Computational and Mathematical Methods in Medicine

Volume 2016 (2016), Article ID 9580724, 10 pages

http://dx.doi.org/10.1155/2016/9580724

## Interaction between Thalamus and Hippocampus in Termination of Amygdala-Kindled Seizures in Mice

^{1}School of Biomedical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China^{2}Department of Neurology, Ren Ji Hospital, School of Medicine, Shanghai Jiao Tong University, Shanghai 200127, China

Received 26 July 2016; Accepted 20 September 2016

Academic Editor: Dong Song

Copyright © 2016 Zhen Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The thalamus and hippocampus have been found both involved in the initiation, propagation, and termination of temporal lobe epilepsy. However, the interaction of these regions during seizures is not clear. The present study is to explore whether some regular patterns exist in their interaction during the termination of seizures. Multichannel in vivo recording techniques were used to record the neural activities from the cornu ammonis 1 (CA1) of hippocampus and mediodorsal thalamus (MDT) in mice. The mice were kindled by electrically stimulating basolateral amygdala neurons, and Racine’s rank standard was employed to classify the stage of behavioral responses (stage 1~5). The coupling index and directionality index were used to investigate the synchronization and information flow direction between CA1 and MDT. Two main results were found in this study. High levels of synchronization between the thalamus and hippocampus were observed before the termination of seizures at stage 4~5 but after the termination of seizures at stage 1~2. In the end of seizures at stage 4~5, the information tended to flow from MDT to CA1. Those results indicate that the synchronization and information flow direction between the thalamus and the hippocampus may participate in the termination of seizures.

#### 1. Introduction

Epilepsy is a kind of chronic neurological disorder characterized by highly synchronized abnormal discharge of neurons. Epileptic seizures can cause serious physiological and psychological damage to patients. Due to that the seizures involve complex interactions across some regions of the brain; insights into the interrelations across some key areas during the evolution of seizures may help us to understand the pathogenesis of epilepsy as well as improve the therapy of epilepsy [1].

Temporal lobe epilepsy (TLE) is the most common type of focal epilepsy in clinic [2]. Recent studies showed that the TLE involves some encephalic regions such as the hippocampus and some of its neighboring regions including the thalamus, amygdala, and entorhinal cortex [3, 4]. Cendes et al. suggested that the most frequent neuropathological change in TLE patients was the hippocampal sclerosis [5]. Many studies have reported that the abnormal electrical activities were often detected in the hippocampus of TLE patients [6–8]. Moreover, during recent years, some researches have reported that the thalamus also plays an important role in TLE. Some studies have suggested that the thalamus is a key part in the initiation and propagation of TLE seizures [9–11]. Bertram found that the cornu ammonis 1 (CA1) of hippocampus and mediodorsal thalamus (MDT) were both involved in amygdala-kindled seizures [1, 3]. Andrade et al. showed that electrically stimulating MDT could remedy TLE [12]. Bertram et al. suggested that the seizure duration would be significantly decreased if strengthening the activity of GABAergic neurons in the MDT in the hippocampus-kindled mice [13]. All of those results are calling for more investigations on the interaction between the thalamus and the hippocampus in the termination of seizures.

