Energetic optimization during over-ground walking in people with and without Down syndrome

Gait & Posture 33 (2011) 630–634

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Energetic optimization during over-ground walking in people with and without Down syndrome Stamatis Agiovlasitis a,*, Robert W. Motl b, Sushant M. Ranadive b, Christopher A. Fahs c, Huimin Yan b, George H. Echols b, Lindy Rossow c, Bo Fernhall b a b c

Department of Kinesiology, Mississippi State University, 233 McCarthy Gym, P.O. Box 6186, Mississippi, MS 39762, United States Department of Kinesiology & Community Health, University of Illinois at Urbana-Champaign, 906 S Goodwin Ave., Urbana, IL 61801, United States Department of Health and Exercise Science, University of Oklahoma, 1401 Asp Ave, Norman, OK 73069, United States

A R T I C L E I N F O

A B S T R A C T

Article history: Received 24 May 2010 Received in revised form 2 February 2011 Accepted 14 February 2011

Individuals with Down syndrome (DS) show reduced gait stability that may increase the metabolic rate (MR) during over-ground walking and alter their energetic cost per unit distance (ECtransport) to speed relationship. If so, the preferred walking speed (PWS) of people with DS may coincide with their speed at minimal ECtransport, reflecting energetic optimization. This study therefore examined whether MR and ECtransport during over-ground walking differ between individuals with and without DS and whether PWS minimizes their ECtransport. Expired gases were collected from 18 individuals with DS and 18 without during six over-ground walking trials, each lasting 6 min, at PWS and at 0.51, 0.76, 1.01, 1.26, and 1.51 m/s. Gross- and net-MR, and gross- and net-ECtransport were expressed in dimensionless form. Energetically optimal walking speeds and minimal gross- and net-ECtransport were determined from the gross- and netECtransport to speed curves for each participant. Individuals with DS showed higher gross-MR, net-MR, grossECtransport, and net-ECtransport. PWS minimized gross-ECtransport in participants with DS, but not in those without. PWS did not minimize net-ECtransport in either group. Therefore, gross-ECtransport minimization during over-ground walking may determine PWS when impairments alter the gross-ECtransport to speed relationship. ß 2011 Elsevier B.V. All rights reserved.

Keywords: Gait Optimization Economy Down syndrome Impairment

1. Introduction It has been proposed that people walk at speeds that optimize the energetic cost per unit distance traveled (ECtransport) [1,2], a tendency thought to have resulted from evolutionary pressure and experience [3–5]. Energetic optimization during walking is still in need of more testing, however. Insight into this theory may be partially gained by studying individuals with conditions that alter the metabolic rate (MR) and the ECtransport to speed relationships [4]. This appears to be the case for individuals with Down syndrome (DS) [6] for whom walking is the most common form of physical activity [7]. Studying MR and ECtransport expressed as either gross (i.e., overall) or net (i.e., gross minus the value of quiet standing) in people with DS may provide additional insight into optimization during walking. Individuals with DS have joint laxity, muscle hypotonia, reduced strength, and deficits of the cerebellum [8,9] collectively

* Corresponding author. Tel.: +1 662 325 4772; fax: +1 662 325 4525. E-mail addresses: [email protected], [email protected] (S. Agiovlasitis). 0966-6362/$ – see front matter ß 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.gaitpost.2011.02.007

considered responsible for their lower mediolateral stability during gait [10,11]. People with DS appear to compensate to reduced stability by walking at given speeds with higher step frequencies and greater active step width adjustments manifested in greater step width variability [10]. These compensations increase the energetic cost [12–14] and, combined with the lower aerobic fitness of people with DS [15], may be responsible for their higher MR during treadmill walking [6]. Children with DS, however, appear to have higher energetic cost than children without DS during treadmill, but not over-ground walking [16]. Therefore, comparisons of MR during over-ground walking are needed. Past research has found that the preferred walking speed (PWS) of people with DS, even when accounting for their shorter leg lengths, is slower than that of people without DS [17], although such findings are not universal [6,16]. It is possible that a preference for slow walking may reflect energetic optimization. Previously, people with and without DS were found to walk faster than the speeds that minimize the net-ECtransport during treadmill walking [6]. PWS, however, was measured over a short distance and over-ground, whereas MR was measured on a treadmill. Furthermore, people with and without DS may be minimizing the

