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Research Reports |
L Fetters, PT, PhD, FAPTA, is Professor, Division of Biokinesiology and Physical Therapy, Department of Pediatrics, Keck School of Medicine, University of Southern California, 1540 Alcazar St, CHP 155, Los Angeles, CA 90033 (USA)
JP Scholz, PT, PhD, is Professor, Department of Physical Therapy and Biomechanics and Movement Science Program, University of Delaware, 307 McKinly Laboratory, Newark, DE 19716 (USA)
Address correspondence to Dr Fetters at: fetters{at}usc.edu
Address correspondence to Dr Scholz at: jpscholz{at}udel.edu
Ohgi et al1 present an interesting approach to investigating differences in the control of spontaneous arm movements in premature infants with and without frank brain injury (BI). The premise of the investigation is that such movements have properties of chaotic systems, requiring nonlinear methods to fully appreciate these properties as well as to distinguish between movements of infants with and without BI. The methods used by the authors provide a promising direction for understanding normal as well as disordered developmental processes. To be truly useful, the results of such analyses should provide new insights about the nature of those processes not obtainable with previous methods. In addition, they should—at least indirectly—motivate ways that clinicians can affect positively the developmental process in infants with BI. We examined the current experimental work with these considerations in mind.
The authors state that their experiment tests 2 hypotheses: "(1) The acceleration time series of upper-extremity spontaneous movements in premature infants demonstrate characteristics of nonlinear dynamics," and "(2) The motor characteristics of infants with BI significantly differ from those without BI, as indicated by increased disorganization of motor control." Because the acceleration profiles of such movements change in time, they are, by definition, a characteristic of a dynamical system. In addition, as the authors correctly point out in the Appendix, "[m]ost physical and physiological systems are inherently nonlinear" (also see Schreiber2). Therefore, this is more of an assumption underlying the authors’ work than a hypothesis.
Regarding their second hypothesis that movement characteristics of infants with BI differ significantly from those of infants without BI, this would not be a surprising finding and already appears in the literature.3–6 The authors imply that linear analyses have failed to identify the differences between infants with and without BI (but see the references cited above). In the current study, they contrasted the results from a linear analysis (power spectral analysis) with 3 nonlinear analyses (comparisons with linearly stochastic surrogate data, embedding dimension, and Lyapunov exponent). The authors’ primary hypothesis then appears to be that differences in movement control between infants with and without BI are best captured by methods of nonlinear time series analysis, based on the assumption that deterministic chaos underlies the movements of infants without BI. The authors predict that the movements of infants with BI will be random, less stable, and more disorganized. Although confirmation of the latter prediction is unlikely to be new, predictions about randomness and instability might be novel (although see below).
Let us consider the single linear method and the 3 nonlinear methods used by these authors and their results. The authors show that analysis of the power spectrum of representative data from each group failed to demonstrate group differences. Indeed, both subjects (one subject from each group) demonstrated frequencies with broad peaks around 1 Hz. The authors state that the high frequency portion of the spectra "seems to follow [a] power law," and, from this, they conclude that the signals suggest a random process. Although the spectra do not differ for the 2 exemplary infants with and without BI, this is insufficient to reject the usefulness of a linear approach in general for the capture of group differences in motor characteristics. This is particularly true because group differences have been demonstrated by other authors3–6 using linear techniques.
The embedding dimension provides a method to estimate the number of dimensions or degrees of freedom (DOFs) required to describe the behavior of a system. However, interpretation of these results may not be straightforward. A system can have a higher number of DOFs because it has more flexibility or because its components are less globally connected through coordination processes. For example, in a study of arm movement synergies underlying reaching to targets by people who have survived a stroke, control subjects who were healthy and people with mild, clinically determined motor impairments appeared to have the ability to couple their joints in more ways than did people with moderate motor impairments (ie, they appeared, effectively, to have more available DOFs).7 This finding was consistent with the relatively fixed hemiparetic synergies in people who had survived a stroke described by Brunnström.8 Moreover, the emergence of infant kicking in full-term infants who are healthy is characterized by increased flexibility of joint coupling, which emerges during the first 6 months of life and replaces the tight coupling of joints seen in the newborn infant and during the first months of life.3,6 Again, an increase in DOFs might describe the development of kicking in infants who are developing typically.
Additionally, although Ohgi and colleagues conclude that their results are consistent with those of Fetters et al3 on infant kicking, indeed, the opposite is true. Fetters and colleagues used spatial-temporal characteristics and joint angle phase characteristics to demonstrate that premature infants with brain damage have constrained stability with less flexibility in their kicking movements when compared with premature infants without brain damage and full term infants who are healthy. These hyper-stabilities have been reported in other populations with neurological damage and are thought to impede functional movement.9 Thus, therapy would be focused on reducing hyper-stabilities and increasing the DOF during the acquisition of functional movement. We might conclude that the opposite therapeutic recommendations might follow from the results of Ohgi et al, but the potential therapeutic implications of their results are not stated.