To investigate the time-varying interactions between different brain areas, a number of methods, such as coupling index (CI) [14, 15] and directionality index (DI) [16, 17], have been suggested. The CI and DI represent the level of synchronization and information flow direction between different brain areas. Due to the nonlinear property of epileptic discharges, the nonlinear methods are preferred in analyzing the interactions between different brain areas during seizures [18]. The information-based method is a representative of nonlinear algorithms, which has been widely applied to analyze the epileptic discharges [10, 18, 19]. Mutual information (MI) is a useful method to study the synchronization between two time series [14]. Stam has demonstrated that MI is more robust for estimation of the changes in neural electrical activity than a linear method of spectral power analysis [20]. Frasch et al. have suggested that MI is suited to measure changes in synchronization of the neural electrical activities in different brain areas, because it is not an amplitude dependent measure [21]. Conditional mutual information (CMI) is an information theory based method to determine the information flow direction between two time series [22]. Recently, the permutation information approach and CMI were integrated, which was called permutation conditional mutual information (PCMI) [23], to estimate the coupling direction between different neuron populations [11]. The stimulation results have shown that this method is superior to CMI for measuring the characteristics of coupling direction between neuron populations [24]. Mi et al. have demonstrated that PCMI can effectively estimate the directionality of local field potentials (LFPs) between CA1 and CA3 in rats [25]. By utilizing MI and PCMI to analyze the LFPs recorded from the hippocampus and the thalamus, the interactions between them in the termination of seizures can be investigated.

The present paper is organized as follows. Section 2 presents the scheme of experimental data acquisition and briefly introduces the algorithms for estimating the MI and PCMI. The results of how the MI and PCMI vary during the evolution of seizures are presented in Section 3. The conclusion is provided in Section 4.

#### 2. Materials and Methods

##### 2.1. Data Acquisition

###### 2.1.1. Animals

Adult (3 to 5 months) male C57BL/6 mice were used in our experiments. The mice were housed in individual cages with food and water ad libitum and kept in a 12 h light/dark cycle. All animal experiments were approved by the Ethic Committee, School of Biomedical Engineering, Shanghai Jiao Tong University. All efforts were made to minimize the number of animals used and their suffering.

###### 2.1.2. Electrophysiological Recordings

Experimental procedures were described in our previous report [26]. In brief, two recording tetrodes were implanted in the MDT of thalamus (with bregma as the reference, anteroposterior (AP), −1.2 mm; mediolateral (ML), −0.6 mm; dorsoventral (DV), −3.1 mm) and the CA1 of right hippocampus (AP, −1.2 mm; ML, −0.6 mm; DV, −1.7 mm), and one stimulation bipolar electrode was implanted in the right basolateral amygdala (BLA, AP, −1.2 mm; ML, −2.6 mm; DV, −4.9 mm). The recording tetrode was formed of four twisted polyester insulated nickel-chrome alloy wires (diameter, 13 *μ*m; California Fine Wire Co., USA). The stimulation electrode was composed of two stainless steel channels (diameter, 50 *μ*m; AM System Co., USA). The recording tetrodes were gilded before being implanted to the target regions to make the impedance in the range 0.5~1.0 MΩ.

Seven days after the electrodes’ implantation, a multichannel in vivo recording system (Plexon Co., USA) and an electrical stimulator (NIHON KOHDEN Co., Japan) were connected to the electrodes. For each mouse, the amplitude of the pulses for stimulating BLA was set as 60 *μ*A (1 s train containing 60 Hz unidirectional pulses) at the first time and increased by 20 *μ*A every 10 min until the duration of the afterdischarge (AD) recorded in the BLA was longer than 5 s; then this stimulating amplitude was used in the further kindling process in this mouse. After the amplitude of the current pulses for stimulating was assigned, the kindling acquisition was achieved by stimulating BLA twice daily with subconvulsive electrical stimulations at a 4-hour interval. During the kindling process, the LFPs in the MDT and CA1 were recorded at a sampling frequency of 1000 Hz and stored for offline analysis. Racine’s rank standard was employed to classify the stage of behavioral responses (stage 1~5) [27]. The mouse in which three consecutive stage 4~5 seizures were induced was regarded as a fully kindled mouse [28]. After the electrophysiological recording finished, the histology check was carried out to inspect whether the electrodes were implanted in the correct positions. If the mouse was fully kindled and passed the histology check, three seizures at stage 1~2 (the first one, the middle one, and the last one) and two seizures at stage 4~5 (the last two) of this mouse were selected for further analysis. Seven fully kindled mice were recruited in this study.

