Isothermal volume contours generated in a freezing gel by embedded cryo-needles with applications to cryo-surgery

Three-dimensional numerical simulations of multi-cryo-needle surgery were performed with cryo-needle temperature variations taken from matched experimental data. The transient temperatures and frozen volumes generated by simultaneously operating up to three 1.47 mm OD cryo-needles embedded in a phase-changing gel simulating the properties of biological tissues, were studied. In all cases studied, the volumes enclosed by the "lethal", -40 degrees C isotherm, achieved most of their final size in the first few minutes of operation, thus obviating the need for long application times. After 30 min of application of the one-, two- or three-cryo-needles, the ablation ratio attained 3%, 3-6% and 3-8%, respectively, depending on cryo-needle placement configurations. Synergistic effects of using multi-cryo-needles were reflected in the increased expansion of both the radial and axial locations of the isothermal contours. Within each number of cryo-needles used, however, the differences in these locations were rather small, and, as a general rule, tended to somewhat decrease with increasing the placement "density" of the cryo-needles. For each two- and three-cryo-needle application, there is a certain combination of placement configuration and application time that would produce the largest, temperature-specific, volume. As a general guideline, multiple cryo-needles should not be placed too close to each other in order to enhance their synergistic effect. Results of this study should be useful in the design of cryo-needle placement and operation protocols and in understanding the limitations of the freezing-ablation process.