The conclusions of many studies of people with BI were based on results obtained by linear analysis techniques.10–15 For example, Reisman and Scholz7 used principal component analyses (PCA) to identify the number of modes of joint coupling required to explain the majority of joint variance during reaching. The conclusion of the current study, that the movements of infants with BI exhibit higher dimensionality (ie, more independent DOFs) than those of infants without BI, is in contrast with the conclusions of these other studies, particularly those of Fetters et al.3 Would a reanalysis of the data from these other studies using similar nonlinear methods lead to a different conclusion? Perhaps it would. However, the conclusion of Fetters et al and others is more consistent with clinical observations about the nature of movements in people with BI (ie, they are more constrained and less flexible).
Moreover, the implications of the authors’ results are not immediately clear. Although the difference between the infant groups in the number of DOFs was significant, the clinical significance of, for example, 6 versus 7 dimensions is not immediately obvious. How are we to interpret what these dimensions represent? For example, does the fact that the analysis is based on the time series of a sensor placed at the wrist imply that the number of dimensions represents how many independent joint movements contribute to the infant's wrist movement? This is probably not the case. Moreover, the reported number of dimensions in both cases is quite large such that, while there may be significant quantitative differences, one wonders whether these dimensions are really different qualitatively. This is not meant to imply that the results of such dimensional analyses cannot be useful. However, the interpretation of the results provided by the authors is inadequate in this regard. In the case of using linear analysis methods such as PCA, one can at least differentiate between which of the movement components contribute most to each PC, each of which accounts for a different proportion of the total variance of the experimental data. Of course, one has to make an a priori commitment to which DOFs are of importance.
Similar arguments can be made about the results based on the Lyapunov exponent. Although the reported differences between groups were significant, how clinically meaningful is a difference in exponent of 0.37, and how should we interpret this in terms of behavior? In other words, can we conclude that these are qualitatively meaningful differences just because they differ quantitatively? The issue is not whether these measures provide a means of distinguishing between such infant populations. If this were the only way to make such distinctions, then such measures would be a useful starting point, but what advantage do they provide over other measures based on linear analysis methods? If we can differentiate between such populations with linear measures that are more readily interpretable, then the usefulness of nonlinear methods without clear interpretation is questionable.
Finally, the authors use surrogate data generated by linear stochastic processes to test the hypothesis that the experimental data have truly chaotic dynamics. The authors report for 2 infants with BI that the prediction error of the original data was higher than the prediction error of the surrogate data. This result led them to conclude that fluctuations of the acceleration time series did not have chaotic characteristics in these 2 infants, but rather were random. However, a more reasonable conclusion would have been that the time series of these infants had a more random character than for the other infants, rather than that they are not chaotic. In fact, the potential problem with this analysis is that the conclusions depend on support for the null hypothesis (ie, that there are no differences between the measures). Failing to reject the null hypothesis is not the same conclusion as stating that the groups are the same. Anyone familiar with statistics knows that rejecting the null hypothesis is difficult to achieve and depends on adequate statistical power. However, the analyses conducted were based on a single 200-second time series from each infant and appear to be based on differences relative to the 95% confidence interval (CI).
Moreover, the conclusions based on the investigators’ results are themselves questionable. For example, Table 2 shows that the prediction error was clearly higher for the original y-axis data for BI group infants 1 and 5. When considering infant 5's result for the x-axis and the z-axis, the prediction error was actually higher for the surrogate data, although the difference was within the 95% CI, which apparently is why the authors draw their conclusion. However, infant 1 of the group without BI had a similar difference for the y-axis that also was within the 95% CI. Why do the authors not consider this infant's data to be based more on random than chaotic processes? Thus, it is unclear what analytical thinking was actually used to draw the authors’ conclusions. Finally, the results test the correspondence of the actual data with linear stochastic data. Thus, even when the results suggest that there is a difference, this does not rule out the possibility that the underlying processes are the result of nonlinear stochastic processes.
Considering a somewhat less critical issue, one also might question whether looking at the 3 movement dimensions separately makes sense. For example, the authors reported that, based on the position of the accelerometer, each axis of movement corresponds to a particular anatomical direction of arm movement. However, with the accelerometer (presumably) strapped to the lateral side of the infant's wrist, medial-lateral (internal-external) arm rotation would change the orientation of the accelerometer, leading a particular arm movement (eg, abduction-adduction) to occur along a different axis of the accelerometer. Therefore, it is not clear that the separation of motion along each axis is actually meaningful or consistent with the authors’ assumptions.
The broader concern of the experimental results presented here is whether the methods were applied such that they can be clearly interpreted. Are such conclusions made from the analysis of one variable—in this case, movement of the wrist joint—appropriate? As pointed out by Schreiber, "bold interpretations of Takens’ theorem [about the embedding dimension],... that we can recover the full dynamics of the human body from a recording of a single variable, is not only in contradiction with common sense but also disproven by mathematical arguments."2(p17) Although the approach provided by the authors is novel and interesting theoretically, the current application of the measures and the extremely limited data set make any conclusions based on them about differences in motor control between infants with and without BI speculative at this time.
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  S. Ohgi, S. Morita, K. K. Loo, and C. Mizuike Author Response Physical Therapy, September 1, 2008; 88(9): 1037 - 1038. [Full Text] [PDF]
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