Hierarchies of damage induced loss of mechanical properties in calcified bone after in vivo fatigue loading of rat ulnae.

During fatigue loading of whole bone, damage to bone tissue accumulates, coalesces and leads to fractures. Whether damage affects tissue material properties similarly at the nanoscale (less than 1 µm), microscale (less than 1 mm), and whole bone scale has not been fully evaluated. Therefore, in this study, we examine scale-dependent loss of calcified tissue material properties in rat ulnae, after fatigue loading of rat forearms using the forearm compression model. In vivo fatigue loading was conducted on the right forearms until a displacement end-point was reached. The non-fatigued left forearms served as contralateral controls. Subsequently, three-point bending tests to failure on excised ulnae demonstrated a 41% and 49% reduction in the stiffness and ultimate strength as compared to contralateral control ulnae, respectively. Depth-sensing microindentation demonstrated an average decrease in material properties, such as elastic modulus and hardness, of 28% and 29% respectively. Nanoindentation measured elastic modulus and hardness were reduced by 26% and 29% in damaged bone relative to contralateral controls, respectively. The increased loss of whole bone material properties compared to tissue material properties measured using indentation is mainly attributed to the presence of a macrocrack located in the medial compressive region at the site of peak strains. The similar magnitude of changes in material properties by microindentation and nanoindentation is attributed to damage that may originate at an even smaller scale, as inferred from 10% differences in connectivity of osteocyte canaliculi in damaged bone.

Correlation between longitudinal, circumferential, and radial moduli in cortical bone: effect of mineral content.

Previous studies indicate that changes in the longitudinal elastic properties of bone due to changes in mineral content are related to the longitudinal strength of bone tissue. Changes in mineral content are expected to affect bone tissue mechanical properties along all directions, albeit to different extents. However, changes in tissue mechanical properties along the different directions are expected to be correlated to one another. In this study, we investigate if radial, circumferential, and longitudinal moduli are related in bone tissue with varying mineral content. Plexiform bovine femoral bone samples were treated in fluoride ion solutions for a period of 3 and 12 days to obtain bones with 20% and 32% lower effective mineral contents. Transmission ultrasound velocities were obtained in the radial, circumferential, and longitudinal axes of bone and combined with measured densities to obtain corresponding tensorial moduli. Results indicate that moduli decreased with fluoride ion treatments and were significantly correlated to one another (r(2) radial vs. longitudinal = 0.80, r(2) circumferential vs. longitudinal = 0.90, r(2) radial vs. circumferential = 0.85). Densities calculated from using ultrasound parameters, acoustic impedance and transmission velocities, were moderately correlated to those measured by the Archimedes principle (r(2)=0.54, p<0.01). These results suggest that radial and circumferential ultrasound measurements could be used to determine the longitudinal properties of bone and that ultrasound may not be able to predict in vitro densities of bones containing unbonded mineral.

A new streaming potential chamber for zeta potential measurements of particulates.

A novel streaming potential measurement device has been validated by determining the average electrokinetic (zeta) potential of densely packed particulate such as human erythrocytes and ground bovine cortical bone. The new streaming potential device used in this study is easy to construct in the laboratory, designed to allow dense packing of particles, and determines zeta potentials for a broad range of particle sizes. The streaming potential device consists of four Plexiglas parts: (i) an upper and (ii) a lower chamber, which act as reservoirs for fluid; (iii) a midchamber which connects the upper and lower chambers and holds the sample holder, and (iv) a sample holder. Pressurization of fluid in the top chamber generates a pressure gradient that induces movement of fluid through the stationary sample and into the bottom chamber. Pressure induced flow through the interconnected pores of the densely packed particulate generates a potential difference across the sample that is measured using electrodes housed in the top and bottom chambers. The measured potential difference is then converted to zeta potentials. The advantage of this chamber is its ability to handle densely packed particulates exhibiting a broad distribution of sizes. Dense packing of particulate is achieved by compacting samples at the bottom of the sample holder under centrifugal forces before the device is assembled. This approach allowed us to determine average zeta potentials of densely packed particulate made of soft and hard materials.

Tensile behavior of cortical bone: dependence of organic matrix material properties on bone mineral content.

