Statistical decision theory and multiscale analyses of human brain data

Highlights

• Combinations of compartmental and mean field models needed in the Big Data era.

• Mathematical proof of a multiscale approach for explaining M/EEG data.

• M/EEG data can reveal laminar differences in neural dynamics.

Abstract

Background

In the era of Big Data, large scale electrophysiological data from animal and human studies are abundant. These data contain information at multiple spatiotemporal scales. However, current approaches for the analysis of electrophysiological data often focus on a single spatiotemporal scale only.

New method

We discuss a multiscale approach for the analysis of electrophysiological data. This is based on combining neural models that describe brain data at different scales. It allows us to make laminar-specific inferences about neurobiological properties of cortical sources using non invasive human electrophysiology data.

Results

We provide a mathematical proof of this approach using statistical decision theory. We also consider its extensions to brain imaging studies including data from the same subjects performing different tasks. As an illustration, we show that changes in gamma oscillations between different people might originate from differences in recurrent connection strengths of inhibitory interneurons in layers 5/6.

Comparison with existing methods

This is a new approach that follows up on our recent work. It is different from other approaches where the scale of spatiotemporal dynamics is fixed.

Conclusions

We discuss a multiscale approach for the analysis of human MEG data. This uses a neural mass model that includes constraints informed by a compartmental model. This has two advantages. First, it allows us to find differences in cortical laminar dynamics and understand neurobiological properties like neuromodulation, excitation to inhibition balance etc. using non invasive data. Second, it allows us to validate macroscale models by exploiting animal data.

Introduction

Recent developments in brain recording techniques allow one to record animal brain data with high spatiotemporal resolution (Jun et al., 2017). At the same time, the ability to collect human brain data from large numbers of subjects have revolutionised the study of neurological diseases and disorders (Braund et al., 2018; Williams et al., 2011). Thus, we can now study details at the scale of a local cortical circuit using animal models and describe differences between very large numbers of individuals at the macroscopic scale with non-invasive human electrophysiology. These developments suggest the need to develop multiscale approaches. These will allow us to connect animal and human models. So far, approaches for the analysis of brain data contain information at a single spatiotemporal scale only. We here discuss a multiscale approach for brain imaging data analysis. This is based on combining neural models that describe brain data at different spatial scales.

We focus on a neural mass model that can explain both animal data obtained with thin laminar probes and human MEG data. Neural masses are biophysical models describing neural population responses where ensemble activity is considered as a point process. For a general introduction to these and similar models, see (Deco et al., 2008; Moran et al., 2013). This and other nomenclature used below are defined in Table 1. Following our earlier work (Pinotsis et al., 2017), we provide a mathematical proof that the neural mass model makes similar predictions to a microscopic, compartmental model. This is based on statistical decision theory (Berger, 2013) and shows that both models can be thought of as rules belonging to the same equivalence class. We show that a Bayesian observer could not distinguish between the data predicted separately by each model. Alternatively, if both models are fitted to the same data using Bayesian inference then these fits will have the same error. This suggests the similarity of their predictions.

As an illustration, we considered laminar differences in the excitation to inhibition balance (E–I) in human MEG data reported in (Schwarzkopf et al., 2012). We asked whether cortical function changes at various depths, and focus on differences in the (E–I) balance relevant to both pathophysiology (Chen et al., 2003) and information processing in the brain (Auksztulewicz and Friston, 2015; Friston et al., 2015a; Pinotsis et al., 2014). We find that differences in the E–I balance are expressed in the recurrent connection strengths of inhibitory interneurons in layers 5/6. Although MEG does not provide direct access to laminar data, the use of a neural mass model that makes laminar predictions allowed us to disclose details about cortical function that would otherwise be accessible only by using invasive recordings. In (Pinotsis et al., 2013a,b), we analysed the same dataset using a neural field model. Here, we used a neural mass model instead. Neural masses are a limiting case of neural fields when intrinsic delays on the cortical manifold are neglected, see also Table 1. We did not use a field model because it does not have the same parameters as the compartmental model considered below (see Lemma 1 in the Theory and Calculations section).

In (Pinotsis et al., 2017), we analysed data from laminar electrodes recorded from a single subject. Compared to that earlier work, our current paper includes two new contributions: the analysis of non invasive data and also of data from multiple subjects. Here we analysed MEG data using a hierarchical Bayesian approach (Parametric Empirical Bayes ; PEB) that downweighs neural model parameter estimates from subjects with less reliable data. The neural models used to explain invasive vs non invasive data are different. Although the neural circuitry is the same, the neural model that explains invasive data outputs responses at different depths, while the model that explains non invasive data sums responses across depths. In our earlier work, laminar predictions were fitted to separate electrode tips. These recorded neural activity from superficial and deep cortical layers separately (cf. Figure 7 in Pinotsis et al., 2017). These recordings corresponded to the outputs of neural populations occupying different cortical layers. Here, we used MEG data. Model fitting entailed summing up output responses across all layers. The best fit was achieved via a joint optimization of different weights with which different populations contribute to the MEG signal as well as observation (lead field) parameters of the virtual electrode. Also, the analysis presented here focuses on variability in the structure and function of neural sources between different people that might account for the variability in observed brain responses.