page_title: Effect of gait parameters on energetic cost
section_title: Constrained Optimization
hierarchical_section_title: Effect of gait parameters on energetic cost / Constrained Optimization
caption_attribution_description: English: Energetic Cost Contour Plot. Coutour lines represent combinations walking speed and step frequency that require the same cost of transport. The green line represents optimization with constrained step frequency (the minimal cost of transport for fixed step frequencies). The red line represents optimization with constrained walking speed. The blue line represents optimization with constrained step lengths.
context_page_description: The effect of gait parameters on energetic cost is a relationship that describes how changes in step length, cadence, step width, and step variability influence the mechanical work and metabolic cost involved in gait. The source of this relationship stems from the deviation of these gait parameters from metabolically optimal values, with the deviations due to environmental, pathological, and other factors.
context_section_description: Since multiple distinct gait parameters have a significant impact on the energetic cost of walking, each of these parameters have to be considered when examining the primary goal of metabolic cost optimization.  The visualization of such an optimization for walking speed, cadence, and step length can be expressed in the form of a contour map, in which parameter combinations that lie on the same contour line share the same cost of transport (cal/kg/m).  The green, red, and blue, dotted lines represent values where cadence, walking speed, and step length are constrained, respectively.  These lines can be formed by finding the tangent points that lines representative of several constant parameter values form with the constant COT contours.  For example, the optimal COT's for constrained walking speeds (red) can be found by drawing vertical lines and noting where they form a tangent with a contour, as seen with point B in the diagram.  A series of these intersections can then form the curve for optimal COT under constrained walking speed.  These constrained optimization values not only reflect the naturally selected preferred gait parameters that are observed by fixing a single parameter at different values, but also form part of a predictive map that allows for the identification of the cost of transport for a multivariate system.
caption: Energetic Cost Contour Plot.  Coutour lines represent parameter combinations that require the same cost of transport.  The colored lines represent optimization to different parameters: (green) step frequency; (red) walking speed; (blue)step length.
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