A porous composite model is developed to analyze the tensile mechanical properties of cortical bone. The effects of microporosity (volksman's canals, osteocyte lacunae) on the mechanical properties of bone tissue are taken into account. A simple shear lag theory, wherein tensile loads are transferred between overlapped mineral platelets by shearing of the organic matrix, is used to model the reinforcement provided by mineral platelets. It is assumed that the organic matrix is elastic in tension and elastic-perfectly plastic in shear until it fails. When organic matrix shear stresses at the ends of mineral platelets reach their yield values, the stress-strain curve of bone tissue starts to deviate from linear behavior. This is referred as the microscopic yield point. At the point where the stress-strain behavior of bone shows a sharp curvature, the organic phase reaches its shear yield stress value over the entire platelet. This is referred as the macroscopic yield point. It is assumed that after macroscopic yield, mineral platelets cannot contribute to the load bearing capacity of bone and that the mechanical behavior of cortical bone tissue is determined by the organic phase only. Bone fails when the principal stress of the organic matrix is reached. By assuming that mechanical properties of the organic matrix are dependent on bone mineral content below the macroscopic yield point, the model is used to predict the entire tensile mechanical behavior of cortical bone for different mineral contents. It is found that decreased shear yield stresses and organic matrix elastic moduli are required to explain the mechanical behavior of bones with lowered mineral contents. Under these conditions, the predicted values (elastic modulus, 0.002 yield stress and strain, and ultimate stress and strain) are within 15% of experimental data.

Tensile damage and its effects on cortical bone.

Plexiform bovine bone samples are repeatedly loaded in tension along their longitudinal axis. In order to induce damage in the bone tissue, bone samples are loaded past their yield point. Half of the bone samples from the damaged group were stored in saline to allow for viscoelastic recovery while the others were decalcified. Tensile tests were conducted on these samples to characterize the effects of damage on the mechanical behavior of the organic matrix (decalcified samples) as well as on bone tissue (stored in saline). The ultimate strain of the damaged decalcified bone is 29% higher compared to that of non-damaged decalcified (control) bone. The ultimate stresses as well as the elastic moduli are similar in both decalcified groups. This phenomenon is also observed in other collagenous tissue (tendon and ligament). This may suggest that damage in bone is caused by shear failure of the organic matrix; transverse separation of the collagen molecules or microfibrils from each other. In contrast, there is a trend towards lowered ultimate strains in damaged bone, which is soaked in saline, with respect to control bone samples (not damaged). The damaged bone tissue exhibits a bi-linear behavior in contrast to the mechanical behavior of non-damaged bone. The initial elastic modulus (below 55 MPa) and ultimate strength of damaged bone are similar to that in non-damaged bone.

Change in creep behavior of plexiform bone with phosphate ion treatment.

The effect of phosphate ions on the mechanical properties of plexiform bone in tension was investigated with an in-vitro model. Bone samples were treated with saline and phosphate ion solutions for three days at 25 degrees C and 37 degrees C and tested in tension. The mechanical properties of the bone samples treated with phosphate were not different than controls (saline treated). Electro kinetic measurements on plexiform bone particles treated with phosphate ions at 37 degrees C showed that phosphate ions alter electro kinetic potentials of bone particles by interacting with bone mineral as compare to saline treated particles near physiological pH. Because of the limited diffusion properties of intact plexiform bone tissue, the tension experiments indicate that, the effect of phosphate ions on the bone mineral-matrix interface is negligible after three days treatment. On the other hand, electro kinetic measurements demonstrated that in a short period of treatment time, phosphate ions diffuse through organic matrix barrier and interact with bone mineral when plexiform bone is in the particle form. As a final experiments bone samples were tested at 37 degrees C in three point bending configuration for three days in saline and phosphate buffer solution. The maximum tension stress generated in bending samples was about 75 percent of the tension yield stress of the samples. The creep experiments showed that the bending rigidity of bone samples tested in phosphate solution reduced in time hence the creep deformation increased compare to control samples tested in saline. This observation is attributed to the acceleration of phosphate ion diffusion into the bending samples due to micro cracks accumulation in bone tissue during the creep experiments which facilitated the phosphate ion interaction with bone mineral.

Effect of bone mineral content on the tensile properties of cortical bone: experiments and theory.

