Effect of misalignment between ultrasound ...

Effect of misalignment between ultrasound piezoelectric transducers on transcutaneous energy transfer Changki Mo*a, Scott Hudsonb, and Leon J. Radziemskic

a

School of Mechanical and Materials Engineering, Washington State University Tri-Cities, 2710 Crimson Way, Richland, WA 99354; bSchool of Electrical Engineering and Computer Science, Washington State University Tri-Cities; cPiezo Energy Technologies, LLC, Tucson, AZ. ABSTRACT

This paper presents power transmission performance of the ultrasound-based piezoelectric recharging system for implantable medical devices. The efficiency of the piezoelectric ultrasonic transcutaneous energy transfer system depends on frequency matching of the transmitter and receiver, electrical, mechanical and acoustical impedance characteristics, distance between the transducers, and misalignment. However, it was realized that the angular misalignment between transmitter and receiver was one of key factors to have effect on the power transmission efficiency. As such, misalignment effect of the piezoelectric ultrasound transmitter and receiver on the power transmission efficiency was investigated by theoretical analysis using finite-difference time-domain method. The pressure field variation in the near field was also estimated to examine the influence of the power transfer performance of the ultrasound-based charging system. Analytical results indicate that the transferred power is greatly reduced by voltage cancellation on the receiver from phase shift due to the misalignment. Furthermore, significant acoustic pressure variation in the near field makes the effect of misalignment on power transmission dependent on the receiver location. Keywords: Transcutaneous energy transmission, Ultrasound piezoelectric transducers, Misalignment, Efficiency of energy transfer.

1. INTRODUCTION Application of the ultrasound power delivery to actual implantable devices is relatively new while biological application of the ultrasound was initiated about a century ago. The method of transmitting power and information to implanted medical device using ultrasonic pitch-catch had been proposed by Kawanabe et al.1 and Suzuki et al.2, and more recently Ozeri et al3,4. Ultrasound recharging system may be an appropriate target to meet the rapidly growing neurostimulator market as Radziemski et al.5 proposed. They carried out in vitro tests and demonstrated that their ultrasound recharging system could transmit significant amounts of power into the implants through tissue mimicking liquid. Conducting performance tests in terms of the factors to influence maximum power transmission for the development process, it was found out that the misalignment of the transmitter and receiver was one of important factors to affect on the power transmission efficiency. A number of experiments indicated that the power delivery went down by 50% if one transducer of diameter of 25mm was even 2° of angle off of parallel. The power transmission efficiency was so sensitive to parallelism of the transducers. In this regard, misalignment effect of the transducers on power transfer performance is investigated in this work. The misalignment issues can be found in open literature only in the ultrasonic non-destructive testing or structural health monitoring area6,7. Some of recent research articles on piezoelectric ultrasonic transcutaneous energy transfer presented power transfer efficiency depending on frequency selection, and axial distance and lateral shift between transducers but not on misalignment of the transducers3,4. In order to investigate the extreme sensitivity of parallelism of the transducers, finite-difference time-domain (FDTD) simulation8-10 for the circular piezoelectric transducers was conducted. The voltage and power generating performance in terms of misaligned angle between the two transducers are examined. A minimum angle between the transducers in net excitation is also included. For design flexibility there should be an optimum angle in terms of the wavelength, and diameter and separation of the transducers. The optimum location of the receiver to capture the radiated energy of the full acoustic pressure field in between near and far field is discussed. *

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Active and Passive Smart Structures and Integrated Systems 2013, edited by Henry A. Sodano, Proc. of SPIE Vol. 8688, 868814 · © 2013 SPIE · CCC code: 0277-786X/13/$18 doi: 10.1117/12.2009895 Proc. of SPIE Vol. 8688 868814-1

In addition, the acoustic pressure field between the transducers is estimated to investigate the pressure distribution and its effect on power transmission performance in the near and far field. In particular, it focuses on the near field pressure estimation because the ultrasound transmitter and receiver are located in the near field for application of the ultrasound power transfer system to implants5. The complex near field estimation has been conducted to estimate the pressure field distribution in the near field by Zemanek11 and many others12-14 since 1971. The formula developed by Kelly13 and McGough et al.14 is adopted to estimate the pressure variation profile in the near field.

