How should we measure and report elasticity in aortic tissue?

BACKGROUND: Different stress-strain definitions are used in the literature to measure the elastic modulus in aortic tissue. There is no agreement as to which stress-strain definition should be implemented. The purpose of this study is to show how different results are given by the various definitions of stress-strain used and to recommend a specific definition when testing aortic tissues.
METHODS: Circumferential specimens from three patients with ascending thoracic aortic aneurysm (ATAA) were obtained from the greater curvature and their tensile properties were tested uniaxially. Three stress definitions (second Piola-Kirchhoff stress, engineering stress and true stress) and four strain definitions (Almansi-Hamel strain, Green-St. Venant strain, engineering strain and true strain) were used to determine the elastic modulus.
RESULTS: We found that the Almansi-Hamel strain definition exhibited the highest non-linear stress-strain relation and consequently may overestimate the elastic modulus when using different stress definitions (second Piola-Kirchhoff stress, engineering stress and true stress). The Green-St. Venant strain definition yielded the lowest non-linear stress-strain relation using different definitions of stress, which may underestimate the values of elastic modulus. Engineering stress and strain definitions are only valid for small strains and displacements, which make them impractical when analysing soft tissues. We show that the effect of varying the stress definition on the elastic modulus measurements is significant for maximum elastic modulus but not when calculating the hypertensive elastic modulus.
CONCLUSIONS: It is important to consider which stress-strain definition is employed when analysing soft tissues. Although the true stress-true strain definition exhibits a non-linear relation, we favour it in tissue mechanics because it gives more accurate measurements of the material's response using the instantaneous values.