Richard A. Harper

Fluid flow in bone in vitro

Recent dielectric measurements suggest that the electromechanical effect in wet (fluid saturated) bone is not due to a piezoelectric effect. This would imply that the electromechanical effect observed in wet bone is due to a streaming potential and is therefore dependent on fluid flow in stressed bone. A model for fluid flow in bone in vitro is presented. This model predicts a rapid decay (of the order of a millisecond or less) for the fluid flow in Haversian systems. The implications of this result for the interpretation of the electromechanical effect in wet bone are discussed.

Dielectric Properties of Fluid-Saturated Bone

The dielectric relaxation of bovine femoral compact bone specimens in vitro, saturated with 0.9 percent NaCI solution is determined by applying a constant current pulse and measuring the change in voltage with time. For specimens in which the current is in the plane perpendicular to the length of the whole bone and along the radial direction (radial specimens), the relaxation is confined to the time domain, t50 ¿s; for longitudinal specimens, the relaxation, if any, would be for t1 ¿s. The long-time resistivity of the latter is ¿45 to 48 ¿m; for the radial specimens, it is ¿3 to 4 times greater. The resistivity of the fluid is 0.72 ¿m. The results indicate that the dielectric behavior of fluid-saturated compact bone in vitro, and, hence, possibly also of in vivo bone, is determined mostly by the fluid-fllled pores. This has implications that contradict some of the commonly accepted views on the electromechanical effect in bone.

Comparison of the electromechanical effects in wet and dry bone

Abstract It has been proposed that the electromechanical properties of bone influence bone remodeling processes. In dry bone the electromechanical effect is known to be due to the piezoelectric behavior of collagen. However, there has been some question whether the stress induced voltages observed in wet bone are due to a piezoelectric effect. Evidence is presented which indicates that the magnitude of the signals observed in bent wet bone are several orders of magnitude larger than one would expect from a piezoelectric effect. This result, along with other experimental observations, implies that the electromechanical effect observed in wet bone is not a piezoelectric effect. Therefore it is suggested that two different mechanisms are responsible for the electromechanical effects in wet and dry bone.

Dielectric relaxation in cortical bone

Measurements of the capacitance and conductance of bovine cortical bone have been performed at body temperature as functions of frequency, time, and humidity. A direct‐coupled low‐frequency bridge containing active circuits was used to study the response below 50 Hz. Results are expressed in terms of permittivity, dielectric loss tangent, and both frequency‐ and time‐dependent electric moduli. The permittivity was found to be extremely sensitive to frequency and humidity; maximum permittivity observed exceeded 105, while the maximum loss tangent was greater than unity. Anisotropy was observed; both the permittivity and the loss tangent were greater if the electric field was parallel to the bone axis.

STRAIN AND FREQUENCY DEPENDENCE OF SHEAR STORAGE MODULUS FOR HUMAN SINGLE OSTEONS AND CORTICAL BONE MICROSAMPLES-SIZE AND HYDRATION EFFECTS*?

Abstract Using a specially designed and laboratory built microtorsional device, the shear storage modulus of single osteons and microsamples containing up to a dozen osteons was investigated for both strain and frequency dependence. The data indicate that an increase in number of osteons in the microsample reduces the storage modulus, and results in smaller strains at which deviation from linearity and plasticity effects are first noticed. Size effects were also noticed, which suggest that an increase in number of osteons, increases the effectiveness of water (hydration of dry samples) in reducing the storage modulus and in increasing the internal energy loss in the sample. Some of the effects were noticed to approach saturation in samples with more than a half dozen osteons, while others appeared to persist (at least up to a dozen osteons). Also noticed, were reductions in shear storage modulus of 10–35% over an approximate frequency reduction of 10 3 –1 Hz for microsamples containing one or more osteons.

Isolation of single osteons and osteon lamellae

Single human osteons were isolated by propagating fractures along their natural boundaries. Furthermore, decalcified osteons were mechanically manipulated to expose their interlamellar interfaces, making possible the study of collagen fibers by means of scanning electron microscopy (SEM). Isolation of single osteons of a wide range of lengths, as described in this paper, makes possible for the first time the study of their mechanical properties in all possible modes. SEM studies of exposed lamellar interfaces reveal that collagen fiber orientations are more complex than previously suggested and suggest further studies in an effort to solve past controversies on collagen fiber orientations in human bone.

New Method of Bone Preparation for Collagen Fiber Orientation Studies by Means of Scanning Electron Microscopy

A sample preparation technique was developed for observing the orientation of collagen fibers in the lamellas of human osteonic bone by means of scanning electron microscopy. Scanning electron micrographs of these fiber orientations are given in the text.

Elastic Constants of the Composite System Hydroxyapatite-Dicalcium Phosphate Dihydrate

In an acidic medium with a pH of less than 4.3, both synthetic OHAp and dental enamel form dicalcium phosphates, mostly the dihydrate form. When the pH level of a system falls, enamel dissolves and is replaced by dicalcium phosphate dihydrate (DCPD). On the surface of a tooth with incipient caries, the plaque and its bacteria drive the local pH to ...4.0; at this point, conditions suit the possibility that an OHAp-DCPD system may exist. In addition, it has been speculated that normal enamel also contains dicalcium phosphates (DAVIDSON, doctoral dissertation, University of Groningen, 1973) . Ultrasonic techniques at high pressures were used to measure the elastic properties of such a composite system. High pressures were used to suppress porosity, if any, to obtain the effective elastic moduli at ideal density. Specimens were made with commercially available OHAp and DCPD. After sieving through a 600-mesh sieve, the powders were mixed in the correct proportions to yield mixtures containing 20, 40, 60, and 80% by volume of DCPD in OHAp and then compacted at a pressure of 30,000 psi. The velocities of transmission of longitudinal and shear ultrasonic waves were measured using an ultrasonic interferometer and a solid-media, high-pressure apparatus (AHRENS and KATZ, J Geophys Res 67: 2935-2944, 1962) . Computer analysis yielded the bulk, shear, and Youngs moduli; atmospheric values were obtained by back extrapolation from the high pressure data. Experience with this system has shown that the precision of a single measurement is + 5%. The illustration shows a plot of the Youngs modulus as a function of composition. The upper line shows the Voigt bound and the lower

Low‐frequency dielectric bridge

This circuit may be used to measure the complex dielectric function (admittance) between 0.01 Hz and 1 kHz in the frequency domain in either the guarded three‐terminal or four‐terminal probe mode, as well as step‐function response (voltage creep or current relaxation) in the time domain. Signals from the unknown impedance and the standard impedance are processed using dc coupled operational amplifiers, the gains of which are varied to balance the bridge.

Strain dependence of dynamic Young's modulus for human single osteons

Abstract The strain dependence of Youngs modulus for human single osteons was investigated at frequencies near 103 Hz by means of a small acoustic speaker. On average, deviations from linear dependence occurred at 2% strain and plasticity followed at 4% strain. The modulus itself averaged at 12–14 GN/m2 and is comparable to values obtained both by Black (1972) and by Smith and Keiper (1965) for samples containing many osteons at frequencies of 350 and 500–3500 Hz respectively.