 Οπότε θα σας δείξω την μακροσκόπικη στιγμή της κατασκευής, μετά στον κόσμο της δημιουργίας και της τρακτογραφίας. Θα μιλήσουμε για ένα πολύ σημαντικό πρόβλημα σε αυτό το κόσμο, πώς θα χρησιμοποιήσεις την πρόσφυγη, αν θέλεις να κάνεις δημιουργία. Ελπίζω ότι όλοι σε αυτό το κόσμο θα αγραίσουν ότι η δημιουργία δημιουργίας έχει been very useful in understanding the brain and in understanding various diseases in the brain. There are many applications that you can look at the books by either Sporn's or the more recent book actually by Bulmore and his co-authors. Many different applications of network analysis in brain science. So most of these network analysis typically is done when we talk about structural networks it is done using diffusion weighted MRI and just to remind you I hope everybody already knows this stuff but just to remind you that diffusion weighted MRI is based on the fact that water molecules basically go through anisotropic diffusion when they are in fibers under different magnetic field gradients and people model this anisotropic diffusion with different models in the simplest case you can model them as an ellipsoid and you can mathematically present that with a tensor or there are more sophisticated models that allow you to consider more complex structures. So after you have these diffusion weighted MRI images then the next step is typically to do the rectography which allows you basically to track these streamlines which we all hypothesize that correspond to fibers and fiber bundles and there are of course many many different rectography methods but at the high level you can distinguish between deterministic and probabilistic. Deterministic typically follows the direction of some principle diffusion eigenvector with probabilistic you can take multiple different directions and these directions are weighted by the anisotropy that you have associated with each direction. So if you want to do network analysis which is where we come from after you have your tractography results you want basically to answer for a given set of regions of interest you want to ask is region X connected to region Y and then if you ask this question for every pair of regions you can construct your network and do your network analysis. So when we first started talking with Helen Mayberg and her group the question that came up basically Helen she will talk about these things tomorrow but they are very interesting in a specific set of regions that are associated with various mental diseases including depression. So we had this set of regions and the question was how do we basically infer a structural network between them. Well what we realized very quickly is that there is a threshold problem right. So if you do probabilistic tractography which is very often done and the Human Connection Project by the way is very big in using probabilistic tractography so if you do that you will have as your input basically what I represent there is this term here. What is this. This is basically the fraction of streamlines that start essentially from a voxel Q of a certain area of a certain region R i and manage to go all the way to your target region which is R j right. So this is basically what this notation represents. Some of these streamlines just don't make it right and so eventually you will have these fractions in this example two out of these three streamlines make it to the target. So if you have these fractions and you want to ask whether this voxel Q of region i is connected to region j you need a threshold typically and if this fraction is more than this threshold then you say that there is a connection there otherwise you say that there is no connection. And of course how you choose the threshold can make a big difference and can significantly change your qualitative and quantitative results. You can have false positives false negatives. Depending on what is the value of tau right this threshold. So let's take a look at the prior work in this space. How do different people different studies have chosen this threshold. Basically in many cases there is just an arbitrary threshold and there isn't really a very good discussion of why that particular threshold was chosen. In some other cases the researchers have chosen the threshold the largest possible threshold to keep the network connected. Anything larger than that will basically cause the network to be partitioned. But again depending on what network you are looking at you know the network may in fact be partitioned if you are not really interested in the whole brain. This is a more recent paper by Dona and others that looked at correlations between the tractography based weights and prior work that used anatomical tracing. And so one of the recommendations in that paper when they because they had the ground truth right so they could basically know what threshold works best and they give some specific values that you see here. Of course they admit that these values these tractography thresholds are specific for this study right. So what do you do if you have a different data set which values should you use. So this is basically what we try to do here. We try to come up with a method for essentially selecting this threshold automatically based and this is our starting point. We are based on the fact that when you do tractography basically you don't have information about the polarity of the connections. You don't know if you see basically that x and y are connected according to tractography. You don't know whether x projects to y or y projects to x. So if in reality the underlying anatomical connection is from x to y you should be able when you do tractography to track these fiber bundles in both directions. So this is a limitation of tractography that we kind of exploit in this work to come up with our threshold. So to say this again when we are basically inferring these networks we try to find a threshold to choose the value of tau that will keep the network basically as symmetric as possible ideally completely symmetric. So how do we quantify symmetry here. You can think of a ratio the denominator is all the existing edges in the network and the numerator is how many of these edges like the red one here appear asymmetric. So in this case this ratio is one out of three edges is asymmetric. So one can think naively that okay this could be my strategy here. I will choose basically that threshold tau that basically minimizes my asymmetry ratio. That sounds as an initial approach but of course this is not really right. Why is it not right? Because as you change your threshold you are changing the density of your network. So this kind of obvious but let me explain it. If your threshold is one which is the largest possible value then you have an empty network the density is zero if your threshold is zero then basically every connection appears and your network would be completely symmetric. So there is basically this relation this decreasing relation between the threshold and the density row of your network. So how is this important? It is important because depending on the density the asymmetry ratio is changing. Here I'm just showing you two examples a sparse network with only 20% of the edges being present and another one with 50% of the edges being present and of course in both cases the networks are randomly constructed and of course here this network has a lower asymmetry just based on chance. It's more likely when you have a denser network that edges will be running in both directions. So actually one can so mathematically that if you have a randomly constructed directed network of density row then you should expect to have an asymmetry ratio of one minus rho. So the larger the density row the lower the asymmetry ratio that you should expect. So based on this very simple observation we decided to normalize the asymmetry. The asymmetry phi that we measure in our tractography based network for a given threshold tau. So we can normalize that by one minus rho which is the