Elastic anisotropy of bivalve hinge-ligament

Compressive stress-strain properties of an elastic ligament of a bivalve, Pseudocardium sachalinensis were investigated in the swollen state in water. The ligament is a calcified tissue, composed of calcium carbonate and insoluble protein which is rich in methionine S-oxide residue [Kikuchi, Y. and Tamiya, N., J. Biochem. (Tokyo) 89, 1975-1976 (1981)]. X-ray diffraction study showed that calcium carbonate existed only in orthorhombic aragonite form, and that all the crystal c-axes of the unit cell orientate nearly in the growing direction of the ligament. The uniaxial compression modulus for the growing direction was appreciably larger than those for the other two directions, while the anisotropy of the modulus was absent for a decalcified ligament. Thus the mechanical anisotropy of the ligament could be explained by means of the uniaxially oriented structure of aragonite crystals being dispersed in a nearly isotropic protein matrix.     

Collagen fibril D-period may change as a function of strain and location in ligament

The purpose of this study was to determine if the characteristic banding pattern (D-period) of collagen fibrils from rabbit medial collateral ligaments changes as a function of gross ligament strain and, if so, whether the changes are location dependent (insertion versus midsubstance). Femur–medial collateral ligament–tibia complexes were strained to 0, 8, or 12% and immediately chemically fixed in situ. Samples were taken from the medial collateral ligament midsubstance and bony insertions, and prepared for and observed under a transmission electron microscope. D-period length was measured and found to increase (albeit not significantly so, p=0.1) as a function of gross strain for samples obtained from the insertion sites but not for samples obtained from the ligament midsubstance. Results suggested that ligament strains are inhomogeneous at the ultrastructural level.     

Elastic properties of woven bone: effect of mineral content and collagen fibrils orientation

Woven bone is a type of tissue that forms mainly during fracture healing or fetal bone development. Its microstructure can be modeled as a composite with a matrix of mineral (hydroxyapatite) and inclusions of collagen fibrils with a more or less random orientation. In the present study, its elastic properties were estimated as a function of composition (degree of mineralization) and fibril orientation. A self-consistent homogenization scheme considering randomness of inclusions’ orientation was used for this purpose. Lacuno-canalicular porosity in the form of periodically distributed void inclusions was also considered. Assuming collagen fibrils to be uniformly oriented in all directions led to an isotropic tissue with a Young’s modulus \(E = 1.90\) GPa, which is of the same order of magnitude as that of woven bone in fracture calluses. By contrast, assuming fibrils to have a preferential orientation resulted in a Young’s modulus in the preferential direction of 9–16 GPa depending on the mineral content of the tissue. These results are consistent with experimental evidence for woven bone in foetuses, where collagen fibrils are aligned to a certain extent.     

The elastic anisotropy of bone

In modeling the anisotropic properties of hydroxyapatite (HAp), Katz found that two kinds of phenomenological relationships held among the elastic stiffness coefficients. Firstly, there are three linear combinations--(c11 + c22 + c33), (c44 + c55 + c66), (c12 + c13 + c23)--which arise naturally when computing the isotropic averages of anisotropic crystal systems over all possible spatial orientations. Secondly, the degree of elastic anisotropy in such crystal systems is characterized by two specific factors: (a) the ratio of the linear compressibility along the unique axis to that perpendicular to it, (c11 + c12 - 2c23)(c33 - c13); and (b) the ratio of the two shear moduli, c44/c66. There have been a number of experiments in recent years which have used either mechanical methods or ultrasonic techniques to measure the anisotropic elastic properties of bovine and human cortical bone. Analyses of data from these experiments show that the above relationships also play a significant role in characterizing the elastic anisotropy in bone.     

The correlation of single-particle diffraction patterns as a continuous function of particle orientation

A statistical model for X-ray scattering of a non-periodic sample to high angles is introduced. It is used to calculate analytically the correlation of distinct diffraction measurements of a particle as a continuous function of particle orientation. Diffraction measurements with shot-noise are also considered. This theory provides a general framework for a deeper understanding of single particle imaging techniques used at X-ray free-electron lasers. Many of these techniques use correlations as a measure of diffraction-pattern similarity in order to determine properties of the sample, such as particle orientation.     

