 This is our last day of lectures and this course is ostensibly about using mathematics, estimation theory, and optimal control to think about how the brain works. And we've done a little bit of that but I thought that at the end we should have an example of how the material can come together for you. So rather than talking about classification, which was scheduled today, I wanted to end with a different story. Pavan Raswani is a graduate student in my lab who took this course two years ago. Yeah, when you're a graduate student, time seems like forever ago when you did anything. Anyway, Pavan has some very preliminary data but I think you're a beautiful example of how to understand behavior using things that we've been talking about. It's like the concepts in optimal control, the notions of Bellman equation and the thought that behavior can be understood if one looks at details and thinking about it mathematically in terms of what is optimization. So what's special about the work that you're going to see is that Pavan is an MD-PhG student so he's interested in clinical applications of this. And I think he's understood something interesting about a particular disease that we would not have been able to understand without the mathematics. So that's what we're going to end the class on, a lecture on how to use some of the stuff that you've learned to understand something about the break. So here's Pavan. Okay, hello everyone. As Raza said, my name is Pavan Raswani. I'm a grad student in Reza's lab and today I'm going to be talking to you about optimal control of saccades in patients with ataxia telangiectasia. And there will be a quiz on how to pronounce that at the end of the lecture, so you rest. No, so I'm going to tell you guys a little bit about this patient group that I've been working with for the last year or so, patients with this disease called ataxia telangiectasia. And then we're going to talk a little bit about their eye movements, their saccades, and the story is kind of thinking about why they make the saccades that they do. So think about that as we go along. And it turns out that we think that perhaps they're actually using some ideas from optimal control and some of the kind of homework and lecture ideas that you've had recently. To make the saccades that they make. So that's a little bit of what we're going to be talking about. This is not math, but I think it's important to understand the patients that we're talking about, the disease that we're talking about, because it kind of informs the point of this work. So ataxia telangiectasia, if we break that down, ataxia means kind of discordination of movement. And telangiectasias are these red kind of spider vein things. They're a dermatologic issue. And so these kids have ataxia, they have telangiectasias, and they have a bunch of other things going on that I'll talk about in a second. But essentially it's an autosomal recessive and for our purposes neurodegenerative disorder. They have a single gene mutation in a gene called ATM, mutated in ataxia telangiectasia, a very creative name. And then gene is involved in the cellular stress response and in DNA repair, double-stranded break repair. It does a lot of things in the cell, so it's not exactly clear which of its mechanisms causes the problems that we see. But nonetheless these kids have a lot of medical problems. And it happens to be the most common progressive cerebellar ataxia, pretending before five years old in the U.S. And it was described in the early 20s and then later in the 40s. So there's been a few families that have it, but it's a pretty rare disease. So in the United States there's maybe five or 600 children that'll have this disease. Hopkins happens to be one of the, it might be the center in the United States that sees them. And there's a few others in the world. So it's kind of also a unique place to get a chance to work with these guys, guys and gals. So a little bit more about the disease. So on MRI and clinically you see a progressive cerebellar degeneration. So their cerebellums get small. You can see on this figure on the right that you can see the gaps between the folia of the cerebellum in a 14-year-old boy. So they have a loss of cerebellar kind of volume. They also have this ataxia that I mentioned. They have oculocutaneous telangiectasia. So they have these bright red spider veins on their eyes and on their skin. They have oculomotorapraxia, which is what we're going to talk about a little more. They also have these coriatic movements. They have immune problems. They're sensitive to radiation. So they have a lot of other things going on. Neurological phenotype is that they have ataxia, kind of a discordination of their movements. And they have oculomotorapraxia, which is you'll see the exact phenotype, but they kind of make the wrong eye movements, it seems like. So that's all the introduction I was going to give about the disease. If anyone has any other questions, I'm happy to answer them. This particular experiment we were looking at saccades in children. And so it's a very simple experiment. So I'm going to give you kind of just a very brief overview. Basically what we would have children, both healthy children and patients do, is sit in front of this fancy high-tech camera. They would be looking at a computer screen and I would present them with a target, a red dot. And then the target would jump to the other side. They would have to look at the other dot. It would jump back. They would have to go look at the first one. Very simple, very straightforward. And the camera would use as an IR kind of IR LED and an image to calculate the position of the gaze by tracking the pupil and the reflection of the cornea. So it's fairly straightforward to use a camera. It's pretty non-invasive. The kids will tolerate it. And it's a pretty simple task. So I looked at the website and so it looks like yesterday for homework you guys actually thought about saccades and how people make the saccades that they do. And you guys went through the calculations for making a saccade with signal-dependent noise and you should have come out with the results that if you have signal-dependent noise the expectation is that when you make a saccade to a target that's pretty far away you should fall a little short. So this is kind of a nice example of data and healthy people. That's in fact what people do. So what I'm plotting here is a healthy 14-year-old boy. On X is time. On Y is the gaze, where he happens to be looking in degrees. The black line shows where the target is. You can see that the target jumps 15 degrees to the left. Then it jumps 15 degrees to the right. 