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State space models and their spectral decomposition in dynamic causal modeling

from Part I - State space methods for neural data

Published online by Cambridge University Press:  05 October 2015

By
R. Moran
Edited by
Zhe Chen
R. Moran
Affiliation:
Virginia Tech Carilion Research Institute
Zhe Chen
Affiliation:
New York University
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Summary

Introduction

Analysis of noninvasive electrophysiological time series (for example, using electroencephalography, EEG) typically culminates in the report of certain data features. These features, namely, event related potentials and spectral compositions have together provided a rich characterization of observable brain dynamics: the N100, the mismatch negativity, the P300, the alpha wave. But what do these features actually represent? What unobservable neural processes generate these different types of features?

Interestingly the field of functional magnetic resonance imaging (fMRI) has had to grapple with a similar type of question. There, equipped with a very indirect, blood-oxygen-level dependent (BOLD) measure of neural function, scientists have used animal preparations and conjoint electrophysiology to show that BOLD responses reflect synaptic input with a particular transmission preference for fast-frequency signals (Logothetis et al. 2001). So if electrophysiological responses serve as “ground truth” for fMRI, what serves as “ground truth” for EEG? Biophysically, EEG represents the effects of summed currents around a population (hundreds of thousands) of active neurons. When measured at the scalp, EEG is specifically thought to reflect the average depolarization of pyramidal cells – due to their regularly oriented dendrites tangential to the cortical surface. So the question then is – from where do these currents arise? Dynamic causal models (DCM) (David & Friston 2003; Kiebel et al. 2008; Moran et al. 2007, 2008) formalize this question using a state space representation of depolarizing and hyperpolarizing current inputs. These states are biophysical, time-dependent descriptions of what is likely occurring in a population of interacting neurons. The models are supposed to embody “ground truth” – or in other words represent a plausible and empirically informed set of operations that our neural wet-ware performs.

In animal studies, cellular physiological investigations such as microdialysis, singlecell or patch-clamp recordings can inform macroscopic electrophysiological measurements of population activity (Fellous et al. 2001). These types of experiments thus link low-level synaptic activity and the emergent dynamics of the cell population. In humans, these experiments are usually not feasible since, with rare exceptions (e.g., pre-surgical evaluation in epilepsy patients), experimental measurements must be noninvasive. One goal of DCM for EEG is to enable inference about low-level physiological processes using noninvasive recordings from the human brain.

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Advanced State Space Methods for Neural and Clinical Data , pp. 114 - 136
Publisher: Cambridge University Press
Print publication year: 2015

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