COMPUTATIONAL ALGORITHM of TWO PARALLEL ULTRASOUND BEAMS of 1D CANCER TISSUE MODEL for SAFE and EFFECTIVE HYPERTHERMIA TREATMENT

Abstract

The mathematical algorithm of two parallel ultrasound beams on a one-dimensional (1D) cancer tissue model for hyperthermia treatment was created using Matlab software. Physically, the model incorporated two beams; the first beam was permanently placed at the center of the tumor, whereas the other was set between the first beam and the tumor. The computational implementation of this technique relies on the Crank-Nicolson method. This technique is a finite different method that offers an exact heat transfer calculation based on the heat analysis of the heat node structure from a 1D biological tissue model. The Matlab software implementation was composed of two stages: tissue temperature profile calculation and optimization computation. To obtain the tissue temperature profile, the beam heat was varied from 45C to 75C (seven different levels of heat from the same source), while the second beam was allowed to move between the first beam and the tumor to locations at distances of 1 to 9mm (nine positions). The obtained tissue temperature profiles were subsequently analyzed to achieve the optimal time, beam position, and beam heat of the treatment. As a result of the optimization, the best position for the second beam was determined to be 5mm from the center of the tumor. Further, all tumor cells were observed to have died, whereas all normal tissues were safe. The optimal time, beam position, and beam heat of the treatment were finally collected to create and fit a mathematical function for further hyperthermia treatment.