Linear Homeomorphic Models for Muscles in the Head–Neck Region

Abstract

The linear homeomorphic muscle model proposed by Enderle and coworkers for the rectus eye muscle is fitted to reflect the dynamics of muscles in the head-neck complex, specifically in muscles involved in gaze shifts. This parameterization of the model for different muscles in the neck region will serve to drive a 3D dynamic computer model for the movement of the head-neck complex, including bony structures and soft tissues, and aimed to study the neural control of the complex during fast eye and head movements such as saccades and gaze shifts. Parameter values for the different muscles in the neck region were obtained by optimization using simulated annealing. These linear homeomorphic muscle models provide non-linear force-velocity profiles and linear length tension profiles, which are in agreement with results from the more complex Virtual Muscle model, which is based on Zajac's non-linear muscle model.

3D Dynamic Modeling of the Head‐Neck Complex for Fast Eye and Head Orientation Movements Research

“…To take into account the different constituents of the head-neck system, different modeling strategies are used. The skeleton (head and cervical vertebrae) are modeled as rigid bodies and muscles by means of Enderle's dynamic model [16], with parameter values obtained through simulated annealing as reported elsewhere [17]. Finally, soft tissues (ligaments, intervertebral disk, and facet joints) are modeled using nonlinear viscoelastic representations.…”

“…We incorporate Enderle et al's model for the rectus eye muscle; individual parameters are estimated and parameterized for each one of the neck muscles [16,17]. Anatomical data about the attachment sites and force-generating parameters for the muscles are presented in [8].…”

“…Enderle's linear model was parameterized for the muscles in the neck used during head movements based on the nonlinear model by Sierra and Enderle [17]. Simulated annealing was used to estimate the linear model's parameter values from the Virtual Muscle nonlinear model, developed by Chen et al [19] and Song et al [20].…”

“…Simulated annealing was used to estimate the linear model's parameter values from the Virtual Muscle nonlinear model, developed by Chen et al [19] and Song et al [20]. This previous report presents on the determination of the parameters of linear muscle models for the head and neck region [17].…”

“…Recently, this linear model was parametrized for the muscles in the neck used during head movements [17], based on the nonlinear model by Zajac [18]. Simulated annealing was used to estimate the linear model's parameter values from the virtual muscle nonlinear model, developed by Chen et al [19] and Song et al [20] The ultimate goal of this work is to address the generation of the neural signals controlling the contraction of the head-neck muscles during fast eye movements.…”