elasticity versus ARF-AoS incidence angle for longitudinal orientation in 2 simulated TI materials with thesame ^^ ^ൌ ^7.2^kPa. It can be observed that when the ARF- AoS incidenceangle is 90°, DoPIo-predicted elasticity is the same for both materials, and thus varies by shear elastic modulus only. Furthermore, as the ARF-AoS incidence angle deviates (increases or decreases) from 90°, DoPIo-predicted elasticity increases, and this increase is greater in the material with the larger longitudinal Young’s moduli (^^). Figure 7B depicts change in DoPIo-derived elasticity relative to measurements at 90° for all materials, which is defined as ∆^^^^^^^^^^. Materials with higher ^^exhibited greater change in DoPIo-derived elasticity for a given change in ARF-AoS incidence angle. To quantify the relationship between ∆^^^^^^^^^^^and ^^, linear regression was performed on the ∆^^^^^^^^^^^ versus ARF-AoS incidence angle data for each material from Figure 7B. The corresponding linear regression lines for all 12 materials are illustrated in Figure 7C. Furthermore, as illustrated in Table II, a strong correlation was observed between ^^and the slope of ∆^^^^^^^^^^ (^ = 0.937, p < 0.0001), whereas weaker, non-significant trends were found for ^்(^ = 0.308, p = 0.330), ^^(^ = 0.417, p = 0.177) and ^்(^ = 0.053, p = 0.871). These results highlight ^^as the primary contributor to angular variation in DoPIo-derived elasticity in longitudinal orientation and support the potential of DoPIo for characterizing ^^in anisotropic tissues such as skeletal muscle, kidney, and breast. . Table II: Spearman’s Correlation Coefficient (^) and corresponding p-values between slopes of linear regression lines fit to ^^^^^^^^^^^ versus ARF-AoS incidence angle data and ^^, ^், ^^, ^்for all materials in the plane of symmetry. Correlation Factor Coefficient p-value Slopes vs. ^^0.937<0.001Slopes vs. ^்0.3080.330Slopes vs. ^^0.4170.177Slopes vs. ^்0.0530.871Meanwhile, Figure 8A illustrates DoPIo measured elasticity versus ARF-AoS incidence angle for transverse orientation in 2 simulated TImaterials with the same ^் ^ൌ ^3.6^kPa. The corresponding ∆^^^^^^^^^^measurements are depicted in Figure 8B. It can be observed that both DoPIo elasticity estimates and ∆^^^^^^^^^^ values remained constant across incidence angles. Furthermore, the slopes of the corresponding linear regression lines for ∆^^^^^^^^^^ (illustrated in Figure 8C) exhibited negligible to weak correlation with any elastic modulus (Table III). Table III: Spearman’s Correlation Coefficient (^) and corresponding p- values between slopes of linear regression lines fit to ^^^^^^^^^^^ versus ARF-AoS incidence angle data and ^^, ^், ^^, ^்for all materials in the plane of Isotropy. Correlation Factor Coefficient p-value Slopes vs. ^^-0.0210.956Slopes vs. ^்0.1790.579Slopes vs. ^^-0.0560.862Slopes vs. ^்0.2200.493Discussion It was demonstrated via in-silico findings within the plane of symmetry that VisR RE measurements taken at non-normal ARF-AoS incidence angles were impacted by both the longitudinal Young’s (^^) and shear (^^) elastic moduli. Moreover, the percent change in RE with varying incidence angles (∆^^) was proportional to the ^^ / ^^ratio. Furthermore, the slopes of linear regression lines fit to the percent change in RE versus ARF-AoS incidence angle distributions demonstrated a strong correlation with the underlying ^^ / ^^of the materials, and these slopes were able to statistically differentiate between TI materials with varying ^^ / ^^ratios. Additionally, it was found that in the plane of isotropy, VisR elasticity measurements remain unaffected by ARF-AoS incidence angle or transverse Young's modulus (^்), providing a reflection solely of the transverse shear elastic modulus (^்). These findings suggest that the rate of change of ∆^^ with incidence angle has the potential to serve as a novel semi-quantitative biomarker for evaluating anisotropic tissues such as kidney, skeletal muscle, and breast, and the authors hope to investigate the in-vivo capabilities of this technique in future studies. When DoPIo ultrasound was used to interrogate the same materials in the plane of symmetry, the change in DoPIo-derived elastic modulus from 90oARF-AoS incidence correlated strongly with the underlying longitudinal Young’s modulus (^^), suggesting that the change in DoPIo-derived elastic modulus with ARF-AoS tilt angle in the plane of symmetry is a viable metric for directly interrogating longitudinal Young’s modulus. It should be noted that variations in the ARF-AoS incidence were achieved in this in-silico evaluation via a combination of beam-tilting and material-tilting. Furthermore, although Table I denotes that ∆^^ is highly correlated with ^^ / ^^at angles with as small a deviation as 78°, from Figure 5B, it seems that ∆^^ is able to distinguish between the various materials with reasonable difference in measure from around 58° onwards. The same observations can be made regarding the DoPIo ∆^^^^^^^^^^ measures given in Figure 7B, where changes greater than 1 kPa occur across all 12 materials from around 58° onwards. Thus, it seems that in order to be an effective biomarker, ∆^^ and ∆^^^^^^^^^^ must be acquired up to 50° ARF-AoS incidence. It is not feasible to obtain such exaggerated ARF-AoS incidence angles via electronic steering using a standard linear array alone (which is limited to a maximum of േ20° in a physical ultrasound machine), but this may be achievable using a curvilinear or other specialized array. This means that effective characterization of ^^ / ^^by VisR or ^^^by DoPIo may not be possible via electronic steering on a standard linear array only, and additional equipment may be required to implement this technique in an ex-vivo or in- vivo setting. Figure 9 is a block diagram illustrating an exemplary system for applying acoustic radiation force ultrasound to non-destructively characterize materials based on longitudinal elasticity metrics. Referring to Figure 9, the system includes an ultrasound transducer 900 for applying acoustic radiation force to a material sample 902. The system further includes a computing platform 904 including at least one processor 906 and a memory 908. The system further includes a controller 910 executable by processor 906 for controlling ultrasound transducer 900 to apply acoustic radiation force at a plurality of different angles of incidence relative to an axis of symmetry of material sample 902. The system further includes a longitudinal elasticity metric determiner 912 executable by processor 906 for measuring, at each of the different angles of incidence, displacements of the material sample caused by the applying of the acoustic radiation force and determining, from the displacements, a metric of longitudinal