Abstract
Background. Datasets consisting of synthetic neural data generated with quantifiable and controlled parameters are a valuable asset in the process of testing and validating directed functional connectivity metrics. Considering the recent debate in the neuroimaging community concerning the use of these metrics for fMRI data, synthetic datasets that emulate the BOLD signal dynamics have played a central role by supporting claims that argue in favor or against certain choices. Generative models often used in studies that simulate neuronal activity, with the aim of gaining insight into specific brain regions and functions, have different requirements from the generative models for benchmarking datasets. Even though the latter must be realistic, there is a tradeoff between realism and computational demand that needs to be contemplated and simulations that efficiently mimic the real behavior of single neurons or neuronal populations are preferred, instead of more cumbersome and marginally precise ones.Methods. This work explores how simple generative models are able to produce neuronal datasets, for benchmarking purposes, that reflect the simulated effective connectivity and, how these can be used to obtain synthetic recordings of EEG and fMRI BOLD signals. The generative models covered here are AR processes, neural mass models consisting of linear and nonlinear stochastic differential equations and populations with thousands of spiking units. Forward models for EEG consist in the simple three-shell head model while the fMRI BOLD signal is modeled with the Balloon-Windkessel model or by convolution with a hemodynamic response function.Results. The simulated datasets are tested for causality with the original spectral formulation for Granger causality. Modeled effective connectivity can be detected in the generated data for varying connection strengths and interaction delays.Discussion. All generative models produce synthetic neuronal data with detectable causal effects although the relation between modeled and detected causality varies and less biophysically realistic models offer more control in causal relations such as modeled strength and frequency location.
Highlights
The field of brain research that studies connectivity relies in an ever evolving array of methods that aim at finding directed or undirected connectivity links from recorded neuronal datasets which pose different challenges such as having nonlinear relations, non-stationary dynamics, low signal-to-noise ratio (SNR), linear mixes or slow dynamics
Most studies that introduce or discuss connectivity metrics use real and simulated datasets for demonstration and validity purposes on a controlled environment. These simulated datasets are obtained through generative models that simulate the conception of neuronal activity, like local field potentials (LFPs), with a certain degree of realism and can be followed by forward biophysical modeling where LFPs are transformed into other neuronal recording datasets like electroencephalography (EEG), magnetoencephalography or functional magnetic resonance imaging blood-oxygen-level dependent (BOLD) signals, for example
As far as directed functional connectivity is concerned, Granger causality (GC) based metrics have been in the center of several studies that discussed their plausibility in the analysis of functional magnetic resonance imaging (fMRI) BOLD datasets due to the inherent low SNR, slow dynamics compared to neuronal activity and confounding effects due to variable vascular latencies across brain regions (Deshpande, Sathian & Hu, 2009; Smith et al, 2010; Valdes-Sosa et al, 2011; Seth, Chorley & Barnett, 2013; Rodrigues & Andrade, 2014)
Summary
The field of brain research that studies connectivity relies in an ever evolving array of methods that aim at finding directed or undirected connectivity links from recorded neuronal datasets which pose different challenges such as having nonlinear relations, non-stationary dynamics, low signal-to-noise ratio (SNR), linear mixes or slow dynamics. As far as directed functional connectivity is concerned, Granger causality (GC) based metrics have been in the center of several studies that discussed their plausibility in the analysis of fMRI BOLD datasets due to the inherent low SNR, slow dynamics compared to neuronal activity and confounding effects due to variable vascular latencies across brain regions (Deshpande, Sathian & Hu, 2009; Smith et al, 2010; Valdes-Sosa et al, 2011; Seth, Chorley & Barnett, 2013; Rodrigues & Andrade, 2014) Most of these studies used simulated datasets to support their claims with generative models such as networks of ‘on–off ’ neurons (Smith et al, 2010), multivariate vector autoregressive (MVAR) processes with real LFPs (Deshpande, Sathian & Hu, 2009; Rodrigues & Andrade, 2014) and columns of thousands of spiking units (Seth, Chorley & Barnett, 2013) and BOLD forward models consisting of linear operations or more biophysically realistic models. All generative models produce synthetic neuronal data with detectable causal effects the relation between modeled and detected causality varies and less biophysically realistic models offer more control in causal relations such as modeled strength and frequency location
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