André M. Bastos

Canonical Microcircuits for Predictive Coding

This Perspective considers the influential notion of a canonical (cortical) microcircuit in light of recent theories about neuronal processing. Specifically, we conciliate quantitative studies of microcircuitry and the functional logic of neuronal computations. We revisit the established idea that message passing among hierarchical cortical areas implements a form of Bayesian inference-paying careful attention to the implications for intrinsic connections among neuronal populations. By deriving canonical forms for these computations, one can associate specific neuronal populations with specific computational roles. This analysis discloses a remarkable correspondence between the microcircuitry of the cortical column and the connectivity implied by predictive coding. Furthermore, it provides some intuitive insights into the functional asymmetries between feedforward and feedback connections and the characteristic frequencies over which they operate.

Attentional stimulus selection through selective synchronization between monkey visual areas.

A central motif in neuronal networks is convergence, linking several input neurons to one target neuron. In visual cortex, convergence renders target neurons responsive to complex stimuli. Yet, convergence typically sends multiple stimuli to a target, and the behaviorally relevant stimulus must be selected. We used two stimuli, activating separate electrocorticographic V1 sites, and both activating an electrocorticographic V4 site equally strongly. When one of those stimuli activated one V1 site, it gamma synchronized (60-80 Hz) to V4. When the two stimuli activated two V1 sites, primarily the relevant one gamma synchronized to V4. Frequency bands of gamma activities showed substantial overlap containing the band of interareal coherence. The relevant V1 site had its gamma peak frequency 2-3 Hz higher than the irrelevant V1 site and 4-6 Hz higher than V4. Gamma-mediated interareal influences were predominantly directed from V1 to V4. We propose that selective synchronization renders relevant input effective, thereby modulating effective connectivity.

Visual areas exert feedforward and feedback influences through distinct frequency channels

Visual cortical areas subserve cognitive functions by interacting in both feedforward and feedback directions. While feedforward influences convey sensory signals, feedback influences modulate feedforward signaling according to the current behavioral context. We investigated whether these interareal influences are subserved differentially by rhythmic synchronization. We correlated frequency-specific directed influences among 28 pairs of visual areas with anatomical metrics of the feedforward or feedback character of the respective interareal projections. This revealed that in the primate visual system, feedforward influences are carried by theta-band (∼ 4 Hz) and gamma-band (∼ 60-80 Hz) synchronization, and feedback influences by beta-band (∼ 14-18 Hz) synchronization. The functional directed influences constrain a functional hierarchy similar to the anatomical hierarchy, but exhibiting task-dependent dynamic changes in particular with regard to the hierarchical positions of frontal areas. Our results demonstrate that feedforward and feedback signaling use distinct frequency channels, suggesting that they subserve differential communication requirements.

Communication through coherence with inter-areal delays.

The communication-through-coherence (CTC) hypothesis proposes that anatomical connections are dynamically rendered effective or ineffective through the presence or absence of rhythmic synchronization, in particular in the gamma and beta bands. The original CTC statement proposed that uni-directional communication is due to rhythmic entrainment with an inter-areal delay and a resulting non-zero phase relation, whereas bi-directional communication is due to zero-phase synchronization. Recent studies found that inter-areal gamma-band synchronization entails a non-zero phase lag. We therefore modify the CTC hypothesis and propose that bi-directional cortical communication is realized separately for the two directions by uni-directional CTC mechanisms entailing delays in both directions. We review evidence suggesting that inter-areal influences in the feedforward and feedback directions are segregated both anatomically and spectrally.

LFP and oscillations-what do they tell us?

Highlights • A brief treatment of dynamic coordination in terms of predictive coding.• Understanding synchronous message passing in terms of hierarchical predictive coding.• Characterising cortical gain control with the dynamic causal modelling of neural fields.• Characterising pathophysiological oscillations with dynamic causal modelling of neural masses.

DCM for complex-valued data: Cross-spectra, coherence and phase-delays

This note describes an extension of Bayesian model inversion procedures for the Dynamic Causal Modeling (DCM) of complex-valued data. Modeling complex data can be particularly useful in the analysis of multivariate ergodic (stationary) time-series. We illustrate this with a generalization of DCM for steady-state responses that models both the real and imaginary parts of sample cross-spectra. DCM allows one to infer underlying biophysical parameters generating data (like synaptic time constants, connection strengths and conduction delays). Because transfer functions and complex cross-spectra can be generated from these parameters, one can also describe the implicit system architecture in terms of conventional (linear systems) measures; like coherence, phase-delay or cross-correlation functions. Crucially, these measures can be derived in both sensor and source-space. In other words, one can examine the cross-correlation or phase-delay functions between hidden neuronal sources using non-invasive data and relate these functions to synaptic parameters and neuronal conduction delays. We illustrate these points using local field potential recordings from the subthalamic nucleus and globus pallidus, with a special focus on the relationship between conduction delays and the ensuing phase relationships and cross-correlation time lags between population activities.

