Estimation of the poroelastic parameters of cortical bone

Mechanical conditions in the initial phase of bone healing

BACKGROUND

Bone healing is sensitive to the initial mechanical conditions with tissue differentiation being determined within days of trauma. Whilst axial compression is regarded as stimulatory, the role of interfragmentary shear is controversial. The purpose of this study was to determine how the initial mechanical conditions produced by interfragmentary shear and torsion differ from those produced by axial compressive movements.

METHODS

The finite element method was used to estimate the strain, pressure and fluid flow in the early callus tissue produced by the different modes of interfragmentary movement found in vivo. Additionally, tissue formation was predicted according to three principally different mechanobiological theories.

FINDINGS

Large interfragmentary shear movements produced comparable strains and less fluid flow and pressure than moderate axial interfragmentary movements. Additionally, combined axial and shear movements did not result in overall increases in the strains and the strain magnitudes were similar to those produced by axial movements alone. Only when axial movements where applied did the non-distortional component of the pressure-deformation theory influence the initial tissue predictions.

INTERPRETATION

This study found that the mechanical stimuli generated by interfragmentary shear and torsion differed from those produced by axial interfragmentary movements. The initial tissue formation as predicted by the mechanobiological theories was dominated by the deformation stimulus.

Corroboration of mechanoregulatory algorithms for tissue differentiation during fracture healing: Comparison with in vivo results

Several mechanoregulation algorithms proposed to control tissue differentiation during bone healing have been shown to accurately predict temporal and spatial tissue distributions during normal fracture healing. As these algorithms are different in nature and biophysical parameters, it raises the question of which reflects the actual mechanobiological processes the best. The aim of this study was to resolve this issue by corroborating the mechanoregulatory algorithms with more extensive in vivo bone healing data from animal experiments. A poroelastic three-dimensional finite element model of an ovine tibia with a 2.4 mm gap and external callus was used to simulate the course of tissue differentiation during fracture healing in an adaptive model. The mechanical conditions applied were similar to those used experimentally, with axial compression or torsional rotation as two distinct cases. Histological data at 4 and 8 weeks, and weekly radiographs, were used for comparison. By applying new mechanical conditions, torsional rotation, the predictions of the algorithms were distinguished successfully. In torsion, the algorithms regulated by strain and hydrostatic pressure failed to predict healing and bone formation as seen in experimental data. The algorithm regulated by deviatoric strain and fluid velocity predicted bridging and healing in torsion, as observed in vivo. The predictions of the algorithm regulated by deviatoric strain alone did not agree with in vivo data. None of the algorithms predicted patterns of healing entirely similar to those observed experimentally for both loading modes. However, patterns predicted by the algorithm based on deviatoric strain and fluid velocity was closest to experimental results. It was the only algorithm able to predict healing with torsional loading as seen in vivo.

Computational fluid dynamics modeling of insertion and advancement of a reamer into the intramedullary canal of a long bone

The effect of reaming velocity on the pressure distribution within the bone was investigated numerically by solving the full three-dimensional momentum equations together with the continuity equation using the finite element technique. Viscosity was also varied to obtain a pressure envelope. It was found that all the experimental data follow the same trends as the envelopes predicted by the finite element model. It was clear that an increase in either the implant insertion rate or the viscosity resulted in an increase in pressure in the intramedullary canal.

Estimation of bone permeability using accurate microstructural measurements

While interstitial fluid flow is necessary for the viability of osteocytes, it is also believed to play a role in bone's mechanosensory system by shearing bone cell membranes or causing cytoskeleton deformation and thus activating biochemical responses that lead to the process of bone adaptation. However, the fluid flow properties that regulate bone's adaptive response are poorly understood. In this paper, we present an analytical approach to determine the degree of anisotropy of the permeability of the lacunar-canalicular porosity in bone. First, we estimate the total number of canaliculi emanating from each osteocyte lacuna based on published measurements from parallel-fibered shaft bones of several species (chick, rabbit, bovine, horse, dog, and human). Next, we determine the local three-dimensional permeability of the lacunar-canalicular porosity for these species using recent microstructural measurements and adapting a previously developed model. Results demonstrated that the number of canaliculi per osteocyte lacuna ranged from 41 for human to 115 for horse. Permeability coefficients were found to be different in three local principal directions, indicating local orthotropic symmetry of bone permeability in parallel-fibered cortical bone for all species examined. For the range of parameters investigated, the local lacunar-canalicular permeability varied more than three orders of magnitude, with the osteocyte lacunar shape and size along with the 3-D canalicular distribution determining the degree of anisotropy of the local permeability. This two-step theoretical approach to determine the degree of anisotropy of the permeability of the lacunar-canalicular porosity will be useful for accurate quantification of interstitial fluid movement in bone.

