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Model-based assessments of the effects of age and ankle fatigue on the control of upright posture in humans
Gait & Posture 30 (2009) 518–522
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Gait & Posture journal homepage: www.elsevier.com/locate/gaitpost
Model-based assessments of the effects of age and ankle fatigue on the control of upright posture in humans Xingda Qu a,*, Maury A. Nussbaum b, Michael L. Madigan c a
School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore Department of Industrial and Systems Engineering, Virginia Tech, Blacksburg, VA, USA c Department of Engineering Science and Mechanics, Virginia Tech, Blacksburg, VA, USA b
A R T I C L E I N F O
A B S T R A C T
Article history: Received 27 March 2009 Received in revised form 21 July 2009 Accepted 30 July 2009
The aim of this study was to investigate how and why age and localized muscle fatigue affect postural control using model-based simulations. A balance control model, based on an optimal control strategy, was used to simulate trials of quiet upright stance both pre-fatigue and following induced ankle plantarflexor fatigue. Empirical data were obtained from an earlier study that included both younger and older participants. Effects of age and ankle fatigue were determined from center-of-pressure (COP) measures and fitted model parameters. Though some discrepancies existed, the simulated effects of age and ankle fatigue were consistent with experimental findings in terms of trends in COP-based measures with age and ankle fatigue. Changes in both COP-based measures and model parameters were used to infer potential underlying causal mechanisms for the observed effects of age and ankle fatigue. For example, the model-based simulations indicated that sensory delay time increased with age and ankle fatigue by 31.1% and 2.9%, respectively, suggesting a potentially important role for such delay in postural control and fall risks. ß 2009 Elsevier B.V. All rights reserved.
Keywords: Balance Postural control Age Ankle fatigue Model-based simulation
1. Introduction Falls are common events in both daily and occupational activities. It was reported that more than 44% of all injuries in 2000 resulted from falls or fall-related incidents [1]. Many falls are subsequent to a ‘‘loss-of-balance’’. Hsiao and Simeonov [2] summarized a number of risk factors that could compromise balance and highlighted the need for better understanding the roles of each factor in the control of balance. Among these diverse risk factors, the present work emphasized two particular intrinsic factors: age and localized muscle fatigue (LMF). These factors are considered of importance since falls occur more frequently in older adults, and LMF is commonly experienced in both daily activities and occupational settings. Both age and LMF affect the way in which humans control balance and posture, and the quality of the postural control mechanisms. For example, aging can decrease strength [3] and the speed of a response to loss of balance [4], both of which result in an increased fall risk [5]. LMF appears to challenge the postural control system, as evidenced by increased COP mean velocity
during upright stance [6,7]. Fatigue induced in simulated occupational tasks, such as repetitive lifting [8] and overhead assembly work [9], has also been found to impair postural control. As an adjunct to biomechanical and neurophysiological studies, mathematical models are often used to study postural control and balance [10,11]. Such models have the advantage of suggesting how the entire system functions and how individual components influence the overall system’s response [12]. Thus, model-based simulation may provide some understanding of underlying postural control mechanisms. We recently presented a balance control model, based on an optimal control strategy, which can simulate spontaneous sway behaviors during quiet upright stance [13]. In the current study, the purposes were to evaluate the ability of the model to simulate age and LMF effects, and to employ the model to investigate how and why age and LMF affect postural control. Based on prior evidence, it was hypothesized that the model would be able to accurately simulate postural changes caused by age and LMF, and that simulation results regarding postural control mechanisms would be consistent with previous findings. 2. Methods 2.1. Participants and experimental procedures
* Corresponding author at: School of Mechanical and Aerospace Engineering, Nanyang Technological University, Blk N3, North Spine, Nanyang Avenue, Singapore 639798, Singapore. Tel.: +65 67904458; fax: +65 67924062. E-mail address: [email protected] (X. Qu). 0966-6362/$ – see front matter ß 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.gaitpost.2009.07.127
Experimental data were obtained from a prior study [14]. As such, the methods and procedures are only presented summarily here, and the reader is referred to the noted publication for details. Thirty-two individuals (16 males and 16 females)
X. Qu et al. / Gait & Posture 30 (2009) 518–522 without self-reported injuries, illness, or musculoskeletal disorders participated in the study. Equal numbers of younger (18–24 years) and older (55–65 years) participants were included, intended as representative of those at the beginning and end of working life, and were balanced across genders. Trials consisting of quiet, bilateral upright stance were conducted both prior to and after fatigue, which was induced in several muscle groups through repetitive, isokinetic, submaximal exercises. Each experimental session involved fatigue at only one joint, and a minimum of two days separated consecutive sessions to avoid residual effects of fatigue at other joints. Only pre- and post-fatigue trials involving fatigue at the ankle were used for three reasons. First, ankle control torque appears to be dominant in postural control during spontaneous sway [15]. Second, our existing balance control model [13] was used, in which the human body is represented by a single inverted pendulum. Thus, the control input to this model is the ankle control torque, and is likely to be affected by ankle fatigue. Third, ankle fatigue has been found to have substantial effects on postural control, as assessed by COP- and