Establishing Reference Values for Isometric Knee Extension and Flexion Strength.

Single-joint isometric and isokinetic knee strength assessment plays an important role in strength and conditioning, physical therapy, and rehabilitation. The literature, however, lacks absolute reference values. We systematically reviewed the available studies that assessed isometric knee strength. Two scientific databases (PubMed and PEDro) were searched for the papers that are published from the inception of the field to the end of 2019. We included studies that involved participants of both genders and different age groups, regardless of the study design, that involved isometric knee extension and/or flexion measurement. The extracted data were converted to body-mass-normalized values. Moreover, the data were grouped according to the knee angle condition (extended, mid-range, and flexed). A meta-analysis was performed on 13,893 participants from 411 studies. In adult healthy males, the pooled 95% confidence intervals (CI) for knee extension were 1.34-2.23Nm/kg for extended knee angle, 2.92-3.45Nm/kg for mid-range knee angle, and 2.50-3.06Nm/kg for flexed knee angle, while the CIs for flexion were 0.85-1.20, 1.15-1.62, and 0.96-1.54Nm/kg, respectively. Adult females consistently showed lower strength than adult male subgroups (e.g., the CIs for knee extension were 1.01-1.50, 2.08-2.74, and 2.04-2.71Nm/kg for extended, mid-range, and flexed knee angle condition). Older adults consistently showed lower values than adults (e.g., pooled CIs for mid-range knee angle were 1.74-2.16Nm/kg (male) and 1.40-1.64Nm/kg (female) for extension, and 0.69-0.89Nm/kg (male) and 0.46-0.81Nm/kg (female) for flexion). Reliable normative for athletes could not be calculated due to limited number of studies for individual sports.

An excursion approach to maxima of the Brownian bridge.

Distributions of functionals of Brownian bridge arise as limiting distributions in non-parametric statistics. In this paper we will give a derivation of distributions of extrema of the Brownian bridge based on excursion theory for Brownian motion. The idea of rescaling and conditioning on the local time has been used widely in the literature. In this paper it is used to give a unified derivation of a number of known distributions, and a few new ones. Particular cases of calculations include the distribution of the Kolmogorov-Smirnov statistic and the Kuiper statistic.