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\title[Diabetes and Wavelets]{Analysis of Type 1 Diabetes with Wavelets and Other Mathematical Tools}% \subtitle{}
\author[Edward Aboufadel]{GVSU REU 2009}
\institute[GVSU REU 2009]{Edward Aboufadel \\ Department of Mathematics \\ Grand Valley State University \\ Allendale, MI 49401}
\date{Summer 2009}

\begin{document}
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\begin{frame}
\titlepage
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\begin{frame}
\frametitle{Presentation Overview}
\begin{enumerate}
\item Introduction Type 1 Diabetes
\pause
\item Introduction to Wavelets
\pause
\item Project 1:  Clustering Diabetics
\pause
\item Project 2:  Glucose Control with a Wavelet-Based Controller
\pause
\item How We'll Get Started
\end{enumerate}
\end{frame}
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\begin{frame}
\frametitle{Type 1 Diabetes}

\begin{textblock}{3}(0,.1)
Zachary Aboufadel:  hockey player, 5th grader, type 1 diabetic
\end{textblock}

\vspace{.1in}

\begin{center}
 \includegraphics[width=350pt]{Zack.pdf}
\end{center}
\pause
\end{frame}

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\begin{frame}
\frametitle{Type 1 Diabetes}

\only<1>{\begin{block}{}
\begin{itemize}
\item Beta cells in the pancreas create \alert{insulin} to regulate the amount of glucose in the blood.
\item Insulin is a hormone that helps the body move the glucose contained in food into cells throughout the body, which use it for energy.
\end{itemize}
\end{block}
}
\only<2>{

\begin{center}
 \includegraphics[width=350pt]{Glucose.pdf}
\end{center}}
\pause

\only<3>{\begin{block}{}\begin{itemize}
\item For people with type 1 diabetes, \alert{the beta cells have been destroyed}.
\item When the beta cells are destroyed, no insulin can be produced, and the glucose stays in the blood instead, where it can cause serious damage to all the organ systems of the body.
\end{itemize}
\end{block}}

\only<4>{

\begin{center}
 \includegraphics[width=350pt]{Pancreas.pdf}
\end{center}
\pause
}
\end{frame}

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\begin{frame}
\frametitle{Type 1 Diabetes}

\begin{block}{}
\begin{itemize}
\item The beta cells are destroyed by \alert{the body's own immune system}, so type 1 diabetes is considered an autoimmune disease.
\item Something happens in the body to activate the immune system to attack the beta cells, but medical scientists are not certain what that is.
\end{itemize}
\end{block}

\begin{block}{}
\begin{itemize}
\item There is growing but inconclusive evidence that type 1 diabetes starts with an infection by a type of virus called a \alert{coxsackie virus}, which are polio-related viruses that cause upper respiratory infections.  After fighting off the virus, the body's immune system turns on the beta cells in the pancreas.
\item However, you cannot catch diabetes from a type 1 diabetic.
\end{itemize}
\end{block}


\end{frame}

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\begin{frame}
\frametitle{Managing Type 1 Diabetes}

\only<1>{\begin{block}{}\begin{itemize}
\item For someone with type 1 diabetes, the most important job is \alert{keeping the blood glucose level under control}.
\item Non-diabetics typically have a blood glucose reading between 80 and 100 mg per dL.
\item For diabetics, that number can range from 20 to over 500.
\end{itemize}\end{block}}

\only<2>{
\begin{block}{Diabetic vs. Non-Diabetic}
\begin{center}
 \includegraphics[width=350pt]{GlucoseChart.pdf}
\end{center}
\end{block}}
\pause

\only<3>{\begin{block}{}\begin{itemize}
\item Many type 1 diabetics use an \alert{insulin pump} to put insulin into their bloodstream 24 hours a day.
\item For research purposes, a \alert{continuous glucose meter} can be used to record glucose levels at 5-minute intervals.
\item For most people, though, a meter with test strips is used four to eight times a day.
\end{itemize}\end{block}}

\only<4>{
\begin{block}{Insulin Pump and Continuous Glucose Monitor}
\begin{center}
 \includegraphics[width=350pt]{Pump.pdf}
\end{center}
\end{block}
}

\only<5>{
\begin{block}{Glucose Meter}
\begin{center}
 \includegraphics[width=350pt]{Meter.pdf}
\end{center}
\end{block}
}

\only<6>{
\begin{block}{Testing With A Meter}
\begin{center}
 \includegraphics[width=350pt]{MeterTest.pdf}
\end{center}
\end{block}
}

