Efficient array design for sonotherapy

Abstract

New linear multi-row, multi-frequency arrays have been designed, constructed and tested as fully operational ultrasound probes to produce confocal imaging and therapeutic acoustic intensities with a standard commercial ultrasound imaging system. The triple-array probes and imaging system produce high quality B-mode images with a center row imaging array at 5.3 MHz and sufficient acoustic power with dual therapeutic arrays to produce mild hyperthermia at 1.54 MHz. The therapeutic array pair in the first probe design (termed G3) utilizes a high bandwidth and peak pressure, suitable for mechanical therapies. The second multi-array design (termed G4) has a redesigned therapeutic array pair which is optimized for a high time-averaged power output suitable for mild hyperthermia applications. The 'thermal therapy' design produces more than 4 W of acoustic power from the low-frequency arrays with only a 10.5 degrees C internal rise in temperature after 100 s of continuous use with an unmodified conventional imaging system or substantially longer operation at lower acoustic power. The low-frequency arrays in both probe designs were examined and contrasted for real power transfer efficiency with a KLM model which includes all lossy contributions in the power delivery path from system transmitters to the tissue load. Laboratory verification was successfully performed for the KLM-derived estimates of transducer parallel model acoustic resistance and dissipation resistance, which are the critical design factors for acoustic power output and undesired internal heating, respectively.

Figure 1a

The multi-array CoLinear common features are two 6mm elevation outside arrays at 1.5MHz and a single 4mm elevation 5.3MHz array (a). The G3 and G4 are different in their outside row designs. The G3 uses a triple layer piezoceramic and two matching layers (b), while the G4 design uses a single layer piezoceramic and single matching layer (c).

Figure 1b

A representative B-mode image acquired during a sonotherapy treatment of a mouse tumor model as a demonstration of the high level of image quality from the use of the 128 element center imaging array in each of the CoLinear probes. In this particular set up, the Antares system, operating as well in spectral Doppler with the low frequency array pair to produce the mild hyperthermia, is in closed loop control with thermocouple feedback with Doppler-PRF modulation to directly maintain a desired target temperature in the range of 41 to 43 °C.

Figure 2

A generalized system interface for a transducer array. The top panel shows the two components of the real power delivered to the array elements as the desired acoustic (P_a) and undesired dissipative (P_d) power. The lower panel shows the principal loss components in power transmission with a simplified tank circuit model at resonance.

Figure 3

The matrix elements of the KLM model used to characterize the CoLinear designs. A general model for a 2-way entire network is shown in (a), our CoLinear design for 1-way system transmission and tissue loading characteristics in (b), and details of the constituents are shown in (c) as a series of 2X2 matrices.

Figure 4

The KLM model calculated spectral response comparisons for the G3 (1a – 1f) and G4 (2a – 2f) low frequency transducer designs, with computational results at f₀ for each case. All paired cases here are performed with unvaried transmit drive voltages (8.5V and 14V, for G3, and G4 respectively) needed to produce 2.1 Watts total acoustic power output with full system and cable. The 1a-2a power spectra with full system and cable pair are derived from (13); the power spectrum pair, 1c-2c, with an ideal voltage source driving the transducers are derived from (19). The efficiency spectra shown in 1b-2b and 1d-2d are derived from (15) and (20) respectively. The “power spectrum efficiency metric” plots of 1e-2e and 1f-2f are derived from (22) and (27) respectively.

Figure 5

The transducer design efficiency (P_{opt_h}) summary spectra for five thicknesses of the graphite composite matching layer in the G4 design, and a single plot comparison for the G3 design with its double layer matching design.

Figure 6

The linear characterization of the two CoLinear designs showing total actual laboratory acoustic power transmitted for a given driving voltage squared.

Figure 7

The acoustic power output spectra, for the G3 design (top) and the G4 design (bottom). The KLM model prediction for power output is stated for f₀=1.54MHz, and as a solid line (see also Fig. 4-1a and Fig. 4-2a); the lab results are shown as points with 10% error bars, and with G3 operating as at a conservatively low power level in this test.

Figure 8

The wave shape comparisons of model (dashed) and lab measurements (solid) of B-mode transmissions for the G3 design (top) and the G4 (bottom).

Figure 9

The normalized, unitless correction factor values at the eleven test frequencies used for G3 and G4 estimates of R_a and R_d resistances. The correction for G4 is near unity due to very light loading on the cable and imaging system transmitters.

Figure 10

The acoustic radiation resistance (R_a) and the dissipation resistance (R_d) for the G3 probe design. The solid and dashed traces are the model predictions for R_a and R_d respectively. The circles and crosses are calculated from lab data based on acoustic power measurements and thermistor step responses in long burst transmission tests. The boxed points at 1.54MHz are unique “seed” points that served as a model-derived reference points for absolute scaling of the lab data.

Figure 11

The acoustic radiation electrical resistance (R_a) and the dissipation electrical resistance (R_d) for the G4 probe design. The solid and dashed traces are the model predictions for R_a and R_d respectively. The circles and crosses are calculated from lab data based on acoustic power measurements and thermistor step responses in long burst transmission tests. The boxed points at 1.54MHz are unique pivot points that served as model-derived reference points for absolute scaling of the lab data.

Figure 12

The backing material embedded thermistor temperature response curves for the G3 and G4 designs at various acoustic outputs. Starting at 23 °C the G4 shows only a 10.5 °C rise at 100 seconds of 4W continuous output.

Figure 13

The acoustic impedances Z1 and Z2 which are the loads for their corresponding interfaces for the direction shown.

Figure 14

Comparison for the analytical estimates of equivalent motional resistance for the G3 design model. The KLM model was used to estimate R_pk, the parallel combination of R_a and R_d. The standard analytical estimate for motional resistance, R_pa, is presented along with the modified version, R_pas, and two simplified single expression estimates.

Figure 15

Comparison for the analytical estimates of equivalent motional resistance for the G4 design model. The KLM model was used to estimate R_pk, the parallel combination of R_a and R_d. The standard analytical estimate for motional resistance, R_pa, is presented along with the modified version, R_pas, and two simplified single expression estimates.