15 degrees to the left, fairly straightforward as I pointed out earlier. And what you see is that for the most part he gets most of the way there when asked to make a saccade to the target. So sometimes he falls a little short and makes a secondary saccade. Sometimes he gets all the way there. But for the most part as you guys should have come out with your homework yesterday people kind of go 95 plus a percent of the way there when they're making a large saccade. And that's also what we see in children. I'm just going to point out that occasionally you see something like this where he jumps maybe two-thirds of the way and then tries to go the rest of the way. But that's relatively rare in healthy people. It's extremely rare in healthy people. You see it occasionally. To summarize these data, the reason I'm doing this plot is because I'm going to highlight the differences between the healthy children and the patients. What I'm going to do is I'm going to basically plot across all the healthy children that I had come in and do the experiment where they're making their saccade to. So to start off with on the right, on the right you see an example of, for example, a single trial which you might expect. And in purple I'm showing that they start off near the start position which is in the dashed line. And they're trying to go to the target which is in the solid line. And it's kind of this summary plot of everyone you see that the dashed line is where they're supposed to be starting. The solid line is supposed to be ending. And they're basically making saccades to a target from positive 20 degrees to negative 20 degrees in this case. And then from negative 20 degrees to positive 20 degrees in the case on the right. And so to start off with in purple you see that this is partially by selection. I make sure that I select trials where they didn't kind of go too early. They didn't anticipate where the target was going to be. So I kind of enforce that they start near the start position. And then we can see where they land after they make their first saccade. So just a little schematic and the colors aren't super clear but that's supposed to be blue. So in the first saccade they tend to land. Most of the way they're on average they fall a little short for the larger saccades. And it seems to be like you probably, you should have come out with in your homework last night or whenever the last homework was. That it's kind of a scaling of the target position. It's just a gain on the distance to the target. So that's about what we see. And then if you ask the men, in some cases they'll make a second saccade, the endpoint of the second saccade as you can see in the schematic on the right is plotted in washed out green. And that's the endpoint of the second saccade. You see they get closer, pretty close to the target by the second saccade. So this is healthy kids' behavior. It kind of comes out nicely with the math that you did last night or whenever. And it's by contrast I'll show you what the patients do. So patients on the other hand here's two example patients. This boy is seven and this young man is 25. So we'll just look at the boy on the left. You see that he is able to get to the target but he seems to do it with multiple steps. So he jumps, jumps, jumps, jumps, jumps, jumps, jumps, jumps. So rather than making one, maybe two saccades in order to achieve the target, you see that these kids tend to go maybe halfway or so, maybe a little more than that and then a little further and then eventually reach the target. So they make what I'm going to call a series of saccades in order to achieve the target instead of basically going most the way there in one step. For those of you who are eye movement aficionados, you can see that this one person happens to have a misdagnus that the eye slides in towards the center and then jumps out. So if anyone notices that, that's what that is. That's why he's not holding the gaze perfectly. And we can summarize these data in the same way that I did for the healthy kids. So we're going to start off by showing that they start off in purple again by kind of construction or this is enforced near the start position, near the starting target. Then the target will jump and they'll make their first saccade. And you see as opposed to making their first saccade, 75% of the way there, 90% of the way there, they seem to only get maybe halfway after the first jump. Then they make a second jump as you can see on the right in green and they get a little further. In third saccade they get closer still and by the fourth, third or fourth saccade they're pretty much smack dab on the target that they're supposed to be getting to. This is a little strange. It's kind of odd that you see these kids, instead of going from left to right, you're left to your right, they kind of go halfway, pause a little further, pause and a little further. And this is actually one of the patients. You can see that they pause for a fair bit of time and I'll talk a little bit more about that later