A mathematical model of dysfunction of the thalamo-cortical loop in schizophrenia

Background

Recent experimental results suggest that impairment of auditory information processing in the thalamo-cortical loop is crucially related to schizophrenia. Large differences between schizophrenia patients and healthy controls were found in the cortical EEG signals.

Methods

We derive a phenomenological mathematical model, based on coupled phase oscillators with continuously distributed frequencies to describe the neural activity of the thalamo-cortical loop. We examine the influence of the bidirectional coupling strengths between the thalamic and the cortical area with regard to the phase-locking effects observed in the experiments. We extend this approach to a model consisting of a thalamic area coupled to two cortical areas, each comprising a set of nonidentical phase oscillators. In the investigations of our model, we applied the Ott-Antonsen theory and the Pikovsky-Rosenblum reduction methods to the original system.

Results

The results derived from our mathematical model satisfactorily reproduce the experimental data obtained by EEG measurements. Furthermore, they show that modifying the coupling strength from the thalamic region to a cortical region affects the duration of phase synchronization, while a change in the feedback to the thalamus affects the strength of synchronization in the cortex. In addition, our model provides an explanation in terms of nonlinear dynamics as to why brain waves desynchronize after a given phase reset.

Conclusion

Our model can explain functional differences seen between EEG records of healthy subjects and schizophrenia patients on a system theoretic basis. Because of this and its predictive character, the model may be considered to pave the way towards an early and reliable clinical detection of schizophrenia that is dependent on the interconnections between the thalamic and cortical regions. In particular, the model parameter that describes the strength of this connection can be used for a diagnostic classification of schizophrenia patients.

     

Development and plasticity of the cerebral cortex: from molecules to maps.

The role played by environmental influences in the development of the nervous system has been subject to intense study for the last three decades. Many laboratories are currently engaged in characterizing the exact contributions of activity-dependent or -independent processes to the development of the mammalian neocortex. Here we introduce a special issue devoted to the topic and briefly review recent progress in this exciting field. At the systems level, many investigators are now distinguishing between an "establishment" phase of cortical connections, where activity-dependent and independent mechanisms could operate, and a later "maintenance" phase, which appears to be controlled by neuronal activity. A particularly interesting recent example of the role of top-down vs. bottom-up influences in the development of cortical connections is the emergence of orientation selectivity in visual cortex: we propose a synthetic view highlighting the role of the thalamo-cortical reciprocal projection in this process. Finally, at the cellular level, NMDA receptors, neurotrophins and many other molecules contribute to activity-dependent rearrangement of cortical connections during appropriate critical periods of development.     

Cross-trial correlation analysis of evoked potentials reveals arousal-related attenuation of thalamo-cortical coupling

We describe a computational method for assessing functional connectivity in sensory neuronal networks. The method, which we term cross-trial correlation, can be applied to signals representing local field potentials (LFPs) evoked by sensory stimulations and utilizes their trial-to-trial variability. A set of single trial samples of a given post-stimulus latency from consecutive evoked potentials (EPs) recorded at a given site is correlated with such sets for all other latencies and recording sites. The results of this computation reveal how neuronal activities at various sites and latencies correspond to activation of other sites at other latencies. The method was used to investigate the functional connectivity of thalamo-cortical network of somatosensory system in behaving rats at two levels of alertness: habituated and aroused. We analyzed potentials evoked by vibrissal deflections recorded simultaneously from the ventrobasal thalamus and barrel cortex. The cross-trial correlation analysis applied to the early post-stimulus period (<25 ms) showed that the magnitude of the population spike recorded in the thalamus at 5 ms post-stimulus correlated with the cortical activation at 6–13 ms post-stimulus. This correlation value was reduced at 6–9 ms, i.e. at early postsynaptic cortical response, with increased level of the animals’ arousal. Similarly, the aroused state diminished positive thalamo-cortical correlation for subsequent early EP waves, whereas the efficacy of an indirect cortico-fugal inhibition (over 15 ms) did not change significantly. Thus we were able to characterize the state related changes of functional connections within the thalamo-cortical network of behaving animals.     

On the origin of the functional architecture of the cortex

The basic structure of receptive fields and functional maps in primary visual cortex is established without exposure to normal sensory experience and before the onset of the critical period. How the brain wires these circuits in the early stages of development remains unknown. Possible explanations include activity-dependent mechanisms driven by spontaneous activity in the retina and thalamus, and molecular guidance orchestrating thalamo-cortical connections on a fine spatial scale. Here I propose an alternative hypothesis: the blueprint for receptive fields, feature maps, and their inter-relationships may reside in the layout of the retinal ganglion cell mosaics along with a simple statistical connectivity scheme dictating the wiring between thalamus and cortex. The model is shown to account for a number of experimental findings, including the relationship between retinotopy, orientation maps, spatial frequency maps and cytochrome oxidase patches. The theory's simplicity, explanatory and predictive power makes it a serious candidate for the origin of the functional architecture of primary visual cortex.     

