Effects of the basic multicellular unit and lamellar thickness on osteonal fatigue life

A remodeling cycle sets the size of the osteon and associated lamellae in the basic multicellular unit. Treatments and aging affect these micro-structural features. We previously demonstrated decreased fatigue life with an unexplained mechanism and decreased osteon size in cortical bone treated with high-dose bisphosphonate. Here, three finite element models were examined: type-1: a single osteon, as a homogeneous unit and with heterogeneous lamellae and interlamellae, type-2: a control, interstitial-only tissue and type-3: the osteon with cement line, set within the interstitial tissue. Models were loaded in simulated, sinusoidal bending fatigue. As osteon size was decreased, lamellar number and lamellar thickness were incrementally adjusted for each model. As hypothesized, lamellae within the larger type-1 models attained greater cycles to failure and the addition of an osteon to type-2 models (generating a type-3 model set) yielded increased fatigue life. However, as the osteon size was decreased, the potential for compressive damage nucleation was increased within the lamellae of the osteons versus the interstitium. Also, osteons with fewer, thicker lamellae displayed increased fatigue life. Osteonal microstructure plays a role in damage initiation location, especially when BMU size is smaller. Previous findings by us and others could partially be explained by this further understanding of increased probability for damage nucleation in smaller osteons.     

An anatomical model for streaming potentials in osteons

An anatomical model for streaming potentials in osteons is developed to characterize the electromechanical effect in bone. The model accounts for the microstructure of the osteon and is based upon first principles of electrochemistry, electrokinetics, continuum mechanics and fluid dynamics. Intra-osteonal potentials and their relaxation times are numerically evaluated. Many of the previously reported observations of potentials in osteons and across macroscopic specimens are explained for the first time in terms of an electrokinetic model. The cusp-like behavior of intra-osteonal potentials is explained, the dependence of the potentials on solution viscosity and conductivity is demonstrated, and insight is gained relative to the time dependence of stress generated potentials.     

Crack propagation in cortical bone is affected by the characteristics of the cement line: a parameter study using an XFEM interface damage model

Bulk properties of cortical bone have been well characterized experimentally, and potent toughening mechanisms, e.g., crack deflections, have been identified at the microscale. However, it is currently difficult to experimentally measure local damage properties and isolate their effect on the tissue fracture resistance. Instead, computer models can be used to analyze the impact of local characteristics and structures, but material parameters required in computer models are not well established. The aim of this study was therefore to identify the material parameters that are important for crack propagation in cortical bone and to elucidate what parameters need to be better defined experimentally. A comprehensive material parameter study was performed using an XFEM interface damage model in 2D to simulate crack propagation around an osteon at the microscale. The importance of 14 factors (material parameters) on four different outcome criteria (maximum force, fracture energy, crack length and crack trajectory) was evaluated using ANOVA for three different osteon orientations. The results identified factors related to the cement line to influence the crack propagation, where the interface strength was important for the ability to deflect cracks. Crack deflection was also favored by low interface stiffness. However, the cement line properties are not well determined experimentally and need to be better characterized. The matrix and osteon stiffness had no or low impact on the crack pattern. Furthermore, the results illustrated how reduced matrix toughness promoted crack penetration of the cement line. This effect is highly relevant for the understanding of the influence of aging on crack propagation and fracture resistance in cortical bone.

     

Adaptation of energy metabolism in under-fed ruminants. Quantification in the whole animal and body tissues]

Ruminants respond to underfeeding by a progressive adaptation until a new equilibrium between dietary supply and requirements is reached. The resulting drop in maintenance energy requirements originates from a decrease in basal metabolism that depends on the level and duration of undernutrition. These modifications are not totally accounted for by changes in live weight but might be explained by differential changes in individual tissue weight and metabolism. Tissues contribute to whole animal expenditure in a disproportionate manner relative to their weight. Thus digestive tract, liver and muscle masses contribute 5-11, 1-2.5 and 35-50% to live weight but about 16-29, 17-31 and about 16% to whole animal energy expenditure, respectively, because of differences in tissue metabolic activity. Underfeeding results in a decrease in the contribution of viscera to energy expenditure, whereas results on muscle mass are scarce. These changes in contribution are due to changes in tissue mass, nutrient supply (blood flow) and/or in metabolic activity.     

