Possible mechanisms to improve sleep spindles via closed loop stimulation during slow wave sleep: A computational study

Abstract

Sleep spindles are one of the prominent EEG oscillatory rhythms of non-rapid eye movement sleep. In the memory consolidation, these oscillations have an important role in the processes of long-term potentiation and synaptic plasticity. Moreover, the activity (spindle density and/or sigma power) of spindles has a linear association with learning performance in different paradigms. According to the experimental observations, the sleep spindle activity can be improved by closed loop acoustic stimulations (CLAS) which eventually improve memory performance. To examine the effects of CLAS on spindles, we propose a biophysical thalamocortical model for slow oscillations (SOs) and sleep spindles. In addition, closed loop stimulation protocols are applied on a thalamic network. Our model results show that the power of spindles is increased when stimulation cues are applied at the commencing of an SO Down-to-Up-state transition, but that activity gradually decreases when cues are applied with an increased time delay from this SO phase. Conversely, stimulation is not effective when cues are applied during the transition of an Up-to-Down-state. Furthermore, our model suggests that a strong inhibitory input from the reticular (RE) layer to the thalamocortical (TC) layer in the thalamic network shifts leads to an emergence of spindle activity at the Up-to-Down-state transition (rather than at Down-to-Up-state transition), and the spindle frequency is also reduced (8-11 Hz) by thalamic inhibition.

Fig 1. The thalamocortical network geometry.

The network is comprised of four cell layers. The top two consist of cortical PY and IN cells. The bottom two, thalamic TC and RE neuron layers, generate sleep spindles. The cortical PY cells layer contains 200 neurons, all other layers contain 40 neurons. Small, green-filled circles symbolize locations of GABA_ARs or GABA_ARs+ GABA_BRs, and the green lines corresponding afferent connections. Red arrowheads point, to AMPARs or AMPARs+ NMDARs receptors, with the red lines indicating the corresponding connections.

Fig 2. Closed loop stimulation (CLS) and driving stimulation (DSt) protocols.

A, In this CLS protocol, stimulation cues (red arrows) were applied immediately after the begin of the SO Down-to-Up-state transition of two successive SOs. After the second cue, SO detection was paused for 2.5 seconds (grey-shaded). B, In this driving stimulation (DSt) protocol, stimulation cues were similarly delivered immediately after the begin of the SO Down-to-Up-state transition. Stimulation was continued for each successive SO as long as the Down-state duration was shorter than 0.5 seconds. C, Different SO states and stimulation points. The dark green circle is the stimulation point immediately after the begin of the Down-to-Up-state transition (“Point 1”, SO detection point), the light green circles present the stimulation points 120 ms (“Point 2”) and 180 ms (“Point 3”) after SO detection, respectively. The red circle is the stimulation point during the Up-to-Down-state transition called “Point 4”. The green and red bars present the SO Down-to-Up and Up-to-Down-state transitions, respectively. The black arrows point to different SO states.

Fig 3. Layer specific network activity.

A, Time-space raster plots exhibit the simultaneous activity of pyramidal (PY) and thalamic layers (200 PY cells, 40 cells in each thalamic layer) for a random 15 sec time interval. The membrane potential of each cell is color coded. TC and RE represent thalamocortical and reticular cells of the thalamic network. B, Corresponding single-cell activity within each neuron layer. C, Zoomed single-cell activity of (blue shaded) one slow oscillation (SO) cycle. D, Cortical LFP (red), calculated as the sum of postsynaptic currents (AMPA, GABA_A NMDA) of pyramidal (PY) cells. Thalamic activity (AMPA current; blue) occurs at the SO Down-to-Up-state transition of. E, Time-frequency spectrogram of cortical LFP revealing SO and sleep spindle activity (calculated by 1 sec moving Fourier transform window; range, 0.1–18 Hz). F, Power spectrum density (PSD) of the cortical LFP, exhibiting a peak in the sleep spindle (10–16 Hz) frequency band. G, The average number of SOs and spindles per minute.

Fig 4. Closed loop stimulation (CLS) simulation results.

A, Power spectral density (PSD) of the cortical LFP across a 300 s time period with “Point 1” (green), “Point 4” stimulation (red), and Control (black) simulation. Spindle power was increased compared to Control when the stimulation cue was applied at “Point 1”. Conversely, spindle power was not increased when the cue was applied at “Point 4”. B, Number of spindles in resultant simulations. Average value of spindle density was increased during “Point 1” (green) compared to “Point 4” stimulation (red) and Control simulation (grey). C, Average value of spindle density was decreased when the stimulation cue was applied at both delays after the “Point 1” point. The stimulation cue was less effective with a larger time delay (180 ms) compared to a smaller time delay (120 ms). D, Average inter-spindle time. The average inter-spindle time period was also significantly reduced when stimulation cues were applied at “Point 1” compared to “Point 4” (red) and Control simulation (grey). * P < .005, two sample t-test.

Fig 5. Driving stimulation (DSt) simulation results.

A, PSD of the cortical LFP across a 300 s time period with “Point 1” (green), “Point 4” stimulation (red), and Control simulation (black). Spindle power was increased compared to Control when the stimulation cue was applied at “Point 1”. Conversely, this power was not increased when the cue was applied at “Point 4”. B, Number of spindles in resultant simulations. Average value of spindle density was increased when the stimulation cue was applied at “Point 1” (green) compared to “Point 4” stimulation (red) and Control simulation (grey). C, The average inter-spindle time period was also significantly reduced when stimulation cue was applied at “Point 1” compared to “Point 4” stimulation (red) and Control simulation (grey). * P < .005, two sample t-test with. D, Number of clicks (cues) in CLS and DSt simulations across the time period of 300 s. The number of clicks was higher in CLS compared to the DSt simulation.

Fig 6. One click closed loop stimulation (sCLS) simulation results.

A, PSD of the cortical LFP across a 300 s time period with “Point 1” (green), “Point 4” stimulation (red), and Control simulation (black). Spindle power was increased compared to Control when stimulation cues were applied at “Point 1” like CLS and DSt. B, Average value of spindle density in Control, “Point 1”, and “Point 4” stimulation. C, PSDs of cortical LFP with control simulation, sCLS, and CLS stimulation at “Point 1” stimulation. The sigma power was higher in CLS than in sCLS.

Fig 7. Possible mechanism of the initiation of fast and slow spindles.

A, A cartoon diagram of fast spindles’ mechanism. The thalamocortical (TC) layer receives a stronger cortical excitatory input (large red plus sign) from the pyramidal layer, whereas the reticular (RE) layer receives a weaker cortical input. Having a relatively strong excitatory input, the TC layer produces fast thalamic activity which is nested with SOs during the Down-to-Up-state transition (left bottom). A1, The cortical LFP (red) with fast thalamic input (blue) which is nested with cortical LFP during the Down-to-Up-state transition. A2, The corresponding activity of single TC (red) and RE (green) cells. A3, PSD of cortical LFP with fast spindles. B, A cartoon diagram of slow spindles’ mechanism. The RE layer receives a stronger cortical excitatory input (large red plus sign) from the pyramidal layer whereas the TC layer receives a weaker cortical input. Having an excitatory input, the RE layer sends a strong inhibitory input to the TC layer and resultantly, the TC layer produces slow thalamic activity during the Up-to-Down-state transition (left bottom). B1, The cortical LFP (red) with a slow thalamic input (blue) which is nested with cortical LFP during the Up-to-Down-state transition. B2, The corresponding activity of single TC (red) and RE (green) cells. The TC cell activity is observed later (~400 ms) during the SO Up to Down-state B3, PSD of cortical LFP with slow spindles.