 Thank you very much for inviting me. It's a pleasure to be here as you just heard. I'm amongst other things co-director of an insurm unit in France Being this a unit in particular focused on system neurosciences Attached to which we have an epilepsy unit so an In-clinic unit and that characterizes actually some of our work quite well. We're trying to carry theoretical neuroscience mathematical principles from The theory through brain network large-scale brain network modeling all the way into the clinic And this is effectively what I'd like to Speak about to you today. It's entitled the virtual brain simulator for large-scale brain network dynamics and what I will do is I will move conceptually theoretically Little in between the last two talks that you heard yesterday on the one-hand side We will talk about connectivity on the other hand. We will talk about Simulating performing simulations as realistically as possible on a chosen level of description so large-scale brain networks a few words on those to motivate our Entry point that we have chosen over the last almost 20 years by now actually When what you see here is a tech cloud from the series of frontiers in neurosciences and there You scale To take the keywords the keywords have been taken from this series and basically whenever the keywords appeared It entered into an index and this index scales The appropriate keyword and you see the predominant Position of fm rye here in particular and when you go to PubMed and type in functional connectivity brain and mr rye just in The last year 28 percent of all citations with regard to this occurred only in the last year out of a Total of three thousand since 1994 Yeah, so connectivity starts connectivity based thinking starts playing a Important and prominent role in the neuroimaging community connectivity there are two Thing at least two definitions to be considered one is the structural and atomical connectivity That is defined by the set of all existing Connections in my case between brain areas number one functional connectivity is a set of Relationships between two areas and relationship is a very general expression They depends on what metric you choose to characterize the Functional the dynamic relationship between two areas So this is a working definition. I'd like to use for functional connectivity What we heard yesterday We heard Michael talk about biomarkers and that's the famous citation that he Brought up also. So one of the hopes is that we can use functional connectivity as a biomarker To at least to distinguish Patient populations from a healthy population and they're seen systematically we do find differences in Pathologies ranging from Alzheimer epilepsy schizophrenia Men also obesity and epilepsy one of the problems. So that we run into this is Much statistical significance we find on the group level but the individual Predictability for a single patient is very low. There is a large inter and intra subject variability and What the belief is is that this may be due to the metrics that we applying we're not applying a good metric. We know that Resting state activity in particular to which the functional connectivity Metrics are being applied Is non-stationary? Yeah, and many of the metrics require a stationarity in order to make Meaningful predictions. So we are in the process to learn about that and Reorienting our thing thinking towards Addressing these issues through better metrics, but also through modeling in order to understand this These phenomena in there yeah through large-scale brain network modeling and that's a mindset in which I would like to have you like As you see here when you decompose a branch into the major branches and the individual needles and lose many of the topological or you use or lose all the topological features and Some aspects of function are not apparent anymore when you look at this some Local aspects of local processing still will be present in each needle But only through the topology on a certain macroscopic level a Functional meaning becomes apparent and that's a mindset that I ask you to have Since with the type of network based large-scale base network based modeling that we Perform this these are the properties That we would like to explore. What are the? Functional consequences upon large-scale brain network dynamics imposed by the constraints are due to topology of the connectivity and One of the big differences when you perform large-scale brain network modeling is That it is still a network, but your nodes Change they are not single neurons anymore number one you deal with local connectivity Which is roughly 50% of all the fibers are into a cortical Yeah, but the other 50% leave the grey matter and perform long distance Connections to far distant areas and there when you look at the propagation speeds that can vary from one to ten A meter per second you run into time delays that are on the time scale that can range to multiple tenths of milliseconds 4050 60 milliseconds depending on the length of the fiber so that they are on a time scale that is important for the dynamics occurring in each of these Network nodes which occurs also on the time scale of multiple tenths of milliseconds So it's not ignorable and computationally that plays a very important role because suddenly All stochastic implementations become a much more sensitive With regards to convergence You have to carry a history along yeah because you have to have For let's say a hundred milliseconds all the memory for the internet work in order to perform the simulation etc So there are issues and consequences for simulations on this type of level of modeling Historically this things like this Or this line of thinking has been performed for more than 20 years here are some Publications of this form new field modeling has been put forward in the 70s by Wilson Kaun newness and there What was missing at that time is a detailed information About the large-scale connectivity