A method and apparatus are disclosed for avoiding fracturing, e.g., thermo-mechanical fracturing, in vitrified biological systems via rapid cooling and/or warming persufflation techniques, by reducing the domain size of fracturing and by reducing thermal gradients. Also disclosed is a system adapted to rapidly cool and warm vitrifiable vascular biological tissue by persufflation, significantly reducing cryoprotectant toxicity from that of surface cooled tissue, in which the system is constructed and configured to use one or more of helium gas, hydrogen gas, neon gas, argon gas, krypton gas, xenon gas, oxygen gas, or various gaseous compounds. The system can be operated under pressure to increase the density and heat capacity of the gas relative to its density and heat capacity at atmospheric pressure and to cool the gas by one or more of mechanical action and by the phase change of a material such as a cryogenic gas or solid.