Self-connection of Thalamic Reticular Nucleus Modulating Absence Seizures

Abstract

Accumulating evidence has suggested that the corticothalamic system not only underlies the onset of absence seizures, but also provides functional roles in controlling absence seizures. However, few studies are involved in the roles of self-connection of thalamic reticular nucleus (TRN) in modulating absence seizures. To this end, we employ a biophysically based corticothalamic network mean-field model to explore these potential control mechanisms. We find that the inhibitory projection from the TRN to specific relay nuclei of thalamus (SRN) can shape the self-connection of TRN controlling absence seizures. Under certain condition, the self-connection of TRN can bidirectionally control absence seizures, which increasing or decreasing the coupling strength of the self-connection of TRN could successfully suppress absence seizures. These findings might provide a new perspective to understand the treatment of absence epilepsy.

Appendix: The Corticothalamic Network Mean-Field Model

To obtain the corticothalamic network mean-field model, we assume that absence seizures are involved in the whole brain, so that the spatial effect is ignored in this model. Also, based on the assumption that intracortical connections are proportional to the synapses involved, we have $V_{i}=V_{e}$ and $Q_{i}=Q_{e}$. Note that both of these assumptions are in line with previous studies [11,12,13, 20, 21]. Accordingly, the corticothalamic network mean-field equations are given in the following:

$$\begin{aligned} \frac{\texttt {d}{\phi _e}(t)}{\texttt {d}t}=\dot{\phi }_{e}(t) \end{aligned}$$

(1)

$$\begin{aligned} \frac{\texttt {d}\dot{\phi }_{e}(t)}{\texttt {d}t}=\gamma _{e}^{2}\left\{ -{\phi _e(t)}+ {F[V_e(t)]}\right\} -2{\gamma _e}{\dot{\phi }_{e}(t)} \end{aligned}$$

(2)

$$\begin{aligned} \frac{\texttt {d}{V_e(t)}}{\texttt {d}t}=\dot{V}_{e}(t) \end{aligned}$$

(3)

$$\begin{aligned} \frac{\texttt {d}\dot{V}_{e}(t)}{\texttt {d}t}={\alpha }{\beta }\left\{ -{V_e(t)}+v_{ee}{\phi _{e}(t)}+v_{ei}{F[V_e(t)]} +v_{es}{F[V_s(t)]}\right\} -({\alpha }+{\beta })\dot{V}_{e}(t) \end{aligned}$$

(4)

$$\begin{aligned} \frac{\texttt {d}{V_r(t)}}{\texttt {d}t}=\dot{V}_{r}(t) \end{aligned}$$

(5)

$$\begin{aligned} \frac{\texttt {d}\dot{V}_{r}(t)}{\texttt {d}t}={\alpha }{\beta }\left\{ -{V_{r}(t)}+v_{re}{\phi _{e}(t)} +v_{rs}{F[V_s(t)]}+v_{rr}{F[V_r(t)]}\right\} -({\alpha }+{\beta })\dot{V}_{r}(t) \end{aligned}$$

(6)

$$\begin{aligned} \frac{\texttt {d}{V_s(t)}}{\texttt {d}t}=\dot{V}_{s}(t) \end{aligned}$$

(7)

$$\begin{aligned} D_{s}={\alpha }{\beta }\left\{ -{V_{s}(t)}+v_{se}{\phi _{e}(t)} +v{_{sr}^{A}}{F[V_r(t)]}+v{_{sr}^{B}}{F[V_r(t-\tau )]}+\phi _{n}\right\} \end{aligned}$$

(8)

$$\begin{aligned} \frac{\texttt {d}\dot{V}_{s}(t)}{\texttt {d}t}=D_{s}-({\alpha }+{\beta })\dot{V}_{s}(t) \end{aligned}$$

(9)

Here, $\phi _{a}$ ($a={e, i, r, s}$) shows the propagating axonal fields of the neural population a, $v_{ab}$ describes the coupling strength from the neural population b to the neural population a. The inverses of $\alpha$ and $\beta$ represent the decay and rise time constants, respectively. $\gamma _{e}$ governs the temporal damping rate of cortical excitatory pulses. $V_{a}$ denotes the mean membrane potential, through which the mean firing rate $Q_{a}$ can be obtained with the sigmoid function $F[{V}_{a}(t)]$ [11, 12, 20] given by

$$\begin{aligned} Q_{a}(t)\equiv {F}[{V}_{a}(t)]=\frac{{Q}_{a}^{max}}{1+{\texttt {exp}}[-{\frac{\pi }{\sqrt{3}}} {\frac{({V}_{a}(t)-{\theta }_{a})}{\sigma }}]} \end{aligned}$$

(10)

where $Q_{a}^{max}$ denotes the maximum firing rate, $\theta _{a}$ shows the mean firing threshold, and $\sigma$ is the standard deviation of the mean firing threshold.