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The Journals of Gerontology Series A: Biomedical Sciences and Medical Sciences
, Volume Advance Article – Feb 17, 2018

6 pages

/lp/ou_press/novel-behavioral-and-neural-evidences-for-age-related-changes-in-force-W7LbsXbxeg

- Publisher
- Oxford University Press
- Copyright
- © The Author(s) 2018. Published by Oxford University Press on behalf of The Gerontological Society of America. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.
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- 1079-5006
- eISSN
- 1758-535X
- D.O.I.
- 10.1093/gerona/gly025
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- See Article on Publisher Site

Abstract This study investigated age-related changes in behavioral and neural complexity for a polyrhythmic movement, which appeared to be an exception to the loss of complexity hypothesis. Young (n = 15; age = 24.2 years) and older (15; 68.1 years) adults performed low-level force-tracking with isometric index abduction to couple a compound sinusoidal target. Multiscale entropy (MSE) of tracking force and inter-spike interval (ISI) of motor unit (MU) in the first dorsal interosseus muscle were assessed. The MSE area of tracking force at shorter time scales of older adults was greater (more complex) than that of young adults, whereas an opposite trend (less complex for the elders) was noted at longer time scales. The MSE area of force fluctuations (the stochastic component of the tracking force) were generally smaller (less complex) for older adults. Along with greater mean and coefficient of ISI, the MSE area of the cumulative discharge rate of elders tended to be lower (less complex) than that of young adults. In conclusion, age-related complexity changes in polyrhythmic force-tracking depended on the time scale. The adaptive behavioral consequences could be multifactorial origins of the age-related impairment in rate coding, increased discharge noises, and lower discharge complexity of pooled MUs. Human Aging, Motor Activity, Muscles, Motor unit Introduction The passage of time impairs the functioning of biological organisms composed of numerous interacting components. A hallmark signature of aging is an increase in the size of behavioral variability but a decline in biological complexity for the loss of structural components and their coupled linkages (1,2). For instance, when older adults exert constant isometric force, their force fluctuations are larger in size but less complex than those of young adults (3,4). Functionally, a larger size of force fluctuations undermines the precision of force control, and a loss of force complexity reduces one’s adaptability to multiple categories of task constraints (2,5). Increases in age-related force variability link to a greater discharge variability of motor units (MUs), particularly at lower target forces (6,7). A key contributor to the reduction in force complexity is degenerative changes in MUs, such that fewer motor neurons of the elderly are coordinated by enhanced low-frequency common oscillatory inputs (3,8,9). Also, the age-related loss of force complexity corresponds to the enhanced regularity of MU discharge times in the elderly (10), due to the limited use of visuospatial information for force gradation (11,12). Nevertheless, it seems that the loss of physiological complexity hypothesis is not universally supported. Vaillancourt and Newell (13) first challenged the hypothesis in a study of mono-rhythmic force contraction (attractor dimension of oscillatory dynamics =1) in older adults. The older adults reduced more variable and complex force behaviors than those of young adults, in terms of larger approximate entropy and less negative spectral slope. The authors argued that the older adults were incapable of reducing intrinsic force dynamics to a lower dimension during sinusoidal force-tracking, supported by decline in firing rate modulation of MUs at the target frequencies (14). Hence, a contrasting perspective, a bi-directional hypothesis, was proposed: age-related physiological complexity is selectively modifiable to task constraints (2,5,15). However, it is not known whether bi-directional hypothesis that adequately accounts for mono-rhythmic force contraction of one attractor dimension of oscillatory dynamics can be generalized to polyrhythmic contraction, when attractor dimension of oscillatory