The pattern of population growth as a function of redundancy and repair

A basic model of hierarchical structure, expressed by simple, linear differential equations, shows that the pattern of population growth is essentially determined by conditions of redundancy in the sub-structure of individuals. There does not exist any possible combination between growth rate and accident rate that could balance population numbers and/or the level of redundancy within the population; all possible combinations either lead to extinction or to positive population growth with a decline of the fraction of individuals with redundant substructure. Declining populations, however, can be held fluctuating between certain limits by periodic phases of sub-unit repair. These results are particularly pertinent to the population dynamics of diploid (polyploid) organisms.     

Complex pattern formation by a self-destabilization of established patterns: chemotactic orientation and phyllotaxis as examples

Stable patterns can be generated by molecular interactions involving local self-enhancement and long-range inhibition. In contrast, highly dynamic patterns result if the maxima, generated in this way, become destabilized by a second antagonistic reaction. The latter must act local and must be long-lasting. Maxima either disappear and reappear at displaced positions or they move over the field as travelling waves. The wave can have unusual properties in that they can penetrate each other without annihilation. The resulting pattern corresponds to those observed in diverse biological systems. In the chemotactic orientation of cells, the temporary signals allow the localized extensions of protrusions under control of minute external asymmetries imposed by the chemoattractant. In phyllotaxis, these signals lead to successive leaf initiation, whereby the longer-lasting extinguishing reaction can cause a displacement of the subsequent leaf initiation site by the typical 137.5 degrees, the golden angle. On seashells, this patterns leads either to oblique lines that can cross each other or to oblique rows of dots. For some of the models animated simulations are available at http://www.eb.tuebingen.mpg.de/abt.4/meinhardt/theory.html.     

Alterations in rat horizontal vestibulo-ocular reflex phase as a function of orientation in gravity

The effect of changes in static and dynamic gravity signals on the phase accuracy of the horizontal vestibulo-ocular reflex (HVOR) was studied in rats using chronically implanted scleral search coils to monitor eye movements. Rats were sinusoidally rotated using a range of different frequencies (0.035-2 Hz) in a plane which always activated the horizontal semicircular canals but in one of three different orientations with regard to gravity which differentially activated the otolith organs: 1) upright-normal static gravity signal, no dynamic otolith activation; 2) inverted-inverted static gravity signal, no dynamic otolith activation; 3) on-side-dynamic activation of the otolith organs. In the upright orientation, the HVOR shows a phase advance at 0.2 Hz and below but not at 0.5 Hz and above. Phase accuracy of the HVOR was further degraded in the inverted orientation with rats showing large phase leads at 0.2 Hz and below. In contrast, accuracy of the HVOR was significantly improved at 0.2 Hz and below in the on-side orientation with phase accurate eye movements down to the lowest frequency tested. The results further support the idea that otolith organs play an important role in VOR generation by supplementing the semicircular canals' response to angular head movements.     

Relative orientation of collagen molecules within a fibril: a homology model for homo sapiens type I collagen

Type I collagen is an essential extracellular protein that plays an important structural role in tissues that require high tensile strength. However, owing to the molecule’s size, to date no experimental structural data are available for the Homo sapiens species. Therefore, there is a real need to develop a reliable homology model and a method to study the packing of the collagen molecules within the fibril. Through the use of the homology model and implementation of a novel simulation technique, we have ascertained the orientations of the collagen molecules within a fibril, which is currently below the resolution limit of experimental techniques. The longitudinal orientation of collagen molecules within a fibril has a significant effect on the mechanical and biological properties of the fibril, owing to the different amino acid side chains available at the interface between the molecules.     

