Localization of Focused-Ultrasound Beams in a Tissue Phantom, Using Remote Thermocouple Arrays

Transcription

1 IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, vol. 61, no. 12, December Localization of Focused-Ultrasound Beams in a Tissue Phantom, Using Remote Thermocouple Arrays Prasanna Hariharan, Seyed Ahmad Reza Dibaji, Rupak K. Banerjee, Srinidhi Nagaraja, and Matthew R. Myers Abstract In focused-ultrasound procedures such as vessel cauterization or clot lysis, targeting accuracy is critical. To investigate the targeting accuracy of the focused-ultrasound systems, tissue phantoms embedded with thermocouples can be employed. This paper describes a method that utilizes an array of thermocouples to localize the focused ultrasound beam. All of the thermocouples are located away from the beam, so that thermocouple artifacts and sensor interference are minimized. Beam propagation and temperature rise in the phantom are simulated numerically, and an optimization routine calculates the beam location that produces the best agreement between the numerical temperature values and those measured with thermocouples. The accuracy of the method was examined as a function of the array characteristics, including the number of thermocouples in the array and their orientation. For exposures with a 3.3-MHz source, the remote-thermocouple technique was able to predict the focal position to within 0.06 mm. Once the focal location is determined using the localization method, temperatures at desired locations (including the focus) can be estimated from remote thermocouple measurements by curve fitting an analytical solution to the heat equation. Temperature increases in the focal plane were predicted to within 5% agreement with measured values using this method. I. Introduction In quality-control testing of focused ultrasound systems in the preclinical phase, as well as in treatment planning, it is important to accurately measure the focal location relative to the intended target. Often the intended target is an object within a tissue phantom, such as a tumor model for a simulated ablation procedure or a vessel model for a simulated cauterization or clot-lysing procedure. In the simulated procedure, it is important to know both the location of the beam (relative to the target, or perhaps a fiduciary marker embedded in the phantom) and the induced temperature rise as a function of position within the phantom. The capability to localize the beam is especially important for phased arrays, for which the focal location cannot be predicted from the transducer geometry. Manuscript received August 20, 2014; accepted September 24, This study was funded by National Science Foundation grants and P. Hariharan, S. Nagaraja, and M. R. Myers are with the Division of Solid and Fluid Mechanics, Center for Devices and Radiological Health, U. S. Food and Drug Administration, Silver Spring, MD ( matthew.myers@fda.hhs.gov). S. A. R. Dibaji and R. K. Banerjee are with the Department of Mechanical and Materials Engineering, College of Engineering and Applied Science, University of Cincinnati, Cincinnati, OH. DOI One method for localizing focused ultrasound beams involves the use of backscatter ultrasound imaging to measure variations in the echo strain induced by localized changes in the speed of sound and thermal expansion [1], [2] caused by temperature increases. Information about changes in the local temperature field, and hence about the beam location, can be inferred from displacements of the radiofrequency ultrasound echoes [1], [3]. These imaging-based methods require the use of an ultrasound imaging system, but are also useful for tissue characterization and treatment monitoring. Another method for localizing focused ultrasound beams is to embed a phantom with a thermocouple, sonicate around the thermocouple junction, and search for the location yielding maximum temperature rise. Because of the small beam width, this is a time-consuming process. Additionally, the temperature recorded by the thermocouple is subject to several significant sources of error, making it difficult to assume that the temperature recorded by the thermocouple is the actual temperature at the focus of the focused ultrasound beam. One source of error associated with direct sonication of thermocouples is the viscous-heating artifact. The relative motion of the thermocouple surface and the surrounding medium (arising from the radiation force of the ultrasound) leads to a frictional heat source that would not occur in the absence of the thermocouple. As reported by Morris et al. [4], this artifact can represent more than half of the temperature rise measured by the thermocouple, depending upon the type of wire and duration of sonication. Huang et al. [5] also reported substantial (over 30%) artifacts with thermocouple measurements in a flow-through phantom. Positioning errors represent another challenge in measuring temperatures by locating beams atop thermocouples. As noted by O Neill et al. [6] and Dasgupta et al. [7], significant temperature errors can result from small positioning errors. A final potential difficulty associated with thermocouple sonication is the interference of the thermocouple with the beam. This is especially true for larger thermocouples that might be used for added strength in an ultrasound phantom [8]. A noninvasive alternative to direct thermocouple sonication is localization using an inverse heat transfer method, wherein the focal location is determined from remote thermocouple measurements. Because the thermocouples are located outside of the beam, there is little motion of the thermocouples or the medium, and thermocouple ar IEEE

2 2020 IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, vol. 61, no. 12, December 2014 tifacts are minimal. Similarly, errors in positioning the beam atop a thermocouple, and interference with the beam by the thermocouple, are not present. Although inverse methods have been applied outside ultrasound applications [9], [10], few studies have used inverse methods in conjunction with ultrasound phantoms. Hariharan et al. [11] employed an inverse algorithm to back calculate the acoustic intensity on the basis of the ultrasound-induced streaming velocities measured in a liquid medium. O Neill et al. [6] moved the focused ultrasound beam focus to 6 locations relative to a single thermocouple, and used a fitting procedure to predict the coordinates of the thermocouple relative to the beam locations. Dasgupta et al. [7] demonstrated how a second thermocouple can be used to better identify the location of the focused ultrasound beam relative to the target thermocouple. In the work of Dasgupta et al. [7], temperature measurements corrupted by positioning errors were refined using an extrapolation technique based upon the improved knowledge of the beam location. However, to the authors knowledge, no examinations have been made into the optimal number of thermocouples to use, or the accuracy as a function of sonication time. This paper describes a study in which a three-dimensional array of thermocouples embedded in a tissue phantom was used in an inverse-heat-transfer procedure to localize the focused ultrasound beam. Within the inverse algorithm, the coordinates of the beam focus are treated as unknowns. The location of the beam is adjusted until the difference between the computed temperature rise at the subarray nodes and measured values at those locations is minimized. The location of minimum error is designated as the beam location. The accuracy of the temperature field predicted by the inverse algorithm is affected by the extent to which the propagation model employed simulates the relevant physical phenomena. In this paper, the Khokhlov Zabolotskaya Kuznetsov (KZK) algorithm, as implemented in the HIFU_Simulator software [12], was employed. This propagation model, as well as others available in the literature, can degrade in accuracy when phenomena such as highly focused beams or cavitation are present. In this case, it is advantageous to use empirical temperature data from the subarray to estimate temperatures at locations of interest. A temperature-prediction strategy will be presented that uses an analytical solution to the heat equation that is