dynamics is larger than 1. In fact, a known polyrhythmic physiological signal is electroencephalography, and age-related complexity changes in electroencephalography was either consistent with the loss of complexity hypothesis (16) or dependent on time scale of entropy measure (17,18). On the other hand, the relative contributions of deterministic and stochastic processes to the changes in force complexity of the elderly have not been specified in the previous studies. In addition to force fluctuation dynamics, the purpose of this study examined MU discharge patterns to reinvestigate age-related loss of behavioral and neural complexity for a polyrhythmic force task. In support of independent verification methods (19), previous studies have validated that spike events of MU discharge can be accurately and reliably decomposed from multielectrode surface electromyography with knowledge-based artificial intelligence algorithm during isometric static (20–22) and rhythmic (23,24) contractions. The particular goals were to capture the stochastic influences on force complexity across various time scales, and to characterize the dimensional changes in the neural noises underlying the complexity modulation in the elderly. For a compound sinusoidal force task, the main hypotheses tested were as follows: (1) multiscale entropy (MSE) of the tracking force and force fluctuations (the stochastic component of the tracking force) would decrease with advanced age; (2) the rate coding of MUs responsible for polyrhythmic force genesis would be undermined with aging, and (3) older adults would produce a greater MU discharge variability and a smaller discharge complexity than those of young adults. Methods Subjects Fifteen young healthy adults (8 female and 7 male, age: 24.2 ± 1.4 years, range 21–32 years) and 15 older healthy adults (8 female and 7 male, age: 68.1 ± 2.0 years, range: 65–78 years) participated in this study. Subjects were volunteers from the local community or a university campus who responded to a poster or a network advertisement. All of the participants were right-handed and had no history of neurological or musculoskeletal diagnoses. They participated in the experiment after signing personal consent forms approved by an authorized institutional human research review board at the University Hospital (No. A-ER-103–413). Experimental Procedures Following verbal instructions and three practice trials, the participants formally performed a polyrhythmic isometric force task with the dominant index finger. Participants were seated 60 cm in front of a computer monitor (spatial resolution: 1920 × 1080 pixels) with the right shoulder abducted by 45°, and the resting forearm was restrained by a thermoplastic splint on the table. The index finger was held slightly abducted (5°), and its abduction force was measured using a force transducer (Model: MB-100, Interface Inc.). The maximal voluntary contraction (MVC) of the first dorsal interosseus (FDI) was predetermined by the maximal force during three 3-s maximal contractions separated by 3 min pauses. The MVC was used to rescale the force output. All participants coupled the force of the index abduction with a compound sinusoidal signal (0.2 and 0.5 Hz) on the monitor. The target signal fluctuated in a small range of 1.5% MVC around a mean level of 30% MVC (Figure 1). To reach the visual target, the participants increased the force output from zero to 30% MVC within 3 s after a latency period of 3 s (slope: 10% MVC/s). After a short steady contraction of 3 s at 30% MVC, they varied the force output to match the compound sinusoidal target signal for another 26 s (the time window of interest: the 9th to 35th s) (Figure 1). Force output returned to the resting state within 3 s following another 3-s latency period. The entire duration of one experimental trial was 44 s. The force output and target signal were sampled at 1 kHz by an analog-to-digital converter with 16-bit resolution (DAQCard-6024E; National Instruments Inc.), controlled by a custom program running on a Labview platform (Labview v.8.5, National Instruments Inc.). Figure 1. View largeDownload slide Decomposition of force data and EMG signal. The target signal and representative tracking force in the time window of interest after removal of a linear trend (the lower right plot). The conditioned tracking force is decomposed into deterministic