2. FDTD SIMUALTION To find the relationship between the misaligned angle θ and the reduced power generated performance, FDTD simulation is conducted in this section. The transducers are assumed to be made of PZT-4 (APC International, Ltd.) and to have the dimension that is the same as those that Radziemski et al.5 tested. Referring to Fig. 1, the misaligned angle θ is considered on the receiver 6,15. The parameters used for the simulation are: transducers diameter D = 25mm, thickness of the transducers w = 2mm, distance between two transducers R = 10mm, frequency f = 1MHz, speed of sound (water) c0 = 1,500m/s, wavelength λ = 1.5mm, spatial resolution of simulation grid ∆s = 75µm, and time step ∆t = 25ns. θ

w

D

R Transmitter

Receiver

Figure 1. Schematic of a transmitter and a misaligned receiver.

Starting at quiescence at t = 0, the transmitter was assumed to generate a pressure wave sin(ω0t) uniformly over its surface. The output voltage of the receiver was taken to be proportional to the integral of the pressure field over its area. The pressure field was evolved using the FDTD method until the output voltage signal reached sinusoidal steady state. This was repeated for each angle θ of interest. Assuming steady-state power is proportional to mean-square voltage, a plot of output power versus θ was generated as shown in Fig. 2. Dots are simulated values and the curve is

with θ0 = 3.5°. This is just slightly larger than 𝜃0 =

𝜆

𝐷

𝑃(𝜃) =

𝜋𝜃 ) 𝜃0

sin (

𝜋𝜃/𝜃0

(1)

= 3.4° as predicted by simple, far-field theory15. The simulated

result indicates that the generated power is reduced to about a half for a misaligned angle of about 1.52° and there is almost no power transmitted for misalignment of 3.5°. It results from voltage cancellation due to out of phase at the upper and lower portions of the receiver. The relationship between the misaligned angle θ and the phase shift φ can also be found by the misaligned receiver considering as an array of two point sources at the upper and the lower with the angle of incidence θ 4,15.

Proc. of SPIE Vol. 8688 868814-2

0.70.6-

n

aa 0.5-

ú 04c e

TT 0.3 w

Li 0.2-

ae

0.10 o

0.5

1

1.5 2 2.5 Misaligned angle (Deg)

4

3.5

3

Figure 2. FDTD simulation for predicted generated power in terms of misaligned angle.

It is noted that the acoustic wave arriving at its surface is assumed to be planar. Only taking into account of the differece 𝐷 ± sin (𝜃) in the phase factor as6,15; 2

𝑘𝐷

𝜙 = � � sin(𝜃) = 2

where k is wave number and ω is wave’s angular frequency.

𝜔𝐷

2𝑐0

𝑠𝑖𝑛(𝜃) =

𝜋𝐷 𝜆

𝑠𝑖𝑛(θ)

(2)

The misalignment angle that makes the upper and lower portions of the receiver out of phase with respect to diameter of receiver is shown in Fig. 3. The larger diameter of the receiver is, the lower misaligned angle causes reduction of output voltages. 9 8

Misaligned angle (Deg)

7 6 5 4 3 2 1 0

0

10

20

30 40 50 Diameter of receiver (mm)

60

70

80

Figure 3. The misaligned angle making the upper and lower portions out of phase in terms of diameter of receiver.

According to the in vitro experimental result by Radziemski et al.5, the angle width of full width at half maximum (FWHM) for the pair of 25mm transducers is 2.8°. The angle shown in Fig. 2 (half of the PET’s measurement) is close to the actual measurement. As a result of the FDTD simulation with simple piezoelectric circular transducers, misaligned angle of the receiver causes to reduce the generated power significantly. The effect of distance between two transducers will be examined with estimation of acoustic pressure profile in the near field next.


3. ESTIMATION OF ACOUSTIC PRESSURE PROFILE In the previous analysis, it is demonstrated that the phase shift due to misaligned angle influenced significantly on generated power of the receiver. In this section, the acoustic pressure field between the two transducers is estimated to investigate the pressure distribution and its effect on power generation performance in the near and far field. The modeling can be started with estimation of the acoustic pressure field at an observation point for the general case of an arbitrary transducer shape and non-uniform vibration distribution by the Rayleigh integral formula3,7,16,17. It can be simplified for the system of a continuous wave sinusoidal excitation and uniformly distributed over the face of a discshape transmitter by approximation for the far field region. However, the transducers used for analysis are 10mm apart and those are in the near field. The near field pressure estimation is very complicated and is requiring huge computational load. The formula established by Kelly13 and McGouch et al.14 is adopted for the analysis. Referring to the definition of the coordinate axes for acoustic pressure field calculation13,14 as depicted in Fig. 4, a single integral expression for the steady-state pressure p by a circular transducer is used. 𝑝(𝑟, 𝑧; 𝑘) = −𝑗𝜔𝜌𝑣𝑒 𝑗𝜔𝑡 𝐻(𝑟, 𝑧; 𝑘)