##### 2.2. Data Analysis

###### 2.2.1. Data Preprocessing

After the LFPs in the MDT and CA1 were collected, notch filtering was performed to filter out the 50 Hz power noise. Due to that the distance between four wires in the recording tetrodes was about 15~25 *μ*m; LFP signals recorded by the wires of a tetrode were highly similar. Therefore, the mean value of LFP signals among the four wires was used to represent the LFP signal recorded by the tetrode. In the following text, the term of LFP in the calculation of coupling index and directionality index refers to the mean value.

###### 2.2.2. Coupling Index-MI

The MI quantifies the shared information between time series based on information theory and is used as the measure of synchronization between those time series [18, 29]. The MI has the maximum value when the two time series are identical, and it is zero when one system is completely independent of the other [29].

Before calculating the MI value, the probability distribution functions (PDFs) of the time series should be calculated. In this study, the permutation information approach [23, 30] was applied to calculate the PDFs of time series. Given a time series which has data points, the PDF of can be calculated by the following steps. Firstly, set a lag to sample the data to build the vectors ( represents continuous sampling, represents dislodging 1 point, and so on) and set an order number of vectors (i.e., the number of points in each vector); the vector composed of points can be arranged into possible permutation patterns ; then we get the vectors from the time series , where , , and so on (when ); thirdly, count the occurrences of each pattern in the time series which is denoted as ; finally, the probability density distribution is inferred by the following equation:

The LFPs recorded from CA1 and MDT are denoted as and , respectively. The PDFs of and are denoted as and . The joint probability functions of and are denoted as . The conditional probability function of given is denoted as .

Based on Shannon’s entropy, the entropy of and is defined as

The conditional entropy of by () is defined as

The joint entropy of and is defined as

The normalized mutual information of and is defined as

In the application of permutation information approach, the value of corresponding with the maximal value of mutual information between and was decided as [24]. was set to be 3.

###### 2.2.3. Directionality Index-PCMI

The permutation conditional mutual information (PCMI) is used to estimate the coupling direction between two time series based on the information theory [23]. After the PDFs of and were estimated by the permutation information approach mentioned in Section 2.2.2, the PCMI between and was calculated by the following equations:where means the information quantity transferred from to (or to ) when lagging behind steps as (or lagging behind steps as ).

The information that is transferred from to (or to ) is defined aswhere and are the minimal and maximal lagging steps, respectively. and are averaged over a range of to decrease the estimation fluctuations. cannot be less than according to Bahraminasab et al.’s study [23]. In this study, and were 3 ms and 20 ms, respectively.

The directionality index is defined as the following equation:

The value of ranges from −1 to 1. means that the information flows from to , and vice versa. means that the interactions between and are symmetrical.

In our study, moving windows were used to analyze the data. The number of data points in the moving window was set to 2000 sample points corresponding to 2 s and shifted forward in 0.5 s steps.

###### 2.2.4. Statistical Analysis

Statistics were performed using Matlab (version 7.0.0, The MathWorks, Inc., Natick, MA, USA). Results were presented as mean ± SEM. One-way analysis of variance (ANOVA) was used for comparison among multiple groups, with indicating significant difference.

#### 3. Result and Discussion

##### 3.1. LFPs Recorded in CA1 and MDT during Amygdala-Kindled Seizures

Neural activities were simultaneously recorded from CA1 of hippocampus and MDT of thalamus during the seizures from 7 fully kindled mice. Typically, seizures initiated immediately after electrically stimulating BLA for 1 s and manifested both behaviorally and electrographically. The epileptiform activities were observable in the hippocampus and the thalamus after the electrical stimulation (Figures 1(a) and 1(b)), and the power of LFPs was raised immediately over a wide frequency band, including theta, alpha, beta, and gamma activity (Figures 1(c)–1(f)). Because the 50 Hz power noises were filtered out, the power density spectral showed a low-power frequency band around 50 Hz.