The adjustment mechanism of the spike and wave discharges in thalamic neurons: a simulation analysis

Abstract

Different from many previous theoretical studies, this paper explores the regulatory mechanism of the spike and wave discharges (SWDs) in the reticular thalamic nucleus (TRN) by a dynamic computational model. We observe that the SWDs appears in the TRN by changing the coupling weights and delays in the thalamocortical circuit. The abundant poly-spikes wave discharges is also induced when the delay increases to large enough. These discharges can be inhibited by tuning the inhibitory output from the basal ganglia to the thalamus. The mechanisms of these waves can be explained in this model together with simulation results, which are different from the mechanisms in the cortex. The TRN is an important target in treating epilepsy, and the results may be a theoretical evidence for experimental study in the future.

Keywords: Computation model; Control; Reticular thalamic nucleus; Spike and wave discharges.

Fig. 1

The BGCT mean-field model (Chen et al. , , ; Van Albada et al. ; Van Albada and Robinson 2009). The neuronal nuclei are abbreviated as follows: r=TRN; s=SRN; $p_2$=GPe; $p_1$=SNr/GPi; $\zeta$=STN; $d_1$=striatal D1 neurons; $d_2$=striatal D2 neurons; e=ECN; i=IIN. Blue lines indicate excitatory connections regulated by glutamate receptors. Yellow lines indicate inhibitory connections regulated by $\gamma$-aminobutyric acids (GABA) receptors

Fig. 2

The different firing states in the TRN, which are obtained by taking $v_{\mathit{ee}}$=0.7, $v_{\mathit{rs}}$=1.5, $v_{\mathit{rs}}$=1 and $v_{\mathit{se}}$=4, respectively. ${\varphi }_r$ is the pulse field of TRN. A A low firing stable state (1). B A simple periodic oscillation state (2). C A typical SWDs state (3), which is a periodic firing phenomenon with two pairs of maxima and minima in a period. D A maximal firing stable state (4). We set $-{\nu }_{\mathit{sr}}$=1.4 and ${\nu }_{p_1\zeta }$=1.8 in all simulations

Fig. 3

A–G The one-dimensional state bifurcation diagrams, which are obtained by changing different parameters ($v_{\mathit{ee}}$, ${\varphi }_n$, $v_{\mathit{re}}$, $v_{\mathit{rs}}$, $v_{\mathit{se}}$, $-v_{\mathit{ei}}$ and $-v_{\mathit{sr}}$, respectively) in the corticothalamic system. ${\varphi }_r$ is the pulse field of TRN. (1),(2),(3) and (4) represent the low firing state, simple periodic oscillation state, SWDs state and maximum firing rate state, respectively. In one cycle, the state (1) and (4) have one extreme point, the state (2) has two extreme points and the state (3) has four extreme points. We set $-{\nu }_{\mathit{sr}}$=1.4 and ${\nu }_{p_1\zeta }$=1.8 in all simulations

Fig. 4

a1–d1 The state bifurcation results in (${\nu }_{p_1\zeta },{\nu }_{\mathit{ee}}$), (${\nu }_{p_1\zeta },-{\nu }_{\mathit{ei}}$), (${\nu }_{p_1\zeta },{\nu }_{\mathit{se}}$) and (${\nu }_{p_1\zeta },-{\nu }_{\mathit{sr}}$), respectively. ${\nu }_{p_1\zeta }$ is the connection strength from the STN to the SNr, which can adjust the activation level of SNr. Different oscillation states are distinguished by four different colors. They show that the SWDs may be inhibited via decreasing or increasing in ${\nu }_{p_1\zeta }$, as indicated by bidirectional arrows. a2–d2 The corresponding DF calculation results, which show that the DF of SWDs state is in 2–4 Hz. In all simulations, we set $-{\nu }_{\mathit{sr}}$=1 in (a); $-{\nu }_{\mathit{sr}}$=1.4 in (b) and (c)

Fig. 5

The effect of the parameter $v_{\mathit{es}}$ on control. a1–e1 The state simulation results in (${\nu }_{p_1\zeta },KK$). Here, we define ${\nu }_{r{p}_1}=KK{\nu }_{s{p}_1}$, and KK is a constant, which represents the competitive relationship between ${\nu }_{r{p}_1}$ and ${\nu }_{s{p}_1}$. They are simulated via taking $v_{\mathit{es}}$=0.8, $v_{\mathit{es}}$=1, $v_{\mathit{es}}$=1.5, $v_{\mathit{es}}$=2 and $v_{\mathit{es}}$=2.3, respectively. Different oscillation states are distinguished by four different colors, which show that the dynamic behaviors have good robustness within some small ranges of parameter changes, such as (a) and (b), or, (c), (d) and (e). And, the $v_{\mathit{es}}$ has great effect on control when it changes greatly. a2–e2 The corresponding DF calculation results

Fig. 6

The polyspike wave discharges (PSWDs) appears in the TRN when the $\tau$ increases to large enough. a and b The state and DF simulation results obtained in (${\nu }_{\mathit{es}},\tau$). Different firing states are expressed by four different colors in (a). P3 represents the polyspike wave discharges state in (a), and the 2–4 Hz PSWDs region is denoted as “PSWDs” in (b). c–h Several time series of the PSWDs, simulated by taking different values of the $\tau$, which show that the number of pulses in one period increases with the increasing in delay. i The MDs of the TRN with the increasing of $\tau$, obtained by setting $v_{\mathit{es}}$=2 mV s. It is shown that the increase of $\tau$ may enhance the activation level of the TRN.

Fig. 7

The inhibition effect of the PSWDs by employing an external stimulus voltage V in the SNr. a–b The state and DF computational results. The PSWDs can be inhibited by tuning V to large enough, indicated by the arrow. c–d The transition process of the time series with the linear increase of the V, simulated by taking $\tau$=0.6 s in (a). In all simulations, we set $v_{\mathit{es}}$=1.5 mV s

Fig. 8

The synchronous resonance phenomenon of EPN, TRN and SRN. a–d represent four different states obtained by setting different values of ${\nu }_{\mathit{es}}$