Mechanical properties of soft human tissues under dynamic loading

The dynamic response of soft human tissues in hydrostatic compression and simple shear is studied using the Kolsky bar technique. We have made modifications to the technique that allow loading of a soft tissue specimen in hydrostatic compression or simple shear. The dynamic response of human tissues (from stomach, heart, liver, and lung of cadavers) is obtained, and analyzed to provide measures of dynamic bulk modulus and shear response for each tissue type. The dynamic bulk response of these tissues is easily described by a linear fit for the bulk modulus in this pressure range, whereas the dynamic shearing response of these tissues is strongly non-linear, showing a near exponential growth of the shear stress.     

Estimates of the peak pressures in bone pore water.

The maximum pore fluid pressures due to uniaxial compression are determined for both the vascular porosity (Haversian and Volkmann's canals) and the lacunar-canalicular porosity of live cortical bone. It is estimated that the peak pore water pressure will be 19 percent of the applied axial stress in the vascular porosity and 12 percent of the applied axial stress in the lacunar-canalicular porosity for an impulsive step loading. However, the estimated relaxation time for the vascular porosity (1.36 microseconds) is three orders of magnitude faster than that estimated for the lacunar-canalicular porosity (4.9 ms). Thus, under physiological loading, which has a stress rise time generally larger than 1 ms, pressures higher than the vascular pressure cannot be sustained in the vascular porosity due to the swift pressure relaxation in this porosity (unless the fluid drainage through the boundary is obstructed). The model also predicts a slight hydraulic stiffening of the bulk modulus due to longer draining time of the lacunar-canalicular porosity. The undrained bulk modulus is 6 percent higher than the drained bulk modulus in this case.     

Propagation of stress waves in inflated sheep lungs

If the lung is an elastic continuum, both longitudinal and transverse stress waves should be propagated in the medium with distinct velocities. In five isolated sheep lungs, we investigated the propagation of stress waves. The lungs were degassed and then inflated to a constant transpulmonary pressure (Ptp). We measured signals transmitted at locations approximately 1.5, 6, and 11 cm from an impulse surface distortion with the use of small microphones embedded in the pleural surface. Two transit times were computed from the first two significant peaks of the cross-correlation of microphone signal pairs. The "fast" wave velocities averaged 301 +/- 92, 445 +/- 80, and 577 +/- 211 (SD) cm/s for Ptp values of 5, 10, and 15 cmH2O, respectively. Corresponding "slow" wave velocities averaged 139 +/- 22, 217 +/- 36, and 255 +/- 89 cm/s. The fast waves were consistent with longitudinal waves of velocity [(K + 4G/3)/p]1/2, where bulk modulus K = 4 Ptp and shear modulus G = 0.7 Ptp. The slow waves were consistent with transverse (and/or Rayleigh) waves of velocity (G/p)1/2, with a G value of 0.9 Ptp. Measured values of K were 5 Ptp and values of G measured by indentation tests were 0.7 Ptp. Thus, stress wave velocities measured on pleural surface of isolated lungs correlated well with elastic moduli of lung parenchyma.     

A mechanical model representation of the in vivo creep behaviour of muscular bulk tissue

In vivo mechanical properties of bulk tissue have not yet been explored sufficiently. One of the major problems researchers face is the lack of agreement between the constitutive models and the standardised methodologies for experimental studies. The object of this study was to obtain bulk modulus of the upper arm under relaxed and controlled contraction that was 25% of the maximum voluntary contraction. A new testing machine was designed to generate constant load on the upper arm and measure the deformation over time. This device is effectively a cuff that applies controllable pressure on a 47-mm wide band of the upper arm. Six different loads (10, 20, 30, 40, 50 and 60 kgf) were applied over a time of up to a maximum of 120 s. The deflection-time curves obtained show strongly non-linear responses of the bulk tissue. The non-linearity manifested by these deflection-time curves is in terms of both time- and load-dependency. A specific mechanical model was developed to represent the creep behaviour of the bulk tissue. The creep behaviour of the upper arm can be simulated by using four Voigt viscoelastic models in series. The three obvious soft tissues of the upper arm, namely skin, fat and muscle, were modelled in series. The effects of blood vessels and connective tissue were also modelled in series with the previous ones. A mechanical model would provide a more controlled method of studying the mechanical properties of the bulk tissue. The purpose of the current research, therefore, was to develop a mechanical model, which would predict the non-linear, viscoelastic behaviour of the human muscular bulk tissue.     

