There are five different types of eye movements: saccades, smooth pursuit, vestibular ocular eye movements, optokinetic eye movements, and vergence eye movements. The purpose of this book series is focused primarily on mathematical models of the horizontal saccadic eye movement system and the smooth pursuit system, rather than on how visual information is processed. In Part 1, early models of saccades and smooth pursuit are presented. A number of oculomotor plant models are described here beginning with the Westheimer model published in 1954, and up through our 1995 model involving a 4th order oculomotor plant model. In Part 2, a 2009 version of a state-of-the-art model is presented for horizontal saccades that is 3rd-order and linear, and controlled by a physiologically based time-optimal neural network. Part 3 describes a model of the saccade system, focusing on the neural network. It presents a neural network model of biophysical neurons in the midbrain for controlling oculomotor muscles during horizontal human saccades. In this book, a multiscale model of the saccade system is presented, focusing on a multiscale neural network and muscle fiber model. Chapter 1 presents a comprehensive model for the control of horizontal saccades using a 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. Chapter 2 presents a biophysically realistic neural network model in the midbrain to drive a muscle fiber oculomotor plant during horizontal monkey saccades. Neural circuitry, including omnipause neuron, premotor excitatory and inhibitory burst neurons, long lead burst neuron, tonic neuron, interneuron, abducens nucleus, and oculomotor nucleus, is developed to examine saccade dynamics. The time-optimal control mechanism demonstrates how the neural commands are encoded in the downstream saccadic pathway by realization of agonist and antagonist controller models. Consequently, each agonist muscle fiber is stimulated by an agonist neuron, while an antagonist muscle fiber is unstimulated by a pause and step from the antagonist neuron. It is concluded that the neural network is constrained by a minimum duration of the agonist pulse, and that the most dominant factor in determining the saccade magnitude is the number of active neurons for the small saccades. For the large saccades, however, the duration of agonist burst firing significantly affects the control of saccades. The proposed saccadic circuitry establishes a complete model of saccade generation since it not only includes the neural circuits at both the premotor and motor stages of the saccade generator, but it also uses a time-optimal controller to yield the desired saccade magnitude. Table of Contents: Acknowledgments / A New Linear Muscle Fiber Model for Neural Control of Saccades\footnotemark / A Physiological Neural Controller of a Muscle Fiber Oculomotor Plant in Horizontal Monkey Saccades\footnotemark / References / Authors' Biographies

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Alireza Ghahari received his B.Sc. degree in electrical engineering from the Sharif University of Technology, Iran, in August 2007. Thereafter, he completed his M.Sc. in electrical and computer engineering at the University of Tehran, Iran, in March 2010. During those years of study, he gained valuable insights into systems engineering by taking courses in a variety of contexts, such as statistical signal processing, information theory and coding, computer vision, and pattern recognition. He started his Ph.D. in the ECE department at University of Connecticut in Fall 2010. His dissertation major advisor was Prof. John Enderle. He has come to realize the profound contributions of Prof. Enderle in the field of theoretical and computational neuroscience,and truly considers John to be a major influence, both academically and personally. His research areas of interest include spiking neural networks analysis and implementation, brain-computer interface, and development of computational techniques. John D. Enderle, Biomedical Engineering Program Director and Professor of Electrical & Computer Engineering at the University of Connecticut, received the B.S., M.E., and Ph.D. degrees in biomedical engineering, and M.E. degree in electrical engineering from Rensselaer Polytechnic Institute, Troy, New York, in 1975, 1977, 1980, and 1978, respectively. After completing his Ph.D. studies, he was a senior staff member at PAR Technology Corporation, Rome, New York, from 1979 to 1981. From 1981-1994, Enderle was a faculty member in the Department of Electrical Engineering and Coordinator for Biomedical Engineering at North Dakota State University (NDSU), Fargo, North Dakota. Dr. Enderle joined the National Science Foundation as Program Director for Biomedical Engineering & Research Aiding Persons with Disabilities Program from January 1994-June 1995. In January 1995, he joined the faculty of the University of Connecticut (UConn) as Professor and Head of the Electrical & Systems Engineering Department. In June 1997, he became the Director for the Biomedical Engineering Program at UConn. Dr. Enderle is a Fellow of the Institute of Electrical & Electronics Engineers (IEEE), the current Editor-in-Chief of the EMB Magazine, the 2004 EMBS Service Award Recipient, Past-President of the IEEE-Engineering in Medicine and Biology Society (EMBS), EMBS Conference Chair for the 22nd Annual International Conference of the IEEE EMBS and World Congress on Medical Physics and Biomedical Engineering in 2000, a past EMBS Vice-President for Publications & Technical Activities and Vice-President for Member and Student Activities, Fellow of the American Institute for Medical and Biological Engineering (AIMBE), an ABET Program Evaluator for Bioengineering Programs, a member of the Engineering Accreditation Commission, a member of the American Society for Engineering Education and Biomedical Engineering Division Chair for 2005, and a Senior member of the Biomedical Engineering Society. Enderle was elected as a Member of the Connecticut Academy of Science and Engineering in 2003, with membership limited to 200 persons. He is also a Teaching Fellow at the University of Connecticut since 1998.