Scaling of Inertial Delays in Terrestrial Mammals

As part of its response to a perturbation, an animal often needs to reposition its body. Inertia acts to oppose the corrective motion, delaying the completion of the movement—we refer to this elapsed time as inertial delay. As animal size increases, muscle moment arms also increase, but muscles are proportionally weaker, and limb inertia is proportionally larger. Consequently, the scaling of inertial delays is complex. Our intent is to determine how quickly different sized animals can produce corrective movements when their muscles act at their force capacity, relative to the time within which those movements need to be performed. Here, we quantify inertial delay using two biomechanical models representing common scenarios in animal locomotion: a distributed mass pendulum approximating swing limb repositioning (swing task), and an inverted pendulum approximating whole body posture recovery (posture task). We parameterized the anatomical, muscular, and inertial properties of these models using literature scaling relationships, then determined inertial delay for each task across a large range of movement magnitudes and the full range of terrestrial mammal sizes. We found that inertial delays scaled with an average of M0.28 in the swing task and M0.35 in the posture task across movement magnitudes—larger animals require more absolute time to perform the same movement as small animals. The time available to complete a movement also increases with animal size, but less steeply. Consequently, inertial delays comprise a greater fraction of swing duration and other characteristic movement times in larger animals. We also compared inertial delays to the other component delays within the stimulus-response pathway. As movement magnitude increased, inertial delays exceeded these sensorimotor delays, and this occurred for smaller movements in larger animals. Inertial delays appear to be a challenge for motor control, particularly for bigger movements in larger animals

Assessment of the gait sensitivity norm as a predictor of falls risk during walking using a neuromusculoskeletal model

Weakness or injury to the neural or musculoskeletal system can compromise an individual’s ability to walk safely and efficiently. Falls are reported to be responsible for 70 percent of accidental deaths in people 75 years of age and older. A practical definition of walking stability is the ability of a person to withstand perturbations and avoid falling. The ability to quantify the stability of an individual’s gait without jeopardizing their safety would be a useful tool in identifying and treating people at risk of falling.Several stability measures derived mainly from dynamical systems theory have been applied to estimate stability of walking. Two of the most notable measures are Floquet multipliers and maximal finite time Lyapunov exponents, but their correlation to falls risk has shown mixed results. The Gait Sensitivity Norm (GSN) is a recently derived variability measure taken from control engineering. It has been shown, under limited circumstances, to correlate well to falls risk on passive dynamic walking machines. However, GSN has not been adequately verified on humans or human-like walking models having active neural control and inherent cycle to cycle variability. The purpose of this work was to assess the ability of GSN to estimate falls risk in a neuromusculoskeletal (NMS) model.Simulated walking data on which stability analyses were run were generated using a computational neuromusculoskeletal model. The model consists of a 2 dimensional 7 segment 18 muscle musculoskeletal model incorporating Hill type muscles. The neural aspects of the model consist of a central pattern generator with 7 neural oscillators and various feedback and feedforward mechanisms. A family of models differing only in a hip stiffness control coefficient was generated. Each model was perturbed until it fell over to estimate actual falls risk. The sensitivity of GSN to the following calculation approaches was evaluated: correcting for steady state variability, data output timestep size, gait parameters and point in the gaitcycle used. Finally, the GSN values obtained for the models were then correlated to actual falls risk using Pearson’s linear correlation coefficients.GSN correlated well to falls risk under some situations. Step velocity and global angle were the gait indicators for which GSN showed good correlation to falls risk. Correlations were moderate to poor when using step time, step length or stride length. GSN was sensitive to the choice of gait indicator, data output timestep size and the point in the gaitcycle used, but not to steady state variability normalization. GSN has the potential to be clinically applied for assessing falls risk. Methods to refine the selection of perturbations applied and the gait parameters studied to ensure accuracy of the stability measure obtained have to be developed.M.S., Biomedical Engineering -- Drexel University, 201