Numerical Simulation of the Effects of a Thermally Significant Blood Vessel on Freezing by a Circular Surface Cryosurgical Probe Compared With Experimental Data

The dynamic thermal interaction between a surface cryosurgical probe (heat sink) and an embedded cylindrical tube (heat source), simulating a thermally-significant blood vessel, has been studied. The cryoprobe was operated by liquid nitrogen while the embedded tube was perfused by water at a constant inlet temperature. Previous experimental data were obtained in a phase-changing medium (PCM) made of 30%/70% by volume mashed potato flakes/distilled-water solution. A parametric study was conducted without the embedded tube, and with flow rates of 30 ml/min and 100 ml/min in the tube, while cooling rates at the tip of the cryoprobe were maintained at $−4°C/min$⁠, $−8°C/min$⁠, or $−12°C/min$⁠. Numerical thermal analysis was performed by ANSYS7.0 and showed good conformity to the experimental data. The results quantify the effects of these parameters on both the shape and extent of freezing obtained in the PCM. For 20 min of operation of the cryoprobe, water temperatures inside the tube remained well above the freezing point for all assumed operating conditions. Frozen volumes of the $0°C$ isotherm, approximating the “frozen front,” and the $−40°C$ isotherm, representing the “lethal temperature,” were smallest for the combination of highest cooling rate at the cryoprobe and the highest flow rate in the tube, (⁠$−12°C/min$ and 100 ml/min). The results indicate that both the flow rates in the embedded tube, and the cooling rates applied at the cryoprobe, have similar qualitative effects on the size of the PCM frozen volumes; increasing either one will cause these volumes to decrease. Under the conditions of this study the effects of flow rate in the tube are more pronounced, however, effecting relative frozen volumes decreases by about 10–20% while those of the cooling rate at the cryoprobe are in the range of 7–14%.