Microstructural mechanical study of a transverse osteon under compressive loading: The role of fiber reinforcement and explanation of some geometrical and mechanical microscopic properties

This Finite Element study aims at understanding the transverse osteon as a composite microstructure, and at differentiating the actions of each of its main components and their interactions. Three components of the osteon have been distinguished: the lamellae mineral-collagen matrix, the lamellae mineral-collagen reinforcement fibers and the Haversian canal content made of intracortical fluid and soft tissues. Numerical compression experiments have been performed, varying the microstructure properties. Our results show that fiber reinforcement of transverse osteons is only efficient at resisting dynamic compressive loadings, but that the improvement of the static compressive properties is very poor. Furthermore, the modeled stress distribution within the matrix and reinforcement fibers may explain why transverse osteons are often limited to a small number of lamellae (<8) and why internal lamellae could be stiffer than external ones.     

Interfacial Strength of Cement Lines in Human Cortical Bone

In human cortical bone, cement lines (or reversal lines) separate osteons from the interstitial bone tissue, which consists of remnants of primary lamellar bone or fragments of remodeled osteons. There have been experimental evidences of the cement line involvement in the failure process of bone such as fatigue and damage. However, there are almost no experimental data on interfacial properties of cement lines in human cortical bone. The objective of this study is to design and assemble a precision and computer controlled osteon pushout microtesting system, and to experimentally determine the interfacial strength of cement lines in human cortical bone by performing osteon pushout tests. Thirty specimens were prepared from humeral diaphyses of four human subjects. Twenty specimens were tested under the condition of a small hole in the supporting plate, in which the cement line debonding occurred. The cement line interfacial strength ranged from 5.38 MPa to 10.85 MPa with an average of 7.31±1.73 MPa. On the other hand, ten specimens were tested under the condition of a large hole in the supporting plate, in which the shear failure inside osteons was observed. The specimens tested under the condition of the large hole resulted in an average shear strength of 73.71±15.06 MPa, ranging from 45.97 MPa to 93.74 MPa. Therefore, our results suggest that the cement line interface between osteon and interstitial bone tissue is weaker than that between bone tissue lamellae.     

"Whither flows the fluid in bone?" An osteocyte's perspective

Bone represents a porous tissue containing a fluid phase, a solid matrix, and cells. Movement of the fluid phase within the pores or spaces of the solid matrix translates endogenous and exogenous mechanobiological, biochemical and electromechanical signals from the system that is exposed to the dynamic external environment to the cells that have the machinery to remodel the tissue from within. Hence, bone fluid serves as a coupling medium, providing an elegant feedback mechanism for functional adaptation. Until recently relatively little has been known about bone fluid per se or the influences governing the characteristics of its flow. This work is designed to review the current state of this emerging field. The structure of bone, as an environment for fluid flow, is discussed in terms of the properties of the spaces and channel walls through which the fluid flows and the influences on flow under physiological conditions. In particular, the development of the bone cell syncytium and lacunocanalicular system are presented, and pathways for fluid flow are described from the systemic to the organ, tissue, cellular and subcellular levels. Finally, exogenous and endogenous mechanisms for pressure-induced fluid movement through bone, including mechanical loading, vascular derived pressure gradients, and osmotic pressure gradients are discussed. The objective of this review is to survey the current understanding of the means by which fluid flow in bone is regulated, from the level of the skeletal system down to the level of osteocyte, and to provide impetus for future research in this area of signal transduction and coupling. An understanding of this important aspect of bone physiology has profound implications for restoration of function through innovative treatment modalities on Earth and in space, as well as for engineering of biomimetic replacement tissue.     

A first estimation of prestress in so-called circularly fibered osteonic lamellae.

The existence and role of prestress in the various hierarchical structures of long bone are long standing questions. In this study, the prestress and associated strain that exist in a component of human bone microstructure, circularly fibered osteonic lamella, are estimated. Such estimates allow the formulation of hypotheses on prestress formation and lamellar stiffness. Dimensional measurements were obtained for eight fully calcified lamellae. These dimensions, before isolation from the surrounding alternate osteon and after strain relief by isolation and axial sectioning, furnish data upon which a geometric lamellar model is constructed. A material model is based on the most likely hypothesis as to lamellar structure. This geometric-material model allows estimation of the preexisting strain. The largest strains occur in shear circumferential-axial and normal axial strain directions, averaging 0.08 and 0.05, respectively. The geometric-material model expresses prestress in terms of as yet unknown elastic moduli. The average prestress magnitude is the largest in shear circumferential-axial direction, compensating for alternate osteon weakness in this direction. The estimated axial prestress confirms long hypothesized alternate osteon precompression, which impedes fractures of areas of collagen bundles transverse to the osteon axis at low stresses. The results of the model support the formulation of the following biological hypotheses: (a) lamellar prestress occurs at a supra-molecular level, namely through collagen bundles which are themselves likely to be prestressed; (b) collagen bundles oblique to the lamellar axis are responsible for shear prestress; (c) prestress ranges up to 0.11 GPa; and (d) the lamella is less stiff than alternate osteon.     

