Exp Brain Res (2013) 231:383–396 DOI 10.1007/s00221-013-3696-9
Research Article
Laterality of quiet standing in old and young Jeffrey M. Kinsella‑Shaw · Steven J. Harrison · Claudia Carello · M. T. Turvey
Received: 22 January 2013 / Accepted: 31 August 2013 / Published online: 27 October 2013 © Springer-Verlag Berlin Heidelberg 2013
Abstract “Quiet standing” is standing without intended movement. To the naked eye, a person “quiet standing” on a rigid surface of support is stationary. In the laboratory quiet standing is indexed by behavior (at the millimeter scale) of the center of pressure (COP), the point location of the vertical ground reaction force vector (GRF). We asked whether quiet standing is lateralized and whether the COP dynamics of the right and left legs differ. In answer, we reexamined a previous quiet standing experiment (Kinsella-Shaw et al. in J Mot Behav 38:251–264, 2006) that used dual, side-by-side, force plates to investigate effects of age and embedding environment. All participants, old (M age = 72.2 ± 4.90 years) and young (M age = 22.8 ± 0.83 years), were right handed and right footed. Cross-recurrence quantification of the anterior–posterior and mediolateral coordinates of each COP revealed that, independent of age, and with no right GRF bias, rightleg coordination was (1) more dynamically stable and less noisy than left-leg coordination and (2) more responsive to changes in degree of visible structure. The results are considered in the context of theories of laterality inclusive of lateralized differences in postural dynamics. J. M. Kinsella‑Shaw (*) Department of Kinesiology, and Center for the Ecological Study of Perception and Action, University of Connecticut, 2095 Hillside Road, U‑1110, Storrs, CT 06269‑1110, USA e-mail: [email protected] S. J. Harrison Department of Psychology, University of Cincinnati, Cincinnati, OH, USA C. Carello · M. T. Turvey Department of Psychology, Center for the Ecological Study of Perception and Action, University of Connecticut, Storrs, CT, USA
Keywords Laterality · Posture · Vision · Dynamics · Aging · Human
Introduction Functional preferences in the use of the upper extremities during manual tasks are so transparent that “motor lateralization” is often treated as synonymous with “handedness.” In a summary of the literature on laterality, Peters (1994, p. 612) highlighted that “… handedness in skilled behavior is an expression of asymmetrically directed attention and … reveals a fundamental aspect of how movement intent is expressed through the hands.” In Bernstein’s (1996) formulation of the body’s functional levels, symmetry rather than asymmetry characterizes the movements constructed at the functional levels of tone (Level A), muscular–articular links or synergies (Level B), and space (Level C). For Bernstein, lateral asymmetry is restricted to activities, mostly manual but also pedal, which typify the level of actions (Level D)—namely sequences of distinct left and right movement patterns, usually involving objects. Standing still or “quiet standing” would seem to be an exemplary non-Level D, nonlateralized, coordination. In the experiment and analyses reported here, we evaluate this apparent symmetry. We do so in the context of experiments by Balasubramaniam et al. (2000), Balasubramaniam and Turvey (2000), and a conjecture by Geschwind and Galaburda (1987). The precision‑aiming postural task Balasubramaniam et al. examined a precision-aiming task in which a horizontal arrow, directed by a laser pointer held in the right-hand firm to the thigh, was controlled by
13
384
Exp Brain Res (2013) 231:383–396
4.5
targets
increasing difficulty
Mean RMS 3.5 (mm)
ML AP
2.5
AP
ML
4.5
Mean RMS (mm) 3.5
2.5
Handedness in quiet standing
AP
ML
Fig. 1 Schematic summary of Balasubramaniam et al. (2000). (Left) Participant with laser pointer in right hand standing parallel to (top) and perpendicular to (bottom) targets of increasing difficulty. Directions of sway, mediolateral (ML) and anterior–posterior (AP), are indicated with respect to the force platform. (Right) Mean RMS (mm) in AP and ML directions for parallel (top) and perpendicular (bottom) orientations to targets. Adapted from Fig. 5 in Balasubramaniam et al. (2000), “Specificity of postural sway to the demands of a precision task.”
the postural system during quiet standing. For all targets, the horizontal visual angle was smaller than the vertical visual angle. The horizontal/vertical ratio decreased, and task difficulty increased, with target distance. Participants performed the task in a parallel (Fig. 1, top) and in a perpendicular (Fig. 1, bottom) orientation of the body’s coronal plane to the targets. The parallel orientation required minimizing mediolateral (ML) sway. The perpendicular orientation required minimizing anteroposterior (AP) sway. In the parallel orientation, the root mean square (RMS) of center of pressure (COP) of ML and AP sway increased and decreased, respectively, with target distance and size (Fig. 1, top right). The pattern reversed in the perpendicular orientation (Fig. 1, bottom right). Nonlinear measures found independence of the two directions of sway and differences in their deterministic structure. Balasubramaniam et al. concluded that the postural organization for upright standing and aiming (as in archery) entails two independent postural subsystems with different but reciprocally related dynamics. They also concluded that some amount of postural variability is needed to ensure stability in quiet standing. As suggested in Fig. 1 (right panels) for each target difficulty, if postural activity was reduced in one direction, it was (partially) compensated for in the other direction.
13
Balasubramaniam et al. raised the question of how one might perform the precision-aiming task in the parallel and perpendicular orientations. They suggested the following formulae. For the parallel case, stiffen the hip muscles in direct relation to the required precision and elevate postural activity in the AP direction to ensure a sufficient level of postural activity for stability. For the perpendicular case, stiffen the ankle muscles in direct relation to the required precision and elevate postural activity in the ML direction to ensure stability. In respect of the formulae, the pattern of data in Fig. 1 indicates an ability to modulate selectively the directions of postural activity at the millimeter scale in response to the demands of suprapostural tasks.