calibrated using array values. A scenario in which the strategy could be used is the following. The beam location is first predicted using a low power setting (where the KZK equation or linear wave equation applies). Once the beam location is determined, the transducer power is increased and the data acquired across the thermocouple array is used in tandem with the estimating function to predict temperatures at non-array locations, including the focus. The following section describes the thermocouple array and the inverse approach. Section III contains results derived using the inverse method on various subarrays, for a variety of sonication times. Section IV discusses the results and draws some conclusions regarding the range of applicability of the inverse method. II. Methods An outline of the study procedure is as follows. Sonications using a focused ultrasound transducer were performed at various target locations within the array. During the sonication period and the subsequent cooling period, temperature measurements were made at all thermocouples comprising the array. Following the experiments, different subarrays of thermocouples were incorporated into the inverse algorithm to estimate the beam location. The accuracy of the inverse method was evaluated as a function of the different numbers and locations of thermocouples comprising the subarray. Accuracy was determined by comparing the coordinates of the beam location derived by the inverse algorithm with those measured by a positioning system. Details regarding phantom construction, ultrasound sonication, temperature measurement, and beam localization are contained in the following sections. A. Phantom Construction A gelrite-based tissue-mimicking material was prepared according to the protocol of King et al. [13]. Acoustic attenuation and speed of sound for the phantom were measured using an ultrasonic time-delayed spectrometry (TDS) system [14]. Thermal conductivity and diffusivity were measured with a thermal property analyzer (KD-2, Decagon Devices Inc., Pullman, WA). Potassium sorbate and calcium chloride were added to the phantom material as preservatives. Properties of the phantom are provided in King et al [13]. The tissue-mimicking material was mixed in liquid form [13] and poured into a cylindrical fixture 8 cm in diameter. Prior to pouring of the liquid mixture into the fixture, the fixture was embedded with an array of eight thin-wire (Chromega-Constantan) thermocouples (0.008 cm diameter), labeled T1 through T8, arranged in four layers with two thermocouples in each layer (Fig. 1). The two thermocouples in each layer were separated by a distance of 4 mm, and each layer was 3 mm in axial extent away from the adjacent layer. To help ensure that the thermocouple leads were perpendicular to the axis of the cylindrical fixture, plastic horizontal cantilevers with grooves for the thermocouple leads were designed that extended radially inward from the fixture surface. The thermocouple leads were fixed within the grooves. The cantilevers each extended to within 0.5 cm of the fixture axis, leaving an unobstructed volume 1 cm in diameter in the center, where the thermocouple junctions resided and sonications were performed. The wires from the 8 thermocouples were connected to an OMB-DAQ-56 (Omega Engineering Inc., Stamford,

3 hariharan et al.: beam localization using thermocouple arrays 2021 Fig. 2. CT scan showing thermocouple wires T1 and T2. Thin, light lines sloping slightly downward from left to right represent thermocouples. Arrows denote thermocouple junctions. Bright spots originate from screws in the fixture; fixture holes without screws appear as dark circles. The dense screws also give rise to artifacts appearing as dark segments connecting all of the screws with each other. Fig. 1. Schematic diagram of thermocouple array. Coordinate system is that established by the CT scanner. CT) data acquisition system. The sampling rate for the system was 1 sample/s. Despite being secured by the cantilevers, the thermocouple wires could undergo slight displacement during pouring of the tissue-mimicking material (TMM). As a result, high resolution (51.4 µm/voxel) micro-computed tomography (micro-ct, Scanco Medical, Basserdorf, Switzerland) was used to more precisely determine thermocouple junction positions. A typical micro-ct image showing the thermocouple junctions is provided in Fig. 2. The three-dimensional micro-ct images revealed an average deviation of 0.4 mm from the distances shown in Fig. 1. B. Acoustic Source The acoustic source was a 1.1-MHz focused ultrasound transducer (Sonic Concepts, Bothell, WA) operating in third-harmonic mode. The operating frequency was thus approximately 3.3 MHz. The transducer diameter and focal length were 6.4 cm and 6.26 cm, respectively. The transducer was driven in continuous-wave mode by a signal generator (33220A, Agilent Technologies Inc., Santa Clara, CA). The driving signal was amplified through the use of a 150-W amplifier (150A100B, Amplifier Research, Souderton, PA). The transducer and the test section resided in a tank of degassed water. The 6-dB beam width of the transducer was 0.52 mm in the radial direction and 3.3 mm in the axial direction. Mounted to the transducer housing was a positioning rod that connected the transducer to an x-y-z positioning system (Fig. 3). The positioning system was capable of adjusting any of the coordinates in discrete mm increments. C. Position Identification The following technique was adopted to experimentally determine the position of the beam within the array. First, a procedure was performed to make the axis of the TMM, the axis of the transducer, and the z-axis of the positioning system parallel. The rim of the transducer was made to contact the surface of the TMM (Fig. 3), making sure contact was made all around the rim. The transducer was then backed away from the TMM using the z-axis screw on the positioning system. Analyses of zoomed-in photographs of the final experimental apparatus from multiple angles revealed slight relative angles between the surface of the TMM and the plane containing the rim of the transducer, as well as between the z-axis of the x-y-z positioning system and the z-axis (axis of rotation) of the transducer/ phantom system. A rotation of 0.7 of the phantom about the x-axis of the positioning system was measured, while the rotation about the y-axis was 1.1. The angle of the zaxis of the transducer/tmm system, measured using the

4 2022 IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, vol. 61, no. 12, December 2014 Fig. 3. Schematic diagram of the positioning system. upper surface of the transducer housing (see Fig. 3), was found to be approximately 1.0 relative to the z-axis of the x-y-z positioning system. For the remainder of the paper, it is assumed that the beam axis was parallel to the z-axis of the x-y-z positioning system and the TMM axis of symmetry residing in the middle of the array, and that the thermocouple wires were perpendicular to the beam axis. This parallel-axis orientation was important, because beam tilt was not built into the mathematical inverse algorithm. (Tilt is discussed further in Section IV.) During the experiments, the transducer was moved along the x-axis of the positioning system. The x-axis of the positioning system corresponded roughly to the x-axis of the array, as defined by the line containing thermocouples T3 and T4. (The y-axis of the array was parallel to the line through T1 and T2.) However, the thermocouple array was not designed so that the x- and y-axes could be accurately identified from outside the fixture, and hence it was not assumed that the x-axis of the thermocouple array corresponded to the x-axis of the positioning system (i.e., some rotation about the z-axis of the two coordinate systems was presumed to have occurred.) As noted in the introduction, precise positioning on top of a thermocouple is difficult for focused ultrasound beams, because of the small beam width and the presence of thermocouple artifacts. Hence, for the purpose of assessing the accuracy of the localization technique, measurements of beam location were not made relative to a position coinciding with one of the thermocouple locations. Instead, measurements