Biaxial mechanical testing of human sclera

The biomechanical environment of the optic nerve head (ONH), of interest in glaucoma, is strongly affected by the biomechanical properties of sclera. However, there is a paucity of information about the variation of scleral mechanical properties within eyes and between individuals. We thus used biaxial testing to measure scleral stiffness in human eyes. Ten eyes from 5 human donors (age 55.4±3.5 years; mean±SD) were obtained within 24 h of death. Square scleral samples (6 mm on a side) were cut from each ocular quadrant 3–9 mm from the ONH centre and were mechanically tested using a biaxial extensional tissue tester (BioTester 5000, CellScale Biomaterials Testing, Waterloo). Stress–strain data in the latitudinal (toward the poles) and longitudinal (circumferential) directions, here referred to as directions 1 and 2, were fit to the four-parameter Fung constitutive equation W=c(e^Q?1), where $Q=c_1{E}_{11}^2+c_2{E}_{22}^2+2c_3{E}_{11}{E}_{22}$ and W, c’s and E_ij are the strain energy function, material parameters and Green strains, respectively. Fitted material parameters were compared between samples. The parameter c₃ ranged from 10^?7 to 10^?8, but did not contribute significantly to the accuracy of the fitting and was thus fixed at 10^?7. The products c?c₁ and c?c₂, measures of stiffness in the 1 and 2 directions, were 2.9±2.0 and 2.8±1.9 MPa, respectively, and were not significantly different (two-sided t-test; p=0.795). The level of anisotropy (ratio of stiffness in orthogonal directions) was 1.065±0.33. No statistically significant correlations between sample thickness and stiffness were found (correlation coefficients=?0.026 and ?0.058 in directions 1 and 2, respectively). Human sclera showed heterogeneous, near-isotropic, nonlinear mechanical properties over the scale of our samples.     

Modelling the mechanical response of elastin for arterial tissue

We compare two constitutive models proposed to model the elastinous constituents of an artery. Holzapfel and Weizsäcker [1998. Biomechanical behavior of the arterial wall and its numerical characterization. Comput. Biol. Med. 28, 377–392] attribute a neo-Hookean response, i.e. $\Psi =c(I_1-3))$, to the elastin whilst Zulliger et al. [2004a. A strain energy function for arteries accounting for wall composition and structure. J. Biomech. 37, 989–1000] propose $\Psi =c(I_1-3{)}^{3/2}$. We analyse these constitutive models for two specific cases: (i) uniaxial extension of an elastinous sheet; (ii) inflation of a cylindrical elastinous membrane. For case (i) we illustrate the functional relationships between: (a) the Cauchy stress (CS) and the Green–Lagrange (GL) strain; (b) the tangent modulus (gradient of the CS–GL strain curve) and linearised strain. The predicted mechanical responses are compared with recent uniaxial extension tests on elastin [Gundiah, N., Ratcliffe, M.B., Pruitt, L.A., 2007. Determination of strain energy function for arterial elastin: experiments using histology and mechanical tests. J. Biomech. 40, 586–594; Lillie, M.A., Gosline, J.M., 2007a. Limits to the durability of arterial elastic tissue. Biomaterials 28, 2021–2031; 2007b. Mechanical properties of elastin along the thoracic aorta in the pig. J. Biomech. 40, 2214–2221]. The neo-Hookean model accurately predicts the mechanical response of a single elastin fibre. However, it is unable to accurately capture the mechanical response of arterial elastin, e.g. the initial toe region of arterial elastin (if it exists) or the gradual increase in modulus of arterial elastin that occurs as it is stretched. The alternative constitutive model ($n=\frac{3}{2}$) yields a nonlinear mechanical response that departs from recent uniaxial test data mentioned above, for the same stretch range. For case (ii) we illustrate the pressure–circumferential stretch relationships and the gradients of the pressure–circumferential stretch curves: significant qualitative differences are observed. For the neo-Hookean model, the gradient decreases rapidly to zero, however, for $n=\frac{3}{2}$, the gradient decreases more gradually to a constant value. We conclude that whilst the neo-Hookean model has limitations, it appears to capture more accurately the mechanical response of elastin.     

Shrinking factors of hyperbranched polysaccharide from fungus

The branched structure properties of hyperbranched polysaccharides (TM3a and TM3b), extracted from sclerotia of Pleurotus tuber-regium, were studied by using laser light scattering and viscometry. The configurational shrinking factor (g) and viscometric shrinking factor (g′) of TM3a and TM3b were discussed, where curdlan and pullulan were taken as the linear references for derivation of g and g′. The dependences of g factor, g′ factor, and Flory factor (Φ_branched) on weight average molecular weight (M_w) were established to be g = 1.07 × 10²$M_{\text{w}}^{-0.48\pm 0.09}$, g′ = 3.63 × 10¹$M_{\text{w}}^{-0.43\pm 0.01}$, and Φ_branched = 7.08 × 10²⁰$M_{\text{w}}^{0.39\pm 0.1}$ for TM3a in 0.25 M LiCl/DMSO at 25 °C, when curdlan acted as the linear reference. A power law relationship g′ = 2.71 × 10^?1g^?0.61±0.1 for TM3a was found, and the exponent was approximately same to 0.60 established by Kurata et al. for polystyrene star molecules. The dependence of g factor on M_w for TM3b was found to be g = 1.99 × 10²$M_{\text{w}}^{-0.53\pm 0.02}$, when pullulan was used as the linear reference. On the basis of Zimm–Stockmayer equation for tetrafunctional units, molecular weight of branching unit (M₀) deduced from nonlinear curve fitting of g versus M_w was 8739 ± 564 g/mol and 3961 ± 1245 g/mol for TM3a and TM3b, respectively. The effect of different linear reference curves and polydispersity was discussed. This work gave valuable information on branched structure characterization and insights into the biosynthetic pathways of the hyperbranched polysaccharide from fungus.