Unconfined compression of articular cartilage: nonlinear behavior and comparison with a fibril-reinforced biphasic model

Mechanical behavior of articular cartilage was characterized in unconfined compression to delineate regimes of linear and nonlinear behavior, to investigate the ability of a fibril-reinforced biphasic model to describe measurements, and to test the prediction of biphasic and poroelastic models that tissue dimensions alter tissue stiffness through a specific scaling law for time and frequency. Disks of full-thickness adult articular cartilage from bovine humeral heads were subjected to successive applications of small-amplitude ramp compressions cumulating to a 10 percent compression offset where a series of sinusoidal and ramp compression and ramp release displacements were superposed. We found all equilibrium behavior (up to 10 percent axial compression offset) to be linear, while most nonequilibrium behavior was nonlinear, with the exception of small-amplitude ramp compressions applied from the same compression offset. Observed nonlinear behavior included compression-offset-dependent stiffening of the transient response to ramp compression, nonlinear maintenance of compressive stress during release from a prescribed offset, and a nonlinear reduction in dynamic stiffness with increasing amplitudes of sinusoidal compression. The fibril-reinforced biphasic model was able to describe stress relaxation response to ramp compression, including the high ratio of peak to equilibrium load. However, compression offset-dependent stiffening appeared to suggest strain-dependent parameters involving strain-dependent fibril network stiffness and strain-dependent hydraulic permeability. Finally, testing of disks of different diameters and rescaling of the frequency according to the rule prescribed by current biphasic and poroelastic models (rescaling with respect to the sample's radius squared) reasonably confirmed the validity of that scaling rule. The overall results of this study support several aspects of current theoretical models of articular cartilage mechanical behavior, motivate further experimental characterization, and suggest the inclusion of specific nonlinear behaviors to models.     

Sex-related effects on venous compliance and capillary filtration in the lower limb

Recent studies in humans have suggested sex differences in venous compliance of the lower limb, with lower compliance in women. Capillary fluid filtration could, however, be a confounder in the evaluation of venous compliance. The venous capacitance and capillary filtration response in the calves of 12 women (23.2 +/- 0.5 years) and 16 men (22.9 +/- 0.5 years) were studied during 8 min lower body negative pressure (LBNP) of 11, 22, and 44 mmHg. Calf venous compliance is dependent on pressure and was determined using the first derivative of a quadratic regression equation that described the capacitance-pressure relationship [compliance = beta1 + (2 x beta2 x transmural pressure)]. We found a lower venous compliance in women at low transmural pressures, and the venous capacitance in men was increased (P < 0.05). However, the difference in compliance between sexes was reduced and not seen at higher transmural pressures. Net capillary fluid filtration and capillary filtration coefficient (CFC) were greater in women than in men during LBNP (P < 0.05). Furthermore, calf volume increase (capacitance response + total capillary filtration) during LBNP was equivalent in both sexes. When total capillary filtration was not subtracted from the calf capacitance response in the calculation of venous compliance, the sex differences disappeared, emphasizing that venous compliance measurement should be corrected for the contribution of CFC.     

The exponential model for a regulatory enzyme. An interpretation of the linear free-energy relationship.

A physical mechanism is suggested to explain the linear free-energy relationship employed in the exponential model for a regulatory enzyme [Ainsworth (1977) J. Theor. Biol. 68, 391-413]. The interpretation depends on the assumption that the structure of the enzyme changes in proportion to its saturation by substrate but at a rate that is low compared with the rates of the association-dissociation reactions of the enzyme-substrate system.     

Prediction in censored survival data: a comparison of the proportional hazards and linear regression models.

Although the analysis of censored survival data using the proportional hazards and linear regression models is common, there has been little work examining the ability of these estimators to predict time to failure. This is unfortunate, since a predictive plot illustrating the relationship between time to failure and a continuous covariate can be far more informative regarding the risk associated with the covariate than a Kaplan-Meier plot obtained by discretizing the variable. In this paper the predictive power of the Cox (1972, Journal of the Royal Statistical Society, Series B 34, 187-202) proportional hazards estimator and the Buckley-James (1979, Biometrika 66, 429-436) censored regression estimator are compared. Using computer simulations and heuristic arguments, it is shown that the choice of method depends on the censoring proportion, strength of the regression, the form of the censoring distribution, and the form of the failure distribution. Several examples are provided to illustrate the usefulness of the methods.     