Balasubramaniam and Turvey asked whether the precisionaiming postural task was sensitive to handedness. Specifically, they asked whether left-handers and right-handers differ in how they modulate postural fluctuations in performance of the task. The question was posed in the parallel orientation, with the laser pointer held equally often in (immobile) right and left hands (Fig. 2, left) across trials. The data pattern shown in the upper panel of Fig. 1 for AP and ML sway as a function of task difficulty was replicated for both left and right-handers. The two major findings of significance to present concerns are depicted in Fig. 2, right: (a) When the pointer was held in the preferred hand, RMS of COP decreased for AP and increased for ML, and (b) the RMS of COP was greater on average for right-handed participants than for left-handed participants, no matter which hand held the laser pointer. An additional finding was that the handedness difference was greater in the ML direction. Geschwind and Galaburda’s conjecture The experiment summarized in Fig. 2 was motivated in part by Geschwind and Galaburda’s (1987) conjecture that the neural substrates of whole-body skills and manual skills, though different, could be lateralized in the same way (see also Waxman 1988, 2003). The choice of the precision-aiming task to test the conjecture was influenced by observations that task asymmetry coordinate with laterality (e.g., a right-hand task bias) can amplify laterality (e.g., Amazeen et al. 1997; Peters 1989, 1994; de Poel et al. 2006). Balasubramaniam and Turvey were concerned that simply standing upright would provide insufficient opportunity for detecting the conjectured laterality at the level of the whole body because it “involves a seemingly even distribution of effort and attention across segments of both sides of the body” and “primary directions of sway” (Balasubramaniam and Turvey, p. 670). However, given the proposals of Peters (1989, 1994) and Bernstein (1996), one might argue that the postural
Exp Brain Res (2013) 231:383–396
385
4.5
ML
hold right
AP
hold le
Mean RMS 3.5 (mm)
ML
AP ML
AP
2.5
right left handers handers
right left handers handers
Fig. 2 Schematic summary of Experiment 1 of Balasubramaniam and Turvey (2000). (Left) Laser pointer in right hand and in left hand. Directions of sway, mediolateral (ML) and anterior–posterior (AP), are indicated with respect to the force platform. (Right) Mean RMS
(mm) in AP and ML directions for right-handers and left-handers as a function of hand holding laser pointer. Means are computed over participants and targets with different degrees of difficulty (see Fig. 1)
precision-aiming task is conducted at Level D, the level of action, given the implicit biasing of attention to the hip against which the handheld laser pointer is held. A true test of Geschwind and Galaburda’s conjecture requires an experimental evaluation that strictly excludes Level D. Experiment 2 of Balasubramaniam and Turvey was such a test. Left-handed and right-handed participants simply stood still while visually fixating a target in a plane parallel to the body’s coronal plane with target distance as a variable. COP variability was affected by target distance but not by handedness. An implication is that, absent imposed asymmetries, the laterality (handedness) of the body is either not detectable in quiet standing or nonexistent.
2008). Blaszczyk et al. (2000), for example, reported that for their younger group, one limb was loaded with 52 % of body weight (whether eyes were open or closed). It also seems that handedness may be a factor in determining which foot is loaded more. In Haddad et al. (2011), 16 of the 22 self-identified right-handed participants (mean age 24 ± 3.2 years; 12 men, 10 women) loaded the right limb more than the left in quiet standing with eyes open. In Gutnik et al. (2008), eight of the 14 right-handed participants (all male, age 18–25 years) identified by the Edinburgh Inventory (100 % laterality quotient) loaded the right limb more than the left in quiet standing with eyes closed. The primary issue is whether LLA is morphological or functional. Blaszczyk et al. (2000) suggested that it was functional in the sense of allowing a person to prepare a preferred leg to make a step should it become necessary due to an unexpected perturbation. For Haddad et al. (2011), evidence of functionality would be a systematic relation between LLA and the dynamics of the right and left COPs. Their failure to find dependence on LLA of the sample entropy (a complexity measure; see Haddad et al. 2006) of the right and left COPs was interpreted as counter to the hypothesis of LLA as functional. Similarly, for Gutnik et al., evidence of functionality would be a systematic relation between LLA and microshifts in the center of mass (changes in magnitude and direction at each successive time step). The absence of such a relation suggested to them that LLA is more likely tied to morphology, for example, known size and strength differences between the muscles and bones of left and right limbs (e.g., Kannus et al. 1994; Matava et al. 2002; Pyöriä et al. 2004).
Limb load asymmetry The hip abductors and adductors are responsible for producing the loading of the limbs (by raising and lowering the body mass above the pelvis), that is, they are responsible for generating the vertical reaction forces under the feet (Winter et al. 1993). It is this loading (and unloading) of the legs that characterizes the hip system’s contribution to standing upright (Winter et al. 1996). Balasubramaniam and Turvey’s Experiment 2 conducted their strict (no Level D) test of quiet standing on a single force platform. The COP so measured was the resultant of the individual left and right contributions. They considered their strict test to be inconclusive: Evaluating Geschwind and Galaburda’s conjecture should be based on the individual right and left contributions, not their resultant. An important dimension of research involving dual force plates is the issue of limb load asymmetry (LLA): the ratio of body weight fraction on more loaded limb to less loaded limb (Blaszczyk et al. 2000). From the evidence to date, it seems that most normal adults stand with their body weight unequally distributed across the two feet (Gutnik et al.
The present investigation Kinsella-Shaw et al. (2006) investigated quiet standing on dual force platforms. Their analysis was in terms of the
13
386
Fig. 3 a Measures derived from dual force plates of the mechanical interaction between each limb and the surface of support (COP and GRF). Each node in the graph represents an output of either the left (L) or right (R) limb with Xs the coordinates of mediolateral (ML) motions, Ys the coordinates of anterior–posterior (AP) motions, and Zs the magnitudes of the GRFs. Each dotted line represents variables that can be paired for cross-recurrence quantification (CRQ). b The nine pairings of variables for assessing inter-limb dynamics through CRQ. Horizontal arrows identify pairings of parallel outputs. Oblique
Exp Brain Res (2013) 231:383–396
arrows identify pairings of nonparallel or orthogonal outputs. c The three pairings of variables of the right limb and of the left limb for the CRQ determination, respectively, of right and left intra-limb dynamics. d Example time series from the present data for a pair of dual force plate measures (XR,YR). ML or X coordinate of the COP under the right foot is shown in gray. AP or Y coordinate of the COP under the right foot is shown in black. Adapted with permission from “Interleg coordination during quiet standing: influence of age and visual environment on noise and stability” by Kinsella-Shaw et al. (2011)
Fig. 4 The two conditions of stationary environmental structure, more (left) and less (right), and the participant’s orientation to them during quiet standing on dual force plates. Adapted with permission from “Interleg coordination during quiet standing: influence of age and visual environment on noise and stability” by Kinsella-Shaw et al. (2011)
reconstructed COP, a variable calculated over the two force plates from the COP of each foot and the vertical force measurements exhibited by each foot (Winter 1995; Winter et al. 1996). Figure 3 shows the full complement of measures on the dual force plates and their potential linkages. The net COP is inclusive of them. The participants in Kinsella-Shaw et al. (2006) were all right handed and right legged and constituted two equal groups of old (65–82 years) and young (aged 22–24 years).
