 So as we've heard in various presentations today already, the organization of the connectivity of the brain at a macroscopic scale is heterogeneous and quite challenging to analyze, quite complex. Likewise, as we've just been reminded by the previous presentation, the organization at a microscopic scale, area intrinsic scale, is also quite complicated, very challenging to analyze. So to bring the two together into a generic model of multi-scale cortical organization appears very challenging indeed, if not impossible, unless there are some rules that link the two levels systematically. And so, like Shrikant and the people he's working with, we're looking for rules that can connect different levels of cortical organization. And that's what I would like to talk about in the next 15 minutes or so. I will outline two of such principles that may help to explain the connection, apply them to a number of data sets from different cortical organizational types, as well as species, and then finally give a first glimpse of how the two scales may be connected. In our work, we're coming from a more top-down perspective as compared to the blue-brain approach, but likewise we're looking for principles. So in that sense, we're actually quite similar in the spirit. So the kind of features that we're interested in are very simple ones. There have been a number of analysis in recent years that look at complex aspect of network topology, network organization, and help try to link them to other levels of brain organization. We're interested in the most basic features of connectivity, such as the existence of specific pathways, or the absence of specific pathways between pairs of regions, as well as their density. And we're also interested in constraining the characteristic patterns of laminar origin and termination in the cortex. So this is the very essential features that are really fundamental for any kind of modeling, and this is what we would like to explain. So let me start by saying a few words about wiring principles. The first and probably the most intuitive one is wiring minimization, or constraining of connectivity by distance. And this is very intuitive as the brain is a physically embedded object, so it makes sense that the wiring should be reduced, also taking inspiration from technical examples such as the wiring of microcircuits, which have inspired some of our beloved system neuroscience diagrams. And indeed there's some evidence for apparent wiring minimization in the brain. However, it's also known that if you look at the actual distributions of projections, there's no strict wiring minimization. So many of the projections are among neighbors in the cortex, but there's also a long tail of quite distant projections. And there are a number of counter examples. So the fact that the optic pathways spend almost the entire diameter of the brain and they're projecting back from the, very back to the front, the thymic nuclei, which are next to each other but unconnected and so on. They argue against a strict wiring minimization principle. And indeed, if you compare directly the wiring minimization of the actual brain connectivity both at the systems level or of C elegance to the theoretically possible minimum or the maximum, you see that it's not quite near the minimum. However, some other organizational features such as the average shortest path links are actually quite close to the theoretically possible minimum. This would be the maximum again. So wiring minimization may not be the full story. Another traditional concept that may help to explain connections is the organization of the brain into gradients of evolutionary development of under genetic development and gene expression patterns, as well as cytooarchitectonic gradients that follow from the combination of those two. And it's quite a traditional hypothesis that these cytooarchitectonic gradients also shape connectivity. So that areas that are more similar in architecture are more frequently and more strongly connected. And there's particularly strong evidence coming from the work of Helen Barber's intergroup over the last three decades or so, that the differences in architecture between different cortical regions, as shown here on the x-axis, help to shape the relative distribution of projections in the cortical layer. So both determination patterns as well as the origin patterns. So these are the central hypothesis that we started with. There are also a number of other hypotheses. So it's been suggested that similarities in cortical thickness, for instance, may correspond to structural connectivity. And you can think of a number of other constraints. And we've tried to explore some of the basic structural parameters that may be relevant in this context. But mostly the cytooarchitectonic hypothesis as well as the distance hypothesis. And we've done so for a number of species, wherever connectivity data sets were available, including the classic work of Feldman and Vanessa on the macaque visual cortical system, a more recent update of the macaque connectome by the group of Henry Kennedy, as well as traditional cat cortical connectomes and more recently available human connectome data from the HCP. As I said, we are focusing on distance and cytooarchitectonic similarity. And in the absence of true information on the length of projections in the brain, we operationalize distance very pragmatically by the border distance. That is the number of borders you have to cross to get from one area to another cortical area or to the Euclidean distance between the mass centers of cortical areas where this information was available. And we quantified cytooarchitectonic similarity in two different ways, starting with the general parameter of the type difference between the origin of a projection and the termination of a projection and defining the architectonic type of an area by the apparent density and prominence of the different cortical layers. So this would be a high type area, think of something like area 17, where you have many very dense cellar layers and a pronounced granular layer, layer 4. And this would be a low type area, limbic areas, such as orbitofrontal cortex, where you can't really discriminate more than three or so cortical layers, two and three together in five and six. Overall density is much reduced. Density of neurons in the cortical layers is also much reduced. So this is the, in this way, we defined eight cortical types for the macaque monkey and five for the cat, based on an ordinal type definition. And where they're available, we also used a simplified metric measure, the neuronal density across the old cortical layers in order to just take the density difference as an indicator of the overall architectonic similarity of cortical areas. So let's get started and let's just see how these parameters play out for