Dynamic permeability of the lacunar-canalicular system in human cortical bone.

A new method for the experimental determination of the permeability of a small sample of a fluid-saturated hierarchically structured porous material is described and applied to the determination of the lacunar-canalicular permeability [Formula: see text] in bone. The interest in the permeability of the lacunar-canalicular pore system (LCS) is due to the fact that the LCS is considered to be the site of bone mechanotransduction due to the loading-driven fluid flow over cellular structures. The permeability of this space has been estimated to be anywhere from [Formula: see text] to [Formula: see text]. However, the vascular pore system and LCS are intertwined, rendering the permeability of the much smaller-dimensioned LCS challenging to measure. In this study, we report a combined experimental and analytical approach that allowed the accurate determination of the [Formula: see text] to be on the order of [Formula: see text] for human osteonal bone. It was found that the [Formula: see text] has a linear dependence on loading frequency, decreasing at a rate of [Formula: see text]/Hz from 1 to 100 Hz, and using the proposed model, the porosity alone was able to explain 86 % of the [Formula: see text] variability.

Quantifying the strain history of bone: spatial uniformity and self-similarity of low-magnitude strains.

We hypothesize that when a broad spectrum of bone strain is considered, strain history is similar for different bones in different species. Using a data collection protocol with a fine resolution, mid-diaphyseal strains were measured in vivo for both weightbearing and non-weightbearing bones in three species: dog, sheep, and turkey, with strain information collected continuously while the animals performed their natural daily activities. The daily strain history was quantified by both counting cyclic strain events (to quantify the distribution of strains of different magnitudes) and by estimating the average spectral characteristics of the strain (to quantify the frequency content of the strain signals). Counting of the daily (12-24 h) strain events show that large strains (> 1000 microstrain) occur relatively few times a day, while very small strains (< 10 microstrain) occur thousands of times a day. The lower magnitude strains (< approximately 200 microstrain) are found to be more uniform around the bone cross-section than the higher magnitude, peak strains. Strain dynamics are found to be well described by a power-law relationship and exhibit self-similar characteristics. These data lead to the suggestion that the organization of bone tissue is driven by the continual barrage of activity spanning a wide but consistent range of frequency and amplitude, and until the mechanism of bone's mechanosensory system is fully understood, all portions of bone's strain history should be considered to possibly play a role in bone adaptation.

Modeling tracer transport in an osteon under cyclic loading.

A mathematical model is developed to explain the fundamental conundrum as to how during cyclic mechanical loading there can be net solute (e.g., nutrient, tracer) transport in bone via the lacunar-canalicular porosity when there is no net fluid movement in the canaliculi over a loading cycle. Our hypothesis is that the fluid space in an osteocytic lacuna facilitates a nearly instantaneous mixing process of bone fluid that creates a difference in tracer concentration between the inward and outward canalicular flow and thus ensures net tracer transport to the osteocytes during cyclic loading, as has been shown experimentally. The sequential spread of the tracer from the osteonal canal to the lacunae is investigated for an osteon experiencing sinusoidal loading. The fluid pressure in the canaliculi is calculated using poroelasticity theory and the mixing process in the lacunae is then simulated computationally. The tracer concentration in lacunae extending radially from the osteonal canal to the cement line is calculated as a function of the loading frequency, loading magnitude, and number of loading cycles as well as the permeability of the lacunar-canalicular porosity. Our results show that net tracer transport to the lacunae does occur for cyclic loading. Tracer transport is found to increase with higher loading magnitude and higher permeability and to decrease with increasing loading frequency. This work will be helpful in designing experimental studies of tracer movement and bone fluid flow, which will enhance our understanding of bone metabolism as well as bone adaptation.

Fluid pressure relaxation depends upon osteonal microstructure: modeling an oscillatory bending experiment.

When bone is mechanically loaded, bone fluid flow induces shear stresses on bone cells that have been proposed to be involved in bone's mechanosensory system. To investigate bone fluid flow and strain-generated potentials, several theoretical models have been proposed to mimic oscillatory four-point bending experiments performed on thin bone specimens. While these previous models assume that the bone fluid relaxes across the specimen thickness, we hypothesize that the bone fluid relaxes primarily through the vascular porosity (osteonal canals) instead and develop a new poroelastic model that integrates the microstructural details of the lacunar-canalicular porosity, osteonal canals, and the osteonal cement lines. Local fluid pressure profiles are obtained from the model, and we find two different fluid relaxation behaviors in the bone specimen, depending on its microstructure: one associated with the connected osteonal canal system, through which bone fluid relaxes to the nearby osteonal canals; and one associated with the thickness of a homogeneous porous bone specimen (approximately 1 mm in our model), through which bone fluid relaxes between the external surfaces of the bone specimen at relatively lower loading frequencies. Our results suggest that in osteonal bone specimens the fluid pressure response to cyclic loading is not sensitive to the permeability of the osteonal cement lines, while it is sensitive to the applied loading frequency. Our results also reveal that the fluid pressure gradients near the osteonal canals (and thus the fluid shear stresses acting on the nearby osteocytes) are significantly amplified at higher loading frequencies.

Testing the daily stress stimulus theory of bone adaptation with natural and experimentally controlled strain histories.

Theories of bone adaptation generally consider that a departure in some feature of the normal homeostatic mechanical stimulus governs mechanical adaptation. Specifically, the 'daily stress stimulus' theory commonly used in computational models of bone adaptation suggests that the mechanical stimulus arises from a synthesis of the peak magnitudes from each loading event during a day. In this study, the homeostatic daily strain history of the adult turkey ulna was established by categorizing and counting the natural wing activities of adult male turkeys over a full 24h period. Strain signals were recorded in vivo for each activity type at three mid-diaphysis sites using stacked rosette strain gages. Following surgical isolation and transverse metaphyseal pinning of the ulnae, additional strain signals were recorded during controlled axial and torsional loading regimens associated with documented maintenance, loss, or addition of bone mass. When the present data were incorporated into the daily stress stimulus formulation, the theory did not consistently discriminate maintenance versus formation regimens, i.e., some maintenance regimens were associated with a substantially higher daily stimulus than some regimens causing bone formation.