A finite element and order of magnitude analysis of cryosurgery in the lung

Cryosurgical freezing of dense lung tumors within health, lung tissue is in vestigated using numerical and order-of-magnitude analyses. The numerical m odel indicates that the freezing: front accelerates as it leaves the tumor and enters the surrounding healthy, low density lung tissue, a prediction c onfirming the earlier analytical work. of Bischof. Bastacky and Rubinsky [1 ]. Order-of-magnitude arguments are used to explain this somewhat counter-i ntuitive: result as well as the qualitative features exhibited by the numer ical freezing simulation In particular, scaling arguments lead to three imp ortant findings : i.) The ratio of freezing front speeds in tumorous and he althy tissue is inversely proportional to the ratio of corresponding tissue densities. Thus. as predicted by the numerical simulation, the Freezing fr ont travels faster in health) tissue. ii.) In either tissue. the speed oi a radially propagating freezing front varies approximately as l/r. where r i s the instantaneous front radius. Thus. the front decelerates as it grows r adially. iii.) Approximate closed form expressions can be derived to estima te the time-varying freezing front location in either tissue type. (C) 1999 Elsevier Science Ltd.