NISHIKAWA, KC; Northern Arizona University: Modeling ballistic jaw movements using equations of motion for a damped mass-spring system. I. Methods.

During ballistic tongue projection, the mm. depressor mandibulae of toads produce high mass specific power (>7 W/g) with little storage of strain energy in tendon or other structures. To account for this high power output, we performed a series of experiments on individual toads, including high-speed (1000 Hz) image analysis with simultaneous EMG recordings from the mm. depressor mandibulae, force-lever experiments, and anatomical measurements. These data were used to model the feeding apparatus as a damped mass-spring system. Digital imaging was used to estimate the distance between upper and lower jaw tips at 1 ms intervals. These data were divided by the in-lever/out-lever ratio to estimate in vivo shortening of the mm. depressor mandibulae at 1 ms intervals, and total shortening during fast mouth opening. EMG was used to measure the duration of mm. depressor mandibulae activation that preceded fast mouth opening. Using the force-lever, muscles were allowed to shorten at a series of reduced loads after 200 ms isometric pre-activation. The distance shortened during the fast phase was measured at each load, and a logarithmic function was used to estimate the displacement from equilibrium that occurred during isometric pre-activation. Stiffness was calculated as force divided by estimated displacement from equilibrium at the in vivo load. Time-dependent behavior was modeled using the characteristic equation for an under-damped mass-spring system. Three parameters (mass, stiffness, and displacement) were estimated from experiments, and the damping coefficient was assumed to be close to the critical value. The fit between data and model was computed as the sum of the squared deviation of predicted from observed results, and a sensitivity analysis was performed for each parameter.