Linear homeomorphic model for human movement

Dynamics of plant mechanics

Muscle and plant dynamics are most important during the high acceleration of saccades. Models have been developed to characterize muscle and plant dynamics. Building these models require an understanding of the length-tension (elastic) and force-velocity (viscous) relationships. Much work has been done to characterize these nonlinear functions, as they are influenced by innervation. However, the active force generator (active-state tension) in the muscle is still poorly understood. Thus, these models serve more to reveal where new studies of muscle behavior are needed than to explain what happens during a saccade.

A Fusion Algorithm for Saccade Eye Movement Enhancement With EOG and Lumped-Element Models

Electrooculography (EOG) can be used to measure eye movements while the eyelids are open or closed and to assist in the diagnosis of certain eye diseases. However, challenges in biosignal acquisition and processing lead to limited accuracy, limited resolution (both temporal and spatial), as well as difficulties in reducing noise and detecting artifacts. Methods such as finite impulse response, wavelet transforms, and averaging filters have been used to denoise and enhance EOG measurements. However, these filters are not specifically designed to detect saccades, and so key features (e.g., saccade amplitude) can be over-filtered and distorted as a consequence of the filtering process. Here we present a model-based fusion technique to enhance saccade features within noisy and raw EOG signals. Specifically, we focus on Westheimer (WH) and linear reciprocal (LR) eye models with a Kalman filter. EOG signals were measured using OpenBCI's Cyton Board (at 250 Hz), and these measurements were compared with a state-of-the-art EyeLink 1000 (EL; 250 Hz) eye tracker. On average, the LR model-based KF produced a 47% improvement of measurement accuracy over the bandpass filters. Thus, we conclude that our LR model-based KF outperforms standard bandpass filtering techniques in reducing noise, eliminating artifacts, and restoring missing features of saccade signatures present within EOG signals.

A Geometrical Approach to Human Saccade Simulation

Modeling and simulation of human eye movement have a wide range of applications in many domains. Various attempts have been made to model and simulate eye movements in a physically accurate manner. All the existing models show limitations and problems in simulating secondary and tertiary eye movements. Recent investigation of pulley models (passive and active hypotheses) in representing human eye motion has recognized mathematical complexity in modeling eye behavior. Sophisticated techniques of modeling are required to investigate eye movements. This paper presents a procedure for eye movement simulation through geometrical modeling (an OpenSim script with its recent MATLAB binding) for binocular vision. First order neural dynamics with Millard's muscle model are used to actuate six Extra Ocular Muscles (EOMs). Pulse-step inputs are used to generate the muscle forces around the eye globe. The implemented model is successful in simulating horizontal and vertical movements of the human eye with respect to the prescribed activation. The developed technique is evaluated using responses from lumped parameter models and EOG recordings.

Estimation of Neural Inputs and Detection of Saccades and Smooth Pursuit Eye Movements by Sparse Bayesian Learning

Eye movements reveal a great wealth of information about the visual system and the brain. Therefore, eye movements can serve as diagnostic markers for various neurological disorders. For an objective analysis, it is crucial to have an automatic and robust procedure to extract relevant eye movement parameters. An essential step towards this goal is to detect and separate different types of eye movements such as fixations, saccades and smooth pursuit. We have developed a model-based approach to perform signal detection and separation on eye movement recordings, using source separation techniques from sparse Bayesian learning. The key idea is to model the oculomotor system with a state space model and to perform signal separation in the neural domain by estimating sparse inputs which trigger saccades. The algorithm was evaluated on synthetic data, neural recordings from rhesus monkeys and on manually annotated human eye movement recordings with different smooth pursuit paradigms. The developed approach shows a high noise-robustness, provides saccade and smooth pursuit parameters, as well as estimates of the position, velocity and acceleration profiles. In addition, by estimating the input to the oculomotor system, we obtain an estimate of the neural inputs to the oculomotor muscles.

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.

Do muscle synergies reduce the dimensionality of behavior?

The muscle synergy hypothesis is an archetype of the notion of Dimensionality Reduction (DR) occurring in the central nervous system due to modular organization. Toward validating this hypothesis, it is important to understand if muscle synergies can reduce the state-space dimensionality while maintaining task control. In this paper we present a scheme for investigating this reduction utilizing the temporal muscle synergy formulation. Our approach is based on the observation that constraining the control input to a weighted combination of temporal muscle synergies also constrains the dynamic behavior of a system in a trajectory-specific manner. We compute this constrained reformulation of system dynamics and then use the method of system balancing for quantifying the DR; we term this approach as Trajectory Specific Dimensionality Analysis (TSDA). We then investigate the consequence of minimization of the dimensionality for a given task. These methods are tested in simulations on a linear (tethered mass) and a non-linear (compliant kinematic chain) system. Dimensionality of various reaching trajectories is compared when using idealized temporal synergies. We show that as a consequence of this Minimum Dimensional Control (MDC) model, smooth straight-line Cartesian trajectories with bell-shaped velocity profiles emerged as the optima for the reaching task. We also investigated the effect on dimensionality due to adding via-points to a trajectory. The results indicate that a trajectory and synergy basis specific DR of behavior results from muscle synergy control. The implications of these results for the synergy hypothesis, optimal motor control, motor development, and robotics are discussed.

