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Summary.tex
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Beamer Presentation
% LaTeX Template
% Version 1.0 (01/07/19)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%----------------------------------------------------------------
% PACKAGES AND THEMES -----------------------------------
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%----------------------------------------------------------------
% TITLE PAGE -------------------------------------------------
%----------------------------------------------------------------
\title[FABCORT]{Fabric-Elasticity Relationships in Cortical Bone}
\author[[email protected]]{\tiny{\bf{Mathieu Simon}}}
\medskip
\date{January, 2025}
\begin{document}
\begin{frame}
\titlepage
\end{frame}
%----------------------------------------------------------------
%----------------------------------------------------------------
%----------------------------------------------------------------
\section{Material and Methods}
\begin{frame}
\frametitle{Material}
\begin{columns}
\column{0.4\linewidth}
\vfill
Data
\begin{itemize}
\item 59 scans
\item 6.5 \textmu m voxel size
\item RUS measurements
\item CTAnalyser
\end{itemize}
\vfill
\column{0.3\linewidth}
\includegraphics[width=\linewidth, trim=200 0 0 0]{01_Fabric/Plots/Scan}\\
\column{0.3\linewidth}
\includegraphics[width=\linewidth, trim=200 0 0 0]{01_Fabric/Plots/Fabric}\\
\end{columns}
\end{frame}
\begin{frame}
\frametitle{Segmentation}
\begin{columns}
\column{0.3\linewidth}
\vfill
\centering
Mean Otsu threshold\\
\vfill
\includegraphics[height=3.75cm, trim=50 0 0 0]{01_Fabric/Results/BVTV_OLS}\\
\vfill
\column{0.5\linewidth}
\vfill
\centering
Fabric distribution\\
\vfill
\includegraphics[height=3.75cm, trim=100 0 0 0]{01_Fabric/Results/Fabric}\\
\vfill
\end{columns}
\end{frame}
\begin{frame}
\frametitle{Resolution Effect - Fabric}
\begin{columns}
\column{0.5\linewidth}
\includegraphics[height=3.25cm]{02_ResolutionEffect/Results/Fabric}\\
\column{0.5\linewidth}
\includegraphics[height=3.25cm]{02_ResolutionEffect/Results/eValues}\\
\end{columns}
\end{frame}
\begin{frame}
\frametitle{Resolution Effect - Elasticity}
\centering
\includegraphics[height=7.5cm, trim=0 0 0 20]{02_ResolutionEffect/Results/Stiffness}\\
\end{frame}
\begin{frame}
\frametitle{Resolution Effect - Elasticity II}
\begin{columns}
\column{0.5\linewidth}
\centering
\includegraphics[height=5cm]{02_ResolutionEffect/Results/BVTV_Downscaling}\\
\column{0.5\linewidth}
\centering
\includegraphics[height=5cm]{02_ResolutionEffect/Results/BVTV_Stiffness}\\
\end{columns}
\end{frame}
\begin{frame}
\frametitle{Convergence Study}
\begin{columns}
\column{0.5\linewidth}
\vfill
Setup
\begin{itemize}
\item 1mm ROI side length
\item 3x3x5 ROIs
\item 65 \textmu m margin
\item Groups of 1, 2, ..., 45 ROIs
\end{itemize}
$\rightarrow$ \textasciitilde 2\textsuperscript{45} possibilities
\vfill
\column{0.4\linewidth}
\includegraphics[width=\linewidth, trim=200 0 0 0]{03_ConvergenceStudy/Results/ROIs}\\
\end{columns}
\end{frame}
\begin{frame}
\frametitle{Convergence Study}
\begin{columns}
\column{0.5\linewidth}
\vfill
Sampling
\begin{itemize}
\item Balanced clustering\\
$\rightarrow$ Linear sum assignment\\
$\rightarrow$ 216*10\textsuperscript{6} possibilities
\item N samples = 1000
\item Norm Error
\item Threshold = 0.05
\end{itemize}
$\rightarrow$ 15-16 ROIs