center-of-mass (COM)-based measures, and these effects have been evident in response to both bilateral [7,16] and unilateral exertions [14]. A commercial dynamometer (Biodex Medical Systems, Shirley, NY) was used to generate fatigue in the ankle plantarflexors through performance of repetitive (12/ min), concentric isotonic exertions at 60% of individual maximum voluntary capacity. Exertions were terminated, and fatigue considered to have been induced, when participants could not complete a preset range of motion (458) for three consecutive repetitions. The mean (SD) durations of the fatiguing ankle exercises were 26.3 (10.9) and 28.3 (13.9) min for the older and younger adults, respectively. Three trials of quiet upright stance were conducted prior to the fatiguing exertions, one of which was randomly selected for analysis here. Several postfatigue trials were performed, the first of which commenced 45 s after the fatiguing exertions and were studied here. During these trials, quiet upright stance was maintained for 75 s while participants stood as still as possible on a force platform (AMTI OR6-7-1000, Watertown, Massachusetts, USA), with barefoot, arms at sides, feet together, and eyes closed. Triaxial ground reaction forces and moments were sampled at 100 Hz, low-pass filtered (5 Hz cut-off, 2nd order, Butterworth) in software, and subsequently used to derive COP time series. 2.2. Model description Our existing balance control model [13] was used to predict the effects of age and ankle fatigue under the conditions described above. In this model, the human body was represented by a single-segment inverted pendulum with feet during quiet upright stance, and the neural controller was assumed to be an optimal controller. Anthropometric measures required by the model were either directly measured or estimated (see [17]). The optimal neural controller generated ankle control torques, and was determined by an infinite-time linear quadratic regulator that minimizes a performance criterion (Eq. (1)) defined by several physical quantities relevant to sway: J¼
1 2
Z
1
2 2 ˙2 ðw1 uˆ ðtÞ þ w2 uˆ ðtÞ þ w3 T 2 ðtÞ þ w4 T˙ ðtÞ þ w5 T}2 ðtÞÞ dt
(1)
0
where uˆ is the delayed ankle angle; T is the ankle torque; and w1 , w2 , w3 , w4 , and w5 are weightings of the respective relevant physical quantities. Several model parameters cannot be specified a priori, specifically the weightings within the performance criterion (Eq. (1)), as well as random disturbance gain (kn) and sensory delay time (td). An optimization procedure was performed to determine the values of these unspecified model parameters, using the following cost function:
E¼
0 12 ^ N X @COPM i COPMi A ^
i¼1
(2)
COPM i ^
where COPMi and COPM i are the ith COP-based measure from the simulation results and from the experimental results, respectively. Heuristic approaches (i.e. a genetic algorithm (GA) and simulated annealing (SA)) were implemented to determine model parameters [18]. Simulation results from this model have been reported to lead to the same general conclusions with experimental findings in terms of agerelated changes in postural control [13], the effects of external loads [17], and the importance of passive and active control of quiet upright stance [19]. 2.3. Dependent COP-based measures A diverse set of measures was desired to represent different aspects of postural control. Using time-domain COP-based measures, numerous studies have demonstrated that aging and LMF increase postural sway [7,20]. Frequency-domain COPbased measures can reflect altered periodicity which is an indicator of reduced physiological functional ability [21] possibly caused by aging and LMF. Statistical mechanics measures have been proposed [22] to account for the dynamic characteristics of the postural control system [23] and were used to identify differences with respect to age and LMF [7,23]. From such observations, we earlier selected eight COP-based measures (including two time-domain, two frequencydomain, and four statistical mechanics measures) to provide a diverse representation of postural control [17]. This same set of measures was used here to investigate
519
Table 1 Glossary of COP-based dependent measures. Acronym
Description
Unit
RMS MV CFREQ FREQD TT TA HS HL
Root mean square distance Mean velocity Centroidal frequency Frequency dispersion Transition time Transition amplitude Short-term scaling exponent Long-term scaling exponent
mm mm/s Hz – s mm2 – –
the effects of age and ankle fatigue (Table 1). When calculating these measures, the initial 10 s and last five seconds of each trial were removed. 2.4. Model simulation and analysis Sixty-four experimental trials of upright stance were simulated using our balance control model (one pre-fatigue and one post-fatigue trials for each of the 32 participants). Each simulation trial was 75 s in duration, with the initial 10 s and last five seconds removed. Simulations involved several steps (see [13] for a detailed description): 1) a set of initial values was assigned to the unspecified model parameters; 2) the human body dynamics, sensory systems, and optimal neural controller were determined; 3) postural sway was simulated; 4) an optimization procedure was used to optimize the cost function through iterative adaptation of the model parameters. Upon completion of the optimization, simulated COP time series and model parameters were retained for subsequent analyses. Two-way repeated measures analyses of variance (ANOVA) were used to identify effects of age and ankle fatigue (p < 0.05) on the control of upright posture. Specifically, for each of the experimental and simulated COP-based measures of postural sway, and model parameters, ANOVA was performed once with age (young vs. old) and ankle fatigue (pre-fatigue vs. post-fatigue) as independent variables. Identified effects were used to posit how and why age and LMF affect postural control. For example, if sensory delay is found to increase with aging, it can be inferred that changes in postural control due to age may be partly caused by an increased sensory delay. To evaluate the performance of the model, model-based predictions and experimental results were compared to identify whether trends in COP-based measures with respect to age and fatigue status were consistent between experimental and simulation results.
