Design and Construction of the Test-cell

To design and construct the test cell some design constraints were applied. The first and most important design constraint was that in making simultaneous electrical impedance and ultrasound propagation velocity measurements there should be similarity in spatial sensitivity between the two measurements. To ensure similarity between the spatial sensitivity of the two measurements, the diameter of the ultrasound element and the electrode spacing was selected so that the position of the last axial maximum in the centre line of the ultrasound field (based on a circular PZT element behaving as a piston) (Figure 3-18) is at the same depth as the peak in the average planar sensitivity for the tetrapolar electrical impedance measurements (section 2.2.3, published in (Islam et al., 2010)).

0 1 2 3 4 5 6 x 10-6 -0.4 -0.35 -0.3 -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 time /s am p li tu d e (n o rm al is ed )

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Figure 3-18 The field distribution of an ideal piston like source generating a continuous ultrasound wave. The near field (Fresnel zone) and far field (Fraunhofer zone) regions are shown in relation to the transducer’s diameter (D) and wave length (λ). (Source:(Hedrick et al., 1995))

Transparent Perspex, which is a premium grade acrylic, was chosen to make the test cell. The test cell, which was cylindrical in shape, holds the sample materials. The depth of the test cell had to be sufficient so that the distance from the base to the transducer was large compared to the wavelength of the ultrasound and that the time of flight for the reflection from the base was long compared to any ‘ringing’ from the transducer. Initial experiments done on the type of ultrasound transducer to be used (section 3.1.1) suggested that ringing following pulse excitation could last up to 30µs without an optimised drive pulse and 6µs with an optimised drive pulse. Therefore, the minimum time of flight from the transducer to a reflective surface was set to 30µs. This corresponds to a depth in the test cell of 22.5mm. This is approximately 13 times the wavelength of the ultrasound in soft tissue. This is small for time of flight measurements, so this was increased to approximately 25 times the wavelength giving a sample chamber depth of 36mm. The diameter of the sample chamber needs to be small to ensure even heating of the sample yet large to enable ultrasound propagation without reflection from the walls. In addition the sensitivity properties of the electrical impedance measurement assume a semi-infinite homogeneous

Distance from transducer (wavelengths)

Re lat iv e In ten sity

Near field (Fresnel zone) Far field (Fraunhofer zone)

Central axis of

𝐷2

𝜆

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media. Therefore, as a compromise, a diameter of 40mm was selected for the test cell. The wall thickness of the cylindrical test cell was chosen to be 2mm as a compromise between robustness and thermal resistance.

Figure 3-19 Perspex test cell showing position of the electrodes and PZT element - (a) Test cell (b) Lid of the test cell and (c) Top of the Test cell.

A cylindrical test cell having internal diameter of 40mm, height of 36mm, vertical walls and its base 2mm thick was constructed from Perspex with the help of the mechanical workshop of the department of Physics at Warwick University (Figure 3-19a). The test cell was threaded around the exterior wall from the top of its open ended side to a depth of 5mm. The lid of the test cell (Figure 3-19b) was designed to incorporate an ultrasound transducer and four electrodes so that simultaneous ultrasound and multi-frequency electrical impedance measurements can be taken. The ultrasound transducer was located at the centre of the lid and the four brass/stainless steel electrodes approximately 5mm in diameter were arranged in square centred on the transducer element. The four electrodes were equi-spaced at a radius of 17mm from the centre forming the corners of a square giving an electrode spacing of 24mm (Figure 3-19b). Apart from the four electrodes there was also an additional electrode for the common connection. Two holes were drilled at a radius of 15mm from the centre line of the lid for insertion of the thermocouple into sample materials to allow the temperature of these to be measured during experiments. Care had been taken to ensure that the positions of the thermocouples were away from the centre line of the test cell to avoid scattering of the ultrasonic waves generated by the

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PZT transducer. Another hole and four recessed regions were cut outside the matching layer in the front side of the lid to allow filling the cell so that sample material made good contact with the electrodes and ultrasound transducer and to allow for its thermal expansion of the materials.

The top of the test cell was held in place by an open ended Perspex cylinder threaded at one end so that it could be screwed on to the threads at the top of the test cell (Figure 3-19c). An O-ring positioned between of lip on the inner surface of the cylinders just above the threaded portion around the top of the test cell in place and provided a seal against liquid ingress. The height of the cylinders, which can be seen in (Figure 3-19a) allowed the test sample to be fully immersed in a water bath for heating.

Figure 3-20 (a) Cross section of the perspex lid of the test cell. Electrode positions are shown as distorted so that al 4 electrodes are visible. (b) The completed Perspex lid – the PZT ultrasound transducer and the electrodes are fitted in the perspex lid.

The diameter of the ultrasonic transducer was chosen based on the sensitivity analysis of electrical impedance measurements discussed in chapter 2. In chapter 2, it was shown that sensitivity of the impedance measurement decreased with the increase of the receive electrode spacing. For a small electrode spacing a high value of sensitivity occurs beneath the electrodes edge. However, for small electrode spacing, the useful sensitivity extends to only a small depth directly beneath the electrodes’ plane. On the other hand, for large electrode spacing, the useful sensitivity distribution extends to a greater depth beneath the electrodes’ plane, but its value is smaller. In addition, the smaller the electrode spacing, the more the impedance measurements will be affected by the local tissue characteristics in the vicinity of the electrodes. From the experimental point of view, it was necessary to make a compromise between the magnitude of sensitivity and the electrode spacings and

1mm 2mm 2mm

14mm

Front: Epoxy matching layer Perspex frame

Electrodes Ground

Drive signal

Rear: Air backed

Recessed region Electrodes

40mm 7 mm

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to make a choice of the optimal electrode spacing for this work. Therefore, an electrode spacing of 24mm was chosen for the present electrical impedance measurement system. It was shown previously that for 4 electrodes arranged in a square, there is a peak in the average sensitivity of a plane at a depth of ⅓ of the electrode separation (section 2.2.3, published in (Islam et al., 2010))- a depth of 8mm in the test cell.

The diameter of the circular element transducer was chosen so that it can produce maximum acoustic pressure amplitude at a distance of 8mm from the front face of the transducer along the centre line of the direction of propagation. If it is assumed that the circular transducer element behaves as a piston, then the axial intensity profile in the direction of propagation has the form of a Bessel function of the 1st type with the last axial maximum at D2/4λ, where D is the radius of the transducer and λ is the wavelength in the media (Figure 3-18). If the frequency of oscillation of the transducer element considered as 1MHz, then the value of λ for 1MHz ultrasound in soft tissue is approximately 1.5mm (considering velocity of sound in soft tissue as 1500ms-1) which gives a transducer diameter of 7mm to align the last axial maxima in the axial ultrasound intensity with the peak in the average sensitivity of a plane in the impedance data.

The Perspex-lid of the test cell was machined to house the circular transducer element. The lid incorporated one hole of 7mm diameter at the centre, into which the 7mm diameter transducer elements would be fitted. The front surface of the lid was recessed around the hole maintaining 14mm diameter and 1mm thickness. The recessed region allowed λ/4 matching layer to be incorporated for the transducer element. Four electrode positioning holes, each of 2.5mm diameters, maintaining 24mm distance between the adjacent holes were drilled in the lid. Another hole for common electrodes was also drilled in the lid of the test cell. Figure 3-20 shows the cross section of the Perspex lid and the completed Perspex lid with PZT and electrodes fitted in it.