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.     

Streaming potential of intact wet bone

The conversion of mechanical loads to bioelectrical signals in bone have been suggested to control repair and remodeling. These signals in wet bone are attributed to the electrokinetic behavior where mechanical forces cause electrical signals due to motion of an ion carrying extracellular fluid in the bone matrix (streaming potentials). Streaming potential experiments were performed on control and chemically treated intact wet bone plugs in aphosphate and phosphate buffers to examine the contribution of bone constituents to the electrokinetic behavior of bone tissue. Data indicate that the organic constituents of bone dominate streaming potentials. Slopes of streaming potential vs pressure are related to the electrokinetic (zeta) potential. The slopes should be analyzed in the low pressure region where data is mainly linear. Comparisons of estimated zeta potentials from streaming potentials with existing data obtained by particle electrophoresis showed similar trends.     

Electromechanical potentials in cortical bone--II. Experimental analysis

The electrokinetic model developed in Part 1 of this paper is used to characterize the electromechanical effect in cortical bone. Low frequency characteristics of stress-generated potentials are measured to provide insight into the origin and generation of these potentials induced in fluid-filled cortical bone. The results support the proposed model and indicate that fluid movement within the microporosity of bone is responsible for observed potentials whose origin is electrokinetic. The microporosity in bone, composed of the fluid spaces in and around mineral crystals encrusting collagen fibrils, constitutes an enormous surface area and appears to dominate surface-related phenomena at low frequencies. Previous experimental results, reported by many researchers, are also supported by this mechanism.     

Electromechanical potentials in cortical bone--I. A continuum approach

An electrokinetic model to characterize the electromechanical effect in cortical bone has been developed using the basic principles of the biphasic theory of porous materials and a simple model for permeability and charge distribution for cortical bone. The model is developed analytically in Part I of this paper and is shown to account qualitatively for the principal experimental results reported to date. Part II of this paper concerns experimental analysis of this model, reporting results of low frequency testing of the dynamic characteristics of stress-generated potentials. Quantitative analysis of these results indicates that the microporosity of bone, made up of the channels around the hydroxyapatite encrusting the collagen matrix, is the compartment responsible for the electromechanical effects in fluid-saturated cortical bone. This microporous compartment would seem to be the obvious source of the electrokinetic effect, because it has the greatest surface area in bone and constitutes the rate limiting fluid flow compartment in deformation-induced fluid flow at low frequency.     

Cartilage electromechanics--I. Electrokinetic transduction and the effects of electrolyte pH and ionic strength

Articular cartilage contains a high fixed charge density under physiological conditions associated primarily with the ionized proteoglycan molecules of the extracellular matrix. Oscillatory compression of cartilage using physiological loads produces electrical potentials that have been shown previously to be the result of an electrokinetic (streaming) transduction mechanism. We have now observed two additional electromechanical phenomena not previously seen in cartilage or other soft tissues: 'streaming current' and 'current-generated stress'. Sinusoidal mechanical compression induced a sinusoidal streaming current density through cartilage disks when the Ag/AgCl electrodes that were used to compress the cartilage were shorted together externally. Conversely, a sinusoidal current density applied to the tissue generated a sinusoidal mechanical stress within the tissue. Both these phenomena were found to be consistent with the same electrokinetic transduction mechanism responsible for the streaming potential. Changes in the measured streaming potential response that resulted from modification of bath ionic strength and pH have provided additional insights into the molecular origins of these transduction processes. Finally, we have now observed streaming potentials in living cartilage maintained in organ culture, as well as in previously frozen tissue.     

Comprehensive Analysis of Human Cells Motion under an Irrotational AC Electric Field in an Electro-Microfluidic Chip

AC electrokinetics is a versatile tool for contact-less manipulation or characterization of cells and has been widely used for separation based on genotype translation to electrical phenotypes. Cells responses to an AC electric field result in a complex combination of electrokinetic phenomena, mainly dielectrophoresis and electrohydrodynamic forces. Human cells behaviors to AC electrokinetics remain unclear over a large frequency spectrum as illustrated by the self-rotation effect observed recently. We here report and analyze human cells behaviors in different conditions of medium conductivity, electric field frequency and magnitude. We also observe the self-rotation of human cells, in the absence of a rotational electric field. Based on an analytical competitive model of electrokinetic forces, we propose an explanation of the cell self-rotation. These experimental results, coupled with our model, lead to the exploitation of the cell behaviors to measure the intrinsic dielectric properties of JURKAT, HEK and PC3 human cell lines.     

