Normalized economical speed is influenced by aging and not by exercise habituation

doi:10.21203/rs.3.rs-2497727/v1

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Normalized economical speed is influenced by aging and not by exercise habituation

https://doi.org/10.21203/rs.3.rs-2497727/v1

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published 05 Oct, 2023

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Objective: A U-shaped relationship between energy cost of walking (C_w; J·kg^-1·m^-1) and walking speed indicates that there is a specific speed minimizing the C_w, called economical speed (ES). It is mostly slower in older adults than young adults; however, effects of leg length on the ES have been ignored. We investigated the effects of aging and exercise habituation on the normalized ES by the leg length (nor-ES). Moreover, the diversity in the stride length (SL) and step frequency (SF) against sinusoidal speed change (SSC) at 30-s and 180-s periods with ±0.56 m･s^-1 among sedentary young (SY), active young (AY), and active elderly (AE) adults was also quantified.

Results: The ES was significantly faster in the following sequence: AY, SY, and AE, whereas nor-ES was faster in the AY and SY than in the AE (no difference was found between AY and SY). Delayed SL and preceding SF were observed at the 180-s SSC in the young adults only. Collectively, greater delay and/or precedence of SL-SF combinations against SSC may reflect locomotive flexibility for passive speed change during walking. The nor-ES was slowed by aging; however, it was not influenced by exercise habituation, at least, in young populations.

Locomotion

Gait

Step variability

Optimal speed

Froude number

The energy cost of walking per unit distance (C_w; J·kg^− 1·m^− 1) presents as a U-shaped curve as a function of walking speed (s; m·s^− 1) [1–3]. This indicates that every individual has a specific walking speed minimizing the C_w [1–13], referred to as economical speed (ES) [1–3]. A biological importance of the ES is that it is well associated with the preferred walking speed (PWS) [13] in healthy populations [3–13].

Using some previous data, the measured ES (m-ES) apparently slowed in the elderly than in the young adults [1,9–12]. Contrary findings were also presented in other studies [13–15]. Thus, it is controversial whether the m-ES is slowed with aging. Different study settings (e.g., measured speeds), anthropometrics (height, obesity, or fitness level), or different calculation of the m-ES render it difficult to obtain a consensus. Of these, anthropometrics, especially in leg length (LL), should be reconsidered because a greater LL proportionally exhibited faster m-ES [1]. Most of the above previous studies have not normalized the m-ES by LL (nor-ES), although LL in association with height was normally greater in the young adults than the elderly adults [1,9,10,12,13]. Furthermore, daily exercise habituation can also be a related factor. Previous studies have compared the m-ES between active (or non-active) young and elderly counterparts [13,15]. Conversely, there is paucity in literatures comparing the m-ES between sedentary and active young adults [13]. As the physical activity level is increased, the m-ES is rendered faster in the elderly adults [14,15]. These results further suggest that the m-ES would be affected by exercise habituation not only in the elderly but also in young adults.

When people walk at a given speed, continuous adjustment of their limbs is required to refrain from falling. This adaptation potentially contributes to minimizing the C_w [16], suggesting that the capability to adjust lower limb motions would be associated with the U-shaped C_w-s relationship. Thus, sinusoidal speed changing (SSC) protocol may be useful to manipulate the lower limb motions [17–19]. To elucidate the effects of aging and exercise habituation in the nor-ES, we investigated whether the nor-ES of the active elderly (AE) adults may not be slower than that of the active young (AY) or sedentary young (SY) adults. Regardless of these issues, peak ankle torque is lower in the elderly adults than in the younger counterparts [20], suggesting that the gait-adjusting capability against SSC may be different among the three groups. Moreover, how step variabilities against SSC is diverse among the three groups was also quantified.

We used additional data from already published paper [19] based on an entirely different perspective. Seventeen SY, 16 AY, and 16 AE adults participated in this study (Table 1). Classification between active and sedentary was conducted using a recent guideline [21]. This study was approved by the ethical committee at Kyusyu Sangyo University and was performed under consideration of the Declaration of Helsinki (no. 2019-0002).

