The document describes the design and testing of a birdcage coil to emulate the RF fields of an MRI machine. The coil was designed to resonate at 128 MHz but was found to resonate at 156 MHz due to unforeseen factors. A quadrature hybrid splitter was designed to drive the coil but was incompatible with its 156 MHz resonance. Testing showed 25-30% power reflection when driving the coil from a single port. An experiment heated a copper wire by 0.7°C over 10 minutes when driven by the coil at 156 MHz. Further modifications are needed to address issues with the coil's resonance frequency and power delivery.

1. Design of Birdcage Coils for Testing of MRI-Safe Devices
Joseph Haystead
Supervisor: Jonathan Scott
ENGG492-15C Honours Research and Management Project
January 2016
1

2. 1 Executive Summary
MRI examinations expose patients to RF elds during examination. Interactions between these
elds and medical implants can cause RF heating, inicting damage to the surrounding tissue. In
order to design MRI-safe electrodes, it is necessary to test them under the same RF conditions
as those found in MRI machines. This can be achieved inexpensively through construction of a
birdcage coil designed to emulate the RF eld of a MRI machine.
This report documents the design process and testing of a birdcage coil and power systems
(quadrature hybrid splitter and power amplier). The coil was designed to resonate at 128 MHz;
however, it was found to resonate at approximately 156 MHz due to unforeseen design parameters.
A quadrature hybrid splitter circuit was designed to divide power and phase-shift an input signal
by 90◦
in order to generate a circularly polarized emission from the coil. Performance analysis
of the splitter indicated that it divided power approximately equally between both output ports
with a phase shift of 85.7◦
when operated at 128 MHz. However, due to the frequency-dependent
behaviour of the splitter (operable only at the designed frequency of 128 MHz), it was found
to be incompatible with the 156 MHz resonance of the coil during testing. A 100W RF power
amplier was constructed and used to power the coil. Despite tuning of the birdcage coil to
match input impedance requirements, SWR measurements from the power amplier indicated that
approximately 25-30% of the power fed to the birdcage coil was reected back to the amplier(when
fed via a single port only). The cause of this is undetermined, but may be due to environmental
interactions resulting in modications to the coil impedance. Finally, an experiment was performed
to attempt RF heating of a 20 cm insulated copper wire placed with a saline-lled phantom. The
coil was fed a 156 MHz signal via a single port (resulting in linear polarization). A ber optic
thermometer measured a 0.7◦
C temperature rise at the tip of the wire over a period of ten minutes.
This report demonstrates that a birdcage coil can be constructed to induce RF heating via the
same mechanisms as those found in MRI machines. The designed coil did not fully match specied
requirements for resonant frequency. Further testing and modications are required to address
these issues.
2

3. 2 Acknowledgment
I would like to express my deepest appreciation and gratitude to my project supervisor and
lecturer Jonathan Scott, for his continual support and encouragement not only in this project,
but throughout the course of my time at Waikato University. His dedication to explaining
electronics concepts has been imperative to the success of my studies.
I would also like to thank Steven McCabe, for his assistance and enthusiasm throughout this
project, and for being integral in steering this project towards a working birdcage coil.
Furthermore, I wish to express gratitude to Brett Nichol, for spending much time and eort on
my behalf to improve my designs and construct the birdcage coil frame and supporting bench.
Finally, I would like to thank my old friend Mark Hubner, for advising me to study engineering.
3

4. Contents
1 Executive Summary 2
2 Acknowledgment 3
3 Background 5
3.1 Principles of MRI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
3.2 Safety of Implanted Medical Devices (IMD) in MRI Machines . . . . . . . . . . . . 8
3.3 Skin Eect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.4 Specic Absorption Rate (SAR) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.5 Reduction of Dielectric Heating in Leads . . . . . . . . . . . . . . . . . . . . . . . . 9
4 Design Overview 10
4.1 Aim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
4.2 Potential Solutions for Testing RF Heating in Leads and Wires . . . . . . . . . . . . 10
4.3 Cost Analysis of Construction of RF Birdcages . . . . . . . . . . . . . . . . . . . . . 12
5 Birdcage Coil Design 13
5.1 Design Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
5.2 Designing Birdcage Coils for Resonant Frequencies . . . . . . . . . . . . . . . . . . . 13
5.3 CAD Design of Coil Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
5.4 Construction of Birdcage Coil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
5.5 Birdcage Coil Power Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
5.5.1 Quadrature Driving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
5.5.2 RF Power Amplier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
6 Performance Analysis of Designed Birdcage Coil 23
6.1 Resonant Frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
6.2 Impedance Matching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
6.3 RF Heating Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
6.4 Post-Experiment Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
6.5 Post-Design Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
7 Conclusion 28
4

