A model of sleep spindles generation
Introduction
Sleep spindles are the characteristic transient phenomena in sleep EEG. They mark the sleep onset and are presumably involved in the gating mechanism blocking the perception of external stimuli. Spindles are characterized by the waxing and waning waves of frequency 7–14 Hz, duration of 0.5–3 s, and the periodic reoccurrence of 3–20 s. Generation of spindles involves two kinds of neural populations: thalamocortical (TC) and reticular (RE) [8].
The main aim of the present model is to provide insight into thalamocortical oscillations observed in humans. Studies in humans show that spindles recorded in frontal derivations have spectra centered approximately at 12 Hz and those recorded in posterior derivations—at 14 Hz. Sleep spindles recorded in the posterior derivations reoccur with period about 4 s, while those in the frontal derivations do not show any specific periodicity [10].
Section snippets
Methods
The model consists of interacting RE and TC populations (Fig. 1). The populations interact with each other by means of pulse densities. Pulse density of a population can be related to the average potential in a population [5], [6], [9].where gTC and gRE are sigmoidal functions and are maximal pulse densities. The pulses generated in one population are transformed in the other population into synaptic currents.
Results
Mechanism of sleep spindle initiation depends on the variance of input noise N. The spindle oscillation is maintained due to reciprocal inhibition of the TC and excitation of the RE population. A spindle terminates spontaneously after a few cycles due to a small increase in resting membrane potential in TC neurons and the decreasing depth of the hyperpolarizations in consecutive spindle cycles, which causes inactivation of ITTC. Those changes result from the progressive activation of Ih. In
Discussion
Results of the simulations support hypothesis that topographical differences observed in vivo in the sleep spindle frequencies are the result of weaker inhibition (by RE) of thalamocortical nuclei projecting to the frontal cortex than the thalamocortical nuclei projecting to the sensory—motor cortex. That hypothesis is further supported by anatomical studies of density of GABA immunoreactive neurons [7]. Weaker inhibition of thalamocortical nuclei projecting to the frontal cortex can explain
Conclusion
The presented model describes rhythmical activity, in which thalamic system is involved, ranging from wakefulness through light to deep sleep and also in slices preparation. It explains topographical sleep spindle frequency, periodicity of their reoccurrence, and the differences of that periodicity in vivo and in vitro. We hypothesize that:
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The low and high frequency spindles are generated in different RE-TC loops characterized by different coupling strengths.
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The periodicity difference between
Jarosław Żygierewicz was born in Warsaw, Poland in 1971. He received the M.Sc. degree in physics in 1995 and the Ph.D. in medical physics in 2000 from the Warsaw University. His research interests are the analysis of biological signals and the modeling of bioelectric phenomena. Currently he is Assistant Professor in Physics Faculty of Warsaw University.
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Cited by (6)
Intracerebral recordings of nocturnal hyperkinetic seizures: Demonstration of a longer duration of the pre-seizure sleep spindle
2007, Clinical NeurophysiologyCitation Excerpt :It is speculated that the two types of sleep spindles (slow spindles in the frontal regions and fast spindles in the parietal regions) are generated by the same mechanism, but in distinct RE-thalamocortical loops, with different durations of GABA receptor-mediated IPSPs in different thalamocortical neurons. Different densities of reticular GABAergic innervation of thalamocortical neurons could explain the various hyperpolarization durations (weaker inhibition by RE of thalamic nuclei projecting to the frontal cortex) (McCormick and Bal, 1997; Zygierewicz et al., 1999; Zygierewicz et al., 2001). The concept of a transformation of the sleep spindles which are generated in the thalamocortical system into epileptic discharges was proposed many years ago from studies performed in a model of absence seizures, the feline generalized penicillin epilepsy (Gloor et al., 1979; Gloor and Fariello, 1988).
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Jarosław Żygierewicz was born in Warsaw, Poland in 1971. He received the M.Sc. degree in physics in 1995 and the Ph.D. in medical physics in 2000 from the Warsaw University. His research interests are the analysis of biological signals and the modeling of bioelectric phenomena. Currently he is Assistant Professor in Physics Faculty of Warsaw University.
Piotr Suffczynski was born in 1970. He studied physics and received the Master's degree in Medical Physics from the Warsaw University, Warsaw, Poland, in 1995. From 1995 till now, he has been a Ph.D. student in the group of Prof. Blinowska at the Laboratory of Medical Physics, Warsaw University. He spent two years of Ph.D. study in the group of prof. Lopes da Silva at the Faculty of Biology, University of Amsterdam, Amsterdam and Institute of Epilepsy, Heemstede, The Netherlands. He is currently finishing his Ph.D. project, which concerns modeling normal and abnormal oscillations in the thalamocortical network.
Katarzyna J. Blinowska received M.Sc. and in 1969 Ph.D. degree in experimental physics from Faculty of Physics, Warsaw University, where she has been employed since graduation till now. In 1979 she received Sc.D. (doctor habilitatus) degree for her research on biological signal analysis. During 1982–1983 she was invited professor at the University of Southern California. Since 1984 she is a head of Medical Physics Laboratory at Warsaw University. In 1994 she became Full Professor. Her main research interests concern investigation of biophysical basis of electrical activity of central nervous system by modeling and signal analysis.