Development and plasticity of cortical areas and networks

The development of cortical layers, areas and networks is mediated by a combination of factors that are present in the cortex and are influenced by thalamic input. Electrical activity of thalamocortical afferents has a progressive role in shaping cortex. For early thalamic innervation and patterning, the presence of activity might be sufficient; for features that develop later, such as intracortical networks that mediate emergent responses of cortex, the spatiotemporal pattern of activity often has an instructive role. Experiments that route projections from the retina to the auditory pathway alter the pattern of activity in auditory thalamocortical afferents at a very early stage and reveal the progressive influence of activity on cortical development. Thus, cortical features such as layers and thalamocortical innervation are unaffected, whereas features that develop later, such as intracortical connections, are affected significantly. Surprisingly, the behavioural role of 'rewired' cortex is also influenced profoundly, indicating the importance of patterned activity for this key aspect of cortical function.     

Reciprocal inhibition and slow calcium decay in perigeniculate interneurons explain changes of spontaneous firing of thalamic cells caused by cortical inactivation

The role of cortical feedback in the thalamocortical processing loop has been extensively investigated over the last decades. With an exception of several cases, these searches focused on the cortical feedback exerted onto thalamo-cortical relay (TC) cells of the dorsal lateral geniculate nucleus (LGN). In a previous, physiological study, we showed in the cat visual system that cessation of cortical input, despite decrease of spontaneous activity of TC cells, increased spontaneous firing of their recurrent inhibitory interneurons located in the perigeniculate nucleus (PGN). To identify mechanisms underlying such functional changes we conducted a modeling study in NEURON on several networks of point neurons with varied model parameters, such as membrane properties, synaptic weights and axonal delays. We considered six network topologies of the retino-geniculo-cortical system. All models were robust against changes of axonal delays except for the delay between the LGN feed-forward interneuron and the TC cell. The best representation of physiological results was obtained with models containing reciprocally connected PGN cells driven by the cortex and with relatively slow decay of intracellular calcium. This strongly indicates that the thalamic reticular nucleus plays an essential role in the cortical influence over thalamo-cortical relay cells while the thalamic feed-forward interneurons are not essential in this process. Further, we suggest that the dependence of the activity of PGN cells on the rate of calcium removal can be one of the key factors determining individual cell response to elimination of cortical input.     

Modulation of Cortical Oscillations by Low-Frequency Direct Cortical Stimulation Is State-Dependent

Cortical oscillations play a fundamental role in organizing large-scale functional brain networks. Noninvasive brain stimulation with temporally patterned waveforms such as repetitive transcranial magnetic stimulation (rTMS) and transcranial alternating current stimulation (tACS) have been proposed to modulate these oscillations. Thus, these stimulation modalities represent promising new approaches for the treatment of psychiatric illnesses in which these oscillations are impaired. However, the mechanism by which periodic brain stimulation alters endogenous oscillation dynamics is debated and appears to depend on brain state. Here, we demonstrate with a static model and a neural oscillator model that recurrent excitation in the thalamo-cortical circuit, together with recruitment of cortico-cortical connections, can explain the enhancement of oscillations by brain stimulation as a function of brain state. We then performed concurrent invasive recording and stimulation of the human cortical surface to elucidate the response of cortical oscillations to periodic stimulation and support the findings from the computational models. We found that (1) stimulation enhanced the targeted oscillation power, (2) this enhancement outlasted stimulation, and (3) the effect of stimulation depended on behavioral state. Together, our results show successful target engagement of oscillations by periodic brain stimulation and highlight the role of nonlinear interaction between endogenous network oscillations and stimulation. These mechanistic insights will contribute to the design of adaptive, more targeted stimulation paradigms.     

Cooperative self-organization of afferent and lateral connections in cortical maps

A self-organizing neural network model called LISSOM for the synergetic development of afferent and lateral connections in cortical feature maps is presented. The weight adaptation process is purely activity-dependent, unsupervised, and local. The afferent input weights self-organize into a topological map of the input space. At the same time, the lateral interconnection weights adapt, and a unique lateral interaction profile develops for each neuron. Weak lateral connections die off, leaving a pattern of connections that represents the significant long-term correlations of activity on the feature map. LISSOM demonstrates how self-organization can bootstrap based on input information only, without global supervision or predetermined lateral interaction. The model gives rise to a nontopographically organized lateral connectivity similar to that observed in the mammalian neocortex as illustrated by a LISSOM model of ocular dominance column formation in the primary visual cortex. In addition, LISSOM can potentially account for the development of multiple maps of different modalities on the same undifferentiated cortical architecture. Received: 12 May 1993/Accepted in revised form: 22 September 1993     