actual connectivity data of the classical filamentous venison data set. So as was to be expected, there are many connections among neighboring areas, here shown existing connections in black bars and absent connections in white bars. But there's also this long tail of projections that go over six, seven or eight cortical borders all across the system. And if you put everything on a relative scale, so that you look at the number of projections that exist for potentially existing connections across a certain length. So all of the connections that could exist at, let's say, border distance eight and see how many of them actually exist. You will find that distance is not really very good predictor of connectivity as it goes down first and then actually goes up again. So you have almost half of the connections that could exist at length eight or seven or so actually present in the system. By contrast, if you look at the type similarity of cortical areas, you find that connections mostly run between areas that are very similar in their architectonic organization and almost entirely absent between areas that are very different in their architecture. Taking the additional measure of thickness similarity, there's a very heterogeneous picture here, maybe that areas that are very different in their thickness don't really form projections among each other. Looking at the rank correlations of the individual data points, we see that indeed the correlation with the structure similarity is greatest. There also appears to be some correlation with the thickness similarity. However, this goes away if you do partial correlations and account actually for the type of these areas. Then it's reduced to zero. There's also a nice relationship in that the most similar areas from the densest connections, although the overall correlations here are reduced, and that's a general observation. Let's look at the lamina profiles of projections. So it's been known for quite some time that there are characteristic patterns of origin and termination of projections in the cortical layers. So it was found that for projections from areas 17 to 18, 18 to 19, and 19 to 20, so projecting from a peripheral chordal to a rostral direction, the projections originated predominantly in apocortical layers, terminating layer four or the deep cortical layers. And they were circulated by projections from the deep cortical layers going back to the boundary of layer two and layer one. So based on this observation from classical work of Rockler and Panier, then all such projection patterns in the brain were classified as forward or feed forward or backward projection patterns or feedback projection patterns. And that's a very, very regular cortical motif, one of the most regular aspects of cortical organization indeed. So taking such patterns and plotting them against the structural parameters that we're interested in, such as border distance or thickness similarity, we don't really find any correlations. So I'm not showing any more pictures than them, because there's not really any good relation with these two aspects. But if you plot, for instance, the laminar characteristics forward and backward pathways against type difference, you find that projections from higher type areas, so more cortical layers, higher neuronal density to lower type areas, form forward projections, as shown here in red, and projections from lower type areas, so more limbic areas, less density, fewer cortical layers to higher areas, form backward projections, shown here in blue. And the highest proportion of lateral pathways of a mobile, bi-laminar balanced projection patterns, shown here in yellow, are actually formed between areas that are very similar in the organization. The same thing can be seen if you operationalize the architectonic similarity with the density difference between the areas. So this is neuronal density differences of the two cortices that you're interested in. Forward projections are associated with projections from denser areas to less dense areas. Feedback from less dense areas to denser areas. And projections with the lateral component exist predominantly between areas that are very similar in the neuronal density. Once again, if you do rank correlations of all the parameters, you find that the correlations are highest most significant for the type differences and the density differences, and much reduced and not significant overall for the distance and the thickness similarity of the areas. So based on these observations, we've arranged cortical areas in this so-called structural model where the areas are placed based on the architectonic type. So the highest type areas are on the outside of this ring. So V1 is up there, V2 and so on. And then you're moving to lower type areas which are more at the center of the organization. And this arrangement actually coincides with the topological arrangement of areas in the brain. So you have areas of the sensory, motor periphery, more to the outside of this diagram and areas that are more on the inside of the brain, as most people would feel intuitively, actually also on the inside of this diagram. Connections are color coded in such a way that connections between areas of the same type or adjacent types are shown in black, two types difference in blue, and more than two types different in red. And the predominance of the black and the blue connections really demonstrates the overall consistency of this kind of model. Connectivity here is identical to Phelaman-Vanesan in the classical diagram. So we sought to validate these findings across a number of other datasets that are available, both for the macaque as well as for other species. And so looking at the recently published connectome from the Kennedy lab, here again are the correlations with the similarity of areas in their density on the log scale. That's a perfect correlation in fact. And the near to perfect correlation there was also found for the distance of projections. We analyzed these two factors, in fact the three factors of the thickness similarity was also included in the multivariate predictive model using SVM and found the highest predictive loading for the density difference of the areas, much higher than of the other individual factors. If you combine the factors, then the best performance was actually achieved by combining the density and the distance difference. And indeed you find that for areas that are very similar in their density and nearby you have a posterior probability of the prediction of 85% that's just what's this line representing here. This line up here represents 15% of chance of existing of a projection. Then we used 10-fold validation prediction in order to see how well using these thresholds and the posterior probabilities, we could actually predict the connectivity from the model and at that level