Optimization of Organ Freezing Protocols with Specified Allowable Thermal Stress Levels

A novel concept of determining optimized cooling protocols for freezing three-dimensional organs has been developed and its feasibility examined computationally. The concept is based on determining correct spatial variation of temperature distribution on the walls of a freezing container at every instant of time during the cooling process so that local thermal stresses in the heterogeneous organ are always kept below a specified level while maximizing the local cooling rates. The cryo-preservation medium must be gelatin which prevents thermal convection. The optimized cooling protocol was simulated by developing a time-accurate finite element computer program to predict unsteady heat conduction with phase change and thermal stresses within a realistically shaped and sized organ made of tissues with temperature-dependent physical properties. A micro-genetic optimization algorithm was then used to achieve nonlinear constrained optimization of parameterized time-varying container wall temperature distribution so that the prescribed maximum allowable thermal stresses are never exceeded in the organ. 1 Graduate research assistant. Student member ASME. 2 Professor. Fellow ASME. 3 Associate Professor. NOMENCLATURE C = specific heat per unit mass E = Young’s modulus of elasticity F = fitness function in the optimization G = shear modulus H = latent heat per unit mass k = thermal conductivity coefficient t = time P = penalty term in the optimization T = temperature u = deformation in x-direction v = deformation in y-direction z = deformation in z-direction x,y,z =Cartesian coordinate directions Greek Letters α = thermal diffusion coefficient β = thermal expansion coefficient ν = Poisson’s ratio σ = stress ρ = density INTRODUCTION Shortage of available human organs is the most serious problem encountered by patients in need of organ transplantation. Using current organ preservation protocols