\only<7>{\begin{block}{}\begin{itemize}
\item About 24 million Americans have diabetes now, with 5-10\% being type 1 diabetes.  There are about \alert{30,000 new cases of type 1 diagnosed each year}.
\item Recent studies suggest that the prevalence of the disease is increasing.
\item  Some well-known type 1 diabetics:  Chicago Bears QB Jay Cutler; Nick Jonas (of the Jonas brothers); actress Sharon Stone; American Idol contestant Elliot Yamin; actress Mary Tyler Moore; musician David Crosby; supreme-court nominee Sonia Sotomayor.
\end{itemize}\end{block}}


\only<8>{
\begin{block}{Diabetic vs. Non-Diabetic}
\begin{center}
 \includegraphics[width=350pt]{GlucoseChart.pdf}
\end{center}
\end{block}}
\end{frame}

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\begin{frame}
\frametitle{Wavelets}

\only<1>{
\begin{block}{}
Wavelets have been developed over the past 30 years.  They are a tool that have been used for image compression, denoising old sound recordings, and many other applications.
\end{block}

~\vspace{0.2in}

\begin{block}{Functions or Filters}\begin{itemize}
\item You can think of \alert{wavelets as functions} that are used to analyze other functions.

\item You can think of \alert {wavelets as filters} that are used to analyze signals.
\end{itemize}
\end{block}}

\end{frame}

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\begin{frame}
\frametitle{Wavelets to Analyze Functions}

\only<1>{

\begin{block}{The Haar mother wavelet}
\begin{center}
 \includegraphics[width=350pt]{HaarMother.pdf}
\end{center}
\end{block}}

\only<2>{

\begin{block}{Shrinking the Haar mother wavelet}
\begin{center}
 \includegraphics[width=350pt]{HaarMother2.pdf}
\end{center}
\end{block}}

\only<3>{

\begin{block}{Dilations and Translations of the Haar mother wavelet}
\begin{center}
 \includegraphics[width=350pt]{HaarMother3.pdf}
\end{center}
\end{block}}


\only<4>{
\begin{block}{Wavelet Multiresolution Analysis of a Function}
$\psi(t)$ is the mother wavelet.  $f(t)$ is the function to be decomposed.

\begin{equation}
f(t) \approx \sum_{j,k} a_{j,k} \psi(2^j t - k)
\end{equation}

\end{block}
}

\only<5>{
\begin{block}{}\begin{itemize}
\item In a wavelet multiresolution analysis, \alert{a set of wavelets forms a basis} for a vector space of functions.
\item Other functions are written as a linear combination of the wavelet basis functions.
\item The coefficients in the linear combination can tell you something about the function you are analyzing, or can be used for other purposes.
\end{itemize}
\end{block}
}

\only<6>{
\begin{block}{The Daubechies father wavelet}
\begin{center}
 \includegraphics[width=350pt]{DaubechiesFather.pdf}
\end{center}
\end{block}}

\only<7>{
\begin{block}{A Daubechies daughter wavelet}
\begin{center}
 \includegraphics[width=350pt]{DaubechiesDaughter.pdf}
\end{center}
\end{block}}

\only<8>{
\begin{block}{Exact reproduction of a linear function}
%{\fontsize{7}{9}
$$\sum_{k=-4}^3 (-2k + 2 + \sqrt{3}) D_4(t-k)$$
%}
\begin{center}
\includegraphics[width=250pt, height=300pt]{DaubLinear.pdf}
\end{center}
\end{block}}

\only<9>{
\begin{block}{Linear Combination of 15 Daubechies wavelet functions}
\begin{center}
 \includegraphics[width=350pt]{DaubAnalysis.pdf}
\end{center}
\end{block}}


\end{frame}

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\begin{frame}
\frametitle{Wavelets to Analyze Signals}

\only<1>{
\begin{block}{}\begin{itemize}
\item The simplest signal is just a sequence of numbers.
\item \alert{A wavelet filter converts a signal into another signal.}  The output can tell you something about the original signal, or can be used for other purposes.
\end{itemize}
\end{block}}