The effect of mineral volume fraction on the tensile mechanical properties of cortical bone tissue is investigated by theoretical and experimental means. The mineral content of plexiform, bovine bone was lowered by 18% and 29% by immersion in fluoride solutions for 3 days and 12 days, respectively. The elastic modulus, yield strength and ultimate strength of bone tissue decreased, while the ultimate strain increased with a decrease in mineral content. The mechanical behavior of bone tissue was modeled by using a micromechanical shear lag theory consisting of overlapped mineral platelets reinforcing the organic matrix. The decrease in yield stress, by the 0.002 offset method, of the fluoride treated bones were matched in the theoretical curves by lowering the shear yield stress of the organic matrix. The failure criterion used was based on failure stresses determined from a failure envelope (Mohr's circle), which was constructed using experimental data. It was found that the model predictions of elastic modulus got worse with a decrease in mineral content (being 7.9%, 17.2% and 33.0% higher for the control, 3-day and 12-day fluoride-treated bones). As a result, the developed theory could not fully predict the yield strain of bones with lowered mineral content, being 12.9% and 21.7% lower than the experimental values. The predicted ultimate stresses of the bone tissues with lower mineral contents were within +/- 10% of the experimental values while the ultimate strains were 12.7% and 26.3% lower than the experimental values. Although the model developed in this study did not take into account the presence of hierarchical structures, voids, orientation of collagen molecules and micro cracks, it still indicated that the mechanical properties of the organic matrix depend on bone mineral content.

Increased ash contents and estimation of dissolution from chemical changes due to in-vitro fluoride treatments.

The in-vitro fluoride treatment technique has been introduced to investigate the composite behavior of bone tissue. Bone tissue with different mechanical properties can be obtained by varying the concentration, pH and immersion time in fluoride ion solutions. The chemical and physical changes in intact pieces of bone treated in-vitro with different concentrations of fluoride ions are studied. The amount of bone mineral that does not contribute to the mechanical behavior of bone tissue is estimated from the dissolution occurring in the fluoride treated bones. Cortical bones from 18-month-old steers were treated in-vitro with 0.145, 0.5 and 2.0 M sodium fluoride (NaF) solutions for three days. The dissolved bone mineral precipitates as calcium fluoride-like (CaF2/P with some phosphate [P] ions) and fluorapatite(FAp)/fluorhydroxyapatite(FHAp)-like materials within the bone tissue. The dissolution estimated from the presence of the precipitated fluoride phases is 5.6, 11.7, and 13.1% of the initial bone mineral content for the 0.145 M, 0.5 M, and 2.0 M NaF treatments respectively. Estimates of dissolution based on the measurements of phosphate and carbonate ions are lower and higher respectively when compared to the fluoride ion measurements. The wet and dry densities decreased slightly due to dissolution and re-precipitation while the ash content (ratio of the ash weight to dry weight) increased a small amount with increasing concentration of fluoride ion treatments. The increased ash content was due to the excess loss of water in the fluoride treated bones as compare to controls (untreated bone samples) during the drying process. The increased removal of water during the drying process may explain the increased ash contents in some in-vivo treatments.

Changing the structurally effective mineral content of bone with in vitro fluoride treatment.

Bovine femur cortical bone specimens were tested in tension after being treated in vitro for 3 days with sodium fluoride solutions of different molarity (0.145, 0.5, and 2.0M). The treatments alter the mechanical properties of the bone samples with different degrees as compared to control samples (untreated). The mechanical properties of the treated samples have lower elastic modulus, yield and ultimate stress, acoustic impedance and hardness, and higher ultimate strain and toughness as compared to control samples. The observed effects were intensified with the increasing molarity of the treatment solutions. This study shows that the fluoride treatment can be used to investigate the composite behavior of bone tissue by altering the structurally important bone mineral content in a controlled manner.

The effects of interphase and bonding on the elastic modulus of bone: changes with age-related osteoporosis.

A simple shear lag model is developed to analyze the physics of the stress transfer between the organic and mineral constituents of bone tissue in the presence of an interphase and changes in bonding. The analytical model is developed assuming interactions between overlapped bone mineral platelets. The platelets are assumed to carry the axial stresses while the organic matrix transfers the stresses from one platelet to another by shear. A decrease in the interphase mechanical properties decreases the elastic modulus due to increased shear between the overlapped platelets. A decrease in bonding decreases the elastic modulus due to an increase in the axial stress transferred from the ends of the platelet. The implications of the changes in parameters on the age-related disorders of bone (osteoporois) are discussed. It is suggested that the aspect ratio and volume fraction of the mineral in the remaining bone tissue would increase due to a reduction in the density of the bone. The mechanical properties of the organic are hypothesized to increase due to a reduction in the density of bone leading to an increased tendency for damage within the organic.

