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ve_analysis.tex
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ve_analysis.tex
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\section{Viscoelastic Material Analysis Metrics}\label{sect:ve_analysis}
The System Dependency and Phantoms Task Force identified that ``simple'',
analytic viscoelastic material models, such as Voigt and Maxwell materials,
inadequately capture the phase velocity trends measured across the energetic
frequency ranges associate with liver shear wave speed characterization.
Instead of using an analytic VE material model, we proposed characterizing the
phantoms using a linear dispersion model of the form
\begin{equation}
c(f) = c_0 + \frac{dc}{df} f.
\end{equation}
This linear model was fit to the 2D Fourier transform of axial velocity data
over a frequency range of 100--400 Hz, and two metrics were used to
characterize the viscoelasticity of materials:
\begin{enumerate}
\item Phase velocity at 200 Hz ($c_{200}$), and
\item Line phase velocity slope from 100--400 Hz ($\frac{dc}{df}$).
\end{enumerate}
This model was applied to human data in patients with liver
fibrosis~\cite{Palmeri2011} (Figure~\ref{fig:phantom_liver_scatter_plot}) to
establish a range of realistic linear dispersion VE material values for healthy
through advanced fibrosis liver health. The 2D Fourier transform data were
processed using the methods described in~\cite{Nightingale2015,Bernal2011}. The
data were also validated using human data acquired using a Philips shear wave
imaging system~\cite{Chen2012a}.
Two important frequency analysis points should be noted:
\begin{enumerate}
\item The choice of frequency range from 100--400 Hz was chosen based on
empirical studies of the Duke human data and should not be considered a
universal recommendation across different imaging systems and clinical
targets. Other choices for estimating a linear phase velocity slope
could include a fixed frequency range about the most energetic center
frequency or an adaptive frequency range based on each dataset.
\item The peak phase velocity data in k-space can be strongly influenced by
the choice of windowed spatial and temporal shear wave velocity
data~\cite{Harris1978}. Inclusion of shear wave data in or adjacent to
the acoustic radiation force excitation can introduce diffraction
effects that can significantly skew the frequency analysis of the
propagating shear waves.
\end{enumerate}
\input{fig_phantom_liver_scatter_plot}
\input{fig_phase2_longitudinal_stability}