Information Technology Reference
In-Depth Information
Chapter 4
Oscillatory Dynamics in Biological Neurons
Abstract
The voltage of the neurons membrane exhibits oscillatory variations after
receiving suitable external excitation either when the neuron is independent from
neighboring neural cells or when the neuron is coupled to neighboring neural cells
through synapses or gap junctions. In the latter case it is significant to analyze
conditions under which synchronization between coupled neural oscillators takes
place, which means that the neurons generate the same voltage variation pattern
possibly subject to a phase difference. The loss of synchronism between neurons
can cause several neurodegenerative disorders. Moreover, it can affect several basic
functions of the body such as gait, respiration, and heart's rhythm. For this reason
synchronization of coupled neural oscillators has become a topic of significant
research during the last years. The associated results have been also used in several
engineering applications, such as biomedical engineering and robotics. For example,
synchronization between neural cells can result in a rhythm generator that controls
joints motion in quadruped, multi-legged, and biped robots.
4.1
Neural Oscillators
Neurons exhibit complicated activation functions, denoted as spiking and bursting.
This activation mechanism is characterized by a silent stage (resting) and a stage
with intensive spike-like oscillations. Bursting activity appears in specific thalamic
cells (this affects, for example, the phases of sleep in people with parkinsonian
tremor and in such a case increased bursting activity appears in neurons which
are found in basal ganglia). Moreover, bursting activity appears in cells which
coordinate breath's rhythm, inside the so-called pre-Botzinger complex.
There is need for two biophysical mechanisms to generate bursting: (1) a
mechanism for the generation of the bursting oscillations, (2) a mechanism for the
switching between the silent phase and the bursting phase.
Spikes are voltage oscillations which are generated by the interaction of an
incoming Na
C
current and an outgoing K
C
current. The slow phase is due to an ionic