of beam location were made relative to an initial sonication location. Accurate measurement of the beam position relative to the previous beam position during successive sonications was possible, because of the precise nature of the x- y-z positioning system. Position measurement began with an initial sonication roughly half way between T3 and T4. The position of the beam was then determined using the inverse algorithm described later. All beam positions for subsequent sonications were measured relative to this initial location, which we took to be the origin of the positioning system. Four additional sonications were executed, at locations 0.25 mm, +0.5 mm, 0.75 mm, and +1.0 mm along the x-axis of the positioning system. At each of these 4 locations, a beam displacement was determined via the algorithm and compared with the displacement measured by the positioning system. It is important to emphasize that the position relative to an initial sonication location was determined only for the purpose of evaluating the accuracy of the method, because beam positions relative to previous beam positions can be measured accurately with the positioning system. The localization procedure yields coordinates of the focus relative to a coordinate system defined by thermocouple junctions in the array. In practice, the coordinates of the target (perhaps a tumor model or vessel model or fiduciary marker) relative to the array would presumably also be known, perhaps through physical connection to the array. Targeting accuracy would be assessed by comparing the coordinates of the ultrasound beam focus with the coordinates of the target. D. Sonication Protocol At each transducer position, the transducer was activated in continuous-wave mode for a period of 30 s. The temperature rise on the full functional array, i.e., thermocouples, T1, T2, T3, T4, T5, T7, and T8, (Fig. 1) was recorded for the 30-s heating period, as well as 20 s of cooling. Thermocouple T6 suffered a malfunction and was not able to record temperature data. Two acoustic power levels were considered, 5 W and 10 W. Sonication at each location was performed 3 times. E. Localization Algorithm In each of the sonication experiments, some of the thermocouples, say N (N 7), were used to define a subarray. The temperature data at the subarray nodes were used in the following algorithm to determine the beam location. A straightforward strategy of stepping through the volume of possible beam focal locations, and computing the difference between the experimental and computational temperature rises across the N-element subarray for each location, was implemented. The computational temperatures were obtained from numerical solutions to the KZK acoustic propagation equation and the heat equation, as implemented in the open-source software HIFU_Simulator. Details of the algorithms are provided in [12]. The metric that was computed for each possible beam location was the average (over the N thermocouples) root-meansquare difference between the experimental temperature rise (T exp ) and numerical temperature rise (T num ) sampled at 1-s (the sampling rate of the data acquisition system) increments: N 1 1 δ = N 50 n= 1 t = 50 s t = 1 s 2 num ( Tnt (,) T(,) nt ). exp (1)

5 hariharan et al.: beam localization using thermocouple arrays 2023 We label the metric δ the optimization difference metric. In (1), the 50 s includes 30 s of heating and 20 s of cooling. For a small number of calculations, durations shorter than 50 s were used in the computations, to examine the influence of sonication time on the accuracy of the method. The location of the beam corresponding to the minimum value of δ was taken to be the derived beam location. The optimization algorithm treats any difference between measured and computed temperatures as localization error, and attempts to reduce the error by finding a new beam position. In order for the algorithm to perform well, differences between experiments and computations not due to localization error should be minimized. To this end, the computed temperatures were normalized by the highest temperature computed, and the experimental temperatures were normalized by the highest temperature measured. This normalization effectively eliminated any problems for the algorithm caused by the source pressure used in the experiments not being exactly the same as that assumed in the computations. With this normalization, all temperature values involved in the optimization process [and input into (1)] were between 0 and 1. To compute the temperature differences required in (1) for a given beam location and thermocouple, the distance from the thermocouple to the beam axis was first computed, along with the axial distance from the thermocouple to the center of the transducer face. The temperature associated with these coordinates could then be easily located in the database of temperature as a function of location. The optimization process thus involved repeated searches through the database as thermocouple number and assumed beam location were changed. Computation of the pressure field and temperature field was only performed once, to compute the values comprising the database. The grid size for the wave-propagation simulation was mm in the axial direction and mm radially. The temperature field in the database was discretized by the heat-equation solver [12] in 0.11-mm increments in the axial direction and mm radially. In attempting to minimize the metric δ in (1), all entries in the database were considered in the calculation. F. Estimation From Remote Measurements The accuracy of the temperature predictions computed within the optimization algorithm is limited by the capability of the acoustic propagation model. These predictions may be sufficiently accurate for beam localization (accuracy of the localization algorithm is addressed in the following section), but for actual temperature prediction at an arbitrary location, temperature prediction using an estimating function with parameters determined using measured temperatures on subarray nodes may be more accurate. (The accuracy of this approach is discussed further in the following two sections.) The estimating function could be constructed from common fitting functions such as polynomials [7], with the unknown parameters determined from the thermocouple measurements. The thermocouple locations would be assumed known at this point because the beam location would be acquired from the localization procedure. Another choice for the estimating function arises when the measurement locations are near the focal plane and sufficiently close to the beam axis say one axial beamwidth. In that case, it is possible to consider the absorbed ultrasound energy as an infinitely long heat source with an intensity profile independent of axial position. This approximation is reasonable because the heat affecting the thermocouple over the recording time originates from a volume of heat roughly constant in strength in the axial direction, because of the zero derivative in the axial beam intensity profile where the beam transitions from converging to diverging. If it is additionally assumed that the heat production has a Gaussian profile, Dillon et al. [15] showed that the estimating function can be written in terms of an exponential integral. The heat production is given by Q = αi exp( r / r ). (2) 2 0 Here, r is the radial coordinate, r 0 is the 1/e beam radius, α is the absorption coefficient, and I 0 is the intensity on the beam axis. The temperature distribution as a function of time is Ir Trt (,) α r r c Ei = p r Ei 2 2 κρ0 0 2 r0 2 ( κt / r0 2 ), where Ei(x) is the exponential integral: 2 s 0 2 (3a) e Ei( x) = d s, (3b) s and κ is the thermal diffusivity, ρ 0 is the density, and c p is the specific heat. By prescribing the unknown intensity and beam width in (3a) and (3b) using temperature data at a given axial coordinate, temperature predictions anywhere in the plane of the given axial coordinate can be made using (3). Temperature predictions using the exponential integral were obtained in the planes of T1/T2, T3/T4, and T7/ T8 (which are perpendicular to the beam axis) by using the data from one thermocouple (the calibration location) as a function of time to determine the parameters of (3a), and predicting the temperature at the other thermocouple location (the prediction location). This procedure was not possible in the T5/T6 plane because of the failure of T6. There were two parameter sets to be determined, the beam radius r 0 and the cluster of constants in front of the square brackets in (3a). The temperature-estimation procedure was performed for all 5 sonication locations described in Section II-C. The prediction location was located in the same plane but on the opposite end of the array from the calibration location. x