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gross-ECtransport. Research in this area is unclear. Optimization of gross-ECtransport appears more plausible from an evolutionary standpoint because it may have allowed early humans to maximize distance traveled on a given amount of metabolic fuel [3,4]. Conversely, it has been suggested that the optimization of netECtransport may be more advantageous for modern humans who do not have to walk long distances, if they seek to minimize their total energetic cost per day [4]. Since DS appears to increase MR during walking and alter the net-ECtransport to speed relationship [6], it may provide a model for the study of energetic optimization. This study therefore examined whether gross- or net-MR and gross- or net-ECtransport across speeds differ during over-ground walking between individuals with and without DS. This study also examined whether over-ground PWS minimizes the gross- or netECtransport in these groups. It was hypothesized that individuals with DS would show higher gross- and net-MR as well as higher gross- and net-ECtransport and that PWS would minimize grossECtransport in both groups. 2. Methods 2.1. Participants Eighteen individuals with DS (10 women and 8 men) and 18 individuals without DS matched for sex participated in this study. The two groups did not differ in age or body mass; however, participants with DS had shorter height and leg length, and greater body mass index (BMI) (p < 0.05; Table 1). The study was approved by the Institutional Review Board. All participants and the legal guardians of participants with DS provided written informed consent. Prior to the experimental session, participants were familiarized with the testing procedures. 2.2. Procedures Participants refrained from food, caffeine, and exercise for at least 3 h prior to testing. Body mass and height were measured, allowing for BMI calculation. Leg length was measured from the right greater trochanter to the floor with shoes on and knees extended during standing. Participants then sat for 10 min to bring physiologic function to resting levels. Thereafter, expired air was collected during quiet sitting, quiet standing, and a set of six walking trials, using a portable opencircuit spirometer (K4b2, Cosmed, Italy). The spirometer was calibrated prior to testing in accordance with manufacturer specifications. Body mass was also measured with participants carrying the spirometer; this value was only used in metabolic calculations. Each of the sitting, standing, and walking trials lasted 6 min. The walking trials were conducted in a quiet rectangular hallway 90 m in perimeter. The first trial was conducted at the PWS of participants. Specifically, participants were instructed to walk at their most comfortable speed and were quietly followed by 2 researchers; one researcher maintained a distance of 1 m from the participant and rolled a distance-measuring wheel (MP301DM, Keson, Aurora, IL), while the other timed the trial. The remaining trials were conducted at target speeds of 0.50, 0.75, 1.00, 1.25, and 1.50 m/s. The order was from the slowest to fastest. The speed was set by the researcher rolling the wheel, also equipped with a cycle computer (Velo 8, Cateye, Osaka, Japan) displaying instantaneous speed. During these paced trials, the researcher rolling the wheel walked at the target speed 1 m in front of the participant, while the second researcher followed the participant, timing the trial and encouraging the participant to maintain the same distance from the pacing researcher. Researchers had practiced extensively these procedures. Consequently, actual average walking speeds, measured as the distance covered over the 6 min, were very close to target speeds. Importantly, speeds during paced walking did not differ between participants with and without DS as shown by non-significant group effect and interaction in 2  5 (group-by-speed) mixedmodel ANOVA. Actual walking speeds for both groups combined were 0.51, 0.76, 1.01, 1.26, and 1.51 m/s. Six minutes of sitting separated the walking bouts.

Table 1 Mean  SD of age and anthropometric indicators of individuals with Down syndrome (DS) and individuals without Down syndrome (non-DS).

Age (years) Body mass (kg) Height (cm)* Leg length (cm)* BMI (kg/m2)*

DS (n = 18)

Non-DS (n = 18)

24.7  6.8 75.7  17.1 153.5  7.9 74.0  3.5 32.3  7.6

26.4  5.1 75.1  22.5 171.9  8.0 88.6  3.9 25.4  7.7

BMI, body mass index. * p < 0.05 between groups in independent samples t-test.

