Background: In radiotherapy treatments for cancer, the ability of normal cells to repair the damage caused by the radiation is slightly better than that of cancer cells. Whilst radiotherapy beams are targeted at the tumour, and the targeting has improved over the past decade with the increasing use of Intensity Modulated Radiotherapy (IMRT), it is inevitable some normal cells will be 'treated'. Any technique that increases the difference in repair rate between normal and cancerous cell has the potential to improve the success of the treatment by killing more cancer cells. One possible technique is mild hyperthermia where the temperature of the tumour, but not the surrounding normal tissue is elevated by about 5oC. The problem is how to selectively heat the tumour. For surface tumours, RF heating using surface coils can be used, but this will not work for deep body tumours.
Ultrasound causes local mechanical vibration in tissues as it propagates through them. At the intensity levels used in medical ultrasound imaging, the temperature rise is too small to measure. However, at high intensities ultrasound can can cause heating. Ultrasound transducers are commonly arrays of elements (figure 1). Ultrasound from such transducers can be focused to create local high intensity levels (figure 2a) and is thus one approach to creating mild hyperthermia in deep body tumours. The focusing is performed by exciting the different elements of a transducer at different times so that at a particular depth constructive interference occurs for the difference wave and they sum to a maximum. An ultrasound transducer of this type is called a phased array transducer.
Figure 2a is a simulation of the field produced by the transducer shown in figure 1 in a water tank and the intensity values were determined by calculating the Rayleigh integral. In figure 2b, the beam from the transducer with the same excitation has been measured in a water tank by scanning the water tank with a 1mm diameter hydrophone. Using these simulations, relationships between the size and poosition of the focal region and the geometry of the array can be established. From figures 2a and 2b it can be seen that for the measured profile the beam is closer to the array than in the measured profile although both were designed to be centred at a depth of 80mm. A full factorial sensitivity analysis suggested that the difference was the result of non-piston like behaviour of the elements.
The approach used to modelling the beam in using the Rayleigh integral: (i) can only be used in a homogeneous medium; and (ii) cannot model the properties of the transducer elements. To do this requires numerical techniques. The wavelength of ultrasound in tissue (water) is small: a 1.5MHz ultrasound wave has a wavelength of 1mm. At least 10 elements/wavelength are required for standard finite element method modelling with the result that: (i) models are very large; and (ii) propagating numerical errors limits the size of the models. The PZFlex/Spectraflex modelling tools overcome these problems and figure 3 shows the 15 element transducer shown in figure 1 modelled with these tools. Using these models the origin of the problem was confirmed and the effect of the diameter of the elements on the position of the focus investigated (figure 4).
Figure 4. The error is focal position as a function of element size
Figure 1. A 15 element phased array ultrasound transducer with a random distribution of 4mm diameter elements.
Figure 2. The modelled (2a) and measured (2b) beam profile of the transducer shown in figure 1. The colour scale is Wm-2 and Z = 0 is the front face of the transducer.
Figure 3. PZflex/SpectraFlex model of the transducer shown in figure 1. The model is 58mm wide x 85mm long with the focus at 60mm. The front face of the transducer is shown as the black line on the left and the colour scale is the Pmax in Pa