Table 1

Physical characteristics in young and elderly participants.
	Sedentary young (8M and 9F)			Active young (11M and 5W)			Active elderly (9M and 7F)			F values	P values
Age, years	20.3	±	0.9	19.9	±	0.6	74.1	±	4.6^#	2185	< 0.001
Height, m	1.613	±	0.083	1.679	±	0.068^*	1.598	±	0.087	4.713	0.014
Body mass, kg	57.2	±	9.8	61.3	±	9.3	58.6	±	7.5	0.892	0.417
BMI, kgཥm^− 2	21.9	±	2.9	21.6	±	2.2	22.9	±	2.0	1.196	0.312
Leg length, m	0.862	±	0.059	0.901	±	0.042^*	0.852	±	0.059	3.908	0.027
Exercise habituation	ཥNone except physical education classes at their university			ཥRecreational sports (volleyball, soccer, tennis, track and field) ཥ90–120 min per day ཥ2–4 days per week			ཥBrisk walking (community walking and mountain club) ཥ40–60 min per day ཥ5–7 days per week
Values are mean±standard deviation. M, men; F, female; BMI, body mass index. * indicates significant difference vs. “Active elderly” and “Sedentary young”, and # indicates significant differences vs. “Sedentary and Active young”.

The participants completed familiarization walking on a motor-driven treadmill (TKK3080, Takei Scientific Instruments Co. Ltd., Niigata, Japan) at several speeds. Thereafter, they performed m-ES determination protocol at 6–7 gait speeds ranging from 0.44 m·s^− 1 to 2.00 m·s^− 1. For that, 6–7 gait speeds were incrementally set at 0.44-0.67-0.89-1.11-1.33-1.56 m·s^− 1 (elderly women up to this speed), -1.67 m·s^− 1 (elderly men), -1.78 m·s^− 1 (young women), and − 2.00 m·s^− 1 (young men). Each speed was maintained for 4 min. Oxygen uptake (VO₂) and carbon dioxide (VCO₂) were continuously measured using a breath-by-breath technique (AE310-S, Minato Medical Science, Osaka, Japan), and an average VO₂ and VCO₂ for the final 2 min at each speed was provided to calculate the C_w with a following equation [22].

C _w (J·kg^− 1·m^− 1) =\(\frac{4.186 \times \left(3.869\times \text{V}\text{O}2 + 1.195\times \text{V}\text{C}\text{O}2\right)}{s}\)

A U-shaped relationship between C_w values and gait speeds was approximated with a quadratic equation [1–3]:

C _w (s) = a·s² + b·s + c

where the coefficients a, b, and c are determined by the least squares methods. The m-ES, at which the U-shaped C_w-s relationship becomes minimal, can be obtained when C_w’ (s) is zero [1–3]. Thus, the m-ES was calculated by a following equation:

The nor-ES was calculated on the “dynamic similarity” theory [23], providing that geometrically similar legged locomotion will walk similarly at the same Froude (F_r) number defined as:

F _r =\(\frac{{\text{m}-\text{E}\text{S}}^{2}}{g･LL}\)

where g is the gravitational acceleration (9.81 m·s^− 2). Energetically optimal gait speed can be obtained when the F_r=0.25 [23]. Thus, the nor-ES was calculated as follows:

nor-ES =\(\frac{0.3193 \times \text{m}-\text{E}\text{S}}{\sqrt{LL}}\)

Biomechanical measurements were conducted on the second visit. The PWS was determined based on a previous study [13]. To capture motion data, eight high speed cameras (Kestrel300, MAC3D System, Rohnert Park, CA, USA) were set with a sampling rate of 100 Hz [19]. The participants walked at their PWS in young adults or 90% PWS in elderly adults for 30-s, thereafter, the treadmill speed was sinusoidally controlled at 30-s and 180-s periods with an amplitude of ± 0.56 m·s^− 1 (± 2 km·h^− 1) in a randomized order. The motion data were used to determine the time delay (TD) of the stride length (SL) and step frequency (SF) against SSC. The SL and SF were approximated using the following equation:

SL and/or SF = A·sin (ωt-TD)

where A, ω, and t represent amplitude, angular frequency, and time (msec), respectively.

Values are mean ± standard deviation. One-way analysis of variance (ANOVA) was used for comparisons in physical characteristics and the m-ES and/or nor-ES among three groups. Two-way (3 groups × 2 sinusoidal periods) repeated measures ANOVA was used for comparisons of the TD of SL (TD_SL) and SF (TD_SF) between two groups. When F values were significant, Ryan’s post-hoc test, which can be used regardless of data distribution [24], was used for further analyses. The statistical significance was set at p < 0.05.