5. 3 Background
3.1 Principles of MRI
In quantum mechanics, a single-proton atomic system (such as hydrogen) has a property known
as spin angular momentum (or simply spin). This spin causes the proton to have a magnetic
moment. In living tissue, these magnetic moments are randomly distributed due to thermal ener-
gies, resulting in a zero net magnetic vector (NMV) over the tissue region volume. The spin and
magnetic moment of an element are related through another property known as the gyromagnetic
ratio (γ). This ratio varies between dierent elements. A MRI machine primarily uses a strong
static magnetic eld (often refered to as the B0 eld, and labelled as being directed in the z-axis).
When the patient is placed within this eld, the protons in their tissue experience torque due to
interaction between their magnetic moments and the B0 eld. This causes the NMV to align with
the magnetic vector (B0) of the B0 eld at the Larmor frequency. Note that the protons will
lack phase-coherence; they will precess at the same speed, but not in phase with each other. The
Larmor frequency is calculated as
ω = γB0. (1)
When a RF pulse (with a magnetic ux component referred to as the B1 eld) at the Larmor
frequency is applied to a region of interest (ROI), the NMV of the protons precessing around the
B0 eld vector will be rotated from alignment with the plane of the B0 eld (longitudinal plane)
into a perpendicular plane (transverse plane). At this time, they will become phase-coherent
(precessing in-phase with each other). For a hydrogen atom (single proton), the gyromagnetic
ratio is approximately 42.57 MHz / T. In some common commercial MRI machines which use a
1.5 T B0 eld, the central Larmor frequency needed for imaging can be calculated as ω = γB0 =
42.57 × 106
× 1.5 = 63.855 MHz. Other MRI machines may generate a 3 T B0 eld to gain higher
resolution images, primarily emitting RF pulses at approximately 127.71 MHz.
The angle to which the NMV will be rotated into the transverse plane depends upon the
strength of the magnetic ux component (B1) of the applied RF pulse and its duration (Tpulse),
and can be calculated as
Θflip ≈ 2πγ · B1 · Tpulse. (2)
To rotate the NMV 90◦
into the transverse plane using a 10µT RF pulse (B1), the duration of
the pulse would need to be approximately 587µs. For this rotation, the NMV could be imagined
as having its precession angle widened from rotating closely around the z-axis (direction of the B0
eld) until its movement traced out a at circle in the x-y plane at a rate dened by the Larmor
frequency.
A RF receive coil aligned such that it is open to the transverse plane (i.e., the at face of
the coil faces a direction perpendicular to the B0 eld, such as the x or y axis) will experience an
induced EMF as the NMV sweeps around the x-y plane (as described previously). This is described
by Faraday's Law of Induction. The induced EMF is proportional to the Larmor frequency, the
applied RF B1 eld pulse, the NMV and the capture area of the receive coil:
EMF ∝ ω
ˆ
B1 · NMVxy · dV (3)
Note that in (3), the B0 eld is assumed to be aligned with the z-axis. Also, maximum EMF is
induced when the B1 eld and the NMV have zero phase angle between them. This implies that
B1 should be circularly polarized for maximum receive signal strength.
5

6. The NMV from the region of interest (ROI) is very weak as it originates from the precessing
atomic spins at the Larmor frequency. The applied RF pulse (B1 eld) will be overwhelmingly
strong at this same frequency, and will mask any EMF induced by the precessing protons. There-
fore, the B1 eld must be removed to allow the RF receive coil to detect signals from the ROI.
However, once the RF pulse has completed (often known as an excitation pulse) and the B1
eld is no longer present, the proton precessions will immediately begin to de-phase and the NMV
will begin to return to its previous equilibrium state, realigning with the B0 eld. This process is
referred to as relaxation.
Two relaxation time decay constants are used to describe the processes occuring at the atomic-
level. The rst decay constant is known as T1, and describes the relaxation process in the z-axis.
It is also known as spin-lattice relaxation, as during this process, energy is released into the
surrounding lattice (or tissue). T1 denes the time taken for the z-component of the NMV to
return to approximately 63% of its pre-excitation pulse magnetization. The second decay constant
is known as T2 (or spin-spin relaxation), and describes the relaxation process in the x-y plane.
T2 denes the time taken for the spins to de-phase to approximately 37% of their pre-excitation
pulse values. Due to dierences in bonds between protons and their parent molecules, T1 relaxation
times can vary. Tightly-bound protons (such as those in fat tissue) will release energy more rapidly
than those in looser-bonds (such as blood/water). T2 relaxation times are also dependent on
the parent molecule type, where de-phasing occurs faster for more tightly-bound protons. The
use of the T2 constant assumes that the B0 eld is completely homogeneous. However, factors
such as dental implants, varying magnetic susceptibilities at interfaces (such as air-to-tissue), or
imperfections in the manufacturing process of the B0 magnet can cause distortions in the B0 eld,
resulting in a faster T2 decay. Therefore, a constant known as T2* (T2-star) is used to include
these eects.
Due to the required positioning of the receive coil (perpendicular to the B0 eld), it is only
possible to detect signals from the T2* relaxation process. As the phase-coherence of the NMV
of the ROI will decrease following the end of the excitation RF pulse (B1 ), the received signal is
known as the T2* decay.
The application of the B0 eld causes the NMV to precess at the same frequency throughout
the body of the patient. Further manipulation of the NMV is needed to discern one location from
another. This is achieved through the use of gradient coils. These coils surround the main B0 coil
and generate magnetic eld gradients which add or subtract to the magnetic eld intensity along
a specic axis. By increasing the magnetic eld intensity at one end of the z-axis and decreasing
it at the other, the Larmor frequency of the precessing protons will become a function of distance
along that axis (Note that the expression mzz describes the magnetic eld gradient in the z-axis
direction):
ω(z) = γB0 + γmzz = ω0 + γmzz. (4)
RF pulses will only excite protons precessing at the same frequency. Slice encoding on
the z-axis enables specic slices along this axis to be targeted without inducing the excita-
tion/relaxation process in other areas. The addition of the gradient eld applied in the y-axis
(up/down) direction adds phase encoding. This causes the protons to precess out of phase,
where the phase shift becomes a function of the distance across the y-axis. The combination of the
z and y axis elds enables the dierentiation of rows within a targetted slice. The x-axis gradient
eld adds frequency encoding. This causes the protons on the left side of the patient to precess
at a dierent frequency to those on the right side. The combination of all three gradient magnetic
6