that happens to be important. So any questions about this so far? The general kind of, the patients that I'm working with, the general observation which is this idea that you might want to make a series of saccades to get to the target. We're going to try to tease that apart a little bit. Any questions? Good. So the first kind of set of questions we're going to ask is whether the saccades are normal. If there's just something messed up about the way they make their eye movements. So prior work has hypothesized that maybe they're trying to get to the target. They're trying to shoot all the way there and then something gets messed up. There's maybe the burst generators in the brainstem are getting somehow suppressed in the middle of the flight of the eye and the saccades are somehow aborted or altered in flight. And so if that were the case, it's a very reasonable hypothesis, if that were the case there's a few things we might expect in the saccade dynamics. So if we look at the profile of the saccade we might expect that it basically terminates in some way, that we can see this termination and somehow altered. And at least initially we should see that saccades shouldn't look like they're going where they actually go, more to the target, because the hypothesis would be that they're somehow getting aborted and kind of shut off in the middle. So they should look at least initially like they're trying to go far and then they fall short. And so basically the saccades may be appropriate in some way for the target distance as opposed to the actual distance they go. So we're going to basically look at some of the saccade dynamics and see if this is the case. As a bit of a hint it turns out it looks like the saccades are normal so it looks like this is not the case. Here's an example of a control young man on the left and a patient on the right. What I've plotted is in time on x, this is in seconds, so the duration of these saccades are 60-70 milliseconds or so for the longest ones. And I'm plotting the velocity in x which is in degrees per second on the y-axis. And they're all aligned to the onset of saccades and I'm basically taking for example in this blue trace all of the 5-ish 5-1 or 5-2 degree saccades and I'm taking the velocity profile in time and I'm averaging them all together and showing you what a typical 5-degree saccade looks like for this healthy young man and then similarly what a typical 5-degree saccade looks like for this patient with AT. And so what you see is and so I'm plotting separately saccades that are about 5, 10, 15, 20, 25 and 30 degrees rightward and then leftward are the negative velocity profiles, that's why they see negative velocities. And so what you see is that at least as far as I picked two nice examples but in general you see this as well the velocity profiles in the patients look smooth they don't look like they're abruptly terminating they look pretty normal relative to the controls and I'll show you some aggregate statistics across the population in a second but basically at least at a visual kind of gross level the saccades look relatively normal minus the fact that they don't like to make big saccades. So I picked someone who happens to have these 30-degree saccades just to show you guys but in most of the patients as you saw in the previous plot for a 40-degree target they go 20 degrees and so the maximum I would get from those people is about 20 but up to those the data that I have the saccades look look normal. So I'm now going to try to show you some kind of aggregate statistics across the population for some of the parameters that we typically measure in saccades and try to hopefully make the saccades look normal. So one measure that we often use is the peak velocity so I showed you the velocity profile in time in the last figure and one parameter we can just extract out of that velocity profile for every saccade that a person makes is the velocity, the peak velocity and that's a pretty typical measure it has a pretty stereotypical relationship in an individual and what I'm going to try to convince you of here is that the peak velocity in patients looks normal so I'm going to pair them to controls. And so what you see on the plot on the left is the amplitude of the saccade. I'm kind of grouping saccades again by in this case in bins of three degrees. This is 18 plus minus one and a half degrees this is 15 plus minus one and a half degrees and so forth for each point just to be able to take an average within an individual and in the shaded regions underneath which are somewhat hard to see, which I apologize for is the control population and I split them up by age range it turns out that this doesn't really have an effect on the velocity the peak velocity but just for kind of completeness I split them up by age range these are in red not that you can see it super clearly would be kids from three to six zeroes old in orange would be six to nine nine to twelve and so forth and so the control data is in the shaded regions underneath and what I've plotted on top of that are the each line is a main sequence this amplitude peak velocity relationship for a single patient and so what you see when I look at the relationship between peak velocity and amplitude is that for the most part the patient data has a nice smooth relationship with the true amplitude of the saccade and it looks appropriate for the amplitude that they're making and as compared to controls it's about the same we know that in healthy people between for example you and I there may be as large as a 50% difference in our peak velocity so there's a few of the kids happen to be a little faster but that's not unexpected given the variance that you see in a typical population of healthy people I pointed out in one of the earlier slides that while peak velocity is a fine point at which to