A new method to measure anatomic knee alignment for large studies of OA: data from the Osteoarthritis Initiative

SummaryObjectiveTo develop and validate a new and improved software method to rapidly determine femur–tibia angle (FTA).MethodsThree readers, two skilled and one unskilled, without any formal medical training, measured FTA in 142 subjects from the Osteoarthritis Initiative (OAI). The reader reliability was assessed using the intra-class correlation coefficient (ICC), root mean square standard deviation (RMSSD), and Bland–Altman plots, comparing the existing and new FTA methods. Gender-specific linear regression assessed the relationship of FTA with the hip–knee–ankle angle (HKA).ResultsThe ICC (RMSSD) for intra- and inter-reader reproducibility of the existing FTA method was 0.96 (0.77°) and 0.92 (1.38°), respectively, and for the new technique was 0.98 (0.25°) and 0.98 (0.37°), with similar results for all three readers. Bland–Altman 95% limits of agreement were greater than ±2° for the existing, and ±1° for the new method. The r-value for the relation of FTA to HKA was 0.68 and 0.72 for the existing and new methods, respectively. Varus (HKA ≤ −2°)/neutral (−2° < HKA < 2°)/valgus (HKA ≥ 2°) alignment based on predicted HKA agreed moderately with measured HKA (weighted kappa = 0.53), and had moderate sensitivity (73%) and specificity (84%) for varus malalignment. The new FTA was related to HKA using a linear equation with a slope of 0.98 and an offset of 4.0°.ConclusionsSince it is largely automated and uses unambiguous anatomical landmarks, the new method is highly reproducible and can be made on a standard posteroanterior (PA) knee radiograph by a relatively unskilled reader

Inference of selection gradients using performance measures as fitness proxies

O.D.F. is supported by the Natural Sciences and Engineering Research Council of Canada and the Madame Vigdís Finnbogadóttir Scholarship. M.B.M. is supported by a University Research Fellowship from the Royal Society (London).1.  Selection coefficients, i.e., selection differentials and gradients, are useful for quantifying selection and for making comparisons across traits and organisms, because they appear in known equations for relating selection and genetic variation to one another and to evolutionary change. However, selection coefficients can only be estimated in organisms where traits and fitness (components) can be measured. This is probably a major contributor to taxonomic biases of selection studies. Aspects of organismal performance, i.e., quantities that are likely to be positively related to fitness components, such as body size, are sometimes used as proxies for fitness, i.e., used in place of fitness components in regression-based selection analysis. To date, little theory exists to inform empirical studies about whether such procedures may yield selection coefficients with known relationships to genetic variation and evolution. 2.  We show that the conditions under which performance measures can be used as proxies for fitness are very limited. Such analyses require that the regression of fitness on the proxy is linear and goes through the origin. We illustrate how fitness proxies may be used in conjunction with information about the performance-fitness relationship, and clarify how this is different from substituting fitness proxies for fitness components in selection analyses. 3.  We apply proxy-based and fitness component-based selection analysis to a system where traits, a performance measure (size; similar to proxies that are commonly used in place of fitness), and a more proximate fitness measure, are all available on the same set of individuals. We find that proxy-based selection gradients are poorly reflective of selection gradients estimated using fitness components, even when proxy-fitness relationships are quite strong and reasonably linear. 4.  We discuss the implications for proxy-based selection analysis. We emphasise that measures of organismal performance, such as size, may in many cases provide useful information that can contribute to quantitative inferences about natural selection, and their use could allow quantitative inference about selection to be conducted in a wider range of taxa. However, such inferences require quantitative analysis of both trait-performance and performance-fitness relationships, rather than substitution of performance for measures of fitness or fitness components.PostprintPeer reviewe

Three-dimensional harmonic oscillator and time evolution in quantum mechanics

The problem of defining time (or phase) operator for three-dimensional harmonic oscillator has been analyzed. A new formula for this operator has been derived. The results have been used to demonstrate a possibility of representing quantum-mechanical time evolution in the framework of an extended Hilbert space structure. Physical interpretation of the extended structure has been discussed shortly, too.Comment: 14 pages; submitted to Phys Rev