Theoretical investigation of a phased-array hyperthermia system with movable apertures

Abstract

A four-applicator phased-array hyperthermia system with movable apertures (MA) is compared with an eight-applicator annular phased-array hyperthermia system with fixed apertures (AA) in terms of the HEP (hyperthermia equipment performance) values, based on two-dimensional models and the bioheat transfer equation. A hybrid element method is used to calculate the z-directed two-dimensional electric field with the inhomogeneities in tissue properties taken into account. The amplitudes and phases of each applicator are then optimized with the objective of uniform power deposition in the tumour and no power deposited in normal tissues. The temperature distributions under different blood flow conditions are obtained by solving the bioheat transfer equation using the finite element method. It is found that among the seven patient models studied, the MA and A A in general perform equally well when the tumour has zero blood flow, or equally poorly when the tumour has a blood flow larger than 5 ml/100 g per min. The performance of AA is often significantly better than that of MA when the tumour blood flow is 2.7 ml/100 g per min. The effects of different weighting functions are evaluated. We show that even if uniform absorbed power density (ARD=absorption rate density) could be achieved in the tumour volume with zero ARD in normal tissue the entire tumour would still not be brought to 43°C or greater. However, it is found that the performance of uniform ARD in the tumour is on average far better than either the AA or MA, and choosing the uniform ARD as the objective function improved 35% of the cases for AA and 16% for MA. The optimization formula includes a weighting function that can be varied for different tissues. By decreasing the weights in regions of high blood flow the HEP values can sometimes be improved quite noticeably. Finally, the importance of the locations of applicators is studied. The results obtained indicate that the applicators should be placed about 5 cm or more away from the patient body (assuming water is the coupling medium) to ensure good HEP ratings.

Key Words:

• movable phased array
• annular phased array
• optimization
• hybrid element method
• and bioheat transfer equation