measure the statistic perhaps the saccades are getting aborted a little later and maybe we're looking too late in the saccade and maybe the velocity early in the saccade is something to look at and that should look appropriate and then somehow it's going to get quenched later so we might expect a difference if I look very early in the saccade versus at the peak velocity and so I'm just showing that on the right I take the velocity instead of at the peak I take the velocity 10 milliseconds into the saccade which is fairly early and again you see the control data in the shaded regions underneath and the patient data one line per patient on top and for the most part it looks like their velocities early in the saccade are normal as compared to controls we can look at a few other pretty kind of normally a few other measured parameters about the saccade dynamics to try to make the case that maybe their saccades are actually normal there's not something wrong with them on the left you see the relationship between the amplitude of the saccade and the duration in milliseconds where I basically just take a velocity threshold and I say when they cross a certain threshold that's the onset and when they go below it and again it's the offset so it's a little noisier but you can see that again for the most part the patients which are in the lines lie right on top of the shaded regions which are the control population and the last thing I'm going to show is the skew so if I go back just for a moment and we look at the velocity profiles oh sorry the velocity profiles of large amplitude saccades are a little bit skewed and that they go up and then there's a little bit of a tail in the velocity profile this is normal we see it in healthy people as you can see a healthy person on the left and so one measure of saccade dynamics maybe the skew that it sometimes looked at and so one way we can assess the skews we take the acceleration phase the time to peak velocity over the total duration if you don't see this tail you'd expect the skew to be one half that is they kind of rise for half of the duration and then they fall for the other half of the duration and if it's less than a half it means you have this tail so if we look at data for the skew again I'm bidding by amplitude and there's skew on the y axis one half as you can see is right up there for control individuals you see that the skew increases you have this longer tail that goes below 50% as you have larger amplitude saccades and you see something similar in the patients maybe a little bit different though this is a less little noisier measure so for the most part I've showed you peak velocity and skew and the velocity profiles themselves looks like patients maybe are making normal appropriate saccades for the amplitude that they are but I haven't and so they look normal relative to controls which is interesting a little surprising given the prior hypothesis the last thing though that would be nice to be able to check and I'm going to show you some data where we take a stab at this is maybe their saccade generators are just different and so they're trying to go to the target and they do it in a weird way so they happen to look normal so we can though within an individual try to ask whether they they're trying to go to the target or they're trying to go the saccades trying to go where it actually goes so we're going to do an intersubject kind of analysis and trying to make the claim that saccades are appropriate for the amplitude that they are as opposed to the distance to the target and again what I'm plotting on X is the amplitude and the peak velocity on Y so first I'm going to take the subset of saccades where the target is suppose 10 degrees away and actually go 10 degrees away and say what's the peak velocity when targets 10 degrees away they go 10 degrees away in this case there's really no ambiguity about whether they're trying to go to the target or they want it to go because they're the same so when you want to go to a target that's 10 degrees away and you go to a target that's 10 degrees away you make a saccade with a peak velocity that's about 400 milliseconds and this is all within all within the patients next thing we can do is we can say okay let's take instead trials where they the amplitude of the saccade was not equal to the target distance they didn't go all the way there this is going to be the majority of those saccades and we can say okay let's take all instances where the target was 10 degrees away if they're trying to go to the target we might expect that when the targets 10 degrees away that's really they should move in the same way as sorry so if we take all instances where the targets 10 degrees away and aggregate them and we get the same relationship as we saw when they both went to and wanted to go and the target was all when they both went 10 degrees away and the target was 10 degrees away that would suggest that they're perhaps trying to go to the target and you see that that's not the case you get something very different that when the target is 10 degrees away they only if I aggregate the saccades they only have a peak velocity of 200 milliseconds which is very different if on the other hand I take these trials where the where the target was some distance and they moved somewhere else and instead I aggregate the saccades based on the actual amplitude not the target distance it looks turns out that the the relationship between amplitude and peak velocity lays right on top of the cases where they went directly to the target so it's a little confusing and I kind of stumble over it but does that make any sense to people who have questions I'm going to do that again that's another question I will ask you the question so what do you mean by amplitude not equal to target yeah so first we can think about if I have these