A general spectral decomposition of causal influences applied to integrated information

Exploring complex and integrated information during sleep

The Integrated Information Theory is a theoretical framework that aims to elucidate the nature of consciousness by postulating that it emerges from the integration of information within a system, and that the degree of consciousness depends on the extent of information integration within the system. When consciousness is lost, the core complex of consciousness proposed by the Integrated Information Theory disintegrates, and Φ measures, which reflect the level of integrated information, are expected to diminish. This study examined the predictions of the Integrated Information Theory using the global brain network acquired via functional magnetic resonance imaging during various tasks and sleep. We discovered that the complex located within the frontoparietal network remained constant regardless of task content, while the regional distribution of the complex collapsed in the initial stages of sleep. Furthermore, Φ measures decreased as sleep progressed under limited analysis conditions. These findings align with predictions made by the Integrated Information Theory and support its postulates.

Emergence of Integrated Information at Macro Timescales in Real Neural Recordings

How a system generates conscious experience remains an elusive question. One approach towards answering this is to consider the information available in the system from the perspective of the system itself. Integrated information theory (IIT) proposes a measure to capture this integrated information (Φ). While Φ can be computed at any spatiotemporal scale, IIT posits that it be applied at the scale at which the measure is maximised. Importantly, Φ in conscious systems should emerge to be maximal not at the smallest spatiotemporal scale, but at some macro scale where system elements or timesteps are grouped into larger elements or timesteps. Emergence in this sense has been demonstrated in simple example systems composed of logic gates, but it remains unclear whether it occurs in real neural recordings which are generally continuous and noisy. Here we first utilise a computational model to confirm that Φ becomes maximal at the temporal scales underlying its generative mechanisms. Second, we search for emergence in local field potentials from the fly brain recorded during wakefulness and anaesthesia, finding that normalised Φ (wake/anaesthesia), but not raw Φ values, peaks at 5 ms. Lastly, we extend our model to investigate why raw Φ values themselves did not peak. This work extends the application of Φ to simple artificial systems consisting of logic gates towards searching for emergence of a macro spatiotemporal scale in real neural systems.

Partial Directed Coherence and the Vector Autoregressive Modelling Myth and a Caveat

Here we dispel the lingering myth that Partial Directed Coherence is a Vector Autoregressive (VAR) Modelling dependent concept. In fact, our examples show that it is spectral factorization that lies at its heart, for which VAR modelling is a mere, albeit very efficient and convenient, device. This applies to Granger Causality estimation procedures in general and also includes instantaneous Granger effects. Care, however, must be exercised for connectivity between multivariate data generated through nonminimum phase mechanisms as it may possibly be incorrectly captured.

Integrated information as a common signature of dynamical and information-processing complexity

The apparent dichotomy between information-processing and dynamical approaches to complexity science forces researchers to choose between two diverging sets of tools and explanations, creating conflict and often hindering scientific progress. Nonetheless, given the shared theoretical goals between both approaches, it is reasonable to conjecture the existence of underlying common signatures that capture interesting behavior in both dynamical and information-processing systems. Here, we argue that a pragmatic use of integrated information theory (IIT), originally conceived in theoretical neuroscience, can provide a potential unifying framework to study complexity in general multivariate systems. By leveraging metrics put forward by the integrated information decomposition framework, our results reveal that integrated information can effectively capture surprisingly heterogeneous signatures of complexity-including metastability and criticality in networks of coupled oscillators as well as distributed computation and emergent stable particles in cellular automata-without relying on idiosyncratic, ad hoc criteria. These results show how an agnostic use of IIT can provide important steps toward bridging the gap between informational and dynamical approaches to complex systems.

Extending the spectral decomposition of Granger causality to include instantaneous influences: application to the control mechanisms of heart rate variability

Assessing Granger causality (GC) intended as the influence, in terms of reduction of variance of surprise, that a driver variable exerts on a given target, requires a suitable treatment of 'instantaneous' effects, i.e. influences due to interactions whose time scale is much faster than the time resolution of the measurements, due to unobserved confounders or insufficient sampling rate that cannot be increased because the mechanism of generation of the variable is inherently slow (e.g. the heartbeat). We exploit a recently proposed framework for the estimation of causal influences in the spectral domain and include instantaneous interactions in the modelling, thus obtaining (i) a novel index of undirected instantaneous causality and (ii) a novel measure of GC including instantaneous effects. An effective procedure to speed up the optimization of parameters in this frame is also presented. After illustrating the proposed formalism in a theoretical example, we apply it to two datasets of cardiovascular and respiratory time series and compare the values obtained within the frequency bands of physiological interest by the proposed total measure of causality with those derived from the standard GC analysis. We find that the inclusion of instantaneous causality allows us to correctly disentangle the baroreflex mechanism from the effects related to cardiorespiratory interactions. Moreover, studying how controlling the respiratory rhythm acts on cardiovascular interactions, we document an increase of the direct (non-baroreflex mediated) influence of respiration on the heart rate in the respiratory frequency band when switching from spontaneous to paced breathing. This article is part of the theme issue 'Advanced computation in cardiovascular physiology: new challenges and opportunities'.