elasticity of material sample 902. In one example, controller 910 and longitudinal elasticity metric determiner 912 may cooperate to control ultrasound transducer 900 to interrogate material sample 902 at different angles of incidence relative to the axis of symmetry of material sample 902 using ViSR ultrasound to determine, at each angle, a ratio of longitudinal Young’s modulus and longitudinal shear modulus of material sample 902. In another example, controller 910 and longitudinal elasticity metric determiner 912 may cooperate to control ultrasound transducer at different angles of incidence relative to the axis of symmetry of material sample 902 to interrogate material sample 902 using DoPIo ultrasound to determine, at each angle, a metric of longitudinal Young’s modulus of material sample. Controller 910 may control the angle of incidence of the application of ultrasound force to material sample 902 by tilting ultrasound transducer 900, material sample 902, both, or neither, in the case where ultrasound transducer 900 includes an array of ultrasound transducer elements capable of generating beams of ultrasound energy at different angles, e.g., using transducer elements transducer elements in the array oriented in different directions or activated with different time delays. To tilt material sample 902, the system may include a tiltable stage or platform (not shown in Figure 9) on which material sample 902 may be placed during ultrasound interrogation. Figure 10 is a flow chart illustrating an exemplary process for applying acoustic radiation force ultrasound to non-destructively characterize materials based on longitudinal elasticity metrics. Referring to Figure 10, in step 1000, the process includes applying, using an ultrasound transducer, acoustic radiation force at a plurality of different angles of incidence relative to an axis of symmetry of a material sample. For example, an ultrasound transducer, the material sample, both, or neither (in the case of an ultrasound transducer array where transducer elements in the array are oriented in different directions or activated with different time delays) may be tilted relative to the axis of symmetry of the material sample to apply acoustic radiation force to the material sample at different angles of incidence relative to the axis of symmetry. In step 1002, the process further includes measuring, at each of the different angles of incidence, displacements of the material sample caused by the applying of the acoustic radiation force. For example, on axis displacement may be measured using the ultrasound transducer that applied the force, a separate ultrasound transducer, or another device capable of measuring axial displacement. In step 1004, the process further includes determining, from the displacements, a metric of longitudinal elasticity of the material sample. For example, if ViSR ultrasound is used as the interrogation method, relative elasticity may be determined from the displacement measurements, a rate of change in relative elasticity with respect to angle of incidence may be determined, and the rate of change may be correlated to a ratio of longitudinal Young’s modulus and longitudinal shear modulus. If DoPIo ultrasound is used as the interrogation method, the time intersection of the first and second displacement profiles obtained from the different tracking beams may be used to determine an elasticity metric at each of the angles of incidence. A rate of change in the elasticity metric relative to the angle of incidence may be determined. The rate of change in elasticity relative to the angle of incidence may be correlated with the longitudinal Young’s modulus. In step 1006, an indication of normality or abnormality of the material sample may be determined based on the semi-quantitative metric of longitudinal elasticity. For example, if the tissue sample is a muscle tissue sample, it is believed that a normal muscle tissue sample will have a different value of the metric of longitudinal elasticity than abnormal muscle tissue, such as muscle tissue with a fibrotic collagen matrix located between muscle fibers. It is believed that by interrogating normal muscle tissue and muscle tissue suspected to have an abnormal condition, the differences in values of the qualitative longitudinal elasticity metrics obtained using the methodologies described herein for the normal and suspected abnormal samples and be used to identify the presence of an abnormality. VisR Ultrasound with Non-Normal ARF-AoS Incidence Interrogates Both Shear and Young’s Elastic Moduli in Transversely Isotropic Materials As described above, Viscoelastic response (VisR) ultrasound has been demonstrated for assessing the shear elastic moduli of transversely isotropic (TI) materials when the applied acoustic radiation force (ARF) excitation is incident normal to the material axis of symmetry (AoS). This study evaluates the potential for non-normal ARF excitations to interrogate both shear and Young’s elastic moduli in TI materials. In silico experiments indicated that VisR relative elasticity (RE) measurements at non-normal ARF-AoS angles were influenced by both the longitudinal Young’s (^^) and shear (^^) moduli. Furthermore, the percent change in RE with varying ARF-AoS incidence angles (∆^^) exhibited a direct correlation with the ^^ / ^^ratio. Additionally, linear regression analysis of ∆^^ versus ARF-AoS incidence angle demonstrated a strong relationship with the underlying ^^ / ^^of the materials, and also successfully differentiated between TI materials with varying ^^ / ^^ratios. These findings were validated ex vivo in chicken pectoralis major and bovine longissimus dorsi muscles, where the rate of change of ∆^^ with incidence angle distinguished the two tissues with statistical significance. The results obtained in this study suggests that the rate of change of ∆^^ with ARF-AoS incidence angle may serve as a novel semi-quantitative biomarker for characterizing anisotropic tissues such as kidney, skeletal muscle, and breast. As described above with regard to Figures 1A-1C, the mechanical properties of TI (transversely isotropic) materials can be described in terms of Young’s and shear moduli. While the mechanical properties of TI materials may be described in terms of Young’s and shear moduli, their interrelationship is more complex than in isotropic materials. The constitutive equation for a linear, elastic material can be written in terms of a generalized Hooke’s lawbetween a stress tensor, ^, and a strain tensor, ^, as ^^^ ൌ ^^^^^^^^,where ^^^^^is a fourth-order stiffness tensor that characterizes the material. Due to rotational and reflective symmetries in a TI material, the stiffness tensor reduces from 81 elastic constants to five independent quantities