The relative contribution of elastic and osmotic adjustments to turgor maintenance of woody species.

To determine how tissue water relations vary and contribute to turgor maintenance in species from contrasting ecological zones, seedlings of jack pine ( Pinus banksiana Lamb.), black spruce ( Picea mariana [Mill] B.S.P.) and flooded gum ( Eucalyptus grandis W. Hill ex Maiden) were subjected to an 8 day drought stress by water withholding with and without prior mild water stress conditioning. Jack pine, a deep-rooted species from dry, sandy boreal sites, lost turgor at the lowest relative water content (75–65%) and water potential, and had lowest maximum bulk elastic modulus (E_max of 5.2–5.8 MPa). Although this suggests a high inherent dehydration tolerance, jack pine did not further adjust its elasticity when repeatedly stressed. Black spruce, a shallow-rooted species from predominantly moist sites in the boreal region, lost turgor at intermediate relative water content (86–76%) and water potential, but could adjust its elasticity to maintain turgor in repeatedly stressed tissues. Flooded gum, a deep-rooted species from moist, warm temperate-subtropical regions, had a low inherent drought tolerance since it lost turgor at higher relative water content (88–84%) and water potential, but was capable of some adjustment when the stress was repeated. Elastic adjustment (<3.7 MPa) was more important for turgor maintenance than osmotic adjustment (<0.13 MPa), which was statistically nonsignificant. Maximum bulk modulus of elasticity, but not osmotic potentials at full turgor, was significantly correlated with the relative water content and water potential at zero turgor in droughted seedlings. These results highlight the importance of tissue shrinkage for dehydration tolerance. Both the inherent capacity for turgor maintenance of a species under drought and its ability to adjust to repeated drought should be considered in genetic selections for drought tolerance.     

Heel-shoe interactions and the durability of EVA foam running-shoe midsoles

A finite element analysis (FEA) was made of the stress distribution in the heelpad and a running shoe midsole, using heelpad properties deduced from published force-deflection data, and measured foam properties. The heelpad has a lower initial shear modulus than the foam (100 vs. 1050 kPa), but a higher bulk modulus. The heelpad is more non-linear, with a higher Ogden strain energy function exponent than the foam (30 vs. 4). Measurements of plantar pressure distribution in running shoes confirmed the FEA. The peak plantar pressure increased on average by 100% after 500 km run. Scanning electron microscopy shows that structural damage (wrinkling of faces and some holes) occurred in the foam after 750 km run. Fatigue of the foam reduces heelstrike cushioning, and is a possible cause of running injuries.     

Use of simultaneous pressure and velocity measurements to estimate arterial wave speed at a single site in humans

It has not been possible to measure wave speed in the human coronary artery, because the vessel is too short for the conventional two-point measurement technique used in the aorta. We present a new method derived from wave intensity analysis, which allows derivation of wave speed at a single point. We apply this method in the aorta and then use it to derive wave speed in the human coronary artery for the first time. We measured simultaneous pressure and Doppler velocity with intracoronary wires at the left main stem, left anterior descending and circumflex arteries, and aorta in 14 subjects after a normal coronary arteriogram. Then, in 10 subjects, serial measurements were made along the aorta before and after intracoronary isosorbide dinitrate. Wave speed was derived by two methods in the aorta: 1) the two-site distance/time method (foot-to-foot delay of pressure waveforms) and 2) a new single-point method using simultaneous pressure and velocity measurements. Coronary wave speed was derived by the single-point method. Wave speed derived by the two methods correlated well (r = 0.72, P < 0.05). Coronary wave speed correlated with aortic wave speed (r = 0.72, P = 0.002). After nitrate administration, coronary wave speed fell by 43%: from 16.4 m/s (95% confidence interval 12.6-20.1) to 9.3 m/s (95% confidence interval 6.5-12.0, P < 0.001). This single-point method allows determination of wave speed in the human coronary artery. Aortic wave speed is correlated to coronary wave speed. Finally, this technique detects the prompt fall in coronary artery wave speed with isosorbide dinitrate.     