Sexual mixing models: a comparison of analogue deterministic and stochastic models.

Models for sexual partner choice are discussed for the case of highly variable sexual activity in the population. It is demonstrated that the variances in the number of infected persons may be extremely large. For the random mixing model, higher order cumulants are also evaluated. On the basis of these results the applicability of deterministic models and models for expectations only are questioned. A general model is proposed for handling nonrandom, or correlated, mixing. The problem of inconsistency is overcome by considering the couples having sex as the natural unit in the model. In the case of s discrete homogeneous groups it is shown that only (s2) parameters defining the interaction between the groups can be chosen freely. Finally, the effect of correlation in partner choice is demonstrated by a bivariate lognormal model for partner choice.     

Decreased capillary filtration but maintained venous compliance in the lower limb of aging women

There are sex-related differences in venous compliance and capillary filtration in the lower limbs, which to some extent can explain the susceptibility to orthostatic intolerance in young women. With age, venous compliance and capacitance are reduced in men. This study was designed to evaluate age-related changes in venous compliance and capillary filtration in the lower limbs of healthy women. Included in this study were 22 young and 12 elderly women (23.1 +/- 0.4 and 66.4 +/- 1.4 yr). Lower body negative pressure (LBNP) of 11, 22, and 44 mmHg created defined transmural pressure gradients in the lower limbs. A plethysmographic technique was used on the calf to assess venous capacitance and net capillary filtration. Venous compliance was calculated with the aid of a quadratic regression equation. No age-related differences in venous compliance and capacitance were found. Net capillary filtration and capillary filtration coefficient (CFC) were lower in elderly women at a LBNP of 11 and 22 mmHg (0.0032 vs. 0.0044 and 0.0030 vs. 0.0041 ml.100 ml(-1).min(-1).mmHg(-1), P < 0.001). At higher transmural pressure (LBNP, 44 mmHg), CFC increased by approximately 1/3 (0.010 ml.100 ml(-1).min(-1).mmHg(-1)) in the elderly (P < 0.001) but remained unchanged in the young women. In conclusion, no age-related decrease in venous compliance and capacitance was seen in women. However, a decreased CFC was found with age, implying reduced capillary function. Increasing transmural pressure increased CFC in the elderly women, indicating an increased capillary susceptibility to transmural pressure load in dependent regions. These findings differ from earlier studies on age-related effects in men, indicating sex-specific vascular aging both in the venous section and microcirculation.     

Carcass conformation and fat cover scores in beef cattle: A comparison of threshold linear models vs grouped data models

Background

Beef carcass conformation and fat cover scores are measured by subjective grading performed by trained technicians. The discrete nature of these scores is taken into account in genetic evaluations using a threshold model, which assumes an underlying continuous distribution called liability that can be modelled by different methods.

Methods

Five threshold models were compared in this study: three threshold linear models, one including slaughterhouse and sex effects, along with other systematic effects, with homogeneous thresholds and two extensions with heterogeneous thresholds that vary across slaughterhouses and across slaughterhouse and sex and a generalised linear model with reverse extreme value errors. For this last model, the underlying variable followed a Weibull distribution and was both a log-linear model and a grouped data model. The fifth model was an extension of grouped data models with score-dependent effects in order to allow for heterogeneous thresholds that vary across slaughterhouse and sex. Goodness-of-fit of these models was tested using the bootstrap methodology. Field data included 2,539 carcasses of the Bruna dels Pirineus beef cattle breed.

