An efficient technique for estimating the two-dimensional temperature distributions around multiple cryo-surgical probes based on combining contributions of unit circles

This study presents an efficient, fast and accurate method for estimating the two-dimensional temperature distributions around multiple cryo-surgical probes. The identical probes are inserted into the same depth and are operated simultaneously and uniformly. The first step in this method involves numerical derivation of the temporal performance data of a single probe, embedded in a semi-infinite, tissue-like medium. The results of this derivation are approximated by algebraic expressions that form the basis for computing the temperature distributions of multiple embedded probes by combining the data of a single probe. Comparison of isothermal contours derived by this method to those computed numerically for a variety of geometrical cases, up to 15 inserted probes and 2–10 min times of operation, yielded excellent results. Since this technique obviates the solution of the differential equations of multiple probes, the computational time required for a particular case is several orders of magnitude shorter than that needed for obtaining the full numerical solution. Blood perfusion and metabolic heat generation rates are demonstrated to inhibit the advancement of isothermal fronts. Application of this method will significantly shorten computational times without compromising the accuracy of the results. It may also facilitate expeditious consideration of the advantages of different modes of operation and the number of inserted probes at the early design stage.