FASE II: LEVANTAMIENTO Y CARACTERIZACIÓN DE LOS

While the results indicated that cross-coupling is weak within the fifteen element array when driven by a 40 V waveform, questions remained as to whether the cross- coupling would be significantly worse for more closely spaced elements and for higher drive voltages. This is important since (as will be discussed in section 8) both a larger number of elements (and therefore closer element spacings) and higher drive voltages would be necessary to create a focal region of sufficient intensity to produce mild hyperthermia in tissue. To allow the crosstalk between more closely spaced elements to be measured, a new transducer array was constructed which was composed of four closely spaced 4 mm diameter elements with a minimum inter-element pitch of 4.4 mm (figure 6.4).

Measurements of the crosstalk in the four element array were made using the same procedure as was used with the fifteen element array. Figure 6.5a shows the 40 V peak-to-peak square-wave drive signal (linei) and the waveforms for crosstalk

−20 0 20 −0.5 0 0.5 −0.5 0 0.5 0 0.5 1 1.5 2 −0.5 0 0.5 Voltage / V Time / µs (i) (ii) (iii) (iv)

Figure 6.5: Typical measured crosstalk waveforms for three different element pairs from the 4 element array. Line ishows the square-wave drive signal while lines ii,iii

and iv show measured crosstalk waveforms for three different element pairs plotted relative to the drive signal. The inter-element pitch for the three element pairs was: (ii) 4.5 mm, (iii) 5.9 mm and (iv) 4.4 mm.

signals measured on three different element pairs in the four element array (lines

ii,iii and iv), with their phases shown relative to the square-wave drive signal. A number of observations can be made from these two plots:

ˆ As with the fifteen element array (figure 6.3a), short, high frequency bursts are present, occurring at the rise and fall of the square-wave drive signal. For each choice of element pairs, these bursts always occur at the same time relative to the drive signal, and it is therefore likely that these are due to electrical cross-coupling, as described in section 6.3.1.

ˆ The measured crosstalk signals also contain a 1 MHz sinusoidal component. The phase of this sinusoidal component is different for each each combination of element pairs, strongly suggesting that it is a result of acoustic coupling between elements, since the time required for the acoustic wave to propagate between elements will depend on the element separation and will therefore be different for each choice of element pair.

Since the crosstalk measurements only required a single active drive chan- nel, measurements were also made while using the higher voltage single-channel

drive electronics (described in section 5.2) to provide the drive signal, enabling the crosstalk to be measured for drive signals up to 280 V peak-to-peak. Figure 6.6a illustrates the combined results for the fifteen element and four element arrays us- ing drive voltages of 40 V and 280 V (peak-to-peak square waveforms). The graph shows that for the fifteen element array and drive voltages of 280 V peak-to-peak, the relationship between the magnitude of the crosstalk and the inter-element pitch is similar to the trend that was seen for a 40 V drive waveform: the crosstalk de- creases very weakly with increasing inter-element pitch. However, for element pairs in the four element array (where the inter-element pitch is smaller) the magnitude of the cross-coupling is strongly dependent on pitch, indicating that acoustic crosstalk dominates at these smaller element spacings (i.e. for element pairs with an inter- element pitch of less than approximately 8 mm). This was true both for drive voltages of 40 V and of 280 V.

Further measurements of the crosstalk were made at intermediate voltages between 40 V and 280 V, and in figure 6.6b the magnitude of the crosstalk is plotted as a function of the drive voltage. For large inter-element pitches (15-30 mm), the crosstalk rose approximately linearly with voltage beyond a drive voltage of 80 V. For small inter-element pitches (4-5 mm) a similar linear increase in the crosstalk with the drive voltage is seen, but the variability of the measured crosstalk is much greater. This large variation suggests that mounting differences between elements are significant in determining the acoustic crosstalk between element pairs.

Although figure 6.6 shows that the measured crosstalk signals were much stronger for closely spaced elements and high drive voltages, the magnitude of the cross-coupling was still relatively weak in comparison to the drive signal. At the minimum inter-element pitch of 4.5 mm and the maximum drive voltage of 280 V the maximum measured RMS crosstalk signal was approximately 1.2 V, which was less than 1.5% of the 280V peak-to-peak drive signal.

In summary, the results indicate that the crosstalk within an array of this type is weak. Cross-coupling between widely spaced elements (where the pitch is greater than about 8 mm) is primarily due to electrical coupling and takes the form

0 5 10 15 20 25 30 35 40 0 200 400 600 800 1000 1200 1400 Inter−element pitch / mm RMS crosstalk / mV 280V 40V 0 50 100 150 200 250 300 0 200 400 600 800 1000 1200

Peak−Peak Drive Voltage / V

Mean RMS crosstalk / mV

4−5mm 15−30mm

(a) (b)

Figure 6.6: Plot (a) shows the measured RMS crosstalk signal against the separation between the drive and receive elements for drive voltages of 40 and 280 V. The data obtained from the fifteen element array are found to the right of the vertical dashed line, while the data obtained from the four element array are found to the left of the line. Plot (b) shows the mean RMS crosstalk signals against drive voltage for element separations within the ranges 4-5 mm and 15-30 mm.

of short, high frequency bursts initiated by the sharp rise and fall of the square- wave drive signal. The strength of this crosstalk is typically less than 0.5% of the drive signal. It will therefore have little influence on the phase of the drive signal at the receiving element. Cross-coupling between closely spaced elements (where the pitch is less than about 8 mm) is more significant and is primarily due to acoustic coupling. The measured waveform for this acoustic crosstalk was sinusoidal.

Acoustic coupling between elements could arise from one of two mechanisms: via transmission of a pressure wave propagating through the Perspex frame, or via a Lamb wave travelling on the surface of the Perspex. The actual mechanism by which acoustic coupling occurred in the four element array has not been identified within the present work. Since the level of the acoustic crosstalk was at most approximately 1.5% of the drive signal, its impact is likely to be small and therefore further inves- tigation of the crosstalk mechanism was not required. However, in arrays composed of a large number of elements it is possible that a small level of crosstalk could impact on the performance of the array, and so simulations investigating this are considered in chapter 7.