Analysis of the effect of partial vitrification on stress development in cryopreserved blood vessels

Thermal stress development in blood vessels, during processes associated with vitrification (vitreous means glassy in Latin), is studied. This paper addresses the limiting case where the specimen completely crystallizes, while the cryoprotectant medium (CPA) completely vitrifies. This case is expected to provide upper boundary estimates for stresses for the more common problem of a partially vitrified sample. The CPA is modeled as a linear viscoelastic medium, with viscosity increasing exponentially with decreasing temperature; given the assumption of complete crystallization, the blood vessel is modeled as linear elastic below the freezing temperature. Consistent with previous observations, the CPA is found to behave linear elastically below a set-temperature, at which point the viscosity rises sufficiently quickly with further cooling. This observation reduces computational efforts and allows for parametric studies based on suitably chosen wholly elastic models. Both 2D concentric cylinder models of the blood vessel in a straight configuration and a 3D model of the vessel curled in a vial of CPA are studied; 2D models are shown to bound the results of the more general 3D problem. It is found that stress in the CPA decreases with increase in CPA volume, at least under conditions where the temperature can be viewed as uniform. Planar cracks are predicted to form transverse to the vessel axis, and to propagate right up to the blood vessel wall. Should such cracks propagate into the vessel, even over only a few mum, the mechanical damage to the lumen, or to endothelial cells, may cause the blood vessel to completely loose its functionality at the end of the cryopreservation protocol.