Assessment of common hyperelastic constitutive equations for describing normal and osteoarthritic articular cartilage.

With the aim of providing information for modelling joint and limb systems, widely available constitutive hyperelastic laws are evaluated in this paper for their ability to predict the mechanical responses of normal and osteoarthritic articular cartilage. Load-displacement data from mechanical indentation were obtained for normal and osteoarthritic cartilage at 0.1 s(-1) and 0.025 s(-1) and converted to the stress-stretch ratio. The data were then fitted to the Arruda-Boyce, Mooney-Rivlin, neo-Hookean, Ogden, polynomial, and Yeoh hyperelastic laws in the MATLAB environment. Although each of the hyperelastic laws performed satisfactorily at the higher rate of loading, their ability to fit experimental data at the lower loading rate varied considerably. For the preferred models, coefficients were provided for stiff, soft, and average tissues to represent normal and degraded tissue at high and low loading rates. The present authors recommend the use of the Mooney-Rivlin or the Yeoh models for describing both normal and degraded articular cartilage, with the Mooney-Rivlin model providing the best compromise between accuracy and required computational power.

In vitro degradation of articular cartilage: does trypsin treatment produce consistent results?

It is common practice in laboratories to create models of degraded articular cartilage in vitro and use these to study the effects of degeneration on cartilage responses to external stimuli such as mechanical loading. However, there are inconsistencies in the reported action of trypsin, and there is no guide on the concentration of trypsin or the time to which a given sample can be treated so that a specific level of proteoglycan depletion is achieved. This paper argues that before any level of confidence can be established in comparative analysis it is necessary to first obtain samples with similar properties. Consequently, we examine the consistency of the outcome of the artificial modification of cartilage relative to the effects of the common enzyme, trypsin, used in the process of in vitro proteoglycan depletion. The results demonstrate that for a given time and enzyme concentration, the action of trypsin on proteoglycans is highly variable and is dependent on the initial distribution and concentration of proteoglycans at different depths, the intrinsic sample depth, the location in the joint space and the medium type, thereby sounding a note of caution to researchers attempting to model a proteoglycan-based degeneration of articular cartilage in their experimental studies.

Generational equity and social insurance.

In recent years, critics have argued that, when inter-generational transfer programs such as Medicare are judged by the standard of "generational equity", these programs are seen to be unfair. It is argued that, under a pay-as-you-go system, future generations are committed to burdens without their consent; that claims are not contractually guaranteed; that early entrants reap windfalls gains; that successive cohorts are tempted to provide insupportably high benefit levels; and, finally, that fluctuations leave future generations at unacceptable risk. Attempts have been made to defend social insurance programs by means of a "lifespan prudential model" of age-group resource allocation, but this defense does not adequately take account of uncertainties and inequities faced by historical birth cohorts. A deeper defense must acknowledge an element of risk-sharing and solidarity while trying to limit inequities within reasonable bounds.