Theoretical modeling of a thermal wave technique to determine the extent of the freezing region surrounding a cryoprobe

Cryosurgery is a clinical technique to ablate undesirable tissues by extreme freezing, exhibiting the merits of minimal invasion, fast recovery, and low cost. A low temperature cryoprobe is used to form a freezing region around the target tissue. Monitoring the extent of the freezing region is critical since including the target tissue within the surgery scope is necessary for precise treatment and minimal damage to the surrounding normal tissue. This paper investigates a thermal wave based monitoring technique similar to the 3ω method for thermal property characterization in order to measure the extent of the freezing region. The method takes advantage of the contrast in thermal properties between the frozen and unfrozen regions and employs different locations on the circumference of the probe for the thermal wave generator and thermal wave sensor. A two-dimensional analytical model in cylindrical coordinates was developed for the thermal wave and was validated by finite element simulations. The analytical model was then employed to determine the influence of several parameters on determining the freezing extent including modulation frequency, the wave generator width, the relative locations of the thermal wave generator and sensor, and the diameter of the cryoprobe. The results obtained indicate the feasibility of the proposed technique since the amplitude and particularly the phase of the thermal wave signal are sensitive to the position of the interface between the frozen and unfrozen regions. For frozen and unfrozen layers with water, thermophysical properties of the measurement sensitive region extend to diameters in the cm range.