6 2024 IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, vol. 61, no. 12, December 2014 TABLE I. Location of the Beam in the Focal Plane Relative to the First Sonication Location, as Determined by the Positioning System (Prescribed Location) and the Inverse Method (Derived Location). Radial displacement Loc 0 Loc 1 Loc 2 Loc 3 Loc 4 Prescribed (mm) Derived (mm) ± ± ± ± 0.02 III. Results A. Determination of Derived Location Using the procedure of Section II-C, an initial beam location was established, and sonications were performed at the 4 other locations along the x-axis of the positioning system. Because the radial beamwidth is much smaller than the axial (a factor of 6 for our transducer), temperature variations in the axial direction were considerably smaller than radial ones, and no motion in the z-direction was considered. Axial coordinates were derived by the algorithm as the beam moved along the x-axis, but they had little temperature variation associated with them and were not reported. As the beam moved along the x-axis, the localization procedure was used to derive the new locations relative to the initial position (labeled the derived positions), and comparisons were made with the locations prescribed by the positioning system (labeled the prescribed positions). The radial distances from the initial position are tabulated in Table I and plotted in Fig. 4. Error bars represent the standard deviation for three measurements. The comparison in Table I is made in terms of distances from the origin (initial sonication location), rather than in terms of x-coordinates, because, as noted in Section II-C, the coordinate system inside the phantom was likely rotated about the z-axis relative to the coordinate system of the positioning system. Changes in both the x- and y-coordinates of the internal system therefore occurred with changes solely in the x-coordinate of the external system. However, distances from the initial location provide a meaningful comparison, as does the degree to which all the sonication locations fall on a line. The average difference between the derived and prescribed distances from the initial location was 0.06 mm. The linearity of the derived locations was measured by the coefficient of determination (R 2 ) for the derived displacements. The R 2 value for the data of Fig. 4 and Table I is In selecting the subarrays for analysis, an attempt was made to choose a representative sample from the space of possible geometries, e.g., it was desired to avoid a large number of arrays in which all thermocouples were aligned vertically. A large variability in the ability of different subarray combinations to predict the radial position can be seen, as well as radial positioning errors of up to almost 1.3 mm. The average position error and the variability as a function of subarray composition decrease with increasing number of thermocouples. When 5 thermocouples are used, the variability between the different combinations is very small (a few hundredths of a millimeter), and the average error in the radial position is about 0.2 mm. The radial positioning error is plotted versus the number of thermocouples in the subarray in Fig. 6. The dependence of the radial positioning error upon number of vertical layers of thermocouples, for a fixed total number of thermocouples, was also investigated. Subarrays of 4 thermocouples, configured in 2, 3, and 4 vertical layers, were used to localize the beam. For the 2-layer configuration, only 3 combinations are possible, because thermocouple T6 was not operative. Five combinations were considered for both the 3-layer and 4-layer subarrays. The error in the radial location is plotted in Fig. 7. Error bars represent the standard deviation for the 3, 5, and 5 arrays for the n = 2-, 3-, and 4-layer cases, respectively. The large standard deviation for the n = 2 case is due to the small number of possible arrays and the large radial positioning error for the (T1, T2, T7, T8) array, also visible in Fig. 5(b). B. Dependence on Number of Thermocouples In Fig. 5, the average (over beam locations 1, 2, 3, and 4 shown in Fig. 4) of the difference between the prescribed and derived radial distances (from the initial location), are shown, as a function of the number of thermocouples. Error bars shown on the plots represent the standard deviation for 12 trials, 3 trials at each of the four positions. For a given number (smaller than the maximum number, 7) of thermocouples, many subarray combinations were possible; some combinations are featured in Figs. 5(a) 5(c). Fig. 4. Radial location of beam referenced from initial sonication location, as measured by positioning system (prescribed shift) and derived by the inverse method (derived shift).

7 hariharan et al.: beam localization using thermocouple arrays 2025 Fig. 5. Average (over the 4 sonication locations) error in the radial position determination, as a function of the composition of the subarray. Error bars represent the standard deviation for 12 measurements: 3 trials at each of the 4 sonication locations. (a) 3-thermocouple subarrays, (b) 4-thermocouple subarrays, and (c) 5-thermocouple subarrays. C. Sensitivity to Sonication Time The location of the beam relative to thermocouple T1 is plotted in Fig. 8(a) as a function of sonication time. Here, all 7 thermocouples were used in the subarray. As a function of sonication time, the localization algorithm converged after about 20 s. The sensitivity of this minimum sonication time to array composition is examined in Fig. 8(b). To reach the final derived location, between 30 and 50 s of temperature tracking were required for all of the subarray combinations considered. (Only one type of subarray for each total number of array elements was examined.) The first 30 s of this time was sonication, with the remainder constituting the cooling phase. D. Temperature Estimation Using Exponential Integral With Empirical Calibration The exponential integral was used to estimate temperatures in the three planes perpendicular to the beam axis containing thermocouples T1 and T2, T3 and T4, and T7 and T8. In each plane, the temperatures measured by one thermocouple were used to compute the unknown parameters in (3). This location was known as the calibration location for the temperature-estimation technique. The exponential integral was then used to estimate the temperature at the other thermocouple location. This second position was termed the prediction location. The estimated temperatures at the prediction locations are compared with the actual thermocouple values in Table II. The radial distance over which the estimation occurred, given by the difference in the radial coordinates of the calibration and prediction locations, is provided, both in terms of absolute distance and numbers of focal beamwidths. (See Section II-B for beamwidth information.) The temperatures estimated using the exponential integral agree with thermocouple values within 5% in the middle (T3/ T4) plane, for both the 5 W and 10 W powers. In the plane closest to the transducer (T1/T2), the discrepancy is about 10% on average. In the plane farthest from the transducer (T7/T8), the average discrepancy is less than 25%. Fig. 6. Error in the determination of the radial location of the beam as a function of the number of thermocouples. Average is performed over all subarray types (shown in Fig. 5) considered containing the given number of thermocouples; error bars represent the standard deviation of all the radial location errors. Fig. 7. Error in determination of the radial location as a function of number of thermocouple layers in the axial direction. Each array contained 4 thermocouples.

