1430
ieee transactions on ultrasonics, ferroelectrics, and frequency control, vol. 49, no. 10, october 2002
Transducer Design for a Portable Ultrasound Enhanced Transdermal Drug-Delivery System Emiliano Maione, K. Kirk Shung, Fellow, IEEE, Richard J. Meyer, Jr., Jack W. Hughes, Robert E. Newnham, Member, IEEE, and Nadine Barrie Smith, Member, IEEE Abstract—For application in a portable transdermal drug-delivery system, novel transducers have been designed to enhance insulin transmission across skin using ultrasound. Previous research has shown transdermal delivery of insulin across skin using commercial sonicators operating at 20 kHz with intensities ranging from 12.5 to 225 mW/cm2 . The goal of this research was to design and construct a small, lightweight transducer or array that could operate with a similar frequency and intensity range as a commercial sonicator used in previous transdermal ultrasound insulin experiments, but without the weight and mass of a sonicator probe. To obtain this intensity range, a cymbal transducer design was chosen because of its light, compact structure and low resonance frequency in water. To increase the spatial ultrasound field for drug delivery across skin, two arrays, each comprising of four cymbal transducers, were constructed. The first array, designated the standard array, used four cymbals transducer elements in parallel. A second array (named the stack array) used four cymbal transducers that used stacked piezoelectric discs to drive the titanium flextensional caps. Under similar driving conditions, the standard array produced intensities comparable to those achieved using a commercial sonicator.
I. Introduction everal noninvasive methods exist for transdermal drug delivery. These include chemical mediation using liposomes and chemical enhancers or physical mechanisms such as iontophoresis, electroporation, and ultrasound (also called sonophoresis or phonophoresis) [1]–[3]. Ultrasound-enhanced transdermal drug delivery offers advantages over traditional drug delivery methods that often are invasive and painful. Recent studies have shown that ultrasound-mediated transdermal drug delivery offers promising potential for noninvasive drug administration [4]–[6]. Currently few drugs, proteins or peptides have been successfully administered transdermally for clinical applications because of the low skin permeability to these relatively large molecules. This low permeability is attributed to the stratum corneum, the outermost skin layer that con-
S
Manuscript received June 22, 2001; accepted May 30, 2002. E. Maione is with Encapsulation Systems Inc., Broomall, PA. 19008. K. K. Shung and N. B. Smith are with the Department of Bioengineering, The Pennsylvania State University, University Park, PA 16802 (e-mail:
[email protected]). R. J. Meyer, Jr., and J. W. Hughes are with the Applied Research Laboratory, The Pennsylvania State University, University Park, PA 16802. R. E. Newnham is with the Material Research Laboratory, The Pennsylvania State University, University Park, PA 16802.
sists of a compact and organized structure of cells named keratinocites surrounded by lipid bilayers. After the drug has traversed the stratum corneum, the next layer is much easier to cross; subsequently, the drug can reach the capillary vessels to be absorbed. The proposed dominate mechanism of sonophoresis, although not completely understood, has been suggested to be the result of cavitation [7], [8], although thermal effects cannot be entirely discounted. Low frequency ultrasound is capable of generating microbubbles in the water and tissue. Investigators have suggested that the cavitation bubbles disrupt the lipid bilayer and allow water channels to be produced within the lipid bilayers [7], [8]. The resulting disorder created in the stratum corneum facilitates the crossing of a hydrophilic drug or molecule. With sonophoresis, previous investigators have found enhanced transdermal drug delivery over various frequency ranges using commercial sonicators. For example, significant transdermal transport of model drugs such as mannitol (MW = 180 Da) and inulin (a plant starch, MW = 5000 Da) have been seen using a 20 kHz commercial sonicator (VCX400, Sonics and Materials, Newtown, CT). Transport of both vassopressin and insulin across in vitro human skin has been demonstrated using a 20 kHz sonicator (Sonicator W385, Heat Systems, Farmingdale, NY) over a period of 5 hours with an intensity as low as 100 mW/cm2 [9]. From in vitro human skin and in vivo rat experiments, the transdermal transport of