[0010] ,

[0011] . These five independent quantities can further be expressed in terms of six engineering constants and one constraint: two Young’s moduli oriented along and across the AoS in longitudinal (L) and transverse (T) directions ( ^^and ^், respectively); two shear moduli, (^^and ^்); two Poisson’s ratios in the plane of isotropy and plane of symmetry (^்்and ^^், respectively); and the constraint, Furthermore, if the material is incompressible, the Poisson’s ratios, ^்்and ^^், have specific values as follows [9],

[0010] : 2 Due to these constraints, an incompressible TI (ITI) material can bedescribed in terms of three material constants: ^், ^^ and ^்⁄ ^^ .TI material properties have been evaluated using Viscoelastic Response (VisR) ultrasound, an on-axis, ARF-based, elastography technique

[0012] ,

[0013] . VisR ultrasound is performed using two successive, spatially co- localized ARF excitations, which generate micrometer-scale displacements to approximate a creep response in the ARF region of excitation (ROE)

[0012] ,

[0013] . The induced displacements are tracked ultrasonically and fit to a three- parameter mass-spring-damper (MSD) model, where one parameter accounts for elasticity, one for viscosity, and the last an inertial component, as described by the following second-order differential equation

[0034] : where ^^^Kg^ is mass, ^^^^^m^ is the axial displacement, ^^^Nmି^s^ is the viscosity, ^^^Nmି^^ is the shear modulus, and ^^^s^ is the time. ^^^^ is the ARF excitation that is described in time as a rectangular function of force magnitude ^ and duration ^^ோிas follows: ^^^^ ൌ ^൫^^^ െ ^^ோி െ ^^^ െ ^^^ െ 2^^ோி െ ^^^൯ ^ ^^^^^^(5) െ^^^ െ ^^ோி^^where ^ is the Heaviside function, and ^^^[s] is the time separating the ARF pushes. Substituting (2) into (1) results in: (6) െ^^^ െ 2^^ோி െ ^^^^where ^^^^sି^^ is the natural frequency, ^^^s^ is the relaxation time constant, and ^^^m^ is the static sensitivity of the system. The values of ^^, ^ and ^ are defined as: Equation (3) is solved for the displacement ^^^^, and thenunconstrained nonlinear optimization is used to fit the ultrasonically tracked displacements at each spatial location to the solution of (3) to estimate ^^, ^ ,and^ . Next, relative elasticity (RE^^mି^^^ and relative viscosity (RV^^mି^^^^ arederived as: Both RE and RV are considered relative to the applied ARF amplitude ^ , which is unknown but assumed to be constant over the imaging field-of-view (FOV). Previous research has demonstrated that VisR RE measurements in TI materials vary as the lateral-elevational long-axis of the ARF point-spread- function (PSF) is rotated from being aligned across (longitudinal orientation) to along (transverse orientation) the AoS, and that the degree of this variation is proportional to the ratio of the underlying shear elastic anisotropy (^^ / ^்). This effect has been demonstrated in silico

[0014] ,

[0015] , as well as in vivo, with the ratio of VisR RE taken along versus across tissue AoS differentiating between patients with versus without Duchenne muscular dystrophy

[0016] and patients with benign versus malignant breast masses

[0017] ,

[0018] However, these prior studies employed ARF excitations that had a 90oincidence angle with respect to the underlying tissue AoS, resulting in observed displacements that predominantly reflected shear elastic moduli

[0034] ,

[0014] ,

[0018] . Conversely, a different study found via finite element method (FEM) simulations and continuous loading experiments that when the incident angle of an applied force varied between 0° and 90° relative to the AoS of glass fiber reinforced polymer (GFRP) — a TI material — the resulting stiffness measurements reflected a combination of Young's and shear elastic moduli

[0035] . Given these findings, it is hypothesized that VisR elasticity measurements taken in TI soft tissues with non-normal ARF-AoS incidence angles will reflect a combination of both Young’s and shear and elastic moduli (^^and ^^). This hypothesis is herein evaluated in silico using FEM simulations mimicking VisR acquisitions in TI media, and the method is translated to physical realization in excised bovine longissimus dorsi and chicken pectoralis major muscles. II. Methods METHODS A. In-silico VisR Simulation Framework The in-silico simulation framework was adapted from the methods developed by Palmeri et al.

