Variability is a critical aspect of a dynamical systems analysis. Because there are a number of numerical techniques that can be used in such an analysis, the calculation of variability has several issues that must be addressed. The purpose of this paper is to present a variety of quantitative methods for investigating variability from a dynamical systems perspective. The paper is divided into two major sections covering discrete and continuous methods. Each of these sections is subdivided into two sections. Within discrete methods, we discuss, first, the calculation of the discrete relative phase from a time-series history of two parameters and, second, the use of return maps. Using continuous methods, we present procedures for using angle-angle plots in the evaluation of relative phase. We then discuss the use of phase plots in the calculation of the continuous relative phase. Each of these methods presents unique problems for the researcher and the method to be used is determined by the nature of the question asked.
Joseph Hamill, Jeffrey M. Haddad, and William J. McDermott
Jeffrey M. Haddad, Laura J. Claxton, Dawn K. Melzer, Joseph Hamill, and Richard E. A. van Emmerik
Posture becomes integrated with other goal-directed behaviors early in infancy and continues to develop into the second decade of life. However, the developmental time course over which posture is stabilized relative to the base of support during a dynamic manual precision task has not been examined. Postural-manual integration was assessed in 7-year-olds, 10-year-olds, and adults using a postural-manual task in which task precision (target fitting size) and postural difficulty (reaching distance to a target) were manipulated. The main dependent variable was postural time-to-contact (TtC). Results indicated systematic age effects in which TtC was shortest in the 7-year-olds, increased in the 10-year-olds, and was longest in the adults. Across all age levels, TtC was longer when performing a precision ft compared with a nonprecision ft and when fitting at a near target compared with fitting at a far target. Finally, TtC increased over the course of the manual fitting task, suggesting that posture became increasingly stable as the hand approached the opening. The ability to modulate postural TtC during the course of the fitting trial was most pronounced in adults as compared with both groups of children. These results suggest that even by 10-years of age, children are not yet able to fully integrate postural movements with goal directed manual tasks at adult-like levels.
Joshua J. Liddy, Amanda J. Arnold, HyeYoung Cho, Nathaniel L. Romine, and Jeffrey M. Haddad
Holding an object has been found to reduce postural sway during quiet standing. However, people normally stand to accomplish suprapostural goals, such as fitting a key into a lock. Postural control should therefore be assessed by examining postural outcomes in the context of suprapostural task performance. This study assessed whether holding an object increased standing postural stability and improved the performance of a concurrent precision manual task. A total of 15 young adults performed a precision manual task with their dominant hand while holding or not holding an object in their nondominant hand. Postural stability was assessed using measures of postural sway and time to boundary. Suprapostural task performance was assessed as an error count. Holding did not influence postural sway or suprapostural task performance. Discrepancies among previous studies coupled with the present findings suggest that the effects of holding an object on standing posture are highly sensitive to the experimental context. The authors provide several explanations for their findings and discuss the limitations of previous suggestions that holding an object may have clinical relevance for balance-compromised populations.
James R. Chagdes, Joshua J. Liddy, Amanda J. Arnold, Laura J. Claxton, and Jeffrey M. Haddad
Portable force-measurement technologies are becoming increasingly popular tools to examine the maturation of postural motor milestones, such as sitting and standing, in infants. These convenient, low-cost devices provide numerous opportunities to characterize postural development outside of the laboratory. However, it is important to understand the unique challenges and technical limitations associated with collecting center of pressure (CoP) data using portable force-measurement technologies in infant populations. This study uses a mathematical model to examine issues that emerge when using portable force-measurement technologies to collect sitting and standing postural data in infants. The results of our mathematical simulations demonstrate that the CoP errors from portable force-measurement technologies depend on the posture examined (e.g., sitting vs. standing), the anthropometrics of the person (e.g., height and weight), the frequency of body sway, and the experimental setup (e.g., an additional support surface being placed on top of the device). Recommendations are provided for developmental researchers interested in adopting these technologies in infant populations.
Jeffrey M. Haddad, Richard E.A. van Emmerik, Jonathan S. Wheat, Joseph Hamill, and Winona Snapp-Childs
A variety of kinematic and kinetic measures are typically used to examine gait symmetry. Here we make the argument that gait asymmetries may be most clearly revealed through higher-order coordinative measures such as continuous relative phase (CRP). Participants walked on a treadmill with a load attached to their nondominant limb. Gait symmetry was then assessed using spatial (angular), temporal (velocity), and higherorder (CRP) symmetry measures. It was found that higher-order measures were most sensitive at assessing asymmetries due to load manipulation at both the distal and proximal segments. Symmetry measures derived from velocity variables were more sensitive than angular measures at detecting asymmetries, but were less sensitive compared with CRP. Asymmetries were also more readily detected using segmental angles compared with joint angles. These results suggest that gait asymmetries that emerge from changing constraints manifest along both spatial and temporal dimensions.
Jeffrey M. Haddad, Jeff L. Gagnon, Christopher J. Hasson, Richard E.A. Van Emmerik, and Joseph Hamill
Postural stability has traditionally been examined through spatial measures of the center of mass (CoM) or center of pressure (CoP), where larger amounts of CoM or CoP movements are considered signs of postural instability. However, for stabilization, the postural control system may utilize additional information about the CoM or CoP such as velocity, acceleration, and the temporal margin to a stability boundary. Postural time-to-contact (TtC) is a variable that can take into account this additional information about the CoM or CoP. Postural TtC is the time it would take the CoM or CoP, given its instantaneous trajectory, to contact a stability boundary. This is essentially the time the system has to reverse any perturbation before stance is threatened. Although this measure shows promise in assessing postural stability, the TtC values derived between studies are highly ambiguous due to major differences in how they are calculated. In this study, various methodologies used to assess postural TtC were compared during quiet stance and induced-sway conditions. The effects of the different methodologies on TtC values will be assessed, and issues regarding the interpretation of TtC data will also be discussed.