insulin has been shown using a 20 kHz ultrasound sonicator operating at intensities from 12.5– 225 mW/cm2 [4]. The major drawback so far in exploiting ultrasound for noninvasive drug delivery is the large size and weight of the ultrasound device. Commercial sonicators are large, heavy, tabletop devices that require power from a standard outlet with the converter (ultrasonic probe) approximately 20 cm in length and weighing almost a kilogram. For practical application of ultrasound-enhanced transdermal drug delivery, a smaller, lighter device is necessary. A practical device should have a flat, low profile that would be situated against the arm or the waist with a reservoir for the insulin located between the transducer and the skin surface. The device also should operate at a frequency similar to a sonicator (i.e., 20 kHz) with intensities that have been shown to transdermally deliver drugs such as insulin. With these goals, the aim of this research was to design a small and lightweight ultrasound transducer system capable of enhancing the permeability of drugs, such as insulin (>7,000 Dalton) through the skin operating at an anal-
c 2002 IEEE 0885–3010/$10.00
maione et al.: design for a portable drug-delivery system
1431
ogous frequency and intensity used with sonicator drugdelivery experiments.
II. Materials and Methods A. Transducer Design Considerations for a Portable Drug-Delivery Device An ideal ultrasonic transducer should be small enough to allow integration into a portable system for transdermal drug release to be positioned on the arm or waist. In order to ensure the portability, the principal specification of the transducer was to be compact and light with a low profile. For delivery without damage to the skin, the maximum temperature rise allowed was no higher than 1– 2◦ C at intensities of approximately 200 mW/cm2 , based on the results from other investigators [4], [9]. Although there are several possible low frequency transducer designs that can be used in a drug-delivery application, such as the low frequency flextensional resonators [10], Tonpilz transducers [11], or “thickness”-type resonators [12], the cymbal transducer design [Fig. 1(a)] most closely matched the specifications. This Class V flextensional transducer has a compact, light structure with a resonance frequency adjustable between 20 and 50 kHz, and a low cost [13]–[17]. With the basic cymbal transducer design [Fig. 1(a)], the caps on the lead zirconate-titanate (PZT) ceramic contained a shallow cavity beneath its inner surface. In the frequency range of 20–50 kHz, the ceramic disc with caps (1 mm thickness and diameter in the range 1–3 cm) had a small radial motion (i.e., the vibration moves from the center of the disc to the edges with radial symmetry). Using this design, the presence of the cavities allowed the caps to convert and amplify the radial displacement of the disc into a much larger axial displacement normal to the surface of the caps. B. Construction of the Single Element Cymbal Transducer The cymbal transducer consisted of a piezoelectric disc sandwiched between two metal caps [Fig. 1(a)]. For the drug-delivery device, the piezoelectric disc was made from PZT-4 (Piezokinetics, Inc., Bellefonte, PA), had a diameter of 12.7 mm, and was 1-mm thick. The PZT-4 was chosen because this material has a high failure voltage threshold compared to ceramics with similar efficiency. The caps were made of 0.25-mm thick (metal basis 5%) titanium (#10385, Alfa Aesar, Ward Hill, MA), and the thin glue layer between the caps and the ceramic disk was made of Eccobond epoxy 45LV with catalyzer 15LV (Emerson & Cuming, Billerica, MA). Soldering between the caps and the coaxial cable used Indalloy Solder #1E (Indium Corporation of America, Utica, NY). The transducer connected to the coaxial cable was encapsulated in a URALITE polymer (FH 3550 part A/B, H.B. Fuller, St. Paul, MN) with an acoustic impedance similar to water. With this coating, the end caps were electrically
Fig. 1. (a) Side view of a single element cymbal transducer (not to scale). Arrows and dashed line show the displacement motion of the transducer and caps. The cymbal transducer consisted of a piezoelectric disc situated between two 0.25-mm thick titanium caps. (b) View of a 12-mm diameter cymbal transducer (right). For experiments, the cymbal transducer was connected with a coaxial cable and housed in polymer material in order to ensure electrical insulation between the end caps (center). The transducer was encased in a housing for stability and positioning in water (left).
