PIERS Proceedings, Moscow, Russia, August 18–21, 2009
1024
Computation of SNR and SAR Based on Simple Electromagnetic
Simulations
R. Rojas and A. O. Rodriguez
Centro de Investigacion en Instrumentacion e Imagenologia Medica, Universidad Autonoma Metropolitana
Iztapalapa, Av. San Rafael Atlixco 186, México DF 09340, México
Abstract— The signal-to-noise ratio is an accepted parameter to measure radiofrequency coil
performance. The specific absorption rate is the only quantifiable safety measure for RF coils.
Analytical expressions can be derived for the simplest cases of surface coils, but more complex coil
configurations require a very complicated mathematical framework to be solved. The numerical
study of the electromagnetic behavior of magnetic resonance imaging coils and interaction with
biological tissues is a good alternative. A numerical method based on the finite element method
to compute the electromagnetic fields of single surface coil is presented here. These numerical
simulations are used to numerical calculate the signal-to-noise ratio and specific absorption rate
for a circular-shaped coil and, the induced currents generated.
1. INTRODUCTION
The quality of the magnetic resonance image is greatly determined by the radiofrequency (RF) coil
performance. The signal-to-noise ratio (SNR) is the widely accepted parameter to measure coil
performance. The SNR depends mainly on the electric field generated by the sample and the coil
magnetic field [1, 2]. The electric field may be regarded as the source of noise and the magnetic
field generated by the coil as the source of stored energy. The specific absorption rate (SAR) is the
safety measure and is a function of the electric field generated by the sample to be imaged. Both
parameters depend on electromagnetic fields generated by both the sample and the RF coils. A
simple numerical approach is proposed in this paper to compute these electromagnetic fields.
2. MATHEMATICAL BACKGROUND
The noise is proportional to the effective resistance Reffec including the interaction with organic
tissue, system electronics, and coil induction [3]. Because, the SNR is proportional to the induced
MR signal (v) and inversely proportional to the RMS of thermal noise voltage in coil, Edelstein
proposed the following expressions for a single coil, along the coil axis [4]:
SNR =
v
rms of thermal noise
(1)
and
v = ωM V B1z
p
rms of thermal noise = 4kT ∆f Reffec
(2)
(3)
where ω is Larmor’s frequency, M magnetization, V voxel volume, B1z magnetic field produced by
the coil in z direction, k Boltzmann’s constant, ∆f bandwidth, and Reffec effective resistance.
Using (2) and (3) in (1), the SNR is:
SNR = p
ωM V B1z
4kT ∆f Reffec
(4)
The effective resistance depends on the power losses P and of the induced current I, then
P = I 2 Reffec
and the power by volume unit is a function of conductivity σ and the electric field
¯ ¯2
dP
¯~¯
= σ ¯E
¯
dV
(5)
(6)
Progress In Electromagnetics Research Symposium Proceedings, Moscow, Russia, August 18–21, 2009 1025
Using the Equations (5) and (6) in (4), we have
ωM V B1z
SNR = √
4kT ∆f σV Ez
simplifying,
¯
¯
¯~ ¯
B
¯
1z ¯
Magnetic field
SNR ∝
= ¯¯ ¯¯
Electricf field
~z¯
¯E
(7)
(8)
(SAR) is the only quantifiable safety measure for RF coils. The interaction between the RF and
organic tissue can increase the temperature and produce biochemical reaction changes or inclusive
a possible burn of tissue [5]. The US FDA recommends that the energy absorption should not be
greater than 0.4 W/kg in body and 3.2 W/kg in head [6]. It is very important the SAR determination
to assure the patient safety. Since SAR is a measure of the energy dissipated in the biological sample,
it can be defined as:
Total energy of RF dissipated in sample
SAR =
(9)
(Exposition time)(Sample weight)
The power losses can be expressed using the Joule effect absorbed by the tissue, which is inversely
proportional to tissue mass density. Finally, SAR can be expressed using Jin’s formulation [7] and
the Equation (9):
P
(10)
SAR =
ρm
Replacing Equation (6) in (10), a good approximation can be obtained:
¯ ¯2
¯~¯
σV ¯E
¯
SAR =
ρm
then
¯ ¯2
¯~¯
SAR ∝ ¯E
¯
(11)
(12)
Analytical expressions for both the SNR and SAR based on Maxwell equations can be derived
for the simplest cases of surface coils, but it is very difficult derive expressions for more complex
geometries due to the complicated mathematical framework involved in it. The numerical study of
the electromagnetic behavior for MRI coils and biological tissues is a good alternative. A numerical
method based on the Finite Element Method (FEM) to compute the electromagnetic fields of single
surface coils is presented here. These numerical simulations are the base to finally calculate the
SNR and SAR for a circular-shaped coil and the induced currents generated by it.