3. Results 3.1. Age and ankle fatigue effects on COP-based measures For the experimental results, significant main effects of age were found on MV, CFREQ, FREQD, TT, and HL (Table 2). More specifically, MV and CFREQ increased, while FREQD, TT, and HL decreased with age (Fig. 1). For the simulated measures, a similar pattern of age effects was found with the exception that the effect on MV was not significant (p = 0.065). Ankle fatigue led to significant changes only in experimental MV, which increased post-fatigue. A significant age ankle fatigue interaction effect was found only for experimental HS. When ankle fatigue was induced, experimental HS decreased in the older group (from 0.829 to 0.801), but increased among younger participants (from 0.795 to 0.810). In contrast to the effects on the experimental COP-based measures, only simulated Hs significantly changed with ankle fatigue. 3.2. Comparison between experimental and simulated measures Comparisons of the influence of age and ankle fatigue on the experimental and simulated measures indicated that almost all the simulated (i.e. model-based) trends were consistent with experimental findings (Fig. 1). Clear discrepancies were only evident in the effects of age on TA, and the effects of ankle fatigue on CFREQ and HS. Most of the significant age and ankle fatigue effects were simulated by the model, as summarized above (Table 2), with exceptions found for MV and HS. More specifically, the simulated data did not reveal the main effects caused by age and ankle fatigue on MV, and the age ankle fatigue interaction effect on HS.
X. Qu et al. / Gait & Posture 30 (2009) 518–522
520
Table 2 Summary of effects of aging and ankle fatigue (p-values from ANOVA tests) on COP-based measured derived from experimental data and model-based simulation. The symbol * indicates a significant (p < 0.05) factor effect. RMS
MV
Experimental Results
Age Fatigue Age Fatigue
0.692 0.836 0.145
0.027* 0.037* 0.217
CFREQ
Simulation Results
Age Fatigue Age Fatigue
0.710 0.440 0.216
0.065 0.109 0.261
TA
HS
HL
0.007* 0.653 0.637
0.003* 0.919 0.507
FREQD
TT 0.039* 0.408 0.175
0.347 1.000 1.000
0.256 0.499 0.032*
0.021* 0.707 0.068
<0.001* 0.152 0.420
0.001* 0.878 0.217
<0.001* 0.324 0.076
0.658 0.347 0.117
0.434 0.019* 0.346
0.017* 0.348 0.144
Fig. 1. Effects of age and ankle fatigue on dependent COP-based measures. Experimental and simulated COP-based measures are normalized to corresponding means for clarity of illustration. F: Post-Fatigue (Fatigued); NF: Pre-Fatigue (No Fatigue); Exp: Experimental Data; Sim: Simulated Data.
Table 3 Means (SD) of model parameters (see Section 2.2 for definitions). The symbol * indicates a significant (p < 0.05) difference. Model Parameters
w1 w2 w3 w4 w5 kn td(ms)
Age
Ankle Fatigue
Age Ankle Fatigue
Young
Old
p-value
Pre-Fatigue
Post-Fatigue
p-Value
p-value
0.285 (0.211) 0.433 (0.170) 0.109 (0.092) 0.147 (0.112) 0.026 (0.034) 124.8 (70.2) 36.6 (18.7)
0.306 (0.234) 0.341 (0.194) 0.201 (0.156) 0.135 (0.084) 0.017 (0.023) 199.3 (113.8) 48.0 (21.1)
0.701 0.054 0.014* 0.656 0.177 0.011* 0.005*
0.305 (0.215) 0.349 (0.177) 0.167 (0.150) 0.152 (0.117) 0.027 (0.036) 156.8 (112.2) 41.7 (18.6)
0.287 (0.237) 0.425 (0.192) 0.143 (0.120) 0.130 (0.075) 0.015 (0.019) 167.4 (80.4) 42.9 (22.7)
0.757 0.102 0.421 0.371 0.141 0.568 0.844
0.749 0.905 0.780 0.998 0.527 0.026* 0.190
3.3. Age and ankle fatigue effects on model parameters
4. Discussion
Several model parameters were significantly altered with age (Table 3), including the weight of ankle control torque (w3 ), random disturbance gains (kn), and sensory delay times (td). Specifically, these parameters were all larger among older participants. In addition, the change of the weight of sway angular velocity (w2 ) approached significance (p = 0.054). In contrast to the effects of age, no main effects of ankle fatigue were found on any model parameters, but a significant age ankle fatigue interaction effect was found for kn.