8 2026 IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, vol. 61, no. 12, December 2014 Fig. 8. (a) Derived beam location in the focal plane, determined using different amounts of temperature data. Number of thermocouples = 7. (b) Deviation from final derived beam location, as a function of the amount of temperature data used, for subarrays containing different numbers of thermocouples. E. Effect of Inherent Uncertainties on Localization Ability Localization using temperature data from thermocouple arrays combined with numerical modeling involves a variety of uncertainties, including imprecise knowledge of material properties, inexact knowledge of thermocouple locations, thermocouple measurement errors, field asymmetries caused by nonuniform transducer pressure distributions, and discretization error. The effect of these uncertainties upon the prediction of beam location can be estimated as follows. The effect of uncertainty in material properties was examined through a series of numerical simulations using extreme values for each of the relevant phantom properties (density, speed of sound, diffusivity, B/A, and a and b in the frequency-dependent attenuation α = af b ). The extreme values were obtained by taking the measured mean value of the parameter and adding and subtracting a standard deviation, with the mean and standard deviation taken from the paper by King et al. [13] from which the phantom recipe was obtained. The standard deviation ranged from 1.5% of the mean for the speed of sound to 10% of the mean for the nonlinearity parameter B/A. The localization procedure was then repeated using the extreme parameter values (one at a time), and the derived beam location for the given parameter values was compared with the derived beam location based upon mean parameter values. This process was performed for all 5 sonication positions listed in Section II-C. The average (over all parameter combinations and sonication positions) difference in beam location compared with the location based upon mean parameter values was mm (2.3% of the beam width). The maximum difference (compared with the value based upon the mean parameter value) for any parameter extreme at any sonication position was mm (8.5% of the beamwidth). This occurred for several parameter extremes, including the lower limit of the attenuation, at Location1. Changes in the diffusivity and exponent b in the frequency-dependent attenuation produced the largest position-averaged changes in the beam position, mm for both, averaged over all sonication positions. To examine sources of uncertainty related to the thermocouples and field asymmetry, we examined 1) the influence of imprecise knowledge of thermocouple location; 2) random noise in thermocouple measurements; 3) a constant bias in the thermocouple output; and 4) an asymmetric temperature field. The analyses were performed by corrupting numerical temperature values in a manner that simulated how temperature measurements would be affected by these uncertainties in practice. The resulting predictions of beam location were compared with beam locations obtained without corruption of the numerical data. The first type of corruption, which simulated imprecise knowledge of thermocouple position, involved shifting four of the seven thermocouples in the array T2, T3, T5, and T8 random amounts from their intended positions. The numerical temperatures computed at the shifted locations were used as the experimental temperatures in the localization algorithm, while still assuming the thermocouples were located at the intended positions during the execution of the algorithm. The amount of shift ranged from 2 mm to 2 mm. This procedure simulated thermocouple shifting, relative to the intended position, that can occur during the array fabrication process, as in the filling of the fixture with the liquid gelatin material. The second type of corruption was to implement thermocouple measurement noise in the form of a random temperature added to the computed temperature value at each time point, for all 7 thermocouples. The size of the added random numbers was varied between 2 C and 2 C. The third type of corruption simulated a thermocouple measurement bias and consisted of a constant value added at all time points. The bias was different for each thermocouple. Biases between 0 C and 4 C were considered.

9 hariharan et al.: beam localization using thermocouple arrays 2027 TABLE II. Temperature Rise at one Thermocouple Location in a Plane Estimated by Calibrating the Estimating Function [Eq. (3)] Using Data at the Other Thermocouple Location. Estimation distance in radial coordinates Estimated temperature rise ( C) Difference between estimated and measured value (%) Location Millimeters Beamwidths 5 W 10 W 5 W 10 W Level 1 (T1/T2) Loc Loc Loc Loc Loc Level 2 (T3/T4) Loc Loc Loc Loc Loc Level 4 (T7/T8) Loc Loc Loc Loc Loc Estimated temperatures are compared with measured values at the same location. Estimation distance is the difference in radial coordinate (from the beam axis) of the calibration and prediction locations, using thermocouples T1 and T2, T3 and T4, and T7 and T8 for levels 1, 2, and 4, respectively; this distance is given in absolute terms (millimeters) and in numbers of ultrasound beamwidths. The fourth type of corruption was to take the temperature field for an axisymmetric transducer, and multiply it by the dimensionless function (1 + ε sin(θ)), where θ is the angle of rotation about the beam axis in the (x, y) plane. The parameter ε was varied between 0 and 0.7. Thus, it was hypothesized that the transducer nonuniformity produced a 2π-periodic modulation with distance around the beam axis. The falloff in temperature with radial distance from the beam axis was not modified. For all four types of corruptions, a temperature uncertainty was determined by computing the rms difference between the uncorrupted numerical temperatures and the corrupted numerical temperatures. This temperature uncertainty is defined in (1), with the experimental temperatures given by the corrupted numerical temperatures, and the numerical temperatures given by the uncorrupted numerical temperatures. The temperature uncertainty was also rendered dimensionless by dividing by the mean temperature across the array at the midpoint of the sonication. The nondimensionalization allows for comparison across different power levels and different values of the material parameters, such as attenuation and conductivity. [See (3) for relevant parameter values.] In Fig. 9, the error in the derived focal location for the four corruption types is plotted as a function of the relative temperature uncertainty. For the thermocouple misalignment, the effect on the accuracy of the localization is multi-valued, depending upon the nature of the misalignment. A line of best fit was also determined for each data set and plotted in Fig. 9. The slopes of the lines are mm deviation/% uncertainty for thermocouple misalignment, for random noise, for constant bias noise, and for asymmetry. Thus, for the sources of uncertainty considered, the localization process is most sensitive to thermocouple misalignment. However, the differences between the slopes are not large (mean slope ± standard deviation = 0.02 ± 0.005), and it can be roughly said that the sensitivity of the localization procedure to uncertainty is 0.02 mm deviation per 1% uncertainty. That is, a 10% uncertainty in the temperature measurement results in an error in the prediction of the radial position of about 0.2 mm. In terms of the asymmetry parameter ε, ε = 0.1 (10% angular modulation in the temperature field) corresponds to a temperature uncertainty of about 7%, and a localization error of about 0.14 mm. Discretization errors contributing to the uncertainty of the present technique include the step size in the propagation model and heat-transfer solver, as well as the grid resolution for the search algorithm. As noted earlier, the grid resolution for the propagation modeling was mm in the axial direction and mm radially. For the heattransfer simulation, the grid resolution was mm. For the search algorithm, the increment was mm in all directions. To study the discretization error, localization calculations were performed using step sizes of mm and mm for the heat-transfer and localization algorithms, for comparison with the working step size of mm. Computations were performed using a single (of the total of 3) experimental data set. The beam location was computed at the 4 locations considered in Table I. It was found that the average (over the 4 locations) error relative to the prescribed location determined by the positioning system was mm for the mm

