44. Considerations for electromagnetic warming of vitrified biomaterials

Abstract

During vitrification, nucleation of ice crystals occurs most rapidly at low temperatures during later stages of cooling, while actual growth of ice crystals is most rapid at warmer temperatures near the solution melting point. Warming rates required to avoid significant ice growth during recovery from vitrification are therefore larger than the cooling rates required during vitrification, when the sample is relatively un-nucleated. Large samples vitrified by external conduction cooling therefore require more rapid warming by internal means if damaging ice growth and cryoprotectant toxicity are to be avoided. Oscillating electric fields coupling to polar molecules (dielectric heating) and mobile ions (ohmic heating) can achieve this. For uniform warming, the oscillation frequency must be low enough to deposit energy inefficiently into the sample (skin depth > > sample size). However the inefficiency cannot be so low that the electric field strength necessary for a desired warming rate causes dielectric breakdown of the sample or surrounding air (arcing). The wavelength inside and outside the sample must also be much larger than the sample to avoid field nodes and antinodes. For vitrified samples of tens or hundreds of grams (human organs), the skin depth and wavelength constraints are met by frequencies of tens of megahertz. Dielectric absorption as a function of frequency is maximal at the Debye relaxation frequency of dipoles. This frequency increases as viscosity decreases, and is therefore temperature-dependent. It’s desirable to choose a frequency with maximal absorption at the temperature at which the ice growth rate is maximal so that the warming rate is fastest when ice growth is fastest. This also promotes temperature uniformity by slowing warming in sample regions that warm past the temperature of maximal energy absorption. In the vitrification solution M22, the target temperature for maximum warming is approximately −60°. The corresponding frequency appears to be on the order of 30 MHz, which fortuitously also meets the aforementioned skin depth and wavelength constraints. Unlike dielectric heating that has a characteristic temperature of maximum absorption for a given frequency, ohmic heating only increases as temperatures increases, leading to “thermal runaway.” It’s therefore desirable to use a cryoprotectant carrier solution of low ionic strength, such as lactose/mannitol-based LM5. Boundary conditions of electric fields at dielectric interfaces also make sample geometry important for achieving a uniform internal field. Previous work in our laboratory with a 27 MHz 200-watt RF source demonstrated peak warming rates of 160 °C during warming a vitrified 20-mL cylindrical volume of M22 in LM5, and half that rate in a vitrified rabbit kidney in the same volume, with 3 °C and 15 °C maximum internal temperature differences respectively. Greater temperature non-uniformity within the organ vs. plain solution reflects decreased dielectric absorption within the non-polar lipid-rich renal pelvis. The maximum warming rate achievable within organs will likely be determined by such differential energy absorption, and the maximum tolerable temperature non-uniformities that result. Future study requires higher power, larger samples, variable frequency, and detailed measurements of cryoprotected tissue electrical properties as a function of frequency to permit accurate modeling.