Molecular dynamics simulations of concentrated aqueous electrolyte solutions

Transport properties of concentrated electrolytes have been analysed using classical molecular dynamics simulations with the algorithms and parameters typical of simulations describing complex electrokinetic phenomena. The electrical conductivity and transport numbers of electrolytes containing monovalent (KCl), divalent (MgCl₂), a mixture of both (KCl+MgCl₂) and trivalent (LaCl₃) cations have been obtained from simulations of the electrolytes in electric fields of different magnitude. The results obtained for different simulation parameters have been discussed and compared with experimental measurements of our own and from the literature. The electroosmotic flow of water molecules induced by the ionic current in different cases has been calculated and interpreted with the help of the hydration properties extracted from the simulations.     

An application of nanoindentation technique to measure bone tissue Lamellae properties

Measuring the microscopic mechanical properties of bone tissue is important in support of understanding the etiology and pathogenesis of many bone diseases. Knowledge about these properties provides a context for estimating the local mechanical environment of bone related cells thait coordinate the adaptation to loads experienced at the whole organ level. The objective of this study was to determine the effects of experimental testing parameters on nanoindentation measures of lamellar-level bone mechanical properties. Specifically, we examined the effect of specimen preparation condition, indentation depth, repetitive loading, time delay, and displacement rate. The nanoindentation experiments produced measures of lamellar elastic moduli for human cortical bone (average value of 17.7 +/- 4.0 GPa for osteons and 19.3 +/- 4.7 GPa for interstitial bone tissue). In addition, the hardness measurements produced results consistent with data in the literature (average 0.52 +/- 0.15 GPa for osteons and 0.59 +/- 0.20 GPa for interstitial bone tissue). Consistent modulus values can be obtained from a 500-nm-deep indent. The results also indicated that the moduli and hardnesses of the dry specimens are significantly greater (22.6% and 56.9%, respectively) than those of the wet and wet and embedded specimens. The latter two groups were not different. The moduli obtained at a 5-nm/s loading rate were significantly lower than the values at the 10- and 20-nm/s loading rates while the 10- and 20-nm/s rates were not significantly different. The hardness measurements showed similar rate-dependent results. The preliminary results indicated that interstitial bone tissue has significantly higher modulus and hardness than osteonal bone tissue. In addition, a significant correlation between hardness and elastic modulus was observed.     

ELECTROKINETIC PHENOMENA : IV. A COMPARISON OF ELECTROPHORETIC AND STREAMING POTENTIALS

1. The conditions are described which are necessary for the comparison of certain types of electrokinetic potentials. An experimental comparison is made of (a) electrophoresis of quartz particles covered with egg albumin; and (b) similar experiments by Briggs on streaming potentials. A slight, consistent, difference is found between the electrophoretic potential and the streaming potential. This difference is probably due to the difference in the protein preparations used rather than to real difference in the electrophoretic and streaming potentials. 2. Data are given which facilitate the measurements and enhance the precision of the estimation of electrical mobilities of microscopic particles.     

Numerical simulation of deformations and electrical potentials in a cartilage substitute

Cartilage exhibits a swelling and shrinking behaviour that influences the function of the cells inside the tissue. This behaviour is caused by mechanical, chemical and electrical loads. It is described by the electrochemomechanical mixture theory, in which the tissue is represented by four components: a charged porous solid, a fluid, cations and anions. By distinguishing between the cations and anions, electrical phenomena can be modelled. This mixture theory is verified by fitting the deformations and the electrical potentials in a uniaxial confined swelling and compression experiment to a mixed finite element simulation. The fitted stiffness, permeability, diffusion coefficients, and osmotic coefficients are in the same range as reported in literature.     

Determination of mechanical properties of human femoral cortical bone by the Hopkinson bar stress technique

The Hopkinson bar stress technique and a universal testing machine (Instron 1125) have been used to investigate the dynamic and static mechanical properties of cortical bone taken from a human femur respectively. We found that the average dynamic Young's modulus value (Ed = 19.9 GPa) to be 23% higher than the average static Young's modulus value (Ed = 16.2 GPa). Furthermore, the Poisson's ratio did not exhibit any significant variation for the two different types of loading. No difference was observed between the values of the dynamic Young's modulus in tension and those found in compression. A comparison was made of the results of this study with those found by other researchers using different techniques, such as ultrasonics, and it was found that they agree well with most of the results of previous studies. Finally, the viscosity for cortical bone found in this study correlates with viscosity reported by Tennyson et al. [Expl Mech. 12, 502-507 (1972)] for ten days post mortem age specimens.     

Cartilage electromechanics--II. A continuum model of cartilage electrokinetics and correlation with experiments

We have formulated a continuum model for linear electrokinetic transduction in cartilage. Expressions are derived for the streaming potential and streaming current induced by oscillatory, uniaxial confined compression of the tissue, as well as the mechanical stress generated by a current density or potential difference applied to the tissue. The experimentally observed streaming potential and current-generated stress response, measured on the same specimens, are compared with the predictions of the theory over a wide frequency range. The theory compares well with the data for reasonable values of cartilage intrinsic mechanical parameters and electrokinetic coupling coefficients. Experiments also show a linear relationship between the stimulus amplitude and the transduction response amplitude, within the range of stimulus amplitudes of interest. This observation is shown to be consistent with the predictions of the linear theory.     

