In situ tensile testing of human aortas by time-resolved small-angle X-ray scattering.

The collagen diffraction patterns of human aortas under uniaxial tensile test conditions have been investigated by synchrotron small-angle X-ray scattering. Using a recently designed tensile testing device the orientation and d-spacing of the collagen fibers in the adventitial layer have been measured in situ with the macroscopic force and sample stretching under physiological conditions. The results show a direct relation between the orientation and extension of the collagen fibers on the nanoscopic level and the macroscopic stress and strain. This is attributed first to a straightening, second to a reorientation of the collagen fibers, and third to an uptake of the increasing loads by the collagen fibers.

Single lamellar mechanics of the human lumbar anulus fibrosus.

The mechanical behavior of the entire anulus fibrosus is determined essentially by the tensile properties of its lamellae, their fiber orientations, and the regional variation of these quantities. Corresponding data are rare in the literature. The paper deals with an in vitro study of single lamellar anulus lamellae and aims to determine (i) their tensile response and regional variation, and (ii) the orientation of lamellar collagen fibers and their regional variation. Fresh human body-disc-body units (L1-L2, n=11) from cadavers were cut midsagittally producing two hemidisc units. One hemidisc was used for the preparation of single lamellar anulus specimens for tensile testing, while the other one was used for the investigation of the lamellar fiber orientation. Single lamellar anulus specimens with adjacent bone fragments were isolated from four anatomical regions: superficial and deep lamellae (3.9+/-0.21 mm, mean +/- SD, apart from the outer boundary surface of the anulus fibrosus) at ventro-lateral and dorsal positions. The specimens underwent cyclic uniaxial tensile tests at three different strain rates in 0.15 mol/l NaCl solution at 37 degrees C, whereby the lamellar fiber direction was aligned with the load axis. For the characterization of the tensile behavior three moduli were calculated: E(low) (0-0.1 MPa), E(medium) (0.1-0.5 MPa) and E(high) (0.5-1 MPa). Additionally, specimens were tested with the load axis transverse to the fiber direction. From the second hemidisc fiber angles with respect to the horizontal plane were determined photogrammetrically from images taken at six circumferential positions from ventral to dorsal and at three depth levels. Tensile moduli along the fiber direction were in the range of 28-78 MPa (regional mean values). Superficial lamellae have larger E(medium) (p=0.017) and E(high) (p=0.012) than internal lamellae, and the mean value of superficial lamellae is about three times higher than that of deep lamellae. Tensile moduli of ventro-lateral lamellae do not differ significantly from the tensile moduli of dorsal lamellae, and E(low) is generally indifferent with respect to the anatomical region. Tensile moduli transverse to the fiber direction were about two orders of magnitude smaller (0.22+/-0.2 MPa, mean +/- SD, n=5). Tensile properties are not correlated significantly with donor age. Only small viscoelastic effects were observed. The regional variation of lamellar fiber angle phi is described appropriately by a regression line |phi|=23.2 + 0.130 x alpha (r(2)=0.55, p<0.001), where alpha is the polar angle associated with the circumferential position. The single anulus lamella may be seen as the elementary structural unit of the anulus fibrosus, and exhibits marked anisotropy and distinct regional variation of tensile properties and fiber angles. These features must be considered for appropriate physical and numerical modeling of the anulus fibrosus.

Determination of constitutive equations for human arteries from clinical data.

Stress-strain analyses of vessel walls require appropriate constitutive equations. Determination of constitutive equations is based on experimental data of (i) diameter and length of a vessel segment subject to internal pressure and external axial force, and (ii) the load-free reference geometry. Typical clinical data, however, provide only pressure-diameter relations in the diastolic-systolic pressure range. In order to overcome this problem, an approach is proposed allowing the determination of constitutive equations from clinical data by means of reasonable assumptions regarding in situ configurations and stress states of arterial walls. The approach is based on a two-dimensional Fung-type stored-energy function capturing the characteristic nonlinear and anisotropic responses of arteries. Examples concerning human aortas from a normotensive and a hypertensive subject illustrate the potential of the approach.