Shear wave elastography can assess the in-vivo nonlinear mechanical behavior of heel-pad

This study combines non-invasive mechanical testing with finite element (FE) modelling to assess for the first time the reliability of shear wave (SW) elastography for the quantitative assessment of the in-vivo nonlinear mechanical behavior of heel-pad. The heel-pads of five volunteers were compressed using a custom-made ultrasound indentation device. Tissue deformation was assessed from B-mode ultrasound and force was measured using a load cell to calculate the force – deformation graph of the indentation test. These results were used to design subject specific FE models and to inverse engineer the tissue’s hyperelastic material coefficients and its stress – strain behavior. SW speed was measured for different levels of compression (from 0% to 50% compression). SW speed for 0% compression was used to assess the initial stiffness of heel-pad (i.e. initial shear modulus, initial Young’s modulus). Changes in SW speed with increasing compressive loading were used to quantify the tissue’s nonlinear mechanical behavior based on the theory of acoustoelasticity. Statistical analysis of results showed significant correlation between SW-based and FE-based estimations of initial stiffness, but SW underestimated initial shear modulus by 64%(±16). A linear relationship was found between the SW-based and FE-based estimations of nonlinear behavior. The results of this study indicate that SW elastography is capable of reliably assessing differences in stiffness, but the absolute values of stiffness should be used with caution. Measuring changes in SW speed for different magnitudes of compression enables the quantification of the tissue’s nonlinear behavior which can significantly enhance the diagnostic value of SW elastography.     

Effects of aging on cardiac and skeletal muscle AMPK activity: basal activity, allosteric activation, and response to in vivo hypoxemia in mice

Although a diminished ability of tissues and organisms to tolerate stress is a clinically important hallmark of normal aging, little is known regarding its biochemical basis. Our goal was to determine whether age-associated changes in AMP-activated protein kinase (AMPK), a key regulator of cellular metabolism during the stress response, might contribute to the poor stress tolerance of aged cardiac and skeletal muscle. Basal AMPK activity and the degree of activation of AMPK by AMP and by in vivo hypoxemia (arterial Po2 of 39 mmHg) were measured in cardiac and skeletal muscle (gastrocnemius) from 5- and 24-mo-old C57Bl/6 mice. In the heart, neither basal AMPK activity nor its allosteric activation by AMP was affected by age. However, after 10 min of hypoxemia, the activity of alpha2-AMPK, but not alpha1-AMPK, was significantly higher in the hearts from old than from young mice (P < 0.005), this difference being due to differences in phosphorylation of alpha2-AMPK. Significant activation of AMPK in the young hearts did not occur until 30 min of hypoxemia (P < 0.01), stress that was poorly tolerated by the old mice (mortality = 67%). In contrast, AMPK activity in gastrocnemius muscle was unaffected by age or hypoxemia. We conclude that the age-associated decline in hypoxic tolerance in cardiac and skeletal muscle is not caused by changes in basal AMPK activity or a blunted AMPK response to hypoxia. Activation of AMPK by in vivo hypoxia is slower and more modest than might be predicted from in vitro and ex vivo experiments.     

Physiological demands of competitive surfing

This study was a performance analysis of surfing athletes during competitive surfing events in an attempt to inform the development of surfing-specific conditioning. Twelve nationally ranked surfers were fitted with heart rate (HR) monitors and global positioning system (GPS) units and videoed during the heats of 2 sanctioned competitions. Means and SDs represented the centrality and spread of analyzed data. From the 32 videos analyzed, the greatest amount of time spent during surfing was paddling (54 ± 6.3% of the total time) (% TT). The remaining stationary represented 28 ± 6.9% TT, wave riding, and paddling for a wave represented only 8 ± 2% TT and 4 ± 1.5% TT, respectively. Surfers spent 61 ± 7% of the total paddling bouts and 64 ± 6.8% of total stationary bouts between 1 and 10 seconds. The average speed recorded via the GPS for all the subjects was 3.7 ± 0.6 km·h(-1), with an average maximum speed of 33.4 ± 6.5 km·h(-1) (45 km·h(-1) was the highest speed recorded). The average distance covered was 1,605 ± 313 m. The mean HR during the surf competitions was 139 ± 11 b·min(-1) (64% HRmax), with a (mean) peak of 190 ± 12 b·min(-1) (87% HRmax). Sixty percent TT was spent between 56 and 74% of the age-predicted HR maximum (HRmax), 19% TT >46% HRmax, and approximately 3% TT >83% HRmax. Competitive surfing therefore involves intermittent high-intensity bouts of all out paddling intercalated with relatively short recovery periods and repeated bouts of low-intensity paddling, incorporating intermittent breath holding. Surfing-specific conditioning sessions should attempt to replicate such a profile.     