One purpose of this study was to examine the ability of our balance control model to accurately simulate age and ankle fatigue effects. Though some discrepancies existed (see Section 3.2), most of the simulated age and ankle fatigue effects on COP-based measures were consistent with experimental findings (Table 2 and Fig. 1). It has been generally accepted that aging adversely affects the accuracy of control signals by increasing sensory noise and elevating sensory thresholds [24–26]. Accuracy of the control signal is influenced in the simulation model by the random
X. Qu et al. / Gait & Posture 30 (2009) 518–522
disturbance gain (kn). With larger disturbance gains, the accuracy of the control signal decreases. In addition, nerve conduction velocity was reported to decrease with aging [27], so sensory delay has also been considered to be larger in the older adults [25]. Since the random disturbance gain (kn) and sensory delay (td) both significantly increased with aging, the proposed balance control model was able to provide a plausible control mechanism that explained the effects of age. It has also been suggested that muscle fatigue slows neural transmission [28], and decreases position sense acuity [29]. Thus, in the present study, the random disturbance gain and simulated sensory delay should have significantly increased with ankle fatigue as well. From the simulation results, the mean random disturbance gain and simulated sensory delay both became larger after ankle fatigue, though not significantly. Thus, the simulation results were partly consistent with previous studies. The above arguments all provide some verification that our model can be used to investigate the effects of age and ankle fatigue on balance. Identifying the changes in COP-based measures and model parameters that occur with either age or fatigue is considered an initial step in developing interventions to reduce age- or fatigue-related falls [30], and models – such as the one employed here – may be useful tools for the development of fallprevention interventions. Another purpose of this study was to employ our model to investigate how and why age and LMF affect postural control. Specifically, changes in model parameters and dependent COPbased measures with age and ankle fatigue may help identify relevant information. For example, we found that the random disturbance gain (kn) and sensory delay (td) both significantly increased with aging. Thus, it might be concluded that increased postural sway due to age is at least partly caused by less accurate control signal and increased sensory delay. Such results have practical implications. For example, in order to improve balance, older adults may benefit from training to enhance the speed of responses to changes in body orientation, and interventions may be developed to minimize the effects of extrinsic factors that contribute to sensory noise. We chose several physical quantities (Eq. (1)) that were considered to be most relevant to postural sway to define the optimal controller’s performance index. Weighting model parameters which can be used to quantify the contributions of these relevant physical quantities to balance control were introduced. A larger weight would indicate that the neural controller places more emphasis on the corresponding physical quantity when maintaining upright balance. For example, the weight of ankle torque (w3 ) was larger in older adults, suggesting that ankle torque plays a more important role in postural control among older versus younger adults. Such results may indicate that training programs designed to increase ankle strength (torque) may be helpful for the prevention of fall incidents among older adults, which is consistent with the findings from previous studies [31–33]. While several studies have suggested a reweighting of sensory input following internal or external perturbations [34,35], our results suggest this may not occur to a substantial effect subsequent to localized fatigue (at least at the ankle), since no changes in weightings occurred with ankle fatigue. However, our modeling approach may have not been sufficiently sensitive to detect such changes, given that it was based on a single, 2-D inverted pendulum. Since simulated COP time series reasonably mirrored the experimental references in terms of the effects of age and ankle fatigue on balance (Fig. 1), simulated COP-based measures could also be used to provide the similar indications regarding age- and fatigue-related postural control mechanisms as the experimental counterparts. For example, the central spectral tendency (CFREQ) in COP became significantly larger in older adults (Table 1 and
521
Fig. 1). Since COP movement is considered to be driven by postural forces [30], this increase suggests an increase in the amplitude of higher frequency components in postural forces. We also found that TT and HL significantly decreased with aging (Table 1 and Fig. 1). Smaller TT and smaller HL indicate a shorter open-loop control scheme and more anti-persistent postural control over long-term intervals, respectively. Open-loop control which dominates short-term intervals has a high level of stochastic activity. Anti-persistent postural control, on the other hand, is utilized over long-term intervals and indicates that past and future COP displacements are negatively correlated [22]. As noted above, some discrepancies existed between the model-based simulations and existing evidence. These discrepancies may be caused by several factors, such as a lack of model sensitivity, insufficient fatigue induced in the ankle plantarflexors, and different protocols adopted to induce fatigue between the current and previous studies. Limitations within the fundamental approach and framework used should also be noted (see [13] for a more complete discussion). For example, it was assumed that the neural controller adopts an optimal control strategy when maintaining upright balance, though this assumption has not been validated. However, this assumption is expected to be reasonable since diverse evidence supports the role of optimality in motor and postural control [36]. In addition, only ankle control torque was considered to contribute to the maintenance of balance; thus, the model adopts an ankle strategy and is only applicable to simulating postural sway with small amplitude. It is important to highlight that the experimental and simulated COP data were not completely independent, since an optimization procedure was used to minimize the difference between them. However, some level of model validation can still be achieved, as was done by comparing the simulated and experimental COPbased measures. If the model structure was not reasonable, it is unlikely that the simulated data could reflect the experimental references, even though the model was designed to do so. In addition, model performance was evaluated by determining whether simulated model parameters (e.g., sensory delay) were consistent with previous studies. Information about these model parameters is new, and could not have been specified from the experimental data before model simulation. Studies have also been done to examine the ability of the model to make predictions for new balance applications. Specifically, we applied our model to predict the effects of external loads on balance control without using additional experimental data under loaded conditions [17]. We consider this as an example of how the model could be used to make predictions, and suggest that other applications are possible (e.g., to simulate effects of pregnancy and rehabilitation). Acknowledgements This work was supported in part by Grant Number R01 OH0078802 from the Centers for Disease Control and Prevention (CDC) and by a Start-up Grant (WBS Element M58050017) from Nanyang Technological University (NTU). Its contents are solely the responsibility of the authors and do not necessarily represent the official views of the CDC or NTU. Conflict of interest The authors declare that we have no financial or personal relationship with other persons or organizations that might inappropriately influence our work presented therein. References [1] Corso P, Finkelstein E, Miller T, Fiebelkorn I, Zaloshnja E. Incidence and lifetime costs of injuries in the United States. Injury Prev 2006;12:212–8.