we achieve a very high accuracy of the prediction indeed. So just combining the architectural similarity in terms of density and the distance information allows you to reproduce the connectivity of the system almost perfectly. We made another interesting observation in that hub areas or core areas in the brain turn out to have much lower density than non-core areas. And this is a general phenomenon whereby areas of low neuronal density have more projections than area of a higher neuronal density. And finally we looked at the connectivity information published in a companion paper by the Kennedy Group and indeed there was a very good correlation between the origin patterns and the density differences of the areas and no other relationships existed. There seemed to be one for the density difference but that again went away if controlled for the density difference. So very, very briefly, similar almost identical results were found in a cat connectome based on the somewhat age data of scanner at all. So perfect rank correlations with distance and type difference. Once again, high predictive values somewhat higher for the type difference than for the distance in a predictive model which allowed to make quite a number of predictions with high reliability also for pathways that have not been tested yet. Once again, we found the difference between the hubs areas which generally have a lower type and the non-hub areas which have a higher type and that's the expression of a general relationship where higher type areas, so more layers, higher neuronal density have fewer connections than the more limbic areas in the brain. And finally, we saw that projections from higher type areas to lower type areas tend to form ascending or forward pathways whereas feedback pathways or descending pathways are formed by projections from lower type areas to higher type areas. So almost identical results to the ones in a monkey. More recently, we used the Elm data and the ZingLab data because they also offer a nice chance to look at apce and contralateral connectivity patterns and an analysis of these data. Alex Goulas, who's here, found that once again, distance and cytoarchitecture predicts significantly the existence of projections somewhat more strongly for the ipsi lateral projections whereas for the contralateral projections, it's more the cytoarchitectural differences that allow the prediction of the projections. So there's a large body of evidence now that the structural model, structural similarities explaining the connection features works for the number of courtesies in the non-human primate as well as across species and there's a very nice poster still up today by Alex Goulas that uses these regularities of cortical organization for cross species predictions. So training a predictor in one species in order to predict connection features in another species in order to demonstrate the universality of the principle and it works just beautifully. So I would encourage you to see this poster over there at the hall. But the question that you may be interested in to know is whether this also works for the human brain and for the human brain, by now we have some connection information for instance for the works of the human connectome project but what we're lacking as yet is detailed architectonic information and until the work of Marcus Ackser and other people in Yulich for instance with the big brain project and Evans also produces much more quantitative and detailed information but for the moment the most detailed comprehensive information about the human brain is actually found in the classical work of Von Ekonimo and Koskinas. And fortunately it's all quantitative so if you transform this information into MNI space which several people have done by now Martijn van den Hevel and we've also made some efforts you can actually use all the quantitative information associated with this classical work and use it in predictive connectomics and what we'll find there so this is just a demonstration to show the connectome data and the architectonic information that's from Von Ekonimo transferred into standard space and done into a standard parcelation you can analyze this and this will result in a very busy diagram I'm afraid but what it shows is that the similarity architectonic similarity particularly of the upper cortical layers indeed is significantly correlated with the existence absence of projections so in fact is the distance but this is a factor that is intrinsic to the diffusion based connectivity data and so it's very difficult to deconvolve that from the actual information of how much distance predicts from the methodological information and this is true both for the right hemisphere as well as for the left hemisphere very early days so we just need to be confirmed in other data sets so what I've tried to convince you of is that the architectonic similarity of cortical areas is consistently correlated with the presence and absence of pathways as well as the laminar patterns of origin and terminations and less consistent relations are indeed seen for the distance or thickness similarity and we've observed similar relationships across different cortices and different species, macaque, mouse and there are also some early results that don't contradict us completely for the human brain. How does this now allow an integration of the last figure in fact? Well last but one. Integration of the micro and the macro scale so just to remind you of what the scheme looks like similar cortices are connected by bilateral origin patterns quite frequently connected quite densely connected whereas this similar cortices have unilateral projection patterns of a more forward and backward nature and so if you take in the additional reflection that the intrinsic connectivity also varies by cortical location so for instance this is a more canonical circuit of sensory areas and the work of the blue brain is also based on something that's more similar to that but limbic areas have a different intrinsic structure you can use the extrinsic connectivity rules to connect more limbic areas in such a fashion and more eulaminate areas in such a fashion and areas of different type in such a fashion. Okay, ending on this one. So I hope that this is a starting ground for bringing in ever more detailed information on the different scales on the macro scale as well as the micro scale in order to build even more detailed models of generic cortical connectivity that then can also be fed into computational models that take these rules into account and some initial version of this work has already found its way into the work of the group of Markus Diezmann, Supercomputational Model of the Makak, Primate Cortics in collaboration with Sascha van der Bader and Rambrandt Backe. Thank you very much and sorry for running over a little bit.