two targets and the eye starts off here and first I'm going to show in green cases where they go all the way to the target so this is in green I'm going to say in this case there's I don't think there's any ambiguity between where you want it where the target is and if you're trying to go to the target and you're trying to go where the saccade lands because they're the same same thing next I'm going to take saccades where they land somewhere else the saccade lands here targets over there and I'm going to say does the the amplitude peak velocity relationship look right for the amplitude of the saccade or does it look right for the target distance right that's what I'm trying to separate and it's nice because as a kind of a control I can take cases where they're the same and I can say this is the nominal relationship for this patient where I'm kind of confident in what it should look like and say now when I take the movements and the trials where they didn't go straight there does it look the relation to the book correct if I think about the patients moving trying to move in a way based on their amplitude or if I think about the patients trying to move to the target and having something get in the way and so the what you see is that the relationship when I think about saccades as their true amplitude which is in red looks right it matches up but when I instead think about the saccades as trying to go to the target just looks very different does that make sense yes it's as if the subject is intending to go halfway to the target that is exactly what I'm trying to say that's the idea it's not that they're intending to try to go to the target and it looks like they're intending to go halfway based on the dynamics of the saccades exactly cool any other questions for the next bit so in summary of this part I've kind of showed you that patients with AT make a geometric series of saccades to shift their gaze they go halfway a little more and they go a little closer and then a little closer and that the saccade dynamics look like they're appropriate for the saccade amplitude and as you pointed out it's kind of what came to my mind when I looked at this data maybe they're trying to go where they actually go maybe they're trying to go halfway and so perhaps this series of saccades that we observe isn't a deficit it's not a problem in their saccades maybe it's somehow an optimal policy maybe it's something that they're doing intentionally because it's somehow good somehow the right thing to do so we can think about why one might make a series of saccades and we can speculate these patients have ataxia what if there's an increase in the signal dependent noise of their movements again if you remember from your homework the last homework set the gain of a saccade was related to the magnitude of the signal dependent noise so if I drastically increase the signal dependent noise which you might be the case in these patients one might expect that the gain should go down and maybe it goes down enough where we see this pretty significant change in the amplitude of their saccades and so as I just said there's an expected change in the saccade gain for a single saccade with an increase in signal dependent noise so this is mostly taken from your homework with a slight tweak so we can think about for example the position of the I X as being a noisy result of making some command U some signal dependent noise and we can think again about a time cost which we think about durations as being linear in the amplitude of the saccade just like you just did before and that the total cost for making a saccade is some accuracy cost JX and some time cost JT where we have a squared accuracy cost and then I'm using a hyperbolic cost of time instead of a quadratic cost of time which is what I think you guys had before so we would expect based on homework last night that they would have a smaller gain we can also think about what if you're allowed to make end saccades so you're allowed to make more than one and so the way I've set that up the solution to these equations ends up being the same thing you guys derived in class so I wasn't going to go through the same derivation it's just the Bellman equation but I'll point out kind of how it works so we're going to think of a system of the IX and after the kth saccade after the kth saccade XK is the position of the I and that position of the I is the position you were at before you made the kth saccade plus the desired amplitude of the kth saccade which is U of K-1 and then plus that single dependent noise term so very similar to what you saw before but I'm now allowing you to make several I movements I'm going to assume that you start off at zero that's not particularly important the duration of the saccades again is for each saccade the duration of the duration T of saccade K-1 is going to be some linear function of the amplitude of that saccade so and this is important the total duration is the sum of the durations of all the saccades if I make three saccades of the sum of the durations but there's also going to be some inter-saccadic interval and in order to kind of improve the or one way to do this effectively is to make an I movement pause for long enough that you can see where you landed and then make another I movement and then pause for long enough that you can see where you landed make another I movement and so if you think about the total duration it's going to be the this doesn't work I get a darker pen it's going to be the duration of the first saccade so I'm just plotting again gays on Y and something like time on X going to be the duration of this first saccade plus some inter-saccadic interval plus the duration of the next saccade plus some inter-saccadic interval plus duration of the third saccade so if I allow three saccades I have two inter-saccadic intervals