on the brain and network level we had subsystems But we didn't have the topological structure of the connectivity so approximations were made homogeneous approximations of which We know that many of those Give us nicely the temple features of the network dynamics, but not the spatial on not at all the spatial temple features so there was basically an outcry for better connectivity information and The first type of modeling using the large-scale connectivity information Was performed here by sorry, but so it was provided by Kutter and wanker and Then the first implementations are of our listed here and that has given a boom to this large-scale Brain connectivity modeling in particular once data also from DTI based information entered allowed Allowing modeling using the two hemispheres and Subcortical structures many applications have been Performed with regard to resting state dynamics right now The first publications are coming out with regard to applications to pathologies such as lesions and Epilepsy I'll give you a more detailed example at the end of my talk with regard to epilepsy What are the network nodes in such a large-scale brain network? It's not individual neurons So we have to make the level of abstraction from individual neurons to what is called neural mass Models we collect the neurons or their neural dynamics in populations and then you have to make a Leap of faith you have to apply a certain metric in order to compress the information And the leap of faith is what do you believe that is actually being coded Within this population. Is it firing rate? Is it the degree of synchronization? Is it spike timing, etc? And depending on This believe There is a mathematical strut or mathematical toolbox that allows you to perform reductions to arrive at what we call the neural mass models where like a synchronization index is being reduced to a variable that evolves Temporally in time. Yes. So these are the population models firing rate would be for instance the well-known Wilson cone model There is an issue though and this issue we run into also already on the single neuron level and that is the Existence of Or the absence of bijectivity in other words when you have a single neuron there so and you describe it to take a Multi-compartment approach for instance. Yeah, there are tons of different Parameter distributions that can give rise to the same emergent dynamics already on the single neuron level this is in particular work by Modern Goya, he nicely reviewed the nature review neuroscience where they have this cartoon based on their empirical data Where they nicely represented in this cartoon imagine you have three? parameters parameter a b and c and then you plot the different Realizations that giving of parameters within one single neurons that give rise to the same characteristic Temporal signature here you have one temple six signature so one characteristic behavior here you have another one and They are lying on so-called manifolds which means this parameter configuration gives you the same Identical dynamics as this parameter configuration if it's convex like this if you take the average over all parameters Actually, you're obtaining a behavior that has absolutely nothing to do with The dynamics that you actually want to observe because it's outside of this manifold So when you make this step from spatial properties spatial features parameters to actually the temporal features There is a certain difficulty involved that must not be underestimated and What we do in order to overcome that in new mass modeling in particular We're trying to understand the invariant features that are present within a Dynamics and this is typically done through the phase flow topology what this means is actually you can characterize the all the dynamics that you observe here on this parameter manifold you can Characterize it by a low-dimensional set of differential equations that gives you a particular Dynamics and this dynamics for 2d and most of the neural mass models are arranged from 2 to 12 dimensions Yeah, you can represent this in a state space and then What you find there this these mathematical equations give you a flow in the state space and Here you have a trajectory when you're sitting here the system evolves towards a particular fixed point so what you have here is a topology that is often used in Decision-making where you have a by stable scenario one stable fixed point another stable fixed point so you have by stability here and This it is this topology that is invariant and that's the type of modeling that we wish to perform a population of neurons even if the parameters are Distributed they give rise to a particular dynamics that we wish to characterize by a state flow that is an unambiguous Representation of the dynamics even if you change the parameters as long as a phase flow remains topologically invariant we deal with the same system and This can be performed Using different mean field techniques and you are dealing with different Neural population models here you have an example From one of the models that we developed ourselves So here you see a simulation of 40 fits you Nogumu neurons this year is a membrane membrane voltage of a single neuron each this year is the variable Representing the opening probability of the channels and what you saw here was a Distribute distribution of initial conditions about 40 neurons that are Coupled and what you see here in this particular case they go down to a fixed point So that corresponded to a discharge a site like this corresponds to an action potential and the system Rests at the fixed point and the red cross represents your mean field so in this case it's a good representation of the mean field dynamics whereas The step from here to here It's the identical system all I have changed a little bit is the dispersion of the parameters Otherwise all parameters are identical and what you see is actually that here The population splits