Statistical characterization of piezoelectric coefficient d23 in cow bone.

In a newly developed, highly sensitive dilatometer we applied pulsatile electric fields to five dry bone samples cut from mid-tibial sections within a 90 degrees angle from the rear to front axis. Samples of five cows were studied. We measured the piezoelectric coefficient d23 establishing its mean and confidence interval for the first time. An analysis of variance detected a significant difference of the coefficient between animals (P < 0.01) but not between samples (P = 0.5). Between animals the coefficient ranged from 9.6 x 10(-14) to 27.1 x 10(-14) C/N. It can no longer be assumed that piezoelectricity is an inherent property of bone, constant between animals.

X-ray diffraction on cyclically loaded osteons.

The results of a study on the fine structural distortion due to the two previously observed types of degradation in cyclically loaded single osteons (i.e., stiffness degradation and pinching effect) are presented. Fully calcified longitudinal and alternate osteons were isolated from 350-microns-thick longitudinal sections of human femoral cortical bone. The samples were prepared from 500-microns-long central cylindrical portions of an osteon, whose two ends were penetrating into rectangular lugs for fixation to an electromechanical device that cyclically loaded the samples. This device was connected to a microwave micrometer and a recorder. The structural distortions induced by cyclic loading were investigated by high- and low-angle X-ray diffraction on conventional and synchrotron radiation sources. Cyclic loading results in a reduction in the degree of orientation of apatite crystallites, especially in longitudinal osteons, in which the most abundant longitudinal lamellae are not protected against buckling by transverse lamellae as they are in alternate osteons. In contrast, the degree of orientation of collagen fibrils does not seem to be affected by cycling loading in the two osteon types, possibly because the disorientation of collagen fibrils is, within limits, a reversible process. Finally, the contrast between the disorientation of inorganic crystallites and the apparently unaltered distribution of collagen fibrils suggests that the degradation of cyclically loaded osteons may be due to a separation of the crystallites from the fibrils.

Pinching in longitudinal and alternate osteons during cyclic loading.

Pinching is a degrading phenomenon which occurs during cyclic loading of certain materials. A change in the slope of the deflection curve reveals pinching lesions, either flexural cracks or bond degradation, cause pinching. This paper investigates pinching for 20 longitudinal and 18 alternate fully calcified osteonic samples of cylindrical shape and 500 micron length. Each sample was axially loaded beyond the proportional limit using an electromechanical device acting as a transducer of the variations in length of the sample into changes in the resonance frequency of a microwave micrometer. A cubic polynomial served as a mathematical model to investigate the stress-strain diagrams at the first and last cycles through the study of strain limits, stiffness and pinching behaviours, and energy absorption. The hysteretic behaviour of the two types of osteons differs and is far from ideal. The presence of pinching may derive from the existence of longitudinal fibrils, in particular the yielding of the incompletely calcified ones. In longitudinal osteons consisting mainly of longitudinal collagen fibrils, the deformation under compression is not protected by lamellae consisting of transverse fibrils, therefore the lesions inducing pinching are magnified. In contrast, in alternate osteons, where the fibrils having a longitudinal orientation are reduced and protected by lamellae containing transversely oriented fibrils, the lesions-inducing pinching are lessened.

Converse piezoelectric effect detected in fresh cow femur bone.

A piezoelectric effect has been reported to exist in biological tissues, in particular in dry bone. Since the precision and resolution now obtainable are much greater, we decided to verify the presence of the converse effect (dimensional change under the application of an electric field) in fresh bone samples, by using a very high sensitivity instrument. We took, in varying orientations, five fresh femur cylindrical bone specimens from a cow leg and placed them as a single piece, or as a stack of 10 thin interlayered slices from one specimen to improve sensitivity, in a special microwave double cavity differential dilatometer. The thickness of the specimen was approximately 10mm. The applied field strength for the nonstacked specimen was near 10 kV m-1. Thickness variation was measured along and across the electric field lines. We applied the electric field as a switched polarity square wave. This allows the thermal dilution of specimen warming and possible electrostriction effects, which are insensitive to the direction of the applied field, to be separated from an electromechanical effect which is sensitive to direction. Using coherent signal averaging over approximately 600 cycles to combat instrumental noise we observed nonthermal, nonelectrostrictional thickness variations in all samples. The amplitudes we observed were near 3 pm for the 1 cm nonstacked specimen, and the bone's responses to electric fields ranged from 26 to 38 fm V-1. With response magnitudes approximating those predicted theoretically for the converse piezoelectric effect in bone we conclude that the piezoelectric theory could not be falsified with our experiments.

An invariance in the isoheptanes of petroleum.

Four isoheptanes in petroleum display a remarkable invariance in a ratio of sums of concentrations. The isoheptanes are not at thermodynamic equilibrium, nor are they fixed to some constant composition. The four isomers display coherent change in relative amounts but maintain invariance in the ratio of sums. Within sets of genetically related petroleum samples, invariance reaches levels that approach the limits of our analytical precision. The invariance is inconsistent with a chemical origin that involves the thermal fragmentation of natural products or their derivatives. It suggests a reaction process at steady state, in which relative rates of product formation are constant. A mechanism is proposed in which the four isoheptanes are formed pairwise and sequentially through two intermediates in a catalytic process that operates at steady state.

Mechanical hysteresis loops from single osteons: technical devices and preliminary results.

The purpose of this paper is to describe an original apparatus for recording hysteresis loops from single osteons and a special microgrinding lathe for preparing osteonic samples for testing. The results obtained by testing isolated osteons, and composite bone samples ground to the same size as an osteon sample justify one to draw the following main conclusions: at an equal degree of calcification, longitudinal osteons show larger hysteresis loops under compression and alternate osteons show larger hysteresis loops under tension; there seems to be little chance of acquiring detailed information on the mechanical effects of osteon calcification recording hysteresis loops; collagen orientation in lamellae is the main factor determining the kind of hysteresis loops displayed by a composite bone sample.