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Lecture 1 1) Introduction to Control Systems 2) Circuitry of Pathway 3) Models Why Study Eye Movements? - No joints in system - Constant inertia (negligible) Saccadic Eye Movements http://web.mit.edu/bcs/schillerlab/pictures/WEB001/GIFs/001-01.gif http://www.optidigit.com/stevens/tutorial/Yarbus.jpg The Premotor Control of Saccades 1.) Cortex 2.) Superior Colliculus 3.) Brainstem Another view Extraocular Muscles 6 muscles per eye 4 recti muscles - lateral/medial - superior/inferior 2 oblique muscles - superior/inferior 6 Muscles → provide 3D of freedom 1. Horizontal (focus of most research) 2. Vertical 3. Torsional Extraocular Muscles 1.) Extraocular muscles consist of 2 distinct layers: a) A global layer with three types of singularly innervated (SI) fibers, and one type of multiply innervated (MI) fiber, and 2) an orbital layer with only 1 type of each (SI and MI). b) Fibers in each layer have different response properties (e.g. fatigability or fusion frequency (contraction time)). c) MRI studies at UCLA (2000) have found sleeves of collagen surrounded by smooth muscle tissue termed “muscle pulleys”. The Global layer runs through the sleeve of the pulley, while the orbital layer appears to insert on the pulley. The function of these pulleys is not yet known: Hypotheses: Linearization of system response and implementation of Listings Law (3D eye motion). Extraocular Muscles 2.) It is not clear that Henneman’s Size Principle holds for extraocular motoneurons: Namely that motoneurons are recruited in an orderly manner according to their cell body size; small neurons have the lowest threshold for synaptic activation and are recruited by the weakest afferent input. 3.) All motoneurons participate in all types of eye movements, fixation, smooth pursuit, saccades, the vestibulo-ocular reflex and optokinetic reflex. The Use of Control Systems for Understanding Eye Movements A system is represented as: Where x(t) is the input, and y(t) is the output. These are signals that very as a function of time. 1) The goal of an engineer, is to design S, so that x results in y. 2) The Neurobiologist already has S, and controls x, observes y Then tries to guess what S is. The VOR as an example: Where: H(t) is head velocity: here a step of velocity and Ė (t) is slow-phase eye velocity (note H(t) and Ė (t) are short hand for dH/dt, dE/dt) So in this case the problem, is to find S, for the VOR Mechanical System analysis: How do you move your eye? Consider some examples of mechanics to relate force to eye movement: 1) Apply a force F to a spring of stiffness K, stretch it to length L. Hooks Law says: F = kL Mechanical System analysis: 2) Apply a force F to a system characterized by a pure viscosity (of coefficient r). A good example is a hypodermic syringe. If you push at a constant force, the plunger moves at a constant velocity dL/dt, such that: F = r dL/dt Mechanical System analysis: 3) Put these 2 elements in series (this is a simplified muscle model): This is called a visco-elasticity. The force is shared by the elasticity (kL) and the viscosity (r dL/dt) so: F = kL + r dL/dt This is a first order differential equation and if our “system” was a visco-elasticity, solving this equation for a given input should produce the observed output. Mechanical System analysis: 4) Now add a mass to the system: From Newton’s law of motion F = m d2L/dt2, where d2L/dt2 is acceleration The system is now described by: F = kL + r dL/dt + m d2L/dt2 Mechanics of Saccadic Eye Movements The oculomotor plant: Plant: devise which produces the final output Oculomotor System: The 1) eye muscles, 2) orbital tissues, 3) globe What is the output? What is the input? Muscle tension, but hard to measure. We can measure motoneuron drive to muscles Eye Movements: Motoneurons 3 Motor Nuclei drive the extraocular muscles For Horizontal Eye Movements: VI = Abducens III = Oculomotor nucleus Description of MN discharge rate Consider 3 experiments: Experiment 1: Monkey looks straight ahead so that: dE/dt = 0, and E = 0 Finding: Neuron fires at a constant rate Fr = Ro Where: (eq 1) Fr → firing rate Ro → is a constant (resting rate) = ~100 spikes/sec Description of MN discharge rate Experiment 2: Monkey fixates (dE/dt = 0) at many angles E. Finding: Fr = Ro + kE (eq 2) Where: k → 5 spike/s Description of MN discharge rate Experiment 3: Monkey makes smooth pursuit movements through zero (E = 0) at many velocities dE/dt. Finding: Fr = Ro + rdE/dt Where: r → 1 (spike/s)/(deg/s) (eq 3) Description of MN discharge rate Description of MN Fr = Ro Fr = Ro + kE Fr = Ro + rĖ Fr = Ro + kE + rĖ All together: Fr-Ro = kE + rĖ ∆Fr = kE + rĖ (eq 1) (eq 2) (eq 3) (eq 4.) Eq 4 provides a good description of MN activity during eye movements, and so the system can be approximated by a first order differential equation and the “system” is described