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Sensitivity of tissue freezing process on changes of time-dependent cryoprobe tip cooling rate

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Mochnacki B. , Siedlecki J.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

2011

tom Vol. 10, nr 2

191-197

In the paper, the problems of thermal interactions between skin tissue and a cylindrical cryoprobe tip are discussed. The cryoprobe tip temperature is time-dependent and its changes from the initial temperature to the final one and back are assumed in the form of a broken line (successive sectors correspond to cooling and heating processes or cooling and heating ones divided by a horizontal sector (a constant freezing temperature)). The aim of the considerations resolves itself in the analysis of dependences between the tip cooling (heating) rate and the course of the freezing process. To solve the problem, the direct approach of sensitivity analysis is used. The mathematical model of freezing is based on the energy equation corresponding to the 'fixed domain method' in which a parameter called 'the substitute thermal capacity' appears. The sensitivity model results from the differentiation of energy equation and boundary-initial conditions with respect to the cooling (heating) rate. At the stage of computations, the finite differences method (FDM) is used. In the final part of paper, examples of computations are presented.