An ex vivo model to study transport processes and fluid flow in loaded bone

Load-induced fluid flow has been postulated to provide a mechanism for the transmission of mechanical signals (e.g. via shear stresses, enhancement of molecular transport, and/or electrical effects) and the subsequent elicitation of a functional adaptation response (e.g. modeling, remodeling, homeostasis) in bone. Although indirect evidence for such fluid flow phenomena can be found in the literature pertaining to strain generated potentials, actual measurement of fluid displacements in cortical bone is inherently difficult. This problem motivated us to develop and introduce an ex vivo perfusion model for the study of transport processes and fluid flow within bone under controlled mechanical loading conditions. To this end, a closed-loop system of perfusion was established in the explanted forelimb of the adult Swiss alpine sheep. Immediately prior to mechanical loading, a bolus of tracer was introduced intraarterially into the system. Thereafter, the forelimb of the left or right side (randomized) was loaded cyclically, via Schanz screws inserted through the metaphyses, producing a peak compressive strain of 0.2% at the middiaphysis of the anterior metacarpal cortex. In paired experiments with perfusion times totalling 2, 4, 8 and 16 min, the concentration of tracer measured at the middiaphysis of the cortex in cross section was significantly higher in the loaded bone than in the unloaded contralateral control. Fluorometric measurements of procion red concentration in the anterior aspect alone showed an enhancement in transport at early stages of loading (8 cycles, 2 min) but no effect in transport after higher number of cycles or increased perfusion times, respectively. This reflects both the small size of the molecular tracer, which would be expected to be transported rapidly by way of diffusive mechanisms alone, as well as the loading mode to which the anterior aspect was exposed. Thus, using our new model it could be shown that load-induced fluid flow represents a powerful mechanism to enhance molecular transport within the lacunocanalicular system of compact bone tissue. Based on these as well as previous studies, it appears that the degree of this effect is dependent on tracer size as well as the mechanical loading mode to which a given area of tissue is exposed.     

Interstitial fluid flow in the osteon with spatial gradients of mechanical properties: a finite element study

Bone remodelling is the process that maintains bone structure and strength through adaptation of bone tissue mechanical properties to applied loads. Bone can be modelled as a porous deformable material whose pores are filled with cells, organic material and interstitial fluid. Fluid flow is believed to play a role in the mechanotransduction of signals for bone remodelling. In this work, an osteon, the elementary unit of cortical bone, is idealized as a hollow cylinder made of a deformable porous matrix saturated with an interstitial fluid. We use Biot’s poroelasticity theory to model the mechanical behaviour of bone tissue taking into account transverse isotropic mechanical properties. A finite element poroelastic model is developed in the COMSOL Multiphysics software. Elasticity equations and Darcy’s law are implemented in this software; they are coupled through the introduction of an interaction term to obtain poroelasticity equations. Using numerical simulations, the investigation of the effect of spatial gradients of permeability or Poisson’s ratio is performed. Results are discussed for their implication on fluid flow in osteons: (i) a permeability gradient affects more the fluid pressure than the velocity profile; (ii) focusing on the fluid flow, the key element of loading is the strain rate; (iii) a Poisson’s ratio gradient affects both fluid pressure and fluid velocity. The influence of textural and mechanical properties of bone on mechanotransduction signals for bone remodelling is also discussed.     