Direct observation of intraparticle equilibration and the rate-limiting step in adsorption of proteins in chromatographic adsorbents with confocal laser scanning microscopy

The adsorption of different proteins in a single biospecific and hydrophobic adsorbent particle for preparative protein chromatography has been observed directly by confocal laser scanning microscopy as a function of time at a constant bulk concentration c(b). The bulk concentration was in the non-linear part of the adsorption isotherm. At all times the concentration of free protein at the particle surface was almost equal to the bulk content indicating that external mass transfer resistance is not rate limiting for the adsorption under these conditions. Inside the particles a distinct maximum in adsorbed and free protein concentration that moved inside to a distance of approximately 0.2 R (R particle radius) from the particle surface, was observed. This is due to a decreasing solid-phase density and adsorptive capacity in the particle between 0.8 R and R indicating that the fraction of macropores (or void space) is larger in the outer than in the inner part of the adsorbent particles. By increasing the bulk concentration by a factor of 10 the equilibration time was reduced by about the same magnitude. This is in agreement with the concentration dependence of the effective pore diffusion coefficient D(p,eff)=D(p)/[epsilon(p)[1+nK/(K +c)(2)]] derived from the mass conservation relations describing the adsorption process. The time dependence protein adsorption up to approximately 90% of the equilibration value q* could be described by a bilinear free driving force model. The rapid equilibration in the outer part of the particle with a half-life time of approximately 100 s in the studied systems accounted for 0.3-0.4 q*. The slower equilibration with a up to ten times longer half-life time, was the adsorption in the inner part of the particle that outside 0.5 R accounts for 0.5-0.6 q*. These data were compared with literature data for batch adsorption of proteins in biospecific, hydrophobic and ion-exchange adsorbents. They could also be described by a bilinear free driving force model, with about the same quantitative results as obtained for similar conditions in the single particle experiments. The static adsorption parameters, maximum binding site concentration n, and dissociation constant for the protein binding to a binding site K, were determined from Scatchard plots. For the same protein-adsorbent system the plots changed from linear to non-linear with increasing n. This change occurred when the average distance between adjacent binding sites become of the same order of magnitude as the size of the binding site or adsorbed protein. This causes a shielding of free binding sites increasing with n and the concentration of adsorbed protein, yielding a concentration dependence in K. These results show that for a high throughput and rapid adsorption in preparative chromatography, the adsorption step should be carried out in the non-linear part of the adsorption isotherm with concentrations up to c(b) where q*/c(b)>/=10 to obtain high protein recoveries. To avoid tailing due to the flow of adsorbed proteins in the inner part of the particles further into the particles at the start of the desorption, and to speed up desorption rates, protein adsorption in the particle within 0.5 R from the particle center should be avoided. This requires the further development of suitable pellicular particles for preparative protein chromatography that meet this requirement.     

Cold acclimation increases basal heart rate but decreases its thermal tolerance in rainbow trout (Oncorhynchus mykiss)

Rainbow trout (Oncorhynchus mykiss, Walbaum) were acclimated to 4 degrees C and 17 degrees C for more than 4 weeks and heart rate was determined in the absence and presence of adrenaline to see how thermal adaptation influences basal heart rate and its beta-adrenergic control in a eurythermal fish species. The basal heart rate in vitro was higher in cold-acclimated than warm-acclimated rainbow trout at temperatures below 17 degrees C. On the other hand, adaptation to cold decreased thermal tolerance of heart rate so that the maximal heart rates were achieved at 17 degrees C (75 +/- 4 bpm) and 24 degrees C (88 +/- 2 bpm) in cold-acclimated and warm-acclimated trout, respectively. Beta-adrenergic response of the heart was enhanced by cold-adaptation, since adrenaline (100 nmol l(-1)) caused stronger stimulation of heart rate in cold-acclimated (29 +/- 14%) than in warm-acclimated fish (10 +/- 1%; P = 0.03). Furthermore, adrenaline strongly opposed the temperature-dependent deterioration of force production in cold-acclimated trout but not in warm-acclimated trout. The results indicate that adaptation to cold increases basal heart rate but decreases its thermal tolerance in rainbow trout. Cold acclimation up-regulates the beta-adrenergic system, and beta-adrenoceptor activation seems to provide cardioprotection against high temperatures in the cold-adapted rainbow trout.     

