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Development and validation of a steep incline and decline metabolic cost equation for steady-state walking

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Abstract

Purpose

The purpose of this study was to develop and validate a data-supported prediction equation (Lankford equation) for walking metabolic cost (\(C_{\text{W}}\)), and to compare this equation to the ACSM, Pandolf, Minetti, and LCDA equations. The current study also investigated how kinematics of incline walking relates to mechanical efficiency and metabolic cost.

Method

Subjects consisted of 145 recreationally fit individuals. Walking speeds were between 1 AND 3 mph with grades ranging from − 18 to 40%. The Lankford equation was then compared to four other reference equations using adjusted R-squared (R2) and Root Mean Square Error (RMSE) as primary metrics to determine correlation with measured CW. Kinematics data collected from reflective markers placed on bony landmarks were compared to CW, incline, and metabolic efficiency to determine the interrelationship between these variables.

Results

The Lankford equation for estimating \(C_{\text{W}}\) was validated with an adjusted R2 = 0.89 and a RMSE of 5.92 Kj min−1, shown to have the highest accuracy among all equations tested. A 0.21 efficiency plateau was observed above 15% incline, and hip, knee, HAT, thigh, and shank angles at foot touch down were found to be highly correlated with \(C_{\text{W}}\) (r > 0.980).

Conclusion

The Lankford equation is a validated and highly accurate prediction equation for steady-state walking across a wide range of inclines and speeds and is applicable to the general public. Altered leg swing observed above 15% incline was found to account for the mechanical efficiency plateau and the rectilinear increase in \(C_{\text{W}}\) with increasing incline.

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Availability of data and material

Private sharing link for source data: https://github.com/BYUIDSS/byui_metabolic_equation_lankford.

Abbreviations

R 2 :

Adjusted R-squared

AIC:

Akaike information criterion

ACSM:

American College of Sports Medicine

BIC:

Bayesian information criterion

BMI:

Body mass index

EE:

Energy expenditure

L :

External load carried (kg)

HAT:

Head, arms, and trunk

HR:

Heart rate

LT:

Lactate threshold

LCDA:

Load Carriage Decision Aid

LogLik:

Log-likelihood

W :

Mass (kg)

\(C_{\text{W}}\) :

Metabolic cost of walking

p :

Number of predictors used

\(\dot{V}{\text{O}}_{2}\) :

Rate of oxygen consumption

RPE:

Rate of perceived exertion

RER:

Respiratory Exchange Ratio:

RMR:

Resting metabolic rate

RMSE:

Root mean square error

n :

Sample size

SS:

Self-selected

S (for the Lankford equation) and V (for all reference equations):

Speed

SSE:

Sum of squared errors

G (percent grade,  %) and i (grade in decimal):

Surface grade

η :

Terrain coefficient

SSTO:

Total sum of squares

VT:

Ventilatory threshold

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Acknowledgment

The authors would like to thank Breanna Neuwirth, Kent Jolley, Emily James, and Michael Dredge for their assistance during data collection and analysis.

Funding

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Author information

Authors and Affiliations

  1. Department of Human Performance and Recreation, Brigham Young University-Idaho, 525 S. Center St, Rexburg, 83460, USA

    D. E. Lankford, Yilin Wu, Jake T. Bartschi & John Hathaway

  2. Department of Human Physiology, Gonzaga University, Spokane, USA

    A. D. Gidley

  3. Department of Kinesiology and Recreation Administration, Humboldt State University, Arcata, USA

    D. E. Lankford

Authors
  1. D. E. Lankford
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  2. Yilin Wu
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  3. Jake T. Bartschi
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  4. John Hathaway
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  5. A. D. Gidley
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Contributions

DEL was the primary investigator who oversaw the study; YW, JB, JH, and AG carried out data collection, data analysis, manuscript preparation, and manuscript editing. All authors have approved the manuscript.

Corresponding author

Correspondence to D. E. Lankford.

Ethics declarations

Conflict of interest

DE. Lankford has performed research consulting for ICON Health & Fitness, manufacturer of the treadmills used in the study.

Ethics approval & Consent to participate

Institutional Review Board at Brigham Young University-Idaho approved the project, and all subjects gave their informed consent prior to the start of the study.

Additional information

Communicated by Jean-René Lacour.

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Lankford, D.E., Wu, Y., Bartschi, J.T. et al. Development and validation of a steep incline and decline metabolic cost equation for steady-state walking. Eur J Appl Physiol 120, 2095–2104 (2020). https://doi.org/10.1007/s00421-020-04428-z

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  • DOI: https://doi.org/10.1007/s00421-020-04428-z

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