A model for the time dependent three-dimensional thermal distribution within iceballs surrounding multiple cryoprobes

A time dependent three-dimensional finite difference model of iceball formation about multiple cryoprobes has been developed and compared to experimental data. Realistic three-dimensional probe geometry is specified and the number of cryoprobes, the cryoprobe cooling rates, and the locations of the probes are arbitrary inputs by the user. The simulation accounts for observed longitudinal thermal gradients along the cryoprobe tips. Thermal histories for several points around commercially available cryoprobes have been predicted within experimental error for one, three, and five probe configurations. The simulation can be used to generate isotherms within the iceball at arbitrary times. Volumes enclosed by the iceball and any isotherms may also be computed to give the ablative ratio, a measure of the iceballʹs killing efficiency. This ratio was calculated as the volume enclosed by a critical isotherm divided by the total volume of the iceball for assumed critical temperatures of -20 and -40 °C. The ablative ratio for a single probe is a continuously decreasing function of time but when multiple probe configurations are used the ablative ratio increases to a maximum and then essentially plateaus. Maximum values of 0.44 and 0.55 were observed for three and five probe configurations, respectively, with an assumed critical temperature of -20 °C. Assuming a critical temperature of -40 °C, maximum ablative ratios of 0.21 and 0.3 for three and five probe configurations, respectively, were observed.