What does the slope of stress-stretch curves tell us about vascular tissue response?

We examined a group of 50 uniaxial stress-stretch curves obtained from human ascending aortic aneurysm tissues. The curves were believed to be associated with elastic response because the stress is monotonically increasing in all curves, and so is the slope. However, 26 curves exhibit exponential-like slope while the remaining 24 curves have sigmoid slopes. We hypothesized that the slope patterns stemmed from collage waviness distribution. A structural constitutive model was introduced to describe the responses. The model employed a unimodal density function to describe the waviness distribution, from which a two-phase response ensued. In the first phase the slope is quasi-exponential, and in the second phase the slope is sigmoid. The model fitted all 50 curves perfectly well. An exponential model was also introduced for a comparison. The model fitted the curves of quasi-exponential slope generally well, but performed worse over the curves of sigmoid slope. The work suggests that the slope may encode significant information about collagen waviness, and underscores a limitation of exponential-based models.