The origin of electrokinetic potentials in bone tissue: the organic phase

The purpose of this study was to determine the relative contributions of the organic and mineral phases of cow cortical bone to its electrokinetic response at room temperature. The technique of particle electrophoresis permitted electrokinetic (zeta) potentials to be calculated and plotted as a function of pH. Control and demineralized bone particles exhibited similar isoelectric points at pH approximately 5.1 (pH at which the zeta potential is zero), well below the isoelectric point of the bone mineral (pH approximately 8.6). In addition, the use of phosphate-containing buffers resulted in a zeta potential sign reversal of the bone mineral but had no effect on both the control and demineralized bone. These key results form the basis from which we suggest that the bone mineral lies within the organic phase (e.g., the mineral is not exposed to the fluid phase) and that the electrokinetic behavior of bone tissue is dominated by its organic ultrastructure.     

The mechanical properties of cranial bone: The effect of loading rate and cranial sampling position

Linear and depressed skull fractures are frequent mechanisms of head injury and are often associated with traumatic brain injury. Accurate knowledge of the fracture of cranial bone can provide insight into the prevention of skull fracture injuries and help aid the design of energy absorbing head protection systems and safety helmets. Cranial bone is a complex material comprising of a three-layered structure: external layers consist of compact, high-density cortical bone and the central layer consists of a low-density, irregularly porous bone structure.In this study, cranial bone specimens were extracted from 8 fresh-frozen cadavers (F=4, M=4; 81±11 years old). 63 specimens were obtained from the parietal and frontal cranial bones. Prior to testing, all specimens were scanned using a μCT scanner at a resolution of 56.9 μm. The specimens were tested in a three-point bend set-up at different dynamic speeds (0.5, 1 and 2.5 m/s). The associated mechanical properties that were calculated for each specimen include the 2nd moment of inertia, the sectional elastic modulus, the maximum force at failure, the energy absorbed until failure and the maximum bending stress. Additionally, the morphological parameters of each specimen and their correlation with the resulting mechanical parameters were examined.It was found that testing speed, strain rate, cranial sampling position and intercranial variation all have a significant effect on some or all of the computed mechanical parameters. A modest correlation was also found between percent bone volume and both the elastic modulus and the maximum bending stress.     

Mechanical properties of single bovine trabeculae are unaffected by strain rate

For a better understanding of traumatic bone fractures, knowledge of the mechanical behavior of bone at high strain rates is required. Importantly, it needs to be clarified how quasistatic mechanical testing experiments relate to real bone fracture. This merits investigating the mechanical behavior of bone with an increase in strain rate. Various studies examined how cortical and trabecular bone behave at varying strain rates, but no one has yet looked at this question using individual trabeculae. In this study, three-point bending tests were carried out on bovine single trabeculae excised from a proximal femur to test the trabecular material's strain rate sensitivity. An experimental setup was designed, capable of measuring local strains at the surface of such small specimens, using digital image correlation. Microdamage was detected using the bone whitening effect. Samples were tested through two orders of magnitude, at strain rates varying between 0.01 and 3.39 s(-1). No linear relationship was observed between the strain rate and the Young's modulus (1.13-16.46 GPa), the amount of microdamage, the maximum tensile strain at failure (14.22-61.65%) and at microdamage initiation (1.95-12.29%). The results obtained in this study conflict with previous studies reporting various trends for macroscopic cortical and trabecular bone samples with an increase in strain rate. This discrepancy might be explained by the bone type, the small sample geometry, the limited range of strain rates tested here, the type of loading and the method of microdamage detection. Based on the results of this study, the strain rate can be ignored when modeling trabecular bone.     

Tensile and compressive properties of cancellous bone

The relationship between the mechanical properties of trabecular bone in tension and compression was investigated by non-destructive testing of the same specimens in tension and compression, followed by random allocation to a destructive test in either tension or compression. There was no difference between Young's modulus in tension and compression, and there was a strong positive correlation between the values (R = 0.97). Strength, ultimate strain and work to failure was significantly higher in tensile testing than in compressive testing.     