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Contents lists available at ScienceDirect
Gait & Posture journal homepage: www.elsevier.com/locate/gaitpost
Model-based assessments of the effects of age and ankle fatigue on the control of upright posture in humans Xingda Qu a,*, Maury A. Nussbaum b, Michael L. Madigan c a
School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore Department of Industrial and Systems Engineering, Virginia Tech, Blacksburg, VA, USA c Department of Engineering Science and Mechanics, Virginia Tech, Blacksburg, VA, USA b
A R T I C L E I N F O
A B S T R A C T
Article history: Received 27 March 2009 Received in revised form 21 July 2009 Accepted 30 July 2009
The aim of this study was to investigate how and why age and localized muscle fatigue affect postural control using model-based simulations. A balance control model, based on an optimal control strategy, was used to simulate trials of quiet upright stance both pre-fatigue and following induced ankle plantarflexor fatigue. Empirical data were obtained from an earlier study that included both younger and older participants. Effects of age and ankle fatigue were determined from center-of-pressure (COP) measures and fitted model parameters. Though some discrepancies existed, the simulated effects of age and ankle fatigue were consistent with experimental findings in terms of trends in COP-based measures with age and ankle fatigue. Changes in both COP-based measures and model parameters were used to infer potential underlying causal mechanisms for the observed effects of age and ankle fatigue. For example, the model-based simulations indicated that sensory delay time increased with age and ankle fatigue by 31.1% and 2.9%, respectively, suggesting a potentially important role for such delay in postural control and fall risks. ß 2009 Elsevier B.V. All rights reserved.
Keywords: Balance Postural control Age Ankle fatigue Model-based simulation
1. Introduction Falls are common events in both daily and occupational activities. It was reported that more than 44% of all injuries in 2000 resulted from falls or fall-related incidents [1]. Many falls are subsequent to a ‘‘loss-of-balance’’. Hsiao and Simeonov [2] summarized a number of risk factors that could compromise balance and highlighted the need for better understanding the roles of each factor in the control of balance. Among these diverse risk factors, the present work emphasized two particular intrinsic factors: age and localized muscle fatigue (LMF). These factors are considered of importance since falls occur more frequently in older adults, and LMF is commonly experienced in both daily activities and occupational settings. Both age and LMF affect the way in which humans control balance and posture, and the quality of the postural control mechanisms. For example, aging can decrease strength [3] and the speed of a response to loss of balance [4], both of which result in an increased fall risk [5]. LMF appears to challenge the postural control system, as evidenced by increased COP mean velocity
during upright stance [6,7]. Fatigue induced in simulated occupational tasks, such as repetitive lifting [8] and overhead assembly work [9], has also been found to impair postural control. As an adjunct to biomechanical and neurophysiological studies, mathematical models are often used to study postural control and balance [10,11]. Such models have the advantage of suggesting how the entire system functions and how individual components influence the overall system’s response [12]. Thus, model-based simulation may provide some understanding of underlying postural control mechanisms. We recently presented a balance control model, based on an optimal control strategy, which can simulate spontaneous sway behaviors during quiet upright stance [13]. In the current study, the purposes were to evaluate the ability of the model to simulate age and LMF effects, and to employ the model to investigate how and why age and LMF affect postural control. Based on prior evidence, it was hypothesized that the model would be able to accurately simulate postural changes caused by age and LMF, and that simulation results regarding postural control mechanisms would be consistent with previous findings. 2. Methods 2.1. Participants and experimental procedures
* Corresponding author at: School of Mechanical and Aerospace Engineering, Nanyang Technological University, Blk N3, North Spine, Nanyang Avenue, Singapore 639798, Singapore. Tel.: +65 67904458; fax: +65 67924062. E-mail address: [email protected] (X. Qu). 0966-6362/$ – see front matter ß 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.gaitpost.2009.07.127
Experimental data were obtained from a prior study [14]. As such, the methods and procedures are only presented summarily here, and the reader is referred to the noted publication for details. Thirty-two individuals (16 males and 16 females)
X. Qu et al. / Gait & Posture 30 (2009) 518–522 without self-reported injuries, illness, or musculoskeletal disorders participated in the study. Equal numbers of younger (18–24 years) and older (55–65 years) participants were included, intended as representative of those at the beginning and end of working life, and were balanced across genders. Trials consisting of quiet, bilateral upright stance were conducted both prior to and after fatigue, which was induced in several muscle groups through repetitive, isokinetic, submaximal exercises. Each experimental session involved fatigue at only one joint, and a minimum of two days separated consecutive sessions to avoid residual effects of fatigue at other joints. Only pre- and post-fatigue trials involving fatigue at the ankle were used for three reasons. First, ankle control torque appears to be dominant in postural control during spontaneous sway [15]. Second, our existing balance control model [13] was used, in which the human body is represented by a single inverted pendulum. Thus, the control input to this model is the ankle control torque, and is likely to be affected by ankle fatigue. Third, ankle fatigue has been found to have substantial effects on postural control, as assessed by COP- and center-of-mass (COM)-based measures, and these effects have been evident in response to both bilateral [7,16] and unilateral exertions [14]. A commercial dynamometer (Biodex Medical Systems, Shirley, NY) was used to generate fatigue in the ankle plantarflexors through performance of repetitive (12/ min), concentric isotonic exertions at 60% of individual maximum voluntary capacity. Exertions were terminated, and fatigue considered to have been induced, when participants could not complete a preset range of motion (458) for three consecutive repetitions. The mean (SD) durations of the fatiguing ankle exercises were 26.3 (10.9) and 28.3 (13.9) min for the older and younger adults, respectively. Three trials of quiet upright stance were conducted prior to the fatiguing exertions, one of which was randomly selected for analysis here. Several postfatigue trials were performed, the first of which commenced 45 s after the fatiguing exertions and were studied here. During these trials, quiet upright stance was maintained for 75 s while participants stood as still as possible on a force platform (AMTI OR6-7-1000, Watertown, Massachusetts, USA), with barefoot, arms at sides, feet together, and eyes closed. Triaxial ground reaction forces and moments were sampled at 100 Hz, low-pass filtered (5 Hz cut-off, 2nd order, Butterworth) in software, and subsequently used to derive COP time series. 2.2. Model description Our existing balance control model [13] was used to predict the effects of age and ankle fatigue under the conditions described above. In this model, the human body was represented by a single-segment inverted pendulum with feet during quiet upright stance, and the neural controller was assumed to be an optimal controller. Anthropometric measures required by the model were either directly measured or estimated (see [17]). The optimal neural controller generated ankle control torques, and was determined by an infinite-time linear quadratic regulator that minimizes a performance criterion (Eq. (1)) defined by several physical quantities relevant to sway: J¼
1 2
Z
1
2 2 ˙2 ðw1 uˆ ðtÞ þ w2 uˆ ðtÞ þ w3 T 2 ðtÞ þ w4 T˙ ðtÞ þ w5 T}2 ðtÞÞ dt
(1)
0
where uˆ is the delayed ankle angle; T is the ankle torque; and w1 , w2 , w3 , w4 , and w5 are weightings of the respective relevant physical quantities. Several model parameters cannot be specified a priori, specifically the weightings within the performance criterion (Eq. (1)), as well as random disturbance gain (kn) and sensory delay time (td). An optimization procedure was performed to determine the values of these unspecified model parameters, using the following cost function:
E¼
0 12 ^ N X @COPM i COPMi A ^
i¼1
(2)
COPM i ^
where COPMi and COPM i are the ith COP-based measure from the simulation results and from the experimental results, respectively. Heuristic approaches (i.e. a genetic algorithm (GA) and simulated annealing (SA)) were implemented to determine model parameters [18]. Simulation results from this model have been reported to lead to the same general conclusions with experimental findings in terms of agerelated changes in postural control [13], the effects of external loads [17], and the importance of passive and active control of quiet upright stance [19]. 2.3. Dependent COP-based measures A diverse set of measures was desired to represent different aspects of postural control. Using time-domain COP-based measures, numerous studies have demonstrated that aging and LMF increase postural sway [7,20]. Frequency-domain COPbased measures can reflect altered periodicity which is an indicator of reduced physiological functional ability [21] possibly caused by aging and LMF. Statistical mechanics measures have been proposed [22] to account for the dynamic characteristics of the postural control system [23] and were used to identify differences with respect to age and LMF [7,23]. From such observations, we earlier selected eight COP-based measures (including two time-domain, two frequencydomain, and four statistical mechanics measures) to provide a diverse representation of postural control [17]. This same set of measures was used here to investigate
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Table 1 Glossary of COP-based dependent measures. Acronym
Description
Unit
RMS MV CFREQ FREQD TT TA HS HL
Root mean square distance Mean velocity Centroidal frequency Frequency dispersion Transition time Transition amplitude Short-term scaling exponent Long-term scaling exponent
mm mm/s Hz – s mm2 – –
the effects of age and ankle fatigue (Table 1). When calculating these measures, the initial 10 s and last five seconds of each trial were removed. 2.4. Model simulation and analysis Sixty-four experimental trials of upright stance were simulated using our balance control model (one pre-fatigue and one post-fatigue trials for each of the 32 participants). Each simulation trial was 75 s in duration, with the initial 10 s and last five seconds removed. Simulations involved several steps (see [13] for a detailed description): 1) a set of initial values was assigned to the unspecified model parameters; 2) the human body dynamics, sensory systems, and optimal neural controller were determined; 3) postural sway was simulated; 4) an optimization procedure was used to optimize the cost function through iterative adaptation of the model parameters. Upon completion of the optimization, simulated COP time series and model parameters were retained for subsequent analyses. Two-way repeated measures analyses of variance (ANOVA) were used to identify effects of age and ankle fatigue (p < 0.05) on the control of upright posture. Specifically, for each of the experimental and simulated COP-based measures of postural sway, and model parameters, ANOVA was performed once with age (young vs. old) and ankle fatigue (pre-fatigue vs. post-fatigue) as independent variables. Identified effects were used to posit how and why age and LMF affect postural control. For example, if sensory delay is found to increase with aging, it can be inferred that changes in postural control due to age may be partly caused by an increased sensory delay. To evaluate the performance of the model, model-based predictions and experimental results were compared to identify whether trends in COP-based measures with respect to age and fatigue status were consistent between experimental and simulation results.