Preparation of dissociated mouse cortical neuron cultures

This video will guide you through the process for generating cortical neuronal cultures from late embryo and early postnatal mouse brain. These cultures can be used for a variety of applications including immunocytochemistry, biochemistry, electrophysiology, calcium and sodium imaging, protein and/or RNA isolation. These cultures also provide a platform to study the neuronal development of transgenic animals that carry a late embryonic or postnatal lethal gene mutation. The procedure is relatively straight forward, requires some experience in tissue culture technique and should not take longer than two to three hours if you are properly prepared. Careful separation of the cortical rind from the thalamo-cortical fiber tract will reduce the number of unwanted non-neuronal cells. To increase yields of neuronal cells triturate the pieces of the cortical tissue gently after the enzyme incubation step. This is imperative as it prevents unnecessary injury to cells and premature neuronal cell death. Since these cultures are maintained in the absence of glia feeder cells, they also offer an added advantage of growing cultures enriched in neurons.     

Effects of the thalamus on the development of cerebral cortical efferents in vitro

The cerebral cortex is a multilayered tissue, with each layer differing in its cellular composition and connections. Axons from deep layer neurons project subcortically, many to the thalamus, whereas superficial layer neurons target other cortical areas. The mechanisms that regulate the development of this pattern of connections are not fully understood. Our experiments examined the potential of the thalamus to attract and/or select neurites from appropriate cortical layers. First, we cocultured murine cortical slices in close proximity to thalamic explants in collagen gels. The amount of neurite outgrowth from deep layer cells was enhanced by, but not attracted to, the thalamic explants. Second, we cocultured cortical slices in contact with thalamic or cortical explants to test for laminar specificity of connections. Specificity was apparent after culture for about a week, in that deep cortical layers contained the highest proportions of corticothalamic cells and superficial cortical layers contained the highest proportions of corticocortical cells. After shorter culture of only a few days, however, specificity was not apparent and there were larger numbers of corticothalamic projections from the superficial layers than after a week. To study how the early nonspecific pattern of corticothalamic connections was transformed into the more specific pattern, we labeled corticothalamic cells early, after 2 days, but let the cultures survive for 8 days. On day 8, the nonspecific pattern of early-labeled cells was still seen. We conclude that although the thalamus does not block the initial entry of inappropriate axons from the superficial layers, many of these axons are subsequently lost. This suggests that contact-mediated interactions between cortical axons and the thalamus allow cortical efferents from appropriate layers to be distinguished from those arising in inappropriate layers. This may contribute to the development of layer-specific cortical connections in vivo.     

Fiber Pathway Pathology,Synapse Loss and Decline of Cortical Function in Schizophrenia

A quantitative cortical model is developed, based on both computational and simulation approaches, which relates measured changes in cortical activity of gray matter with changes in the integrity of longitudinal fiber pathways. The model consists of modules of up to 5,000 neurons each, 80% excitatory and 20% inhibitory, with these having different degrees of synaptic connectiveness both within a module as well as between modules. It is shown that if the inter-modular synaptic connections are reduced to zero while maintaining the intra-modular synaptic connections constant, then activity in the modules is reduced by about 50%. This agrees with experimental observations in which cortical electrical activity in a region of interest, measured using the rate of oxidative glucose metabolism (CMR_glc(ox)), is reduced by about 50% when the cortical region is isolated, either by surgical means or by transient cold block. There is also a 50% decrease in measured cortical activity following inactivation of the nucleus of Meynert and the intra-laminar nuclei of the thalamus, which arise either following appropriate lesions or in sleep. This occurs in the model if the inter-modular synaptic connections require input from these nuclei in order to function. In schizophrenia there is a 24% decrease in functional anisotropy of longitudinal fasciculi accompanied by a 7% decrease in cortical activity (CMR_glc(ox)).The cortical model predicts this, namely for a 24% decrease in the functioning of the inter-modular connections, either through the complete loss of 24% of axons subserving the connections or due to such a decrease in the efficacy of all the inter-modular connections, there will be about a 7% decrease in the activity of the modules. This work suggests that deterioration of longitudinal fasciculi in schizophrenia explains the loss of activity in the gray matter.     