10 2028 IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, vol. 61, no. 12, December 2014 Fig. 9. Error in the prediction of the radial beam location as a function of temperature measurement uncertainty, for simulated temperature data corrupted in four ways: 1) Simulated numerical temperatures are stored at each location in the computational domain, including the designed thermocouple locations. At some of the thermocouple locations, the temperature trace is replaced by the trace at a nearby location, simulating thermocouples measuring temperatures at different locations than designed, because of shifting during the fabrication of the phantom. This created a difference between the true (i.e., simulated) temperature field and the corrupted temperature field that was a function of the amount of shift to the nearby location. Four (T2, T3, T5, and T8) of the seven thermocouples were shifted by amounts up to 2 mm. 2) Random perturbations of up to 2 C were added to each time point, for all 7 thermocouples. 3) A bias that was constant in time, but different for different thermocouples, was added to each temperature trace. 4) An asymmetric temperature field of the form T = T s (1 + ε sin(θ)), was imposed, where T s is the temperature field for a symmetric transducer, θ is the angle of rotation about the beam axis, and ε is a parameter that was varied between 0 and 0.7. resolution grid, mm for the mm grid, and mm for the mm grid. IV. Discussion The results of Table I and Fig. 4 showed that the localization method was able to determine the radial location of the focused ultrasound beam with an accuracy of approximately 0.06 mm. For the 0.5 mm ultrasound beam width (full-width at half-maximum) applicable to this study, this error is approximately 12% of the beam width. The localization algorithm also predicted that the 4 derived beam locations were essentially collinear (R 2 = 0.98), which is important because the coordinate changes were accomplished by moving the positioner along its x- axis. These conclusions regarding the capability of the technique are based upon a 7-thermocouple array. As noted in Fig. 6, comparable accuracy can be obtained using 6 or 5 thermocouples. Similar accuracy can even be achieved using 4 or 3 thermocouples, for some thermocouple combinations (e.g., T3, T4, T5, and T7 in Fig. 5). However, with fewer than 5 thermocouples, the localization accuracy is highly dependent upon the type of array chosen and the given beam location. Because the beam location is not typically well known before the localization process, we recommend that arrays containing at least 6 thermocouples be constructed. The 6-node array ensures good localization accuracy even in the event of one thermocouple failure. The failure of thermocouple T6 prevented a thorough study of the sensitivity of the localization technique to the number of vertical layers (Fig. 7), because only 3 possible subarrays could be designed from 4 thermocouples in 2 layers. It does seem to be the case, based upon Fig. 7, that 3 and 4 vertical layers are equally capable of localizing the beam, for a fixed number of 4 thermocouples. It also appears that the accuracy of the localization method is more sensitive to the total number of thermocouples (Fig. 6) than the number of layers (Fig. 7). Derived focal locations for varying sonication time demonstrated that for the array dimensions used in this study, approximately 50 s of acquisition time are required for the coordinates of the derived focal location to attain their asymptotic and most accurate values (Fig. 8). For short focused ultrasound procedures, e.g., exposure for a few seconds, it must be understood that acquisition of temperature data for only the exposure time of the procedure will likely result in a less accurate estimate for the focal location. Hence, even if a 10-s procedure is to be performed in a phantom or excised animal tissue,

11 hariharan et al.: beam localization using thermocouple arrays 2029 a preliminary exposure of longer duration (at least 50 s with cooling) should be executed to accurately ascertain the focal position. These exposures used for localization can be performed at low powers, with temperatures above the noise levels of the thermocouples, but below levels at which thermal effects occur, perhaps 5 C or 6 C. Alternatively, arrays with closer positioning (less than the 4 mm employed in the present apparatus) of the thermocouples can be constructed. The drawback of this approach is that as the radial distance between thermocouples decreases, the likelihood of an intense portion of the beam interacting with the junction increases, thereby generating potentially large thermocouple artifacts. Temperature prediction using empirical calibration of the exponential integral function was most accurate in the T3/T4 plane (Table II), which is the plane of the thermocouple array closest to the focus (i.e., axial location of maximum intensity, about 2 mm in front of geometric focus). The T7/T8 plane is between 6 and 7 mm beyond the focus. For the narrow 3.3-MHz beam used in this study, this represents approximately 2 axial beamwidths. At this distance, spreading of the beam probably violates the line-source assumption upon which the exponentialintegral formulation is based, resulting in lower accuracy for the method. The T1/T2 plane is roughly one axial beamwidth above the focus and some beam spreading has likely reduced the accuracy relative to that in the focal plane. Accuracy at the T1/T2 axial location is still about 10%, however. The success of the exponential-integral method at locations sufficiently near the focal plane illustrates the potential of the technique for estimating temperatures in focused ultrasound procedures. Because the data used to calibrate the temperature prediction function are acquired at locations remote from the beam, thermocouple artifacts are minimal. Additionally, because the acoustic parameters (intensity, beamwidth) required by the model are determined empirically, limitations of the propagation model are also minimized. They emerge only in the determination of the beam location. In other words, the exponential integral primarily models heat transfer from the source region. As noted previously, the primary obstacle to accurate temperature predictions for the temperature estimator is beam curvature. In cases where beam curvature prevents accurate temperature estimation, such as a heterogeneous medium that leads to defocusing, beam localization can still be accomplished, provided the accompanying propagation model can treat the beam focusing with sufficient accuracy. In some cases in which the propagation model produces significant error, accurate beam location may still be possible. Because the localization algorithm works in terms of normalized temperatures, the effect of incorrect pressure and temperature magnitudes on localization is minimal. More important is the prediction by the propagation model of the shape of the heat source. One example in which the localization algorithm produces accurate results under challenging conditions for the propagation model is the case of strong focusing. In the present study, the f-number of the transducer is approximately 1, a case