components and stochastic component (or force fluctuations) (the lower left plot). The deterministic components are of the same spectral ingredients as the target signal. The surface EMG is decomposed to motor unit spike trains with the previously proved algorithm (the upper plots). Figure 1. View largeDownload slide Decomposition of force data and EMG signal. The target signal and representative tracking force in the time window of interest after removal of a linear trend (the lower right plot). The conditioned tracking force is decomposed into deterministic components and stochastic component (or force fluctuations) (the lower left plot). The deterministic components are of the same spectral ingredients as the target signal. The surface EMG is decomposed to motor unit spike trains with the previously proved algorithm (the upper plots). Electromyographic Recordings Multielectrode surface electromyography (Bagnoli sEMG system, Delsys Inc) was used to record the activity of the FDI muscle following skin preparation and proper sensor application. Five surface pin-sensors with blunted ends (0.5 mm diameter) were placed at the corners and at the center of a 5 × 5 mm square. The analog EMG signals from each pin-sensor were amplified (gain = 1,000) and band-pass filtered (cut-off frequencies 20 and 450 Hz, 80 dB/octave roll-off) (23). The conditioned EMG signal of each channel was sampled at 20 KHz to avoid phase skew across channels (20,21). EMG works v.4.1 (Delsys Inc) was used to separate the superimposed action potentials of the entire data collection period (44 s) from the four EMG channels under the framework of artificial intelligence (20,21). The decomposition processing resulted in binary spike trains that coded the timing of discharge events for MUs with values of 0 or 1 (Figure 1). Surface decomposition algorithms have been shown to produce convincing decomposition results via independent verification methods (19). The Decomposition-Synthesis–Decomposition-Compare (DSDC) test was used to validate the accuracy of the EMG decomposition of each motor unit action potential train (MUAPT) (20,25), showing that the decomposition accuracy of the MUAPTs of the algorithm ranged from 92.5 to 97.6%. In this study, MUs of low decomposition accuracy (<90%) were automatically discarded from further analysis. Data Analysis To exclude force data irrelevant to visuomotor processes and error correction (such as 8–12 Hz physiological tremor) (26), the real force was conditioned with a low-pass filter (cut-off frequency: 6 Hz). Task error was denoted as the root mean square (RMS) value of mismatch between the tracking force and target signal. A force decomposition process was conducted to separate deterministic force components containing the target frequencies (0.2 and 0.5 Hz) and stochastic force fluctuations (Figure 1). The force fluctuation profile was obtained by conditioning the force output with a zero-phasing notch filter that passes all frequencies except for target rates at 0.2 and 0.5 Hz. The transfer function (H(z)) of the notch filter was: H(z)=b0(1−ejw0z−1)(1−e−jw0z−1)(1−ejw1z−1)(1−e−jw1z−1)(1−rejw0z−1)(1−re−jw0z−1)(1−rejw1z−1)(1−re−jw1z−1)r = 0.9995, w0 = π/900, w1 = π/360. Subtracting the force fluctuation profile from the force output resulted in a deterministic force component spectrally identical to the target rates. RMS was applied to the deterministic force component and the force fluctuations. RDet/Fc was defined as the RMS of the deterministic force component divided by the RMS of the force fluctuations. The force spectral profile of the tracking force was estimated with a fast Fourier transform and the Welch method (Hanning window, window length: 13 s, overlapping time segment: 20% window length) with a spectral resolution of 0.01 Hz. The spectral peaks of the target frequencies of 0.2 Hz (P.2max) and 0.5 Hz (P.5max) were featured. The percentages of the residual low-frequency (Pres_l) and high-frequency components (Pres_h) were denoted as the spectral areas lower than 0.1 Hz and above 1 Hz divided by the overall spectral area of the force output, respectively. After a down-sampling process at 100 Hz (13,27), the complexity of the tracking force and force fluctuations was quantified with MSE via a coarse-graining process to reveal a sample entropy (SampEn) curve across different time scales. The mathematical formula of sample