3. Results 3.1. Age and ankle fatigue effects on COP-based measures For the experimental results, significant main effects of age were found on MV, CFREQ, FREQD, TT, and HL (Table 2). More specifically, MV and CFREQ increased, while FREQD, TT, and HL decreased with age (Fig. 1). For the simulated measures, a similar pattern of age effects was found with the exception that the effect on MV was not significant (p = 0.065). Ankle fatigue led to significant changes only in experimental MV, which increased post-fatigue. A significant age ankle fatigue interaction effect was found only for experimental HS. When ankle fatigue was induced, experimental HS decreased in the older group (from 0.829 to 0.801), but increased among younger participants (from 0.795 to 0.810). In contrast to the effects on the experimental COP-based measures, only simulated Hs significantly changed with ankle fatigue. 3.2. Comparison between experimental and simulated measures Comparisons of the influence of age and ankle fatigue on the experimental and simulated measures indicated that almost all the simulated (i.e. model-based) trends were consistent with experimental findings (Fig. 1). Clear discrepancies were only evident in the effects of age on TA, and the effects of ankle fatigue on CFREQ and HS. Most of the significant age and ankle fatigue effects were simulated by the model, as summarized above (Table 2), with exceptions found for MV and HS. More specifically, the simulated data did not reveal the main effects caused by age and ankle fatigue on MV, and the age ankle fatigue interaction effect on HS.
X. Qu et al. / Gait & Posture 30 (2009) 518–522
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Table 2 Summary of effects of aging and ankle fatigue (p-values from ANOVA tests) on COP-based measured derived from experimental data and model-based simulation. The symbol * indicates a significant (p < 0.05) factor effect. RMS
MV
Experimental Results
Age Fatigue Age Fatigue
0.692 0.836 0.145
0.027* 0.037* 0.217
CFREQ
Simulation Results
Age Fatigue Age Fatigue
0.710 0.440 0.216
0.065 0.109 0.261
TA
HS
HL
0.007* 0.653 0.637
0.003* 0.919 0.507
FREQD
TT 0.039* 0.408 0.175
0.347 1.000 1.000
0.256 0.499 0.032*
0.021* 0.707 0.068
<0.001* 0.152 0.420
0.001* 0.878 0.217
<0.001* 0.324 0.076
0.658 0.347 0.117
0.434 0.019* 0.346
0.017* 0.348 0.144
Fig. 1. Effects of age and ankle fatigue on dependent COP-based measures. Experimental and simulated COP-based measures are normalized to corresponding means for clarity of illustration. F: Post-Fatigue (Fatigued); NF: Pre-Fatigue (No Fatigue); Exp: Experimental Data; Sim: Simulated Data.
Table 3 Means (SD) of model parameters (see Section 2.2 for definitions). The symbol * indicates a significant (p < 0.05) difference. Model Parameters
w1 w2 w3 w4 w5 kn td(ms)
Age
Ankle Fatigue
Age Ankle Fatigue
Young
Old
p-value
Pre-Fatigue
Post-Fatigue
p-Value
p-value
0.285 (0.211) 0.433 (0.170) 0.109 (0.092) 0.147 (0.112) 0.026 (0.034) 124.8 (70.2) 36.6 (18.7)
0.306 (0.234) 0.341 (0.194) 0.201 (0.156) 0.135 (0.084) 0.017 (0.023) 199.3 (113.8) 48.0 (21.1)
0.701 0.054 0.014* 0.656 0.177 0.011* 0.005*
0.305 (0.215) 0.349 (0.177) 0.167 (0.150) 0.152 (0.117) 0.027 (0.036) 156.8 (112.2) 41.7 (18.6)
0.287 (0.237) 0.425 (0.192) 0.143 (0.120) 0.130 (0.075) 0.015 (0.019) 167.4 (80.4) 42.9 (22.7)
0.757 0.102 0.421 0.371 0.141 0.568 0.844
0.749 0.905 0.780 0.998 0.527 0.026* 0.190
3.3. Age and ankle fatigue effects on model parameters
4. Discussion
Several model parameters were significantly altered with age (Table 3), including the weight of ankle control torque (w3 ), random disturbance gains (kn), and sensory delay times (td). Specifically, these parameters were all larger among older participants. In addition, the change of the weight of sway angular velocity (w2 ) approached significance (p = 0.054). In contrast to the effects of age, no main effects of ankle fatigue were found on any model parameters, but a significant age ankle fatigue interaction effect was found for kn.