Bone as an ion exchange organ: evidence for instantaneous cell-dependent calcium efflux from bone not due to resorption

The current study tests the hypothesis that basal level and minute-by-minute correction of plasma Ca2+ by outward and inward Ca2+ fluxes from and into an exchangeable ionic pool in bone is controlled by an active partition system without contributions from the bone remodeling system. Direct real-time measurements of Ca2+ fluxes were made using the scanning ion-selective electrode technique (SIET) on living bones maintained ex vivo in physiological conditions. SIET three-dimensional measurements of the local Ca2+ concentration gradient (10 microm spatial resolution) were performed on metatarsal bones of weanling mice after drilling a 100-mum hole through the cortex to expose the internal bone extracellular fluid (BECF) to the bathing solution, whose composition mimicked the extracellular fluid (ECF). Influxes of Ca2+ towards the center of the cortical hole (15.1+/-4.2 pmol cm-2 s-1) were found in the ECF and were reversed to effluxes (7.4+/-2.9 pmol cm-2 s-1) when calcium was depleted from the ECF, mimicking a plasma demand. The reversal from influx to efflux and vice versa was immediate and fluxes in both directions were steady throughout the experimental time (>or=2 h, n=14). Only the efflux was nullified within 10 min by the addition of 10 mM/L Na-Cyanide (n=7), demonstrating its cell dependence. The timeframes of the exchanges and the stability of the Ca2+ fluxes over time suggest the existence of an exchangeable calcium pool in bone. The calcium efflux dependency on viable cells suggests that an active partition system might play a central role in the short-term error correction of plasma calcium without the contribution of bone remodeling.

Comparison of biophysical stimuli for mechano-regulation of tissue differentiation during fracture healing

Most long-bone fractures heal through indirect or secondary fracture healing, a complex process in which endochondral ossification is an essential part and bone is regenerated by tissue differentiation. This process is sensitive to the mechanical environment, and several authors have proposed mechano-regulation algorithms to describe it using strain, pore pressure and/or interstitial fluid velocity as biofeedback variables. The aim of this study was to compare various mechano-regulation algorithms' abilities to describe normal fracture healing in one computational model. Additionally, we hypothesized that tissue differentiation during normal fracture healing could be equally well regulated by the individual mechanical stimuli, e.g. deviatoric strain, pore pressure or fluid velocity. A biphasic finite element model of an ovine tibia with a 3mm fracture gap and callus was used to simulate the course of tissue differentiation during normal fracture healing. The load applied was regulated in a biofeedback loop, where the load magnitude was determined by the interfragmentary movement in the fracture gap. All the previously published mechano-regulation algorithms studied, simulated the course of normal fracture healing correctly. They predicted (1) intramembranous bone formation along the periosteum and callus tip, (2) endochondral ossification within the external callus and cortical gap, and (3) creeping substitution of bone towards the gap from the initial lateral osseous bridge. Some differences between the effects of the algorithms were seen, but they were not significant. None of the volumetric components, i.e. pore pressure or fluid velocity, alone were able to correctly predict spatial or temporal tissue distribution during fracture healing. However, simulation as a function of only deviatoric strain accurately predicted the course of normal fracture healing. This suggests that the deviatoric component may be the most significant mechanical parameter to guide tissue differentiation during indirect fracture healing.

A quantum biological hypothesis of human secondary dentinogenesis

It is hypothesized that human coronal secondary dentin (SD) is a final classical mechanical (CM) response to a chain of prior quantum mechanical (QM) transductions of the information of initial CM occlusal loadings of enamel. Such CM energy is transduced into QM quanta (as protons) that are translocated centripetally via clustered water (CW), (as "proton wires"), that is structurally related to both enamel prism sheath and hydroxyapatite crystal hydration shells. These quanta pass into odontoblastic cell processes (OP), lying within dentinal tubules (DT). OP's contain abundant parallel arrays of cylindrical microtubules (MT). These are the sites of two further CW-related QM events: (i) proton translocation associated with conformal changes of MT tubulin protein dimers; and (ii) coherent energetic oscillations within the CW filling the MT's hollow cores. Finally, these quanta pass into the odontoblastic soma, where QM wave function collapse transduces this information into a final CM state that initiates the processes of SD formation. A critical portion of this hypothesis may be experimentally tested.