entropy was SampEn(m,r,N)=−log(∑i=1N−mAi∑i=1N−mBi) where r = 15% of the standard deviation of the force channel, m is the length of the template (m = 2), and N is the number of data points in the time series. Ai is the number of matches of the ith template of length m + 1 data points, and Bi is the number of matches of the ith template of length m data points. The complexity measure was performed, and each time scale represented 10 ms. MSE areas were denoted as summations of SampEn for the time scales of 1–10, 11–20, 21–30, 31–40, 41–50, and 51–60. A larger MSE area represented a noisier force structure, and vice versa. The discharge variables of the MUs in the time window of interest were determined based on the whole decomposed EMG data. Inter-spike intervals (ISImean) was the mean value of all ISI for an individual MUAPT, and the ISIGAV was the averaged value of the ISImean for all MUs. The temporal variability of a single MU was assessed with the coefficient of variation of ISI (CV-ISI) in one MUAPT, and CV-ISIGAV was the mean value of CV-ISI for all MUs in an experimental trial. Experimentally observed ISI variability among MUs was represented with the CV of the ISImean of all MUs (CV-ISImean) in an experimental trial. The rate code spectrum of each MU was estimated with a fast Fourier transform and the Welch method using the same parameter settings for force data. Then we determined the percentage of MUs that discharged at the target frequencies in an experimental trial with the rate code spectrum of each MU. As force behaviors are tuned to pooled MU discharges, the cumulative discharge rate (CDR) was characterized by convolution of the cumulative spike trains of all identifiable MUs with a Hanning window of 400 ms in duration (25). The resulting CDR, which reflects low-frequency neural drive to a muscle, is a function of force fluctuations (28). After down-sampling the CDR at 100 Hz like force data, the complexity of the CDR was measured with MSE. The MSE areas of the CDR for the time scales of 1–10, 11–20, 21–30, 31–40, 41–50, and 51–60 were determined. All of the force variables and discharge variables of the three experimental trials were averaged subject-by-subject. Signal processing were completed in Matlab (Mathworks Inc.). Statistical Analysis Independent t statistics were used to examine differences in MVC, tracking-force variables, force fluctuation variables, and MU discharge variables between the young and older groups. Data are presented as group means ± 1 standard error of the mean. All statistical analyses were performed in IBM SPSS Statistics (v19). The level of significance was 0.05. Results Force Characteristics The young adults exhibited a greater MVC (23.2 ± 1.4 N) than that of the older adults (18.1 ± 1.4 N) (t28 = 2.567, p = .016). The task errors (Young: .665 ± .037 % MVC; Older: 1.743 ± 0.250% MVC, t28 = −4.572, p < .001) and force fluctuations (Young: 0.450 ± 0.031% MVC; Older: 1.153 ± 0.175% MVC, t28 = −3.994, p < .001) of the older adults were greater than those of the young adults. The ratio of the amplitude of the deterministic force component to that of force fluctuations (RDet/Fc) was smaller for the older adults (0.389 ± 0.028) than for the young adults (0.956 ± 0.091) (t28 = −5.458, p < .001). Figure 2A shows the pooled power spectra of the detrended tracking force for young and older adults. Figure 2B contrasts the spectral variables of the tracking force of the young and older adults. The spectral peaks at 0.2 Hz (P.2max) (t28 = 5.193, p < .001) and 0.5 Hz (P.5max) (t28 = 6.890, p < .001) of the older adults were smaller than those of the young adults. The older adults had larger low-frequency (Pres_l) (t28 = −3.802, p = .001) and high-frequency (Pres_h) (t28 = −4.776, p < .001) residual powers as compared to the young adults. Figure 2. View largeDownload slide (A) Pooled power spectra of the tracking force. (B) The contrast of population means of all the spectral variables between the young and older groups. (P.2max and P.5max: spectral peaks of force at 0.2 and 0.5 Hz: Pres_l: residual low-frequency force power; Pres_h: residual high-frequency force power). Figure 2. View largeDownload slide (A) Pooled power spectra of the tracking force. (B) The contrast of population means of all the spectral variables between the young and older groups. (P.2max and P.5max: spectral peaks of force at 0.2 and 0.5 