Neural masses and fields in dynamic causal modeling

Abstract

Dynamic causal modeling (DCM) provides a framework for the analysis of effective connectivity among neuronal subpopulations that subtend invasive (electrocorticograms and local field potentials) and non-invasive (electroencephalography and magnetoencephalography) electrophysiological responses. This paper reviews the suite of neuronal population models including neural masses, fields and conductance-based models that are used in DCM. These models are expressed in terms of sets of differential equations that allow one to model the synaptic underpinnings of connectivity. We describe early developments using neural mass models, where convolution-based dynamics are used to generate responses in laminar-specific populations of excitatory and inhibitory cells. We show that these models, though resting on only two simple transforms, can recapitulate the characteristics of both evoked and spectral responses observed empirically. Using an identical neuronal architecture, we show that a set of conductance based models-that consider the dynamics of specific ion-channels-present a richer space of responses; owing to non-linear interactions between conductances and membrane potentials. We propose that conductance-based models may be more appropriate when spectra present with multiple resonances. Finally, we outline a third class of models, where each neuronal subpopulation is treated as a field; in other words, as a manifold on the cortical surface. By explicitly accounting for the spatial propagation of cortical activity through partial differential equations (PDEs), we show that the topology of connectivity-through local lateral interactions among cortical layers-may be inferred, even in the absence of spatially resolved data. We also show that these models allow for a detailed analysis of structure-function relationships in the cortex. Our review highlights the relationship among these models and how the hypothesis asked of empirical data suggests an appropriate model class.

Neural mass model-based tracking of anesthetic brain states

“…The JR neural mass model (Jansen & Rit, 1995) of population activity in cerebral cortex, or modifications thereof, forms the basis of many current approaches to infer underlying physiological variables from sparsely sampled electrophysiological recordings (Wendling et al, 2002;Moran et al, 2013;Chong et al, 2011;Postoyan et al, 2012;Chong et al, 2012aChong et al, ,b, 2015Freestone et al, 2011Freestone et al, , 2013Freestone et al, , 2014. This combined with the simplicity of the JR model makes it a suitable first choice in the search for the simplest neural mass model that is both accurate, informative and efficient enough for clinical application in anesthesia.…”

“…The main idea behind these approaches is that different regions of parameter space of neural mass models describe different types of state dynamics of these models, such as limit cycles and fixed points, which in turn result in different types of modelled EEG amplitude spectra that can be related to real EEG data and spectra (Freestone et al, 2013; 25 Moran et al, 2013). Methods that estimate the parameters of these neural mass models using real EEG data can then be used to infer and track key physiological variables, such as post-synaptic potential (PSP) amplitudes and rate constants, and these estimates in turn can be used to determine the current brain state (e.g.…”

“…Methods that estimate the parameters of these neural mass models using real EEG data can then be used to infer and track key physiological variables, such as post-synaptic potential (PSP) amplitudes and rate constants, and these estimates in turn can be used to determine the current brain state (e.g. awake, anesthetised, asleep, or seizure) based on their relationship to the EEG signal dynamics and amplitude spectra (Freestone et al, 2013;Moran et al, 2013;Kuhlmann et al, 2015a).…”

“…Various approaches for parameter estimation of neural mass models have been developed (Wendling et al, 2002;Moran et al, 2013;Chong et al, 2011;Postoyan et al, 2012;Chong et al, 2012aChong et al, ,b, 2015Freestone et al, 2011Freestone et al, , 2013Freestone et al, , 2014. Given that neural mass models are generally nonlinear and related noise sources can be considered to be Gaussian white noise (Liley et al, 2002;Nunez & Srinivasan, 2006), this paper presents the application of the unscented Kalman filter (UKF) to state and parameter estimation of a neural mass model of population activity in 35 cerebral cortex.…”

Dynamic causal modelling of seizure activity in a rat model

“…Dynamic causal models allow one to predict observed electrophysiological activity (in our case spectral density) in terms of electromagnetic sources that comprise coupled neuronal populations, driven by endogenous neuronal activity (Moran et al, 2009(Moran et al, , 2011a. These models are equipped with parameters encoding intrinsic connection strengths, synaptic rate constants and the spectral form of endogenous (afferent) input: for a more detailed discussion of the models see (Moran et al, 2013). By epoching electrophysiological data around the point of seizure onset, one can effectively track the trajectory of synaptic parameters that best explains epoch by epoch changes in spectral density during seizure onset.…”