+ Can diffusion MRI determine structural connectivity?
    Roland Henry

We aim to highlight issues involved in inferring brain structural connectivity from diffusion MRI data. At the outset fundamental problems arise from the mismatch in scale of in-vivo diffusion MRI and axons; to wit diffusion MRI is a relatively coarse pixilated sampling of the underlying axonal structure. Given this basic limitation, a number of assumptions must be made to arrive at models of structural connectivity, and these assumptions deeply affect our ability to determine connectivity. In summary, technical and methodological issues including modeling the diffusion signal and experimental noise significantly affect the determination of structural connectivity by diffusion MRI and dictate the types of questions that can be answered with this method.

+ What can diffusion MRI really tell us about microstructure?
    Saad Jbabdi

The last few years have witnessed an explosion of studies reporting structural variations in the brain white matter that are related to behaviour or disease. Diffusion MRI is playing a leading role, since it is sensitive to tissue biophysical and geometrical properties. For example, changes in diffusion anisotropy are generally attributed to changes in myelination, calibre or packing of white matter axons, amongst other factors. However, diffusion-derived measures are not very specific, rendering the interpretation of changes in diffusivity far from being straightforward. Little effort has been made in trying to isolate the effects of the various tissue microstructural features on water diffusion. We will present experimental relaxometry and diffusion MR data, as well as simulations supporting the idea that myelin might not be related to diffusion anisotropy in a simple way, as most researchers have assumed in the last years. These data urge us to develop more accurate and realistic models for intra-voxel diffusion, and support the need for combining different sources of data to better characterise brain microstructure in-vivo.

+ A methodological approach to MRI tractography
    Xavier Gigandet

Diffusion MRI, providing information about the size and orientation of the multiple compartments lying inside an imaging voxel, has proved to be a powerful tool to probe in vivo and non-invasively the tissue microstructure. From the widely used Diffusion Tensor Imaging (DTI) to higher angular resolution MRI methodologies such as Diffusion Spectrum Imaging (DSI), diffusion measurements in the brain white matter have given a new breath to fiber tract architecture studies, thus opening a window on global brain anatomical connectivity. However, from the beginning of the development of MRI tractography we are faced with many challenges. First, the resolution of diffusion MR acquisitions is currently limited to about 2mm, several orders of magnitude bigger than the size of axons. Next, it is very difficult to obtain a gold standard against which we can test the tractography methods. Furthermore, whilst the current techniques allow very interesting individual studies, there is still a lot of work before we can perform group comparison studies. In this presentation, we will review and discuss some of the proposed solutions to tackle these problems. More particularly, we will present a method to normalize the connection matrices obtained by tractography. Then, we will focus on the creation of a gold standard for tractography based on tracing studies performed on a macaque monkey.

+ Network science and the brain: From structural connections to brain dynamics
    Olaf Sporns

Network science investigates the structure and dynamics of complex networks, seeking to uncover principles of network organization across a variety of scientific disciplines, ranging from the physical to the social sciences. In neuroscience, a central theoretical issue concerns the relationship between structural brain networks and the neural dynamics they support across multiple time scales. I will discuss two recent studies that apply network science approaches to the structure and dynamics of cerebral cortex. First, a large-scale simulation study of macaque cortical networks aimed at the relation between structural networks and functional networks, and at how fast time-scale dynamics can give rise to dynamical patterns at slower time scales. Second, a detailed analysis of structural brain networks of human cortex performed in collaboration with Patric Hagmann demonstrates the existence of a densely interconnected core in posterior medial cortex, as well as strong correlations between structural and resting-state functional connections across the entire human brain. These studies enable us to build detailed forward models of human brain dynamics that are constrained by anatomical connections and physiology.

+ Exploring interhemispheric connections through a dynamical model of the neocortex
    Jorge Riera