actually in three clusters. Yeah, so the parameters are Identical except the dispersion of one single parameter in this particular case the threshold is a little wider And you see that the behavior is completely different the mean field is absolutely meaningless It does not capture the characteristics You have to actually two three population one that is hanging out here at the fixed point So shows sub threshold oscillations You see how it moves to left right and then two populations that fire in anti-phase So we can capture this type of behavior It will not work with a mean field firing rate dynamics and in particular This will be important when you deal with time delays because when time delays do not matter when you have fixed points Equilibrium states, but as soon as you have oscillatory dynamics becomes a very very important issue So if you believe that rhythms and oscillations in the brain play a role, you have to take this type of approach and consider time delays So this can be done This can be done here in particular for instance in the two-dimensional Stefanesco-Jerza model where you can take coupled Fiziu-Gnogumu neurons for global coupling and collapse it then mathematically on the Individual clusters that you saw so you can obtain a mode Representation of the population dynamics you get a dimension reduction from very high-dimensional to low-dimensional in this case where these variables here are still differential equations, but Correspond to the clusters that were moving as population means within the state space that I showed you and you obtain a very good representation of the qualitative features of the dynamics here you have the fully Microscopic network model. So we are still talking about one single population one single neural mass In this case composed of let's say a few hundreds neurons neurons This is the dispersion of the the threshold parameter I spoke about and that's the coupling strength and you have highly synchronized the dynamics here Then you have partially synchronized dynamics here with multi-stable solutions and you have desynchronized behavior here so this is a fully microscopic network and when you represent this complex behavior in the same parameter space but Reproduce it with a reduced system using these population modes. You'll see that many features quantitatively are different, but the characteristics of the parameter space are The same you identify the correct regions and how they change where the critical lines of Changes from one behavior to the other are to be found and this is actually what we want to do in the virtual brain here You have another example of a full Network model based on single neuron simulations again dispersion and here you have a time delay parameter What we have done here is there we took now a two-dimensional sheet with local couplings probabilistic coupling of individual neurons and then long-range connection exactly the way we have it in large-scale brain networks where we have a Melange mix between global connectivity and local connectivity and the major point is if we replace this continuously this This continuous sheet composed of distributed neurons with this type of connection characteristics by a Network of coupled neural masses Can we represent the topology of the different behaviors in the parameter space? This is what you find here So here I changed the propagation of velocity along the fibers dispersion of the parameter This is a synchronization index large synchronization De-synchronization you see a wavy feature and if we reduce a number of neurons in the fully microscopic Network we arrive at a smoothening out of this wavy structure in the Microscopic network and if we now replace all the neurons by low-dimensional representations of neural masses that has still the same Topology of connectivity then we actually represent Or reproduce these parametric changes in the topology of the parameter Space Quantitatively, it's wrong, but I don't care what we want to do is we want to build human brains on this Microscopic level of description and then manipulate our parameters in order to understand that Changes may be due to pathology. Maybe due to far a pharmacology of parameters the qualitative changes of parameters On this reduced level of description So this is a mindset and for this we have developed over the last 10 years a simulation platform That allows us to bring all these features together informatics Visualization computation simulation stochastic with time delays, etc. So this group Came together the first time in 2005 and the virtual rain itself project has developed started in 2010 it was funded by The James McDonald Foundation. It was Randy McIntosh who brought all of us together and people to be highlighted there is the Petra Ritter from Berlin who is responsible for the educational platform Kathy Price who is leading the clinical efforts Randy I already mentioned who is the coordinator of the group and I'm responsible for the technological Developments of the platform. So the idea is introduce Realistic connectivity in three-dimensional physical space for individual subjects individual patients so patients specific handle the data geometry and connectivity in a three-dimensional space and Introduce neural mass modeling to different levels of representation on a degree of complexity In order to perform large-scale brain simulations We have chosen to as a front and we have chosen a Browser based operation you can download all the information from our website and also the software The software itself is open source and runs on either a high-performance cluster or on your laptop on my laptop So depending on the complexity that you Wish to use at the core is a simulator with all the difficulties and complexities I talked about time delays representation of neural masses. It has to be scalable for different patient brains We bring in all the information about structural connectivity Coupling time