A DCM study of spectral asymmetries in feedforward and feedback connections between visual areas V1 and V4 in the monkey

This paper reports a dynamic causal modeling study of electrocorticographic (ECoG) data that addresses functional asymmetries between forward and backward connections in the visual cortical hierarchy. Specifically, we ask whether forward connections employ gamma-band frequencies, while backward connections preferentially use lower (beta-band) frequencies. We addressed this question by modeling empirical cross spectra using a neural mass model equipped with superficial and deep pyramidal cell populations—that model the source of forward and backward connections, respectively. This enabled us to reconstruct the transfer functions and associated spectra of specific subpopulations within cortical sources. We first established that Bayesian model comparison was able to discriminate between forward and backward connections, defined in terms of their cells of origin. We then confirmed that model selection was able to identify extrastriate (V4) sources as being hierarchically higher than early visual (V1) sources. Finally, an examination of the auto spectra and transfer functions associated with superficial and deep pyramidal cells confirmed that forward connections employed predominantly higher (gamma) frequencies, while backward connections were mediated by lower (alpha/beta) frequencies. We discuss these findings in relation to current views about alpha, beta, and gamma oscillations and predictive coding in the brain.

Simultaneous Recordings from the Primary Visual Cortex and Lateral Geniculate Nucleus Reveal Rhythmic Interactions and a Cortical Source for Gamma-Band Oscillations

Oscillatory synchronization of neuronal activity has been proposed as a mechanism to modulate effective connectivity between interacting neuronal populations. In the visual system, oscillations in the gamma-frequency range (30–100 Hz) are thought to subserve corticocortical communication. To test whether a similar mechanism might influence subcortical-cortical communication, we recorded local field potential activity from retinotopically aligned regions in the lateral geniculate nucleus (LGN) and primary visual cortex (V1) of alert macaque monkeys viewing stimuli known to produce strong cortical gamma-band oscillations. As predicted, we found robust gamma-band power in V1. In contrast, visual stimulation did not evoke gamma-band activity in the LGN. Interestingly, an analysis of oscillatory phase synchronization of LGN and V1 activity identified synchronization in the alpha (8–14 Hz) and beta (15–30 Hz) frequency bands. Further analysis of directed connectivity revealed that alpha-band interactions mediated corticogeniculate feedback processing, whereas beta-band interactions mediated geniculocortical feedforward processing. These results demonstrate that although the LGN and V1 display functional interactions in the lower frequency bands, gamma-band activity in the alert monkey is largely an emergent property of cortex.

Granger causality revisited

This technical paper offers a critical re-evaluation of (spectral) Granger causality measures in the analysis of biological timeseries. Using realistic (neural mass) models of coupled neuronal dynamics, we evaluate the robustness of parametric and nonparametric Granger causality. Starting from a broad class of generative (state-space) models of neuronal dynamics, we show how their Volterra kernels prescribe the second-order statistics of their response to random fluctuations; characterised in terms of cross-spectral density, cross-covariance, autoregressive coefficients and directed transfer functions. These quantities in turn specify Granger causality — providing a direct (analytic) link between the parameters of a generative model and the expected Granger causality. We use this link to show that Granger causality measures based upon autoregressive models can become unreliable when the underlying dynamics is dominated by slow (unstable) modes — as quantified by the principal Lyapunov exponent. However, nonparametric measures based on causal spectral factors are robust to dynamical instability. We then demonstrate how both parametric and nonparametric spectral causality measures can become unreliable in the presence of measurement noise. Finally, we show that this problem can be finessed by deriving spectral causality measures from Volterra kernels, estimated using dynamic causal modelling.

Contrast gain control and horizontal interactions in V1: a DCM study

Using high-density electrocorticographic recordings – from awake-behaving monkeys – and dynamic causal modelling, we characterised contrast dependent gain control in visual cortex, in terms of synaptic rate constants and intrinsic connectivity. Specifically, we used neural field models to quantify the balance of excitatory and inhibitory influences; both in terms of the strength and spatial dispersion of horizontal intrinsic connections. Our results allow us to infer that increasing contrast increases the sensitivity or gain of superficial pyramidal cells to inputs from spiny stellate populations. Furthermore, changes in the effective spatial extent of horizontal coupling nuance the spatiotemporal filtering properties of cortical laminae in V1 — effectively preserving higher spatial frequencies. These results are consistent with recent non-invasive human studies of contrast dependent changes in the gain of pyramidal cells elaborating forward connections — studies designed to test specific hypotheses about precision and gain control based on predictive coding. Furthermore, they are consistent with established results showing that the receptive fields of V1 units shrink with increasing visual contrast.