Influence of fluid-flow direction on effective permeability of the vertebral end plate: an analytical model

Convective transports in the vertebral end plate (VEP) play a significant role in the homeostasis of the spine. A few studies hypothesised that the hydraulic resistance or effective permeability of the VEP could be dependant upon fluid-flow direction. Results were influenced by species, region of interest within the end plate and pathology. Some results were contradictory. We propose an analytical model based on steady-state Newtonian flows in capillary media to develop a phenomenological analysis of convective transport through the VEP. This dependence was established using a biquadratic analytical function involving porosities of subchondral bone, capillary bed and cartilage end plate. Discussion of results provided a theoretical justification for variable and/or contradictory experimental results concerning the amount of energy lost by fluid during its course through the end plate. Tissue porosities and, especially, those relative to the capillary bed could strongly influence the dependence of fluid energy loss on flow direction and could potentially modify tissue homeostasis related to the day and night cycle.     

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.     

Hysteretic pinching of human secondary osteons subjected to torsion

The mechanical behavior of bone tissue's ultra- and micro- structure is fundamental to assessment of macroscopic bone mechanics. This paper explores the ultra-structural characteristics of human femoral tissue responsible for energy absorption of secondary osteons under mechanical loading. A novel mathematical interpretation of single osteon mechanics elucidates the behavior of the collagen-apatite interface. Fully calcified single osteon specimens were mechanically tested quasi-statically under cyclic torsional loading about their longitudinal axis. On each hysteretic diagram, all cycles after the initial monotonic cycle appear pinched and share two points. Stiffness degradation and pinching degradation were investigated on the torque versus deflection-angle-per-unit-length diagrams as the number of cycles increases, in relation to the appearance of osteons in cross-section under circularly polarized light microscopy. Material science's Bauschinger effect, originally defined for metals and later extended to structures reinforced with metal bars, is adapted to describe pinching. Material science's prying effect, defined as amplification of eccentric tensile load through lever action, is employed to explain pinching. The presence of the two points shared by all complete cycles is analyzed in terms of the mathematical fixed point theorem. The results allow formulation of the following conjectures: (1) the prying of carbonated apatite crystallites at the interface with the 40 nm long bands of non-calcified collagen fibrils causes pinching; (2) the prying effect increases with the increasing percentage of collagen-apatite elements that form a larger angle with the osteon axis; and (3) micro-cracks increase more in number than in length as the number of cycles increases.     

Osteon interfacial strength and histomorphometry of equine cortical bone

The interfacial strength of secondary osteons from the diaphysis of the Thoroughbred equine third metacarpal was evaluated using the fiber pushout test. The pushout was performed on 300-500 microm sections of 4x4x15 mm bone blocks machined from four anatomic regions of the cortex. Pushout strength was evaluated from proximal to distal location within the diaphysis on four osteon types classified under polarized light on adjacent histologic sections from each block. The shear strength of the interfaces were estimated from shear lag theory. Differences were found in the interfacial strength of osteons based on appearance under polarized light with bright field having the highest interfacial strength (40.3 MPa). The lowest strength was found in the dark field osteons (22.8 MPa). The dorsal region had the highest shear strength and toughness compared to all other regions. The cement line and interlamellar interfaces are similar in strength, but exhibit regional dependence--specifically, the palmar region strength is less (17.5 MPa) than the osteon interlamellar interfaces (30.4 MPa) and osteon type dependent (alternating significantly weaker than other types). Histomorphometry revealed significant regional differences (p<0.0001) in osteon area fraction among the four osteon types as well as differences in the osteon diameter (p=0.01), with dorsal regions having larger osteons (170 microm) than the palmar region (151 microm). Fatigue life and fracture toughness of Haversian bone are reported in the literature to be regionally dependent and are known to be associated with osteon pullout--an osteon interfacial phenomenon. Therefore, the results presented in this study are important to further the understanding of the mechanisms of fragility and damage accumulation in cortical bone.     

Influence of cortical canal architecture on lacunocanalicular pore pressure and fluid flow

Bone is a dynamic tissue that undergoes structural modification in response to its mechanical environment, but how bone cells sense and respond to loading conditions remains incompletely understood. Current theories focus on strain-induced fluid flow for the primary means of mechanotransduction. To examine the influence of age-related cortical rarefaction on lacunocanalicular fluid characteristics, coupled fluid flow and mechanical computational models of bone specimens representing young, mid-age and aged samples were derived artificially from the same original micro-computed tomography image data. Simulated mechanical loading was applied to the bone models to induce pressure-driven interstitial fluid flow. Results demonstrated a decrease in pore pressure and fluid velocity magnitudes with age as a result of increased cortical porosity. Mean canal separation, as opposed to canal size, was implicated as a primary factor affecting age-related fluid dynamics. Future investigations through refinement of the model may implicate fluid stasis or inadequate nutrient transport experienced by osteocytes as a key factor in the initiation of cortical remodelling events.     

