Fractional order viscoelasticity of the aortic valve cusp: An alternative to quasilinear viscoelasticity

Background: Quasilinear viscoelasticity (QLV) theory has been widely and successfully used to describe the time-dependent response of connective tissues. Difficulties remain, however particularly in material parameter estimation and sensitivities. In this study, we introduce a new alternative: the fractional order viscoelasticity (FOV) theory, which uses a fractional order integral to describe the relaxation response. FOV implies a fractal-like tissue structure, reflecting the hierarchical arrangement of collagenous tissues. Method of Approach: A one-dimensional (I-D) FOV reduced relaxation function was developed, replacing the QLV "box-spectrum" function with a fractional relaxation function. A direct-fit, global optimization method was used, to estimate material parameters from stress relaxation tests on aortic valve tissue. Results: We found that for the aortic heart valve, FOV had similar accuracy and better parameter sensitivity than QLV particularly for the long time constant (tau 2). The mean (n = 5) fractional order was 0.29, indicating that the viscoelastic response of the tissue was strongly fractal-like. Results summary: mean QLV parameters were C = 0.079, tau 1 = 0.004, tau 2 = 76, and mean FOV parameters were 8 = 0.29, r = 0.076, and p = 1.84. Conclusions: FOV can provide valuable new in-sights into tissue viscoelastic behavior. Determining the fractional order can provide a new and sensitive quantitative measure for tissue comparison.