Changes in perceived contrast of suprathreshold gratings as a function of orientation and spatial frequency

Orientation anisotropy for suprathreshold gratings of different spatial frequencies was measured using a contrast matching procedure. Observers matched the contrast of sine-wave gratings of various orientations to a vertical reference grating set at different reference contrasts. At threshold, the size of the anisotropy increased with spatial frequency, confirming previous results. When the reference grating contrast was set above threshold, the anisotropy declined, and eventually disappeared for gratings of medium spatial frequencies. At higher spatial frequencies, although the relative anisotropy became smaller, it did not disappear within the range of contrasts used in this study. For medium, but not for high spatial frequencies, the data are consistent with Kulikowski's (1976) model of effective contrast constancy.     

Elastic modulus of trabecular bone material

An ultrasonic technique was used to measure both the elastic modulus (Young's modulus) of trabecular bone material and the elastic modulus of the cancellous structure. The average trabecular modulus, measured on specimens obtained from three human and one bovine distal femora, was 13.0 GPa (S.D. 1.47) and 10.9 GPa (S.D. 1.57), respectively. On human specimens the structural elastic modulus was found to be related to the structural (apparent) density raised to the 1.88 power. The elastic modulus from the bovine specimens showed a more linear relationship with the density of the cancellous structure (density raised to the 1.57 power).     

Expanded polytetrafluoroethylene as a microvascular graft: a study of four fibril lengths

The utility for a prosthetic microvascular graft is well demonstrated, but previous studies have been inconclusive. Expanded polytetrafluoroethylene (Gore-Tex) has been most widely tested as a prosthetic graft. Polytetrafluoroethylene is composed of transverse nodules connected by long fibrils. This study evaluates the effect of fibril length on observed patency in a 1-mm inner-diameter system. Fibril lengths tested were 30, 60, 90, and 120 micron. One-hundred and sixty-three grafts were implanted in the abdominal aorta of Sprague-Dawley rats by a single surgeon using a standardized technique. No anticoagulants were used. Grafts were harvested at predetermined times and evaluated macroscopically, by scanning electron microscope, and by standard histology. The highest patency observed was 97.7 percent in the 90-micron fibril-length grafts. Fibril morphology also affected patency. Increased patency was associated with an amorphous fibril pattern. The graft functioned as a matrix for the formation of a pseudoartery, complete with monocell-thick intima and smooth-muscle media. A foreign-body reaction was observed in the 60-micron fibril-length graft only. Expanded polytetrafluoroethylene does show promise as a microvascular graft. Both fibril length and morphology affect observed patency.     

Spatial organization of the lacunar-canalicular system in the structures of bone lamellae

By means of light microscopical techniques and scanning electron microscopy spatial organization of the lacunar-canalicular system (LCS) has been studied in structures of a mature lamellar bone. A method for making corrosive casts of osseous lacunae and canaliculi is suggested, owing to which their spatial organization can be analysed. Certain data on interconnections of the osseous lacunae with each other and with vascular canals and natural surfaces of the bone are presented. The role of LCS as a component of the microcirculatory bed of the lamellar bone is discussed.     

Collinear effects on 3-Gabor alignment as a function of spacing, orientation and detectability.

Our ability to align three Gabor patches depends upon their internal carrier orientation; we are better at aligning vertical or horizontal patches than oblique patches (Keeble and Hess, 1998). However, the tuning of alignment to patch orientation has not studied in detail. We measured the alignment of a vertical target with reference patches varying in orientation and found it tuned to vertical (collinear) patches at centre-to-centre separation of three carrier periods, with a steep increase for oblique references and slight downturn for horizontal (orthogonal) references. Next, we increased separation between the patches, testing collinear, side-by-side, orthogonal and oblique configurations. Surprisingly, we found that the tuning for collinear patches was preserved. All ten observers tested had lower alignment thresholds for collinear patches. This effect extended to an inter-patch separation of 10 carrier periods (20 envelope standard deviations). Additionally, we measured contrast detection thresholds for the reference patches using the same stimuli. The collinear facilitation of alignment was even greater than the collinear facilitation of detection.