7. elds allows for specic volume elements (known as voxels) to be targetted in three dimensions.
The thickness of the z-axis slice is dependent on the steepness of the gradient magnetic eld and
the bandwidth of the RF pulse. A steeper gradient eld will allow for thinner slices to be analyzed.
Likewise, a smaller RF pulse bandwidth will also enable thinner slice encoding.
The sequence used to gain a signal from a targetted voxel consists of several steps. First, the
z-axis gradient eld is turned on to add slice-encoding to the ROI. A RF pulse is applied to select a
specic slice (often called a slice-select pulse). This causes the protons within this slice to rotate
(as described previously). When the slice-select pulse is complete, the NMV of the selected slice
begins to return to equilibrium and so the x and y axis gradient elds need to be quickly applied
to encode the voxels within the slice. The x-axis gradient coil is switched on momentarily (for a
time Tx) to apply phase encoding (known as a phase encode pulse). Following this, the proton
precessions will return to the original Larmor frequency of the slice, but will be out of phase by
an amount kx = γmxTx(where mx is the magnetization gradient along the x-axis). Following the
phase-encode pulse, the y-axis gradient coil is switched on (known as a frequency encode pulse).
At this time, the x-axis gradient is zero (mx = 0) and the Larmor frequency becomes y-dependent.
The signal is read by the RF receive coil and can be approximated as
S(t) ∝
ˆ
ROI
ω(B1 · |NMV (x, y)|e−j(ω0t+kxx+kyy)
)dkxdky (5)
where ky = γmyt. By calculating the inverse Fourier transform of S(t) in the equation above,
a measure of the NMV of the targetted voxel within the slice (NMV (x, y)) can be obtained. This
measurement relates to the spin density of the voxel, and therefore the voxel composition and tissue
type can be determined. Note that the equation above assumes that the distribution of spin density
in the slice is generated by B0 and B1 elds that are spatially homogeneous. Any inhomogeneities
or distortions in these elds (such as those that may be caused by dental implants, or varying
magnetic susceptibilities at interfaces) can alter the NMV (x, y) and cause image degradation.
As the components of S(t) are related to amplitude and phase of the B1 eld, signicant con-
straints must be placed on the design of the RF electronics to ensure that no unwanted frequencies
are produced and that these two components remain linear (i.e., the RF transmitter must produce
uniform amplitude across the frequencies used in the MRI machine).
The RF receive coil does not detect a signal that is directly viewable as an image. Instead,
a Fourier representation is received. For each slice, a sequence of phase and frequency encodings
are performed to populate a two-dimensional array (known as k-space). The phase encode pulse
sets up ky information for a given kx value, and so a series of measurements of kx for a line of
ky is performed. If a 256x256 k-space representation is used with a pulse repetition rate of 1 kx
measurement per second, it will take approximately 4 minutes to obtain a single image. From this
point, the digitized RF signal is in a form which can be processed to generate an image, as well as
compensate for items that degrade the image such as potential image aliasing, patient movement,
and other nonidealities that can be corrected using sophisticated techniques. [1]
7