\vfill
\column{0.4\linewidth}
\vfill
\includegraphics[width=\linewidth, trim=75 0 0 0]{03_ConvergenceStudy/Results/NormError}\\
\vfill
\end{columns}
\end{frame}
\begin{frame}
\frametitle{Material Effect}
\vfill
\includegraphics[width=\linewidth]{04_MaterialEffect/Material}\\
\vfill
\end{frame}
\begin{frame}
\frametitle{Homogenization}
\begin{columns}
\column{0.5\linewidth}
\vfill
Setup
\begin{itemize}
\item Downsampling factor: 2
\item 16x1mm\textsuperscript{3} ROIs
\item Isotropic vs transverse
\item Mean $\mathbb{S}$ / Sample
\end{itemize}
\vfill
\column{0.4\linewidth}
\vfill
\includegraphics[width=\linewidth, trim=200 0 0 0]{05_Homogenization/Plots/ROIs}\\
\vfill
\end{columns}
\end{frame}
\section{Results}
\begin{frame}
\frametitle{Simulations vs RUS}
\centering
\begin{columns}
\column{0.45\linewidth}
\centering
\includegraphics[width=\linewidth]{05_Homogenization/Plots/Elasticity_IsoRUS}\\
Isotropic Material
\column{0.45\linewidth}
\centering
\includegraphics[width=\linewidth]{05_Homogenization/Plots/Elasticity_TraRUS}\\
Transverse Isotropic Material
\end{columns}
\end{frame}
\begin{frame}
\frametitle{Anisotropy}
\vfill
\begin{columns}
\column{0.5\linewidth}
\centering
\includegraphics[width=\linewidth]{05_Homogenization/Plots/Anisotropy}\\
\column{0.5\linewidth}
\centering
\includegraphics[width=\linewidth]{05_Homogenization/Plots/AnisotropyBVTV}\\
\end{columns}
\vfill
\end{frame}
\begin{frame}
\frametitle{Homogenization}
\centering
\begin{columns}
\column{0.33\linewidth}
\centering
\includegraphics[width=\linewidth]{05_Homogenization/Plots/Regression_Iso}\\
Isotropic
\column{0.33\linewidth}
\centering
\includegraphics[width=\linewidth]{05_Homogenization/Plots/Regression_Tra}\\
Transverse
\column{0.33\linewidth}
\centering
\includegraphics[width=\linewidth]{05_Homogenization/Plots/Regression_IsoVsTra}\\
Comparison
\end{columns}
\end{frame}
\begin{frame}
\frametitle{Comparison with Trabecular Bone}
\centering
$\mathbb{S}_{Ts} = \mathbb{S}_{T} / ||\mathbb{S}_{T}|| * ||\mathbb{S}_{I}||$
\begin{table}
\resizebox{\textwidth}{!}{%
\begin{tabular}{l|cc|ccccc|c}
Study & Bone type & Resolution & $\lambda_0$ & $\lambda_0$' & $\mu_0$ & k & l & DA \\
\hline
Gross et al. & Trab. & 18 & 4609 & 3692 & 3738 & 1.60 & 0.99 & 1.67 \\
Panyasantisuk et al. & Trab. & 36 & 3841 & 3076 & 3115 & 1.60 & 0.99 & 1.54 \\
Simon et al & Trab. & 61 & 2738 & 1662 & 2187 & 1.60 & 0.99 & 1.99 \\
Present study & Cort. ($\mathbb{S}_{I}$) & 13 & 5389 & 5307 & 4023 & 1.60 & 0.99 & 2.02 \\
Present study & Cort. ($\mathbb{S}_{Ts}$) & 13 & 5574 & 5511 & 3077 & 1.60 & 0.99 & 2.02 \\
\end{tabular}}
\end{table}
\end{frame}
\begin{frame}
\frametitle{Comparison $l$ Exponent}
\begin{columns}
\column{0.5\linewidth}
Reference: Transverse isotropic
\begin{itemize}
\item $\mathbb{S}_{Is} = \mathbb{S}_{I} / |\mathbb{S}_{I}| * |\mathbb{S}_{T}|$
\item $\lambda_0 = 11096$
\item $\lambda_0$'$ = 10970$
\item $\mu_0 = 6124$
\item $k = 2.18$
\end{itemize}
\column{0.5\linewidth}
\resizebox{\textwidth}{!}{%
\begin{tabular}{l|cc}
Matrix & Isotropic & Transverse \\
\hline
$l$ & -0.04 & 0.46 \\
95\% CI Low & -0.12 & 0.39 \\
95\% CI High & 0.04 & 0.52 \\
\end{tabular}}
\end{columns}
\end{frame}
%----------------------------------------------------------------
%----------------------------------------------------------------
%----------------------------------------------------------------
\end{document}