A New Device for Mechanical Testing of Blood Vessels at Cryogenic Temperatures

Abstract

As part of an ongoing program to study the thermo-mechanical effects associated with cryopreservation via vitrification (vitreous in Latin means glassy), the current study focuses on the development of a new device for mechanical testing of blood vessels at cryogenic temperatures. This device is demonstrated on a bovine carotid artery model, permeated with the cryoprotectant cocktail VS55 and a reference solution of 7.05M DMSO, below glass transition. Results are also presented for crystallized specimens, in the absence of cryoprotectants. Results indicate that the elastic modulus of a specimen with no cryoprotectant, at about −140°C (8.6 and 15.5°C below the glass transition temperature of 7.05M DMSO and VS55, respectively), is 1038.8 ± 25.2 MPa, which is 8 and 3% higher than that of a vitrified specimen permeated with 7.05M DMSO and VS55, respectively. The elastic modulus of a crystallized material at −50°C is lower by ∼20% lower from that at −140°C.

Appendix

1.1 Uncertainty Analysis

The elastic modulus is given by:

$$ E = \frac{\sigma } {\varepsilon } = \frac{{L_{o} F}} {{LA}} $$

(1)

where σ is the stress, ɛ is the strain, F is the load, L is the elongation, L _o is the effective length, and A is the cross-sectional area. Following a standard engineering analysis of uncertainty [20], the uncertainty in estimation of the modulus of elasticity can be calculated as:

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

(2)

where δL, δL _o , δA, and δF are the estimated uncertainties in measurement of the displacement, effective length, cross-sectional area, and load, respectively; the typical corresponding values are: 1.3 × 10⁻² 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, respectively. From equation (2), the uncertainty in elasticity modulus calculation is estimated as 97 MPa, which is of the same order of magnitude as the standard deviation in experimental data. This agreement indicates that the uncertainty in the experimental apparatus and method of operation is adequate for the study of mechanical response in frozen blood vessels.

The uncertainty in temperature measurement is generated 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 overall uncertainty in temperature measurement is estimated as ±0.8°C. This value, however, is negligible when compared with the temperature distribution along a single specimen.