8. 3.2 Safety of Implanted Medical Devices (IMD) in MRI Machines
Complications can arise for patients who require a MRI examination and possess an IMD such as
a pacemaker, debrillator or deep brain stimulator. These complications arise due to interactions
between implant materials and geometries and the magnetic and RF elds produced by MRI
machines during examinations. The magnetic elds used may impart strong forces upon implants
manufactured using magnetic materials, potentially moving them within the body. Electrodes and
leadwires of IMDs can act as antennas which concentrate RF elds, resulting in heating of tissue
and potential injury [3].
3.3 Skin Eect
The skin eect is the mechanism by which alternating electric currents (AC) tend to distribute
within a conductor such that the current density is greatest close to the surface. For a cylindrical
conductor (such as a wire), approximately 63% of an alternating current ows within a radial
distance (known as the skin depth, δ) from the conductor surface (gure 1). The skin depth
is a function of the conductor material properties and the alternating current frequency. At
higher frequencies, the skin depth is smaller and so the AC resistance of the conductor is greater
[4]. Electronically, it is desirable to have the lowest resistance possible for implant wires so that
stimulation currents can be lower, extending the battery-life of connected IMDs. However, by
using a material with low resistance, the wire may be more susceptible to large currents induced
by RF elds, and therefore greater dielectric heating.
Figure 1: The skin eect. Approximately 63% of alternating current ows within a radial distance
(known as the skin depth, δ). Image accessed from [4].
3.4 Specic Absorption Rate (SAR)
The specic absorption rate (SAR) is a measure of the rate at which RF power is absorbed per
mass of human body tissue (W/kg). A 3-Tesla MRI machine can deliver peak pulses in the order
of 20 kW at 128Mhz, leading to signicant heating of a patient. The International Commission
on Non-Ionizing Radiation Protection (ICNIRP) recommends maximum localized temperatures of
38◦
C in the head and 39◦
C in the torso, allowing for a 1−2◦
C rise above body temperature (37◦
8

9. C) induced by RF heating. The SAR is typically averaged over the whole body, whole head, or
local regions of 10 g mass [2]. Limits for SAR delivered during MRI are specied in [11]. For the
whole body, the SAR value must not exceed 2 W/Kg. For exposed body parts, the SAR must not
exceed 2 - 10 W/Kg (limit scales with ratio of exposed patient mass / total patient mass). For
the head region, the SAR must not exceed 3.2 W/kg. Local SAR (spherical volume of 10g mass)
values dier, specifying limits of 10 W/Kg for the head and trunk, and 20 W/Kg for extremities.
However, there is strong evidence [2] to suggest that a 10g region is too large for averaged local
SAR values, and therefore may not be reliable for study of implant safety in MRI machines.
3.5 Reduction of Dielectric Heating in Leads
Research has been conducted into improving the safety of implants for use in MRI machines by
reducing the eect of RF-induced dielectric heating. Reference [5] reports of a design for a deep
brain stimulator (DBS) lead design which utilizes a non-uniform diametered coil, as opposed to a
standard uniform diameter along the length of the lead. The design was tested using a phantom
and MRI machine and compared against a standard lead. Maximal temperature rises were found
to be reduced from 4.6◦
C to 2.0◦
C , with an average reduction of 59%. By altering the geometry of
the lead components, the transmission line parameters of the lead were modied and the impedance
under RF was increased. This may have reduced the amplitude of the electric eld induced in the
lead by the RF eld.
Reference [6] also discusses how modications to lead geometry can signicantly change RF
heating. Simulation software was used to experiment with the eect of dielectric heating when
applying resistive sheets to a 4 mm segment at both ends of a 60 cm insulated copper wire. The
wires were exposed to a plane wave (with electric eld of the RF wave parallel to wire axis). The
simulation used a 64MHz RF eld (as is used in 1.5 T MRI machines). Average electric eld
strengths were recorded within a 1 cm
3
volume centered on the end of the wire. Resistance of the
sheet was varied from 0.1 to 100 kΩ. For a 10 kΩ load resistance, the average electric eld strength
was recorded as being 64% of that recorded from a baseline unloaded wire. This was calculated
to correspond to a 41% reduction in dielectric heating. Further simulation was performed into the
eect of the wire length. The load at the end of the wire was set to 5 kΩ, and the wire length was
varied from 50 cm to 65 cm. The results showed that for lengths of wire near resonance, the load
applied to the end of the wire decreased RF-induced electric eld strength and heating.
Reference [2] investigates and discusses the eect of electrode wire insulation properties. Sim-
ulations were performed to predict the eect of insulation on the electric eld within a wire. Both
wires had a diameter of 800 µm. One wire was bare, and the other was insulated with a 350
µm thick coating. The simulation showed that the insulation shifted the resonant frequency of
the wire and increased the maximum electric eld strength by a factor of three. A phantom was
constructed using saline gel to compare the simulation results with measurements. Wire samples
were placed in the phantom and tested using a commercial 3 T (128 MHz) MRI machine. Tem-
perature was measured after 5 minutes of MRI scanning for wires of varying length and wires of
varying insulation thickness. The recorded measurements showed that at the worst-case length (at
resonance), a wire with 700 µm of insulation thickness experienced a 25.7◦
C rise in temperature.
A wire with half this thickness (350µm) increased in temperature by 21.3◦
C, while another wire
with only 21µm of insulation thickness increased in temperature by 3.7◦
C. The simulations and
measurements both show that RF heating increases proportionally with increased wire insulation
thickness.
Reference [7] explores the eect of lead tip area, lead conductor material, and lead insulation
9