insulated, and multiple reflections between the interface polymer-water were minimized. A photograph of the cymbal transducer [Fig. 1(b), right], cymbal with polymer coat [Fig. 1(b), center], and the final cymbal transducer with housing and coaxial cable connections [Fig. 1(b), left] are shown. C. Finite Element Simulations of the Single Element Cymbal Transducer In order to obtain a resonance frequency of about 20 kHz with high efficiency, the key parameters (i.e., disc thickness, cap depth, and cap material) were optimized by
1432
ieee transactions on ultrasonics, ferroelectrics, and frequency control, vol. 49, no. 10, october 2002
means of a finite element analysis model as described in detail elsewhere [17]. Finite element analysis of the cymbal transducer was performed using the ANSYS software package (Swanson Analysis Systems, Inc., Hoston, PA) with a Pentium III personal computer (Dell Computer Corporation, Austin, TX). Two models of the cymbal transducer were implemented. In the first model, the cymbal transducer was surrounded by air, and the input admittance was simulated using circuit models. Experimental input admittance parameters were determined using a network analyzer (HP 4194A, Hewlett Packard, Palo Alto, CA). The second model analyzed the cymbal transducer completely surrounded by water in order to examine the effect of water loading on the resonance frequency of the transducer. From the finite element model, it was possible to construct a circuit model for frequencies close to the resonance frequency using the circuit simulator software PSpice (Cadence Design Systems, Inc., San Jose, CA); implementation of transducer components was straightforward. The pressure, in decibels, was normalized to micropascals at 1 meter from the source with 1 volt input at the transducer electrodes for initial evaluation. Pressure measurements were determined experimentally using a calibrated hydrophone (described in more detail later).
Fig. 2. For the standard array made up of four cymbal transducers, the cymbal elements were connected in parallel, encased in URALITEr polymer, and arranged in a two-by-two elemental pattern. The dimensions of the array were 37 × 37 × 7 mm3 .
D. Two-by-Two Standard Array and Stack Array In order to utilize fully the potential of the low profile cymbal transducer and increase the spatial ultrasound field for drug delivery, four cymbal transducers were arranged in a two-by-two pattern. For the standard array, four cymbal transducers were connected in parallel and encased in URALITE polymer (FH 3550, H.B. Fuller, St. Paul, MN). The ceramics and physical size of the single elements of the array were identical to the cymbal transducer, and the final array dimensions were 37×37×7 mm3 (Fig. 2). A second array design stacked two piezoelectric discs (Fig. 3); this stacked cymbal transducer had two piezoelectric discs connected mechanically in series and electrically in parallel. The polar directions of the two ceramic discs were opposite to one another so that the ground electrode was on the outer sides of the stack with the powered electrode on the inner and common sides of the discs. In this configuration, the total capacitance of the transducer was increased by a factor of two, and the mechanical strain remained unchanged. The input admittance at low frequencies was mainly related to the clamped capacitance; if the clamped capacitance was doubled, the total absorbed power and the total energy stored was doubled. For increased efficiency, four stacked cymbal transducers were used to make a two-by-two array similar in size (37×37×7 mm3 ) to the standard array. The drawbacks of the stacked array design were higher cost and increased device complexity [18]. The two-by-two stack array consisted of four stacked cymbal transducers connected in parallel and encased in URALITE polymer as for the standard
Fig. 3. The stacked cymbal transducer made from two piezoelectric discs with the polar directions of the discs opposite in order to have the ground electrode on the outer sides of the stack and the powered electrode on the common side of the discs. The stack array was composed of four stacked cymbal transducer elements and has dimensions identical to the standard array.