Results

Differences in carcass conformation and fat cover scores among slaughterhouses could not be totally captured by a systematic slaughterhouse effect, as fitted in the threshold linear model with homogeneous thresholds, and different thresholds per slaughterhouse were estimated using a slaughterhouse-specific threshold model. This model fixed most of the deficiencies when stratification by slaughterhouse was done, but it still failed to correctly fit frequencies stratified by sex, especially for fat cover, as 5 of the 8 current percentages were not included within the bootstrap interval. This indicates that scoring varied with sex and a specific sex per slaughterhouse threshold linear model should be used in order to guarantee the goodness-of-fit of the genetic evaluation model. This was also observed in grouped data models that avoided fitting deficiencies when slaughterhouse and sex effects were score-dependent.

Conclusions

Both threshold linear models and grouped data models can guarantee the goodness-of-fit of the genetic evaluation for carcass conformation and fat cover, but our results highlight the need for specific thresholds by sex and slaughterhouse in order to avoid fitting deficiencies.     

Mechanisms of cardiac cell excitation with premature monophasic and biphasic field stimuli: a model study.

The mechanisms by which extracellular electric field stimuli induce the (re)excitation of cardiac cells in various stages of refractoriness are still not well understood. We modeled the interactions between an isolated cardiac cell and imposed extracellular electric fields to determine the mechanisms by which relatively low-strength uniform monophasic and biphasic field stimuli induce premature reexcitations. An idealized ventricular cell was simulated with 11 subcellular membrane patches, each of which obeyed Luo-Rudy (phase 1) kinetics. Implementing a standard S1-S2 pulse protocol, strength-interval maps of the cellular excitatory responses were generated for rectangular monophasic and symmetric biphasic field stimuli of 2, 5, 10, and 20 ms total duration. In contrast to previously documented current injection studies, our results demonstrate that a cardiac cell exhibits a significantly nonmonotonic excitatory response to premature monophasic and, to a much lesser degree, biphasic field stimuli. Furthermore, for monophasic stimuli at low field strengths, the cell is exquisitely sensitive to the timing of the shock, demonstrating a classic all-or-none depolarizing response. However, at higher field strengths this all-or-none sensitivity reverts to a more gradual transition of excitatory responses with respect to stimulus prematurity. In contrast, biphasic stimuli produce such graded responses at all suprathreshold stimulus strengths. Similar behaviors are demonstrated at all S2 stimulus durations tested. The generation of depolarizing (sodium) currents is triggered by one or more of the sharp field gradient changes produced at the stimulus edges-i.e., make, break, and transphasic (for biphasic stimuli)-with the magnitude of these edge-induced current contributions dependent on both the prematurity and the strength of the applied field. In all cases, however, depolarizing current arises from the partial removal of sodium inactivation from at least part of the cell, because of either the natural process of repolarization or a localized acceleration of this process by the impressed field.     

Decreased venous compliance in dogs with chronic renal hypertension.

Femoral vein (FV) pressure-volume relationships were measured in vitro in 14 dogs with chronic (more than 4 weeks), one-kidney perinephritic hypertension and in 13 unilaterally nephrectomized normotensive control dogs. Segments of FV were also examined histologically and analyzed for their water and electrolyte contents. Compared to controls: (I) the FV pressure-volume curves of hypertensive dogs were shifted toward the pressure axis (P is less than 0.05); (ii) calcaulated vagous compliance in the pressure range of 0-15 mm Hg was decreased (P is less than 0.05); and (iii) the water and sodium contents of vwins from hypertensive dogs were increased (P is less than 0.05). Histological examination of the FV from hypertensive and control dogs did not reveal significant differences. The findings indicate that the decreases in venous compliance that we have previously observed in the early stages (less than 4 weeks) of perinephritic hypertension in dogs persist into the chronic stage of hypertension. Venous wall "edema" may account for the decreased venous compliance in this form of hypertension.     

Toward a mathematical model of the assembly and disassembly of membrane microdomains: comparison with experimental models

We study a model system in which lipid bilayers are created using variable (precisely known) proportions of phosphatidylcholine and cholesterol. The model membranes exhibit cholesterol-enriched microdomains that are analogous to the so-called "lipid rafts" that form in living cells. After briefly presenting some experimental results, we formulate and solve a novel mathematical model based on the Smoluchowski equations for coagulation and fragmentation. We present a comparison between the distribution of lipid-raft areas observed in experimental lipid bilayers, and that distribution predicted by the theoretical model. Excellent agreement between the experiments and theory is obtained, with minimal parameter fitting.     