Trajectory prediction of saccadic eye movements using a compressed exponential model

Gaze-contingent display paradigms play an important role in vision research. The time delay due to data transmission from eye tracker to monitor may lead to a misalignment between the gaze direction and image manipulation during eye movements, and therefore compromise the contingency. We present a method to reduce this misalignment by using a compressed exponential function to model the trajectories of saccadic eye movements. Our algorithm was evaluated using experimental data from 1,212 saccades ranging from 3° to 30°, which were collected with an EyeLink 1000 and a Dual-Purkinje Image (DPI) eye tracker. The model fits eye displacement with a high agreement (R² > 0.96). When assuming a 10-millisecond time delay, prediction of 2D saccade trajectories using our model could reduce the misalignment by 30% to 60% with the EyeLink tracker and 20% to 40% with the DPI tracker for saccades larger than 8°. Because a certain number of samples are required for model fitting, the prediction did not offer improvement for most small saccades and the early stages of large saccades. Evaluation was also performed for a simulated 100-Hz gaze-contingent display using the prerecorded saccade data. With prediction, the percentage of misalignment larger than 2° dropped from 45% to 20% for EyeLink and 42% to 26% for DPI data. These results suggest that the saccade-prediction algorithm may help create more accurate gaze-contingent displays.

Unconscious priming by illusory figures: the role of the salient region

In this study we provide evidence that unconscious priming can be obtained as a result of the processing of the salient region (SR) of illusory figures and without that of illusory contours (ICs). We used a metacontrast masking paradigm where illusory figures were masked by real figures. In Experiment 1 we found a clear priming effect when participants were asked to discriminate between square and diamond masks preceded by congruent or incongruent illusory square or diamond primes. It is likely that metacontrast impairs the processing of ICs but not of the SR; therefore the above result strongly suggests that the priming effect was specifically related to the processing of the SR. In Experiment 2 participants were tested in the same task as in Experiment 1 with additional primes in which the inducers were presented in the same locations but their shapes were changed so as to modify the global configuration. We termed these primes High, Low, and No Salient Region (HSR, LSR, and NSR, respectively). The HSR condition replicated Experiment 1, whereas in the LSR and NSR conditions the priming effect got progressively smaller. The results of Experiment 1 were replicated with the priming effect significantly larger in the HSR than in all other conditions. It was also larger in the HSR than in LSR condition and smallest but still present in the NSR condition. Taken together, these results indicate that the unconscious processing of only the SR yields a priming effect and that a reduction of the saliency of the SR leads to a reduction of the priming effect, while its elimination does not abolish it.

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.

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

The characteristics of a muscle model are analyzed using rectus eye muscle parameter values and compared to rectus eye muscle data. The muscle is modeled as a viscoelastic parallel combination connected to a parallel combination of active state tension generator, viscosity element, and length tension elastic element. Each of the elements is linear and their existence is supported with physiological evidence. The static and dynamic properties of the muscle model are compared to rectus eye muscle data. The length-tension characteristics of the model are in good agreement with the data within the operating region of the muscle. With the muscle model incorporated into a lever system to match the isotonic experiment paradigm, simulation results for this linear system yield a nonlinear force-velocity curve. Moreover, the family of force-velocity curves generated with different stimulus rates reported in the literature match the predictions of the model without parametric changes. The results of this paper are important in studies involving the oculomotor plant and oculomotor neural networks. Additionally, these results may be applicable to other muscles.

Frequency response analysis of human saccadic eye movements: estimation of stochastic muscle forces

A frequency response method is used to estimate parameters of a fourth-order model of the oculomotor system and the active state tensions during a saccadic eye movement. The lateral and medial rectus muscle of each eye is modeled as a parallel combination of an active state tension generator with a viscosity and elastic element, connected to a series elastic element. The eyeball is modeled as a sphere connected to a viscosity and elastic element. Each of these elements is assumed to be ideal and linear. The active state tension for each muscle is modeled by a low-pass filtered pulse-step waveform. Initial estimates of the oculomotor mechanical components are based on physiological evidence. Initial estimates of the active state tension are based on an extrapolation of the eye movement trajectory. Horizontal saccadic eye movements were recorded from infrared signals reflected from the anterior surface of the cornea and then digitized. Parameter estimates were calculated for the model by using a conjugate gradient search program which minimizes the integral of the absolute value of the squared error between the model and the data. The predictions of the model are shown to be in good agreement with the data. Final estimates of motoneuronal activity demonstrate that the agonist muscle is maximally stimulated during the early portion of a saccadic eye movement regardless of the amplitude of the saccade; only the duration of the maximal stimulation affects the size of the saccade. The antagonist muscle is completely inhibited during the period of maximum agonist muscle stimulation. Furthermore, it is demonstrated that saccade motoneuronal activity is a stochastic phenomenon.

Dependence of jumping performance on muscle properties when humans use only calf muscles for propulsion

Using optimal control techniques, maximum height jumps were simulated for humans who held their body rigid except for the ankle. Three dynamic models of ankle torque generation based on known calf muscle properties were used. Force and kinematics obtained from the simulations using nominal and perturbed parameters were compared with data obtained from humans who had performed this type of jump. One torque model incorporated the series elastic, force-length and force-velocity properties of muscle. Our results suggest that higher jumps would be achieved by those who have the most compliant and fastest contracting muscles. It was also found that height attained depended much more on the ability of muscles to generate isometric force at long lengths than at short lengths. Studies of forward and strictly vertical jumps using similar computer methods suggest that for any maximal jump the optimal strategy is first to achieve a unique state (position, velocity and acceleration) with the feet flat on the ground, and then to maximally activate one's calf muscles until lift-off.

Model emulates human smooth pursuit system producing zero-latency target tracking

Humans can overcome the 150 ms time delay of the smooth pursuit eye movement system and track smoothly moving visual targets with zero-latency. Our target-selective adaptive control model can also overcome an inherent time delay and produce zero-latency tracking. No other model or man-made system can do this. Our model is physically realizable and physiologically realistic. The technique used in our model should be useful for analyzing other time-delay systems, such as man-machine systems and robots.