An Improved Waveform Diversity Method for Optimizing 3-D Power Dispositions
In an effort to improve conformal tumor heating for hyperthermia and heat modulated drug delivery, simulations using waveform diversity were run in a 3-D model with a spherical-section phased array to generate temperatures in a deep-seated spherical tumor. Waveform diversity generates several beam patterns to match a desired power distribution, and results show that compared to spot scanning, waveform diversity has greatly reduced intervening tissue heating.
The phased array used has 1444 square elements, each 0.24 cm x 0.24 cm, and has opening angels in the lateral dimensions of 60°. The center of the array is set as the origin of the coordinate system, with a geometric focus at 12 cm. The tumor used for these results has a diameter of 3 cm and is centered at (0,0,12) cm. Computational grid used is set as a 15 cm x 15 cm x 15.9 cm volume with -7.5 cm ≤ x,y ≤ 7.5 cm, and 4.05 cm ≤ z ≤ 19.95 cm. The acoustic and thermal properties used are: ρ=1000 kg/m3, c=1500 m/s, α=0.5 dB/cm/MHz, Wb=5 kg/m3/s, K=0.55 W/m/<°C, and Cb=4000 J/kg/°C. The array uses an excitation signal with center frequency 1 MHz, giving wavelength λ=1.5 mm.
In order to lower the computational cost, the number of transducer elements in the array was reduced by using mode scanning combined with waveform diversity. This makes it possible to run the same case for waveform diversity with only one quarter of the focal points defined for spot scanning. In the case for the results shown in figure 1, 33 of these focal points are tumor control points, and 144 are normal tissue control points. The normal tissue control points are uniformly distributed within a square grid, 0.825 cm x 0.825 cm, located at z=9.45 cm in the xy-plane with 0.075 mm (λ/2) spacing in each direction. The results using this distribution of control points gives 56.5% of the tumor heated to 4°C or more. The temperature distribution is shown in figure 1.
Figure 1: Temperature rise in the xz-plane evaluated at y=0, the center of the tumor model is located at z=12 cm, the tumor radius is 3 cm, and control points are uniformly distributed throughout the tumor with weighting of 1.
To improve upon the results shown in figure 1, all of the control points that reached a temperature of 5°C or above were removed and the simulation was repeated. Results for the temperature rise are shown in figure 2. Unlike the case for figure 1, the area inside the tumor that reached a temperature of 5°C or more was much greater, even in comparison with the area of figure 1 that reached a temperature of 4°C or more. The percentage of the tumor that achieved 5°C or more was 60.343% while the percentage of the tissue heating for 5°C or more was only .010581%. This result brought about a new direction to proceed with for modifying the distribution of tumor control points.
Figure 2: Temperature rise in the xz-plane evaluated at y=0, the center of the tumor model is located at z=12 cm, the tumor radius is 3 cm, with the removal of all control points that reached a temperature of 5°C or more from the case ran in figure 1. All remaining control points are uniformly distributed throughout the tumor with weighting of 1.