of substantial focusing. Soneson [16] showed that, for the transducer characteristics in this paper, the KZK equation was in error relative to the more general Westervelt equation by about 8% in pressure, or about 16% in intensity. However, Soneson [17] showed that the radial beam width predicted by the KZK equation is within 1% of the value predicted by the Westervelt equation. The normalized heat source is therefore modeled accurately by the KZK equation, allowing for radial localization errors of less than a tenth of a millimeter (Table I). Temperature calculations (Table II), which depend primarily upon experimental temperatures measured on array nodes, are affected by the propagation model only through determination of the beam location. A second example of where the localization algorithm can produce useful results under challenging conditions for the propagation model is the case of highly nonlinear propagation effects. The beam location could be determined at a low power, and additional temperature measurements made across the thermocouple array at a high power. The radial location of the beam would likely be unchanged with the increase in power, though the axial location of the focus could change slightly. Temperatures computed using the exponential-integral function would be accurate if the beam could be modeled using a single intensity and beamwidth. For additional accuracy, a heat source in the form of a sum of line sources representing the different intensity modes (with different amplitudes and beamwidths) could be considered, similar to that considered by Myers and Soneson [18]. Parameter estimation should be manageable if the number of modes is small. Inclusion of nonlinear propagation effects constitutes an important regime for further testing of the localization and temperature-prediction techniques. For the three numerical procedures propagation modeling, heat-transfer simulation, and optimization involved in the localization procedure, the grid spacing should be kept small enough that discretization error is not the limiting source of uncertainty. The simple criterion initially used for choosing the grid sizes in the present study is that the grid spacing should be a small fraction (a tenth or less) of the beam width for all three procedures. The beam width for the transducer used in our study is 0.52 mm (Section II-B). However, with the aid of the temperature uncertainty sensitivity study presented in Fig. 9, the following more rigorous procedure for selecting the grid spacing can be defined. The algorithms used in this paper to solve the KZK and energy equations are both second-order accurate. Assuming the pressure and temperature fields are smooth, and the relevant length scale in the radial direction is the ultrasound beamwidth b 0, then the relative error in the pressure and temperature are of the order (Δ p /b 0 ) 2 and (Δ T /b 0 ) 2 respectively, where Δ p and Δ T are the grid sizes in the radial direction for the pressure and temperature prediction algorithms. For the 0.52 mm beam width and

12 2030 IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, vol. 61, no. 12, December 2014 the grid sizes of Section II-E, (Δ p /b 0 ) 2 is on the order of and (Δ T /b 0 ) 2 is approximately We can use Fig. 9 to transform these uncertainties to uncertainties in beam localization. We consider uncertainty in the square of the pressure, which is equal to 2(Δ p /b 0 ) 2 or 0.004, to be the uncertainty in the heat source, and also a rough measure of temperature uncertainty, given that temperature is proportional to heat production for small times. Likewise, (Δ T /b 0 ) 2 = is also measure of temperature uncertainty. From the average slope of the fitting lines in Fig. 9 (0.02 mm/% deviation), the pressure and temperature uncertainties translate to uncertainties in beam localization of roughly mm and mm. For the search algorithm in the optimization procedure, a reasonable measure of the uncertainty is half of the grid resolution, or mm in this case, because all locations are examined in the optimization procedure. To determine if the grid spacing is sufficiently small, these three localization uncertainties (0.008 mm, mm, and mm) are then compared with the localization uncertainty associated with temperature measurement. The localization uncertainty associated with the thermocouple temperature measurements can also be estimated using the average correlation (0.02 mm/% deviation) in Fig. 9. Thermocouple uncertainty is typically on the order of 1 C for fine-wire thermocouples [19], which corresponds to perhaps 10 percent of the temperature rise at the array locations remote from the beam axis. From Fig. 9, this translates to a localization uncertainty of about 0.2 mm. This localization uncertainty is larger than that associated with discretization, indicating that no grid refinement is necessary. The fact that the ultimate error attributed to the localization procedure is about 0.06 mm somewhat smaller than the 0.2 mm estimate may be due to the fact that the uncertainty in the array of thermocouples is less than that for a single thermocouple. As further evidence that the discretization errors were sufficiently small, the average localization error reduced minimally (0.070 mm to mm) when the grid spacing was halved, from mm to mm (Section III-E). The localization algorithm presented in this paper can be considerably faster than techniques based upon sonication atop a single thermocouple and searching for the maximum temperature rise. In the present approach, only a single sonication is required, with the localization being accomplished through post-processing. Execution of the optimization algorithm required to attain the focal location required approximately 5 min using the exhaustive marching algorithm to search. Implementation of a more sophisticated optimization algorithm (e.g., Hariharan et al. [11]) could reduce the localization time considerably, though care must be taken to ensure that the convergence properties are well understood. The localization algorithm presented in this paper represents the first step toward a practical tool for localizing focused ultrasound beams. The present algorithm assuming a single-element, axisymmetric transducer, can be generalized to treat more complicated geometries and phased arrays. Any new transducer geometry must be accompanied by a propagation model that can adequately model the propagation. In addition to nonaxisymmetric transducers, an important generalization is the incorporation of beam tilt. All of the beams in the present study were aligned with the z-axis of the array. In focused ultrasound clinical procedures, the focused ultrasound beam might be rotated with respect to an axis perpendicular to the center of the array, possibly in both polar and azimuthal directions. Besides more general transducers, more general media such as a heterogeneous material can be treated by the localization model, provided again that the accompanying propagation model can adequately model the propagation. Further validation of the temperature-prediction capabilities of the present technique, in the form of comparisons with the estimated focal temperatures with those determined noninvasively by MR thermography, also constitutes an important future direction. V. Conclusions A technique has been presented for localizing a focused ultrasound beam using temperature measurements on an array of sensors remote from the beam. The technique does not suffer from thermocouple artifacts or positioning uncertainties associated with locating beams atop thermocouple junctions. Arrays with as few as three thermocouples were able to localize the beam to within a distance of about 0.06 mm, or about a tenth of a beamwidth for the 3.3-MHz transducer used in this study. However, performance of the arrays with 3 or 4 thermocouples was sensitive to the locations of the thermocouples. The localization ability of arrays with 5 or more