Manh Nguyen Trong

Associating spontaneous with evoked activity in a neural mass model of visual cortex

Spontaneous activity of the brain at rest frequently has been considered a mere backdrop to the salient activity evoked by external stimuli or tasks. However, the resting state of the brain consumes most of its energy budget, which suggests a far more important role. An intriguing hint comes from experimental observations of spontaneous activity patterns, which closely resemble those evoked by visual stimulation with oriented gratings, except that cortex appeared to cycle between different orientation maps. Moreover, patterns similar to those evoked by the behaviorally most relevant horizontal and vertical orientations occurred more often than those corresponding to oblique angles. We hypothesize that this kind of spontaneous activity develops at least to some degree autonomously, providing a dynamical reservoir of cortical states, which are then associated with visual stimuli through learning. To test this hypothesis, we use a biologically inspired neural mass model to simulate a patch of cat visual cortex. Spontaneous transitions between orientation states were induced by modest modifications of the neural connectivity, establishing a stable heteroclinic channel. Significantly, the experimentally observed greater frequency of states representing the behaviorally important horizontal and vertical orientations emerged spontaneously from these simulations. We then applied bar-shaped inputs to the model cortex and used Hebbian learning rules to modify the corresponding synaptic strengths. After unsupervised learning, different bar inputs reliably and exclusively evoked their associated orientation state; whereas in the absence of input, the model cortex resumed its spontaneous cycling. We conclude that the experimentally observed similarities between spontaneous and evoked activity in visual cortex can be explained as the outcome of a learning process that associates external stimuli with a preexisting reservoir of autonomous neural activity states. Our findings hence demonstrate how cortical connectivity can link the maintenance of spontaneous activity in the brain mechanistically to its core cognitive functions.

Modeling spatio-temporal effects of propofol using a neural field approach

Anesthetic agents like propofol induce global changes of brain states and behavior [1]. Yet the relation to the observed spatio-temporal patterns of EEG and fMRI has not been fully understood. In this study, we use a biologically inspired neural field model to explain these patterns in the human brain induced by propofol.

A neural field model using advanced anatomical connectivity information

We propose a mathematical framework for a neural field model that can accommodate empirical information on connectivity strength between different parts of the brain, and axonal caliber information of these connections. Furthermore, we use integro-differential equations to describe the mean dynamics (i.e., firing rate and mean membrane potential) [1]. We demonstrate the framework at the example of the rat brain. Here, we specify the propagation velocity distributions by a linear relationship using empirical, position-variant, axonal diameter distributions of myelinated and unmyelinated callosal axons [2]. We approximate the experimentally estimated histograms of axonal diameters using alpha functions. By interpolating these alpha functions in space, weighted by the fiber densities of the myelinated and unmyelinated axons, we compute the velocity probability density (see Figure ​Figure1B).1B). Diffusion tensor imaging is used to reconstruct axonal projections through the white matter. We use an atlas-based parcellation of the rat brain [3] to allocate the reconstructed projections to specific brain regions, yielding a connectome (see Figure ​Figure1A).1A). The structures that are most strongly interconnected are the hippocampus, the thalamus, the motor and the sensory cortices. A simulation of the electrocorticogram demonstrates the impact of distal over local connections on brain function (see Figure ​Figure1C1C). Figure 1 A. Connectome B. Velocity probability density C. Electrocorticogram

Spontaneous state switching in realistic mean-field model of visual cortex with heteroclinic channel