array. The electrical impedance of both the standard and stack array was tuned using an external LC (L = inductor, C = capacitor) π-network. Using a calibrated hydrophone, the transmitting voltage response was measured for both arrays with and without electrical tuning. E. Exposimetry of the Cymbal Transducer and Arrays For determining the transmitting voltage response (TVR) from the cymbal transducer, calibrated hydrophone (Naval Research Laboratory, Washington, DC Type F33, s/n A118) was used in a 7.9 × 5.3 × 5.5 m3 tank containing distilled water. The transducer (or array) and hydrophone were positioned at a depth of 2.74 m and were separated by a distance of 3.16 m. The radio frequency (RF) signal driving the cymbal transducer or array was
maione et al.: design for a portable drug-delivery system
generated by a frequency pulse/function generator (Model 81, Wavetek Inc., San Diego, CA) and amplified by an RF amplifier (Model 40A12, Amplifier Research, Souderton, PA). A pure tone sinusoidal pulse signal of 2-ms duration was applied to the transducer or array, and its acoustic output was monitored with the hydrophone. The TVR, source level, and input impedance for the device under test were recorded. For determining the intensity at a plane 1 mm from the transducer face, the ultrasonic intensities from the cymbal transducer, standard array, and stack array were measured with a calibrated miniature omnidirectional reference hydrophone (Model TC4013, RESON, Inc., Goleta, CA) in a 51 × 54 × 122 mm3 partially anechoic tank containing degassed, distilled water. A signal generator and amplifier was used to drive the transducers. The RF signal driving a transducer was generated by an arbitrary waveform generator (AWG, Model 393, Wavetek Inc., San Diego, CA) and amplified by an RF amplifier (Model 40A12, Amplifier Research, Souderton, PA). Pulse period, duty cycle, and exposure time of the signal from the frequency generator and hydrophone was acquired using an Agilent 54622A 100 MHz digitizing oscilloscope (Agilent, Palo Alto CA). The signal generator operated at 20 kHz with a 1 V (peakto-peak) output. The pulsed signal had a pulse duration of 200 ms and pulse repetition period of 1 second (i.e., 20% duty cycle); the amplifier gain was set to 50 dB. A computer-controlled exposimetry positioning system was used for automated scanning. The scanning step size for each device was 1 mm, but the scanning area was different for the cymbal and arrays due to their different sizes. The scanning area was 30, 40, and 100 mm2 for the cymbal transducer, stack array, and standard array, respectively. Spatial peak-temporal peak intensity (Isptp ), and spatial peak-temporal average (Ispta ) was determined over a plane 1 mm from each transducer face using the hydrophone based on 3–5 scannings of each transducer for a mean and standard deviation of the results [19], [20].
III. Results and Discussion A. Single Element Cymbal Transducer: Simulated and Experimental Results in Air and Water PSpice software was used to model the single element transducer circuit in both air and water for its response. In air, the input admittance of the single element cymbal transducer was simulated using the component values shown in Fig. 4(a). The results of modeling the input admittance from the cymbal transducer as a circuit over a frequency range (30–50 kHz) is shown in Fig. 4(b). Plotted against the simulated results are the experimental input admittance results measured with the HP 4194A network analyzer. Both the simulated and experimental input admittance results indicate a mechanical resonance frequency at approximately 41 kHz. From Fig. 4, the experimental input admittance results were only slightly less than the
1433
Fig. 4. (a) Using the PSpicer simulation program, modeling of the single element cymbal transducer determined its input admittance as a function of frequency in air using the components shown. (b) The simulation results of the input admittance from the single element cymbal transducer as a circuit in air was evaluated against experimental results for the transducer determined using a network analyzer. Simulated and experimental results show a mechanical resonance frequency at approximately 41 kHz.