delays the geometry cortical surface different models the TVB is completely model agnostic There are different algorithms for the simulation available and it links directly through forward solutions to eG MEG bolt signal or As eG stereotypic eG as I will show you later. This is a snapshot of the interface So where you define the different population models Parcelations play a role you have a connectivity editor Which is one very important feature because what you want to do is you want to load in your Connectome for a patient and then you want to quantify it using the brain connectivity toolbox developed by Olaf Sporn's and colleagues For instance, you want to visualize the time delays as a function of the connectivity You want to introduce lesion lesions and basically work with the connectivity matrix and Then you can perform simulations and visualize it again in 3d. Here. We have a Parcelation of 96 areas for two hemispheres with sub cortical Areas included and you see the areas actually for 96 actually pretty big you Here in this case you have a representation of the local field potential and You can put the Skull around that and calculate the eG again time resolved and then basically treat it as if it were experimental data you can focus on individual areas and basically Manipulate individual time series. It's not a data analysis platform It's really focused on the simulation and the treatment of the data and bringing everything together so This was a graphical user interface there is a python command line interface all of us Mostly work on the command line interface But for the less experienced user in particular when you want to do visualization the graphical user interface is actually very Useful all the pictures you will see today have been made Almost all the pictures have been made by TVB and are coming out of this Just as a proof of concept for the generic nature of the platform when the L netlas For the mouse connector came out. We basically downloaded the data and we read it in Into TVB and they worked without any problems here. You have the connectivity yeah time delays Sorry fiber tracks and the fiber track lengths and this is the Surface yeah within the TVB interface. We've not worked with it yet. We just start working with that which will give us a very nice Validation of all these DTI based approaches as compared to the tracker based Connectome that we obtained here. Yeah so a little overview of the Background that is within TVB. I told you it's agnostic with regard to the Neural mass model everyone has certain preferences whether you look at firing rate based models or oscillatory models We're not dealing with single neural models. Yeah, it's all based on the population level and these are the models that are currently implemented and it's open source and there are more and more models coming from the outside community being contributed and Then implemented in the official version. Yeah, so But all of the models which needs to be emphasized are described by ordinary differential equations So all of them your mass models and what we have implemented there is actually a nice phase flow Visualizer so you implement the equations mathematically you can and then you can visualize The equations through there now you have to know mathematics a little bit through the new clients the intersections are the fixed points You click somewhere here and it basically does it takes a point where you click that may as an initial condition it shows you different trajectories and then you can hear change the parameters and Introduce dispersion of parameters. It's very useful. I like myself. I like to work visually like this rather than changing the parameters. I You get immediately in Visual impression of how the flow changes whether it's a limit cycle that comes up, etc Working with these phase flows and then the times here's Occur immediately mathematically we have This is this rough basically the essential part of the TBB equation it is a differential equation with integral terms and Time delays where this represents the neural mass model X is space the cortical space on the cortical surface or sub cortical areas which are centered in In between and below the two Hemispheres then you have local connectivity which does not undergo a delay a connectivity function that needs to be specified and again It's arbitrary that you can specify and the global connectivity coming from typically DTI data undergoes a time delay with the time delay is identical to a scaled the fiber length that you have and scaled by your velocity For the coupling functions, there are different Choices that can be made and as usual it depends on the modeler and what you want to do Geometry Parcelations certain choices need to be made. Yeah, so this is a representative Parcelation for the 96 areas We are the the integral cortex is being tessellated and then you can make Tessellated and typically we have something between 10 to a hundred thousand vertex points for both hemispheres Then you have to make a modeling choice. You can either take a brain area As in your parcellation as a network mode and a network node Then you basically run this mode of operation and you can still represent it in in This geometry to calculate forward solutions or you can perform surface-based modeling But then you have a significantly higher dimensionality where you take basically every single vertex point and Perform a high-dimensional network simulation This is for instance something that we do on Our high performance cluster because it takes a significant time the code is not paralyzed But when we perform parameter sweeps you can run on each core a parameter configuration independently But there you can basically let it run. So here we do What I typically use is sixteen thousand eight hundred hundred and forty thousand we have done only once as a proof of concept Yeah, so TVB connectivity data are coming from DTI data Then they are represented