[0022] and later implemented by Hossain et al.

[0013] ,

[0014] ,

[0023] . The LS-DYNA3D (Livermore Software Technology Corporation, Livermore, CA, USA) FEM solver was used to predict TI material responses to VisR ARF impulses. Firstly, the acoustic intensity field for an ARF push characterized by the parameters provided in Table I was calculated using the Field II ultrasound simulation package

[0023] . The calculated intensity values were scaled to a peak intensity of 5000^^ / ^^ଶ, and the radiation force magnitude was derived according to the following expression

[0023] : ^2^^^(10) ^ൌ^ where ^ is the absorption coefficient of the medium (assigned as 0.5^^^ / ^^ / ^^^ for soft tissue), ^ is the speed of sound in the medium (assumed to be 1540^^ / ^ as in soft tissue), and ^^is the temporal average beam intensity over a volume. As described in (10), point load forces were calculated by spatially sampling the volumetric radiation force ^^. Next, TI materials were defined using the LS-DYNA3D “MAT_ORTHOTROPIC_ELASTIC” material model. Twelve different TI materials were analyzed in this study. Their mechanical properties were chosen to coincide with those published for TI soft tissues such as skeletalmuscle, kidney, and breast: ^் ൌ 11.74 െ 24.96 kPa, ^^ ൌ 35.23 െ 82.78 kPa,^் ൌ 3.20 െ 6.80 kPa, and ^^ ൌ 4.80 െ 40.80 kPa

[0023] -

[0030] . Each material wasdefined for a finite element (FE) mesh that spanned 7^to^42^mm^axially, െ8^to^8^mm^laterally, and െ8^to^8^mm^elevationally, with each element havingdimensions of 0.2 ൈ 0.2 ൈ 0.2^mmଷ

[0015] ,

[0023] . Furthermore, for each TImaterial, a 6-element thick perfectly matched layer (PML) was implemented around the mesh using the LS-DYNA3D “MAT_PML_ELASTIC” material model. The purpose of the PML was to simulate an infinite medium and remove spurious wave reflections from the boundaries of the mesh

[0014] ,

[0015] ,

[0023] . TABLE IV PARAMETERS USED TO SIMULATE THE ARF FIELD AND ULTRASONIC TRACKING, AS WELL AS NCC PARAMETERS USED FOR DISPLACEMENT TRACKING. THE SAME PARAMETERS WERE ALSO USED FOR EXPERIMENTAL ACQUISITIONS. * Aperture growth and dynamic Rx focusing enabled The previously calculated point loads were then applied to each material mesh twice to simulate the two VisR ARF pushes. The point loads' magnitude was kept constant for 70^^^, and the ARF pushes were separated by 0.4^^^. Each material was assessed in two different orientations: (i) with the long axis of the lateral-elevational ARF PSF aligned across the material AoS (i.e., interrogating the plane of symmetry in longitudinal orientation), and (ii) with the long axis of the lateral-elevational ARF PSF aligned along the material AoS (i.e., interrogating the plane of isotropy in transverse orientation). In each orientation, variations in the ARF-AoS incidence angle were achieved by tilting the simulated ARF pushes to െ20°, 0°, and 20° and by tilting the material by 0°, 12°, and 24°, for a total of nine incidence angles per orientation, as shown in Figure 3A for the plane of symmetry and Figure 3B for the plane of isotropy. Note that, although it is expected that VisR RE will vary with ARF-AoS incidence angle in only the plane of symmetry, experiments in the plane of isotropy were included to confirm the expectation. Simulations were allowed to run for a total of 4.35^^^, and displacement data were sampled every 0.1^^^ between the two ARF impulses and following the second ARF impulse to represent a conventional ultrasound imaging ensemble with a pulse repetition frequency (PRF) of 10^^^^

[0015] ,

[0016] ,

[0023] . To simulate ultrasonic tracking, 3D scatterer phantoms were defined in Field II to span the volume of the FEM mesh. For each simulated TI material with a specific orientation and ARF-AoS incidence angle, ten unique scatterer realizations were generated (for a total of 180 unique iterations per TI material: 2 orientations x 9 ARF-AoS incidence angles x 10 unique scatterer realizations). The LS-DYNA3D-derived displacements were used to linearly interpolate the scatterer positions for every time step in the VisR simulation ensemble using MATLAB (Mathworks Inc., Natick, MA, USA). After generating the scatterer position matrices for each time step, the corresponding RF lines were simulated using Field II. White Gaussian noise was added to each RF line using the awgn function in MATLAB to simulate a system SNR of 40^^^, which is typical of commercially available clinical ultrasound imaging systems. Motion tracking was performed on the RF lines using 1D axial normalized cross-correlation (NCC) with parameters listed in Table IV and using procedures described in