simulated results of the cymbal transducer and had a difference no greater than 1 kHz. The second model analyzed the cymbal transducer completely surrounded by water using two simulation programs. ANSYS optimized the shape of the elements in the finite-element mesh in order to avoid the presence of any triangular elements. It also was possible to obtain an equivalent circuit of the finite element model [Fig. 5(a)]. From this model, it was possible to obtain the mean value of the velocity of the radiating surface, given by the current Iv in the resistor-inductor-capacitor (RLC) branch of the circuit of Fig. 5(a) using an electroacoustic analogy. From a similar electrical input, Fig. 5(b) shows the comparison of the calculated pressure determined using both ANSYS and PSpice along with the radiated pressure measured experimentally as functions of frequency. Fig. 5 plots the results as a function of the TVR, which represents the transfer function (pressure/voltage) of the transducer. From Fig. 5, the resonance frequencies for the simulated and experimental results were slightly less than 20 kHz and within about 1 kHz of each other. In order to obtain the optimal power transfer between the generator and the transducer, and shift the resonance closer to 20 kHz, a tuning network was used. The simplest circuit was an inductor being the complex conjugate impedance of the input impedance of the transducer calculated at the resonance frequency. Insertion of a 33 mH
1434
ieee transactions on ultrasonics, ferroelectrics, and frequency control, vol. 49, no. 10, october 2002
Fig. 6. Optimal power transfer to the load was obtained by placing a 33 mH series inductor between the generator and the transducer in Fig. 5(a). From this tuning the irradiated pressure increased 10 dB to a maximum TVR of 135 dB compared to the pressure obtained without the inductor [Fig. 5(b)]. Simulated and experimental results are shown.
Fig. 5. (a) Modeling of the single element cymbal transducer in water as a function of frequency was performed using PSpicer with the circuit components shown. (b) The single element cymbal transducer was modeled using two different simulation programs, ANSYSr and PSpicer . The experimental result was compared against the simulations and plotted as a function of the TVR. The resonance frequencies for the simulated and experimental results were slightly less than 20 kHz, yet within about 1 kHz of each other.
series inductor between the generator and the transducer in Fig. 5(a) resulted in a increase in the TVR due to minimalization of the electrical reflections within the cable. Fig. 6 shows the results of the simulated circuit with the series inductor and the measured results from the cymbal transducer. A drawback with using the tuning was the high resistive losses at these frequencies with standard components. To reduce these losses, the inductor was made from a toroid core. With tuning, the pressure irradiated increased 10 dB to a maximum TVR of 135 dB compared to the pressure obtained without the inductor (TVR = 125 dB) at the same applied voltage. B. Exposimetry of the Cymbal Transducer, Standard and Stack Array Using similar driving conditions, the intensity was determined in a plane 1 mm from the transducer face. All three devices (i.e., cymbal transducer, standard array, and stack array) were driven with a 1 Vpp signal with a 20% duty cycle amplified by 50 dB with a 1 s pulse repetition period. Each device was scanned 3–5 times to produce
a mean and standard deviation of the intensity results. Fig. 7(a) shows a typical two-dimensional scanning plot of the temporal peak intensity for the single element cymbal transducer over a 30 × 30 mm2 area with 1-mm steps. For Fig. 7, the single element cymbal transducer has a spatial peak-temporal peak intensity (Isptp ) of approximately 16 mW/cm2 over a 5 × 5 mm2 area. Under similar driving conditions, a 40 × 40 mm2 two-dimensional plot of the temporal peak intensity was acquired for the four element stack array Fig. 7(b)]. For the stack array, the Isptp was only slightly larger in value and area than the single element cymbal transducer. The standard array produced the largest temporal peak intensity compared to the single element cymbal transducer and the stack array under similar driving settings. Fig. 7(c) shows representative 100 × 100 mm2 twodimensional temporal peak intensity plot for the standard array. From Fig. 7(c), the temporal peak intensity was approximately one order of magnitude larger than both the cymbal transducer and the stack array and produced a larger intensity field. From the scannings of the three devices, the spatial peak-temporal peak and spatial peaktemporal average intensities were averaged. Table I lists the mean and standard deviation (x ± s.d.) of the intensity results for the cymbal transducer, standard array, and stack array. From Table I, the standard array had the largest Isptp and Ispta values in the plane 1 mm from the face of the transducer. Although the stack array was designed to produce an intensity larger than the standard array, it unfortunately only produced intensities similar to the single element cymbal. As expected, the arrays produced a larger spatial intensity area due to a larger effective radiating area compared to the single element device. These results indicate that the standard array is a good candidate for a portable device for ultrasound-enhanced
maione et al.: design for a portable drug-delivery system
1435
transdermal delivery of drugs producing intensities that previously have been shown to transport insulin.
