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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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