[0033] . A dataset describing axial displacements versus time was generated for each independent speckle realization, and the temporal displacement profiles were then fit to the MSD model using a custom C++ implementation of Nelder-Mead non-linear least squares minimization

[0012] . VisR RE values for each speckle realization were then derived according to (8), and RE measurements were analyzed in terms of mean and standard deviation of values from the same region-of-interest (ROI) (a 2^^ region about the focal depth) across the 10 speckle realizations for each unique TI material with specific orientation and ARF-AoS incidence angle. B. Ex-vivo Data Acquisition To physically translate in silico results, ex-vivo experiments were performed on bovine longissimus dorsi and chicken pectoralis major samples purchased from a local butcher shop. These muscles were chosen due to their structure and visible alignment of muscle fibers. Samples were kept at room temperature for 2-3 hours before being placed in a room-temperature water bath for imaging on a motion isolation table (Newport, Irvine, California, USA). For each sample, fiber orientation was determined by visual inspection of the surface and by B-mode imaging. Samples were then positioned to acquire data in both longitudinal and transverse orientations with respect to the AoS, which was indicated by the muscle fibers’ long axes. VisR data were acquired using a Siemens S3000 Helix imaging system with a 9-L4 transducer (Siemens Healthineers, Ultrasound Division, Issaquah, WA, USA). The transducer was mounted on a 6-DoF serial robotic arm (Meca500, Mecademic, Montreal, Quebec, Canada), which was used to acquire data starting at normal (90°) ARF-AoS incidence, followed by 10°, 20°, 30°, and 40° tilting of the transducer about a fixed center axis (corresponding to 80°, 70°, 60° and 50° ARF-AoS incidence angles) in both longitudinal and transverse orientations. This acquisition configuration is illustrated in Figure 11. Three separate VisR acquisitions were repeated at each location without moving the transducer. For each scan, the imaging focal depths in the chicken and bovine samples were 20^^ and 30^^, respectively, due to the thickness of the specific samples. Apart from the focal depths, the same imaging parameters (center frequencies, focal configurations, ARF pulse duration, PRF) outlined in Table IV for in silico data generation were implemented for the ex vivo data acquisitions. VisR data were collected in ensembles consisting of two reference pulses, two ARF impulses with 6 tracking lines between, and then additional tracking lines. The ensembles of VisR data were acquired in 40 lateral positions evenly spaced across a 2^^ lateral field-of-view (FOV) for 2D imaging. ARF-induced displacements were measured using 1D NCC, also with the same parameters listed in Table IV as with the in silico experiments. The temporal displacement profiles were then fit to the MSD model using non- linear least squares minimization, as described above, to form 2D parametric images of VisR RE for each acquisition. From these parametric images, VisR RE was analyzed in terms of mean and standard deviation in a 2^^ ROI about the focal depth across the 3 acquisitions taken at each location. III. RESULTS Figure 4A illustrates VisR RE versus ARF-AoS incidence angle for longitudinal orientation in four simulated TI materials. The materials are clustered by longitudinal shear modulus values, with two materials having^^ ^ൌ ^16.20^kPa and two materials having ^^ ^ൌ ^4.80^kPa. Three observationsare notable. First, when the ARF- AoS incidence angle is 90°, RE varies by shear elastic modulus only. Second, as the ARF-AoS incidence angle deviates (increases or decreases) from 90°, RE increases. Finally, for a given shear elastic modulus, the degree of this RE increase is greater in the material with the larger Young’s modulus. For all simulated materials, the percentage change in RE at different ARF- AoS incidence angles compared to the RE measured at 90° was calculated and defined as ∆^^. Figure 4B shows ∆^^ versus ARF-AoS incidence angle for materials with different ratios of longitudinal shear-to- Young’s elastic moduli (^^ / ^^^. Materials with lower ^^ / ^^exhibited greater percent change in RE for a given change in ARF-AoS incidence angle. The statistical relationship between ∆^^ and ^^ / ^^was assessed using Spearman’s correlation test. The correlation coefficients, reported in Table V, indicate a strong correlation, particularly for 78oand smaller incidence angles. To quantify the relationship between ∆^^^and ^^ / ^^, linear regression was performed on the ∆^^ versus ARF-AoS incidence angle data for each material from Figure 4B. The slopes of the fitted lines, representing the rate of change of ∆^^ with respect to ARF-AoS incidence angle, were then extracted. These slopes were plotted against the corresponding ^^ / ^^ratios of the materials, as shown in Figure 5. It can be observed that slope decreases with increasing ^^ / ^^ratio. Wilcoxon rank sum tests (with 95% confidence intervals) indicated that the slopes of materials with the same or similar ^^ / ^^values (0.26, 0.26, 0.26, and 0.27) were not statistically different, while the slopes of all other materials with adjacent ^^ / ^^values