so it's going to be n-1 the number of saccades minus 1 times the inter-saccadic interval ISI plus the duration of the K-saccades and there's some again cost of accuracy the nth step we don't really care about your accuracy after before that we care about your endpoint accuracy you want to be there at the end and so there's some total time cost which is a hyperbolic cost function as you guys have discussed the other important point that that's a little slightly different is that we assume that the system is fully observable so that you know where you landed as I pointed out earlier you make a saccade you see where you landed and then you make the next one for the results that I'm going to show you and so we'll start off by looking at what we would expect in control individuals if anyone's interested in the actual values of all the parameters I have them but the general qualitative results I think are what are interesting so and so the way I solve this is just actually I used some of the notes from when I took the class you can just use the Bellman equation to say to find the optimal policy given the signal dependent noise given that you have n time steps and you just solve the system in the same way and so if we can think about what the what the behavior is of control subjects and what you might expect with an increasing number of saccades so for a control individual as you increase the number of saccades they are more accurate if I go 95% of the way on the first saccade making a second saccade is going to help me even if I'm 99% of the way on the second saccade making a third saccade is always going to help my accuracy so there's really no penalty to accuracy for having more saccades you obviously do better the more saccades you make but the trade off as we know is that there's a cost of time and so doing things slowly and definitely isn't really ideal you eventually actually would like to fixate the target and move on with the rest of your life and so we can think about a cost of accuracy that goes down with the number of saccades we have a hyperbolic cost of time that goes up with the number of saccades this is driven largely by the inner saccadic interval because that's going to be much longer than the duration of an eye movement which is fairly short and then we can take the total cost which is shown in blue on the top line and you see that the minimum for the total cost is going to be in this case the optimist could make one saccade as you for the most part observe in healthy people if I instead if I only increase the signal dependent noise in my simulations the results are what you see on the right so you can see that the the time cost is the same for the two sides that is it's a hyperbolic cost of time it goes up with the number of saccades it's driven largely by the inner saccadic interval but the accuracy cost for making just one saccade is much, much larger because they have a greater signal dependent noise as you would expect and it indeed does come down with more eye movements, again it's fairly intuitive but because this cost is so much higher for making a large single movement or two kind of large-ish movements you actually see that the optimal policy is to make something like three-ish saccades, three-four saccades which is kind of what we see in the patient so it's kind of nice that it works out that way but I haven't shown you that the patients actually have an increased signal dependent noise so this is what the math predicts is that if the patients have signal dependent noise a much increased signal dependent noise in this case, I think I increased by a factor of three, two or three the results are about the same for increases of about that magnitude and the, oh, I'm sorry I get a question Did these results change at all if you don't assume that the induced saccade interval is the same? As long as it is long enough that you get feedback these results are going to be about the same if you make the induced saccade interval shorter, significantly obviously the time cost is going to shift a little bit because that drives the time cost but as long as it's long enough that you can see where you are or see where you go the results are going to be the same I think the question is more than one why do you have the assumption that the induced saccade interval is the same after each step longer at so it's not going to change that much so if you saw the data I'll show you the spread of the induced saccade interval in a couple of slides but as long as it's not changing by in order of magnitude you're going to still see ascending cost of time on average the expected cost of time is going to go up and the accuracy is going to go down so it's going to trade off close to this point I can make the induced saccade interval variable but as long as it's about this magnitude the expected value of the induced saccade interval is about what I use which I use 300ms which is what the data or 400ms which is what the data is if the expected value of the induced saccade interval is that you're going to get very similar results I'll just skip to that since that's coming up so what I'm going to show on this slide is the induced saccade interval as I said for the model I assume that they have a fully observable system so that they know where they land before they make the next saccade I'm going to be plotting a histogram of the inter-saccadic interval when they make two saccades on a single trial and so for control individuals and for patients it's just a histogram of the inter-saccadic interval frequency is on Y the mean of both you see that they tend to not have inter-saccadic intervals less than about 150ms which is about what it might take for you to get visual feedback and plan a new saccade more or less and the means of the inter-saccadic interval is fairly similar it's 400ms in