as visco-elasticic. Test of the model Another Experiment: Different approach (Robinson 1964) Put a suction contact lens on the eye 1) attach to a rod, which restrains the eye, 2) Cover the eye, and 3) Have subject fixate at different positions with other Finding: F = a + bE Test of the model Yet another Experiment: Put a suction contact lens on the eye 1) Tie a thread to it, 2) Cover the eye, and 3) Have subject fixate straight ahead (∆Fr = 0) with the other THEN: Pull the covered eye to one side and let go Finding: F = a + bE + cĖ c/b = ~ 200 ms Test of the model Yet one last Experiment: Put a suction contact lens on the eye 1) Attach a ball and socket joint to it, 2) and attach to a little cart on a friction-less sled 3) eye now has 100X normal inertia THEN: Then ask subject to make saccades Finding: Eye still lands in right place, so: - system is not affected by the mass of eye – inertia is not important Description of MN discharge rate Recall: 1) Fr = Ro + KE + rĖ ↓ 2) Fr – Ro = KE + rĖ if τe = r/k E(t) = R(1- e –t/τe) E(t) = R(1- e –1) if t = τe = R(1 – 1/e) = R(1 –1/2.7) = R x .37 If : r =1, K =5, then τe = 250 ms.. Eye Dynamics with a step command of FR would be too slow. Saccades can be on target in less than 100ms. Recall: : Mechanical System analysis: We put 2 elements in series (this is a simplified muscle model): This is called a visco-elasticity. The force is shared by the elasticity (kL) and the viscosity (r dL/dt) so: F = kL + r dL/dt This is a first order differential equation and if our “system” was a visco-elasticity, solving this equation for a given input should produce the observed output. How Do Motoneurons Drive Eye Movement? Fr = Ro + KE + rĖ SO: to make a saccade a step change in discharge would not work. What signal do the ocular motoneurons send to the extraocular muscles to generate saccades? Analysis of Motoneuron Signals 3) So what is the MN command to drive saccades? Pulse: Need an extra “burst” (pulse) in MN command signal in order to complete saccade in a shorter time. Note, The pulse resembles velocity + The step resembles position Linearity and Superposition: The MN equation took the results from 3 experiments, and added them together. Assumption: The system is linear. If we put in 2 signals, the output is the same as as the sum of the response of each alone. Analysis of Motoneuron Signals 3) So what is the MN command to drive saccades? Where do pulse and step come from? Hypothesis: A neural network integrates the pulse to create the step. Sensory endings in extraocular fibers Two types of mechanoreceptors are found in extraocular muscles Muscle Spindles (stretch) and Golgi tendon organs (tension). Early studies at the turn of the century led Sherrington to suggest that the muscle spindles in these muscles mediated a stretch reflex similar to that which he observed in skeletal muscles. Briefly, the stretch reflex is evoked by stimulation of the muscle spindles; passively stretching a muscle causes that muscle and its synergists to contract, and its antagonists to relax, in effect opposing the stretching force. However, experiments in alert animals demonstrated that there is no stretch reflex in the extraocular muscles. So what do the proprioceptors do? Experiments in which a lesion was made in this pathway by cutting the opthalmic nerve have demonstrated that during vergence eye movements, the non-dominant eye tends to drift medially. Recording from a neuron in the left abducens nucleus: A: The left eye is held relatively fixed by the experimenter. B: A normal conjugate saccade of the same amplitude intended in A. Step Command and the Neural Integrator • The “integrator” is not perfect: it is “leaky”. In the dark, the human eye drifts from attempted eccentric positions with a time constant of 25s. → This is generally not a problem • Model of the oculomotor neural integrator: Most utilize a system of reverberating collaterals. Motoneuron Discharges Step The “pulse” command drives the saccade but still needs a “step” to hold the eye in its new position. Proposal: Neural Integration (mathematical) of pulse command produces step. Evidence: Lesions of the nucleus prepositus and medial vestibular nuclei cause problems with “gaze holding”. Lecture II Physiological and Theoretical Models of Saccade Generation Lateral rectus Basic Anatomical Circuit: Horizontal Eye Movements Abducens nerve Excitatory burst neuron Motor neuron Nucleus Prepositus hypoglossi Inhibitory burst neuron Basic Circuit: Horizontal Eye Movements The Premotor Control of Eye Movements 1.) Cortex 2.) Superior Colliculus 3.) Brainstem Robinson model SSaccades are very accurate: Feedback Model to explain MModel structure - Local feedback (E*) used to bring eyes accurately on target − NOTE: feed-back is not visual. Latencies of visual pathways are too long (a minimum of 100ms). MMain Features of Model • • • • - Burst of activity from BN’s drives the saccade. - Burst from BN’s is integrates by NI to hold eyes at new position. - Internal estimate of eye position (E*) is fed back for comparison with desired eye position (Ed). Ed – E* = em → when em=0, no drive to BN’s → end. Main limitation of this model Ed is in head centered coordinates, Superior colliculus (SC) is in not, it is in eye centered (retinocentric) coordinates. → Neurophysiological studies had demonstrated that the SC saccade cells discharge the same for a saccade at a given amplitude and direction, regardless of initial eye position. Superior Colliculus 1) Superficial Layers: Visual Responses, Discharge after appearance of a target to limited part of the visual field. 