Spontaneous switching between cortical states in the visual cortex of cat was reported by Kenet et al.[1]: a succession of spatial activation patterns normally associated with visual input was observed even in the absence of external input. Using a Wilson-Cowan network, Blumenfeld et al.[2] proposed a model for this phenomenon that generated multistability by applying unstructured noise. Here we use the biologically realistic mean-field model of Jansen & Rit [3], together with the heteroclinic channel theory proposed by Rabinovich et al., cf. Ref. [5], to propose a mechanism how such spontaneous switching between states could occur independent of extrinsic noise. A hypercolumn in V1 is made up of orientation preference columns (OPC), which selectively respond to specifically oriented stimuli. Our model of an OPC consists of 3 neuronal populations: pyramidal neurons (PN) and excitatory (Ex. IN) / inhibitory interneurons (Inh. IN), see Fig. ​Fig.1A.1A. Their connectivity decays exponentially with orientation difference, see Fig. ​Fig.1B.1B. These decays, and the spatial layout shown in Fig. ​Fig.1C(I,II),1C(I,II), are derived from the data of Gilbert & Wiesel [4]. The interactions between the OPCs are described by integral differential equations: Figure 1 A. Basic model setup. B. Assumed decay of connectivity with orientation difference [4]. C. Spatial layout of OPCs and examples of the simulated evoked and spontaneous activity. [Θ: 2nd order differential operator, V: membrane potentials, W: connectivity, S: sigmoid function, I: input, K: gain] Evoked activity was simulated by applying input to a specific hypercolumn, yielding patterns that are very similar to the OPC distribution maps - compare Fig. ​Fig.1C(Evok.)1C(Evok.) with ​with1C1C(IV,V). Importantly however, even without any external stimulus the system spontaneously switches from one state to another, see Fig. ​Fig.1C1C(Spon.). In state space the system evolves in a heteroclinic channel, made up by the trajectories near a chain of saddle points (representing the OPCs) and associated unstable separatrixes. The inhibitory connectivity governs this sequence of activation. Imposing noise on this connectivity can introduce randomness into the sequence of activation. In this study we have combined mean-field and heteroclinic channel theory in order to describe the experimental observation of spontaneous state switching [1]. In contrast to Ref. [2], we do not need to impose unstructured noise to create multistability here. Furthermore, manipulations of our inhibitory connectivity matrix can vary the resulting sequence of states, e.g., in order to accommodate expectations about the next stimulus.

Neural field model of rat's cortex based on realistic connectivity from diffusion weighted MRI and neural morphology

Generative models of neural circuits may help to create a link between neural mechanisms and observable data. We propose a model of rats cortex using a neural field model containing biologically plausible anatomical connections from tractography based on dwMRI data and from the neural morphological database NeuroMorpho [1]. There are three principal types of anatomical connections in the cortex: Local, long-range and distal connections [2]. For specifying local connections we use neural morphologies from [1]. We consider each voxel in the model as a neural mass and distribute randomly drawn neurons from the database therein. After that we use bootstrap methods to determine the total number and variability of synaptic contacts. For the distal connectivity we estimated the degree of anatomical connectedness using white matter tractography on the basis of diffusion weighted MRI [3]. Our neural field consists of 5 layers. For each layer we assume three different neural masses: pyramidal cells, excitatory and inhibitory interneurons [4]. The mutual interactions between neural masses will be described by a system of integral differential equations: where V is the state vector (mean membrane potentials), T the time delays in the dendritic arbors, S the sigmoidal output function, W the connection coefficients between the neural elements, I the input, and t(d) is the distance dependent time delays. Figure ​Figure1A1A shows the estimated spatial dependency of local connectivity, which is in accordance with anatomical observations [2]. The distal connectivity map of 28 regions is displayed in Fig. ​Fig.1B.1B. An example map of simulated activity on the cortex in response to a stimulus to somatosensory cortex is illustrated in Fig. ​Fig.1C.1C. Figure 1 (A) Local connectivity profile between a pyramidal cell in layer V and an interneuron in layer III (grid size 250 µm). (B) Distal connectivity map estimated from dwMRI between 28 regions

A neural field model for spatio-temporal brain activity using a morphological model of cortical connectivity

Electroencephalography and magnetoencephalography(EEG and MEG) are brain signals with high temporal res-olutions and are believed to reflect neural mass action. Formodeling the neuronal structures, which are responsiblefor the generation of EEG/MEG, one can use so-calledneural mass models, like the one of Jansen and Rit [1]. Insuch models, a brain area (