Effect of oscillating fluid shear on solute transport in cortical bone

The consequences of an oscillatory fluid shear mechanism on nutrient transport in bone during physical activity and ultrasonic therapy are discussed. During movement, periodic stress on bone creates transient pressure gradients that circulate interstitial fluid through calcified bone. A transport model derived from oscillatory Taylor-Aris dispersion phenomena was used to predict a ratio of effective-to-molecular diffusivity, K/D, for solutes of varying sizes up to 50 nm in diameter, in pores filled with interstitial fluid and pericellular matrix. The magnitude of the estimated transport enhancement depended on the molecular size, pore dimension, applied frequency and the displacement of the fluid during pressurization. For oscillation frequencies and amplitudes corresponding to those experienced during normal human activity, transport enhancements of up to 100 fold are expected for molecules larger than 5 nm in diameter. Enhancements of up to one order of magnitude, due to ultrasound stimulations in the MHz frequency range, are also expected for 7-nm-sized solutes. No effects are anticipated for ions, whose molecular diffusion time is too fast relative to the oscillation frequency. This model is expected to be useful for understanding differences in bone growth as a function of type of movement or to develop new physical therapies.

“Culture shock” from the bone cell's perspective: emulating physiological conditions for mechanobiological investigations

Bone physiology can be examined on multiple length scales. Results of cell-level studies, typically carried out in vitro, are often extrapolated to attempt to understand tissue and organ physiology. Results of organ- or organism-level studies are often analyzed to deduce the state(s) of the cells within the larger system(s). Although phenomena on all of these scales—cell, tissue, organ, system, organism—are interlinked and contribute to the overall health and function of bone tissue, it is difficult to relate research among these scales. For example, groups of cells in an exogenous, in vitro environment that is well defined by the researcher would not be expected to function similarly to those in a dynamic, endogenous environment, dictated by systemic as well as organismal physiology. This review of the literature on bone cell culture describes potential causes and components of cell “culture shock,” i.e., behavioral variations associated with the transition from in vivo to in vitro environment, focusing on investigations of mechanotransduction and experimental approaches to mimic aspects of bone tissue on a macroscopic scale. The state of the art is reviewed, and new paradigms are suggested to begin bridging the gap between two-dimensional cell cultures in petri dishes and the three-dimensional environment of living bone tissue.

Tissue growth and remodeling

The growth and remodeling of a tissue depends on certain features in the history of its mechanical environment as well as its genetic makeup. The mechanical environment influences the tissue's developing morphology, the process of simply increasing the size of existing morphological structures, and the formation of the proteins of which the tissue is constructed. The relationships between genetic information, various epigenetic mechanisms and tissue development are discussed. The developmental growth and remodeling of most structural tissues are enhanced by the use of those tissues and retarded by their disuse. The mechanical or mathematical modeling of tissue growth and development using cellular automata models and continuum mechanical models is reviewed.

Strain-derived canalicular fluid flow regulates osteoclast activity in a remodelling osteon--a proposal

The concept of bone remodelling by basic multicellular units is well established, but how the resorbing osteoclasts find their way through the pre-existing bone matrix remains unexplained. The alignment of secondary osteons along the dominant loading direction suggests that remodelling is guided by mechanical strain. This means that adaptation (Wolff's Law) takes place throughout life at each remodelling cycle. We propose that alignment during remodelling occurs as a result of different canalicular flow patterns around cutting cone and reversal zone during loading. Low canalicular flow around the tip of the cutting cone is proposed to reduce NO production by local osteocytes thereby causing their apoptosis. In turn, osteocyte apoptosis could be the mechanism that attracts osteoclasts, leading to further excavation of bone in the direction of loading. At the transition between cutting cone and reversal zone, however, enhanced canalicular flow will stimulate osteocytes to increase NO production, which induces osteoclast retraction and detachment from the bone surface. Together, this leads to a treadmill of attaching and detaching osteoclasts in the tip and the periphery of the cutting cone, respectively, and the digging of a tunnel in the direction of loading.

A case for strain-induced fluid flow as a regulator of BMU-coupling and osteonal alignment

Throughout life, human bone is renewed continuously in a tightly controlled sequence of resorption and formation. This process of bone remodeling is remarkable because it involves cells from different lineages, collaborating in so-called basic multicellular units (BMUs) within small spatial and temporal boundaries. Moreover, the newly formed (secondary) osteons are aligned to the dominant load direction and have a density related to its magnitude, thus creating a globally optimized mechanical structure. Although the existence of BMUs is amply described, the cellular mechanisms driving bone remodeling-particularly the alignment process-are poorly understood. In this study we present a theory that explains bone remodelling as a self-organizing process of mechanical adaptation. Osteocytes thereby act as sensors of strain-induced fluid flow. Physiological loading produces stasis of extracellular fluid in front of the cutting cone of a tunneling osteon, which will lead to osteocytic disuse and (continued) attraction of osteoclasts. However, around the resting zone and the closing cone, enhanced extracellular fluid flow occurs, which will activate osteocytes to recruit osteoblasts. Thus, cellular activity at a bone remodeling site is well related to local fluid flow patterns, which may explain the coordinated progression of a BMU.