ANALYSIS OF THE INVERSE PROBLEM OF FREEZING AND THAWING OF A BINARY-SOLUTION DURING CRYOSURGICAL PROCESSES

Art integral solution for a one-dimensional inverse Stefan problem is presented. Both the freezing and subsequent thawing processes are cons idered. The medium depicting biological tissues, is a nonideal binary solution wherein phase change occurs over a range of temperatures rath er than at a single one. A constant cooling, or warming, rate is impos ed at the lower temperature boundary of the freezing/thawing front. Th is condition is believed to be essential for maximizing cell destructi on rate. The integral solution yields a temperature forcing function w hich is applied at the surface of the cryoprobe. An average thermal co nductivity, on both sides of the freezing front, is used to improve th e solution. A two-dimensional, axisymmetric finite element code is use d to calculate cooling/warming rates at positions in the medium away f rom the axis of symmetry of the cryoprobe. It was shown that these coo ling/warming rates were always lower than the prescribed rate assumed in the one-dimensional solution. Thus similar, or even higher, cell de struction rates may be expected in the medium consistent with existing in vitro data. Certain problems associated with the control of the wa rming rate during the melting stage are discussed.