Adaptation of passive rat left ventricle in diastolic dysfunction.

This article deals with providing a theoretical explanation for quantitative changes in the geometry, the opening angle and the deformation parameters of the rat ventricular wall during adaptation of the passive left ventricle in diastolic dysfunction. A large deformation theory is applied to analyse transmural stress and strain distribution in the left ventricular wall considering it to be made of homogeneous, incompressible, transversely isotropic, non-linear elastic material. The basic assumptions made for computing stress distributions are that the average circumferential stress and strain for the adaptive ventricle is equal to the average circumferential stress and strain in the normotensive ventricle, respectively. All the relevant parameters, such as opening angle, twist per unit length, axial extension, internal and external radii and others, in the stress-free, unloaded and loaded states of normotensive, hypertensive and adaptive left ventricle are determined. The circumferential stress and strain distribution through the ventricular wall are also computed. Our analysis predicts that during adaptation, wall thickness and wall mass of the ventricle increase. These results are consistent with experimental findings and are the indications of initiation of congestive heart failure.

Noninvasive light-reflection technique for measuring soft-tissue stretch.

A novel, to our knowledge, sensor for measuring the stretch in soft tissues such as skin is described. The technique, which is a modification of two-dimensional polarization imaging, uses changes in the reflectivity of polarized light as a monitor of skin stretch. Measurements show that the reflectivity increases with stretch. Measurements were made on guinea pig skin and on nonbiological materials. The changes in reflectivity result from the changes that take place in the interface roughness between skin or material layers and the consequential changes in the diffuse reflective characteristics of the skin. Conceptually, as the roughness of an interface decreases, a smoother reflecting interface is produced, resulting in a commensurate increase in specular reflection. A simple roughness model correctly predicts the main experimental results. Results can be extended easily to real-time stretch analysis of large tissue areas that would be applicable for predicting stresses in skin during and after the surgical closure of wounds.

Optimal patterns for suturing wounds.

A mathematical model for computing stresses in sutured human skin wounds is presented. The model uses the incremental law of elasticity and elastic constants valid for in vivo orthotropic skin. The model is applied to compute the principal stress and displacements resulting from suturing small elliptical and circular wounds in a large flat sheet of skin, in order to determine the optimal suturing patterns. It is observed that the average stress index for a circular wound sutured toward the center is almost double that of a wound sutured transverse to the diameter. Thus, the latter type of suturing pattern is preferable. Similarly, suturing an elliptical wound transversely produces a lower average stress index than a circular wound of the same area. It is also found that the optimal ratio of semi-major to semi-minor axis of an elliptical wound is near 3 (for abdominal wounds), i.e., this ratio produces the most uniform stresses along the wound edges, where wound healing is slowest. Since high stresses have adverse effects on healing and blood flow, this work, depicting regions of high stresses, may be used along with other biological factors to help predict regions of slower healing in sutured wounds.

Varying the mechanical properties of bone tissue by changing the amount of its structurally effective bone mineral content.

The effect of fluoride ions on the mechanical properties of bone tissue in tension was investigated with an in vitro model. Structurally effective Bone Mineral Content (BMC) of bovine bone tissue was changed by fluoride ion treatment. First, bovine cortical bone specimens were treated with a detergent solution in order to increase the diffusion rates of the treatment ions across the samples. After the initial treatment, different ion solutions were used to treat the tension samples (fluoride, sodium and chloride). Ionic strength and pH were varied. Experimental results showed that the sodium chloride solutions of different ionic strengths, at physiological and high pH, do not affect the mechanical properties of bone tissue in tension. However, uniform fluoride treatment across the samples reduced the mechanical strength of bone tissue by converting small amounts of bone mineral to mostly calcium fluoride. This action reduces the structurally effective BMC and also possibly effects the interface bonding between the bone mineral and the organic matrix of the bone tissue.

The effect of in vitro fluoride ion treatment on the ultrasonic properties of cortical bone.

The mechanical properties of composites are influenced, in part, by the volume fraction, orientation, constituent mechanical properties, and interfacial bonding. Cortical bone tissue represents a short-fibered biological composite where the hydroxyapatite phase is embedded in an organic matrix composed of type I collagen and other noncollagenous proteins. Destructive mechanical testing has revealed that fluoride ion treatment significantly lowers the Z-axis tensile and compressive properties of cortical bone through a constituent interfacial debonding mechanism. The present ultrasonic data indicates that fluoride ion treatment significantly alters the longitudinal velocity in the Z-axis as well as the circumferential and radial axes of cortical bone. This suggests that the distribution of constituents and interfacial bonding amongst them may contribute to the anisotropic nature of bone tissue.