were statistically different. Figure 6A illustrates VisR RE versus ARF-AoS incidence angle for transverse orientation in 4 simulated TI materials. The materials are clustered by transverse shear modulus values, with two materials having ^் ^ൌ ^3.60^kPaand two materials having ^் ^ൌ ^3.20^kPa. It can be observed that RE variesby ^்but is not impacted by the ARF-AoS incidence angle. Furthermore, from Figure 6B, it is notable that ∆^^ values are negligible across all simulated materials regardless of the ARF-AoS incidence angle. Figures 12A-12I illustrate B-mode and parametric RE images of chicken pectoralis major at ARF-AoS incidence angles of 90°, 70°, and 50° in longitudinal orientation. Across the incidence angles, variation in the muscle fiber alignment with respect to the transducer can be seen in the B-mode images. The corresponding parametric RE images demonstrate a progressive increase in measured elasticity as the incidence angle decreases from 90°. Figures 13A-13I demonstrate B-mode and parametric RE images obtained in transverse orientation for the same chicken sample. It can be observed that the measured elasticity is nearly constant across the different incidence angles. Figures 14A and 14B illustrate VisR RE versus ARF-AoS incidence angle for longitudinal orientation in both chicken pectoralis major and bovine longissimus dorsi.^Percent change in RE relative to RE at 90oARF-AoS incidence for both tissues is illustrated in Figure 14B. It is notable that ∆^^ increases more rapidly for chicken pectoralis major than for bovine longissimus dorsi. Figure 10 similarly shows VisR RE (Figure 14A) and ∆^^^^°^ Figure 14B) versus ARF-AoS incidence angle for both chicken and bovine samples, but for transverse orientation interrogating the plane of isotropy. Consistent with in silico results, VisR RE was nearly constant as the ARF-AoS incidence angle varied. Figures 15A and 15B illustrate the slopes of linear regression lines fit to ∆^^ versus ARF-AoS incidence angle for both chicken and bovine samples in longitudinal orientation (Figure 15B). Wilcoxon rank sum tests (95% confidence interval) indicated that the slopes for chicken and bovine muscleswere statistically significantly different (^ ^ 0.05, indicated IV. DISCUSSION This study evaluated the potential for VisR ultrasound to interrogate both shear and Young’s elastic moduli in TI materials using non-normal ARF- AoS incidence angles. Figures 4A, 4B, 12A-12I, 14A, and 14B demonstrate that VisR RE measurements taken using non-normal ARF-AoS incidence angles in the plane of symmetry vary with ARF-AoS incidence angle to a degree that is proportional to the longitudinal Young’s modulus (^^). On the contrary, VisR measurements taken in the plane of isotropy do not vary with ARF-AoS incidence. These results have several meaningful implications. First, the result that percent change in RE versus ARF-AoS incidence angle in the plane of symmetry is highly correlated to the underlying ratio of ^^ / ^^(Figure 4B and Table II) highlights the opportunity to interrogate ^^ / ^^as an independent biomarker. The potential relevance of such is demonstrated in Figure 14B, in which chicken and bovine muscles were differentiated by trends in RE. Considering the data in Figures 14A and 14B more carefully, bovine muscle had higher RE at 90oARF-AoS incidence in both the plane of symmetry (suggesting a higher ^^^^and in the plane of isotropy (Figure 14A, suggesting a higher ^்^, and the percent change in RE with ARF-AoS incidence in the plane of symmetry was lower (suggesting a larger ^^ / ^^) relative to chicken. The relevance of interrogating ^^ / ^^is further demonstrated in Figures 5 and 16, in which the linear regression slope of change in RE versus ARF-AoS incidence angle, a semi-quantitative parameter, statistically discriminated TI materials with different ^^ / ^^in silico and chicken and bovine muscle ex vivo. These results demonstrate that obtaining VisR elasticity measurements across a range of ARF-AoS incidence angles in the plane of symmetry can enable interrogation of ^^ / ^^in anisotropic tissues. The clinical relevance of this finding will be evaluated in future studies. Second, variations in the ARF-AoS incidence were herein achieved using a combination of beam tilting and material tilting in silico and transducer tilting ex vivo. While electronic beam steering would enable more efficient data collection, the steering range of േ20° that is typical for commercial systems would not support the wide range of ARF-AoS incidence angles used in this study. The sufficiency of an ARF-AoS incidence range of േ20° for interrogating ^^ / ^^would need to be determined. Although Table II denotes that ∆^^ is highly correlated with ^^ / ^^at incidence angles as close to 90oas 78° (12° steering), from Figure 4B, ∆^^ distinguishes between materials with ^^ / ^^that are close in value when the ARF-AoS incidence angle is 58° or smaller (32osteering or more). Consistent results were obtained ex vivo (Figures 14A and 14B), when ∆^^ was able to differentiate between chicken and bovine tissues at 60° and 50° ARF-AoS incidence angles, suggesting that about േ30° steering may be needed. An additional complication introduced by electronic steering is the associated alterations to beam properties

