A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue

@article{Wilson2004AMT,
  title={A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue},
  author={Hugh R. Wilson and Jack D. Cowan},
  journal={Kybernetik},
  year={2004},
  volume={13},
  pages={55-80}
}
It is proposed that distinct anatomical regions of cerebral cortex and of thalamic nuclei are functionally two-dimensional. On this view, the third (radial) dimension of cortical and thalamic structures is associated with a redundancy of circuits and functions so that reliable signal processing obtains in the presence of noisy or ambiguous stimuli.A mathematical model of simple cortical and thalamic nervous tissue is consequently developed, comprising two types of neurons (excitatory and… Expand
A Population Model of the Thalamus and its Wave Interactions with the Cortex
TLDR
A population model of the thalamus based on the mean-field cortex developed by Steyn-Ross et al. Expand
Topology and dynamics of the canonical circuit of cat V1
TLDR
A model of co-operative competitive processing that is consistent with the observed connectivity in the superficial layers of the cortex is discussed, and also how the topology of the overall cortical circuit could be configured dynamically through average inhibition is considered. Expand
Co-operative Populations of Neurons: Mean Field Models of Mesoscopic Brain Activity
TLDR
The aim of this chapter is to outline the historical genesis of this important modelling framework, and to detail its many successes in accounting for the experimentally observed neuronal population activity in cortex. Expand
Anisotropic connectivity and cooperative phenomena as a basis for orientation sensitivity in the visual cortex
TLDR
In this paper, orientation sensitivity arises through cooperative interactions among neurons having anisotropic excitatory, and isotropic inhibitory connections. Expand
Modeling and analyzing the thalamocortical system
Physiological evidence localizes the thalamocortical system as the functional unit being responsible for the perception of sensory input. In this thesis the dynamical processes in the thalamus duringExpand
Corticonic models of brain mechanisms underlying cognition and intelligence
TLDR
It is suggested that a Parametrically Coupled Logistic Map network (PCLMN) is a minimal model of the thalamo–cortical complex and that marrying such a network to a suitable associative memory with re-entry or feedback forms a useful, albeit, abstract model of a cortical module of the brain that could facilitate building a simple artificial brain. Expand
Multi-scale modeling of complex neuronal networks: a view towards striatal cholinergic pattern formations
  • H. R. Noori
  • Computer Science, Medicine
  • Journal of biological physics
  • 2012
TLDR
This study introduces an abstract mathematical model of a deterministic nature that provides a robust integral transformation of the microscopic activities into macroscopic spatiotemporal patterns within the structure of the dorsal striatum of rats. Expand
COALIA: a computational model of human EEG for consciousness research
TLDR
A physiologically-grounded computational model is presented, attempting to account for the main micro-circuits identified in the human cortex, while including the specificities of each neuronal type, which provides a quantitative framework to accelerate the study of the physiological mechanisms involved in the emergence, maintenance and disruption of consciousness. Expand
Equations governing dynamics of excitation and inhibition in the mouse corticothalamic network
TLDR
It is concluded that mean-field models can accurately summarize cortical dynamics, but only when the cortex is considered as part of a dynamic corticothalamic network. Expand
Characteristics of neuronal systems in the visual cortex
TLDR
A model system of variable complexity that is spatially two-dimensional and time-dependent, uses feedback for iteration and smoothing, includes the mapping of the cortical networks and can be nonlinear as the case requires is proposed. Expand
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 70 REFERENCES
Brain functions and neural dynamics.
TLDR
A model based on observations of netlets is presented, in which it is assumed that the netlets are the fundamental building blocks out of which nets of considerable complexity may be as embled and the concepts of netlet interaction are applied in conjunction with the principle of synaptic facilitation to information processing in the cortex. Expand
Modality and topographic properties of single neurons of cat's somatic sensory cortex.
TLDR
Observations upon the modality and topographical attributes of single neurons of the first somatic sensory area of the cat’s cerebral cortex, the analogue of the cortex of the postcentral gyrus in the primate brain, support an hypothesis of the functional organization of this cortical area. Expand
THE TONIC CONTROL OF CORTICAL RESPONSIVENESS BY INHIBITORY AND FACILITATORY DIFFUSE INFLUENCES.
TLDR
Data show that a driving mechanism, having its main descending circuit in the periventricular and periaqueductal gray matter, interacts with the RF, establishing a positive feedback circuit, to maintain tonic arousal, which would explain the impairment of enduring wakefulness and the occurrence of ECoG spindles in animals with central gray or posterior hypothalamic lesions. Expand
The representation of the visual field on the cerebral cortex in monkeys
TLDR
On the basis of his extensive and elegant anatomical investigations on the visual cortex, Poliak (1932) suggested that a mathematical projection of the retina on the cerebral cortex must exist and this work has made such a surface, folded it and compared it with the calcarine cortex of the monkey. Expand
The probability of neural connexions
  • A. M. Uttley
  • Biology, Medicine
  • Proceedings of the Royal Society of London. Series B - Biological Sciences
  • 1955
In some areas of a nervous system there is no obvious plan of connexions. If it is assumed, first, that in these areas fibre growth is random, and secondly, that connexions are formed if axon andExpand
Analog simulation of prepyriform cortex in the cat
Abstract The prepyriform cortex contains three types of intracortical feedback loops, negative, positive excitatory, and positive inhibitory, representing the possible modes of interaction in a mixedExpand
Some properties of isolated cerebral cortex in the unanaesthetized cat
  • B. Burns
  • Medicine
  • The Journal of physiology
  • 1951
TLDR
It proved possible to decerebrate cats in such a way that a part of one cerebral hemisphere remained in the cranial cavity, with all its nervous connexions cut but with undisturbed blood supply. Expand
Functional synaptic organization of primary visual cortex neurones in the cat
TLDR
The findings suggest that from each eye less than 5 geniculo-cortical afferent converging fibres have a major effect on the activity of one cortical cell, and that inhibitory afferents may be indirect and relayed through another cortical pyramidal cell. Expand
Inhibition in Thalamic and Cortical Neurones and its Role in Phasing Neuronal Discharges
TLDR
Most of the cells in the ventrobasal complex of the thalamus have been identified as thalamo‐cortical relay (TCR) cells, namely activation by contralateral afferent volleys and antidromic invasion from the ipsi‐lateral somato‐sensory cortex. Expand
Excitatory and inhibitory interactions in localized populations of model neurons.
TLDR
It is proved that the existence of limit cycle dynamics in response to one class of stimuli implies theexistence of multiple stable states and hysteresis in responseTo this work, coupled nonlinear differential equations are derived for the dynamics of spatially localized populations containing both excitatory and inhibitory model neurons. Expand
...
1
2
3
4
5
...