Quadratically convergent algorithm for computing real root of non-linear transcendental equations

Objectives

The present paper describes a new algorithm to find a root of non-linear transcendental equations. It is found that Regula-Falsi method always gives guaranteed result but slow convergence. However, Newton–Raphson method does not give guaranteed result but faster than Regula-Falsi method. Therefore, the present paper used these two ideas and developed a new algorithm which has better convergence than Regula-Falsi and guaranteed result. One of the major issue in Newton–Raphson method is, it fails when first derivative is zero or approximately zero.

Results

The proposed method implemented the failure condition of Newton–Raphson method with better convergence. Error calculation has been discussed for certain real life examples using Bisection, Regula-Falsi, Newton–Raphson method and new proposed method. The computed results show that the new proposed quadratically convergent method provides better convergence than other methods.

     

The dynamics of a hydrogel strip.

A hydrogel strip relaxes when it is stretched. The decay in tensile stress can be ascribed primarily to strain-induced swelling of the polymer network--a result that follows from a continuum model of the gel-solvent system. An equation of motion and a linear constitutive law of the polymer network, Darcy's law, and the conservation of mass of the network and interstitial fluid are solved with boundary and initial conditions appropriate for a stress-relaxation experiment. This model predicts that the time constant of decay depends inversely upon the square of the thickness of the sample. This result is confirmed by experiments. In addition, the network shear modulus, mu, bulk modulus, k, and hydraulic permeability, 1/f, which are estimated by non-linear regression, all agree with measurements obtained using other methods.     

Linear relationship between electromyography and shear wave elastography measurements persists in deep muscles of the upper extremity

Recent works have demonstrated a linear relationship between muscle activation and shear modulus in various superficial muscles. As such, it may be possible to overcome limitations of traditional electromyography (EMG) methods by assessing activation using shear wave elastography. However, the relationship has not been wholly validated in deep muscles. This study measured the association between squared shear wave velocity, which is related to shear modulus, and activation within superficial and deep muscles. This relationship was also compared between surface and intramuscular EMG electrodes. We simultaneously recorded EMG and shear wave velocity in one deep (brachialis) and one superficial (brachioradialis) muscle in ten healthy individuals during isometric elbow flexion across a wide range of contraction intensities. Muscle activation and squared shear wave velocity demonstrated good reliability (ICC > 0.75) and showed a linear relationship (P < 0.05) for all muscle/EMG electrode type combinations (study conditions) after down-sampling. Study condition was not a significant within-subject factor to the slope or intercept of the relationship (P > 0.05). This work demonstrates that activation of both superficial and deep muscles can be assessed noninvasively using ultrasound shear wave elastography and is a critical step toward demonstrating elastography’s utility as an alternative to EMG.     

A fast strong coupling algorithm for the partitioned fluid–structure interaction simulation of BMHVs

The numerical simulation of Bileaflet Mechanical Heart Valves (BMHVs) has gained strong interest in the last years, as a design and optimisation tool. In this paper, a strong coupling algorithm for the partitioned fluid–structure interaction simulation of a BMHV is presented. The convergence of the coupling iterations between the flow solver and the leaflet motion solver is accelerated by using the Jacobian with the derivatives of the pressure and viscous moments acting on the leaflets with respect to the leaflet accelerations. This Jacobian is numerically calculated from the coupling iterations. An error analysis is done to derive a criterion for the selection of useable coupling iterations. The algorithm is successfully tested for two 3D cases of a BMHV and a comparison is made with existing coupling schemes. It is observed that the developed coupling scheme outperforms these existing schemes in needed coupling iterations per time step and CPU time.     

Time course and quantitative analysis of the adaptive responses to 85% oxygen in the rat lung and heart

The phenomenon of oxygen tolerance (resistance to 100% O(2) in rats previously exposed to 85% O(2)) constitutes one of the few models of adaptive responses to oxidative stress in mammals. In vitro studies suggest that reactive oxygen species mediate this response. To test this hypothesis in vivo, we followed the time course of oxidative stress, enzyme induction, and edema in the lung, heart and liver of rats exposed to 85% O(2) for 1 to 5 days. Interestingly, not only the lung, but also the heart of rats exposed to 85% O(2) showed increases in the production of O(*-)(2) (aconitase inactivation) early during the exposure. Increases in O(*-)(2) were associated to oxidative stress (increased in situ chemiluminescence) and transient edema in both tissues. Both the lung and heart displayed induction of superoxide dismutase and reversion of the oxidative stress and damage. The adaptive response in the heart was faster and more efficient, suggesting that this tissue is at a more critical risk when exposed to elevated O(2) concentrations.     

