**Thalamo-Cortical Interactions
Modeled by Weakly Connected Oscillators: Could Brain Use FM Radio Principles?**

*BioSystems *(1998)48:85-94

Frank C. Hoppensteadt and Eugene M. Izhikevich

*Systems Science Center, Box 7606,
Arizona State University,
Tempe, AZ 85287-7606. *

**Abstract.** We model
a thalamo-cortical system using the following two assumptions: 1.) Each
cortical column is an autonomous oscillator. 2.) Connections between cortical
columns and the thalamus are weak. Our goal is to deduce from these assumptions
general principles of thalamo-cortical interactions that are independent
of the equations describing the system.

We find that the existence of synaptic connections between any two cortical columns does not guarantee that the columns interact: They interact only when there is a certain nearly resonant relation between their frequencies, which implies that the interactions are frequency modulated (FM). When the resonant relation holds, the cortical columns interact through phase modulations. Thus, communications between weakly connected cortical oscillators employ an FM radio principle: the frequency of oscillation encodes the channel of communication, while the information is transmitted via phase modulations.

If the thalamic input has an appropriate frequency, then it can dynamically link any two cortical columns that would otherwise be unlinked. Thus, by adjusting its temporal activity, the thalamus has control over information processing taking place in the cortex.

Our results can be interpreted in terms of single neurons as follows: The mean firing rate (frequency) of a periodically spiking neuron does not carry any information other than identifying a channel of communication. Information (i.e., neural code) is carried through modulations of interspike intervals.

**Keywords:** Weakly connected
oscillators, quasiperiodic oscillators, canonical model, FM interactions,
thalamo-cortical system

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