[0035] , including changes in beam shape, focal position, prominence of side lobes, etc. The impact of such changes on VisR RE measurements will be evaluated in future work. If it is ultimately determined that electronic steering is not optimal, then specialized devices to support efficient mechanical steering could be designed to make in vivo data collection by mechanical steering convenient. Third, since VisR ultrasound derived RE provides an inherently qualitative indication of elasticity, it necessitates relying on distributions of percent change in RE to compare across different tissue types. However, employing quantitative on-axis elastography techniques, such as Double Profile Intersection (DoPIo)

[0037] ,

[0038] or Quantitative VisR (QVisR)

[0039] , may enable relating the absolute differences in modulus estimates across a range of ARF-AoS incidence angles directly to the underlying ^^. This can potentially lead to quantification of both ^^and ^^in the plane of symmetry, and ^்in the plane of isotropy for more complete characterization of anisotropic tissues. An important additional outcome of this work is the knowledge that VisR assessments of longitudinal shear elastic modulus (^^), which are made in longitudinal orientation, could be confounded by the longitudinal Young’s modulus (^^) if the radiation force is not delivered normal to the underlying AoS. This is especially important to consider when evaluating anisotropic tissues in vivo because the underlying AoS may not be aligned with the skin surface, such as in bipennate muscles

[0040] ,

[0041] or in the context of altered collagen organization caused by cancers

[0042] ,

[0043] or other pathologies

[0044] . However, the results in Figures 4A and 4B also suggest that, in such cases, it would be possible to electronically or mechanically sweep data acquisitions to identify the angle that provides the lowest elasticity measure, as our findings demonstrate that normal radiation force incidence is associated with the minimum value of RE (Figures 4A, 4B, 12A-12I, 14A, and 14B). Alternatively, the confounding effects of non-normal ARF-AoS incidence can be avoided by performing VisR in only the plane of isotropy with transverse orientation, as shown in Figures 6A, 6B, 13A-13I, 15A, and 15B, but this would limit elasticity characterization to only the transverse shear elastic modulus (^்). A limitation in the study design was that in silico results were obtained from a collection of 12 simulated TI materials. Although the elasticities of the evaluated materials spanned the wide range of values expected for various types of soft tissue, including skeletal muscle, kidney and breast, a larger investigation using more materials could help to clarify optimal ARF-AoS incidence angle range and step-size, as well as the potential for electronic steering in clinical settings. Another limitation was that tissue experiments were conducted ex vivo with no aberrating layer between the transducer and the target tissue. Defocusing from aberration (or other causes) would widen the ARF excitation, resulting in a stronger contribution from ^்in VisR RE measures in the plane of symmetry, which could decrease sensitivity to ^^ / ^^. Future studies will include aberrating layers and consider the impact of increasing the ARF focal configuration. VI. CONCLUSION This study has shown that VisR ultrasound can be used to interrogate both shear and Young’s elastic moduli in TI materials. In silico findings within the plane of symmetry revealed that VisR RE measurements taken at non- normal ARF-AoS incidence angles were impacted by both the longitudinal Young’s (^^) and shear (^^) elastic moduli. Moreover, the percent change in RE with varying incidence angles (∆^^) was proportional to the ^^ / ^^ratio. Furthermore, the slopes of linear regression lines fit to the percent change in RE versus ARF-AoS incidence angle distributions demonstrated a strong correlation with the underlying ^^ / ^^of the materials, and these slopes were able to statistically differentiate between TI materials with varying ^^ / ^^ratios. It was found that in the plane of isotropy, VisR elasticity measurements remained constant over ARF-AoS incidence angle. These in silico results were translated to ex vivo application in chicken pectoralis major and bovine longissimus dorsi muscles. The rate of change of ∆^^ with incidence angle, indicative of ^^ / ^^, distinguished between the two tissues with statistical significance. These findings suggest that the rate of change of ∆^^ with incidence angle has the potential to serve as a novel semi-quantitative biomarker for evaluating anisotropic tissues such as kidney, skeletal muscle, and breast. The disclosure of each of the following references is incorporated herein by reference in its entirety. References [1] J. Ophir et al., “Elastography: Ultrasonic estimation and imaging of the elastic properties of tissues,” Proc. Inst. Mech. Eng. [H], vol.213, no.3, pp. 203–233, Mar.1999, doi: 10.1243 / 0954411991534933. [2] T. Shiina et al., “WFUMB Guidelines and Recommendations for Clinical Use of Ultrasound Elastography: Part 1: Basic Principles and Terminology,” Ultrasound Med. Biol., vol.41, no.5, pp.1126–1147, May 2015, doi: 10.1016 / j.ultrasmedbio.2015.03.009. [3] K. Nightingale, M. S. Soo, R. Nightingale, and G. 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Claims

1. CLAIMS What is claimed is:

1. A method for applying acoustic radiation force ultrasound to non- destructively characterize materials based on longitudinal elasticity metrics, the method comprising: applying, using an ultrasound transducer, acoustic radiation force at a plurality of different angles of incidence relative to an axis of symmetry of a material sample; measuring, at each of the different angles of incidence, displacements of the material sample caused by the applying of the acoustic radiation force; and determining, from the displacements, a metric of longitudinal elasticity of the material sample.

2. The method of claim 1 wherein applying the acoustic radiation force at different angles of incidence relative to the axis of symmetry of the material sample includes tilting the ultrasound transducer and / or the material sample to vary the angle of incidence of a beam of ultrasound energy generated by the ultrasound transducer relative to the axis of symmetry of the material sample.

3. The method of claim 1 wherein the ultrasound transducer includes an array of transducer elements and applying the acoustic radiation force at different angles of incidence relative to the axis of symmetry of the material sample includes using transducer elements in the array oriented in different directions or activated with different time delays to generate beams of ultrasound energy that impact the material sample at different angles relative to the axis of symmetry of the material sample.

