Neural masses and fields in dynamic causal modeling

Dynamic causal modeling (DCM) provides a framework for the analysis of effective connectivity among neuronal subpopulations that subtend invasive (electrocorticograms and local field potentials) and non-invasive (electroencephalography and magnetoencephalography) electrophysiological responses. This paper reviews the suite of neuronal population models including neural masses, fields and conductance-based models that are used in DCM. These models are expressed in terms of sets of differential equations that allow one to model the synaptic underpinnings of connectivity. We describe early developments using neural mass models, where convolution-based dynamics are used to generate responses in laminar-specific populations of excitatory and inhibitory cells. We show that these models, though resting on only two simple transforms, can recapitulate the characteristics of both evoked and spectral responses observed empirically. Using an identical neuronal architecture, we show that a set of conductance based models—that consider the dynamics of specific ion-channels—present a richer space of responses; owing to non-linear interactions between conductances and membrane potentials. We propose that conductance-based models may be more appropriate when spectra present with multiple resonances. Finally, we outline a third class of models, where each neuronal subpopulation is treated as a field; in other words, as a manifold on the cortical surface. By explicitly accounting for the spatial propagation of cortical activity through partial differential equations (PDEs), we show that the topology of connectivity—through local lateral interactions among cortical layers—may be inferred, even in the absence of spatially resolved data. We also show that these models allow for a detailed analysis of structure–function relationships in the cortex. Our review highlights the relationship among these models and how the hypothesis asked of empirical data suggests an appropriate model class

LFP and oscillations - what do they tell us?

This review surveys recent trends in the use of local field potentials—and their non-invasive counterparts—to address the principles of functional brain architectures. In particular, we treat oscillations as the (observable) signature of context-sensitive changes in synaptic efficacy that underlie coordinated dynamics and message-passing in the brain. This rich source of information is now being exploited by various procedures—like dynamic causal modelling—to test hypotheses about neuronal circuits in health and disease. Furthermore, the roles played by neuromodulatory mechanisms can be addressed directly through their effects on oscillatory phenomena. These neuromodulatory or gain control processes are central to many theories of normal brain function (e.g. attention) and the pathophysiology of several neuropsychiatric conditions (e.g. Parkinson's disease)

Dynamic causal modelling of eye movements during pursuit: Confirming precision-encoding in V1 using MEG

This paper shows that it is possible to estimate the subjective precision (inverse variance) of Bayesian beliefs during oculomotor pursuit. Subjects viewed a sinusoidal target, with or without random fluctuations in its motion. Eye trajectories and magnetoencephalographic (MEG) data were recorded concurrently. The target was periodically occluded, such that its reappearance caused a visual evoked response field (ERF). Dynamic causal modelling (DCM) was used to fit models of eye trajectories and the ERFs. The DCM for pursuit was based on predictive coding and active inference, and predicts subjects' eye movements based on their (subjective) Bayesian beliefs about target (and eye) motion. The precisions of these hierarchical beliefs can be inferred from behavioural (pursuit) data. The DCM for MEG data used an established biophysical model of neuronal activity that includes parameters for the gain of superficial pyramidal cells, which is thought to encode precision at the neuronal level. Previous studies (using DCM of pursuit data) suggest that noisy target motion increases subjective precision at the sensory level: i.e., subjects attend more to the target's sensory attributes. We compared (noisy motion-induced) changes in the synaptic gain based on the modelling of MEG data to changes in subjective precision estimated using the pursuit data. We demonstrate that imprecise target motion increases the gain of superficial pyramidal cells in V1 (across subjects). Furthermore, increases in sensory precision – inferred by our behavioural DCM – correlate with the increase in gain in V1, across subjects. This is a step towards a fully integrated model of brain computations, cortical responses and behaviour that may provide a useful clinical tool in conditions like schizophrenia

Electrophysiological Data and the Biophysical Modelling of Local Cortical Circuits