In order to properly estimate effective connections among cerebral cortices from EEG data, we need to keep our mind on two important questions:
1. How do the rigid anatomical structures of the neocortex impact on the dynamics of neuronal networks?
2. Which are the physical principles underlying the relationship between the neuronal activity and the data?
To address these two issues, in this work we proposed a novel dynamic forward model for EEG data as well as a methodology based on filtering techniques to solve the corresponding inverse problem, i.e. to estimate the time course of synaptic inputs into the neocortex. The proposed inverse method, which can be obtained on either individual or group cortical surfaces, takes into consideration: a) the variability of the neocortex in terms of its shape and thickness (Lerch and Evans 2005, Lyttelton et al., 2007) and b) the cortical micro-circuitry as the crucial element determining the dynamics of the extracellular current sources (Riera et al., 2006, 2007). In such a formulation, large areas enclosing synchronously activated pyramidal cells (PC), especially the tufted layer V PCs which have apical trunks oriented in parallel and pointing perpendicularly to the cortical surface, are modeled from an electrotonic viewpoint with emphasis in layer distributed synaptic inputs. We used the proposed methodology to study inward and outward connections within the somatosensory cortex of Wistar rats, assuming the existence of interconnected basic units (i.e. the barrels). For that purpose, massively parallel microelectrode recordings [i.e. local field potentials (LFP)] were obtained concurrently with skull EEG data during the stimulation of the ipsi- and contra- lateral whiskers (10ms air-puffs, frequencies: 1Hz, stimulus durations 32s). A craniotomy of 2mm in diameter was performed on the barrel cortex of five Wistar rats (8 weeks). LFP recordings were obtained by using silicon-substrate probes (1D-shank, silicon dioxide/nitride insulation, 16 linearly arranged iridium electrodes) connected to a 50 KHz amplifier and a processing unit (PZ2/RZ2, TDT), with a stereotaxic system and a probe-stage both customized for in vivo experiment using small rodents. Skull EEG data were recorded using BrainVision amplifiers (32 channels) and used to estimate the superficial distributions of cortical synaptic inputs and extracellular current sources. We estimated the dynamics of the connection strength between both hemispheres by: a) evaluating the functional connectivity at the level of the estimated extracellular current sources and b) performing a correlation analysis among (estimated) inputs and (predicted) outputs to barrels in both ipsi and contra lateral hemispheres. We compared the results obtained by both approaches with the connectivity analysis performed locally from the LFPs.

+ Data-driven effective connectivity analysis in fMRI and MEG
    Alard Roebroeck

Since its introduction, effective connectivity has become one of the central concepts in the neuroimaging field, influencing both data analysis strategies and the nature of model formulation. Effective connectivity approaches have traditionally focused on a limited set of pre-specified regions of interest (ROIs), testing a causal model of the influences between them. This contrasts with functional connectivity approaches, which quantify correlation (or mutual information) between large arrays of data channels and do not require specification of a generative model. One of the tenets of ROI-based effective connectivity analysis is that it forces a researcher to be explicit about a generative anatomical model underlying cognitive task performance. One of its major drawbacks, however, is that omission of relevant areas can lead to spurious influences and misleading inference within preconceived models. This talk will discuss data-driven effective connectivity approaches that avoid the need for a restrictive structural ROIbased model, starting instead from whole brain data. Recent developments will be presented in Granger causality analysis and sparse autoregressive modeling of fMRI data that make the implementation of such a strategy possible. The talk and ensuing discussion will touch upon topics such as: Bias/variance trade-off, Model-comparison and overfitting, and multimodal strategies (i.e. incorporating E/MEG, diffusion tractography data). It would be interesting to discuss whether effective connectivity models can be defined that have an adjustable trade-off between hypothesis-based anatomical models and data-driven exploration. And, if so, where on this continuum the useful middle-ground is found between inference bias (inherent to strict models) on one hand and high estimation variance and overfitting (ensuing from overly explorative strategies) on the other.

+ Effects of anatomo-functional connectivity changes on simulated brain dynamics: A model-based study
    Nelson Trujillo-Barreto

The development of novel Neuroimaging techniques, as well as of new methods of analysis and models during the last two decades or so, has led to a breakthrough in the field of neuroscience. We can now answer with reliable accuracy to the question of where (spatial location) and when (timing) a neural event is generated. Nevertheless it was only recently that we were able to give the first steps to address the old and intriguing question of why (causation) these neural events are produced and give rise to more complex brain processes. A central problem in this respect is to determine the causal relationships (functional connectivity) between brain regions that form a given neural network in the activated brain. The models and methods of analysis developed to this end typically involve a huge number of unknown (connectivity) parameters, which make model identification a challenging task. To overcome this, the use of prior information or constraints during the estimation process becomes crucial. A tempting procedure is to incorporate anatomical connectivity priors to encourage functional connections between those areas that are anatomically connected, in pretty much the same way that source activations activations (in M/EEG source reconstruction for example) are constrained to anatomical regions where the probability of grey matter is significant. To explore this issue, we use a biophysical model of realistically interconnected neural mass models (NMMs) to study the type of activity that this model is able to generate and how this activity is affected by changes in the anatomical connections pattern used. Each NMM is used to model the activity within one voxel and is connected to other NMMs via short range connections (SRC) (connections between voxels of the same brain area) and long range connections (LRC) (connections between voxels of different brain areas). SRC are assumed to decay exponentially with distance between voxels while LRC are estimated from actual DWI recordings. We also explore how the activity generated by the model is affected by changes in other parameters of the network like the time delay and intensity (mean number of active synapses in the unit of time) of the connections.