IV. Conclusions
Fig. 7. The temporal peak intensity was determined in a spatial plane 1 mm from the face of the transducer for the (a) single element cymbal transducer, (b) stack array, and (c) standard array under identical driving conditions. All three were driven with a 1 Vpp signal with a 20% duty cycle amplified by 50 dB with a 1 s pulse repetition period.
Based on the requirements needed for a small, lightweight ultrasonic transducer to be integrated in a transdermal drug-delivery system, the cymbal transducer design was chosen mainly because of its compact structure and low resonance frequency. Simulation of the cymbal transducer using a circuit model obtained from finite element analysis was compared to experimental results and agreed well. The performance of the impedance tuned single element cymbal transducer showed promise. Unfortunately, in order to reach adequate intensity levels, a very high drive voltage was required. In order to overcome this weakness, the cymbal design was modified to consist of a stack of two piezoelectric discs instead of one. Of the three devices designed, the standard array produced the largest intensity under similar driving conditions, which indicates it was the most electrical efficient compared to the cymbal and stack arrays. The standard array achieved intensities analogous to ultrasound delivery sonicator intensities; however, this device was capable of producing higher intensities, although the upper limits were not fully explored at this time to avoid destructive evaluation. The goal of this research was to produce a low profile transducer device that could generate intensities comparable to a sonicator used for ultrasonic transdermal insulin transport operating at a similar frequency. Sonicators have been shown to transdermally deliver insulin across in vitro and in vivo skin using intensities as low as 12.5 mW/cm2 [4]. Based on the spatial peak temporal peak intensity results, the standard array produced intensities that previously were shown to transdermally deliver insulin across skin using a sonicator. Although a commercial sonicator has been an excellent device for demonstrating drug delivery, the next stage is for a similar but practicable ultrasonic method. The ultrasonic probe or converter from a commercial sonicator can weigh almost a kilogram; but the standard array weighs less than 22 gm. Additionally, the probe tip on a sonicator is small, covering only 10-mm diameter; the standard array covers a 37 × 37 mm2 area. Conquering Diabetes, a research report from the Congressionally-Established Diabetes Research Group funded by the National Institutes of Health, specified overarching goals to potentially prevent, cure, treat, and manage this disease [21]. Specifically among these research challenges are methods to optimize glucose control. The recommendations from the NIH Research Group include: “Increase basic and clinical research to discover novel approaches to controlling hyperglycemia in diabetes. These approaches should include developing technologies that enable administration of insulin by routes other than injection.” This research forms the cornerstone to developing a clinically approved device for transdermal insulin delivery.
1436
ieee transactions on ultrasonics, ferroelectrics, and frequency control, vol. 49, no. 10, october 2002 TABLE I Mean and Standard Deviations for Transducers and Arrays.∗ Intensity (mW/cm2 )
Single element cymbal
2 × 2 Stack array
2 × 2 Standard array
Isptp Ispta
16.6 ± 4.3 2.2 ± 3.1
17.1 ± 5.0 5.5 ± 2.3
204.9 ± 20.1 67.8 ± 0.4
∗ For
the experiments. the three transducers were electrically driven under similar conditions. The pulsed signal (f = 20 kHz) from the signal generator was at 1 Vpp with a pulse duration of 200 ms and pulse repetition period of 1 second (i.e., 20% duty cycle). Amplifier gain was 50 dB. Intensity results in mW/cm2 were determined over a plane 1 mm from the transducer face.
Acknowledgments The support provided by Encapsulations Systems, Inc (Broomall, PA) to this work is gratefully acknowledged.