controls and 378ms in patients and the proportion of ISIs that are less than 150ms just a cutoff I defined is 5% in controls in patients and these distributions look at least to the eye similar I don't think there's any significant difference between them does that answer your guys' questions to some degree okay so the two kind of premises of the model the two assumptions one is that they're pausing long enough to actually get feedback to make the next saccade that's what I just showed you and the second bit is that they actually have an increase in single dependent noise and it's about the right size to get this effect because if the single dependent noise is 5% that's not the simulations kind of increase that's much larger than that if the single dependent noise is going up by a thousand fold then obviously you'd expect some different behavior so here's the data I'm going to try to measure single dependent noise in two ways the first way is I'm going to take when they make a saccade in X I'm going to say the first saccade I'm going to assume I'm going to go to the same place just an assumption and I'm going to say the first saccade where does it tend to land up for a given target amplitude and a given individual and then what's the variance of that endpoint for the individual and I'm going to aggregate it across people and so what you see on and I'm just grouping over both leftwards and rightwards saccades so just taking the leftwards and rightwards trial so I'm taking the absolute value of the target position and as a result the saccade amplitude so for controls for example they may make a saccade you know on average their first saccade in some trials maybe about 12 degrees or 12-13 degrees and they have some variance which goes up as the magnitude of the first saccade increases this is a nice demonstration that there is some sense of single dependent noise whereas if I plot the same data for control for the patients we see that the slope is much steeper much increased kind of rate of increase of the variance as the amplitude of the saccade goes up yes these are the MATLAB gummed up the labeling and I made this figure like this afternoon so that's why I haven't cleaned it up this is everyone there's about 30 controls and about 10 patients and I'm sorry that the I threw this figure in this afternoon so I apologize for that this is all pretty fresh stuff so the so it's 30 controls and 10 patients together the other way we can look at it is we can say that first way assumes that they're trying to go to the same place on every trial another way we can look at it is because my targets are always aligned in X they're always horizontal it's fair to assume that they're trying to make a saccade that's actually horizontal and so we can look at the variance in Y as a function of the X amplitude as a way to kind of measure it without having to assume assume that they're trying to go or make some assumptions of where they're trying to go and what you see is that it's a little noisier but in controls that there's really not much variability in the there's not much change in the variability in the Y component but with patients it goes up quite a bit and they're making for example a 20 degree saccade there's a much larger variance in Y on average for a typical patient and as I pointed out they have these inter-saccadic intervals that are long enough where they could be getting visual feedback so together at least they suggest that maybe so we see that patients do have an increase in the independent noise that they sit for long enough at each of the endpoints that they're they could be getting visual feedback so and we know that if those two were the case an optimal feedback controller would would want to make three, four saccades which is what we see in the patients so it kind of works out nicely that that the math kind of makes a prediction and that we see some evidence for those predictions in the patients data so in summary the patients make a series of saccades to shift their gaze that series may be an optimal policy not a deficit based on the fact that their saccade dynamics look normal and that an optimal policy with increased signal dependent noise actually is to make a series of saccades and we do see that they have an increase in signal dependent noise in the patients and that's basically it just some acknowledgments that patients are usually very generous many of them fly from very far away to come to Hopkins in general and then they'll sit around they'll stick around on their vacation to do the experiments and the MD-PhD program, the AT Children's Center and then our funding sources have all been very helpful and generous so thank you guys and I am more than happy to take questions more questions from here to there for these patients it takes more than a second often yes it'll take them more than a second because if they make three saccades the ISIs are about three, four hundred milliseconds it's going to be about a second to go shift their gaze effectively for the large margin how long is this time system thing to go somewhere how long is it so it depends on how in depth you mean by understand but the visual signal is going to hit v1 I think within a hundred milliseconds or so and you can plan I think a second saccade in 150 to 200 milliseconds it's pretty normal so that's why I kind of set the threshold number based on the time it takes for visual information to reach cortex it may not actually be needed it may not need to reach cortex but to reach cortex I think is on the order I mean to stop for shorter periods of time because they train to do that because they need to manage saccades they train themselves to do all this faster to do to get the signal I don't know if they're getting visual feedback any faster than healthy people I don't have any evidence for that but I do think