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The visualization method to evaluate the
performance of an RF coil array for MRI
Marlon Perez, Daniel Hernandez, Dongeun Kim, Yongmoon Park,
Min Hyoung Cho, Soo Yeol Lee
Biomedical Engineering, Kyung Hee University
e-mail : marlonperezr@gmail.com, sylee01@khu.ac.kr
Abstract
We present a method for evaluation and
visualization of the array RF coil performance in
MRI (Magnetic Resonance Imaging). The parameters
to evaluate are the spatial sensitivity distribution,
SNR, g-factor, and the noise correlation matrix of
the array RF coil. For easy and efficient evaluation
of the coil performance, we visualize the sensitivity
and SNR maps of each coil element on the relative
axial-, sagittal-, and coronal-planes which are
defined with respect to the plane of the
corresponding coil element. We made the 3D model
of a helmet-style array coil using a commercial 3D
modeling software after we had measured the 3D
geometry of the coil using a 3D scanner. With the
3D model, we simulated the coil performance
parameter maps using a FDTD solver. Then, we
displayed the simulated parameter maps and
experimentally obtained parameter maps in parallel
on the three orthogonal planes defined relative to
the each coil plane. We think the proposed method
can be used for quality control of array RF coils.
I. Introduction
The array coils, in MRI, are used for parallel
imaging [1]; this is practical for its ability to
acquire independent signal from a specific area of
the imaging object. Surface coils are well known for
acquire images with high SNR, where the maximum
SNR occurs at a distance proportional to the
diameter of the coil [2].
When there is a combination of surface coils into
an array, the high SNR is preserved along the
covered FOV (Field-of-view) [2].
The coil construction could be based on
simulations, generating a computer model and test it
on the computer [3]. However, to achieve the correct
decoupling between channels, the coil might change
during the construction process, changing here the
coil shape and the expected performance based on
the first simulation.
The array might have different geometric pattern
for each coil element in order to cover an specific
area of the body, for example in a helmet style coil
array, the coils facing the upper frontal part will
differ from the one in the occipital or parietal area
of the head. In this case each element of the array
coil has different shape and consequently the coil
sensitivity profile vary from coil to coil. The coil
performance can be evaluated based on the image
quality acquired by each coil element. With that
been said, a comparison of the performance, between
elements of the array coil, with only considering the
images in the cartesians planes will result
inaccurate, and requires normalization. Because the
coils are distributed in 3D, their sensitivity profiles
must be visualized by viewing the images in
different planes that pass through different rows of
coils [4]. Our method normalizes the coil sensitivity,
and further the SNR. It is based on the selection of
relative axial and transversal planes to the coil, at a
distance given by the coil maximum diameter. To
generate the planes, it is necessary to know the
spatial location of the coils and the geometric shape.
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Then, after the coil construction and fine tuning, we
would like to obtain the final geometry of the whole
coil array structure in order to obtain a
computerized 3D model. It was used Fast Scan
(from Polhemus), that is a 3D scanner, which will
acquire the spatial data points that represents the
position and orientation of each coil element in the
array structure. The points will be loaded to
AutoCAD (from Autodesk), once in there, the full
geometric of the coil is constructed.
With all the previous data acquired, a new
simulation is performed. Now, with the final coil
array structure acquired and having a 3D real
model, an accurate simulation using SEMCAD X
(from speag) is realized in order to evaluate the coil
performance [5]. Further the SNR map, g-factor and
noise correlation matrix is computed with MUSAIK
(an add-on from SEMCAD). In the other hand of
simulation, experimental data from a 3D MRI image
of a phantom will be acquired, this will be the one
we want to compare with the simulation data from
SEMCAD. A similar approach but in the reverse
way have been seen in [6]. This experimental data
will be scaled and fitted to the AutoCAD geometry
model. At this point the location of the coil elements
to the imaged object is calculated, to later generate
the relative normal planes to the coils. SNR maps
are extracted using the generated relative planes to
the coil. Three planes views are acquire from each
coil, rAxial, rCoronal and rSagittal; it is important to
notice that the planes have as reference the normal
vector of the coil element pointing out from the
imaged object, and are independent to other coil
element plane.
For the last point, a code in Matlab/c++ was
written to show the arbitraries slices of selected
coils. The application allows comparison between
coils, from experiment data and simulation data.
II. The relative views
2.1 Co-registration
In order to compute the SNR, 3D MRI data is
acquired. Moreover, in the coil array structure three
points are required from each element in order to
localize them in a 3D space, this is done with a 3D
scanner. At this point the MRI volumetric data is
combined with the model obtained with the 3D
scanner.
By computing the MRI data isocenter, both the
MRI data and the coil 3D model matched to share
the same spatial domain. However, before they could
be matched, both models should be scaled to the
same dimensions, i.e. millimeters.
2.2 Coil localization
The blue circles in figure 1 represent the spatial
point acquired with the 3D scanner, at three specific
points along each coil, and differ from the
measurement taken to generate the AutoCAD model.
The reason behind acquire only 3 point per coil, is
that, it is sufficient to create a plane where the coil
is laying. Given the plane equation, on equation 1.
(1)
That can be simplifying by the vector notation as
denoted in equation 2.
(2)
Where n is a nonzero normal vector to the plane
and
is a distance to a point in the plane.
Another way to write the plane equation if one
knows three points is presented in equation 3.
(3)
Again n is the normal vector, P1, P2 and P3 are
the measured points along the coil.
