\documentclass{article}
\usepackage{amsmath,amsfonts,amssymb,graphicx}

\title{Dependence of Action Potential Duration (APD) on Cardiomyocyte $\textil{g_{K_{r}}}$ and $\textil{\tau_{K_{r}}}$ in MATLAB Long QT Syndrome Type II Simulations}
\author{BME 301 - Bioelectricity \\\ \\\ Professor Emilia Entcheva \\\ \\\ Steven Leigh \\\ Kerri Keng \\\ Bill Dusch \\\ Sybil Baby \\\ Adriana Gomez}
\date{May 2007}
\maketitle
\pagebreak
\begin{document}

  \begin{figure}
  \includegraphics[scale=0.45]{LQT2.png}
  \caption{Synergistic interaction between $\tau_{K_{r}}$ and $\textil{g_{K_{r}}}$ produces marked increase or decrease in APD.}
  \end{figure}

Sensitivity analysis determines how deviations in a system parameter affect the entire system. Sometimes it is interesting or necesary to see how changes in more than one variable affect the greater system. In this case, we consider action potential duration and it's dependence on changes in both the time constant and membrane conductance of the rapidly-activating potassium current, I_{K_{r}}.

In single variable terms, the x-axis is membrane conductance and $\frac{\partial}{\partial x}$ is the system's sensitivity in milliseconds per percent deviation of $\textil{g_{K_{r}}}$. Similarly, $\frac{\partial}{\partial y}$ is the system's sensitivity to a change in the current's time constant. For each given x- or y-value, the alternate partial derivative is found and the series of lines obtained from these derivatives are then connected, which creates a plane (Figure 1) that represents what happens to action potential duration as a function of both $\tau_{K_{r}}$ and $\textil{g_{K_{r}}}$.

Since an increase or decrease in \textsl{both} variables produces a corresponding decrease and increase in the system, the variables work together (synergistically) in their effects on action potential duration.
\end{document}