in this matrix connected structural connectivity matrix brain areas Plotted or plugged into other brain areas Left hemisphere right hemisphere intermospheric connections Represented in 3d then as I told you either local coupling for the surface-based modeling You have a local connectivity and the large-scale connectivity so both can be treated independently For the local connectivity you can choose different type of connectivity functions that are then defined over the curved surface of the cortex and You can introduce yeah here you have a representation of the local coupling on the curved surface here in Gaussian type of local coupling as it decays from this point and One feature that is very important is then the time delay and this as I said earlier we get from the Track lengths here you have a representation of the connectivity over the time delays As so basically we deal with a tensor Yeah matrix and then a third dimension that plots the time delays which you have to carry along Yeah parameters can be dispersed and You can stimulate individual areas again the stimulation location can also be dispersed so that's roughly the current functionality you can run systematic parameter space explorations within the platform and Basically perform simplest analysis such as variance synchronization index But as I said if you want to perform a more detailed analysis download the data and load it into curry or some better professional software that is dealing that is focused on analysis Applications most of it so far has been done for the resting state and there the general Approach using TVB has been the following you load in your Connectivity matrix you build a Parcelation and the geometry of the cortex basically build your brain model you put in your neural mass model on each brain Area so most of these modeling Studies have performed region based modeling rather than surface based modeling actually only one has performed No to have performed surface based modeling and then you Run your model and you get Your time series out of the neural mass if it's firing rate or local field potential it depends on your Neural mass model Using the balloon wind castle model which is implemented. It gives you the bolt signal and then you start Comparing it to empirical data one possibility Mostly used as you can compute a functional connectivity matrix Brain region on brain region and the cross correlation or covariance between brain regions This gives your matrix and you compare and fit and optimize your parameters When comparing it to the empirical functional connectivity matrix. So I mentioned non-stationarity has been a big issue and The functional connectivity matrices are typically not fit to capture these non-stationarity's but Studying the model has helped us a lot to the non-stationarity's are also present in the model Yeah That's a different talk But the model has helped us a lot to understand the nature of the non-stationary behavior within the resting state and then has Taught us how to change our analysis in order to get a better and deeper understanding of the resting state Activity and the non-stationarity is present in the functional connectivity. Yeah, so and Legioning is performed with lesion patient studies by an assault in California. That is another branch that is coming Being pushed forward what I want to do is I want to This where my heart is closest to at the moment is epilepsy. Yeah, and this is preliminary work Some aspects have been published, but I want to Show you the vision where we want to go what we want to do. Yeah, this is specific patient data of a female patient out of our clinics 30 years old so local Marseille and We reconstructed her Geometry Cortical and sub cortical, which is not that necessary. We are not using this information But the cortical is in from important and the connect them. Yeah, so this is a representation of the fiber tracks of this particular patient and Then this is a representation a lot matrix of the weights left hemisphere right hemisphere Into hemispheric and the lengths of this particular patient of the tracks of this particular patient this is experimental data and With this patient or a few general words 1% of the human population has epilepsy suffers from epilepsy a third of this 1% is is Pharmaceutical resistant so their only hope for relief is actually surgery and Pre-surgical Treatment or analysis is EG MEG. We do also MEG and fMRI and You basically take what you get in order to find out where is the epileptogenic zone that then shall be the target or one of the possible targets for surgical removal, yeah What is being done in our clinics also is SEG Stereotactic EEG which has been developed by Talarak and Banco. These are individual needles about that length Yeah, you have about 10 electrodes on each needle spaced multiple millimeters away from each other and It's a volume metric approach. You see them here So these are the needles that were introduced in the patient's brain. Yeah, so initially it was thought based on the analysis of EEG and MRI and fMRI where the clinicians were looking for seizure for lesions it was thought that it is mostly on the right hemisphere yeah, no, sorry on the left hemisphere and So they placed eight electrodes on the left hemisphere one two three four five and six and Two vertical and two other electrodes on the other hemisphere because it was suspected There may be also a part of the epileptogenic zone. Yeah, so each point represents an electrode and they are color-coded and These are the time series. So these are roughly This would so the dynamics here that would be roughly one minute 30 seconds something like that the time scale doesn't matter here so much Roughly one minute 10 time series for the brown electrode with the individual points and then other color other color other color So that is a setup. This what you observe that would be the resting state of the EEG typically these needles are being