4. The method of claim 1 wherein applying the acoustic radiation force at different angles of incidence includes varying an angle of incidence of the acoustic radiation force through angles ranging from about -45° to about 45° relative to a normal to the axis of symmetry of the material sample.

5. The method of claim 1 wherein applying the acoustic radiation force and measuring the displacements includes utilizing Viscoelastic Response (VisR) ultrasound in which, at each of the angles of incidence, applying the acoustic radiation force includes applying a plurality of pulses of ultrasound energy to the material sample and measuring the displacements includes measuring on-axis displacements of the material sample caused by each of the pulses.

6. The method of claim 5 wherein determining the metric of longitudinal elasticity includes determining a relative elasticity of the material sample from the displacements, determining a rate of change in the relative elasticity relative to the angle of incidence, and correlating the rate of change in the relative elasticity to a ratio of longitudinal Young’s modulus and longitudinal shear modulus of the material sample.

7. The method of claim 1 wherein applying the acoustic radiation force and measuring the displacements includes using Double Profile Intersection (DoPIo) ultrasound in which, at each of the angles of incidence, applying the acoustic radiation force includes applying a pulse of ultrasound energy and measuring the displacements includes measuring on-axis displacements using first and second tracking beams of different focal configurations and obtaining first and second displacement profiles of the material sample from the first and second tracking beams.

8. The method of claim 7 wherein determining the metric of longitudinal elasticity includes using a time intersection of the first and second displacement profiles to determine an elasticity metric at each of the angles of incidence, determining a rate of change in the elasticity metric relative to the angle of incidence, and correlating the rate of change in the elasticity metric to a longitudinal Young’s modulus.

9. The method of claim 1 wherein the material sample comprises a tissue sample.

10. The method of claim 9 comprising using the metric of longitudinal elasticity to detect an abnormality in the tissue sample.

11. A system for applying acoustic radiation force ultrasound to non- destructively characterize materials based on longitudinal elasticity metrics, the system comprising: an ultrasound transducer; a computing platform including at least one processor and a memory; a controller executable by the at least one processor for controlling the ultrasound transducer to apply acoustic radiation force at a plurality of different angles of incidence relative to an axis of symmetry of a material sample; and a longitudinal elasticity metric determiner executable by the at least one processor for measuring, at each of the different angles of incidence, displacements of the material sample caused by the applying of the acoustic radiation force and determining, from the displacements, a metric of longitudinal elasticity of the material sample.

12. The system of claim 11 wherein applying the acoustic radiation force at different angles of incidence relative to the axis of symmetry of the material sample includes tilting the ultrasound transducer and / or the material sample to vary the angle of incidence of a beam of ultrasound energy generated by the ultrasound transducer relative to the axis of symmetry of the material sample.

13. The system of claim 11 wherein the ultrasound transducer includes an array of transducer elements and applying the acoustic radiation force at different angles of incidence relative to the axis of symmetry of the material sample includes using transducer elements in the array oriented in different directions or activated with different time delays to generate beams of ultrasound energy that impact the material sample at different angles relative to the axis of symmetry of the material sample.

14. The system of claim 11 wherein applying the acoustic radiation force at different angles of incidence includes varying an angle of incidence of the acoustic radiation force through angles ranging from about -45° to about 45° relative to the axis of symmetry of the material sample.

15. The system of claim 11 wherein applying the acoustic radiation force and measuring the displacements includes utilizing Viscoelastic Response (VisR) ultrasound in which, at each of the angles of incidence, applying the acoustic radiation force includes applying a plurality of pulses of ultrasound energy to the material sample and measuring the displacements includes measuring on-axis displacements of the material sample caused by each of the pulses.

16. The system of claim 15 wherein determining the metric of longitudinal elasticity includes determining a relative elasticity of the material sample from the displacements, determining a rate of change in the relative elasticity relative to the angle of incidence, and correlating the rate of change in the relative elasticity to a ratio of longitudinal Young’s modulus and longitudinal shear modulus of the material sample.

17. The system of claim 11 wherein applying the acoustic radiation force and measuring the displacements includes using Double Profile Intersection (DoPIo) ultrasound in which, at each of the angles of incidence, applying the acoustic radiation force includes applying a pulse of ultrasound energy and measuring the displacements includes measuring on-axis displacements using first and second tracking beams of different focal configurations and obtaining first and second displacement profiles of the material sample from the first and second tracking beams.

18. The system of claim 17 wherein determining the metric of longitudinal elasticity includes using a time intersection of the first and second displacement profiles to determine an elasticity metric at each of the angles of incidence, determining a rate of change in the elasticity metric relative to the angle of incidence, and correlating the rate of change in the elasticity metric to a longitudinal Young’s modulus.

19. The system of claim 11 wherein the material sample comprises a tissue sample.

20. A non-transitory computer readable medium having stored thereon executable instructions that when executed by a processor of a computer control the computer to perform steps comprising:controlling an ultrasound transducer to apply acoustic radiation force at a plurality of different angles of incidence relative to an axis of symmetry of a material sample; measuring, at each of the different angles of incidence, displacements of the material sample caused by the applying of the acoustic radiation force; and determining, from the displacements, a metric of longitudinal elasticity of the material sample.

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