update article

Results Diffusion

article/article.tex

@@ -286,14 +286,15 @@
 
   % Модель 1
   \subsection*{Model 1: Diffusion}
-  In the case of the diffusion mechanism simulations were conducted without Eq.(\ref{eqn:phi}), and with Eq.(\ref{eqn:theta}) set to $\theta = \varphi$.
+  In the case of the diffusion mechanism simulations were conducted without Eq.(\ref{eqn:phi}), and with Eq.(\ref{eqn:theta}) set to $\theta = \varphi$. The diffusion was considered to be equal in both spatial directions $x$ and $y$. The resulted model's behaviour at the point is consistent with the homogeneous case, and the observations from multiple points allows us to calculate additional characteristics of the model such as wave's velocity and length. We start from the point's description of the model, continue with a comparison of measurements at multiple points and finally look at the spatial picture of the resulted potassium wave.
 
+  The central point of the domain shows a population activity with periodic spontaneous IDs (Fig \ref{fig:diff_K_point_center_period}). The period is about 90 seconds. Each ID is characterized by a high rate of activity for about 20 seconds (Fig \ref{fig:diff_K_point_center}), and consists of SBs resembling IIDs (Fig \ref{fig:diff_K_point_center}A). $[K]_o$ dynamics determines the time length of an ID. As soon as its slow increase reaches a certain maximum level (around 4mM), the increase velocity jumps to a higher value and gives a start to an ID. The velocity keeps growing until it is balanced by the Na-K-pump. After that the velocity decreasing and the potassium concentration starts returning to its baseline. The concentration approaching the baseline defines the ID's termination. The peak of $[K]_o$ takes place at the middle of an ID, and the form of $[K]_o$ wave is symmetric about this middle. The $Na^+/K^+$ pump in its turn peaks at the end of an ID. The form of the pump's wave is shifted towards the ID's end as its activity keeps increasing until the original potassium concentration is restored. The sodium concentration starts its increase together with the jump of the potassium concentration velocity. After that it keeps increasing until it reaches the maximum at the end of an ID and slowly decays to the original concentration before the next ID. Both the increase and the decrease of the sodium concentration are approximately linear.
 
   \begin{figure}
     \centering
-    \makebox[\textwidth][c]{\includegraphics[width=1.2\textwidth]{diff/K_board.png}}
-    \caption{Potassium concentration patterns during one ID}
-    \label{fig:diff_K_board}
+    \includegraphics[width=1.0\textwidth]{diff/x40y40_period.png}
+    \caption{Periodic activity of series of IDs recorded in the center of the cortical domain(Fig.\ref{fig:diff_K_board}). \textbf{A}, the representative neuron membrane depolarization $U$. \textbf{B}, the total input current $u$. \textbf{C}, The ionic concentrations $[K]_o$ and $[Na]_i$, and the $Na^+/K^+$ pump current $I_{pump}$. \textbf{D}, the somatic firing rate $\nu$ and the synaptic resource $x^D$}.
+    \label{fig:diff_K_point_center_period}
   \end{figure}
   \begin{figure}
     \centering
@@ -301,12 +302,7 @@
     \caption{An ictal discharge recorded in the center of the cortical domain (Fig.\ref{fig:diff_K_board}). \textbf{A}, the representative neuron membrane depolarization $U$. \textbf{B}, the total input current $u$. \textbf{C}, The ionic concentrations $[K]_o$ and $[Na]_i$, and the $Na^+/K^+$ pump current $I_{pump}$. \textbf{D}, the somatic firing rate $\nu$ and the synaptic resource $x^D$}.
     \label{fig:diff_K_point_center}
   \end{figure}
-  \begin{figure}
-    \centering
-    \includegraphics[width=1.0\textwidth]{diff/x40y40_period.png}
-    \caption{Periodic activity of series of IDs recorded in the center of the cortical domain(Fig.\ref{fig:diff_K_board}). \textbf{A}, the representative neuron membrane depolarization $U$. \textbf{B}, the total input current $u$. \textbf{C}, The ionic concentrations $[K]_o$ and $[Na]_i$, and the $Na^+/K^+$ pump current $I_{pump}$. \textbf{D}, the somatic firing rate $\nu$ and the synaptic resource $x^D$}.
-    \label{fig:diff_K_point_center_period}
-  \end{figure}
+
   \begin{figure}
     \centering
     \begin{minipage}{0.5\linewidth}
@@ -325,6 +321,13 @@
     \end{minipage}
   \end{figure}
 
+  \begin{figure}
+    \centering
+    \makebox[\textwidth][c]{\includegraphics[width=1.2\textwidth]{diff/K_board.png}}
+    \caption{Potassium concentration patterns during one ID}
+    \label{fig:diff_K_board}
+  \end{figure}
+
   % Модель 2
   \subsection*{Model 2: Axo-dendritic spread}
   \label{Results_Model2}