asymmetry that you should expect in a random network just based on chance for that given density. So again let me say this once more. We normalize the asymmetry that we observe by the asymmetry that we should expect just based on chance for that given density. So if we do that we can describe our method which by the way we call MANIA. What does it stand for? Minimum asymmetry network inference algorithm. So what does MANIA do? It selects basically the threshold tau that minimizes this normalized asymmetry ratio. So if you look at the graph here at the right the red curve shows the not normalized the unnormalized asymmetry ratio which of course gradually decreases as the density increases. But the blue curve is what we care about. This one shows essentially what is the normalized asymmetry ratio and we're trying to find the minimum of this curve. The point at which the network is as symmetric as possible. And that is essentially the threshold that we use. That is, of course there is a relation between the threshold that we use and the corresponding density. So we choose the threshold that gives us this specific density that has the minimum normalized asymmetry ratio. So let's go back to where we started from when Ellen gave us this list of other ways. We were looking only at the bilateral connections. And so for a single subject in that study we had a set of 28 subjects female in healthy subjects around 20 years old. And basically for this specific subject this is the network that we were getting. And in this case it's completely symmetric for this given threshold that many had chose. Take a look here at this specific area B825 has a very special interest in depression and Helen will talk about this more tomorrow. We will come back to this picture in a few minutes. What I want to show though is that this is only for a single subject, right? You would like ideally to have something more statistically significant if you have a larger number of samples. So by the way a common criticism here is that many doesn't produce a weighted network it produces only a binary network. We only know if the edges are there or not. Well that's kind of true but not exactly. We can actually quantify our confidence for each edge. And the way we do that, I will be very brief here, the way we do that is by essentially finding for each edge what is the minimum density, right? At which this edge first appears. So as you kind of change your threshold from one to zero you gradually see more and more edges and the edges that appear first at lower densities you're more confident that they exist and gradually of course you have weaker confidence. So if this is your optimal threshold that many had chose this distance between this threshold and the threshold at which you first saw that edge that is basically how we compute our metric of confidence for each edge. I'm not giving all the details here. I just want to say that based on this confidence metric we can now go and rank the edges in terms of confidence. We can say that edge W is more likely to appear than edge Y and Z. So how do we do based on this confidence values our group level analysis? Again the naive approach would be just to somehow average the tractography data or perhaps to construct a network for each subject and then somehow put the networks together. What we do is based on a more non parametric ranking based method where we say that well for every subject we can basically rank the edges in terms of confidence using this confidence metric that I just described earlier. So we can say for subject one for example W is more likely than Y and so on. And then we are dealing with a very classical problem computer science which is if you have a number of rankings for different subjects how can you basically quote unquote average the rankings or aggregate the rankings. So there are many algorithms to do that. The basic algorithm that we use is that you say that a certain edge appears before another edge if that is the ordering of those two edges in most of your subjects, very simple algorithm. So I have two more minutes so let me just show you that if we do that we get this network going back to the network for all our 28 subjects. And an interesting thing again is that if we analyze this network in terms of how central each of these edges is this particular edge between the B25 and the ACP area this is basically the edge that shows up as the most central edge in this network. This is a very interesting result because actually that is one of the fiber bundles that are often the target of deep brain stimulation in depression patients. So I'm running out of time here. I was planning to also show you some results for how we evaluated this method. Very briefly we used fiber cap which is a particular structure. People have created. It has several, it has basically seven actual fiber bundles. Some of them are pretty challenging. There is some splitting going on here. There is some kissing going on here. There are overlaps, there are sharp turns. So when we actually examine what does MANIA do in this case it produces a threshold which is this particular point here. The point that minimizes the normalized symmetry ratio which is very close but not exactly the same with the optimal threshold that you could have chosen now that you know the ground truth. So we don't actually find the perfect threshold but we find something quite close to it. And when you actually look at the network that we infer most of the connections are there but there is a false positive here and there are two false positives and one false negative actually in the MANIA results. And if you look more closely at the probabilistic you know the connectivity maps that come out of probabilistic tractography you can basically understand that the problem is not really so much with MANIA itself but with these probabilistic tracts, streamlines that are going their own way essentially. So I guess I ran out of time. I will not show any results for our synthetic evaluation and if you have any questions I'll be glad to answer them. Thank you. Be a presentation of an interesting method. Question is the positive input. Hi. I was wondering why you go for the most symmetric network rather than one that has a degree of asymmetry that has been observed for instance in tracing data which as far as I know is around 10%. Right, so let me be again clear about this. The underlying anatomical connections are indeed asymmetric as you said. But tractography cannot really see the polarity of the connections. According to tractography you wouldn't be able to see that some connections are asymmetric. So there is a difference between the asymmetry that actually exists in the brain and the asymmetry that you observe with tractography. With tractography ideally you shouldn't really see that but still you could perhaps obtain a better connection matrix if you took into account the asymmetry that the brain has rather than that would be given by your measurement modality. Right, but I mean tractography wouldn't really give you some hints, some clues in terms of which direction you should prefer. It would be nice if we had a hint so that we keep some edges as not symmetric but what would be that hint? If in general you think that the degree of asymmetry of the network as a whole is important then in some sense you would obtain a better matrix if you had that degree of asymmetry even if the specific edges that you choose to be unidirectional and not the correct ones I mean it depends on what you use it for afterwards but... I mean I see your point it would be very nice if we had that kind of asymmetry in the final result but again tractography doesn't give us the right hints here. You might start from an asymmetry constraint and then go back and approach it again and see if you can see some more asymmetric information out in the second one. That's an interesting idea, yeah, we can look at that. Thank you. We're going to have to move on. Thank you very much.