Modeling single probe cryosurgery

A time dependent three dimensional model of iceball formation about a single cryoprobe is described and extensively compared to experimental data. A realistic three dimensional probe geometry is specified and cryoprobe temperature may be arbitrarily set as a function of time in the model. Thermal histories for several points around a CRYOprobe$\sp{\rm TM}$ have been predicted to high accuracy. Temperature distributions with time within iceballs are presented and compared to the results of the infinite cylinder equilibrium solution of the Fourier heat equation. Infinite cylinder approximations are shown to be grossly inaccurate. A novel concept, termed the ablative ratio, is introduced as the ratio of the volume of ablated tissue divided by the total volume of the iceball. This concept assumes necrosis occurs when cells have been dropped below some critical temperature. For the purposes of illustration, we will assume a $-20\sp\circ$C isotherm completely kills target tissue. The simulated results indicate that the killing efficiency of an iceball, as measured by the ablative ratio, decreases with time as the iceball increases with size. Calculations of isotherm locations with the infinite cylinder solution are shown to yield overestimates of the ablative ratio.