Fokker-Planck dynamics of macroscopic cortical activity as measured with MEG
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1
VU University Amsterdam, Netherlands
Macroscopic electrical activity emerging from human cortex is known to be involved in several cognitive and behavioral processes. Currently there is no consensus however, on its precise role. Understanding the dynamical principles underlying the macroscopic patterning of brain activity is an important aspect of research on the neuronal underpinnings of cognition and behavior. In this study we investigate the use of Fokker-Planck equations to capture the dynamics of EEG/MEG recordings. A Fokker-Planck equation describes the time-evolution of the probability density of the solution to a stochastic differential equation. It contains a deterministic term (drift) and a stochastic term (diffusion) and the resulting dynamics is a result of the interplay between drift and diffusion. Although Fokker-Planck equations have been fitted to time-series of several complex systems, the statistical issues are not always dealt with in a correct way. Moreover, their application to neuroscientific datasets is limited to a handful of studies [1]. In this study [2] we discuss three important issues that arise when estimating drift and diffusion parameters from a given time-series and propose methodology to deal with these issues. Moreover, we apply the proposed methodology to several MEG experiments. First, the construction of consistent estimators provides a challenge because we observe the continuous-time process only at discrete time points. This finite-time effect becomes an issue especially when the sampling frequency is low. We adopt the method proposed in [3] which yields consistent estimators irrespective of the sampling frequency. Secondly, we propose a strategy for model verification by 
using appropriate residuals. And finally, the asymptotic 
theory in [3] is adapted to provide confidence intervals for 
the estimated model parameters.
References
1. Prusseit J, Lehnertz K. (2007) Stochastic qualifiers of epileptic brain dynamics. PRL 98, 138103.
2. Hindriks R, Bijma F, van der Vaart AW. Data-driven Fokker-Planck models of macroscopic neuronal activity. (in preparation).
3. Bibby BM, Sorensen M. (1997) Martingale estimation functions for discretely observed diffusion processes. Bernoulli 1(1/2), 017-039.
Conference:
Biomag 2010 - 17th International Conference on Biomagnetism , Dubrovnik, Croatia, 28 Mar - 1 Apr, 2010.
Presentation Type:
Poster Presentation
Topic:
Signal proccessing
Citation:
Hindriks
R,
Bijma
F and
Vaart
AV
(2010). Fokker-Planck dynamics of macroscopic cortical activity as measured with MEG.
Front. Neurosci.
Conference Abstract:
Biomag 2010 - 17th International Conference on Biomagnetism .
doi: 10.3389/conf.fnins.2010.06.00126
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Received:
24 Mar 2010;
Published Online:
24 Mar 2010.
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Correspondence:
Rikkert Hindriks, VU University Amsterdam, Amsterdam, Netherlands, hindriks@few.vu.nl