13
They performed quiet standing in the setting depicted in Fig. 4 under two levels of illumination and two levels of optical structure. This 2 (age) × 2 (illumination) × 2 (structure) design was directed at two primary predictions and two secondary predictions. The primary predictions were that fluctuations of quiet standing in a stationary environment (1a) are influenced by the visible environment’s structure with the effect greater for older than for younger adults and (1b) depend on the level of environmental
Exp Brain Res (2013) 231:383–396
387
Fig. 5 a Left and right force platforms. b Phase space reconstruction of left platform data. The series X1(t) (black dashed lines) and series X2(t) (solid gray lines), depicted as sinusoids for simplicity, are embedded in a reconstructed phase space. Time-delayed copies of X(t) are used as surrogate dimensions X(t + τ) and X(t + 2τ) for a threedimensional embedding (a minimal and picturable case). CRQ of two embedded time series is shown with intersecting trajectories counted as recurrent points for Cross RECUR calculations and the longest parallel trajectory of X1(t) and X2(t) for Cross MAXLINE calculations. Adapted with permission from “Concurrent cognitive task modulates coordination dynamics,” by Pellecchia et al. 2005
illumination with the effect more pronounced for older than for younger adults. The two secondary predictions were that the effects of the environment’s structure and illumination on fluctuations of quiet standing are (2a) dependent on the fluctuation measure, given the different control and coordination properties that such measures quantify, and (2b) correlated with visual contrast sensitivity separately from chronological age. The experiment’s results were in agreement with the primary predictions: Both reduced illumination and reduced environmental structure affected the postural behavior of the older participants more than the postural behavior of the younger participants. The experiment’s results were also in agreement with the secondary predictions: The effects of the environmental variables were measure dependent and, in some instances, predictable by visual contrast sensitivity separately from chronological age. Kinsella-Shaw et al. (2011) reanalyzed the data of Kinsella-Shaw et al. (2006) in terms of Fig. 3b, that is, the subset of potential linkages defining inter-limb coordination. Arguably, it is this subset that is most directly responsible for modulating axial rotations and fluctuations. The reanalysis used cross-recurrence quantification (CRQ) (see present Fig. 5 and “Appendix”) as the means of measuring the degree of linkage between any two nodes identified in Fig. 3b. The CRQ measures of the three parallel cases (e.g.,
XL(t), XR(t)) were found to be larger in magnitude than the CRQ measures of the six nonparallel cases (e.g., XL(t), ZR(t)), with the largest CRQ measures associated with the linkage between YL(t) and YR(t). The CRQ measures indicated that inter-leg coordination was least noisy and most dynamically stable in the direction faced by the participants (see Fig. 4), as would be expected if fluctuations of a participant’s coronal plane were modulated to preserve axial orientation to the visible environment. The foregoing observations of Kinsella-Shaw et al. (2011) set the stage for evaluating Balasubramaniam and Turvey’s interpretation of their Experiment 2 as showing that lateralization of legs and trunk is not detectable in quiet standing, in the absence of imposed asymmetries. In the present paper we reanalyze Kinsella-Shaw et al.’s (2006) data in terms of the subset of potential linkages shown in Fig. 3c, that is, the subset of potential linkages defining intra-limb coordination. Arguably, it would be this subset that would be most directly involved in any left–right asymmetries manifest in the fluctuations of quiet standing. At issue is whether the CRQ (X, Y), (X, Z), (Z, Y) measures, either some or all, are more pronounced in the right leg of the right-handed participants independently of LLA. If such were the case, the strong version of Geschwind and Galaburda’s (1987) conjecture would be favored: The asymmetry of the lower limbs is no less basic than the asymmetry
13
388
of the upper limbs. Parallels of predictions (1a) and (1b) advanced in Kinsella-Shaw et al. (2006) were also of interest. Would the visible environment’s structure affect right limb CRQ measures more than left limb CRQ measures in an age-dependent manner? Would the level of environmental illumination affect right limb CRQ measures more than left limb CRQ measures in an age-dependent manner?
Method Participants Seven men and five women constituted the group of young adults (22.8 ± .83 years), and six men and six women constituted the group of old adults (72.2 ± 4.9 years). All participants were living independently in the community and driving. All participants gave their consent in accordance with the University of Connecticut Institutional Review Board’s regulations for studies with human participants. None of the participants used any kind of assistive devices, orthoses or prostheses, for ambulation or maintaining upright stance. All had normal or corrected-to-normal visual acuity. Cutaneous sensation of the feet was assessed by a licensed physical therapist using Semmes–Weinstein monofilaments and was intact for all participants. A history of falls over the previous 6 months, medical procedures, and medication use was obtained from each participant. None of the young adults had a history of falls. Of the older adults, seven had zero falls, two had one fall, and three had two falls. All reported falls were noninjurious and self-corrected. None of the participants had a history of use of any medication known to compromise balance. Height of the young adults ranged from 155 cm to 188 cm, with a mean of 163 cm. Weight for this group ranged from 46.34 kg to 92.10 kg, with a mean of 67.62. For the older adults, height ranged from 152 cm to 191 cm, with a mean of 171 cm. Weight for the older group ranged from 56.22 kg to 95.78 kg, with a mean of 73.93 kg. Each person in each group was paid $10 for participating. Determination of the functionally preferred lower extremity The screening procedure for lower limb functional preference incorporated prospective participants’ self-reports and three functional tests. There were three trials per test. The leg selected for use on all three trials of each test was identified as the functionally preferred leg for that test. For all 24 participants, the leg spontaneously self-selected for the three functional tests was consistent with the self-report of right-side functional dominance of the upper extremity. Four prospective participants were excluded from the study
13
Exp Brain Res (2013) 231:383–396
as a result of a discrepancy between self-reports of rightside functional preference and an observed preference for the use of the left leg during some trials of the functional testing. The screening procedure was as follows: 1. Using the Edinburgh Handedness Inventory, the prospective participant reported that the right upper extremity was functionally dominant, which is the preferred limb for tasks requiring greater coordination. Functional preference was then demonstrated by writing. 2. The prospective participant was required to kick a soccer ball with moderate force to the experimenter, who was kneeling directly in front of the kicker at a distance of 4 meters. The leg used to kick the ball was identified as the preferred leg. The accuracy of the kick was not part of the assessment. 3. The prospective participant was required to demonstrate single-leg stance three times and to maintain it for “as long as possible without discomfort.” The leg most frequently selected for unilateral stance was identified as preferred. 4. The prospective participant was required to step up onto a 15-cm-high platform. The leg selected to step with was identified as the preferred limb. Apparatus and data collection COP data were obtained at a sampling rate of 100 Hz using two Advanced Mechanical Technology Incorporated force platforms and a 64-Channel Run Technologies Datapac 2000 Analog-to-Digital Collection System. A Peak Performance Technologies Synchronization Trigger System synchronized data collection across the force plates networked with a dedicated Dell Optiplex GX300 workstation. In each trial, participants stood barefoot on the platforms, arms relaxed at their sides, legs abducted 10–12 deg, with heels 12 cm apart, one foot on each platform. (The platforms were embedded in the floor and separated by a 4-mm gap.) Participants were instructed to stand still and relaxed, and to look at the depth-grating (“more structure”) or at the (“less structure”) whiteboard, depending on the experimental condition (see Fig. 4). COP under each foot was obtained independently from the two force plates. For each foot, COPx and COPy were calculated from the time series of shear forces (F) and moments (M) recorded from the force platforms as follows (Richardson et al. 2007):
COPx =
(Fx · COPz ) − My , Fz
COPy =
(Fy · COPz ) − Mx Fz