kept for two weeks in The brain and the patient has been monitored 24 hours out of 24. Yeah, here you see inter eclospikes Yeah, in the in the blue electrode here and Here you see a simple seizure But please note the simple seizure Starts on the other hemisphere on the right hemisphere where actually we have only two electrodes and Not here on the left hemisphere where the patient received eight electrodes so a simple seizure means it starts locally and it stays locally and a This year you have a zoom into the seizure dynamics and this very characteristic for siege development fast so spontaneous on set faster discharge Development of a spike wave complex determined by a big amplitude spike fast discharges than the slowing down Quiet zone and then discharge again. Yeah, so this is here. We are on the second range. Yeah from year to year That's roughly 10 seconds. Yeah, but it happens on the right hemisphere And here you have a complex partial seizure, which means actually the seizure starts here again on the right hemisphere Yeah Please see the when the amplitude gets high of the discharges. Yeah, I increase the size of the Sphere representing the location in the brain of the patient Yeah, and then it propagates to the other hemisphere and to these areas. So that's actually hippocampus and Tlamic structure you will see that in detail. Yeah, so this is actually the Propagation from one hemisphere to the other hemisphere. So we took this brain. We reconstructed it. We Implemented neural mass models that are capable of performing this type of seizure dynamics with the temple features that I described to you we implemented a Forward model of structural EEG. So what you see here is the Needles like in the patient. This is not the virtual brain. Yeah, the needles are Implemented at the same locations and they the network nodes from all of the patient are the brain regions Represented by the red dots. So this is what we did not see in the patient data What we see in the patient data is only what is measured by these needles the network nodes are in red And this is what we used for modeling The time series are here and here you see a spontaneous simple seizure and What you can do with a virtual brain approach and that is beneficial So this has been published in brain just recently and we will get something out in a journal of neuroscience with regard to the Coupling and the actual virtualization is of the interpatient is still in preparation But what we can do with regard to the mathematics is now we can perform mathematics because the models are lower dimensional For the epileptogenic zone we use the clinicians eye to identify us. What are the candidates that gives us settings of parameters where we can increase the epileptogenicity parameter in the model Yeah, we can perform a linear stability analysis Using the connect them of this particular patient plus the distribution of the parameters in order to Calculate the paths of propagation of seizure propagation as we observed it in the data That gives us a setting of epileptogenicity parameters that we can implement in the model and then we can Systematically scan and vary the other parameters that we will believe that are relevant. Yeah, this is what we are doing here So we have actually a low dimensional parameter set inspired by the clinical knowledge mathematical analysis that Determines and a low dimensional parameter set that we can computationally vary. These are the results So here you see the simple seizure propagation. It stays here and then for The zoom the fastest charges this without noise now the fastest charges and the slowing down Development of a spike wave complex and the termination of the simple seizure and here the complex seizure Yeah Starting on the right hemisphere. So a epileptogenicity values are higher on the right hemisphere and on the left Hemisphere it starts here on the right hemisphere hippocampus in red You see the activity of the neural mass model in TVB But this is what is measured through the forward solution in the s e g electrode Then it continues. It spreads to the thalamus. Please note that in the thalamus We have an augmentation of the activity which we did not see in the s e g because there were no Electrodes in there, but the mathematical analysis showed us actually that the propagation always in this particular case for this Distribution of a epileptogenicity values always has to go through the thalamus, which we did not before know before that from the thalamus it recruits a left hippocampus and Goes to the temporal lobe to the left temporal lobe fast discharges here and basically then terminates Initially the mathematical analysis showed us that in order we will never be able to get this propagation here deterministically, but with the simulations of Noise it turned out actually in the presence of noise the order flips of how the individual areas are being Recruited and this is a reproducible the underlying mathematical mechanism for this We don't understand yet fully, but this is what we observed in the simulations. So here once again in the video it starts on The right hemisphere Please note here how it increases the activity Brown areas then it travels through the thalamus increased activity and recruits on the left hemisphere Paribocampus and Temporal lobe again dynamically represented Scaling up the size of the individual red blobs in the other colors you have the se genitals So this is what we're doing Initially the patient has not been considered for surgery because the epileptogenic zone is on both hemispheres So that's an immediate stop for surgery now There are renegotiations with the clinicians we see if we can find different avenues Etc at least to stop the seizure from propagation, but again that is a vision for the future Though this is what we're doing working together with our clinical colleagues. So in summary The vision is to develop individualizable Simulators on this macroscopic the