Hz: Pres_l: residual low-frequency force power; Pres_h: residual high-frequency force power). Figure 3A shows the pooled MSE curves (SampEn versus time scale) of tracking force and force fluctuations of the young and older adults. Of note was that the age-related variations in MSE curve for tracking force seemed to be scale-dependent. Figure 3B is summary results of independent t statistics for the MSE areas of the tracking force and force fluctuations of the two age groups in various time scales. For the tracking force (Figure 3B, the left plot), the MSE1–10 of the older adults was greater than that of the young adults (t28 = −2.523, p = .018), whereas the MSE31-40 (t28 = 2.881, p = .008), MSE41–50 (t28 = 4.318, p < .001), and MSE51–60 (t28 = 5.599, p < .001) of the older adults were smaller than those of the young adults. In contrast, the MSE areas of force fluctuations (time scales: 11–60)(Figure 3B, the right plot) of the older adults were largely smaller than those of the young adults (MES11–20: t28 = 2.085, p = .046; MES21–30: t28 = 2.551, p = .016; MES31-40: t28 = 3.155, p = .004; MES41–50: t28 = 3.136, p = .004; MES51–60: t28 = 2.736, p = .012), except for MSE1–10 (t28 = 1.167, p = .117). Figure 3. View largeDownload slide (A) The contrast of pooled multiscale entropy (MSE) curves of tracking force and force fluctuations for different time scales between the young and older groups. (B) The contrast of MSE areas of tracking force and force fluctuations for different time scale intervals between the two groups. Each time scale represents 10 ms. (SampEn: Sample entropy). Figure 3. View largeDownload slide (A) The contrast of pooled multiscale entropy (MSE) curves of tracking force and force fluctuations for different time scales between the young and older groups. (B) The contrast of MSE areas of tracking force and force fluctuations for different time scale intervals between the two groups. Each time scale represents 10 ms. (SampEn: Sample entropy). MU Discharge Characteristics The average numbers of analyzed MUs in an experimental trial for the young and older adults were 27.1 ± 1.1 and 26.8 ± 1.2, respectively. Table 1 contrasts discharge variables between the young and older adults. The grand average of the mean inter-spike interval (ISIGAV) of the older adults was greater than the ISIGAV of young adults (p = .043). The grand average of the coefficient of variance for the inter-spike interval (CV-ISIGAV) and the coefficient of variance of the mean inter-spike interval among MUs (CV-ISImean) was group dependent (p < .05), which indicated a greater variability of the inter-spike interval of a single MU and a greater variance of the mean inter-spike interval among MUs for the older adults. Figure 4A displays the rate code spectra of three typical MUs consisting of target frequencies of 0.2 and/or 0.5 Hz. The discharge spectrum of MU C contained both target frequencies, while MU A and MU B discharged at either 0.2 or 0.5 Hz. The upper plot of Figure 4B shows the averaged peak amplitude of the rate code spectra at 0.2 and 0.5 Hz for the young and older adults. The results of independent t statistics revealed that the peak amplitude of 0.2 Hz for the young adults was larger than that of the older adults (t28 = 2.227, p = .034). Only a marginally significant age effect was found on the peak amplitude of 0.5 Hz (t28 = 1.871, p = .072). The percentage of MUs with rate codes at 0.2 Hz was age-dependent, and the young adults had a higher percentage of MUs with rate codes at 0.2 Hz as compared to the older adults (t28 = 3.339, p = 0.002). The percentage of MUs with rate codes at 0.5 Hz was not significantly age-dependent (t28 = 1.555, p = 0.131). Figure 5A contrasts the pooled MSE curves of the CDR between the young and older adults. Figure 5B shows scale-dependent differences in CDR MSE area between young and older adults. The MSE area of the older adults was smaller than that of the young adults at the time scales of 31–40 (t28 = 2.133, p = 0.042) and 41–50 (t28 = 2.104, p = 0.045). Table 1. Discharge Variable of Motor Units Discharge Variables Young Older Statistics ISIGAV (ms) 60.75 ± 2.23 68.22 ± 2.72 t28 = −2.120, p = .043 CV-ISIGAV 0.214 ± 0.004 0.232 ± 0.026 t28 = −2.355, p = .026 CV-ISImean 0.241 ± 0.014 0.291 ± 0.008 t28 = −3.114, p = .004 Discharge Variables Young Older Statistics ISIGAV (ms) 60.75 ± 2.23 68.22 ± 2.72 t28 = −2.120, p = .043 CV-ISIGAV 0.214 ± 0.004 0.232 ± 0.026 t28 = −2.355, p = .026 CV-ISImean 0.241 ± 0.014 0.291 ± 0.008 t28 = −3.114, p = .004 Note: CV-ISIGAV: grand average of coefficient of variance of spike intervals in a spike train for all motor units. CV-ISI mean: coefficient of variance of mean inter-spike interval among all motor units; ISIGAV: grand average of mean inter-spike interval for all motor units. View Large Table 1. Discharge Variable of Motor Units Discharge Variables Young Older Statistics ISIGAV (ms) 60.75 ± 2.23 68.22 ± 2.72 t28 = −2.120, p = .043 CV-ISIGAV 0.214 ± 0.004 0.232 ± 0.026 t28 = −2.355, p = .026 CV-ISImean 0.241 ± 0.014 0.291 ± 0.008 t28 = −3.114, p = .004 Discharge Variables Young Older Statistics ISIGAV (ms) 60.75 ± 2.23 68.22 ± 2.72 t28 = −2.120, p = .043 CV-ISIGAV 0.214 ± 0.004 0.232 ± 0.026 t28 = −2.355, p = .026 CV-ISImean 0.241 ± 0.014 0.291 ± 0.008 t28 = −3.114, p = .004 Note: CV-ISIGAV: grand average of coefficient of variance of spike intervals in a spike train for all motor units. CV-ISI mean: coefficient of variance of mean inter-spike interval among all motor units; ISIGAV: grand average of mean inter-spike interval for all motor units. View Large Figure 4. View largeDownload slide (A) Rate coding spectra of typical motor units. (B) The mean amplitude of the spectral peaks and the percentages of MUs that discharge at target frequencies. Figure 4. View largeDownload slide (A) Rate coding spectra of typical motor units. (B) The mean amplitude of the spectral peaks and the percentages of MUs that discharge at target frequencies. Figure 5. View largeDownload slide Pooled multiscale entropy (MSE) of different time scales (A) and population means of respective MSE areas (B) of cumulative discharge rate (CDR) for the young and older groups. Figure 5. View largeDownload slide Pooled multiscale entropy (MSE) of different time scales (A) and population means of respective MSE areas (B) of cumulative discharge rate (CDR) for the young and older groups. Discussion The purpose of this study was to reinvestigate age-related changes in behavioral and neural complexity for a force task with two attractor dimension of oscillatory dynamics. Despite that the older adults demonstrated greater MSE of tracking force at shorter time scales, MSE area at longer time scales of the older adults was conversely smaller than those of the young adults. The MSE of force fluctuations (the stochastic component) that consisted of a greater portion of tracking force for older adults was generally lower as compared to that of young adults, in collaboration with the lower complexity of the CDR at longer time scales in the older adults. This study clearly revealed that the age-related force complexity of polyrhythmic isometric contraction depended on the time scale of the entropy measure. The behavioral results and neural correlates are critical to rethinking of the theoretical position on the modulation of biological complexity with aging. The loss of physiological complexity in the neurobehavioral system (such as cardiac rhythm, postural control, etc.) is a generic feature of aging (1,29). For static isometric contraction at low and medium levels, the age-related loss of complexity in force fluctuations (13,30) and EMG signals (1) was reported. But the hypothesis was challenged by a pioneering study based on sinusoidal force tracking at 1 Hz (13). Vaillancourt and Newell (13) found that older adults had a higher approximate entropy and less negative spectral slope of tracking force when the target constraint was mono-rhythmic (attractor dimension of task intrinsic dynamics = 1). This postulation was also examined with MSE (27). The exception of age-related complexity loss for the limit-cycle attractor task led to the loss of adaptive hypothesis (2,5,15), which assumes a bidirectional changes (increase or decrease) in force complexity with respect to attractor dimension of task intrinsic dynamic. In this study, a polyrhythmic force task was investigated, in an attempt to generalize the bi-directional hypothesis (2,5,15). Also, we extended MSE measures at longer time scales (200–600 ms) than explored previously, considering that the longer-range correlations could more reliably index the system flexibility (30,31). Consistent with the results of Vaillancourt et al. (27), the MSE1–10 of tracking force at shorter time scales (10–100 ms) was