\only<2>{
\begin{block}{Example with Daubechies Filters}
\begin{itemize}
\item Here is the signal we are going to analyze:  $s = [1.02, 2.01, 2.99, 4.05, 5.12, 6.03, 7.09, 7.98, 9.14, 10.05, 11.02, 12.00]$.
\item Here are the filters:
\item  Low-pass filter:  $H$ = [0.483, 0.837, 0.224, --0.129 ].
\item  High-pass filter: $G$ = [--0.129, --0.224, 0.837, --0.483].
\item  When filtering, we basically compute the dot product between four entries in the signal and the four entries in the filter.
\item  The low-pass filter will compute some sort of \alert{average} of the signal entries.  The high-pass filter will pick up changes or \alert{differences} in the signal.
\end{itemize}
\end{block}
}

\only<3>{
\begin{block}{Example with Daubechies Filters}
\begin{itemize}
\item $s = [1.02, 2.01, 2.99, 4.05, 5.12, 6.03, 7.09, 7.98, 9.14, 10.05, 11.02, 12.00]$.
\item Low-pass results:  $Hs$ = [2.32234, 5.20303, 8.07881, 10.85464, 13.74695].
\item High-pass results:  $Gs$ = [--0.03534, 0.08004, 0.06879, 0.09390, --0.00252].
\item The high-pass results are close to zero because \alert{the signal is practically linear}.
\item Filtering can be reversed, but you can tweak the output before reversing as a way to clean up data, or hide messages, or something else.
\end{itemize}
\end{block}
}

\end{frame}



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\begin{frame}
\frametitle{REU 2008:  Imitating Chuck Close}

\only<1>{

\begin{block}{Artwork by Chuck Close}
\begin{center}
 \includegraphics[width=350pt]{Close.pdf}
\end{center}
\end{block}}

\only<2>{

\begin{block}{Artwork by Chuck Close}
\begin{center}
 \includegraphics[width=350pt]{CloseClose.pdf}
\end{center}
\end{block}}

\only<3>{
\begin{block}{by Clara Madsen and Sarah Boyenger}
\begin{center}
 \includegraphics[width=350pt]{Emily.pdf}
\end{center}
\end{block}}

\only<4>{
\begin{block}{Something More Abstract}
\begin{center}
 \includegraphics[width=350pt]{Lincoln.pdf}
\end{center}
\end{block}}

\end{frame}

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\begin{frame}
\frametitle{REU 2009:  Project 1 -- Clustering Diabetics}

\only<1>{
\begin{block}{}\begin{itemize}
\item The AIDA Online Diabetes Simulator can generate \alert{blood glucose time sequences} for many sample cases.
\item If we think of each sequence as a node in a graph, can we develop a way to determine which sequences are adjacent, using wavelets?  (I have a few ideas, and perhaps you will, too.)
\item If so, we can use a new method of data analysis called the \alert{Laplacian eigenmap method} to cluster the diabetics.
\item The reason to do this:  diabetics in a cluster might be managed in a certain way, while diabetics in another cluster might need a different type of treatment.
\end{itemize}
\end{block}}

\only<2>{
\begin{block}{}
\begin{itemize}
\item I am about to get access to \alert{real data} (time sequences) from 137 diabetics who wore continuous glucose monitors for a full year.
\item We can apply our wavelet-based clustering methods to this data to see what we can determine.
\end{itemize}
\end{block}
}
\end{frame}

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\begin{frame}
\frametitle{REU 2009:  Project 2 -- A Wavelet-Based Controller for an Artificial Pancreas}

\only<1>{
\begin{block}{}\begin{itemize}
\item In industry, PID controllers are used to minimize errors in manufacturing.
\item PID = \alert{Proportional, Integral, Derivative}.
\item P = the immediate error.
\item I = the accumulated error.
\item D = the immediate change in the error.
\end{itemize}
\end{block}}

\only<2>{
\begin{block}{}
\begin{itemize}
\item One idea that is being used in \alert{research for an artificial pancreas} is to have it work like a PID controller.
\item There is some evidence that a normal pancreas really works that way.
\item I have a paper from 2005 proposing a wavelet-based PID controller.
\item Is it a good proposal?  Can we do better?  How could we apply this to glucose control?
\end{itemize}
\end{block}
}

\end{frame}
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\begin{frame}
\frametitle{REU 2009:  Getting Started}

\begin{block}{}\begin{itemize}
\item A lot of \alert{reading to do this week}:  Diabetes, Wavelets, Eigenmap.
\item We should be able to get the eigenmap method up-and-running without too much trouble.
\item At least one of the team members needs to have some experience with programming.
\item We can't go in to this thinking we'll really make a difference, but it will be fun to try.
\end{itemize}
\end{block}
\end{frame}

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\end{document} 