Influence of cortical canal architecture on lacunocanalicular pore pressure and fluid flow

Bone is a dynamic tissue that undergoes structural modification in response to its mechanical environment, but how bone cells sense and respond to loading conditions remains incompletely understood. Current theories focus on strain-induced fluid flow for the primary means of mechanotransduction. To examine the influence of age-related cortical rarefaction on lacunocanalicular fluid characteristics, coupled fluid flow and mechanical computational models of bone specimens representing young, mid-age and aged samples were derived artificially from the same original micro-computed tomography image data. Simulated mechanical loading was applied to the bone models to induce pressure-driven interstitial fluid flow. Results demonstrated a decrease in pore pressure and fluid velocity magnitudes with age as a result of increased cortical porosity. Mean canal separation, as opposed to canal size, was implicated as a primary factor affecting age-related fluid dynamics. Future investigations through refinement of the model may implicate fluid stasis or inadequate nutrient transport experienced by osteocytes as a key factor in the initiation of cortical remodelling events.     

Osteon remodeling dynamics in the Cayo Santiago Macaca mulatta: The effect of matriline

At the microstructural level, bones remodel throughout life. This process is recorded in bone cortex as osteons. A more comprehensive understanding of the interaction between genetic regulation and environmental factors in osteon remodeling will increase the value of this skeletal record and enable more accurate reconstruction of individual life histories. The purpose of this study was to examine the contribution of maternal lineage to normal age and sex variation in osteon remodeling dynamics in Macaca mulatta. Femoral cross sections from 57 Cayo Santiago-derived rhesus macaques representing five matrilines were examined to evaluate the effect of genetic relatedness on osteon remodeling dynamics. Analysis of variance revealed an effect of maternal lineage on osteon area and Haversian canal area. The other variables did not differ significantly among matrilines. Analysis of covariance revealed no significant interactions among age, sex, and matriline for any of the microstructural variables.     

Osteomyelitis in a 265-million-year-old titanosuchid (Dinocephalia,Therapsida)

Abstract

Analytical palaeohistology techniques have allowed a better understanding of the microstructure of fossil bone, as well as of bone pathologies of extinct animals. Osteomyelitis is one of the oldest identified bone pathologies, occurring in Synapsida dating back as far as the Lower Permian. Here we show the presence of this pathology in the femur of Jonkeria parva, an omnivorous titanosuchid from the Tapinocephalus Assemblage Zone of the Karoo Basin of South Africa. The pathology is characterised by bony radial spicules growing perpendicular to the normal orientation of the unaffected fibrolamellar bone tissue, and shows localised increase in vascular canal size. Puncture marks on the femur suggests that an attack by a predator may have resulted in a bacterial infection that caused contiguous and subjacent osteomyelitis.     

A finite element analysis for the prediction of load-induced fluid flow and mechanochemical transduction in bone

Interstitial fluid flow through the lacunocanalicular cavities of mechanically loaded bone provides the biophysical basis for a number of postulates regarding mechanotransduction in bone. Recently, the existence of load-induced fluid flow and its influence on molecular transport through bone has been confirmed using tracer methods to visualize fluid flow induced by in vivo four-point-bending of rat tibiae. In this paper, we present a theoretical two-stage approach for the calculation of load-induced flow fields and for the evaluation of their influence on molecular transport in bone loaded in four-point bending, analogous to the aforementioned experimental model. In the first stage, the fluid velocities are calculated using a three-dimensional, poroelastic finite element model. In the second stage, mass transport analysis, this calculated fluid flow serves as a forced convection flow and its contribution to the total transport potential is determined. Based on this combined approach, the overall tracer concentration in the loaded bone is significantly higher than that in the unloaded bone. Furthermore, augmentation of mass transport through convective flow is more pronounced in the tension band of the tissue, as compared to the compression band. In general, augmentation of tracer concentration via convective mechanisms is most pronounced in areas corresponding to lowest fluid velocities, which is indicative of fluid flow direction and areas of increased "dwell time" or accumulation during the loading cycle. This theoretical model, in combination with the corresponding experimental model, provides unique insight into the role of mechanical loads in modulating local flow distributions and concentration gradients within bone tissue.