+ Connectivity : Model free and generic bilinear approaches to detecting and classifying neuronal interactionsed
    Gary Green

Current important techniques for investigating connectivity, such as Dynamic Causal Modelling, make particular assumptions about model structure or about the parameters that should be used as a metric. Although techniques such as Bayesian model selection can help in selecting the most probable model, formal model comparison is difficult as differing model parameters contribute in complex ways to determining model performance. An associated problem is found in techniques such as the use of synchronisation indices where the use of specific observables also make assumptions about neuronal connectivity dynamics and interactions. We will argue that the use of measures of the local manifold shape of connected systems can be used as a model free approach to the detection and classification of network behaviour. We will also argue that an extension to this approach, which takes into account exogenous inputs or conditions, can be formulated as a generic bilinear system, or generalised DCS, where the underlying dimension or formulation of the system is not needed. In both cases, Bayesian methods can be exploited, but without the need for an assumed underlying model structure or combination of observables. Moreover, the gDCS approach allows a formal comparison of traditional DCMs. Examples from MEG data will be discussed.

+ Relating neural dynamics to functional and effective connectivity
    Barry Horwitz

At this workshop, I will discuss the neurobiological basis of functional and effective connectivity. This issue is particularly acute for fMRI-based measures of functional/effective connectivity, given the temporal and spatial limitations of the data. I will stress the importance of neuronal heterogeneity as a source of task-related changes in connectivity. We also will point out the need for caution in interpreting differences in connectivity between patient groups and normal subjects. I will illustrate these issues using a neurobiologically realistic computational model that can simultaneously simulate fMRI time series and neuronal activity in multiple, connected brain regions. Unlike the situation with experimental data, where the underlying pattern of connectivity and neuronal activity are largely unknown, in the model we know what each neuron is doing at all time points, and we know the full connectivity of each neuron. Thus, the model provides a testing ground for understanding how well fMRI functional and effective connectivity patterns are reflected in the underlying neurobiology. Some published references to this work are the following:
Horwitz, B., et al. Phil. Trans. Roy. Soc. Lond. B 360: 1093-1108, 2005.
Lee, L., Friston, K.J., Horwitz, B.: NeuroImage 30: 1243-1254, 2006.
Kim, J., Horwitz, B.: Magnetic Resonance Imaging 2008 Jan 9; [Epub ahead of print].
Marrelec, G., Kim, J., Doyon, J., Horwitz, B. Human Brain Mapp. (in press).

+ Phase amplitude coupling and the interaction between cortical inputs
    Kai J. Miller

Having recently validated our hypothesis of functional changes in a cortical spectral power law with local activity in human cortex, we move to the significance of this finding. Using a PCA based method on electrocorticographic recordings in humans, we were able to decouple this power law behavior from the classic α and β rhythms, revealing its presence at low frequencies. The projection of the dynamic spectrum to this power law, which we denote "χ" is able to capture the dynamics of specific finger movement in specific electrodes. We examined the relationship of changes in the amplitude of this power law to the phase of intrinsic low frequency rhythms. We will then demonstrate that χ couples to the phase of the beta rhythm (so called phase-amplitude coupling – PAC). During periods of movement, this PAC is less pronounced than during periods of rest. We show how a simple, small-scale, model of synaptic organization may provide intuition for the large scale phase-amplitude correlation we report. In this model: 1) χ reflects asynchronous summation of a large number of cortico-cortical inputs between pyramidal neurons. 2) Synchronous, sub-cortical or distant cortical, projections to pyramidal neurons are reflected in the β rhythms. The β rhythm constrains local computation, and this is the basis for the phase-amplitude coupling. During local computation, the amplitude of χ goes up, β goes down, and the PAC decreases.

+ Observing the observer: Meta-Bayesian models of learning and decision making
    Jean Daunizeau

In this paper, we describe a generic meta-Bayesian procedure (i.e., a Bayesian treatment of Bayesian predictions) for inferring the optimisation schemes used by subjects during learning and decision making. We start with the premise that subjects represent or infer the causes of their sensory inputs and optimise their behaviour on the basis of this inference. From a Bayesian perspective, the brain is an observer of its own sensory signals. In other words, subjects invert some forward or generative model of sensory inputs to represent the unobserved (hidden) causes of that input. Under ideal Bayesian assumptions, the quantities encoding these representations are defined uniquely, for any model the subject might be using. This means one can use measured (behavioural or physiological) responses to infer the most likely model employed by a subject. Furthermore, under rationality assumptions that subjects make optimal decisions on the basis of their (posterior) beliefs; one can evaluate the likelihood of observed choice or action-sequences, under different utility or loss-functions. This means that when we observe the observer (i.e., the brain), we can infer prior beliefs, implicit in a subject’s model, and their utility-functions from psychophysical or neurophysiological (e.g. neuroimaging) measures. This model selection induces a key distinction between the subject’s (perceptual) model, which predicts sensory signals and an experimenter’s (response) model, which predicts evoked responses or explicit actions. We illustrate the utility of this approach by applying it to reaction-time data from a simple cue-outcome associative learning task.