3. METHODOLOGY
An anatomical pixel model of the human head (brain and skin) was developed using the software
tool, AUTODESK 3DS MAX (V. 3.2 Autodesk, San Rafael, CA, USA). This pixel model was
imported to the software tool, COMSOL MULTIPHYSICS (V. 3.2, COMSOL, Burlington, MA,
USA). A single loop coil was also developed with the same tool and placed over the head model
as shown in Fig. 1(a) the electric and magnetic fields were computed with COMSOL using the
tissue properties reported in [8] for the resonant frequency of 128 MHz. In the first run, the coil
was operated in transmission mode and the electric current density induced in the head model by
the coil was estimated. In the second run, the induced currents were used to numerically compute
the electric field produced by the head. With these data, matrices were formed to numerically
compute the SNR and the SAR using specially-written programmes in MATLAB (Math Works,
USA). Fig. 1(b) shows a three-dimensional illustration of the electric field in sagittal orientation.
Figure 2 shows a coronal cut of model (a) gives an image of the coil magnetic field in the
transmission-mode operation, (b) shows the electric field generated by the sample after the excitation (reception coil operation).
Using the magnetic and electric fields data in Fig. 2, the SNR and the SAR were computed for
this particular configuration.
PIERS Proceedings, Moscow, Russia, August 18–21, 2009
1026
(a)
(b)
Figure 1: (a) Anatomical pixel model of human head, (b) three-dimensional electric field of the sample in
sagittal orientation with the coil in transmission mode only.
(a)
(b)
Figure 2: (a) Magnetic field generated by the coil in transmission mode, (b) electric field generated by the
sample after excitation by the RF coil.
(a)
(b)
Figure 3: (a) Surface coil SNR operating in transmission-mode, (b) SAR generated by the sample.
Figure 4: Current density induced over the brain measured from the centre towards the brain border.
Progress In Electromagnetics Research Symposium Proceedings, Moscow, Russia, August 18–21, 2009 1027
Figure 4 shows profiles of current density as a function of position for two different frequencies.
An increase in the induced currents is observed at the surface of the brain, this is due to the electric
properties of the brain and that higher frequency leads to a higher current density. Additionally,
induced currents were also computed and showed an expected pattern. Therefore, the induced
current intensity increases as a function of the frequency.
4. CONCLUSION
It has been proved that it is possible to numerically compute the electromagnetic fields for a simple
coil configuration together with a pixel model. A circular-shaped coil was chosen for simplicity,
however this approach can also be extended to more complex coil configurations such as the birdcage
or coil arrays. Other pixel anatomical models of human organs can be constructed and numerically
simulated with this method for higher resonant frequencies applications too. This numerical method
can offer a graphical tool to illustrate the behavior of the SNR and SAR. It can be particularly
useful for those students and researches starting to familiarise with the development of RF coil for
MRI, since the simulation method is easy to implement. The induced current intensity obtained,
may serve as guidelines to study safety issues involving RF coils.
A simple numerical method to assess the SNR and SAR is presented using he FEM and this
can be extended to other coil configurations and regions of interest. The numerical results showed
the viability of this method to study the coil performance of simple coil configurations involving
models simulating human organs.
ACKNOWLEDGMENT
• Centro de Investigacion en Instrumentación e Imagenologia Medica. Universidad Autonoma
Metropolitana Iztapalapa.
• National Council of Science and Technology of Mexico for a Ph.D. scholarship.
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