A significantly greater height and LL were observed in the AY than the other groups with no differences in body weight and body mass index among the groups (Table 1). The m-ES was 1.304 ± 0.068 m·s^− 1 (SY), 1.361 ± 0.058 m·s^− 1 (AY), and 1.250 ± 0.061 m·s^− 1 (AE), respectively (Fig. 1A). The nor-ES was 0.448 ± 0.018 (SY), 0.458 ± 0.018 (AY), and 0.433 ± 0.021 (AE), respectively (Fig. 1B). The m-ES was significantly faster in the order of AY, SY, and AE (F = 11.781, p < 0.001, Fig. 1A). A significant group effect was observed in the nor-ES (F = 6.824, p = 0.003), and a post-hoc test revealed that the nor-ES was significantly slower in the AE than in the AY (t = 3.658, p < 0.001, Fig. 1B) and SY (t = 2.303, p < 0.026, Fig. 1B). The nor-ES was not significantly different between AY and SY (t = 1.410, p = 0.165, Fig. 1B).

Non-significant main effects of groups (F = 1.657, p = 0.202, Fig. 2A) and period (F = 0.058, p = 0.811, Fig. 2A) were found in the TD_SL with no significant interaction effect (F = 2.253, p = 0.117). There was a significant interaction effect in the TD_SF (F = 3.889, p = 0.028, Fig. 2B). Although the TD_SF was not significantly different among the three groups at the 30-s period (F = 0.023, p = 0.977), significant simple main effects of the period were found at the 180-s period in the SY (F = 7.821, p = 0.008) and AY (F = 11.819, p = 0.001) than the AE (Fig. 2B). A post-hoc test revealed that the TD_SF at the 180-s period was significantly lesser in the SY (t = 3.094, p = 0.004) and AY (t = 3.497, p < 0.001) than the AE (Fig. 2B).

On average, a relatively smaller difference was observed in the nor-ES (~ 3.9%) than the m-ES (~ 6.2%) between AE and the other two groups (Fig. 1), suggesting that the LL plays a key role in determining the individual ES. Additionally, no significant differences were observed between SY and AY in the nor-ES (Fig. 1B), indicating that exercise habituation did not affect the nor-ES, at least, in young adults. The increased muscular co-activation of the thigh muscles is attributed to age-related increase in the C_w [9,11,25–27], but it can contribute to enhance gait stability. Thus, such an age-related increase in the muscular co-activation of the thigh muscles is a trade-off between gait stability and EE during walking in the elderly adults. However, an age-related upward shift of the C_w-s curve is normally accompanied with a leftward shift of that curve, resulting in a slower m-ES [1,9,12]. It was noteworthy noting that the C_w-s curve and/or C_w at some selected gait speeds was lower in elderly distance runners than in elderly habitual walkers [13–15,28]. Remarkably, compared to healthy young adults, neither leftward nor upward shifts of the U-shaped curve were observed in elderly runners compared to healthy young adults [14,15], and nor-ES seemed to be faster in these well-trained elderly adults than healthy young adults [15]. These previous results and our present results suggest that the m-ES could be maintained if elderly adults could execute locomotive exercises at a sufficiently high- or moderate-intensity level.

Both elderly and young adults present a similar U-shaped C_w-s curve [1,9,12,14,15], suggesting that similar gait-related biomechanical factors would affect the U-shaped curve regardless of age. An upper and leftward shift of the C_w-s curve in the elderly adults may be attributed not only to thigh muscle co-activation but also to an increased step width because it can induce a considerable increase in the C_w [29]. However, the step width of the AE in our original study was not different from that of younger counterparts [19]. Instead, elderly adults normally present a shorter SL compared to the young adults [30]. In that case, a faster SF is necessary because gait speed should correspond to the product of the SL and SF. During SSC condition, quick optimization of the SL and SF is continuously required to catch up with the speed change. The AE presented a quite smaller TD_SL (Fig. 2A) and TD_SF (Fig. 2B); otherwise, the AY and SY presented combinations of greater positive TD_SL (Fig. 2A) and negative TD_SF (Fig. 2B) values especially at the 180-s period. Indeed, physiological variability during exercise is normally regarded as a flexibility representing exercise tolerance (e.g., heart rate variability [31]). However, excessive gait variability would predispose to link an increase in fall risk [32], suggesting that a greater TD and precedence of the SL and SF combinations at the 180-s period in young adults (Fig. 2) may reflect a greater locomotive flexibility to adjust appropriate SL-SF combinations for passive speed change during treadmill walking. At the 180-s period, relatively greater variations of the TD_SF and TD_SL were observed in the SY and AE than the AY adults (Fig. 2). At faster gait speeds, a lesser ankle torque [20] and gait instability [33] were reported in the elderly populations than the younger counterparts. Greater variations of the TD_SF and TD_SL at the 180-s period would be associated with these previous studies because a 180-s period involves fast gait speeds for a longer duration compared to the 30-s period protocol. Although our datasets could not provide clear mechanism(s), both exercise habituation and aging may influence variations of the TD_SF and TD_SL.