2) Intermediate Layers: Saccade related burst neurons, Discharge prior to saccadic eye movements Superior Colliculus: Motor Map A) Stimulation studies: Features of Motor Map: Iso-amplitude line: medial/lateral Iso-direction lines: rostral/caudal Saccade vector is independent of initial eye position. Coordinated Eye-Head Gaze Shifts Stimulation of Superior Colliculus at 2 Different Caudal Sites 1) A caudal site 2) A more caudal site Freedman, Stanford, and Sparks, 1996 Superior Colliculus: Intermediate Layers A) Cartoon Neurons active before a large (40 deg) saccade B) Size of active zone Top: Analysis of movement fields of 4 cells for which the optimal amplitude was 2, 5, 9 and 16 deg. Amplitude converted: deg to mm. Bottom: Same curves but normalized and aligned. Size of active population is the same for all amplitude saccades. Jurgen’s Model for Saccade Generation Main features of model - To account for SC neurophysiology; the model input is the desired change in eye position (∆Ed), not absolute eye positioning space. - A second integrator is added which feedbacks an internal estimate ∆E* rather than E* - ∆Ed - ∆E* = eµ → when eµ = 0, no drive to BN ∴ end of saccade. Superior Colliculus: Saccade-Related Burst Neurons - Projects to PPRF (brainstem BN’s) There is ambiguity in encoding direction (deg) vs amplitude (deg) Example: For a single neuron: saccades F & 6 produce the same discharge. Motor Map of Intermediate Layers of SC Observation Neurons in the SC burst for saccades of a certain direction and amplitude. QQuestion What is discharge of neurons in the SC related to: • The appearance of a target at a particular location on the retinal map? OR T The generation of a saccadic eye movement of a • particular amplitude? Superior Colliculus: Sensory or Motor Response Animal initially fixates a target (O) in all paradigms. B, C : Single saccades trials: Target O to target A – neurons fires (but not for O to B). D: Double-step saccade trial: Target O to target B back to target O – before the B-O saccade (which is of same amplitude as the O-A). Jurgen’s Model for Saccade Generation Main features of model - To account for SC neurophysiology; the model input is the desired change in eye position (∆Ed), not absolute eye positioning space. - A second integrator is added which feedbacks an internal estimate ∆E* rather than E* - ∆Ed - ∆E* = eµ → when eµ = 0, no drive to BN ∴ end of saccade. The Moving Mountain Hypothesis The models of Robinson and Jurgens employ an error signal (em) to drive the burst neurons. 1) Most recent models of saccade generation create the error signal in the brainstem within the PPRF. 2) However, it has also been recently argued that the output of the superior colliculus in an error signal. So the question arises: Is the superior colliculus in the feedback loop? Activity of: 10 burst cells (left) and 10 buildup cells (right) during a 50 deg horizontal saccade. Spatial Distribution of : burst cell (left) and buildup cell (right) activity prior to a 50 deg horizontal saccade. Spatial Distribution of : burst cell (left) and buildup cell (right) activity during a 50 deg horizontal saccade. A Neurophysiological Model for Saccades Test of Model? Test: Moving Mountain Hypothesis A.) Experimental Logic: Injection of muscimol at a rostral location should influence trajectory, but not amplitude of large saccade. B.) Experimental Results: Trajectories and amplitude of 10 deg saccades are affected. Only trajectories of 20 deg saccades are affected. Test: Fixation Zone Hypothesis A.) Experimental Logic: Bilateral stimulation in rostral zone should increase neuron activity, which in turn will inhibit Burst and Buildup cells, so saccades can not be made. B.) Experimental Results: During rostral zone stimulation, monkeys are unable to make saccades to visual targets, until the stimulation is turned off. Fixation Zone: Neurons Encode Gaze Error A.) Experimental Logic: Record from neurons in cats during multiple step gaze shifts B.) Experimental Results: Linear relationship between GPE and FR at end of plateau Bergeron and Guitton, 2000 The Premotor Control of Eye Movements 1.) Cortex 2.) Superior Colliculus 3.) Brainstem