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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 (1-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 [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. [DOI: 10.1115/1.1933900] Keywords: Fractional Calculus, Viscoelasticity, Nonlinear Elasticity, Aortic Valve, Fractals, Soft Tissue

Understanding the complex relationships between microstructural organization and macromechanical function is fundamental to our knowledge of the differences between normal, diseased/injured, and healing connective tissues. The long-term success of functional tissue-engineered constructs or scaffolds may largely depend on our understanding of the structural organization of the original tissue. Although innovative techniques have been used to characterize and measure the microstructural properties of collagen fibers, a large gap remains in our knowledge of the behavior of intermediate scale (i.e., 'mesostructural') groups of fiber bundles in larger tissue samples. The objective of this study was to develop a system capable of directly measuring deformations of these smaller mesostructures during application of controlled loads. A novel mesostructural testing system (MSTS) has been developed to apply controlled multiaxial loads to medium (meso-) scale tissue specimens, while directly measuring local nonuniform deformations using synchronized digital video capture and 'markerless' image correlation. A novel component of the MSTS is the use of elliptically polarized light to enhance collagen fiber contrast, providing the necessary texture for accurate markerless feature tracking of local fiber deformations. In this report we describe the components of the system, its calibration and validation, and the results from two different tissues: the porcine aortic valve cusp and the bovine pericardium. Validation tests on prepared samples showed maximum error of direct strain measurement to be 0.3%. Aortic valve specimens were found to have larger inhomogeneous strains during tensile testing than bovine pericardium. Clamping effects were more pronounced for the valve specimens. A new system for direct internal strain measurement in connective tissues during application of controlled loads has been developed and validated. The results from the two different tissues show that significant inhomogeneous deformations can occur even in simple tensile testing experiments. [DOI: 10.1115/1.3116155] Keywords: biomechanics, tissue engineering, collagen, connective tissues, structural properties, material properties, digital image correlation, fibers