A general linear framework for the comparison and evaluation of models of sensorimotor synchronization

Sensorimotor synchronization (SMS), the temporal coordination of a rhythmic movement with an external rhythm, has been studied most often in tasks that require tapping along with a metronome. Models of SMS use information about the timing of preceding stimuli and responses to predict when the next response will be made. This article compares the theoretical structure and empirical predictions of four two-parameter models proposed in the literature: Michon (Timing in temporal tracking, Van Gorcum, Assen, 1967), Hary and Moore (Br J Math Stat Psychol 40:109–124, 1987b), Mates (Biol Cybern 70:463–473, 1994a; Biol Cybern 70:475–484, 1994b), and Schulze et al. (Mus Percept 22:461–467, 2005). By embedding these models within a general linear framework, the mathematical equivalence of the Michon, Hary and Moore, and Schulze et al. models is demonstrated. The Mates model, which differs from the other three, is then tested empirically with new data from a tapping experiment in which the metronome alternated between two tempi. The Mates model predictions are found to be invalid for about one-third of the trials, suggesting that at least one of the model’s underlying assumptions is incorrect. The other models cannot be refuted as easily, but they do not predict some features of the data very accurately. Comparison of the models’ predictions in a training/test procedure did not yield any significant differences. The general linear framework introduced here may help in the formulation of new models that make better predictions.     

A biphasic model for micro-indentation of a hydrogel-based contact lens

The stiffness and hydraulic permeability of soft contact lenses may influence its clinical performance, e.g., on-eye movement, fitting, and wettability, and may be related to the occurrence of complications; e.g., lesions. It is therefore important to determine these properties in the design of comfortable contact lenses. Micro-indentation provides a nondestructive means of measuring mechanical properties of soft, hydrated contact lenses. However, certain geometrical and material considerations must be taken into account when analyzing output force-displacement (F-D) data. Rather than solely having a solid response, mechanical behavior of hydrogel contact lenses can be described as the coupled interaction between fluid transport through pores and solid matrix deformation. In addition, indentation of thin membranes ( approximately 100 microm) requires special consideration of boundary conditions at lens surfaces and at the indenter contact region. In this study, a biphasic finite element model was developed to simulate the micro-indentation of a hydrogel contact lens. The model accounts for a curved, thin hydrogel membrane supported on an impermeable mold. A time-varying boundary condition was implemented to model the contact interface between the impermeable spherical indenter and the lens. Parametric studies varying the indentation velocities and hydraulic permeability show F-D curves have a sensitive region outside of which the force response reaches asymptotic limits governed by either the solid matrix (slow indentation velocity, large permeability) or the fluid transport (high indentation velocity, low permeability). Using these results, biphasic properties (Young's modulus and hydraulic permeability) were estimated by fitting model results to F-D curves obtained at multiple indentation velocities (1.2 and 20 microm/s). Fitting to micro-indentation tests of Etafilcon A resulted in an estimated permeability range of 1.0 x 10(-15) to 5.0 x 10(-15) m(4)N s and Young's modulus range of 130 to 170 kPa.     

Characterizing activity-dependent processes with a piecewise exponential model

The response of some biological processes is dependent on the frequency of stimulation. With first-order processes, the response is driven exponentially to an equilibrium determined by the value of the driving function. When the stimulus or driving function is viewed as switching between constant values the resulting response is piecewise exponential. With periodic excitation, the time course of a point fixed in time relative to the initiation time of each stimulus is shown to be exponential with a rate and steady state that are linearly dependent on the rates and equilibria associated with each component exponential. This linearity can be exploited and leads to a simple estimation procedure for the apparent state-dependent rates.     

Data-guide for brain deformation in surgery: comparison of linear and nonlinear models

Background  

Pre-operative imaging devices generate high-resolution images but intra-operative imaging devices generate low-resolution images. To use high-resolution pre-operative images during surgery, they must be deformed to reflect intra-operative geometry of brain.