10. material. Larger lead tip area was found to have a greater eect on reduction of RF heating (as
much as 50% reduction in a specic lead). Leads with greater DC resistance were found to have
lower RF heating. Lead insulation material was found to have signicant eect on RF heating.
Leads insulated using silicon were found to experience a maximum tip temperature increase of
approximately 37◦
C, whereas a bare lead with no insulation was found to increase by only 5◦
C. Leads insulated with silicon, along with an outer conductive coating of nickel were found to
increase in temperature by approximately 17◦
C, and a lead insulated with silicon and coated with
conductive graphite was found to increase in temperature by approximately 8◦
C.
Solutions that involve external devices have also been researched. Reference [8] describes the
use of a cylindrical shield to surround the area containing an electrode lead and suppress the RF
eld within it. Temperature was measured as increasing by 4.5◦
C without the shield (when used
in a 1.5 T MRI machine) and by only 0.2◦
C with the shield. Reference [9] demonstrates how
changes in the MRI RF transmitter coil design can be used to decrease RF heating in implanted
electrodes. Up to 90% reduction in heating was measured when replacing the body coil (a type of
coil used for imaging) by an optimized parallel transmit excitation with same nominal ip angle.
4 Design Overview
4.1 Aim
Patients implanted with medical devices (such as pacemakers, debrillators, deep brain stimulators)
are unable to undergo examination in MRI machines due to interactions between the materials
of the implants and the RF elds. These RF elds can cause rapid heating of tissue surrounding
implant wires and leads, resulting in injury. It is estimated that a patient with an implanted
pacemaker is denied a MRI examination every 3 minutes in the U.S., and every 6 minutes in
Europe [14]. Therefore, it is important that wires and leads be developed to prevent RF heating
during MRI examinations.
In order to develop MRI-safe leads, it is necessary to test them under conditions which reproduce
the RF exposure of an MRI examination. However, MRI machines can cost millions of dollars even
when purchased second-hand. Large additional costs may also incur due to installation (power,
cooling, shielding), maintainence and other technical requirements. Rental of MRI machines can
cost hundreds of dollars per hour. Combined with the slow time-dependant nature of testing
temperature rises in leads, this can quickly make testing new designs nancially infeasible. Thus,
a low-cost solution capable of replicating the RF emissions of a MRI machine is desired. This
project aimed to design, construct and test such a device.
4.2 Potential Solutions for Testing RF Heating in Leads and Wires
The cost of the hardware required to enable the strict magnetic specications used in the MRI
machine far exceeds that of the hardware used to transmit the RF pulses. As the strong magnetic
eld of MRI machines is of little relevance to testing leads for RF heating, it may be nancially
feasible to construct test apparatus which exposes the leads to RF radiation in a similar (or
identical) way to that of a MRI machine.
The most widely used RF coil in MRI machines is the birdcage coil. These coils produce circu-
larly polarized, highly uniform, transverse radiofrequency (RF) magnetic elds within a cylindrical
volume. Details of the calculations required to model birdcages can be found in reference[10].
10