With the coils plane calculated, the next step is to
compute the three planes relative to the coil. One
plane is parallel to the coils plane, and is only
moved a distance D’ inside the phantom, we called
to this relative axial plane, the relative coronal and
sagittal planes are calculated as the transversal
planes from the rAxial plane.
Figure 1, coil fitting to the 3D model of the phantom
The three points can be defined as:
P1= point at which the rSagittal plane will lie with
a central point as reference.
P2= the central point.
P3= point at which the rCoronal plane will lie with
a central point as reference.
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2.3 The relative planes
The procedure to obtain the rSagittal and rCoronal
planes is based on the creation of these planes with
the plane equation.
Fig. 2 Rotation of planes around the line P2 to P3
A diagram of the process to generate these planes
is show in figure 2. It starts with the selection of
P2 and P3 to draw a line between each other, which
is show as a dotted line in figure 2; is the reference
or pivot for the rotation of P1 by 90 degrees, in
order to have a new point (P4). Now the new point
P4 in combination with P2 and P3 represents a new
plane perpendicular to the axial plane.
For P2 = (a,b,c), P3= (d,e,f) and a vector
between them <u,v,w> = < d-a, e-b, f-c >
R= (4)
The rotational matrix is given by the equation 4.
The rotation angle is
and
.
The rAxial plane will be created with P1, P2 and
P3, and will be translated a distance D from the
original position. The rCoronal plane will be created
with P2, P3 and P4. The rSagittal plane will be
created with P1, P2 and P4. All this procedure will
be repeated for the remaining coils.
The distance at which the rAxial plane penetrates
the phantom is a parameter that eventually becomes
a user choice, in order to verify the coil’s
homogeneity.
With the arbitraries planes calculated, the
extraction data from the phantom is done with
simple interpolation.
A comparison between the normal orthogonal view
and the proposed approach (relative view) is
illustrated in figure 3.
Fig. 3 Comparison between orthogonal and relative views.
Camera orientation in y=0, in the left column. Camera
orientation observing all the axes, in the right column.
Orthogonal view approach in the top row. Proposed method
in the bottom row. The green points represents the coil
structure. The pink circle represents one coil element.
Ⅲ. Results
The performance analysis for a 36 channel coil
was evaluated, the structure 45 cm height, by 30 cm
width. The coil is built with cooper strip lines of 4
mm width and 0.23 mm height. The coil covers the
neck and the head in a helmet style. The coil model
was created using a 3D scanner and combined in
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AutoCAD, as show in figure 4.
Followed by the modeling of the coil, we perform
simulation using SEMCAD X.
Fig. 4 Generation of 3D model using AutoCAD
Each channel was simulated separated, with a
harmonic voltage signal, at 123.5 MHz. for a
simulation time of 10 periods; we used a GPU
accelerated engine, for FDTD computation. We use a
water based phantom of 100 mm radius and 400
mm height, with relative permittivity of 76.7 and
electrical conductivity 0.6 S/m. For the coils strip
lines, we assigned cooper properties, similar to a
perfect conductor.
Figure 5 shows some of the B1 fields in the axial
plane, for some of the 36 coils. The position of the
axial plane varies from coil to coil.
Fig. 5 B1 field profile for the simulation of some of the 36
channels, all the profiles are on the Z slice.
In the other hand, 3D MRI experiment was done
using the 36 channel coil, using a 3D gradient echo
we obtain 128 slices.
The 3D experimental data were loaded to Matlab
to create a model to fit the coil, thereafter we
applied the algorithm to compute the relative slices
in order to extract, the coil sensitivity, SNR of each
coil.
By selecting the coil of interest, the coil
sensitivity is displayed as experimental or simulation
data. The final visualization for this method can be
observed in figure 6, in this example we used only
the simulation data to compare the performance
between each channel. We can observe that among
the three compared channels, the one that is in the
last row presents the highest sensitivity, meaning
that the others need some adjustment.
Fig 6 Visualization of the relative slices.
Ⅳ. Conclusions
We have developed the evaluation method of the
MRI RF coil arrays. The developed method
visualizes the sensitivity and SNR maps of each coil
element on the its own relative axial-, sagittal-, and
coronal-planes with respect to the coil element. The
method looks helpful for the analysis of MRI RF
coil arrays and is useful for coil design.
References
[1] Roemer P. B. The NMR Phased Array. MRM;
1990;16;192-225.
[2] Charles A. McKenzie, and Daniel K. Sodickson,
Coils, Receivers, and Parallel Imaging: A Technical
Perspective, ISMRM 2006 Morning Categorical
Course Technical Advances and Their Impact on
Body MR.
[3] Wong et al. Computer Simulations for
Optimization of Design Parameters for Intravascular
Imaging Microcoil Construction. Proc. Intl. Soc. Mag.
Reson. Med. 11 (2003).
[4] Wiggins et al. 32-Channel 3 Tesla Receive-Only
Phased-Array Head Coil With Soccer-Ball Element
Geometry. MRM;2006;56;216-223.
[5] Christopher M. Collins and Michael B. Smith,
Calculations of B1 Distribution, SNR, and SAR for
a Surface Coil Adjacent to an
Anatomically-Accurate Human Body Model, MRM,
2001;45;692-699.
[6] Constantinides et al. Intercomparison of
performance of RF coil geometries for high field
mouse cardiac MRI. Concepts in Magnetic
Resonance Part A Bridg Educ
Res;2011;38A(5);236-252.
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