thermocouples was nearly independent of the configuration of the array. The combination of remote temperature measurements and a fitting function in the form of an exponential integral showed considerable potential for predicting temperatures at any desired location, including the focus, with minimal complication due to thermocouple artifact. References [1] J. Civale, I. Rivens, G. ter Haar, H. Morris, C. Coussios, P. Friend, and J. Bamber, Calibration of ultrasound backscatter temperature imaging for high-intensity focused ultrasound treatment planning, Ultrasound Med. Biol., vol. 39, no. 9, pp , [2] G. Speyer, P. J. Kaczkowski, A. A. Brayman, and L. A. Crum, Displacement analysis of diagnostic ultrasound backscatter: A methodology for characterizing, modeling, and monitoring high intensity focused ultrasound therapy, J. Acoust. Soc. Am., vol. 128, no. 1, pp , [3] A. Anand and P. J. Kaczkowski, Noninvasive measurement of local thermal diffusivity using backscattered ultrasound and focused ultrasound heating, Ultrasound Med. Biol., vol. 34, no. 9, pp , [4] H. Morris, I. Rivens, A. Shaw, and G. Ter Haar, Investigation of the viscous heating artefact arising from the use of thermocouples in a focused ultrasound field, Phys. Med. Biol., vol. 53, no. 17, pp , [5] J. Huang, R. G. Holt, R. O. Cleveland, and R. A. Roy, Experimental validation of a tractable numerical model for focused ultrasound

13 hariharan et al.: beam localization using thermocouple arrays 2031 heating in flow-through tissue phantoms, J. Acoust. Soc. Am., vol. 116, no. 4, pp , [6] B. O Neill, H. Vo, M. Angstadt, K. P. C. Li, T. Quinn, and V. Frenkel, Pulsed high intensity focused ultrasound mediated nanoparticle delivery: Mechanisms and efficacy in murine muscle, Ultrasound Med. Biol., vol. 35, no. 3, pp , [7] S. Dasgupta, P. Hariharan, R. K. Banerjee, and M. R. Myers, Beam localization in HIFU temperature measurements using thermocouples, with application to cooling by large blood vessels, Ultrasonics, vol. 51, no. 2, pp , [8] D. M. Nell and M. R. Myers, Thermal effects generated by highintensity focused ultrasound beams at normal incidence to a bone surface, J. Acoust. Soc. Am., vol. 127, no. 1, pp , [9] O. Cortés, G. Urquiza, and J. A. Hernández, Inverse heat transfer using Levenberg-Marquardt and particle swarm optimization methods for heat source estimation, Appl. Mech. Mater., vol. 15, pp , [10] D. Maillet, R. Pasquetti, and A. Degiovanni, Inverse heat conduction applied to the measurement of heat transfer coefficient on a cylinder: Comparison between an analytical and a boundary element technique, J. Heat Transf., vol. 113, no. 3, pp , [11] P. Hariharan, M. R. Myers, R. A. Robinson, S. Maruvada, J. Sliva, and R. K. Banerjee, Characterization of high intensity focused ultrasound transducers using acoustic streaming, J. Acoust. Soc. Am., vol. 123, no. 3, pp , [12] J. E. Soneson, A user-friendly software package for HIFU simulation, AIP Conf. Proc., vol. 1113, pp , [13] R. L. King, Y. Liu, S. Maruvada, B. A. Herman, K. A. Wear, and G. R. Harris, Development and characterization of a tissue-mimicking material for high-intensity focused ultrasound, IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 58, no. 7, pp , [14] P. Gammell, S. Maruvada, and G. Harris, An ultrasonic time delayspectrometry (TDS) system employing digital processing, IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 54, no. 5, pp , [15] C. R. Dillon, U. Vyas, A. Payne, D. A. Christensen, and R. B. Roemer, An analytical solution for improved HIFU SAR estimation, Phys. Med. Biol., vol. 57, no. 14, pp , [16] J. E. Soneson, A parametric study of error in the parabolic approximation of focused axisymmetric ultrasound beams, J. Acoust. Soc. Am., vol. 131, no. 6, pp. EL481 EL486, [17] J. E. Soneson, Wide-angle parabolic approximation for strongly focused axisymmetric ultrasound beams, presented at 14th Int. Symp. Therapeutic Ultrasound, Las Vegas, NV, April [18] M. R. Myers and J. E. Soneson, Temperature modes for nonlinear Gaussian beams, J. Acoust. Soc. Am., vol. 126, pp , [19] American Limits of Error Thermocouple Tolerances. ASTM E230 ANSI MC 96.1 Standard, Seyed Ahmad Reza Dibaji received his B.S. and M.S. degrees in mechanical engineering in 2004 and He is currently a Ph.D. candidate at the University of Cincinnati, working in the field of therapeutic ultrasound for cancer treatment. Since 2011, he has been working as a scholar-in-residence for the Center for Devices and Radiological Health of the U.S. Food and Drug Administration. He has been involved in different computational and experimental projects related to high intensity therapeutic ultrasound. Rupak K. Banerjee received his B.S. degree in mechanical engineering and his M.S. degree in biological sciences in 1984 from the Birla Institute of Technology and Science, Pilani, India; his M.S. degree in applied mechanics in 1987 from the Indian Institute of Technology, New Delhi, India; and his Ph.D. degree in mechanical engineering and mechanics in 1992 from Drexel University, Philadelphia, PA. He has been a Professor in the Mechanical and Biomedical Engineering Departments at the University of Cincinnati since His primary research areas include cardiovascular hemodynamics, characterization of thermal ablation using high-intensity focused ultrasound and radio-frequency, ocular and tumor drug delivery, micro- and nanofluidics, and oxygen transport under microgravity in biological systems. He was elected as a Fellow of ASME and the chair of the Biotransport committee of the Bioengineering Division and the K-17 committee of the Heat Transfer Division of ASME. He is a registered Professional Engineer. Srinidhi Nagaraja earned a B.S. degree in mechanical engineering from the University of Michigan in 1999 and a Ph.D. degree in mechanical engineering from the Georgia Institute of Technology in His dissertation examined how aging decreases the stress/strain threshold to initiate damage in trabecular bone. Dr. Nagaraja joined the U.S. Food and Drug Administration s Office of Science and Engineering Laboratories in His research interests are in the mechanical safety of implantable cardiovascular and orthopedic devices. Dr. Nagaraja has used micro-ct for more than 14 years to understand bone microstructure and the interaction of medical devices with surrounding biological tissues. Prasanna Hariharan was born in Madurai, India in He obtained his Ph.D. degree in mechanical engineering from the University of Cincinnati in Since 2008, he has been working as a mechanical engineer for the U.S. Food and Drug Administration s Center for Devices and Radiological Health (CDRH). He is engaged in a variety of research projects focusing on ultrasonics, fluid dynamics, heat transfer, and drug delivery in medical devices. This includes development of new computational models and bench-test methods to evaluate the performance of therapeutic ultrasound and cardio-vascular devices. He is also interested in using computational fluid dynamics (CFD) and computational heat transfer (CHT) to evaluate the thermal and mechanical effects of therapeutic ultrasound devices. Matthew R. Myers received his doctorate in applied mathematics from the University of Arizona. He worked in the research and development laboratory of Corning Glass Works, where he performed mathematical modeling of fiber drawing and other processes involving molten glass. Dr. Myers was later employed as an acoustics consultant with BBN Systems and Technologies. In 1990, Dr. Myers joined the Center for Devices and Radiological Health of the U.S. Food and Drug Administration. He has performed mathematical modeling in the areas of drug delivery, cardiovascular implants, virus transport, and most recently, therapeutic ultrasound. His current research areas include noninvasive methods for preclinical testing of focused-ultrasound surgery devices, and applications of high-intensity focused ultrasound to the study of traumatic brain injury.