Stress-Strain Measurements and Viscoelastic Response of Blood Vessels Cryopreserved by Vitrification

Abstract

To gain increased insight into thermo-mechanical phenomena during cryopreservation, tensile stress relaxation experiments were conducted on vitrified blood vessels (vitreous in Latin means Glassy), and the results compared with various viscoelastic models. Using a recently presented device, isothermal stress-relaxation results were obtained for a bovine carotid artery model, permeated with the cryoprotectant cocktail VS55 and a reference solution of 7.05 M DMSO. After a rapidly applied tensile strain, experimental results display exponential decay of stress with time; the stress at a given time increases with decreasing specimen temperature. Among the viscoelastic models investigated, the Williams–Landel–Ferry model was found to best-fit the variation of the stress relaxation data with temperature, while a Maxwell–Weichert model is used to represent the exponential decay of the stress with time. Blood vessel properties were found to dominate at temperatures above roughly −100 °C, while the properties of the cryoprotectant dominate below this temperature. A suitably defined steady-state viscosity displayed a similar behavior for both cryoprotectants, when normalized with respect to the cryoprotectant glass transition temperature.

Appendix A: Uncertainty Analysis

Following standard practice,3 the uncertainty in this procedure is estimated as:

$$ \delta E = {\sqrt {{\left( {\frac{{\partial E}} {{\partial L}}\delta L} \right)}^{2} \, + \,{\left( {\frac{{\partial E}} {{\partial L_{{\text{o}}} }}\delta L_{{\text{o}}} } \right)}^{2} + {\left( {\frac{{\partial E}} {{\partial A}}\delta A} \right)}^{2} + {\left( {\frac{{\partial E}} {{\partial F}}\delta F} \right)}^{2} } } $$

(A.1)

where δL, δL _o, δA, and δF are the estimated uncertainties in measurement of the displacement, effective length, cross-sectional area, and load, respectively; typical corresponding values are: 3.4 × 10⁻³ mm (corresponding to the average elongation of the stainless steel rods under the load present during an experiment), 1 mm, 1.15 mm² (9%), and 0.15 N. When substituting the relaxation modulus from Eq. (1) into Eq. (A.1), the uncertainty is estimated as 12.5% of the long time value of the relaxation modulus for each case. The latter value represents the uncertainty introduced by the experimental apparatus,6 not taking into consideration variations between different specimens, which are expected to have a greater effect on measurements.

Uncertainty in temperature measurements is introduced by A/D conversion (22 bits at 0.333 Hz) in the data acquisition module, cold-junction compensation, and quality of the thermocouple material. The combined effect of these uncertainties is estimated as ±0.8 °C. This value, however, is small when compared with the temperature distribution along a single specimen (typically 5 °C).