Short communication Changes in power curve shapes as an indicator of fatigue during dynamic contractions Fermin Mallor a , Teresa Leon b,n , Martin Gaston a , Mikel Izquierdo c a Department of Statistics and Operations Research, Public University of Navarre, Pamplona, Spain b Department of Statistics and Operations Research, University of Valencia, Valencia, Spain c Studies, Research and Sport Medicine Center, Government of Navarre, Pamplona, Navarre, Spain article info Article history: Accepted 13 January 2010 Keywords: Muscle fatigue Functional data analysis Functional principal components Cluster analysis Granulometric size distribution abstract The purpose of this study was to analyze exercise-induced leg fatigue during a dynamic fatiguing task by examining the shapes of power vs. time curves through the combined use of several statistical methods: B-spline smoothing, functional principal components and (supervised and unsupervised) classification. In addition, granulometric size distributions were also computed to allow for comparison of curves coming from different subjects. Twelve physically active men participated in one acute heavy-resistance exercise protocol which consisted of five sets of 10 repetition maximum leg press with 120 s of rest between sets. To obtain a smooth and accurate representation of the data, a basis of 180 B-splines was used. Functional principal component (FPC) analysis was used to find the dominant modes of variation in the curves. A multivariate cluster over the FPC scores and a k-nearest neighbor classification led to three interpretable groups corresponding to different levels of fatigue. Fatigue-induced changes in the shapes of the power curves were evident, in which curves progressively flatten and develop a second power peak. In a practical setting FPC analysis greatly reduces dimensionality and the use of granulometries allows for comparison of the curve shapes without distorting the time scale. In contrast to the present methodology, which considers each curve as a datum, classical statistical approaches using summary parameters of time series may lead to limited information about the impact of dynamic fatiguing protocols on kinematic and kinetic time-course changes in curve shapes. & 2010 Elsevier Ltd. All rights reserved. 1. Introduction Exercise-induced fatigue is defined as the reversible reduction in force- or power-generating capacity of the neuromuscular system (Fitts, 1994; Bigland-Ritchie et al., 1981). Assessment of exercise-induced leg fatigue is usually made before and immedi- ately after isometric fatiguing exercise (Vollestad et al., 1988; Gandevia et al., 1995). In doing so, quantification of peripheral fatigue is based on comparison between pre- vs. post-exercise measures. Classically, these methods include either the assessment of effort-dependent contraction force (i.e., maximal voluntary isometric contraction force or isometric relaxation time) or effort- independent force generated by evoked muscle contractions (Amann and Calbet, 2008, Enoka and Duchateau, 2008). Despite the fact that most muscles shorten during athletic and voluntary physical activities, many studies have frequently used isometric rather than dynamic fatiguing tasks to examine muscle fatigue (Izquierdo et al., 2006). During dynamic contractions, the impact of exercise-induced fatigue is classically assessed by measuring velocity and/or muscle power changes (i.e., peak or the mean velocity) over a set of repetitions at a given percentage of the maximal dynamic strength (1RM). Thus, it has been previously reported that, over a set of repetitions to failure muscle contraction, velocity slows naturally as fatigue increases (Izquier- do et al., 2006). Although extracting discrete variables, such as peak, maximum or average values or time-integrated power/velocity values from data has remained the norm for biomechanical analysis (Ryan et al., 2006), this practice does not consider the unique waveform structure that may contain additional information about subtle changes in power/velocity vs. time relationships. Functional data analysis (FDA) is an extension of multivariate analyses that provides a way to analyze the dynamic nature of power curves (Ramsay and Silverman, 2005). The use of FDA in biomechanics has not yet been widely implemented but some recent examples are the study of patterns in sit-to-stand movement (Page et al., 2006; Epifanio et al., 2008), and the identification of the variation in kinematic and kinetic waveforms resulting from fatigue experienced over a 45-min lifting task (Godwin et al., 2009). The purpose of the present study was to analyze exercise- induced leg fatigue during a dynamic fatiguing task by examining the shapes of power curves through the combined use of several ARTICLE IN PRESS Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/jbiomech www.JBiomech.com Journal of Biomechanics 0021-9290/$ - see front matter & 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.jbiomech.2010.01.038 n Corresponding author. Tel.: + 34 96 3543088. E-mail address: teresa.leon@uv.es (T. Leon). Journal of Biomechanics 43 (2010) 1627–1631