that particularly since this is a developmental disorder it's very reasonable that they've learned to adopt this policy given the deficits in their system so in terms of having trained to do the behavior itself I think that's possible I don't know if they have trained to your second question I don't know if they've trained to get visual feedback any faster than healthy people that's your question yeah the answer is out of it yeah to some degree so we know that the cerebellum in many examples is involved in computing a forward model that is when you make a command I think you guys have talked about this you make a command it takes time for feedback to come back to your brain and so it's useful to have a system that predicts what the consequences of that command are going to be and it's thought that the cerebellum does that to some degree and these kids we know have a vastly shrunken cerebellum and they have atexia so perhaps they have an impaired forward model they can't predict where they're going to go as well as you or I and so as a result they're not able to compensate in advance or compensate before they get feedback and so then that would predict that they should have an increase in the signal of pain noise because for larger commands you know the other parts of the system have an increase in signal of pain noise and you can't correct for those factors so that actually that is consistent that might be one reason why they have an increase in the signal of pain noise does this sort of and this is just like a curious question is this sort of like change in the pattern of saccades have really any practical cause any practical deficits for these kids relative to other results of like that are kind of common in the cerebellum or lesions as a result of that destruction of the forward model so for these kids and specifically for their eye movements if that's where we can focus on I don't know if the series is necessarily the issue but the increase in noise certainly is so for example when you read reading is a classic example these are children there in school when you read, reading involves moving your eye very accurately from one part of a word to another part of a word or from one word to the next word and because they have an increase in the variance excuse me it's difficult for them to land right on the word after one movement and so they'll have to sometimes make two or three and it takes them a second to get from word to word so reading is slower it's more effortful they have to remember what they, the word that they read before much more than you or I would and as a result particularly in the patients that have worse eye movement deficits reading can be quite fatiguing and quite difficult and so in practice they a lot of them use audiobooks and that sort of thing but that's one practical clinical consequence of the, of this phenotype if time is less costly then they should make more saccades so the if the cost of time is changed it has to change because this is a kind of a discreet thing it has to change a fair bit and there's enough noise if I, if you remember from the example there's enough noise in kind of trial to trial where the saccades land so I'm not sure that I have, I can look at that specifically I haven't actually looked at the first half and second half to say that convincingly I haven't looked at the first half and second to say that convincingly but that's an that is the prediction that if you significantly change the cost of time within an individual or perhaps across individuals that you should see a shift in the number of saccades people make that's exactly true yeah of course why do we blink our eyes so often so blinking blinking serves in part to hydrate the sclera and cornea so the sclera and cornea are not particularly your cornea is not well vascularized you don't have blood vessels that run across your cornea that would be bad you wouldn't be able to see and so it's not well vascularized and so it's not hydrated it's not you know and so to hydrate those cells you need that's in part one of the reasons why one might blink is to hydrate the cornea and that's why if you don't blink or you have dry eyes from a medical condition one of the major consequences is corneal abrasions that's the bad thing that happens if you don't if you have dry eyes so random but that's I think the answer this just might be the I mean as you said like the model probably wouldn't see the result wouldn't significantly change with this but if you go back to the slide with the inter-psychotic intervals those histograms are pretty like apparently bimodal and again from your plot it's pretty obvious that the inter-psychotic intervals are different over the course of the trial if you separated those out for like inter-psychotic interval for the first saccade and inter-psychotic interval for the second saccade it looks like you'd be able to separate those separate the modes in those plot which might it probably will give you the same result but it might be an augmentation you could make to the model in terms of actually having the inter-psychotic intervals be fixed values but be different for after each saccade so that's a good question I actually have looked at this I've done these histograms for first saccade second saccade and I don't have very many third saccade in control so it's not easy to it's not as meaningful to do that the first saccade is always one mode in the second the first ISI is one mode and the second ISI is another this happens to be the example that I picked but that's not always the case you see a similar shape obviously it's smaller numbers it's a little noisier but similar shape for just the first saccade distribution and just the second saccade distribution or second ISI distribution that's a good question more questions? miscellaneous questions cool thank you