Analysis of compressive creep behavior of the vertebral unit subjected to a uniform axial loading using exact parametric solution equations of Kelvin-solid models--Part II. Rhesus monkey intervertebral joints

The simulation of long-term creep response behavior, observed on 54 Rhesus monkey intervertebral joints subjected to a constant axial compressive stress, is attempted by two- and three-parameter-solid models utilizing the Burns- Kaleps 'exact analysis scheme'. Model parameters identified by the analysis of each specimen's experimental strain data were optimized via a computer program and the mechanical properties (Young's moduli and the viscosity coefficient) appropriate to each model were calculated for individual spinal segments. Simulation results for the two-parameter-solid (one- Kelvin -unit) model demonstrate its general ineptness in predicting the observed strain-time behavior of normal spinal sements . The three-parameter-solid model yielded excellent results in the simulation of observed spinal segment compressive creep phenomena. It produced an average error between the model predicted and experimental strain values that ranged from a low of 0.4000% to a high of 3.290% for the 54 Rhesus monkey intervertebral joints, with a collective average error for all specimens of only 1.363%.     

Analysis of Bone Remodeling Under Piezoelectricity Effects Using Boundary Elements

Piezoelectric materials exhibit a response to mechanical-electrical coupling,which represents an important contribution to the electrical-mechanical interaction in bone remodeling process.Therefore,the study of the piezoelectric effect on bone remodeling has high interest in applied biomechanics.The effects of mechano-regulation and electrical stimulation on bone healing are explained.The Boundary Element Method (BEM) is used to simulate piezoelectric effects on bones when sheafing forces are applied to collagen fibers to make them slip past each other.The piezoelectric fundamental solutions are obtained by using the Radon transform.The Dual Reciprocity Method (DRM) is used to simulate the particular solutions in time-dependent problems.BEM analysis showed the strong influence of electrical stimulation on bone remodeling.The examples discussed in this work showed that,as expected,the electrically loaded bone surfaces improved the bone deposition.BEM results confirmed previous findings obtained by using the Finite Element Method (FEM).This work opens very promising doors in biomechanics research,showing that mechanical loads can be replaced,in part,by electrical charges that stimulate strengthening bone density.The obtained results herein are in good agreement with those found in literature from experimental testing and/or other simulation approaches.     

Apparent Young's modulus of human radius using inverse finite-element method

The ability to assess the elastic and failure properties of cortical bone at the radial diaphysis has a clinical importance. A new generation of quantitative ultrasound (QUS) devices and peripheral quantitative computed tomography (p-QCT) has been developed to assess non-invasively bone material and structural properties at the distal radius. This anatomical site is characterized by a thin cortical thickness that complicates traditional mechanical testing methods on specimens. Until now, mechanical properties of cortical bone at distal radius (e.g., elastic modulus, yield stress and strain) remain rarely studied probably due to experimental difficulties. The present study introduces an inverse finite-element method strategy to measure the elastic modulus and yield properties of human cortical specimens of the radial diaphysis. Twenty millimeter-thick portions of diaphysis were cut from 40 human radii (ages 45-90) for biomechanical test. Subsequently the same portion was modeled in order to obtain a specimen-specific three dimensional finite-element model (3D-FEM). Longitudinal elastic constants at the apparent level and stress characterizations were performed by coupling mechanical parameters with isotropic linear-elastic simulations. The results indicated that the mean apparent Young's modulus for radial cortical bone was 16 GPa (SD 1.8) and the yield stress was 153 MPa (SD 33). Breaking load was 12,946 N (SD 3644), cortical thickness 2.9 mm (SD 0.6), structural effective strain at the yield (epsilon(y)=0.0097) and failure (epsilon(u)=0.0154) load were also calculated. The 3D-FEM strategy described here may help to investigate bone mechanical properties when some difficulties arise from machining mechanical sample.     

Non-invasive assessment of failure torque in rat bones with simulated lytic lesions using computed tomography based structural rigidity analysis

This study applies CT-based structural rigidity analysis (CTRA) to assess failure torque of rat femurs with simulated lytic defects at different locations (proximal and distal femur) and diameters (25% and 50% of the cross-section at the site), and compared the results to those obtained from mechanical testing. Moreover, it aims to compare the correlation coefficients between CTRA-based failure torque and DXA-based aBMD versus actual failure torque. Twenty rats were randomly assigned to four equal groups of different simulated lesions based on size and location. Femurs from each animal underwent micro-computed tomography to assess three-dimensional micro-structural data, torsional rigidity using structural rigidity analysis and dual energy X-ray absorptiometry to assess bone mineral density. Following imaging, all specimens were subjected to torsion. Failure torque predicted from CT-derived structural rigidity measurements was better correlated with mechanically derived failure torque [R(2)=0.85] than was aBMD from DXA [R(2)=0.32]. In summary, the results of this study suggest that computed tomography based structural rigidity analysis can be used to accurately and quantitatively measure the mechanical failure torque of bones with osteolytic lesions in an experimental rat model. Structural rigidity analysis can provide more accurate predictions on maximal torque to mechanical failure than dual energy X-ray absorptiometry based on bone mineral density.