Bayesian inference in populations of cortical neurons: a model of motion integration and segmentation in area MT

A major issue in cortical physiology and computational neuroscience is understanding the interaction between extrinsic signals from feedforward connections and intracortical signals from lateral connections. We propose here a computational model for motion perception based on the assumption that the local cortical circuits in the medio-temporal area (area MT) implement a Bayesian inference principle. This approach establishes a functional balance between feedforward and lateral, excitatory and inhibitory, inputs. The model reproduces most of the known properties of the neurons in area MT in response to moving stimuli. It accounts for important motion perception phenomena including motion transparency, spatial and temporal integration/segmentation. While integrating several properties of previously proposed models, it makes specific testable predictions concerning, in particular, temporal properties of neurons and the architecture of lateral connections in area MT. In addition, the proposed mechanism is consistent with the known properties of local cortical circuits in area V1. This suggests that Bayesian inference may be a general feature of information processing in cortical neuron populations. Received: 3 December 1997 / Accepted in revised form: 21 July 1998     

Structural study of the development of ocularity domains using a neural network model

We present a model for the development of ocularity domains in the visual cortex of mammals during the embryonic stage. We model the thalamo-cortical pathway with a self-organising neural network with two source layers, each of them serving different retinae, and one target layer, where the connections end. The connectivity between the source layers and the target layer is driven by Hebbian learning. In both the source layers and the target layer we assume excitatory lateral signal diffusion between proximal neurons that causes them to be correlated. According to the developmental state being modelled, we do not consider either correlation or anti-correlation between the signals originated in neurons of different retinae. The basic assumptions made are proved to be sufficient to attain a distribution of connections arranged in ocularity domains. The dependence of the geometry of the ocularity domains on the parameters of the model is analysed and a correlation between the width of the signal diffusion and the extent of the domains is found. The generality of the assumptions made allows an easy translation of the model to explain the development of other elements of the sensory nervous system.     

Cell type specificity of local cortical connections

The function of the cerebral cortex is dependent on the precise organization of the circuits formed by its component neurons. The connections between neurons are not random, but are specific at multiple levels of organization. For example, each cortical area connects to only a selected subset of other areas and within any given area the axonal and dendritic arbors of individual neurons arborize in precise, layer-specific patterns (for review see Felleman & Van Essen, 1991; Callaway, 1998) . In each layer there are dendrites from multiple cell types including cells with somata both within and outside that layer. Anatomical studies have shown that axons arborizing in a particular cortical layer can connect selectively onto dendrites of some cell types in the layer, while avoiding the dendrites of other cell types (e.g. Freund & Gulyas, 1991; Hornung & Celio, 1992; Staiger et al., 1996). These cell type specific connections are, however, difficult to elucidate with anatomical methods, so the frequency of such specificity has remained elusive. Recent experimental methods combining intracellular recording of single neurons with focal neuronal stimulation by uncaging glutamate with light (“photostimulation”) have made the analysis of cell type specific cortical connections more tractable. These studies show that cell type specificity of connections is prevalent in cortex. Here I review photostimulation-based studies investigating the laminar sources of cortical input to distinct cell types in the visual and somatosensory cortices of rats and the primary visual cortex of monkeys.     

Formation of plastic connections of the visual system during ontogenesis of the rabbit

Analysis of evoked potentials and unit activity in the visual cortical projection area of rabbits revealed a definite succession of forming of interneuronal connections in ontogeny. In early postnatal period, the neuronal reactions were characterized by stable responses with one excitatory phase corresponding to initially negative surface evoked potential. Similarity of reactions of neurones situated in the same vertical column was observed and explained by functioning of a system of rigid connections of the thalamic relay nuclei afferents with cortical pyramidal neurones. Beginning from the third week of postnatal life of rabbits the neuronal reactions assumed a distinctly expressed phasic character, and variability of responses was seen along the vertical line. The changes revealed correlated with formation of a system of interneurones providing a possibility of plastic neuronal interaction. A study of the influence of preliminary cortical stimulation of the associative areas showed that intercentral cooperation mediated by cortical interneurones providing a systemic analysis of visual information began to form from the third week of postnatal life and reached the definitive level at later stages of development.     

Homeostatic plasticity in the CNS: synaptic and intrinsic forms

The study of experience-dependent plasticity has been dominated by questions of how Hebbian plasticity mechanisms act during learning and development. This is unsurprising as Hebbian plasticity constitutes the most fully developed and influential model of how information is stored in neural circuits and how neural circuitry can develop without extensive genetic instructions. Yet Hebbian plasticity may not be sufficient for understanding either learning or development: the dramatic changes in synapse number and strength that can be produced by this kind of plasticity tend to threaten the stability of neural circuits. Recent work has suggested that, in addition to Hebbian plasticity, homeostatic regulatory mechanisms are active in a variety of preparations. These mechanisms alter both the synaptic connections between neurons and the intrinsic electrical properties of individual neurons, in such a way as to maintain some constancy in neuronal properties despite the changes wrought by Hebbian mechanisms. Here we review the evidence for homeostatic plasticity in the central nervous system, with special emphasis on results from cortical preparations.