Frequency Domain Repercussions of Instantaneous Granger Causality

Using directed transfer function (DTF) and partial directed coherence (PDC) in the information version, this paper extends the theoretical framework to incorporate the instantaneous Granger causality (iGC) frequency domain description into a single unified perspective. We show that standard vector autoregressive models allow portraying iGC's repercussions associated with Granger connectivity, where interactions mediated without delay between time series can be easily detected.

Steady state evoked potential (SSEP) responses in the primary and secondary somatosensory cortices of anesthetized cats: Nonlinearity characterized by harmonic and intermodulation frequencies

When presented with an oscillatory sensory input at a particular frequency, F [Hz], neural systems respond with the corresponding frequency, f [Hz], and its multiples. When the input includes two frequencies (F1 and F2) and they are nonlinearly integrated in the system, responses at intermodulation frequencies (i.e., n1*f1+n2*f2 [Hz], where n1 and n2 are non-zero integers) emerge. Utilizing these properties, the steady state evoked potential (SSEP) paradigm allows us to characterize linear and nonlinear neural computation performed in cortical neurocircuitry. Here, we analyzed the steady state evoked local field potentials (LFPs) recorded from the primary (S1) and secondary (S2) somatosensory cortex of anesthetized cats (maintained with alfaxalone) while we presented slow (F1 = 23Hz) and fast (F2 = 200Hz) somatosensory vibration to the contralateral paw pads and digits. Over 9 experimental sessions, we recorded LFPs from N = 1620 and N = 1008 bipolar-referenced sites in S1 and S2 using electrode arrays. Power spectral analyses revealed strong responses at 1) the fundamental (f1, f2), 2) its harmonic, 3) the intermodulation frequencies, and 4) broadband frequencies (50-150Hz). To compare the computational architecture in S1 and S2, we employed simple computational modeling. Our modeling results necessitate nonlinear computation to explain SSEP in S2 more than S1. Combined with our current analysis of LFPs, our paradigm offers a rare opportunity to constrain the computational architecture of hierarchical organization of S1 and S2 and to reveal how a large-scale SSEP can emerge from local neural population activities.

Integrated information structure collapses with anesthetic loss of conscious arousal in Drosophila melanogaster

The physical basis of consciousness remains one of the most elusive concepts in current science. One influential conjecture is that consciousness is to do with some form of causality, measurable through information. The integrated information theory of consciousness (IIT) proposes that conscious experience, filled with rich and specific content, corresponds directly to a hierarchically organised, irreducible pattern of causal interactions; i.e. an integrated informational structure among elements of a system. Here, we tested this conjecture in a simple biological system (fruit flies), estimating the information structure of the system during wakefulness and general anesthesia. Consistent with this conjecture, we found that integrated interactions among populations of neurons during wakefulness collapsed to isolated clusters of interactions during anesthesia. We used classification analysis to quantify the accuracy of discrimination between wakeful and anesthetised states, and found that informational structures inferred conscious states with greater accuracy than a scalar summary of the structure, a measure which is generally championed as the main measure of IIT. In stark contrast to a view which assumes feedforward architecture for insect brains, especially fly visual systems, we found rich information structures, which cannot arise from purely feedforward systems, occurred across the fly brain. Further, these information structures collapsed uniformly across the brain during anesthesia. Our results speak to the potential utility of the novel concept of an “informational structure” as a measure for level of consciousness, above and beyond simple scalar values.

The physical basis of consciousness remains elusive. Efforts to measure consciousness have generally been restricted to simple, scalar quantities which summarise the complexity of a system, inspired by integrated information theory, which links a multi-dimensional, informational structure to the contents of experience in a system. Due to the complexity of the definition of the structure, assessment of its utility as a measure of conscious arousal in a system has largely been ignored. In this manuscript we evaluate the utility of such an information structure in measuring the level of arousal in the fruit fly. Our results indicate that this structure can be more informative about the level of arousal in a system than even the single-value summary proposed by the theory itself. These results may push consciousness research towards the notion of multi-dimensional informational structures, instead of traditional scalar summaries.