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

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.

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.

We found that for the aortic heart valve, FOV had similar accuracy and better parameter sensitivity than QLV, particularly for the long time constant (tau2). 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, tau1 = 0.004, tau2 = 76, and mean FOV parameters were beta = 0.29, tau = 0.076, and rho = 1.84.

FOV can provide valuable new insights into tissue viscoelastic behavior Determining the fractional order can provide a new and sensitive quantitative measure for tissue comparison.