References [1] M. R. Prausnitz, “A practical assessment of transdermal drug delivery by skin electroporation,” Adv. Drug Deliv. Rev., vol. 35, pp. 61–76, 1999. [2] M. R. Prausnitz, “Reversible skin permeabilization for transdermal delivery of macromolecules,” Crit. Rev. Ther. Drug Carrier Syst., vol. 14, pp. 455–483, 1997. [3] F. Montorsi, A. Salonia, G. Guazzoni, L. Barbieri, R. Colombo, M. Brausi, V. Scattoni, P. Rigatti, and G. Pizzini, “Transdermal electromotive multi-drug administration for Peyronie’s disease: Preliminary results,” J. Androl., vol. 21, pp. 85–90, Jan. 2000. [4] S. Mitragotri, D. Blankschtein, and R. Langer, “Ultrasoundmediated transdermal protein delivery,” Science, vol. 269, pp. 850–853, 1995. [5] ——, “Transdermal drug delivery using low-frequency sonophoresis,” Pharm. Res., vol. 13, pp. 411–420, 1996. [6] S. Mitragotri and J. Kost, “Low-frequency sonophoresis: A noninvasive method of drug delivery and diagnostics,” Biotechnol. Prog., vol. 16, pp. 488–492, 2000. [7] S. Mitragotri, D. A. Edwards, D. Blankschtein, and R. Langer, “A mechanistic study of ultrasonically-enhanced transdermal drug delivery,” J. Pharm. Sci., vol. 84, pp. 697–706, Jun. 1995. [8] S. Mitragotri, D. Blankschtein, and R. Langer, “An explanation for the variation of the sonophoretic transdermal transport enhancement from drug to drug,” J. Pharm. Sci., vol. 86, pp. 1190–1192, Oct. 1997. [9] I. Zhang, K. K. Shung, and D. A. Edwards, “Hydrogels with enhanced mass transfer for transdermal drug delivery,” J. Pharm. Sci., vol. 85, pp. 1312–1316, Dec. 1996.
[10] D. Stansfield, Underwater Electroacoustic Transducers. Bath, UK: Bath Univ. Press, 1990. [11] O. B. Wilson, An Introduction to the Theory and Design of Sonar Transducers. Los Altos, CA: Peninsula Publ., 1988. [12] K. K. Shung, M. B. Smith, and B. Tsui, Principles of Medical Imaging. San Diego: Academic, 1992. [13] R. E. Newnham, Q. C. Xu, and S. Yoshikawa, “Transformed stress direction acoustic transducer,” U.S. Patent 4,999,819, Mar. 12, 1991. [14] ——, “Metal-electroactive ceramic composite actuators,” U.S. Patent 5,276,657, Jan. 4, 1994. [15] A. Dogan, K. Uchino, and R. E. Newnham, “Composite piezoelectric transducer with truncated conical endcaps ‘cymbal’,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 44, pp. 597–605, 1997. [16] R. E. Newnham and A. Dogan, inventors, “Metal-electroactive ceramic composite transducer,” U.S. Patent 5,729,077, Mar. 17, 1998. [17] J. F. Tressler, W. Cao, K. Uchino, and R. E. Newnham, “Finite element analysis of the cymbal-type flextensional transducer,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 45, pp. 1363–1369, 1998. [18] J. Zhang, “Miniaturized flextensional transducers and arrays,” Ph.D. dissertation, The Pennsylvania State University, University Park, PA, 2000. [19] IEEE Guide for Medical Ultrasound Field Parameter Measurements, New York: Institute of Electrical and Electronics Engineers, Inc., 1990. [20] Acoustic Output Labeling Standard for Diagnostic Ultrasound Equipment, Laurel, MD: American Institute of Ultrasound in Medicine, 1998. [21] Congressionally-Established Diabetes Research Working Group, “Conquering Diabetes: A Strategic Plan for the 21st Century,” Bethesda, MD: National Institutes of Health (NIH), Publication No. 99-4398, p. 12.