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2.3. Data analyses The rates of oxygen uptake and carbon dioxide production were measured in ml/ min as the respective averages over the last 3 min of each trial. The first 3 min were discarded, allowing participants adequate time to achieve steady-state [18]. Steady-state was confirmed by minimal change in oxygen uptake rate (<100 ml/ min) during the last 3 min. This criterion was not demonstrated during the PWS trials by four participants with DS and one participant without DS; therefore, their MR and ECtransport at PWS were not used in subsequent analyses. The gross metabolic power was first determined in Watts from the rates of oxygen uptake and carbon dioxide production, using a published formula [19]. The net metabolic power during walking was also determined in Watts by subtracting the standing from the gross metabolic power. To account for differences between groups in body size, the gross- and net-MR were expressed in dimensionless form pffiffiffiffiffi [MR ¼ P=Mg gL, where P is either the gross or the net metabolic power (W), M is body mass (kg), g is the acceleration of gravity (9.81 m/s2), and L is the leg length (m)] by [14]. Dimensionless gross- and net-ECtransport were, respectively, calculated pffiffiffiffiffi dividing the gross and net dimensionless MR by dimensionless speed [¼ v= gL, where v is walking speed (m/s), g is the acceleration of gravity, and L is the leg length] [14]. PWS was expressed in m/s, but also in dimensionless form to account for the shorter legs of participants with DS. The minimal gross-ECtransport and the minimal net-ECtransport as well as the speeds at which they occurred were mathematically determined from the individual third-order polynomial regressions of the grossECtransport and net-ECtransport as a function of actual walking speed (m/s). Differences between groups in gross- and net-MR as well as gross- and netECtransport as a function of speed were each analyzed using 2  5 (group-by-speed) mixed-model ANOVA. The Greenhouse–Geisser adjustment was applied as appropriate. When the interaction was significant, independent t-tests between groups, with Bonferroni-adjusted alpha (0.01), were performed at each speed. To account for the higher BMI of participants with DS, the mixed-model analyses were also conducted with BMI as a covariate followed by ANCOVA at each speed with Bonferroni-adjusted alpha. Differences between DS and non-DS groups in resting MR, PWS, and energetically optimal speeds were analyzed with independent ttests. Within-group differences between PWS and energetically optimal speed as well as differences between ECtransport at PWS and the predicted minimal ECtransport were tested with paired t-tests; these analyses were conducted for both gross- and net-ECtransport. The relationships among PWS and speeds at minimal net- and grossECtransport were examined with Pearson correlations. The alpha level was 0.05.

3. Results The responses of gross-MR and net-MR as a function of walking speed differed between groups as shown by significant interactions (p < 0.001; Fig. 1). Participants with DS had higher gross-MR and higher net-MR at all speeds (p < 0.001). These results did not change with BMI as a covariate. The difference in net-MR between DS and non-DS participants was not due to resting MR which did not differ between groups (Table 2). Similarly, the relationships of gross- and net-ECtransport to walking speed were different between groups as revealed by significant group-by-speed interactions (p  0.001; Fig. 2). Individuals with DS had greater gross-ECtransport and greater netECtransport at all speeds than individuals without DS (p  0.001). Covarying for BMI did not change these results. PWS appeared to minimize the gross-ECtransport in participants with DS, but not in those without DS (Fig. 2a and Table 2). For individuals with DS, PWS did not differ from speed at minimal gross-ECtransport. Similarly, their gross-ECtransport at PWS did not differ from the minimal gross-ECtransport. For individuals without DS, however, PWS was faster than speed at minimal grossECtransport (p = 0.001). Furthermore, their gross-ECtransport at PWS was significantly higher than their minimal gross-ECtransport (p = 0.002). The speed at minimal gross-ECtransport was significantly slower in participants with DS than participants without DS (p < 0.001). Participants with DS showed slower absolute and dimensionless PWS than participants without DS (p < 0.05). For both groups combined, PWS was moderately correlated with speed at minimal gross-ECtransport (r = 0.54; p < 0.01). In contrast, PWS did not minimize the net-ECtransport of participants with and without DS (Fig. 2b). PWS was significantly faster than the speed at minimal net-ECtransport in each group (p  0.002). Similarly, net-ECtransport at PWS was significantly higher than the minimal net-ECtransport in each group (p < 0.05).