One purpose of this study was to examine the ability of our balance control model to accurately simulate age and ankle fatigue effects. Though some discrepancies existed (see Section 3.2), most of the simulated age and ankle fatigue effects on COP-based measures were consistent with experimental findings (Table 2 and Fig. 1). It has been generally accepted that aging adversely affects the accuracy of control signals by increasing sensory noise and elevating sensory thresholds [24–26]. Accuracy of the control signal is influenced in the simulation model by the random
X. Qu et al. / Gait & Posture 30 (2009) 518–522
disturbance gain (kn). With larger disturbance gains, the accuracy of the control signal decreases. In addition, nerve conduction velocity was reported to decrease with aging [27], so sensory delay has also been considered to be larger in the older adults [25]. Since the random disturbance gain (kn) and sensory delay (td) both significantly increased with aging, the proposed balance control model was able to provide a plausible control mechanism that explained the effects of age. It has also been suggested that muscle fatigue slows neural transmission [28], and decreases position sense acuity [29]. Thus, in the present study, the random disturbance gain and simulated sensory delay should have significantly increased with ankle fatigue as well. From the simulation results, the mean random disturbance gain and simulated sensory delay both became larger after ankle fatigue, though not significantly. Thus, the simulation results were partly consistent with previous studies. The above arguments all provide some verification that our model can be used to investigate the effects of age and ankle fatigue on balance. Identifying the changes in COP-based measures and model parameters that occur with either age or fatigue is considered an initial step in developing interventions to reduce age- or fatigue-related falls [30], and models – such as the one employed here – may be useful tools for the development of fallprevention interventions. Another purpose of this study was to employ our model to investigate how and why age and LMF affect postural control. Specifically, changes in model parameters and dependent COPbased measures with age and ankle fatigue may help identify relevant information. For example, we found that the random disturbance gain (kn) and sensory delay (td) both significantly increased with aging. Thus, it might be concluded that increased postural sway due to age is at least partly caused by less accurate control signal and increased sensory delay. Such results have practical implications. For example, in order to improve balance, older adults may benefit from training to enhance the speed of responses to changes in body orientation, and interventions may be developed to minimize the effects of extrinsic factors that contribute to sensory noise. We chose several physical quantities (Eq. (1)) that were considered to be most relevant to postural sway to define the optimal controller’s performance index. Weighting model parameters which can be used to quantify the contributions of these relevant physical quantities to balance control were introduced. A larger weight would indicate that the neural controller places more emphasis on the corresponding physical quantity when maintaining upright balance. For example, the weight of ankle torque (w3 ) was larger in older adults, suggesting that ankle torque plays a more important role in postural control among older versus younger adults. Such results may indicate that training programs designed to increase ankle strength (torque) may be helpful for the prevention of fall incidents among older adults, which is consistent with the findings from previous studies [31–33]. While several studies have suggested a reweighting of sensory input following internal or external perturbations [34,35], our results suggest this may not occur to a substantial effect subsequent to localized fatigue (at least at the ankle), since no changes in weightings occurred with ankle fatigue. However, our modeling approach may have not been sufficiently sensitive to detect such changes, given that it was based on a single, 2-D inverted pendulum. Since simulated COP time series reasonably mirrored the experimental references in terms of the effects of age and ankle fatigue on balance (Fig. 1), simulated COP-based measures could also be used to provide the similar indications regarding age- and fatigue-related postural control mechanisms as the experimental counterparts. For example, the central spectral tendency (CFREQ) in COP became significantly larger in older adults (Table 1 and
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Fig. 1). Since COP movement is considered to be driven by postural forces [30], this increase suggests an increase in the amplitude of higher frequency components in postural forces. We also found that TT and HL significantly decreased with aging (Table 1 and Fig. 1). Smaller TT and smaller HL indicate a shorter open-loop control scheme and more anti-persistent postural control over long-term intervals, respectively. Open-loop control which dominates short-term intervals has a high level of stochastic activity. Anti-persistent postural control, on the other hand, is utilized over long-term intervals and indicates that past and future COP displacements are negatively correlated [22]. As noted above, some discrepancies existed between the model-based simulations and existing evidence. These discrepancies may be caused by several factors, such as a lack of model sensitivity, insufficient fatigue induced in the ankle plantarflexors, and different protocols adopted to induce fatigue between the current and previous studies. Limitations within the fundamental approach and framework used should also be noted (see [13] for a more complete discussion). For example, it was assumed that the neural controller adopts an optimal control strategy when maintaining upright balance, though this assumption has not been validated. However, this assumption is expected to be reasonable since diverse evidence supports the role of optimality in motor and postural control [36]. In addition, only ankle control torque was considered to contribute to the maintenance of balance; thus, the model adopts an ankle strategy and is only applicable to simulating postural sway with small amplitude. It is important to highlight that the experimental and simulated COP data were not completely independent, since an optimization procedure was used to minimize the difference between them. However, some level of model validation can still be achieved, as was done by comparing the simulated and experimental COPbased measures. If the model structure was not reasonable, it is unlikely that the simulated data could reflect the experimental references, even though the model was designed to do so. In addition, model performance was evaluated by determining whether simulated model parameters (e.g., sensory delay) were consistent with previous studies. Information about these model parameters is new, and could not have been specified from the experimental data before model simulation. Studies have also been done to examine the ability of the model to make predictions for new balance applications. Specifically, we applied our model to predict the effects of external loads on balance control without using additional experimental data under loaded conditions [17]. We consider this as an example of how the model could be used to make predictions, and suggest that other applications are possible (e.g., to simulate effects of pregnancy and rehabilitation). Acknowledgements This work was supported in part by Grant Number R01 OH0078802 from the Centers for Disease Control and Prevention (CDC) and by a Start-up Grant (WBS Element M58050017) from Nanyang Technological University (NTU). Its contents are solely the responsibility of the authors and do not necessarily represent the official views of the CDC or NTU. Conflict of interest The authors declare that we have no financial or personal relationship with other persons or organizations that might inappropriately influence our work presented therein. References [1] Corso P, Finkelstein E, Miller T, Fiebelkorn I, Zaloshnja E. Incidence and lifetime costs of injuries in the United States. Injury Prev 2006;12:212–8.
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