Four 100-watt work lamps, controlled from a central custom-built rheostat, were the source used in the low illumination (3 lx) (entailing mesopic vision). The overhead
Exp Brain Res (2013) 231:383–396
fluorescent lights were the source for the high illumination (440 lx) (entailing photopic vision). Ambient illumination levels were verified with an Extech Instruments Heavy Duty Light Meter (Model 407026) for each experimental condition for every participant. The light meter was calibrated at the beginning of each data collection session. (The Extech light meter was used because of its compensatory circuits that ensure accuracy under both incandescent and fluorescent light sources.) The depth-grating (“more structure”) consisted of nine rows of 1.8-cm-diameter aluminum rods (conduits) arrayed three deep, for a total of 27 potentially visible rods. The rods in each row were placed 8 cm apart, with successive rows separated by a distance of 18 cm. Participants stood on the platforms at a distance of 122 cm from the nearest row of the display, positioned such that their eyes were directed roughly at its center (Fig. 4). As a whole, the depth-grating measured 92 cm wide and 105.6 cm high. Consequently, the first row subtended a visual horizontal angle of 41.32 deg and a visual vertical angle of 46.8 deg. The “less structure” condition consisted of a rectangular section of 5-mm-thickness white foam core board of the same vertical and horizontal dimensions as the depth-grating apparatus. It was presented at the same location relative to the participants’ vantage point as the depth-grating, thereby preserving all the same visual angle relationships. The foam core board surface had a flat-white homogeneous finish with no detectable texture or other surface features. An identical section of white foam core board provided a backdrop for the depth-grating apparatus and was affixed flush to the posterior surfaces of the most distant (third) row of rods. In either condition, participants were instructed to simply “look at the array” and were not instructed to focus specifically on the rods or the white screen (see Fig. 4). Data collection was initiated once the participant was in position and indicated that they were comfortable and that their breathing was regular. Procedure There were eight trials in each of the five experimental conditions: (1) eyes closed, (2) eyes open, 3 lx, planar array, (3) eyes open, 3 lx, depth-grating array, (4) eyes open, 440 lx, planar array, and (5) eyes open, 440 lx, depth-grating array. Conditions 2–5 were collected as blocks of eight trials with 5 min separating data collection in each block to allow for full, stable levels of adaptation to the level of available illumination [This method of presentation is consistent with the recommended protocol for testing contrast sensitivity which was important to Kinsella-Shaw et al. (2006). It assures that all the participants had the same opportunity for light–dark adaptation (McMurdo and Gaskell 1991)]. The eyes-closed condition was used to establish a baseline
389
for postural variability in the total absence of visual support, and data in this condition were collected in two fourtrial blocks. The first block preceded data collection in all other conditions; the second block of eyes-closed trials was the final episode of data collection. Subsequent analysis of variance (ANOVA) conducted on all of the obtained measures of COP variability revealed no significant differences between the trials collected in the two eyes-closed blocks for any of the participants. Trials lasted 35 s each, with the initial 5 s excluded from the analysis to eliminate any possible transients that could bias the analysis of the steady-state trajectories. The analyzed portion of each trial yielded 3,000 data points. Participants were allowed to rest as needed. As in Blaszczyk et al. (2000), participants were allowed to freely select a limb load distribution strategy. Data analysis Data analysis took advantage of the provision, by the dual force plates in Kinsella-Shaw et al. (2006), of simultaneous and independent recordings of COPx(t), COPy(t), and GRFz(t) generated under each foot (see Fig. 3a). These data were submitted to LLA and CRQ analyses. Measures of LLA This quantity was calculated in two ways: (1) as the percentage of load on the right foot according to Right Load % = [Right GRFz/(Right GRFz + Left GRFz)] × 100, and (2) as the ratio of body weight fraction put on the more loaded limb to the less loaded limb, alternatively the absolute degree to which loading differs from a 50:50 weight distribution (i.e., independent of direction). Method of CRQ Adding to the remarks on CRQ made above and in the “Appendix,” %Cross RECUR in Fig. 5 is the percentage of states relative to all the states sampled that are returned to (are proximate to each other in phase space under a preestablished distance criterion during the period of observation) by the systems or subsystems under investigation. %Cross MAXLINE expresses the maximum number of states that remain close (satisfy the pre-established distance criterion) over time forming a line of recurrent states arrayed diagonally in phase space, relative to the longest possible line (the line of symmetry), indicative of complete between-systems state-transition congruence (Marwan et al. 2007). Diagonal lines of this kind are present in the common phase space when stable, deterministic, dynamical coordination exists between systems’ trajectories. In CRQ, independently generated time series (such as COPx(t), COPy(t), and GRFz(t)) are embedded in their
13
390
Exp Brain Res (2013) 231:383–396
respective phase spaces and then used to compute a %Cross RECUR plot, providing a graphical representation of: m CRi,j = �(ri − �xi − yi �),
i = 1, . . . , Nx , j = 1, . . . , Ny
This is the equation for the %cross-recurrence matrix, CRm, where N is the number of considered (sampled) states xi (from the first time series) and yj (from the second time series), so that any point xi or yj is said to be %cross-recurrent (an element of the matrix) if the Euclidean distance between the two normalized vectors is less than or equal to the threshold radius r. (This is equivalent to εi, the cutoff distance in simple recurrence quantification analysis.) This threshold distance provides the radius for the sphere (see Fig. 5, Cross RECUR) defined with xi at its center such that any yj falling within the sphere represents a recurrent state in the shared state-space and is plotted as a point. Therefore, the percentage of points that are %Cross RECUR points is given by:
%Cross RECUR =
N 1 m CRi,j N2 i,j=1
The %Cross RECUR measure derived in this manner has been shown to be highly sensitive to even small amounts of stochastic (random) noise. Thus, %Cross RECUR provides a measure of the density of %cross-recurrent points within the CRQ plot and corresponds to the probability of identifying truly recurrent points as such (Thiel et al. 2002; Marwan 2003). As this measure captures the proportion of points that are recurrent relative to the total number of points, its inverse can be interpreted as analogous to Q, the index of system noise measurable in bidirectionally, coupled-pendulum systems (Kudo et al. 2006; Richardson et al. 2007; see “Appendix”). In CRQ, %Cross MAXLINE is the longest shared trajectory (see Fig. 5) and is a measure of the shared activity of the two observed processes (e.g., COPx(t) of right limb and COPy(t) of right limb). More specifically, if the two processes have the same or similar time evolution, parts of the two trajectories in phase space will occupy the same region of phase space and do so for a certain length of time. The longer the time, the longer the shared trajectory or, equivalently, the longer is the line that represents it. The maximum length of the diagonal lines in the %Cross RECUR plot excluding the line i = j is given by:
%Cross MAXLINE = max(li ; i = 1 . . . Ni ) Here li is a diagonal sequence of recurrent points, and Nl is the total number of diagonal lines. As noted above, the quantity MAXLINE, derived from single recurrence or %Cross RECUR, follows from expressing observed MAXLINE as a percentage of the maximum recurrent line length
13
that is possible (Kudo et al. 2006; Richardson et al. 2005). For the coordination of independently controlled systems (see “Appendix”), %Cross MAXLINE can be interpreted as a measure of entrainment (Marwan 2003; Richardson et al. 2007). Under this interpretation, %Cross MAXLINE quantifies mutual convergence of state dynamics at a local space– time scale, comparable to λ (Lyapunov exponent), providing a measure of local attractor strength (Kudo et al. 2006; Richardson et al. 2007). In the present case, the provision is for intra-limb coordination. Parameters for CRQ Before performing phase space reconstruction, all output variables were rescaled (normalized) on a unit interval (0–1). Consistent with our earlier analysis (Kinsella-Shaw et al. 2006, 2011), phase space reconstruction was performed using nine embedding dimensions and a time lag of 0.1 s. Criterion for recurrence was set at 5 % of the maximum distance between points in the distance matrix.