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0.35 0.3

a

*

DS Non-DS

0.25

*

0.2 0.15

*

0.1

*

*

0.05 0 0.25

0.50

0.75

1.00

1.25

1.50

1.75

Gross-ECtransport (Dimensionless)

a Gross-MR (Dimensionless)

632

0.7

*

DS Non-DS

0.6

*

0.5

†

0.3 0.2 0.25

0.50

0.75

Non-DS

*

0.15 0.1 0.05 0 0.25

*

0.50

*

*

0.75

1.00

1.25

1.50

1.75

Speed (m/s)

1.25

1.50

1.75

0.5 0.45

DS Non-DS

0.4

*

* * *

0.35

*

0.3

†

0.25

†

0.2 0.15 0.25

0.50

0.75

1.00

1.25

1.50

1.75

Speed (m/s)

Fig. 1. Mean  SD metabolic rate (MR) as a function of actual average walking speed in individuals with Down syndrome (DS) and individuals without Down syndrome (nonDS). (a) Gross-MR; curves are the second-order polynomials fitted to means for individuals with DS [gross-MR = 0.14 (speed)2  0.11 (speed) + 0.13, R2 = 1.00] and individuals without DS [gross-MR = 0.06 (speed)2  0.05 (speed) + 0.09, R2 = 1.00]. (b) Net-MR; curves are the second-order polynomials fitted to means for individuals with DS [net-MR = 0.14 (speed)2  0.11 (speed) + 0.09, R2 = 1.00] and individuals without DS [net-MR = 0.06 (speed)2  0.05 (speed) + 0.05, R2 = 1.00]. For calculation of dimensionless MR, see Section 2. *p < 0.001 between groups.

Table 2 Mean  SD preferred walking speed (PWS), energetically optimal walking speeds, and resting metabolic rate (MRrest) of individuals with Down syndrome (DS) and individuals without Down syndrome (non-DS). p-Value*

Group

PWS (m/s) PWS (dimensionless) Speed at minimal gross-ECtransport (m/s) Speed at minimal net-ECtransport (m/s) MRrest (dimensionless)

b Net-ECtransport(Dimensionless)

Net-MR (Dimensionless)

*

DS

0.2

1.00

Speed (m/s)

0.3 0.25

*

0.4

Speed (m/s)

b

*

*

DS

Non-DS

1.07  0.26 0.40  0.09 1.01  0.11 0.87  0.12y 0.05  0.01

1.37  0.17 0.47  0.06 1.20  0.11y 1.03  0.16y 0.04  0.01

<0.001 0.013 <0.001 0.001 0.256

ECtransport, energetic cost of transport; MRrest, standing metabolic rate. For calculation of dimensionless MRrest and dimensionless PWS, see Section 2. * Comparison between DS and non-DS individuals. y Within-group difference between speed at minimal gross- or net-ECtransport and PWS (m/s) statistically significant (p  0.002).

The speed at minimal net-ECtransport was significantly slower in participants with DS than participants without (p = 0.001). For both groups combined, PWS was moderately correlated with speed at minimal net-ECtransport (r = 0.49; p < 0.01) and speed at minimal net-ECtransport was highly correlated with speed at minimal gross-ECtransport (r = 0.78; p < 0.01). 4. Discussion This study examined whether MR and ECtransport during overground walking differ between individuals with and without DS and whether these groups prefer to walk over-ground at speeds that optimize their ECtransport.

Fig. 2. Mean  SD of energetic cost of transport (ECtransport) as a function of actual average walking speed in individuals with Down syndrome (DS) and individuals without Down syndrome (non-DS). (a) Gross-ECtransport; curves are the third-order polynomials fitted to means for individuals with DS [gross-ECtransport = 0.42 (speed)3 + 1.75 (speed)2  2.23 (speed) + 1.32, R2 = 1.00] and individuals without DS [gross-ECtransport = 0.15 (speed)3 + 0.77 (speed)2  1.22 (speed) + 0.92, R2 = 1.00]. (b) Net-ECtransport; curves are the third-order polynomials fitted to means for individuals with DS [net-ECtransport = 0.26 (speed)3 + 1.09 (speed)2  1.27 (speed) + 0.74, R2 = 1.00] and individuals without DS [net-ECtransport = 0.01 (speed)3 + 0.16 (speed)2  0.34 (speed) + 0.37, R2 = 1.00]. For calculation of dimensionless ECtransport, see Section 2. *p < 0.001 between groups. Filled circles and triangles show the ECtransport at the preferred walking speed (PWS) for individuals with and without DS, respectively. Dashed and solid vertical lines indicate the energetically optimal walking speeds for individuals with and without DS, respectively. (y) Significant difference between ECtransport at PWS and minimal ECtransport and between PWS and energetically optimal walking speeds for individuals with and without DS (p < 0.05).