11. Construction of birdcage coils for the purpose of testing RF heating in leads has already been
performed. Reference [12] details methods used to test a large series of wires and leads in a 1.5
T RF coil. A full-sized birdcage RF coil (length 113 cm, inner diameter 62 cm) with 16 legs
was constructed. Tuning capacitors were placed on each of the legs (joining to a ring on either
end of the cylinder) to form a low-pass structure. It is reported that this system is the same as
those used in 1.5 T clinical systems. The coil was fed by a quadrature power divider to produce
circularly polarized B1 elds. The birdcage was housed within an anechoic chamber (a room
designed to completely absorb the reection of electromagnetic waves), and the coil was powered
by a RF amplier specied to deliver 130 Watts at 64 MHz. Testing was conducted via a series
of exposure protocols. First, an initial base temperature measurement with no RF exposure was
taken for 60 seconds, followed by 200 seconds of RF exposure, followed by another 200 seconds for
cooling. A preliminary study was conducted into the calorimetry of a saline (without gelling agent)
phantom that was to be used in the wire heating tests. This allowed the total power delivered to
the phantom (whole body SAR) to be calculated. The power delivered to the birdcage coil was
approximately 55 W, producing a whole body average SAR within the phantom of approximately
1 W/Kg (for comparison, the whole body SAR limit is 2 W/Kg [11]). By determining the whole
body SAR, the RF heating data collected from tested wires and leads could be extrapolated to
values that could be expected to occur in a clinical MRI system.
More tests involving the contributors of [12] are detailed in [13]. A 1.5 T birdcage is again
constructed (with minor dierences; length 112cm, inner diameter 60cm). However, the birdcage
is powered by a 150 W RF amplier at 64 MHz and housed within a metal cage for RF shielding.
The same calorimetric study method is used to determine the power required from the birdcage
coil to deliver a whole body SAR of 1 W/Kg to a phantom inside the coil.
Yet another report [14] from the contributors of [12] and [13] demonstrates the behaviours of
a simulated birdcage coil and a physical constructed equivalent. A head-sized coil (16 cylindrical
copper legs, diameter 6 mm, length 30 cm, along with two external rectangular aluminium rings;
12 mm x 8 mm, 30 cm diameter ring) was designed using CAD software, and simulation software
was used to perform a broadband analysis (40 - 80 MHz) to determine the values of the tuning
capacitors required to maximize the resonance of the coil (for the given dimensions) at 64 MHz.
Measurements were performed on the physical birdcage coil to compare against the simulation
analysis. It was found that resonance occured at 64 MHz for capacitors of 17.2 pF. To obtain a
circularly polarized eld, two quadrature signals (90◦
phase-shifted) were applied to the RF ports
of the coil. The amplitude of these signals was adjusted to have a total forward power of 470
mW. Further tests were performed on a scaled version of the birdcage (length 62 cm, diamter
62 cm). Simulated analysis determined that the coil would be resonant for tuning capacitors of
70 pF. The simulated quadrature signals were adjusted to produce an average SAR of 1 W/Kg
inside a phantom. The physical birdcage was constructed using parallel copper plates, divided
by a thin layer of dielectric material, resulting in a distributed capacitance. It is reported that
this construction method is commonly used in 1.5 T clinical MRI machines. The birdcage was
housed in an anechoic chamber and fed by a 130 W 64 MHz RF amplier. Calorimetry studies
were again performed to determine the amplitude of the quadrature signals needed to deliver an
averaged whole body SAR of 1 W/Kg.
Following numerical validation of the constructed birdcage, an implant lead was tested inside
a phantom placed within the coil. Initially, the birdcage coil was excited by a quadrature voltage
with an amplitude that induced a whole-body mean SAR of 1 W/Kg inside a HVD (human visible
dataset; a phantom capable of reproducing 34 dierent human tissues with spacial resolution of 2
mm) with no implant. This resulted in an averaged local (over 1 mg tissue) SAR of 143.9 W/Kg
11

12. at the tip of the implant lead. Therefore, it can be seen that a birdcage can be constructed to
simulate MRI RF exposure at standard SAR levels (1 W/Kg) in order to demonstrate unsafe levels
of induced heating in experimental leads and wires.
Reference [15] describes the use of a constructed birdcage coil to induce RF currents in a
wire. The report states that the birdcage RF safety test platform replicates the eld (and,
heating) patterns seen within an MRI scanner to study the resonance properties of guidewires at
a comparatively negligible fraction of the cost of a complete MRI system and without the need to
face the challenges posed by the static magnetic eld during the initial stage of developing new
safety devices. The birdcage was 100 cm long and 60 cm in diameter, and was inserted inside a RF
shield of length 150 cm and diameter 82 cm. End-ring capacitors were 66 pF, while each leg rung
was comprised of three capacitor segments: the outer two were 18 pF, and the middle segment was
22 pF. In the testing, the birdcage was linearly polarized (unlike in references [12], [13], [14]). To
account for this, wires were placed in a plane orthogonal to the applied B1 RF eld where electric
eld strength would be at a maximum. A 200 W 64 MHz RF amplier was used. The RF delivered
to the coil was varied from 3.5 to 55 W. It is reported that Even at these power levels, with light
loading, this birdcage could still create RF electromagnetic elds and heating comparable to that
of an MRI scanner. Under a 100 Kg load, a continuous 200 W excitationneglecting radiation
and coil losses, as is standardshould still be able to produce 2 W/Kg SAR, comparable to many
MRI sequences. These statements and birdcage design principles appear to concur with those
presented in references [12], [13], [14].
4.3 Cost Analysis of Construction of RF Birdcages
The birdcages constructed in references [12] to [15] could be replicated using relatively inexpensive
materials and hardware. A quick web search of RF ampliers on the order of 100 to 200 W yields
many retail listings costing only hundreds of dollars (in some cases, as little as $40 USD). These
ampliers are typically of narrow spectrum, but modications may be possible to tune them to
single frequencies (such as 64 MHz, or 128 MHz). For comparison, MRI RF amplier units typi-
cally have kilowatts of output power, and prices are usually only available through manufacturer
quotation. RF power dividers (such as those used in [12]) can also be found inexpensively, typically
for less than $100 USD. For the RF phase shift (to produce a circularly polarized signal), it may
be possible to construct a simple phase shift circuit using few inexpensive electronic components.
The cost of the materials needed for the construction of the birdcage structure vary, but are
still inexpensive relative to the cost of an MRI machine. Reference [15] displays a gure which
appears to show the birdcage supporting structure constructed from a frame of wood and shielded
using copper plating. The remaining costs (capacitors, metal leg rungs) may vary, but are likely
to be almost negligible by comparison.
12