Ethanol enhances carbachol-induced protease activation and accelerates Ca2+ waves in isolated rat pancreatic acini

Alcohol abuse is a leading cause of pancreatitis, accounting for 30% of acute cases and 70-90% of chronic cases, yet the mechanisms leading to alcohol-associated pancreatic injury are unclear. An early and critical feature of pancreatitis is the aberrant signaling of Ca(2+) within the pancreatic acinar cell. An important conductor of this Ca(2+) is the basolaterally localized, intracellular Ca(2+) channel ryanodine receptor (RYR). In this study, we examined the effect of ethanol on mediating both pathologic intra-acinar protease activation, a precursor to pancreatitis, as well as RYR Ca(2+) signals. We hypothesized that ethanol sensitizes the acinar cell to protease activation by modulating RYR Ca(2+). Acinar cells were freshly isolated from rat, pretreated with ethanol, and stimulated with the muscarinic agonist carbachol (1 μM). Ethanol caused a doubling in the carbachol-induced activation of the proteases trypsin and chymotrypsin (p < 0.02). The RYR inhibitor dantrolene abrogated the enhancement of trypsin and chymotrypsin activity by ethanol (p < 0.005 for both proteases). Further, ethanol accelerated the speed of the apical to basolateral Ca(2+) wave from 9 to 18 μm/s (p < 0.0005; n = 18-22 cells/group); an increase in Ca(2+) wave speed was also observed with a change from physiologic concentrations of carbachol (1 μM) to a supraphysiologic concentration (1 mM) that leads to protease activation. Dantrolene abrogated the ethanol-induced acceleration of wave speed (p < 0.05; n = 10-16 cells/group). Our results suggest that the enhancement of pathologic protease activation by ethanol is dependent on the RYR and that a novel mechanism for this enhancement may involve RYR-mediated acceleration of Ca(2+) waves.     

Stress wave velocities in bovine patellar tendon.

The velocity of longitudinal stress waves in an elastic body is given by the square root of the ratio of its elastic modulus to its density. In tendinous and ligamentous tissue, the elastic modulus increases with strain and with strain rate. Therefore, it was postulated that stress wave velocity would also increase with increasing strain and strain rate. The purpose of this study was to determine the velocity of stress waves in tendinous tissue as a function of strain and to compare these values to those predicted using the elastic modulus derived from quasi-static testing. Five bovine patellar tendons were harvested and potted as bone-tendon-bone specimens. Quasi-static mechanical properties were determined in tension at a deformation rate of 100 mm/s. Impact loading was employed to determine wave velocity at various strain levels, achieved by preloading the tendon. Following impact, there was a measurable delay in force transmission across the specimen and this delay decreased with increasing tendon strain. The wave velocities at tendon strains of 0.0075, 0.015, and 0.0225 were determined to be 260 +/- 52 m/s, 360 +/- 71 m/s, and 461 +/- 94 m/s, respectively. These velocities were significantly (p < 0.01) faster than those predicted using elastic moduli derived from the quasi-static tests by 52, 45, and 41 percent, respectively. This study has documented that stress wave velocity in patellar tendon increases with increasing strain and is underestimated with a modulus estimated from quasi-static testing.     

Assessment of the effect of mesh density on the material property discretisation within QCT based FE models: a practical example using the implanted proximal tibia

A three-dimensional, quantitative computed tomography based finite element model of a proximal implanted tibia was analysed in order to assess the effect of mesh density on material property discretisation and the resulting influence on the predicted stress distribution. The mesh was refined on the contact surfaces (matched meshes) with element sizes of 3, 2, 1.4, 1 and 0.8 mm. The same loading conditions were used in all models (bi-condylar load: 60% medial, 40% lateral). Significant variations were observed in the modulus distributions between the coarsest and finest mesh densities. Poor discretisation of the material properties also resulted in poor correlations of the stresses and risk ratios between the coarsest and finest meshes. Little difference in Young's modulus, von Mises stress and risk ratio distributions were observed between the three finest models; hence, it was concluded that for this particular case an element size of 1.4 mm on the contact surfaces was enough to properly describe the stiffness, stress and risk ratio distributions within the bone. Poor convergence of the material property distribution occurred when the element size was significantly larger than the pixel size of the source CT data. It was concluded that unless there is convergence in the Young's modulus distribution, convergence of the stress field or of other parameters of interest will not occur either.