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LETTER TO THE EDITOR
The present study examined the time and frequency structure of force output in adult humans to determine whether the changes in complexity with age are dependent on external task demands. Healthy young (20–24 yr), old (60–69 yr), and older-old (75–90 yr) humans produced isometric force contractions to constant and sine wave targets that also varied in force level. First, force variability on each force task increased with advancing age. Second, both time and frequency analysis showed that the structure of the force output in the old and older-old adults was less complex in the constant-force level task and more complex in the sine wave force task. Third, the alterations in force output with aging were primarily due to low-frequency bands <4 Hz. These results support the postulation that the observed increase or decrease in physiological complexity with aging is influenced by the relatively fast time scale of external task demands (Vaillancourt DE and Newell KM. Neurobiol Aging 23: 1–11, 2002).
Age-related changes in complexity depend on task dynamics
To the Editor: The changes in complexity most frequently cited in both aging and diseased systems have physiological output consistent with a loss of complexity (3). However, across the cardiovascular, nervous, and endocrine systems, both increases and decreases in complexity with aging and disease occur, collectively termed the bidirectional complexity hypothesis (7). Our recent study tested the bidirectional complexity hypothesis in young (21–35 yr), old (60–75 yr), and older-old (75–90 yr) participants during constant and sinusoidal isometric force production tasks (6). The findings were consistent across all dynamical metrics in showing bidirectional changes in complexity with age that were dependent on the intrinsic dynamics of the experimental task.
The bidirectional complexity hypothesis has been criticized for relying on entropy-based metrics that ignore sequential properties across multiple time scales, thereby misinterpreting the changes of reduced complexity with aging and disease (1, 2). The critique is based on the notion that greater entropy values are not always associated with an increase in physiological complexity. For instance, a white Gaussian noise time series returns a high entropy value even though there is no underlying dynamical structure in the time series. An aggregate analysis method, multiscale entropy analysis (MSE), has been suggested to overcome the limitations of single-scale entropy measures by calculating entropy over different variations of the same data set following a moving average window that varies in length or scale (1).
The purpose of this commentary is to reexamine our previous findings (6) using the MSE method to determine whether the finding of age-related bidirectional changes in complexity was due to biological variation or because of the use of dynamical measures that do not account for scales other than the shortest one. Figure 1 depicts the results from the MSE analysis, in which sample entropy (SampEn) (5) was calculated over different time scales during constant (Fig. 1A) and sinewave (Fig. 1B) force production tasks. ANOVA statistics were used to examine the SampEn (m = 2; r = 0.2) changes across age (3-between subject factor), task (2-repeated factor), and time scale (20-repeated factor) with a Type I 
-level set to 0.05. In both constant and sinewave force production tasks, the SampEn values increase from between 0.25 and 0.50 at the shortest time scale, to greater than 1.25 at the highest MSE time scale (time scale effect, P < 0.05). Although the directionality of age differences in SampEn values was maintained across all time scales, there was a bidirectional change in SampEn with age, depending on the force production task (age by task interaction, P < 0.05). We further explored the age-by-task interaction by conducting two separate two-way ANOVAs for age and time scale. The constant force task (see Fig. 1A) supports the loss of complexity viewpoint, that is, that SampEn was reduced with aging at each time scale (age effect, P < 0.05). In contrast, Fig. 1B demonstrates the opposite finding during the sinewave task, in which the older-old adults had greater SampEn values compared with the young subjects (age effect, P < 0.05).
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GRANTS
This work was supported by grants from the National Institutes of Health (F32-NS-44727, T32-AG-00048, and R01-HD-46918).
ACKNOWLEDGMENTS
We thank Dr. Randall Moorman and Dr. Douglas Lake for supplying the algorithm to calculate sample entropy.
REFERENCES
Department of Movement Sciences and Center for Magnetic Resonance Research, University of Illinois at Chicago, Chicago, Illinois 60612. court1@uic.edu
1Departments of Kinesiology and 3Biobehavioral Health, and 2Gerontology Center, The Pennsylvania State University, University Park, Pennsylvania 16802
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), old (60–75 yr; 
), and older-old (75–90 yr; 
) groups. The task required participants to abduct their index finger against the compressive force load cell, matching the visually determined constant (A) and 1-Hz sinewave (B) force targets.