(3)

Where, ρ is the density of medium and v is a constant normal velocity evaluated at the surface of the transducer. The origin (O) is defined as the intersection between the z and r axes in the cylindrical coordinate system13,14.

r

ϕ a O z Transmitter

Receiver

Figure 4. Definition of coordinated axes for this analysis.

The formulation for H in the Eq. (3) can be expressed as13,14; 𝐻(𝑟, 𝑧; 𝑘) =

𝜋 𝑎 𝑟𝑐𝑜𝑠𝜑−𝑎 ∫ 𝑗𝑘𝜋 0 𝑟 2 +𝑎2 −2𝑎𝑟𝑐𝑜𝑠𝜑

× �𝑒 −𝑗𝑘�𝑟

2 +𝑎2 −2𝑎𝑟𝑐𝑜𝑠𝜑+𝑧 2

− 𝑒 −𝑗𝑘𝑧 � 𝑑𝜑

(4)

As in the Eqs. (3) and (4), the pressure amplitude is proportional to the magnitude of H(r,z;k), so the near field pressure can be calculated with one integration. Using the Eqs. (3) and (4), the simulation result for the near field pressure amplitude generated by a circular transducer with radius a= 8.3λ in MATLAB is shown in Fig. 5. The near field acoustic pressure profile in the figure is identical as those results in previous works11-14 except different radius and wavelength. Instead of using normalized values for all axes, actual dimension for the radius of 12.5mm, the distance of 400mm between the transducers, and the pressure amplitude of 72kPa are used to generate the plot. Figure 5 shows only the axial distance up to 15mm because the distance between the transducers is z = 10mm for the case of Radziemski et al.5.


4

x 10 8

Acoustic pressure (Pa)

7 6 5 4 3 2 1 0 15 0

10 4

2

6

5

8 10 12

0

Axial distance (mm)

Radial distance (mm)

Figure 5. Near field pressure amplitude generated by a circular transducer with radius a= 8.3λ.

It clearly shows that variation of acoustic pressure field in the near field is significant. Unlike the pressure in the far field, the axial pressure amplitude in the near field goes through a series of peaks and nulls. The number of peaks and nulls in the near field depends on the value of a/λ15. The Rayleigh distance R0, which is approximately the end of the near field, the beginning of the far field, or the near to far field transition can be found as15; 𝑅0 ≡

𝐴 𝜆

=

𝜋𝑎2 𝜆

=

𝜋(12.5)2 1.5

= 327.25 𝑚𝑚

(5)

But Zemanek11 concluded that the far field begins much earlier, at about R0/4. In addition, Ozeri and Shmilovitz6 used a different formula for the near field calculation. If their formula is used to find our near field distance, then; 𝐿≈

𝑎2 𝜆

=

12.52 1.5

= 104.17 𝑚𝑚

(6)

So the transducers of 25mm diameter lead to the near to far field transition at about 100mm or more. Figure 6 depicts the magnitude of acoustic pressure variation with respect to axial distance up to 400mm.


4

8

x 10

7


6

5

4

3

2

1

0

0

50

100

150

200 250 Axial distance (mm)

300

350

400

Figure 6. Magnitude of acoustic pressure variation with respect to axial distance.

Based on Eq. (6), Fig. 6 demonstrates that the pressure field is not expanding in the near field, not until it gets past the near field to far field region. It shows that the transition from the near field to far field begins at the axial distance of about 100mm as indicated in Eq. (6). The magnitude of acoustic pressure variation for the axial distance of 12mm which is close to the test setup by Radziemski et al.5 is shown in Fig. 7. A series of peaks and nulls in the axial pressure amplitude in this field can be seen. Figure 7 indicates that the voltage or power generating performance can be affected by not only the phase shift due to misalignment of the transducers but also suitable location of the receiver. The effect of misalignment for each location on power generating performance is different, as the receiver is placed at the peaks, the nulls, or between those of the pressure field. 4

8

x 10

7


6

5

4

3

2

1

0

0

2

4

6 Axial distance (mm)

8

10

12

Figure 7. Magnitude of acoustic pressure variation for the axial distance of 12 mm.

