+ 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.
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