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\begin{document}
\title{Prelim}
\author[ ]{Trong Nguyen}
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\date{}
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\section*{Goals:}
{\label{896397}}
Quantitative ultrasound (QUS) characterization based on frequency
analysis of the backscatter radio frequency (RF) data has seen success
in a number of applications.
Theoretical models have been developed to relate the gated normalized
power spectrum to the scattering properties of investigated tissue.
Localized changes in compressibility and density induce local changes in
the gated RF. The autocorrelation of the medium is approximated equal to
the Fourier transform of RF. Under the Born approximation and plane wave
sonification, closed form solution for the scattering size and
scattering concentration can be derived. Specifically, the slope and
intercept of the linear fit to the log of the normalized power spectrum
over the squared of~the analysis frequencies are related to the
scattering diameter and acoustic concentration.~
However, normalized spectrum analysis requires the use of a reference
phantom or a planar reflector to remove the system dependent transfer
function and diffraction effects. This usage of the reference phantom
hinders the adoption of QUS into clinical practice. For in vivo
application, this technique does not account for the layers in front of
the tissue, cannot fully account for the division of the diffraction
effects.~
The attenuation and backscattering changes might not be simultaneous.
The pathological changes in tissues will induce the change in
attenuation or backscatter coefficient at the same time.~
\par\null
Question: to what extent QUS do not need the reference phantom? Which is
to say the scattering and attenuation variations are dominating the
diffraction and acoustical-electro conversion variations. For the task
of classification, the power spectrum might be sufficient.~
Can we do QUS with a simpler and more practical reference phantom for
some specific applications? By embedded a sphere inside a body in a
semi-invasive procedure, we have more reliable calibration.
Layers effect: no work has been done to compensate for the layer before
the tissue in question. The layer effect compensation is important for
QUS to be accurate and applicable.
There is a need to publish the data publicly in ultrasonic tissue
characterization for more collaboration.~~
An example: BSC measurement inter laboratory gave inconsistent results
for tissue-mimicking phantom \cite{Madsen_1999}.
\section*{Relationship between Gated Power Spectrum and Tissue
Microstructure}
{\label{236876}}
$$S(f, z) = TG(f)D(f,z)A(f,z)B(f)$$
f: frequency, z: depth of the ROI,~
S(f, z): power spectrum of the ~backscattered signal.~
G(f): transducer effects from transmitting and receiving an RF signal.
D(f,z) : diffraction effect.~
A(f, z): attenuation~
B(f): backscattered coefficients.~
T is the transmission loss.
~
Using the reference phantom technique~\cite{Yao_1990}, where s
denotes sample, and r denotes reference phantom, the ratio of power
spectrum is:~
\par\null\par\null
$$RS(f,z) = \frac{S_s(f,z)}{S_r(f,z)}= \frac{T_s}{T_r}\frac{B_s(f)A_s(f,z)}{B_r(f)A_r(f,z)}$$
$$R(f,z)=\frac{b_sf^{n_s}}{b_rf^{n_r}} exp\{-4(\alpha_s-\alpha_r)fz\}$$
\(\)
$$lnR(f,z) = (b_s-b_r)+(n_s-n_r)lnf-4(\alpha_s-\alpha_r)fz$$
\par\null
Transmission loss does not affect the estimation of (ns-nr) and
(as-ar).~
Plane wave approximation. focal zone approximation. Born approximation
(single scattering event).
~
backscattered power spectrum = scattering * attenuation * diffraction *
transmission loss * system transfer function.
if attenuation + transmission loss is estimated: classification using
the scattering.
if we assume scattering model, we can get the scattering diameter and
scattering concentration.
these parameters have physical meaning.
The relationship between BSC and PS.~ ~~
\par\null\par\null
The normalized power spectrum ~\cite{Lizzi_1997}:
$$W(f) = \frac{{185L{q^2}a_{eff}^6\rho z_{{\text{var}}}^2{f^4}}}{{[1 + 2.66{{(fq{a_{eff}})}^2}]}}{e^{ - 12.159{f^2}a_{eff}^2}}$$
\section*{}
{\label{250104}}
\section*{Machine learning}
{\label{250104}}
using PCA to reduce dimension of the features. PCA on the calibrated
power spectrum. Use only a few components for classification.
using random forest / SVM for classification.
PCA to capture other nuances of the data that linear fit left out.
\section*{Study design}
{\label{596788}}
The study includes 60 rabbits. Already have 37 rabbits, 20 more to come.
largest in-vivo animal study for fatty \& fibrosis dataset.
