Research Interest

Transducer modelling

GR ter Haar, I Rivens, S Woodford, J Civale in collaboration with P Gelat National Physical Laboratories, Teddington and N Saffari University College, London
Source of funding: EPSRC

A primary aim of this project is the design of a phased-array transducer for the guidance, delivery and monitoring for therapeutic ultrasound treatment of liver tumours. The majority of the liver lies behind the acoustically opaque rib cage, and there is significant liver motion during both the respiratory and cardiac cycles. Both these greatly complicate the delivery of conformal ultrasound induced thermal therapy. The drive electronics under development in this project have 256 transmit channels, half of which will also have receive-capabilities for imaging and monitoring. The phased-array ultrasound source may thus have up to 256 elements active at any one time. Extensive computer modelling is being undertaken on several fronts to determine the optimum numbers and distribution of therapeutic and imaging elements for use in the clinical demonstrator device being developed.   

Mathematical models for the “construction” of transducer arrays, whether they consist of regularly or randomly distributed elements, (which may be circular or rectangular in shape), have been written earlier in this project. Using an existing linear acoustic propagation code, extended to predict the acoustic field profile in 3D, we aim to assess the capability of different transducer designs in terms of their treatment efficacy. In order to facilitate such a study it has first been necessary to identify useful performance indicators. We have identified these to be the following:

A. Steering error – i.e. the difference between intended position of the focal peak intensity and the actual position (in each of 3 cartesian coordinates)
B. Steering cost – the loss of focal intensity at the steered position, compared to that at the geometric (unsteered) focus.
C. Secondary peak damage risk – the ratio of the highest secondary peak intensity to the steered focal peak intensity, after accounting for attenuation in soft-tissue, was used to indicate whether unwanted thermal damage could occur at that position.  The use of a limit for this quantity of between 20 – 40% of the steered focal peak allowed us to define the maximum (safe) steering distance.
D. Maximum treatment depth at maximum steering distance – an assumption that each element was excited at 10 Wcm-2 at its surface, allowed the free-field spatial-peak intensity to be calculated.
E. Treatable volume – this has been approximated as the full width and length of the unsteered focal beam multiplied by the maximum steering distance.

Preliminary data for one transducer is shown in Figure 1

Figure 1. Left : Layout of 254 randomly distributed 6 mm diameter elements with a minimum spacing of 0.2 mm placed on a 16.5 cm diameter transducer with a 13 cm radius of curvature. Right : the steering capability of such a device at 1.5 MHz.  Each coloured line represents a different rotational orientation of the transducer, and the spread of data demonstrates the orientation dependence of the results. Using the constraint that the highest secondary maximum (after depth dependent attenuation correction at 1 dB/cm) cannot exceed 20% of the steered focal peak intensity gives a maximum steering distance of 1.4 cm. The maximum treatment depth was 10.7 cm, and the treatable volume was 0.51 cc

Figure 2. shows the random transducer of the previous figure, left: blue represents the shadow of the focal region caused by a regular distribution of 4 mm wide ribs with 12 mm intercostal spacing when the ribs are located 7 cm in front of the transducer. Right: the ability of the device to steer in the direction parallel to the ribs (green curve) and across the ribs (red curve). The data show increased secondary peaks at all steering distances. The potential to steer along the gap between the ribs greatly exceeds the potential to steer across them. The best treatable volume in this rib-restricted case is 0.45 cc and the maximum treatment depth is 4.0 cm insufficient to allow treatment at clinically useful depths.   

We have extended this study to begin to account for the presence of ribs by approximating the effect that a uniformly spaced rib cage will have in terms of blocking the propagating ultrasound field. In order to achieve this we have back projected the shadow of the ribs onto the transducer surface, taking into account the finite width of the focal region. Thus a wider focal region, which will treat a greater volume of tissue, will widen the shadow of the ribs on the transducer. We have used the shadowing effect of the ribs to identify a subset of elements which would be available for the delivery of therapy, assuming that in order to minimise the risk of rib surface heating, shadowed elements should not be used. For the designs investigated, to date we have found that requiring entire elements to be “unshadowed” reduces a 256 element transducer to as few as 10% residual useable elements. In terms of energy delivery alone this renders the device unuseable, and the steering capability of such a device is extremely poor. Relaxing the conditions such that any element is used for which the central point on its surface is “unshadowed” results in around 40-50% of elements remaining useable.

The next stage of the design process is to optimise the transducer and imaging aperture sizes, as well as the number, size, and inter-element spacing between elements for transcostal treatments.