Results LLA The left and right GRFz means were 378.73 ± 115.87 and 352.92 ± 87.88 for the younger group, and 383.53 ± 73.35 and 388.21 ± 68.78 for the older group. Analysis of variance (ANOVA) revealed that effects of Leg, F (1, 22) = 1.72, p = .20, Age, (F
Research Article
Laterality of quiet standing in old and young Jeffrey M. Kinsella‑Shaw · Steven J. Harrison · Claudia Carello · M. T. Turvey
Received: 22 January 2013 / Accepted: 31 August 2013 / Published online: 27 October 2013 © Springer-Verlag Berlin Heidelberg 2013
Abstract “Quiet standing” is standing without intended movement. To the naked eye, a person “quiet standing” on a rigid surface of support is stationary. In the laboratory quiet standing is indexed by behavior (at the millimeter scale) of the center of pressure (COP), the point location of the vertical ground reaction force vector (GRF). We asked whether quiet standing is lateralized and whether the COP dynamics of the right and left legs differ. In answer, we reexamined a previous quiet standing experiment (Kinsella-Shaw et al. in J Mot Behav 38:251–264, 2006) that used dual, side-by-side, force plates to investigate effects of age and embedding environment. All participants, old (M age = 72.2 ± 4.90 years) and young (M age = 22.8 ± 0.83 years), were right handed and right footed. Cross-recurrence quantification of the anterior–posterior and mediolateral coordinates of each COP revealed that, independent of age, and with no right GRF bias, rightleg coordination was (1) more dynamically stable and less noisy than left-leg coordination and (2) more responsive to changes in degree of visible structure. The results are considered in the context of theories of laterality inclusive of lateralized differences in postural dynamics. J. M. Kinsella‑Shaw (*) Department of Kinesiology, and Center for the Ecological Study of Perception and Action, University of Connecticut, 2095 Hillside Road, U‑1110, Storrs, CT 06269‑1110, USA e-mail: [email protected] S. J. Harrison Department of Psychology, University of Cincinnati, Cincinnati, OH, USA C. Carello · M. T. Turvey Department of Psychology, Center for the Ecological Study of Perception and Action, University of Connecticut, Storrs, CT, USA
Keywords Laterality · Posture · Vision · Dynamics · Aging · Human
Introduction Functional preferences in the use of the upper extremities during manual tasks are so transparent that “motor lateralization” is often treated as synonymous with “handedness.” In a summary of the literature on laterality, Peters (1994, p. 612) highlighted that “… handedness in skilled behavior is an expression of asymmetrically directed attention and … reveals a fundamental aspect of how movement intent is expressed through the hands.” In Bernstein’s (1996) formulation of the body’s functional levels, symmetry rather than asymmetry characterizes the movements constructed at the functional levels of tone (Level A), muscular–articular links or synergies (Level B), and space (Level C). For Bernstein, lateral asymmetry is restricted to activities, mostly manual but also pedal, which typify the level of actions (Level D)—namely sequences of distinct left and right movement patterns, usually involving objects. Standing still or “quiet standing” would seem to be an exemplary non-Level D, nonlateralized, coordination. In the experiment and analyses reported here, we evaluate this apparent symmetry. We do so in the context of experiments by Balasubramaniam et al. (2000), Balasubramaniam and Turvey (2000), and a conjecture by Geschwind and Galaburda (1987). The precision‑aiming postural task Balasubramaniam et al. examined a precision-aiming task in which a horizontal arrow, directed by a laser pointer held in the right-hand firm to the thigh, was controlled by
13
384
Exp Brain Res (2013) 231:383–396
4.5
targets
increasing difficulty
Mean RMS 3.5 (mm)
ML AP
2.5
AP
ML
4.5
Mean RMS (mm) 3.5
2.5
Handedness in quiet standing
AP
ML
Fig. 1 Schematic summary of Balasubramaniam et al. (2000). (Left) Participant with laser pointer in right hand standing parallel to (top) and perpendicular to (bottom) targets of increasing difficulty. Directions of sway, mediolateral (ML) and anterior–posterior (AP), are indicated with respect to the force platform. (Right) Mean RMS (mm) in AP and ML directions for parallel (top) and perpendicular (bottom) orientations to targets. Adapted from Fig. 5 in Balasubramaniam et al. (2000), “Specificity of postural sway to the demands of a precision task.”
the postural system during quiet standing. For all targets, the horizontal visual angle was smaller than the vertical visual angle. The horizontal/vertical ratio decreased, and task difficulty increased, with target distance. Participants performed the task in a parallel (Fig. 1, top) and in a perpendicular (Fig. 1, bottom) orientation of the body’s coronal plane to the targets. The parallel orientation required minimizing mediolateral (ML) sway. The perpendicular orientation required minimizing anteroposterior (AP) sway. In the parallel orientation, the root mean square (RMS) of center of pressure (COP) of ML and AP sway increased and decreased, respectively, with target distance and size (Fig. 1, top right). The pattern reversed in the perpendicular orientation (Fig. 1, bottom right). Nonlinear measures found independence of the two directions of sway and differences in their deterministic structure. Balasubramaniam et al. concluded that the postural organization for upright standing and aiming (as in archery) entails two independent postural subsystems with different but reciprocally related dynamics. They also concluded that some amount of postural variability is needed to ensure stability in quiet standing. As suggested in Fig. 1 (right panels) for each target difficulty, if postural activity was reduced in one direction, it was (partially) compensated for in the other direction.
13
Balasubramaniam et al. raised the question of how one might perform the precision-aiming task in the parallel and perpendicular orientations. They suggested the following formulae. For the parallel case, stiffen the hip muscles in direct relation to the required precision and elevate postural activity in the AP direction to ensure a sufficient level of postural activity for stability. For the perpendicular case, stiffen the ankle muscles in direct relation to the required precision and elevate postural activity in the ML direction to ensure stability. In respect of the formulae, the pattern of data in Fig. 1 indicates an ability to modulate selectively the directions of postural activity at the millimeter scale in response to the demands of suprapostural tasks.
Balasubramaniam and Turvey asked whether the precisionaiming postural task was sensitive to handedness. Specifically, they asked whether left-handers and right-handers differ in how they modulate postural fluctuations in performance of the task. The question was posed in the parallel orientation, with the laser pointer held equally often in (immobile) right and left hands (Fig. 2, left) across trials. The data pattern shown in the upper panel of Fig. 1 for AP and ML sway as a function of task difficulty was replicated for both left and right-handers. The two major findings of significance to present concerns are depicted in Fig. 2, right: (a) When the pointer was held in the preferred hand, RMS of COP decreased for AP and increased for ML, and (b) the RMS of COP was greater on average for right-handed participants than for left-handed participants, no matter which hand held the laser pointer. An additional finding was that the handedness difference was greater in the ML direction. Geschwind and Galaburda’s conjecture The experiment summarized in Fig. 2 was motivated in part by Geschwind and Galaburda’s (1987) conjecture that the neural substrates of whole-body skills and manual skills, though different, could be lateralized in the same way (see also Waxman 1988, 2003). The choice of the precision-aiming task to test the conjecture was influenced by observations that task asymmetry coordinate with laterality (e.g., a right-hand task bias) can amplify laterality (e.g., Amazeen et al. 1997; Peters 1989, 1994; de Poel et al. 2006). Balasubramaniam and Turvey were concerned that simply standing upright would provide insufficient opportunity for detecting the conjectured laterality at the level of the whole body because it “involves a seemingly even distribution of effort and attention across segments of both sides of the body” and “primary directions of sway” (Balasubramaniam and Turvey, p. 670). However, given the proposals of Peters (1989, 1994) and Bernstein (1996), one might argue that the postural
Exp Brain Res (2013) 231:383–396
385
4.5
ML
hold right
AP
hold le
Mean RMS 3.5 (mm)
ML
AP ML
AP
2.5
right left handers handers
right left handers handers
Fig. 2 Schematic summary of Experiment 1 of Balasubramaniam and Turvey (2000). (Left) Laser pointer in right hand and in left hand. Directions of sway, mediolateral (ML) and anterior–posterior (AP), are indicated with respect to the force platform. (Right) Mean RMS
(mm) in AP and ML directions for right-handers and left-handers as a function of hand holding laser pointer. Means are computed over participants and targets with different degrees of difficulty (see Fig. 1)
precision-aiming task is conducted at Level D, the level of action, given the implicit biasing of attention to the hip against which the handheld laser pointer is held. A true test of Geschwind and Galaburda’s conjecture requires an experimental evaluation that strictly excludes Level D. Experiment 2 of Balasubramaniam and Turvey was such a test. Left-handed and right-handed participants simply stood still while visually fixating a target in a plane parallel to the body’s coronal plane with target distance as a variable. COP variability was affected by target distance but not by handedness. An implication is that, absent imposed asymmetries, the laterality (handedness) of the body is either not detectable in quiet standing or nonexistent.