As hypothesized, gross- and net-MR were higher across speeds and both variables increased at faster rates with increases in speed in individuals with than without DS. These responses to speed had similar shapes in both groups, suggesting a systematic cause of the difference in MR. This cause does not appear related to the higher BMI of participants with DS which did not confound the results. Individuals with obesity show similar gross-MR, but higher netMR than lean individuals likely because of their lower resting MR [20,21]. In contrast, resting MR did not differ between the present individuals with and without DS, in accord with previous research [22]. These results, combined with the reasonable assumption that net-MR reflects primarily the energetic cost of walking [14], suggest that differences in gross- and net-MR between groups may be partially due to the gait characteristics of individuals with DS. Similar relationships between net-MR and speed for people with and without DS have been documented for treadmill walking [6], implying that the causes of the difference in MR may apply to both treadmill and over-ground walking. Among the potential causes of the differences in gross- or netMR between groups are the gait patterns and compensations of people with DS. Specifically, the greater mediolateral body motion during walking of individuals with DS [10,11] may increase the

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energetic cost required to redirect their body center of mass between steps [13]. Furthermore, individuals with DS show greater step width variability and higher step frequencies [10]. These factors, respectively, increase the energetic costs associated with mediolateral stabilization and with the forced motion of the swinging leg [12–14,23]. Notably, differences in body motion and stepping behaviors between people with and without DS increase at faster speeds [10], potentially explaining the present widening of the difference in gross- or net-MR with increases in speed. It is also possible that higher MR in individuals with DS may be due to greater co-contraction of antagonistic muscles [16]. Finally, the lower fitness of individuals with DS [15] may also contribute to higher MR [24]. A result of higher gross- and net-MR in participants with DS was that gross- and net-ECtransport were, respectively, higher than those of participants without DS. For both variables, the difference appears to increase at fast speeds apparently due to the widening of the between-group difference in MR. Consequently, the relationships of gross- or net-ECtransport to walking speed differed between groups, such that the respective minima occurred at slower speeds for participants with DS. The present speed at minimal gross-ECtransport of participants with DS is the first ever reported value and cannot be compared to other studies; however, the speed at minimal gross-ECtransport of individuals without DS and the speeds at minimal net-ECtransport of participants with and without DS were within the range previously reported [1,2,4,6,20,25]. Similarly, PWS of individuals with and without DS was within the range previously observed [1,2,6,20]. Importantly, PWS was slower in participants with than without DS even after accounting for differences in leg length. This is in agreement with one [17], but not all previous investigations [6,16]. This disparity may reflect differences between studies in PWS determination and age or activity levels of participants. Nevertheless, the question of interest is whether PWS in people with and without DS minimizes either the gross- or the net-ECtransport. The present participants with DS preferred to walk over-ground at speeds that minimized their gross-ECtransport, whereas participants without DS did not. The preference of participants without DS to walk faster than their speed at minimal gross-ECtransport is in contrast to early suggestions that people naturally walk at their most economical speeds [1,2]. Early work, however, did not evaluate this hypothesis statistically. Instead, it based the energetic optimization proposition on the proximity between PWS and speed at optimal gross-ECtransport and on the observation that gross-ECtransport at PWS does not appear much higher than the minimal gross-ECtransport. Recent work, however, has found grossECtransport at PWS to be statistically higher than the minimal grossECtransport in women with and without obesity, although the difference appeared small [21]. It is therefore possible that energetic optimization becomes a primary goal when conditions such as DS, alter the gross-ECtransport to speed relationship in a way that makes walking faster than PWS too costly. Healthy individuals, however, may be able to bypass energetic concerns when other constraints predominate. In fact, the moderate correlation between PWS and speed at optimal grossECtransport suggests that PWS may be partially determined by energetic demands, but also by other factors. In support of this argument, PWS around the world varies widely as a function of population size and is thought to reflect the ‘‘pace of life’’ [26,27]. Furthermore, PWS was moderately correlated with speed at optimal net-ECtransport, suggesting that this variable may also partially determine PWS. This argument appears weakened, however, by the observation that PWS in participants with and without DS did not minimize net-ECtransport, a finding confirming past research [6]. Furthermore, it is possible that speed at optimal net-ECtransport is associated with PWS simply because it shares common variance