+ Linking cortical connectivity to attention and awareness
    John-Dylan Haynes

The degree to which cortical integration of information is required for conscious perception and attention is still a matter of debate. Here we provide evidence for the important role of cortical connectivity during tasks involving spatial attention and visual perception. We conducted a series of experiments that investigated cortical connectivity between the precise retinotopic representations of stimuli in various visual areas. Selective spatial attention is reflected in increased connectivity between the representations of multiple selected stimuli and decreased connectivity between unselected distractors. These changes in connectivity are present both within single retinotopic areas and between brain areas. In visual masking, the connectivity between remote regions in early and high-level visual cortex was significantly increased when stimuli were more visible. Taken together these findings suggest that both attention and awareness require intact large-scale connectivity within the visual system.

+ Transient cognitive dynamics: The brain modes competition
    Mikhail Rabinovich

The dynamical modeling of the temporal structure of cognitive processes is a key step for understanding cognition. Cognitive functions such as sequential learning, working memory and decision making in a changing environment cannot be understood using only the traditional view of brain dynamics based on computation with attractors, i.e., static or rhythmic brain activity. The execution of cognitive functions is a transient dynamical process. Any dynamical mechanism underlying cognitive processes has to be robust against noise, reproducible from experiment to experiment in similar environmental conditions and, at the same time, it has to be sensitive to changing internal and external information. We propose here a new dynamical object that can represent robust and reproducible transient brain dynamics. This object is a sequence of metastable cognitive states connected by transients according to cause-effect conditions. We also propose a new class of models for the analysis of transient dynamics with uncertainty, which can be applied for sequential decision making. We emphasize that many kind of the dynamical phenomena (stable transient) that would be nongeneric in an arbitrary complex dynamical system can become generic when constrained by a specificity of variables (like a positivity of the cognitive mode activity in our case). We also discuss the relationship of the cognitive network organization with the networks topology in the phase space (mutual connections of the metastable states, separatrixes, and attractors).

+ Cortical dynamics at rest: The role of fluctuations and delays
    Gustavo Deco

In this talk, we discuss the intrinsic structural and dynamical causes of brain's dynamics during rest. In particular, we focus on the role of stochastic fluctuations and temporal delays on the resting state neurodynamics. For that purpose, we perform an exhaustive dynamical and statistical analysis of a cortical system based on the anatomical connectivity matrix of one hemisphere obtained from the CoCoMac database. Anticorrelation patterns and slow 0.1 Hz oscillations of the related fMRI-BOLD signals can be explained as fluctuations driven explorations of the dynamics capabilities of the underlying network.

+ DEM: A variational treatment of dynamic systems
    Karl Friston

We present a variational treatment of dynamic models that furnishes the time-dependent conditional densities of a system's states and the time-independent densities of its parameters. These obtain by maximizing the variational free energy of the system with respect to the conditional densities. The ensuing free energy represents a lower-bound approximation to the models marginal likelihood or log-evidence required for model selection and averaging. This approach rests on formulating the optimization of free energy dynamically, in generalized co-ordinates of motion. The resulting scheme can be used for on-line Bayesian inversion of nonlinear dynamic causal models and eschews some limitations of existing approaches, such as Kalman and particle filtering. We refer to this approach as dynamic expectation maximization (DEM). Our proposal is that the brain uses exactly the same scheme to infer on the causes of its sensory inputs.

+ Some hidden physiology in naturalistic spike rasters
    Bruce Knight

It is very unusual for a vertebrate central nervous system to commit an information processing duty to a single cell. So reasonably we may think of a typical part of the brain as a collection of interconnected neuron subpopulations, which receive inputs, and issue outputs, and talk among themselves, through tracts of parallel nerve fibers. A central goal of this system is to generalize from diversity: to recognize an important pattern in diverse inputs and respond with strong activity on a specific output tract. In the design of such a system, clearly there could be major advantages if two different input sets, which shared the same pattern of relative input strengths but differed greatly in their absolute input levels, were both able to cleanly activate the same output tract. One suspects strong evolutionary pressures toward such design. Though neuron models of the broadly Hodgkin-Huxley type display highly nonlinear dynamics, nonetheless, remarkably, they include a subset of mathematical designs which fulfill the above demand. Such model neurons do this by yielding a time-varying firing rate which (for a large population) is a perfect copy of the time-varying synaptic input current which drives them. There are realistic neuron models which well approximate this behavior over a reasonably broad dynamic range. In rasters of spike responses to repeated naturalistic stimuli, such perfect copy neurons leave a hidden signature. Experimental rasters from some real cells reveal close to this signature, and yield neuron models with near perfect copy behavior which reasonably replicate the laboratory data.