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 (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. CONCLUSIONS: 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.

Stress relaxation preconditioning of porcine aortic valves.

In uniaxial tensile testing, load preconditioning is used to generate repeatable load/elongation curves and set a "reference state" for subsequent tensile tests. We have observed however, that for porcine aortic valve (PAV) tissues, preconditioning does not lead to repeatable stress relaxation curves. We thus investigated possible experimental protocols that could be used to generate repeatable load/elongation and stress relaxation curves. To quantify repeatability of stress relaxation, we compared normalized loads at the same time points from repeated stress relaxation curves and computed a repeatability ratio. We found that PAV specimens can generate repeatable stress relaxation curves (repeatability ratio >0.95) if they are subjected to at least five cycles of repeated load preconditioning and stress relaxation. We also found that a single cycle of loading/unloading prior to each stress relaxation phase is sufficient to generate repeatable stress relaxation curves. Stress relaxation preconditioning is therefore required to generate repeatable load/elongation and stress relaxation curves. It is expected that such curves will generate more accurate material constants for the characterization and modeling of PAV mechanics.

The effect of strain rate on the viscoelastic response of aortic valve tissue: a direct-fit approach.

Knowledge of strain-rate sensitivity of soft tissue viscoelastic and nonlinear elastic properties is important for accurate predictions of biomechanical behavior and for quantitative assessment of the effects of disease or surgical/pharmaceutical intervention. Soft tissues are known to exhibit mild rate sensitivity, but experimental artifacts related to testing system control can confound estimation of these effects. "Perfect" ramp-and-hold stress-relaxation tests become difficult at high strain rates because of problems related to undershoot/overshoot error and vibrations. These errors can introduce unwanted bias into parameter estimation methods that rely on idealizations of the applied ramp-and-hold displacement. To address these problems, we describe a new method for estimating quasilinear viscoelastic (QLV) parameters that directly fits the QLV constitutive model to the actual point-wise stress-time history of the test, using an adaptive grid refinement (AGR) global optimization algorithm. This new method significantly improves the accuracy and predictivity of QLV parameter estimates for heart valve tissues, compared to traditional methods that use idealized displacement data. We estimated QLV parameters for aortic valve tissue over a range of physiologic displacement rates, finding that the viscoelastic content parameter (C) increased slightly with increasing strain rate, but the fast (tau1) and slow (tau2) time constants were strain rate insensitive.

A new method of estimating gauge length for porcine aortic valve test specimens.

Porcine aortic valve (PAV) cusps are folded and wrinkled in the in vitro state. In the tensile testing of PAV specimens, estimating gauge length (the length at which a specimen starts to offer measurable resistance to load) is often difficult and subjective. We have therefore developed a new method for estimating the gauge length of such tissues. The method is based on the observation that the specimen's gauge length can be associated with a stationary point on the slope of its load-length curve if loaded from a wrinkled state, or a state of slight compression. We represented the load-length response of test specimens in the low-load, high-compliance region by a cubic function and determined the stationary point on the slope of the function using elementary calculus. The cubic function representation is fine-tuned by reducing or expanding an originally selected "test region" until the correlation coefficient of the cubic fit is maximized. The new method was applied to data obtained from the tensile testing of strips of heart valve tissue and was found to be objective, repeatable and robust.