2008). Blaszczyk et al. (2000), for example, reported that for their younger group, one limb was loaded with 52 % of body weight (whether eyes were open or closed). It also seems that handedness may be a factor in determining which foot is loaded more. In Haddad et al. (2011), 16 of the 22 self-identified right-handed participants (mean age 24 ± 3.2 years; 12 men, 10 women) loaded the right limb more than the left in quiet standing with eyes open. In Gutnik et al. (2008), eight of the 14 right-handed participants (all male, age 18–25 years) identified by the Edinburgh Inventory (100 % laterality quotient) loaded the right limb more than the left in quiet standing with eyes closed. The primary issue is whether LLA is morphological or functional. Blaszczyk et al. (2000) suggested that it was functional in the sense of allowing a person to prepare a preferred leg to make a step should it become necessary due to an unexpected perturbation. For Haddad et al. (2011), evidence of functionality would be a systematic relation between LLA and the dynamics of the right and left COPs. Their failure to find dependence on LLA of the sample entropy (a complexity measure; see Haddad et al. 2006) of the right and left COPs was interpreted as counter to the hypothesis of LLA as functional. Similarly, for Gutnik et al., evidence of functionality would be a systematic relation between LLA and microshifts in the center of mass (changes in magnitude and direction at each successive time step). The absence of such a relation suggested to them that LLA is more likely tied to morphology, for example, known size and strength differences between the muscles and bones of left and right limbs (e.g., Kannus et al. 1994; Matava et al. 2002; Pyöriä et al. 2004).
Limb load asymmetry The hip abductors and adductors are responsible for producing the loading of the limbs (by raising and lowering the body mass above the pelvis), that is, they are responsible for generating the vertical reaction forces under the feet (Winter et al. 1993). It is this loading (and unloading) of the legs that characterizes the hip system’s contribution to standing upright (Winter et al. 1996). Balasubramaniam and Turvey’s Experiment 2 conducted their strict (no Level D) test of quiet standing on a single force platform. The COP so measured was the resultant of the individual left and right contributions. They considered their strict test to be inconclusive: Evaluating Geschwind and Galaburda’s conjecture should be based on the individual right and left contributions, not their resultant. An important dimension of research involving dual force plates is the issue of limb load asymmetry (LLA): the ratio of body weight fraction on more loaded limb to less loaded limb (Blaszczyk et al. 2000). From the evidence to date, it seems that most normal adults stand with their body weight unequally distributed across the two feet (Gutnik et al.
The present investigation Kinsella-Shaw et al. (2006) investigated quiet standing on dual force platforms. Their analysis was in terms of the
13
386
Fig. 3 a Measures derived from dual force plates of the mechanical interaction between each limb and the surface of support (COP and GRF). Each node in the graph represents an output of either the left (L) or right (R) limb with Xs the coordinates of mediolateral (ML) motions, Ys the coordinates of anterior–posterior (AP) motions, and Zs the magnitudes of the GRFs. Each dotted line represents variables that can be paired for cross-recurrence quantification (CRQ). b The nine pairings of variables for assessing inter-limb dynamics through CRQ. Horizontal arrows identify pairings of parallel outputs. Oblique
Exp Brain Res (2013) 231:383–396
arrows identify pairings of nonparallel or orthogonal outputs. c The three pairings of variables of the right limb and of the left limb for the CRQ determination, respectively, of right and left intra-limb dynamics. d Example time series from the present data for a pair of dual force plate measures (XR,YR). ML or X coordinate of the COP under the right foot is shown in gray. AP or Y coordinate of the COP under the right foot is shown in black. Adapted with permission from “Interleg coordination during quiet standing: influence of age and visual environment on noise and stability” by Kinsella-Shaw et al. (2011)
Fig. 4 The two conditions of stationary environmental structure, more (left) and less (right), and the participant’s orientation to them during quiet standing on dual force plates. Adapted with permission from “Interleg coordination during quiet standing: influence of age and visual environment on noise and stability” by Kinsella-Shaw et al. (2011)
reconstructed COP, a variable calculated over the two force plates from the COP of each foot and the vertical force measurements exhibited by each foot (Winter 1995; Winter et al. 1996). Figure 3 shows the full complement of measures on the dual force plates and their potential linkages. The net COP is inclusive of them. The participants in Kinsella-Shaw et al. (2006) were all right handed and right legged and constituted two equal groups of old (65–82 years) and young (aged 22–24 years).
