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First published online January 17, 2007
Journal of Experimental Biology 210, 484-494 (2007)
Published by The Company of Biologists 2007
doi: 10.1242/jeb.02662
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Predicting the energy cost of terrestrial locomotion: a test of the LiMb model in humans and quadrupeds

Herman Pontzer

Washington University, 119 McMillan Hall, St Louis, MO 63130, USA


Figure 1
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  		Fig. 1. Representative vertical GRF traces for three steps of a human running trial at 2.5 m s–1. Solid line: raw vertical GRF trace. Note the noise imposed by the treadmill. Dotted line: mean vertical force of the GRF.

 

Figure 2
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  		Fig. 2. Kinematic, energetics and estimated force data for three subjects: one human (Mb=69.0 kg, hindlimb L=95cm, red circles), one goat (Mb=23, L=43.5, yellow triangles), and one dog (Mb=26.3, L=39, blue squares). Each point represents one subject at one speed. Open-centered points indicate walking trials, while filled points represent running trials. (A) The rate of oxygen consumption (i.e. COL), (B) excursion angle {phi}, (C) stride frequency f and (D) mean muscle force generated per step, as estimated by the LiMb model, versus speed. (E) The rate of muscle force generation, predicted by the LiMb model, versus the observed rate of oxygen consumption. The estimated rate of force production is a product of mean muscle force per step (D) and step frequency (2f; C).

 

Figure 3
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  		Fig. 3. LiMb model-predicted rate of force production (N kg–1 s–1) versus observed COLwalk (open circles) and COLrun (ml O2 kg–1 s–1) (filled circles) for humans (N=10 subjects). This pattern is similar to that reported previously for a different group of humans (Pontzer, 2005Go). Broken lines indicate LSR for COLwalk and COLrun, solid line indicates LSR for all trials. LSR equations and coefficients of determination are given in the figure.

 

Figure 4
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  		Fig. 4. LiMb model-predicted rate of force production (N kg–1 s–1) versus observed COL (ml O2 kg–1 s–1) for 4 humans (red circles), 4 goats (yellow triangles) and 4 dogs (blue squares). Walking and running trials are combined; symbols with open centers indicate walking trials. Broken line indicates LSR for all data (y=0.0035x+0.0433, r2=0.90, N=76 trials, P<0.001).

 

Figure 5
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  		Fig. 5. The performance of the LiMb model compared to other predictors of locomotor cost. (A) r2 values (coefficients of determination) for the LiMb model (black bars), contact time (tc–1) (light grey bars), Froude number (U2L–1g–1) (dark grey bars) and hindlimb length (UL–1) (white bars), calculated via LSR with observed COL (ml O2 kg–1 s–1). r2 values are given above each bar. Numbers in parentheses indicate sample size (number of subjects). Interspecific comparison (`All') is calculated for dogs (N=4), goats (N=4) and a subset of humans (N=4), as shown in Fig. 4. (B) r2 values for the LiMb model (black bars) contact time (tc–1U–1) (light grey bars), hindlimb length (L–1) (dark grey bars) and body mass (white bars), calculated via LSR with observed COT (ml O2 kg–1 m–1).

 

Figure 6
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  		Fig. 6. Predicted versus observed mean vertical GRF. (A) Because the point of foot–ground contact shifts forward between heel-strike and toe-off, standing hip height, L, underestimates the effective length of the hindlimb, L'. (Adapted from Gottschall and Kram, 2005Go.) (B) Using L to predict vertical GRF via the LiMb model consistently overestimates vertical GRF (open squares), while L' provides a reasonably good fit (closed circles). Broken line indicates y=x.

 

Figure 7
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  		Fig. 7. The relative contributions of vertical (black), horizontal (gray), and leg-swing (white) forces to total force production predicted by the LiMb model for (A) walking and (B) running. Sample sizes (subjects) are given in parentheses. For humans, walking values are for speeds near subjects' preferred speed (1.5 m s–1).

 

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© The Company of Biologists Ltd 2007