### Meeting Abstract

**S1-3.14** Jan. 5 **Bipedal Running: "No muscle work and all tendon play" is energetically beneficial even with an energy cost for isometric force production.** *SRINIVASAN, Manoj; Princeton University, Princeton* msriniva@princeton.edu

Muscles consume energy whether or not they perform work, as long as they exert a force while active. An energy-economizing animal will presumably minimize its total metabolic expenditure during locomotion, rather than minimizing, say in particular, the mechanical work performed or the force exerted. However, the major muscles that produce forces during stance in running turkeys do little mechanical work --- most of the positive and negative work required to redirect the center of mass velocity seem to be provided by the passive stretch and recoil of elastic tendons. This strategy superficially seems coincident with minimizing stance work. However, it is not clear why an animal would prefer to minimize just the muscle work, while the close-to-isometric muscles do expend metabolic energy as they need to provide a force that is equal at all times to the force in the series tendons. Here we use a simple mathematical model of a bipedal animal: one consisting of a point-mass body and legs with a telescoping actuator (muscle) and a series spring (tendon), to study the overall energetic optimality or otherwise of this strategy. We set up a mathematical optimization problem to minimize a few simple models of energy expenditure (during stance) that penalize isometric force as well as mechanical work. For a range of parameters of these simple models, we find that the minimization of the overall cost is indistinguishable from minimizing mechanical work alone. That is, the optimal locomotion strategies in these idealized models involved little or no muscle work and only tendon work, as observed in real animals. As a result, in these optimal locomotor strategies, the total metabolic cost during stance seems to be dominated by the metabolic cost for the production of isometric force, as also suggested by various experiments.