A comparison of static and dynamic characteristics between rectus eye muscle and linear muscle model predictions

Closed-loop optogenetic neuromodulation enables high-fidelity fatigue-resistant muscle control

Closed-loop neuroprostheses show promise in restoring motion in individuals with neurological conditions. However, conventional activation strategies based on functional electrical stimulation (FES) fail to accurately modulate muscle force and exhibit rapid fatigue because of their unphysiological recruitment mechanism. Here, we present a closed-loop control framework that leverages physiological force modulation under functional optogenetic stimulation (FOS) to enable high-fidelity muscle control for extended periods of time (>60 minutes) in vivo. We first uncovered the force modulation characteristic of FOS, showing more physiological recruitment and significantly higher modulation ranges (>320%) compared with FES. Second, we developed a neuromuscular model that accurately describes the highly nonlinear dynamics of optogenetically stimulated muscle. Third, on the basis of the optogenetic model, we demonstrated real-time control of muscle force with improved performance and fatigue resistance compared with FES. This work lays the foundation for fatigue-resistant neuroprostheses and optogenetically controlled biohybrid robots with high-fidelity force modulation.

Dynamic Characteristics of a New Three-Dimensional Linear Homeomorphic Saccade Model

A linear homeomorphic eye movement model that produces 3D saccadic eye movements consistent with anatomical and physiological evidence is introduced in this second part of a two-paper sequence. Central to the model is the implementation of a time-optimal neural control strategy involving six linear muscle models that faithfully represent the dynamic characteristics of 3D saccades. The muscle is modeled as a parallel combination of viscosity [Formula: see text] and series elasticity [Formula: see text], connected to the parallel combination of active-state tension generator [Formula: see text], viscosity element [Formula: see text], and length tension elastic element [Formula: see text]. The neural input for each muscle is separately maintained while the effective pulling direction is modulated by its respective pulley. The results demonstrate that a time-optimal, 2D commutative neural controller, together with the pulley system, actively functions to implement Listing's law during both static and dynamic simulations and provide an excellent match with the experimental data. The parameters and neural input to the muscles are estimated using a time domain system identification technique from saccade data, with an excellent match between the model estimates and the data. A total of 20 horizontal, 5 vertical and 62 oblique saccades are analyzed.

Static Characteristics of a New Three-Dimensional Linear Homeomorphic Saccade Model

A linear homeomorphic saccade model that produces 3D saccadic eye movements consistent with physiological and anatomical evidence is introduced. Central to the model is the implementation of a time-optimal controller with six linear muscles and pulleys that represent the saccade oculomotor plant. Each muscle is modeled as a parallel combination of viscosity [Formula: see text] and series elasticity [Formula: see text] connected to the parallel combination of active-state tension generator [Formula: see text], viscosity element [Formula: see text], and length tension elastic element [Formula: see text]. Additionally, passive tissues involving the eyeball include a viscosity element [Formula: see text], elastic element [Formula: see text], and moment of inertia [Formula: see text]. The neural input for each muscle is separately maintained, whereas the effective pulling direction is modulated by its respective mid-orbital constraint from the pulleys. Initial parameter values for the oculomotor plant are based on anatomical and physiological evidence. The oculomotor plant uses a time-optimal, 2D commutative neural controller, together with the pulley system that actively functions to implement Listing's law during both static and dynamic conditions. In a companion paper, the dynamic characteristics of the saccade model is analyzed using a time domain system identification technique to estimate the final parameter values and neural inputs from saccade data. An excellent match between the model estimates and the data is observed, whereby a total of 20 horizontal, 5 vertical, and 64 oblique saccades are analyzed.

A new linear muscle fiber model for neural control of saccades

A comprehensive model for the control of horizontal saccades is presented using a new muscle fiber model for the lateral and medial rectus muscles. The importance of this model is that each muscle fiber has a separate neural input. This model is robust and accounts for the neural activity for both large and small saccades. The muscle fiber model consists of serial sequences of muscle fibers in parallel with other serial sequences of muscle fibers. Each muscle fiber is described by a parallel combination of a linear length tension element, viscous element and active state tension generator.

An updated time-optimal 3rd-order linear saccadic eye plant model

A linear third-order model of the ocular motor plant for horizontal saccadic eye movements is presented consisting of a linear ocular motor plant and a time-optimal saccadic controller based on physiological considerations. The ocular motor plant consists of the eyeball and two extraocular muscles. All parameters and initial conditions are estimated or measured from physiological data. The neural inputs are described by pulse-slide-step waveforms with a post inhibitory rebound burst and based on a time-optimal controller. Model parameters are estimated using the system identification technique. The static and dynamic behaviors of the model are in excellent agreement with the experimental data.

3D dynamic computer model of the head-neck complex

A 3D dynamic computer model for the movement of the head is presented that incorporates anatomically correct information about the diverse elements forming the system. The skeleton is considered as a set of interconnected rigid 3D bodies following the Newton-Euler laws of movement. The muscles are modeled using Enderle's linear model. Finally, the soft tissues, namely the ligaments, intervertebral disks, and zigapophysial joints, are modeled using the finite elements approach. The model is intended to study the neural network that controls movement and maintains the balance of the head-neck complex during eye movements.

Neural control of saccades

Quantitative models of the oculomotor plant and control of the saccadic eye movement system are presented in this chapter. Oculomotor plant models described here are linear, including a second-order model by Westheimer (1954), Bahill et al. (1980) and Enderle et al. (2000). The model of the saccade generator is initiated by the superior colliculus and terminated by the cerebellar fastigial nucleus that operates under a time optimal control strategy. A common mechanism for all types of saccades is described, including those with dynamic overshoot and glissadic behavior. Conflicting evidence exists regarding the operation of the excitatory burst neuron during saccades. The excitatory burst neuron operates within two states: complete inhibition, and without inhibition that is characterized by high firing at rates of up to 1000 Hz. While there is direct evidence of projections from the superior colliculus to the paramedian pontine reticular formation, there is conflictory evidence regarding the connections from the superior colliculus to the excitatory burst neuron, with the most recent experimental results supporting no direct connections. A model of the excitatory burst neuron is described using a Hodgkin-Huxley model of the neuron that fires at 1000 Hz automatically and without stimulation when released from inhibition. SIMULINK simulations using this neuron model have all of the characteristics of the excitatory burst neuron firing rate during a saccade. This model eliminates the need to introduce BIAS inputs that causes bursting in some models of the saccade generator. Such a model is also appropriate for modeling the Omnipause neurons.