13. 5 Birdcage Coil Design
5.1 Design Parameters
Birdcage coils are a class of resonator which create circularly polarized, highly uniform RF magnetic
elds within their cylindrical volume. These elds are the result of currents which ow along the
surface of legs or rungs, arranged at equally-spaced angular intervals around the curvature of the
cylinder. The legs of the coil are connected at the ends of the cylinder via circular end ring
segments.
By applying a current density sinusoidally across the surface of a cylinder, a uniform tranverse
magnetic eld can be formed. A birdcage coil approximates this behaviour through the combination
of discrete leg currents. Circular polarization is achieved by rotating the current pattern at the
desired Lamor frequency. The currents in the birdcage coil occur as a result of the ladder network
consisting of N equal sections (where N is the count of legs), each containing one inductive element
(from leg), inductive elements from sections of both end rings, and capacitors either on the end
rings (connected between legs; known as high-pass), on the legs (connected between end rings;
known as low-pass ), or a combination of both (known as hybrid, or band-pass). By increasing
the number of these sections, the eld homogeneity is improved (though mostly in the transverse
direction). The resulting number of modes of resonance is an integer between 1 and N, and
determines the RF eld pattern and operating frequency of the coil. Only modes of order equal to
1 (the rst resonant mode) will result in a homogeneous eld. A cylindrical RF shield can also be
axed to the outer surface of the coil, but will reduce transverse eld homegeneity and amplitude.
In addition to the self inductances of the coil legs and end rings, mutual inductances occur
between all nonorthogonal inductive elements due to magnetic coupling through space. The eect
of these mutual inductances is signicant and complicates the analysis of the ladder network beyond
the capabilities of standard lter design theory [10].
5.2 Designing Birdcage Coils for Resonant Frequencies
The birdcage coil to be designed was expected to meet several requirements. Firstly, it needed
to be of sucient size to house a full-scale torso phantom placed within it (both in length and
radius). Secondly, the resonating frequency of the coil needed to be as similiar as possible to that
of an MRI machine. These dimensions required an internal cylindrical volume of approximately
90 cm in length with a 30 cm radius.
To model the elds and resonant properties for a birdcage coil of specic parameters, it is
necessary to compute the mutual inductances between the legs and end rings of the coil. A
software package (called Birdcage Builder [16]) was found that could automatically perform the
analysis required, presenting a single capacitance value for a given birdcage coil geometry (see
gure 2). Using this software, the end-ring capacitor values for a high-pass birdcage operating at
128 MHz with the required dimensions (length 90 cm, radius 30 cm, leg/end ring width 1.9 cm,
with no shield) was found to be approximately 7.5 pF.
13

14. Figure 2: Birdcage builder software.
(a) Physical dimensions and resonance requirements are
entered.
(b) Values for the end ring capacitors are calculated from
the given parameters on the settings page.
(c) Calculations of self, mutual, and thus eective induc-
tances of birdcage leg and end ring segments.
14

15. 5.3 CAD Design of Coil Structure
A CAD software was used to design the birdcage to the required dimensions. A support bench
was included in this design to allow ease of movement of a phantom through the centre of the coil
(gure 3).
Figure 3: Initial design CAD render of birdcage coil frame, with phantom and support bench.
A later revision of the CAD model included modications to allow ease of construction. The
end rings were divided into quarter sections that could be layered and interlocked using segments
of dowel rods and wood glue. This also allowed the end rings to be laser-cut during construction
(gure 4). The placement of the legs was modied such that their inner surfaces became coincident
with the interior surfaces of the end rings. Conductive strips were also added to the legs and end
rings of the model.
15

16. Figure 4: CAD schematic of laser-cut end ring section.
16

17. Figure 5: Second revision of birdcage CAD model.
5.4 Construction of Birdcage Coil
The coil was constructed as per the specications of the CAD model. The legs were cut from
sections of MDF. The end ring sections were made from plywood, and were laser-cut to the
designed dimensions. The end ring quarter sections were layered twice (with the second layer
being rotated 45◦
) and fastened together using dowel rods and wood glue. The legs were also
glued to the end rings. Metallic fasteners (such as screws) were avoided so as not to have any
interaction with the RF elds of the coil.
The supporting bench was redesigned during construction (gure 6). The new structure allowed
both birdcage coil and phantom to be moved along the length of the bench. Nylon screws and
wood glue were used to construct the bench. A RF shield was also created during construction
from wire fencing material, but was later removed before testing of the coil performance.
For the conductive strips on the legs and end rings, an adhesive copper tape was used (0.035
mm thickness, 19 mm width). The traces of the legs were soldered at the intersections with the
end ring traces. Small gaps (~1 mm width) were cut from the copper traces half-way between the
leg connections on the end rings to allow space for the capacitors.
The capacitors specied by the birdcage calculation software were 7.5 pF. The closest value of
capacitor available during construction was 8.2 pF. This caused the calculated resonant frequency
to decrease to approximately 124 MHz, but was deemed acceptable as the resulting change in
wavelength would be minimal.
17