Technological considerations are necessary. Two comparative studies presented phase shift in degree [17,18], equivalent to the TD_SL and TD_SF in the present study. Surprisingly, both TD_SF and TD_SL in healthy young adults showed negative values over 4-s in SF and 1.5-s in SL even at 60-s SSC protocol [18]. However, the trend of our results completely different from those of our previous studies (Fig. 2). This could be attributed to the different calculation techniques. Both previous studies used interpolated 1-s data for calculating the phase shift of the SF and SL. That is, TD_SL and TD_SF values with a sampling frequency of 1.0 Hz were treated based on the discrete Fourier transform. If SF and/or SL variabilities occurred above 0.5 Hz that corresponded to the Nyquist folding frequency of the original sampling frequency (1.0 Hz), those variabilities could contaminate low-frequency spectrums, so-called “aliasing” [34].

Limitations

In the present study, sedentary elderly adults were not recruited. Considering their safety and potential risk management as presented [4], testing of these populations was not conducted. Additionally, an electromyography study was not performed since it did not align with the purpose of the original study [19].

active elderly

ANOVA

analysis of variance

active young

C_w

energy cost of walking

energy expenditure

m-ES

measured economical speed

nor-ES

normalized economical speed

leg length

PWS

preferred walking speed

speed

standard deviation

step frequency

stride length

SSC

sinusoidal speed change

sedentary young

time delay

TD_SF

time delay of step frequency

TD_SL

time delay of stride length

VO₂

oxygen uptake

VCO₂

carbon dioxide output.

Acknowledgements

We specially thank Mr. Akinobu Sakamoto, Mr. Tomokazu Iwatani, Mr. Hiromichi Ikegami, Mr. Takeshi Saito, Mr. Masaru Hashimura, and Mr. Shizuo Takatoh (Takei Scientific Instruments Co., Ltd.) for customizing the treadmill to control the gait speed sinusoidally. We also thank Enago

Author contributions

All authors designed the original study settings on consensus. DA, KM, MH, and TT performed measurements. DA, TT, MH, AS, and KM analyzed and interpreted the data. MH and DA prepared figure presentations and drafted the first manuscript. DA and AS revised the manuscript. All authors have read and approved the final manuscript.

Funding

This study was financially supported by Grant-in-Aid for Scientific Research from the Japan Society for the Promotion of Science (JP19K11541 and JP22K11517 to DA, JP20K19623 to KM, JP21K17613 to AS, and JP18K11012 to MH). Equipment and software installation were also supported by Grant-in-Aid for Kyushu Sangyo University (KSU) Scientific Research and Encouragement of Scientists (K035124 and R035027 to DA).

Availability of data and materials

The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.

Ethical approval and consent to participate

All study procedures were approved by the ethical committee at Kyusyu Sangyo University.

Consent for publication

Not appreciable.

Competing interests

The authors declare that they have no competing interests.

Author details

¹National Institute of Fitness and Sports in KANOYA, Shiromizu-1, Kanoya city, Kagoshima, 8912393, Japan. ²Center for Health and Sports Science, Kyushu Sangyo University, 2-3-1 Matsukadai, Higashi-ku, Fukuoka 813-8503, Japan. ³CNP Design, 4-1-5 Shimobaru, Higashi-ku, Fukuoka 813-0002, Japan.

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No competing interests reported.

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Journal Publication

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Editorial decision: Major revision
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You are reading this latest preprint version

Normalized economical speed is influenced by aging and not by exercise habituation

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Abstract

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Introduction

Material And Methods

Results

Discussion

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Abbreviations

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References

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