Viscoelastic spectrum analysis and the identification of a fung viscoelastic material

Despite its many limitations, the Fung “quasi-linear viscoelastic” constitutive model continues to serve as a workhorse of the biomechanics community. A central challenge in applying the model is that it requires a specific form for the relaxation spectrum that is difficult to relate to easily obtained experimental spectra such as a generalized Maxwell relaxation spectrum. Here, we present a simple and general technique for obtaining a from relaxation data a viscoelastic spectrum appropriate to the Fung model. We apply the model to identify several biomaterials that are modeled reasonably by a Fung model, and many more that are not

Confidence Intervals for Concentration and Brightness from Fluorescence Fluctuation Measurements

AbstractThe theory of photon count histogram (PCH) analysis describes the distribution of fluorescence fluctuation amplitudes due to populations of fluorophores diffusing through a focused laser beam and provides a rigorous framework through which the brightnesses and concentrations of the fluorophores can be determined. In practice, however, the brightnesses and concentrations of only a few components can be identified. Brightnesses and concentrations are determined by a nonlinear least-squares fit of a theoretical model to the experimental PCH derived from a record of fluorescence intensity fluctuations. The χ2 hypersurface in the neighborhood of the optimum parameter set can have varying degrees of curvature, due to the intrinsic curvature of the model, the specific parameter values of the system under study, and the relative noise in the data. Because of this varying curvature, parameters estimated from the least-squares analysis have varying degrees of uncertainty associated with them. There are several methods for assigning confidence intervals to the parameters, but these methods have different efficacies for PCH data. Here, we evaluate several approaches to confidence interval estimation for PCH data, including asymptotic standard error, likelihood joint-confidence region, likelihood confidence intervals, skew-corrected and accelerated bootstrap (BCa), and Monte Carlo residual resampling methods. We study these with a model two-dimensional membrane system for simplicity, but the principles are applicable as well to fluorophores diffusing in three-dimensional solution. Using simulated fluorescence fluctuation data, we find the BCa method to be particularly well-suited for estimating confidence intervals in PCH analysis, and several other methods to be less so. Using the BCa method and additional simulated fluctuation data, we find that confidence intervals can be reduced dramatically for a specific non-Gaussian beam profile

Physically-Induced Cytoskeleton Remodeling of Cells in Three-Dimensional Culture

<div><p>Characterizing how cells in three-dimensional (3D) environments or natural tissues respond to biophysical stimuli is a longstanding challenge in biology and tissue engineering. We demonstrate a strategy to monitor morphological and mechanical responses of contractile fibroblasts in a 3D environment. Cells responded to stretch through specific, cell-wide mechanisms involving staged retraction and reinforcement. Retraction responses occurred for all orientations of stress fibers and cellular protrusions relative to the stretch direction, while reinforcement responses, including extension of cellular processes and stress fiber formation, occurred predominantly in the stretch direction. A previously unreported role of F-actin clumps was observed, with clumps possibly acting as F-actin reservoirs for retraction and reinforcement responses during stretch. Responses were consistent with a model of cellular sensitivity to local physical cues. These findings suggest mechanisms for global actin cytoskeleton remodeling in non-muscle cells and provide insight into cellular responses important in pathologies such as fibrosis and hypertension.</p> </div

Fibrocartilage Tissue Engineering: The Role of the Stress Environment on Cell Morphology and Matrix Expression

Although much is known about the effects of uniaxial mechanical loading on fibrocartilage development, the stress fields to which fibrocartilaginous regions are subjected to during development are mutiaxial. That fibrocartilage develops at tendon-to-bone attachments and in compressive regions of tendons is well established. However, the three-dimensional (3D) nature of the stresses needed for the development of fibrocartilage is not known. Here, we developed and applied an in vitro system to determine whether fibrocartilage can develop under a state of periodic hydrostatic tension in which only a single principal component of stress is compressive. This question is vital to efforts to mechanically guide morphogenesis and matrix expression in engineered tissue replacements. Mesenchymal stromal cells in a 3D culture were exposed to compressive and tensile stresses as a result of an external tensile hydrostatic stress field. The stress field was characterized through mechanical modeling. Tensile cyclic stresses promoted spindle-shaped cells, upregulation of scleraxis and type one collagen, and cell alignment with the direction of tension. Cells experiencing a single compressive stress component exhibited rounded cell morphology and random cell orientation. No difference in mRNA expression of the genes Sox9 and aggrecan was observed when comparing tensile and compressive regions unless the medium was supplemented with the chondrogenic factor transforming growth factor beta3. In that case, Sox9 was upregulated under static loading conditions and aggrecan was upregulated under cyclic loading conditions. In conclusion, the fibrous component of fibrocartilage could be generated using only mechanical cues, but generation of the cartilaginous component of fibrocartilage required biologic factors in addition to mechanical cues. These studies support the hypothesis that the 3D stress environment influences cell activity and gene expression in fibrocartilage development