The acoustic pressure variation across the radial axis for various axial distances from 8.7mm to 400mm is depicted in Fig. 8 to examine the pressure variation profile across the receiver in terms of the receiver location.


Distance between two transducers

8.7mm 10mm 11.7mm 20mm 50mm 51.8mm 100mm 400mm

10

Radial distance (mm)

5

0

-5

-10

0

1

2

3 4 5 Acoustic pressure (Pa)

6

7

8 4

x 10

Figure 8. Acoustic pressure variation across the radial axis for different axial distances.

At 400mm the pressure field shows obvious far field region and the transition occurs at around 100mm. Placing the receiver at 10mm or 20mm may produce the same generated power, but placing at around 11.7mm, a null point could reduce the generated power since very lower pressure field is applied to the central area of the receiver. In addition, placing the receiver at around 100mm makes insensitive to the misalignment, even though it may not be practical for implants.

4. CONCLUSION The effect of misalignment of the ultrasound transmitter and receiver on the power transmission efficiency is investigated by theoretical analysis using FDTD simulation. The pressure field variation in the near field was also estimated to examine the influence of the power transfer performance of the ultrasound-based charging system. Analytical results indicate that power transfer efficiency is extremely sensitive to the misalignment of the transducers by voltage cancellation due to phase shift. In addition, according to the estimation of pressure variation profile in the near field, the effect of misalignment on the power transmission is highly dependent on the receiver location.

AKNOWLEDGEMENTS The authors acknowledge the support of the National Institutes of Health – National Institute of Bioimaging and Bioengineering, under grant 1 R41 EB007421-01A1. The conclusions stated in this publication are solely those of the authors and not the National Institutes of Health.

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[5] Radzienski, L. J., Denison, A. B., Bell, S., Dunn, F., and Cochran, E. R., “In-vitro tests of a rapid, stable-temperature, ultrasound-based recharging system for implantable batteries,” J. Med. Devices, 4(2), 027523 (2010). [6] Lamancusa, J. S. and Figueroa, J. F., “Ranging errors caused by angular misalignment between ultrasonic transducer pairs,” J. Acoust. Soc. Am., 87(3), 1327-1335 (1990). [7] Kichou, H. B., Chavez, J. A., Turo, A., Salazar, J., and Garcia-Hernandez, M. J., “Lamb waves beam deviation due to small inclination of the test structure in air-coupled ultrasonic NDT,” Ultrasonics, 44, 1077-1082 (2006). [8] Schneider, J. and Hudson, S., “The finite-difference time-domain method applied to anisotropic material,” IEEE Trans. on Antennas and Propagation, 41(7), 994-999 (1993). [9] Hallaj, I. M. and Cleveland, R. O., “FDTD simulation of finite-amplitude pressure and temperature field for biomedical ultrasound,” J. Acoust. Soc. Am., 105(5), L7-12 (1999). [10] Hosokawa, A., “Simulation of ultrasound propagation through bovine cancellous bone using elastic and Biot’s finite-difference time-domain methods,” J. Acoust. Soc. Am., 118(3), 1782-1789 (2005). [11] Zemanek, J., “Beam behavior within the nearfield of a vibrating piston,” J. Acoust. Soc. Am., 49(1), Pt. 2, 181-191 (1971). [12] Lockwood, J. C. and Willette, J. G., “High-speed method for computing the exact solution for the pressure variations in the nearfield of a baffled piston,” J. Acoust. Soc. Am., 53(3), 735-741 (1973). [13] Kelly, J. K., “Nearfield pressure calculations for circular transducers,” Report for MTH 843, Michigan State University (2003). [14] McGouch R. J., Samulski, T. V., and Kelly, J. F., “An efficient grid sectoring method for calculations of the nearfield pressure generated by a circular piston,” J. Acoust. Soc. Am., 115(5), 1942-1954 (2004). [15] Blackstock, D. T., [Fundamentals of physical acoustics], John Wiley & Sons, Inc, New York (2000). [16] Cobbold, R. S. C., [Foundations of biomedical ultrasound], Oxford University Press, New York (2007). [17] Vives, A. A. (Ed.), [Piezoelectric transducers and Application], Springer, Berlin (2008).