This paper shows how recordings of gamma oscillations – under different experimental conditions or from different subjects – can be combined with a class of population models called neural fields and dynamic causal modeling (DCM) to distinguish among alternative hypotheses regarding cortical structure and function. This approach exploits inter-subject variability and trial-specific effects associated with modulations in the peak frequency of gamma oscillations. It draws on the computational power of Bayesian model inversion, when applied to neural field models of cortical dynamics. Bayesian model comparison allows one to adjudicate among different mechanistic hypotheses about cortical excitability, synaptic kinetics and the cardinal topographic features of local cortical circuits. It also provides optimal parameter estimates that quantify neuromodulation and the spatial dispersion of axonal connections or summation of receptive fields in the visual cortex. This paper provides an overview of a family of neural field models that have been recently implemented using the DCM toolbox of the academic freeware Statistical Parametric Mapping (SPM). The SPM software is a popular platform for analyzing neuroimaging data, used by several neuroscience communities worldwide. DCM allows for a formal (Bayesian) statistical analysis of cortical network connectivity, based upon realistic biophysical models of brain responses. It is this particular feature of DCM – the unique combination of generative models with optimization techniques based upon (variational) Bayesian principles – that furnishes a novel way to characterize functional brain architectures. In particular, it provides answers to questions about how the brain is wired and how it responds to different experimental manipulations. For a review of the general role of neural fields in SPM the reader can consult e.g. see [1]. Neural fields have a long and illustrious history in mathematical neuroscience, see e.g. [2] for a review. In summary, neural fields include horizontal intrinsic connections within layers or laminae of the cortical sheet and prescribe the time evolution of cell activity – such as mean depolarization or (average) action potential density. These models characterize current fluxes as continuous processes on the cortical sheet, using partial differential equations (PDEs). The key advance that neural field models offer, over other population models (like neural masses), is that they embody spatial parameters (like the density and extent of lateral connections). This allows one to model responses not just in time but also over space. Conversely, these models are particularly useful for explaining observed cortical responses over different spatial scales; for example, with high-density recordings, at the epidural or intracortical level. However, the impact of spatially extensive dynamics is not restricted to expression over space but can also have profound effects on temporal (e.g., spectral) responses at one point (or averaged locally over the cortical surface). This means that neural field models may also play a key role in the modelling of non-invasive electrophysiological data that does not resolve spatial activity directly. Our overview comprises two parts: in the first part, we use neural fields to simulate neural activity and distinguish the effects of post synaptic filtering on predicted responses in terms of synaptic rate constants that correspond to different timescales and distinct neurotransmitters. This application of neural fields follows the tradition of many studies, in which neural fields (and mean field models in general) have been used to explain cortical activity based on qualitative changes of models activity induced by changes in model parameters, like synaptic efficacy and connection strengths, see e.g.[3–8] . We will focus on the links between neuronal oscillations – mediated by the lateral propagation of neuronal spiking activity – using a field model that incorporates canonical cortical microcircuitry, where each population or layer has a receptor complement based on findings in cellular neuroscience. In the second part of this paper, we follow a different route, and use neural fields quantitatively – that is to fit empirical data recorded during visual stimulation, see e.g. [9–12]. We focus on neuromodulatory effects and discuss particular applications of DCMs with neural fields to explain invasive and non-invasive data. We present two studies of spectral responses obtained from the visual cortex during visual perception experiments: in the first study, MEG data were acquired during a task designed to show how activity in the gamma band is related to visual perception. This experiment tried to determine the spectral properties of an individual's gamma response, and how this relates to underlying visual cortex microcircuitry. In the second study, we exploited high density – spatially resolved – data from multi-electrode electrocorticographic (ECoG) arrays to study the effect of varying stimulus contrast on cortical excitability and gamma peak frequency. These data were acquired at the Ernst Strüngmann Institute for Neuroscience, in collaboration with the Max Planck Society in Frankfurt. We will consider neural field models in the light of a Bayesian framework for evaluating model evidence and obtaining parameter estimates using invasive and non-invasive recordings of gamma oscillations. We will first focus on model predictions of conductance and convolution based field models and showed that these can yield spectral responses that are sensitive to biophysical properties of local cortical circuits like cortical excitability and synaptic filtering; we will also consider two different mechanisms for this filtering: a nonlinear mechanism involving specific conductances and a linear convolution of afferent firing rates producing post synaptic potentials. We will then turn to empirical MEG data and looked for potential determinants of the spectral properties of an individual's gamma response, and how they relate to underlying visual cortex microcircuitry and excitation/inhibition balance. We found correlations between peak gamma frequency and cortical inhibition (parameterized by the excitatory drive to inhibitory cell populations) over subjects. This constitutes a compelling illustration of how non-invasive data can provide quantitative estimates of the spatial properties of neural sources and explain systematic variations in the dynamics those sources generate. Furthermore, the conclusions fitted comfortably with studies of contextual interactions and orientation discrimination suggesting that local contextual interactions in V1 are weaker in individuals with a large V1 area [13, 14]. Finally, we will use dynamic causal modeling and neural fields to test specific hypotheses about precision and gain control based on predictive coding formulations of neuronal processing. We exploited finely sampled electrophysiological responses from awake-behaving monkeys and an experimental manipulation (the contrast of visual stimuli) to look at changes in the gain and balance of excitatory and inhibitory influences. Our results suggest that increasing contrast effectively increases the sensitivity or gain of superficial pyramidal cells to inputs from spiny stellate populations. Furthermore, they are consistent with intriguing results showing that the receptive fields of V1 units shrinks with increasing visual contrast. The approach we will illustrate in this paper rests on neural field models that are optimized in relation to observed gamma responses from the visual cortex and are – crucially – compared in terms of their evidence. This provides a principled way to address questions about cortical structure, function and the architectures that underlie neuronal computations. <br/