The rabbits were on a combination of fatty + normal diet. ~140 g of diet
daily. Injection of CCL4 weekly.
Different weeks of fatty diet: 0, 1, 2, 3, 6 weeks.
different CCL4 concentration was injected to induce fibrosis. CCL4
injection was based on weight.
have exact amount of food + CCL4 injection.
born on the same day, same gender, feed at the same time, same light -
dark cycle.
Transducer L9-4, C5-2. Two sides of liver.
\textbf{Ground truth}:
Folch assay. Hydroxyproline assay. There was missing data due to
experiment error.~
\section*{Results:}
{\label{199967}}
\textbf{Classification results using BSCs:}
\textbf{1.~~~} \textbf{Methods:}
Split the data into training and testing set. Two classes:
Class 0 (blue): Smaller than 5\% lipid
Class 1 (orange): larger than 5\% lipid.
Testing rabbits set: 10 rabbits.
Training rabbits set: 25 rabbits.
{[}L736, L759, L767, L741, L740, L743, L746, L753, L755, L757{]}. The
number of class 0 is smaller due to the imbalance of the lipid in all
the rabbits.
~
Method 1: Apply PCA to BSC to get 35 principal components. These
components were used to get 35 features for each example in the
training/testing set. ~
Method 2: Linear fit to the BSC to get slope and intercept.
~
\textbf{1.~~~} \textbf{Classifier: Random Forest. ~}
~
Confusion matrix using PCA + Random Forest.
\textbf{1.~~~} \textbf{Confusion matrix using linear fit. ~Linear fit
cannot discriminate the two classes.}
\textbf{I.~~~~~~~~~~~~~~} \textbf{Classification results using
Attenuation:}
\textbf{~}
\textbf{Attenuation slope at 4 MHZ (dB/cm). Correlation coefficient =
0.698.}
\textbf{1.~~~} \textbf{Attenuation slope and intercept (linear fit to
attenuation curve) and classified using SVM.~ Class 0 is less than 5\%,
Class 1 is \textgreater{}5 \% (same as BSCs). There are three examples
misclassified (in red).}
Figure 5 Attenuation slope and intercept\textbf{}
\textbf{~}
~
\section*{\texorpdfstring{{}Layer
effect}{Layer effect}}\label{layer-effect}
no work has been found on compensating the transmission loss for
backscattering and attenuation calculation.
important for in-vivo work.
estimation of transmission loss in layer before the liver.
{}
{}
$$|{S_{ri}}(f)| = |{S_{ti}}(f)||H(f)|T_1^2T_2^2...T_{i - 1}^2{R_i}{M_i}{e^{ - 2f\sum\limits_{}^i {{\alpha _n}{X_n}} }} $$
$$T_1^2T_2^2...T_{i - 1}^2{R_i}{M_i} = {\left( {\frac{{2{Z_1}}}{{{Z_1} + {Z_2}}}} \right)^2}{\left( {\frac{{2{Z_2}}}{{{Z_2} + {Z_3}}}} \right)^2}...{\left( {\frac{{2{Z_{i - 1}}}}{{{Z_{i - 1}} + {Z_i}}}} \right)^2}\frac{{{Z_{i + 1}} - {Z_i}}}{{{Z_{i + 1}} + {Z_i}}}\frac{{{Z_1}}}{{{Z_i}}}$$
\par\null
~
\(S_i\): amplitude of the frequency spectrum for the ith
received echo
\(S_t\): amplitude of the frequency spectrum for the
transmitted waveform.
\textbar{}H(f)\textbar{}: amplitude spectrum of the impulse response for
the transmitter- transducer-receiver system.
: amplitude transmission coefficients at specular reflecting boundaries
between tissue segments where Zn is the acoustic impedance of the nth
tissue segment.
R\_i: amplitude reflection coefficient at the specular reflecting
boundary of the ith tissue segment = (Z\_i+1 -- Z\_i)/(Z\_i+1 + Z\_i)
M\_i = Z1/Zi
X\_n = thickness of the nth tissue segment.
Alpha n = attenuation coefficient for the nth tissue segment.
\section*{QUS without reference
phantom.}\label{qus-without-reference-phantom.}
Use an embedded sphere.
Can be inserted into the body.
\section[More
questions]{\texorpdfstring{\protect\hypertarget{header-n71}{}{}More
questions}{More questions}}\label{more-questions}
do these techniques apply to other dataset?
thyroid dataset.
\par\null
\par\null
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