# The Keith Worsley workshop on Computational Modeling of Brain Dynamics: from stochastic models to Neuroimages (09w5092)

## Organizers

Viktor Jirsa (Theoretical Neuroscience Group)

Pedro A. Valdés-Sosa (Cuban Neuroscience Center)

Keith Worsley (McGill University)

## Objectives

We are at a critical stage in understanding the neural underpinning of human cognitive processes with a sharp contradiction between the enormous amounts of data gathered by available neuroimaging technologies and the relatively low level of application of theoretical models to explain in detail the observed phenomena. The objective of this workshop is to bring together leading experts of the Human Brain Mapping Project together with computational neuroscientists, mathematicians and statisticians in order to assess the current state of database construction, neural modeling, numerical methods, computational technologies and statistical procedures that could bridge the gap between existing theory and the explanation of individually recorded brain images. We will emphasize the interpretation of data obtained from the human electroencephalogram (EEG) and functional magnetic resonance imaging (MRI), especially the understanding of oscillatory activity recorded in concurrent EEG-fMRI experiments. We hope to create links between several lines of work that have been developing in isolation and that are apparently ready to cross-fertilize. In fact if the workshop is approved the detailed questions enumerated below could be distributed and work advanced previous to the workshop. During the workshop the insights provided and collaborations that would be enhanced would have a positive impact in future research into normal brain function and its alterations in neuropsychiatric disorders as well as stimulating new areas of work in applied mathematics, statistics and biophysics. An additional objective would be to place an overview of the workshop in a high impact factor journal such as NeuroImage or Human Brain Mapping possibly accompanied by a selection of requested papers.

We propose to dedicate sessions successively to review and discuss the following areas:

1. Neural Mass Modeling (Day 1): The field of mesoscopic neural mass modeling based has been vigorously developed [1]. Currently local models formulated in terms of stochastic ordinary differential equations [2;2;3] are able to simulate normal and pathological EEG signals and have provided n insight into the nonlinear dynamics of the brain. More recently these models have been extended to global models based on stochastic partial differential equations [4-6]. The main difficulties to apply this modeling to actual data until recently has been: i) the lack of specific data for a given subject regarding cortical morphology, brain connectivity , and head volume conductor properties; ii) Limitations in numerical methods for the simulation and estimation of stochastic ordinary and partial differential equations, iii) Paucity of statistical methods that can adequately address the huge amounts of data provided by neuoroimages. More specifically in this session we will consider :

a. [7]An overview of the basic physiology and results of neural mass modeling: (Freeman[3], Lopes da Silva [2]

b. The current state and limitations of local models: Deco [8], Faugeras, Robinson [9], Suffcynzki and Wendling [10].

c. The current state and limitations of global models: Breakspear [11], Jirsa, Nunez [6], Wright [12].

d. Stochastic characterization of states and bifurcations of nonlinear local and global models: Faugeras , Harrison [13], Wennekers [14].

e. The basic information about brain morphology and connectivity, head volume conductor properties, population characteristics of hemodynamic and EEG characteristics that should be provided by the Human Brain Mapping initiative.

2. Structural constraints on brain dynamics provided by the Human Brain Mapping Project (Day 2): Over the past decade a wealth of information has been acquired and integrated into publicly available databases about the detailed cyto-architecture [15], gross brain morphology [16] and connectivity [17] of the human brain. This can provide the information that has been lacking for detailed neural modeling. New questions must be addressed and combined functional/morphological information gathered. More specifically in this session we will consider :

a. Current state of anatomical databases: Evans [18], ,Zilles [19],

b. General principles of brain connectivity, relevance for neural modeling:, Hilgetag [20;21] , Kotter [22], Sporns [21], Amunts [23].

c. In vivo determination of head volume conductor parameters and connectivity measures: Valdes-Hernandez [24].

3. Integration and estimation of neural stochastic models: In this session recent advances in the integration of stochastic differential equations will be examined. Particular emphasis will be places on the use of exponential integrators in order to preserve the qualitative dynamics of continuous neural mass models when discretized. Emphasis will also be placed on filtering and maximum likelihood estimation. More specifically in this session we will consider :

a. An Overview on bridging dynamical system and nonlinear time series theory: Ozaki .[25-27]

b. Simulation and estimation of ordinary stochastic differential equations, differential algebraic equations , and delay equations.: Jimenez [28;29], Burrage [30],Biscay [28;31], Roy [32].

c. Integration of stochastic partial differential equations: Berland [33].

4. Large scale simulations of neural networks (Day3): In this session we shall look at the computational issues of large and medium scale modeling of neural masses with emphasis on methods for producing simulations that can be checked against experimental results. This would be in themorning and the afternoon would be dedicated to group discussions and a walkabout the BIRS area.

a. Overview of large scale modeling, what exhaustive modeling can tell us aout neural masses: Markram [34].

b. Medium scale models: Deco [8], Horwitz [35].

5. Statistical inference on Brain images based on neural modeling (Day 4): In this session we

shall examine the current state and limitations of Statistical Parametric Mapping (SPM) of Neuroimages. The use of Bayesian state space models shall be examined in detail as well as procedures to deal with p much larger than n (p=numbr of variables, n=number of observations).

a. Overview of inference for statistical images: Worsley [36;37], Friston [38].

b. SPM of EEG/ERP models: David [38], Demiralp [39], Moran, Sotero [40].

c. SPM modeling functional images: Trujillo [40-42], Uludag [43].

d. SPM models for joint EEG/fMRI recordings: Babajani [44], Riera [45], Valdes[22;25;46]

6. Wrap up (Day 5): Overall discussion of issues, planning of collaborations and of publications.

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