--- title: Assignment: The Nonlinear Saccade model --- # Assignment: The Nonlinear Saccade model ```{objectives} - Converted from LaTeX to MyST (first pass) - Please verify equations, figures, and references ``` ## Exercises \begin{exercise}[amplitude] First, run the Saccade model with its default parameter set (these are already set, see Table {ref}`tab:saccademdl`). Then change the saccade amplitude by changing the value of the Synaptic Gain block to 1.0 (the Synaptic Gain the connection strength of a particular SC site to the saccade generator). [label=**\alph***] - How is saccade amplitude related to the Synaptic Gain? - How would you obtain saccade amplitudes of 1, 5, 10, 20, and 30 deg? \end{exercise} \begin{exercise}[Main Sequence] In this exercise, you will see how the **main sequence** is affected by the Burst Generator. First, ensure that the parameters of the Pulse-Step generator part of the model (Neural Integrator, Direct path, and Oculomotor Plant), the Burst Generator, and the Superior Colliculus (SC), are chosen at their default values (see Table {ref}`tab:saccademdl`). Tip: To obtain the main sequence, you can obtain the amplitude, peak velocity and duration of each saccade by reading out the Scope displays using the Cursors (rulers). Saccade duration may be taken as the time interval where eye velocity exceeds about 10\% of its peak velocity. Make tables (on paper or on spreadsheet) where you indicate the parameters used, and note saccade amplitude, peak velocity and duration. Make a graph of (\mcode{plot}) the main sequences in your report (label clearly, use correct units, indicate the different parameter settings that were used). Example Matlab code: \begin{lstlisting} A = [0 10 20 30]; Vpeak = [0 100 200 300]; D = [100 100 100 100]; figure(1); clf; subplot(2,1,1); plot(A,D,'ko'); subplot(2,1,2); plot(A,Vpeak,'ko'); \end{lstlisting} [label=**\alph***)] - Obtain the main sequence of normal saccades (see e.g. Fig. {ref}`fig:mapfig0`). Generate saccades with different saccade amplitudes (1, 5, 10, 20, and 30 deg; see exercise {ref}`exc:saccademdlamplitude`). - Then, vary the saturation level (Bmax) of the Burst Generator (to 1400 and 7000 deg/s). Determine the main sequence again. - Then, vary the angular constant (A0) of the Burst Generator (to 3 and 140 deg). Determine the main sequence again. - How does the Burst Generator (changes in parameters) affect the behavior of the main sequence? \end{exercise} \begin{table}[ht] \begin{tabular}{l l l l l l} \toprule **Stage** & **Symbol** & **Meaning** & **Range** & **Default** & **Unit** \\ \midrule SC & FR & firing rate, burst height & [0 - 1000] & 800 & Hz \\ & D & burst duration & [0 - 0.20] & 50 & ms \\ Synaptic Gain & R & SC-BS connection strength & [0.1 - 1.5] & 0.5 & - \\ Burst Generator & Bmax & Pulse height max & [0 - 1000] & 700 & deg/s \\ & A0 & Angular constant & [1 - 100] & 7 & deg/s \\ OPNs & Bias & fixation OPN firing rate & [50-500] & 80 & Hz \\ & Delay & Trigger moment from SC & [0-50] & 15 & ms \\ & SC Gain & Attenuates SC burst & [0-1] & 0.2 & - \\ Feedback Path & Gain (K) & Feedback Gain & [0 - 5] & 1.0 & - \\ \midrule Neural Integrator & G & Gain & [0 - 1.0] & 1.0 & - \\ Direct Path & Gain (K) & Forward Gain & [0 - 0.5] & 0.15 & - \\ Oculomotor Plant & T1 & Long Time Constant & [0.05 - 0.30] & 0.15 & s \\ & T2 & Short Time Constant & [0 - 0.03] & 0.020 & s \\ \bottomrule \end{tabular} \caption{Paremeters of the Simulink saccade model. SC = superior colliculus, OPNs = OmniPause Neurons, BS = brainstem} \end{table} \begin{exercise}[Linearity] Try to obtain a **main sequence** of saccades after 'linearizing' the model. How would you do that? Verify the result, by making a main sequence graph, and compare this with your own expectations expressed in Question 1 (see 'Dutch' Syllabus). \end{exercise} \begin{exercise}[Influence of the feedback gain] Start with the default parameters, and concentrate on 20 deg amplitude saccades produced by the default settings. Vary the gain in the feedback loop between 0.5, 1.0, and 2.0. Plot the eye position and velocity traces. Try to explain the resulting effects. \end{exercise} \begin{exercise}[OPN] Keep the amplitude of the saccade fixed at 20 deg. Now only change the timing of the OPNs, by changing the delay of the SC-trigger burst (10, 15, 25, 50, 75 ms). Describe the effect on the LLBN burst of these changes , and on the kinematics of the resulting saccades. Explain your observations (hint: look under the LLBN mask, and determine when feedback kicks in). \end{exercise} \begin{exercise}[Superior Colliculus] Keep the amplitude of the saccade fixed at 20 deg. Now only change the parameters of the SC burst (everything else being default). First ensure, however, that the total number of spikes in the burst (i.e. the integral of the pulse: width $x$ height) remains fixed. Describe the effects on the saccades, and explain (Hint: what does the burst represent? How many spikes does it contain? ). Subsequently, drop the demand on the number of spikes and explain the effect of either a change in burst intensity and/or a change in burst duration. \end{exercise} \begin{exercise}[Valium] Fig. {ref}`fig:diazepam` shows the effect of 7 mg Valium on human saccades. Try to explain the (average) experimental results with the Saccade model, if we assume that benzodiazepines have no effect on the mechanical properties of the plant, but only affect the CNS. Support your explanation with simulations. \end{exercise} ```{figure} images/diazepam.png :name: fig:diazepam Effect of an intravenous injection of Diazepam (Valium) on human saccades toward flashed targets: although the Valium saccades (right) are still quite accurate, their kinematics are much more variable and slower than normal responses (left). Note also the differences in the reconstructed Pulse-Step signals (bottom). (After: Van Opstal et al., Vision Res., 1985) ```