13
They performed quiet standing in the setting depicted in Fig. 4 under two levels of illumination and two levels of optical structure. This 2 (age) × 2 (illumination) × 2 (structure) design was directed at two primary predictions and two secondary predictions. The primary predictions were that fluctuations of quiet standing in a stationary environment (1a) are influenced by the visible environment’s structure with the effect greater for older than for younger adults and (1b) depend on the level of environmental
Exp Brain Res (2013) 231:383–396
387
Fig. 5 a Left and right force platforms. b Phase space reconstruction of left platform data. The series X1(t) (black dashed lines) and series X2(t) (solid gray lines), depicted as sinusoids for simplicity, are embedded in a reconstructed phase space. Time-delayed copies of X(t) are used as surrogate dimensions X(t + τ) and X(t + 2τ) for a threedimensional embedding (a minimal and picturable case). CRQ of two embedded time series is shown with intersecting trajectories counted as recurrent points for Cross RECUR calculations and the longest parallel trajectory of X1(t) and X2(t) for Cross MAXLINE calculations. Adapted with permission from “Concurrent cognitive task modulates coordination dynamics,” by Pellecchia et al. 2005
illumination with the effect more pronounced for older than for younger adults. The two secondary predictions were that the effects of the environment’s structure and illumination on fluctuations of quiet standing are (2a) dependent on the fluctuation measure, given the different control and coordination properties that such measures quantify, and (2b) correlated with visual contrast sensitivity separately from chronological age. The experiment’s results were in agreement with the primary predictions: Both reduced illumination and reduced environmental structure affected the postural behavior of the older participants more than the postural behavior of the younger participants. The experiment’s results were also in agreement with the secondary predictions: The effects of the environmental variables were measure dependent and, in some instances, predictable by visual contrast sensitivity separately from chronological age. Kinsella-Shaw et al. (2011) reanalyzed the data of Kinsella-Shaw et al. (2006) in terms of Fig. 3b, that is, the subset of potential linkages defining inter-limb coordination. Arguably, it is this subset that is most directly responsible for modulating axial rotations and fluctuations. The reanalysis used cross-recurrence quantification (CRQ) (see present Fig. 5 and “Appendix”) as the means of measuring the degree of linkage between any two nodes identified in Fig. 3b. The CRQ measures of the three parallel cases (e.g.,
XL(t), XR(t)) were found to be larger in magnitude than the CRQ measures of the six nonparallel cases (e.g., XL(t), ZR(t)), with the largest CRQ measures associated with the linkage between YL(t) and YR(t). The CRQ measures indicated that inter-leg coordination was least noisy and most dynamically stable in the direction faced by the participants (see Fig. 4), as would be expected if fluctuations of a participant’s coronal plane were modulated to preserve axial orientation to the visible environment. The foregoing observations of Kinsella-Shaw et al. (2011) set the stage for evaluating Balasubramaniam and Turvey’s interpretation of their Experiment 2 as showing that lateralization of legs and trunk is not detectable in quiet standing, in the absence of imposed asymmetries. In the present paper we reanalyze Kinsella-Shaw et al.’s (2006) data in terms of the subset of potential linkages shown in Fig. 3c, that is, the subset of potential linkages defining intra-limb coordination. Arguably, it would be this subset that would be most directly involved in any left–right asymmetries manifest in the fluctuations of quiet standing. At issue is whether the CRQ (X, Y), (X, Z), (Z, Y) measures, either some or all, are more pronounced in the right leg of the right-handed participants independently of LLA. If such were the case, the strong version of Geschwind and Galaburda’s (1987) conjecture would be favored: The asymmetry of the lower limbs is no less basic than the asymmetry
13
388
of the upper limbs. Parallels of predictions (1a) and (1b) advanced in Kinsella-Shaw et al. (2006) were also of interest. Would the visible environment’s structure affect right limb CRQ measures more than left limb CRQ measures in an age-dependent manner? Would the level of environmental illumination affect right limb CRQ measures more than left limb CRQ measures in an age-dependent manner?
Method Participants Seven men and five women constituted the group of young adults (22.8 ± .83 years), and six men and six women constituted the group of old adults (72.2 ± 4.9 years). All participants were living independently in the community and driving. All participants gave their consent in accordance with the University of Connecticut Institutional Review Board’s regulations for studies with human participants. None of the participants used any kind of assistive devices, orthoses or prostheses, for ambulation or maintaining upright stance. All had normal or corrected-to-normal visual acuity. Cutaneous sensation of the feet was assessed by a licensed physical therapist using Semmes–Weinstein monofilaments and was intact for all participants. A history of falls over the previous 6 months, medical procedures, and medication use was obtained from each participant. None of the young adults had a history of falls. Of the older adults, seven had zero falls, two had one fall, and three had two falls. All reported falls were noninjurious and self-corrected. None of the participants had a history of use of any medication known to compromise balance. Height of the young adults ranged from 155 cm to 188 cm, with a mean of 163 cm. Weight for this group ranged from 46.34 kg to 92.10 kg, with a mean of 67.62. For the older adults, height ranged from 152 cm to 191 cm, with a mean of 171 cm. Weight for the older group ranged from 56.22 kg to 95.78 kg, with a mean of 73.93 kg. Each person in each group was paid $10 for participating. Determination of the functionally preferred lower extremity The screening procedure for lower limb functional preference incorporated prospective participants’ self-reports and three functional tests. There were three trials per test. The leg selected for use on all three trials of each test was identified as the functionally preferred leg for that test. For all 24 participants, the leg spontaneously self-selected for the three functional tests was consistent with the self-report of right-side functional dominance of the upper extremity. Four prospective participants were excluded from the study
13
Exp Brain Res (2013) 231:383–396
as a result of a discrepancy between self-reports of rightside functional preference and an observed preference for the use of the left leg during some trials of the functional testing. The screening procedure was as follows: 1. Using the Edinburgh Handedness Inventory, the prospective participant reported that the right upper extremity was functionally dominant, which is the preferred limb for tasks requiring greater coordination. Functional preference was then demonstrated by writing. 2. The prospective participant was required to kick a soccer ball with moderate force to the experimenter, who was kneeling directly in front of the kicker at a distance of 4 meters. The leg used to kick the ball was identified as the preferred leg. The accuracy of the kick was not part of the assessment. 3. The prospective participant was required to demonstrate single-leg stance three times and to maintain it for “as long as possible without discomfort.” The leg most frequently selected for unilateral stance was identified as preferred. 4. The prospective participant was required to step up onto a 15-cm-high platform. The leg selected to step with was identified as the preferred limb. Apparatus and data collection COP data were obtained at a sampling rate of 100 Hz using two Advanced Mechanical Technology Incorporated force platforms and a 64-Channel Run Technologies Datapac 2000 Analog-to-Digital Collection System. A Peak Performance Technologies Synchronization Trigger System synchronized data collection across the force plates networked with a dedicated Dell Optiplex GX300 workstation. In each trial, participants stood barefoot on the platforms, arms relaxed at their sides, legs abducted 10–12 deg, with heels 12 cm apart, one foot on each platform. (The platforms were embedded in the floor and separated by a 4-mm gap.) Participants were instructed to stand still and relaxed, and to look at the depth-grating (“more structure”) or at the (“less structure”) whiteboard, depending on the experimental condition (see Fig. 4). COP under each foot was obtained independently from the two force plates. For each foot, COPx and COPy were calculated from the time series of shear forces (F) and moments (M) recorded from the force platforms as follows (Richardson et al. 2007):
COPx =
(Fx · COPz ) − My , Fz
COPy =
(Fy · COPz ) − Mx Fz
Four 100-watt work lamps, controlled from a central custom-built rheostat, were the source used in the low illumination (3 lx) (entailing mesopic vision). The overhead