Effect of electromagnetic stimulation with different waveforms on cultured chick tendon fibroblasts.

An energy efficient electromagnetic stimulator device for fracture healing was compared to a commercially available device in stimulating cell growth in tissue cultures. The energy efficient device, which conserves energy by using a bidirectional time-dependent magnetic wave form, and the commercially available stimulator, which uses a unidirectional time-dependent magnetic wave form, were tested on chick tendon fibroblasts in primary culture. Comparing non-stimulated control and cells electromagnetically stimulated with unidirectional and bidirectional waveforms showed that at the growth phase between days 2 and 3, both electrical stimulation techniques increased cell division as measured by DNA synthesis. When cells were dividing rapidly, collagen synthesis was reduced. When the cells reached the confluence there was no difference among the groups (control, unidirectionally stimulated, and bidirectionally stimulated) in terms of number of cells or collagen produced.

Compressive properties of cortical bone: mineral-organic interfacial bonding.

Bone tissue is an anisotropic non-homogeneous composite material composed of inorganic, bone mineral fibres (hydroxyapatite) embedded in an organic matrix (type I collagen and non-collagenous proteins). Factors contributing to the overall mechanical behaviour include constituent volume fraction, mechanical properties, orientation and interfacial bonding interactions. Interfacial bonding between the mineral and organic constituents is based, in part, on electrostatic interactions between negatively charged organic domains and the positively charged mineral surface. Phosphate and fluoride ions have been demonstrated to alter mineral-organic interactions, thereby influencing the mechanical properties of bone in tension. The present study explores the effects of phosphate and fluoride ions on the compressive properties of cortical bone.

Ion concentration effects on bone streaming potentials and zeta potentials.

Electrical potentials are dependent on the properties of the solid and fluid phases of bone. The solid phase in bone is composed of an organic matrix and inorganic bone mineral fibre, while the fluid phase is separated into compartments associated with the vascular channel system and mineralized matrix. Recently, a piezoelectric and electrokinetic response following mechanical deformation was demonstrated in fully hydrated bone. However, alterations in the fluid phase and the effects on streaming potentials where flow through the sample due to pressure on the fluid phase without prior solid matrix mechanical deformation have not been examined. Streaming potentials in high ionic strength solutions reveal a flow-dependent streaming potential in the absence of mechanical deformation not previously observed in stress-generated potentials. Streaming potentials in high ionic strength sodium chloride solutions (0.75 M) of control and deproteinized samples suggest that organic molecules and ions in the electrical double layer may be susceptible to flow-induced alterations which can modify the streaming potentials generated. Alterations in properties of the fluid phase can modify the streaming and zeta potentials and may play a role in the biofeedback response to bone tissue.

The role of ions and mineral-organic interfacial bonding on the compressive properties of cortical bone.

Bone tissue is a composite material composed of an inorganic stiff mineral phase embedded in a compliant organic matrix. Similar to other composites, the mechanical properties of bone depend upon the properties, volume fraction, and orientation of its constituents as well as the bonding interactions. Interfacial bonding between the mineral and organic constituents are based, in part, on electrostatic interactions between negatively charged organic domains and positively charged mineral surface. Phosphate and fluoride ions can alter mineral-organic interfacial causing a permutation in the mechanical properties. Partial debonding between the mineral and organic constituents of bone may play an important role in the mechanical properties of aged and diseased bone. The present study examines the effects of phosphate and fluoride ion treatment on the compression properties of cortical bone and the reversibility of the effect.

Electrokinetic behavior of intact wet bone: compartmental model.

Streaming potential experiments were performed on chemically-treated intact wet bone plugs equilibrated in potential-determining ion buffers. Comparison of calculated zeta (zeta) potentials from intact wet bone streaming potentials and bone particle electrophoresis indicates different values. Intact streaming potential experiments, where fluid is forced through the samples, represents flow, primarily through the vascular channel system, and contribution of the organically-lined channels to the electrokinetic zeta potential. Bone particle electrophoresis represents mainly the electrokinetic contribution of exposed mineralized matrix. The organic linings present in the vascular channel system limit potential-determining ions' access to the mineralized matrix. These linings may have an important role in mineral homeostasis and control of ion fluxes between bone compartments.