Gamma Oscillations and Neural Field DCMs Can Reveal Cortical Excitability and Microstructure

This paper shows how gamma oscillations can be combined with neural population models and dynamic causal modeling (DCM) to distinguish among alternative hypotheses regarding cortical excitability and microstructure. This approach exploits inter-subject variability and trial-specific effects associated with modulations in the peak frequency of gamma oscillations. Neural field models are used to evaluate model evidence and obtain parameter estimates using invasive and non-invasive gamma recordings. Our overview comprises two parts: in the first part, we use neural fields to simulate neural activity and distinguish the effects of post synaptic filtering on predicted responses in terms of synaptic rate constants that correspond to different timescales and distinct neurotransmitters. We focus on model predictions of conductance and convolution based field models and show that these can yield spectral responses that are sensitive to biophysical properties of local cortical circuits like synaptic kinetics and filtering; we also consider two different mechanisms for this filtering: a nonlinear mechanism involving specific conductances and a linear convolution of afferent firing rates producing post synaptic potentials. In the second part of this paper, we use neural fields quantitatively—to fit empirical data recorded during visual stimulation. We present two studies of spectral responses obtained from the visual cortex during visual perception experiments: in the first study, MEG data were acquired during a task designed to show how activity in the gamma band is related to visual perception, while in the second study, we exploited high density electrocorticographic (ECoG) data to study the effect of varying stimulus contrast on cortical excitability and gamma peak frequency

Extracting novel information from neuroimaging data using neural fields

We showcase three case studies that illustrate how neural fields can be useful in the analysis of neuroimaging data. In particular, we argue that neural fields allow one to: (i) compare evidences for alternative hypotheses regarding neurobiological determinants of stimulus-specific response variability; (ii) make inferences about between subject variability in cortical function and microstructure using non-invasive data and (iii) estimate spatial parameters describing cortical sources, even without spatially resolved data

Augmenting Human Selves Through Artificial Agents - Lessons From the Brain

Much of current artificial intelligence (AI) and the drive toward artificial general intelligence (AGI) focuses on developing machines for functional tasks that humans accomplish. These may be narrowly specified tasks as in AI, or more general tasks as in AGI - but typically these tasks do not target higher-level human cognitive abilities, such as consciousness or morality; these are left to the realm of so-called "strong AI" or "artificial consciousness." In this paper, we focus on how a machine can augment humans rather than do what they do, and we extend this beyond AGI-style tasks to augmenting peculiarly personal human capacities, such as wellbeing and morality. We base this proposal on associating such capacities with the "self," which we define as the "environment-agent nexus"; namely, a fine-tuned interaction of brain with environment in all its relevant variables. We consider richly adaptive architectures that have the potential to implement this interaction by taking lessons from the brain. In particular, we suggest conjoining the free energy principle (FEP) with the dynamic temporo-spatial (TSD) view of neuro-mental processes. Our proposed integration of FEP and TSD - in the implementation of artificial agents - offers a novel, expressive, and explainable way for artificial agents to adapt to different environmental contexts. The targeted applications are broad: from adaptive intelligence augmenting agents (IA's) that assist psychiatric self-regulation to environmental disaster prediction and personal assistants. This reflects the central role of the mind and moral decision-making in most of what we do as humans