A theory of cortical responses

Abstract

This article concerns the nature of evoked brain responses and the principles underlying their generation. We start with the premise that the sensory brain has evolved to represent or infer the causes of changes in its sensory inputs. The problem of inference is well formulated in statistical terms. The statistical fundaments of inference may therefore afford important constraints on neuronal implementation. By formulating the original ideas of Helmholtz on perception, in terms of modern-day statistical theories, one arrives at a model of perceptual inference and learning that can explain a remarkable range of neurobiological facts.It turns out that the problems of inferring the causes of sensory input (perceptual inference) and learning the relationship between input and cause (perceptual learning) can be resolved using exactly the same principle. Specifically, both inference and learning rest on minimizing the brain's free energy, as defined in statistical physics. Furthermore, inference and learning can proceed in a biologically plausible fashion. Cortical responses can be seen as the brain's attempt to minimize the free energy induced by a stimulus and thereby encode the most likely cause of that stimulus. Similarly, learning emerges from changes in synaptic efficacy that minimize the free energy, averaged over all stimuli encountered. The underlying scheme rests on empirical Bayes and hierarchical models of how sensory input is caused. The use of hierarchical models enables the brain to construct prior expectations in a dynamic and context-sensitive fashion. This scheme provides a principled way to understand many aspects of cortical organization and responses. The aim of this article is to encompass many apparently unrelated anatomical, physiological and psychophysical attributes of the brain within a single theoretical perspective. In terms of cortical architectures, the theoretical treatment predicts that sensory cortex should be arranged hierarchically, that connections should be reciprocal and that forward and backward connections should show a functional asymmetry (forward connections are driving, whereas backward connections are both driving and modulatory). In terms of synaptic physiology, it predicts associative plasticity and, for dynamic models, spike-timing-dependent plasticity. In terms of electrophysiology, it accounts for classical and extra classical receptive field effects and long-latency or endogenous components of evoked cortical responses. It predicts the attenuation of responses encoding prediction error with perceptual learning and explains many phenomena such as repetition suppression, mismatch negativity (MMN) and the P300 in electroencephalography. In psychophysical terms, it accounts for the behavioural correlates of these physiological phenomena, for example, priming and global precedence. The final focus of this article is on perceptual learning as measured with the MMN and the implications for empirical studies of coupling among cortical areas using evoked sensory responses.

Figure 1

Schematic illustrating hierarchical structures in the brain and the distinction between forward, backward and lateral connections. This schematic is inspired by Mesulam's (1998) notion of sensory-fugal processing over ‘a core synaptic hierarchy, which includes the primary sensory, upstream unimodal, downstream unimodal, heteromodal, paralimbic and limbic zones of the cerebral cortex’ (see Mesulam 1998 for more details).

Figure 2

Upper panel: schematic depicting a hierarchical predictive coding architecture. Here, hierarchical arrangements within the model serve to provide predictions or priors to representations in the level below. The upper circles represent error units and the lower circles functional subpopulations encoding the conditional expectation of causes. These expectations change to minimize both the discrepancy between their predicted value and the mismatch incurred by their prediction of the level below. These two constraints correspond to prior and likelihood terms, respectively (see main text). Lower panel: a more detailed depiction of the influences on representational and error units.

Figure 3

Schematic adapted from Zeki (1993) summarizing the functional segregation of processing pathways and the relationship of simulated RFs to the stripe structures in V2. LGN, lateral geniculate nucleus; P, parvocellular pathway; M, magnocellular pathway. These RFs were obtained by minimizing the free energy of a model neuronal system when exposed to moving natural scenes. See Friston (2000) for details.

Figure 4

Repetition suppression as measured with fMRI in normal subjects. Top panel: estimated hemodynamic responses to the presentation of faces that were (red), and were not (blue), seen previously during the scanning session. These estimates were based on a linear convolution model of fMRI responses in the most significant voxel in the corresponding statistical parametric map. Lower panel: statistical parametric maps, overlaid on a cortical rendering of a single subject, showing areas that responded to all faces (left) and the region showing significant repetition suppression. For details, see Henson et al. (2000).

Figure 5

Schematic using empirical results reported in Baldeweg et al. (2004) relating the MMN to a predictive error suppression during perceptual learning. The idea is that perceptual synthesis (E-step) minimizes prediction error ‘online’ to terminate an early negativity, while perceptual learning (M-step) attenuates its expression over repeated exposures (solid black bars). The magnitude of MMN increases with number N of standards in each ‘roving’ stimulus train. This may be due to the suppression of an N1-like component over repeated presentation of the standards (dotted lines) that reveals the MMN.

Figure 6

This schematic shows the state equations describing the dynamics of one source. Each source is modelled with three subpopulations (pyramidal, spiny stellate and inhibitory inter neurons) as described in Jansen & Rit (1995) and David & Friston (2003). These have been assigned to granular and agranular cortical layers which receive forward and backward connection, respectively.

Figure 7

Upper right: transparent views of the cortical surface showing localized sources that entered the DCM. A bilateral extrinsic input acts on primary auditory cortices (red), which project reciprocally to orbito-frontal regions (green). In the right hemisphere, an indirect pathway was specified via a relay in the superior temporal gyrus (magenta). At the highest level, orbito-frontal and left posterior cingulate (blue) cortices were assumed to be laterally and reciprocally connected (broken lines). Lower left: schematic showing the extrinsic connectivity architecture of the DCM used to explain empirical data. Sources were coupled with extrinsic cortico-cortical connections following the rules of Felleman & Van Essen (1991). A1, primary auditory cortex; OF, orbitofrontal cortex; PC, posterior cingulate cortex; STG, superior temporal gyrus (right is on the right and left on the left). The free parameters of this model included extrinsic connection strengths that were adjusted to best explain the observed ERPs. Critically, these parameters allowed for differences in connections between the standard and oddball trials. Lower right: The results of a Bayesian model selection are shown in terms of the log evidence for models allowing changes in forward (F), backward (B), forward and backward (FB) and forward, backward and lateral connections (FBL). There is very strong evidence that both backward and lateral connections change with perceptual learning as predicted theoretically.

Figure 8

Auditory oddball paradigm: DCM results for the FBL model of the previous figure. Upper panel: the data are the projection of the original scalp time-series onto the three first spatial modes or eigenvectors. Note the correspondence between the measured ERPs (thin lines) and those generated by the model (thick lines). Lower panel: the response of each source is shown for the standard (grey) and oddball (black) trials based on the conditional expectation of the DCM parameters. Changes in coupling are shown alongside each connection in terms of the relative strength (oddball to standard). The percentages refer to the conditional confidence this change is non-zero (i.e. a relative strength of more than one). Changes with over 95% confidence are shown as solid lines. A1, primary auditory cortex; OF, orbitofrontal cortex; PC, posterior cingulate cortex; STG, superior temporal gyrus.