large-scale brain network level of organization to ask questions that are appropriate to ask on this level of organization namely brain connectivity to reproduce Invasive and non-invasive near imaging data in a realistic fashion So that requires all the near informatics efforts to put them together in order to have an immediately usable Yeah, open source platform for simulation available that allows us basically to vary in pathologies parameters that are linked to this macroscopic level and that's typically connectivity Yeah, and as I showed you in the beginning many pathologies have at least a connectivity component that we'd like to address here Many people are involved in this. These are our funding agencies that have helped us to develop At least different parts of the virtual brain platform and people I would like to highlight that are contributing heavily to this is of course Randy Gustavo, Petra, and this is my team and the clinical team that is working with us on This project. Thank you very much Thank you On one of your slides you were showing I think Some kind of forward model. I'm not sure whether I understood it You showed this model wave of parameters and then you create data From which you create a connectivity matrix and this connectivity matrix you compare with the reconnectivity matrix And then I think the idea was to optimize the parameters in your model to fit the the real data So I was wondering how do you? Handle the problem that you can run in some kind of local optimum when you try to optimize this Parameters in particular when it comes to clinical applications So parameter optimization is Not the focus of this here because that is part of the outside analysis That was the one slide where I showed you how it has been done with regard to the resting state And was actually quite critical with regard to this optimization because the functional connectivity is Kind of questionable that depending on how what metric what measure you choose for the functional connectivity There are many assumptions behind that so I'd be Very cautious with regard to the optimization because even the metric that we use here I would look at it Very carefully. Yes, so we have not invested much effort at the moment with regard to the Optimization of this. Yeah, what we are doing what we have Pointed this out because it has been done in some studies in order to find an optimal operating point and there With regards to optimization what has been done until then is a greedy search number one and Using many different initial conditions typically a thousand initial conditions in the parameter space But more sophisticated aspects or approaches have not been performed so far what we have focused upon is And because you asked with regard to clinical approaches is to take an approach where we Perform an informed parameter Search where we perform the simulations for different parameter settings But in a low-dimensional parameter space as I showed you with the epileptic patient that we perform in initial mathematical analysis using all expert eye clinical knowledge like the Fabrice Patelme our Head of epilepsy. He told us basically we would identify these areas as the epileptogenic zone this we took as a starting Point then we performed the linear stability analysis and identified all the different paths that the system can take Yeah, and then we had a reduced set of parameters that we then computationally sweep out perform The simulations yeah, and then it depends again on what metric you use effectively to represent Propagation of an epileptic seizure. That's non-trivial. Also. Do you look at signatures of synchronization, etc, etc? so I'm actually very conscious with regard to Optimization because what do you optimize when you look at so complex phenomena? Yeah Sorry to say Kind of complicated answer, but it is a very complicated problem. Yeah, so this is a probably a related question that goes to the question of stability in large nonlinear dynamical systems, so I wonder with all of these Weight matrices that you get from your connect terms and so on Whether you have any sense of what it requires to keep your systems bounded and whether there's anything about the way that you build the model which addresses this point maybe also comment on the Possible function of instabilities Yeah Can just for clarification when you say to keep the system bounded. Do you mean? Algorithmically bounded so to say that the algorithms converge or bounded in order not to Explore go away from an unstable fixed point dynamically bounded dynamically bounded. Okay, so the question is when we have so many parameters neural mass models we build the network and We have no idea Where to start with the different parameters, how can we? Make sure that our starting point is not somewhere in parameter space where the system basically Explodes so what we are doing is the default settings of it depends a little on What the task is and so far much of the work is focused on resting state conditions Yeah, so new the approach has been take the new mass models in The default settings all of them have an equilibrium point and then they differ if they are able to show limit cycle oscillations Etc. Etc. But you start at the equilibrium point and then Connector connectivity is at zero C equals zero and the first parameter You start increasing as you keep the topology of the connectum Invariant and then you start increasing the scaling the scalar scaling of the connectum And you guide the system through a series of bifurcations Purely through the connectivity So you do not touch the parameter in the neural mass models unless of course you have questions about Distributions of excitability or epileptogenicity as we had with the epileptic patient But with the resting state we kept all of them invariant We have not used any automatic method we have worked very close With the empirists together so it's close to the experimental eye. Yes. Thank you