title: A simple procedure for determining spatial and transient variations of cooling rate within a specimen during cryopreservation. Part 2: Graphical solutions.
abstract: The ability to analyse the cooling rate history and its spatial distribution is useful in predicting the response of a biological specimen to a specific cryopreservation protocol. Although analytical and numerical methods exist for performing rigorous analyses of these thermal processes, their practical use requires considerable time and/or mathematical sophistication. In Part 1 of this paper a theoretical basis was presented for the development of a graphical analysis procedure for determining cooling rate that is quick and straightforward to apply. In this paper derived graphs are presented, from which the instantaneous cooling rate may be determined for specimens of a wide range of physical shapes. These dimensions graphs have been derived for determination of cooling rate as a function of time, position, the system's physical properties and the thermal boundary conditions. Numerical examples are presented for analysing the cooling of biological specimens for specific preservation protocols, illustrating solution both by computation using the tabulated constants from tables in the first paper and by reading directly from the graphed solutions.
authors: MRC Medical Cryobiology Group, University Department of Surgery, Cambridge.
authors: K R
authors: KR
authors: Diller
mesh_terms: D015925:Cryopreservation / Q000379:methods*; D005583:Fourier Analysis; D008433:Mathematics; D008954:Models, Biological