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with the speed at optimal gross-ECtransport as suggested by the high correlation between these variables. As previously proposed, minimization of gross-ECtransport may be a stronger optimality criterion than minimization of net-ECtransport because it may have resulted from long periods of evolutionary pressure, allowing humans to maximize distance traveled on given fuel resources [4]. The following limitations warrant consideration. First, measurement of MR and ECtransport at PWS may have been affected by speed variations during the trial. All of the participants included in the analyses, however, showed steady-state oxygen uptake. Second, people with DS appear to age faster than people without DS [28], potentially contributing to their present higher MR and ECtransport because age affects balance and energetic cost of walking [23]. Finally, the reported correlations should be interpreted with caution due to small sample size. In conclusion, individuals with DS show higher MR and ECtransport during over-ground walking than individuals without DS. PWS is slower in people with DS and minimizes their grossECtransport. In contrast, PWS in people without DS is faster than their speed at minimal gross-ECtransport. Individuals with and without DS do not appear to minimize the net-ECtransport. Therefore, minimization of gross-ECtransport may contribute to PWS during overground walking when disabling conditions drastically alter the gross-ECtransport to speed relationship. Acknowledgment Funded by Special Olympics Healthy Athletes Health Professions Student Grant. Conflict of interest statement The authors have no conflicts of interest. References [1] Corcoran PJ, Brengelmann GL. Oxygen uptake in normal and handicapped subjects, in relation to speed of walking beside velocity-controlled cart. Arch Phys Med Rehabil 1970;51:78–87. [2] Ralston HJ. Energy-speed relation and optimal speed during level walking. Int Z Angew Physiol 1958;17:277–83. [3] Alexander RM. Optimization and gaits in the locomotion of vertebrates. Physiol Rev 1989;69:1199–227. [4] Srinivasan M. Optimal speeds for walking and running, and walking on a moving walkway. Chaos 2009;19:026112. [5] Sparrow WA, Newell KM. Metabolic energy expenditure and the regulation of movement economy. Psychon Bull Rev 1998;5:173–96. [6] Agiovlasitis S, McCubbin JA, Yun J, Widrick JJ, Pavol MJ. Economy and preferred speed of walking in adults with and without Down syndrome. Adapt Phys Activ Q 2009;26:118–30. [7] Draheim CC, Williams DP, McCubbin JA. Prevalence of physical inactivity and recommended physical activity in community-based adults with mental retardation. Ment Retard 2002;40:436–44. [8] American Academy of Pediatrics. Health supervision for children with Down syndrome. Pediatrics 2001;107:442–9. [9] Pinter JD, Eliez S, Schmitt JE, Capone GT, Reiss AL. Neuroanatomy of Down’s syndrome: a high-resolution MRI study. Am J Psychiatry 2001;158:1659–65. [10] Agiovlasitis S, McCubbin JA, Yun J, Mpitsos G, Pavol MJ. Effects of Down syndrome on three-dimensional motion during walking at different speeds. Gait Posture 2009;30:345–50. [11] Kubo M, Ulrich B. Coordination of pelvis-HAT (head, arms and trunk) in anterior-posterior and medio-lateral directions during treadmill gait in preadolescents with/without Down syndrome. Gait Posture 2006;23:512–8. [12] Doke J, Donelan JM, Kuo AD. Mechanics and energetics of swinging the human leg. J Exp Biol 2005;208(Pt 3):439–45. [13] Donelan JM, Shipman DW, Kram R, Kuo AD. Mechanical and metabolic requirements for active lateral stabilization in human walking. J Biomech 2004;37:827–35. [14] Kuo AD. The six determinants of gait and the inverted pendulum analogy: a dynamic walking perspective. Hum Mov Sci 2007;26:617–56. [15] Fernhall B, Pitetti KH, Rimmer JH, McCubbin JA, Rintala P, Millar AL, et al. Cardiorespiratory capacity of individuals with mental retardation including Down syndrome. Med Sci Sports Exerc 1996;28:366–71. [16] Ulrich BD, Haehl V, Buzzi UH, Kubo M, Holt KG. Modeling dynamic resource utilization in populations with unique constraints: preadolescents with and without Down syndrome. Hum Mov Sci 2004;23:133–56.

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