Exp Brain Res (2013) 231:383–396
fluorescent lights were the source for the high illumination (440 lx) (entailing photopic vision). Ambient illumination levels were verified with an Extech Instruments Heavy Duty Light Meter (Model 407026) for each experimental condition for every participant. The light meter was calibrated at the beginning of each data collection session. (The Extech light meter was used because of its compensatory circuits that ensure accuracy under both incandescent and fluorescent light sources.) The depth-grating (“more structure”) consisted of nine rows of 1.8-cm-diameter aluminum rods (conduits) arrayed three deep, for a total of 27 potentially visible rods. The rods in each row were placed 8 cm apart, with successive rows separated by a distance of 18 cm. Participants stood on the platforms at a distance of 122 cm from the nearest row of the display, positioned such that their eyes were directed roughly at its center (Fig. 4). As a whole, the depth-grating measured 92 cm wide and 105.6 cm high. Consequently, the first row subtended a visual horizontal angle of 41.32 deg and a visual vertical angle of 46.8 deg. The “less structure” condition consisted of a rectangular section of 5-mm-thickness white foam core board of the same vertical and horizontal dimensions as the depth-grating apparatus. It was presented at the same location relative to the participants’ vantage point as the depth-grating, thereby preserving all the same visual angle relationships. The foam core board surface had a flat-white homogeneous finish with no detectable texture or other surface features. An identical section of white foam core board provided a backdrop for the depth-grating apparatus and was affixed flush to the posterior surfaces of the most distant (third) row of rods. In either condition, participants were instructed to simply “look at the array” and were not instructed to focus specifically on the rods or the white screen (see Fig. 4). Data collection was initiated once the participant was in position and indicated that they were comfortable and that their breathing was regular. Procedure There were eight trials in each of the five experimental conditions: (1) eyes closed, (2) eyes open, 3 lx, planar array, (3) eyes open, 3 lx, depth-grating array, (4) eyes open, 440 lx, planar array, and (5) eyes open, 440 lx, depth-grating array. Conditions 2–5 were collected as blocks of eight trials with 5 min separating data collection in each block to allow for full, stable levels of adaptation to the level of available illumination [This method of presentation is consistent with the recommended protocol for testing contrast sensitivity which was important to Kinsella-Shaw et al. (2006). It assures that all the participants had the same opportunity for light–dark adaptation (McMurdo and Gaskell 1991)]. The eyes-closed condition was used to establish a baseline
389
for postural variability in the total absence of visual support, and data in this condition were collected in two fourtrial blocks. The first block preceded data collection in all other conditions; the second block of eyes-closed trials was the final episode of data collection. Subsequent analysis of variance (ANOVA) conducted on all of the obtained measures of COP variability revealed no significant differences between the trials collected in the two eyes-closed blocks for any of the participants. Trials lasted 35 s each, with the initial 5 s excluded from the analysis to eliminate any possible transients that could bias the analysis of the steady-state trajectories. The analyzed portion of each trial yielded 3,000 data points. Participants were allowed to rest as needed. As in Blaszczyk et al. (2000), participants were allowed to freely select a limb load distribution strategy. Data analysis Data analysis took advantage of the provision, by the dual force plates in Kinsella-Shaw et al. (2006), of simultaneous and independent recordings of COPx(t), COPy(t), and GRFz(t) generated under each foot (see Fig. 3a). These data were submitted to LLA and CRQ analyses. Measures of LLA This quantity was calculated in two ways: (1) as the percentage of load on the right foot according to Right Load % = [Right GRFz/(Right GRFz + Left GRFz)] × 100, and (2) as the ratio of body weight fraction put on the more loaded limb to the less loaded limb, alternatively the absolute degree to which loading differs from a 50:50 weight distribution (i.e., independent of direction). Method of CRQ Adding to the remarks on CRQ made above and in the “Appendix,” %Cross RECUR in Fig. 5 is the percentage of states relative to all the states sampled that are returned to (are proximate to each other in phase space under a preestablished distance criterion during the period of observation) by the systems or subsystems under investigation. %Cross MAXLINE expresses the maximum number of states that remain close (satisfy the pre-established distance criterion) over time forming a line of recurrent states arrayed diagonally in phase space, relative to the longest possible line (the line of symmetry), indicative of complete between-systems state-transition congruence (Marwan et al. 2007). Diagonal lines of this kind are present in the common phase space when stable, deterministic, dynamical coordination exists between systems’ trajectories. In CRQ, independently generated time series (such as COPx(t), COPy(t), and GRFz(t)) are embedded in their
13
390
Exp Brain Res (2013) 231:383–396
respective phase spaces and then used to compute a %Cross RECUR plot, providing a graphical representation of: m CRi,j = �(ri − �xi − yi �),
i = 1, . . . , Nx , j = 1, . . . , Ny
This is the equation for the %cross-recurrence matrix, CRm, where N is the number of considered (sampled) states xi (from the first time series) and yj (from the second time series), so that any point xi or yj is said to be %cross-recurrent (an element of the matrix) if the Euclidean distance between the two normalized vectors is less than or equal to the threshold radius r. (This is equivalent to εi, the cutoff distance in simple recurrence quantification analysis.) This threshold distance provides the radius for the sphere (see Fig. 5, Cross RECUR) defined with xi at its center such that any yj falling within the sphere represents a recurrent state in the shared state-space and is plotted as a point. Therefore, the percentage of points that are %Cross RECUR points is given by:
%Cross RECUR =
N 1 m CRi,j N2 i,j=1
The %Cross RECUR measure derived in this manner has been shown to be highly sensitive to even small amounts of stochastic (random) noise. Thus, %Cross RECUR provides a measure of the density of %cross-recurrent points within the CRQ plot and corresponds to the probability of identifying truly recurrent points as such (Thiel et al. 2002; Marwan 2003). As this measure captures the proportion of points that are recurrent relative to the total number of points, its inverse can be interpreted as analogous to Q, the index of system noise measurable in bidirectionally, coupled-pendulum systems (Kudo et al. 2006; Richardson et al. 2007; see “Appendix”). In CRQ, %Cross MAXLINE is the longest shared trajectory (see Fig. 5) and is a measure of the shared activity of the two observed processes (e.g., COPx(t) of right limb and COPy(t) of right limb). More specifically, if the two processes have the same or similar time evolution, parts of the two trajectories in phase space will occupy the same region of phase space and do so for a certain length of time. The longer the time, the longer the shared trajectory or, equivalently, the longer is the line that represents it. The maximum length of the diagonal lines in the %Cross RECUR plot excluding the line i = j is given by:
%Cross MAXLINE = max(li ; i = 1 . . . Ni ) Here li is a diagonal sequence of recurrent points, and Nl is the total number of diagonal lines. As noted above, the quantity MAXLINE, derived from single recurrence or %Cross RECUR, follows from expressing observed MAXLINE as a percentage of the maximum recurrent line length
13
that is possible (Kudo et al. 2006; Richardson et al. 2005). For the coordination of independently controlled systems (see “Appendix”), %Cross MAXLINE can be interpreted as a measure of entrainment (Marwan 2003; Richardson et al. 2007). Under this interpretation, %Cross MAXLINE quantifies mutual convergence of state dynamics at a local space– time scale, comparable to λ (Lyapunov exponent), providing a measure of local attractor strength (Kudo et al. 2006; Richardson et al. 2007). In the present case, the provision is for intra-limb coordination. Parameters for CRQ Before performing phase space reconstruction, all output variables were rescaled (normalized) on a unit interval (0–1). Consistent with our earlier analysis (Kinsella-Shaw et al. 2006, 2011), phase space reconstruction was performed using nine embedding dimensions and a time lag of 0.1 s. Criterion for recurrence was set at 5 % of the maximum distance between points in the distance matrix.
Results LLA The left and right GRFz means were 378.73 ± 115.87 and 352.92 ± 87.88 for the younger group, and 383.53 ± 73.35 and 388.21 ± 68.78 for the older group. Analysis of variance (ANOVA) revealed that effects of Leg, F (1, 22) = 1.72, p = .20, Age, (F
