Fig 1.
Measurement of foot paths and energy expenditure on outdoor terrain.
Subjects walked on different terrains while wearing a portable respirometry system, a global positioning system (GPS) device, and one inertial measurement unit (IMU) per foot. Sample data from one subject show traces for walking speed and elevation from GPS, rates of oxygen consumption and carbon dioxide production, and angular velocity and translational acceleration vs. time. Terrains included Sidewalk, Gravel, Grass, Woodchip, and Dirt, along with transitions between them (gray lines, not analyzed). Walking speed was loosely regulated via GPS (average speeds listed); terrain segments were selected to avoid large net changes in elevation during trials.
Fig 2.
Sample foot path trajectories and associated measurements, as viewed from above and from the side.
Forward vs. lateral foot displacements from each trial were used to compute stride covariances. Vertical path of foot was used to determine virtual clearance, relative to straight line between start and end of stride.
Fig 3.
Representative foot path trajectories for each terrain (from one representative subject), as viewed from above and from side.
All strides were arranged to have common origin, to emphasize variation among strides. Color of trajectories varies gradually between beginning (blue) and end (red) of trial, to indicate time course of strides.
Fig 4.
Summary measures of energetic cost and stride measures on five different terrains.
Energy expenditure in terms of net metabolic rate and net metabolic cost of transport (energy per unit distance and weight). Stride measures are shown as mean and root-mean-square (RMS) variability: virtual clearance, lateral swing distance, stride height, stride length, stride width (variability only), and walking speed. Bars denote across-subject means; error bars denote standard deviation across subjects (N = 10).
Table 1.
Stride measures and energy expenditure for five terrains.
Table 2.
Linear relationship between net metabolic rate (outcome variable) and individual stride measures.
Fig 5.
Principal components and linear discriminants of stride measures, shown as a series of columns of horizontal bars, each row representing a stride measure.
First five principal components (PCs) are shown, as well as two linear discriminants, for (LD1) Gravel vs. Grass, and (LD2) Sidewalk vs. Dirt (with constant offsets listed). Stride measures from all subjects and all terrains contributed to this analysis.
Fig 6.
Stride measures for all subjects (N = 10) and all terrains, plotted in two ways: (top) stride length vs. speed, and (bottom) Linear discriminants against each other (i.e. a projection of multi-dimensional data onto two discriminants).
Each data point represents one subject’s average measures for one terrain. Stride lengths and speeds (filled symbols) were highly correlated with each other, and overlapped for different terrains. As an example of within-trial variations, top graph also shows all strides from all terrains for a single representative subject (smaller, lightly shaded symbols). Linear discriminants improve separation between two pairs of terrains (separators denoted by dashed lines).
Fig 7.
Net metabolic rate for all subjects and all terrains, fitted vs. observed.
Observed refers to empirical measurements (five terrains, N = 10 each). Fitted refers to three ways to predict metabolic rate: Principal components regression from first two PCs (PCR; adjusted R2 = 0.46); Partial least squares regression (PLSR; adjusted R2 = 0.52); and from virtual clearance in a single-variable linear regression (Clearance; overall adjusted R2 = 0.34; shown fitted with subject-specific offsets, R2 = 0.49). Fit types are denoted by symbol shape, and terrains by color.