larger for the older adults (Figure 3A and B), the left plots). In contrast, the MSE areas of the tracking force at longer time scales (MSE31–40, MSE41–50, and MSE51–60) in the older adults were conversely smaller than those of the young adults. Theoretically, this loss of complexity across the longer scales related mostly to low-frequency oscillations (or potentiation of Pres_l) and complexity enhancement in the lower scales were subject to non-linear interaction of information about both high- and low-frequency oscillations (or potentiation of Pres_l and Pres_h) (Figure 2A and B) (32), following age-related flattering of the force power spectrum. Age-related flattering of the power spectrum was attributable to atypical increases in MU discharge variability (6,33), lower mean discharge rate (34) (Table 1), and decoupling of the populating spiking activity from the oscillatory regimen (Figure 4B) (35,36). Interestingly, the shift in entropy with respect to time scale for polyrhythmic tracking force with age was nicely compatible with that for Electroencephalography (EEG) signal with multi-oscillatory dynamics (17,18), contrary to increase in complexity of mono-rhythmic force task (13,14) and decrease complexity of static force task (3,4) in the healthy elderly. Based on the theorem of Fourier approximation, mono-rhythmic force, polyrhythmic force in this study, and static force can be modeled with one, two, and infinite spectral components, respectively (or attractor dimensions =1, 2, and infinite). The time-scale-dependent effect in this study is reminiscent of a shift in the trend of force complexity modulation in the elderly with respect to attractor dimension of oscillatory dynamics. Force complexity of the older adults potentiates in the very low attractor dimension, and it progressively decreases for increasing attractor dimension of oscillatory dynamics. Hence, age-related complexity modulation of polyrhythmic force was a transitional phase, manifested with both increase and decrease in force complexity at various time scales. Behavioral expression of the loss of complexity hypothesis for a polyrhythmic force could be masked by a lacking of distinguishing the relative contributions of stochastic processes to the changes in the complexity of polyrhythmic force. The dedifferentiation of stochastic force components with advanced age is worthy of note (Figure 3A and B), the right plots). As the force fluctuations functionally serve to additive accuracy control to minimize force tracking deviations (37,38), the low structural complexity with large force fluctuations for the elderly indicated that their force gradation strategy was governed by simple causality. The older adults could not meet task constraints by preserving stability along with flexibility. At the motoneuronal level, we also noted the dedifferentiation of the CDR, or the effective neural drive to predict force steadiness (28,39), at longer time scales (MSE31–40 and MSE41–50) (Figure 5A and B). The complexity reduction in MU discharge linked to the degenerative changes in an aging neuromuscular system, including enhanced common oscillatory inputs to fewer but larger MUs due to collateral sprouting (9,40). In conclusion, age-related modulation of complexity for a polyrhythmic force task depends on time scale of entropy measures. Age-related complexity modulation of a polyrhythmic force task seems to be the transitional stage of age-related complexity modulations between a static force task and a mono-rhythmic force task. Nevertheless, aging does reduce the complexity in the stochastic component of tracking force (force fluctuations) and CDRs of MUs during the polyrhythmic force task. Namely, force gradation strategy to remedy tracking deviations for older adults is not as rich and flexible as compared with that for young people. Funding This research was partially supported by grants from the Ministry of Science and Technology, Taiwan, R.O.C., under Grant no. MOST 105-2410-H-040-009. Conflicts of Interest The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. References 1. Lipsitz LA, Goldberger AL. Loss of ‘complexity’ and aging. 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The Journals of Gerontology Series A: Biomedical Sciences and Medical Sciences – Oxford University Press

**Published: ** Feb 17, 2018

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