18. To provide power to the coil, two 50 Ω coaxial cables were soldered to one of the end rings.
Each cable connected in parallel across a capacitor on the end ring. The cables were spaced 4 legs
apart (90◦
of the end ring) to provide a quadrature power feed to the coil, and were soldered
such that their polarities faced in the same direction along the end ring (i.e., +/-, +/-).
Figure 6: The constructed birdcage coil, with supporting bench and phantom.
18

19. Figure 7: Rear view of constructed birdcage coil.
19

20. 5.5 Birdcage Coil Power Systems
5.5.1 Quadrature Driving
In order to create circularly polarized RF elds, birdcage coils must be powered by a quadrature
feed. This requires two feeding ports on the coil, which are excited by currents at the Larmor
frequency with a 90◦
phase dierence between them. The power fed to each port must be equal
to ensure circular polarization.
A λ/8 transmission line hybrid splitter was designed to divide and phase-shift power fed to the
birdcage coil ports (gure 8). The circuit consisted of an etched PCB, two 50 Ω coaxial cables,
two capacitors, and a resistor (used for dissipating power reected from coil). BNC connectors
were soldered to the PCB for the single input and two output ports. The outer shields of the
coaxial cables were soldered to the PCB ground plane. The length of the coaxial cables was
determined by the required wavelength of the birdcage coil and the velocity factor (VF) of the
cable used [18]. To divide power at 128 MHz, the required cable length was approximately 19.7 cm
(λ/8×V F = 0.299×0.66). The required capacitor values were calculated as C = (50Ω×ω)−1
= 25
pF.
Figure 8: λ/8 transmission line hybrid created to split and phase-shift power at 128 MHz.
The constructed splitter was tested using a vector network analyser (VNA). A S12 analysis
was performed to determine the phase angle between the output ports of the splitter. The input
of the splitter was connected to the rst port of the VNA, with one splitter output connected to
the second VNA port and the other terminated via a 50 Ω load (output congurations alternated
between tests). By sweeping the output frequency of the VNA, the phase shift at each splitter
output could be observed. The phase shift between the splitter input and outputs at 128 MHz
was found to be approximately 43.8◦
for the rst output, and −41.9◦
for the second output. This
resulted in a total phase shift of 85.7◦
between the splitter outputs.
The splitter was also tested using a RF generator and oscilloscope to analyse the magnitude
of the power division. Both outputs of the splitter were fed into the oscilloscope. By sweeping
the frequency of the generator, it was found that the power amplitudes of the output ports were
approximately equal at 122.3 MHz (gure 9). However, operation at this frequency caused the
phase-shift to decrease further from the desired value. The cause of the dierence between the cal-
culated and measured operating frequency of the splitter is possibly due to component tolerances,
and may be removed via tuning capacitors. Further testing would be required to conrm this.
20

21. Figure 9: Oscilloscope trace of splitter outputs (operated at 122.3 MHz).
21

22. 5.5.2 RF Power Amplier
A RF power amplier (PA) was used to feed the quadrature splitter and the birdcage coil. The PA
was constructed from a kit purchased from an online store, and was specied as being suitable for
providing up to 100W of power over a range of 80 - 180 MHz (gure 10). An aluminium heatsink
was created and attached to the amplier. BNC connectors were soldered to the input and output
of the amplier. The circuit included a standing-wave ratio (SWR) meter to allow measurements
of the power absorbed and reected by the antenna.
Figure 10: RF amplier (100W, 80 - 180 MHz) used to power the birdcage coil.
22

23. 6 Performance Analysis of Designed Birdcage Coil
6.1 Resonant Frequency
Following construction, the S11 parameters of the birdcage coil ports were analysed using a VNA.
The largest signal absorption/loss was expected to occur at approximately 128 MHz; However, the
closest frequency where a signicant signal loss to the coil could be observed was approximately
160 MHz. The cause of this dierence between calculated and actual resonant frequency is unde-
termined, but may be related to the methods used by the Birdcage Builder software. It was later
observed that the software does not request the thickness of the metal used for the birdcage coil
legs and end rings. As the calculations are heavily dependant on the self and mutual inductance
of the birdcage components, this may account for the dierence in calculated and actual resonant
frequencies.
After this analysis, the birdcage coil RF emission was tested using an oscilloscope. The coil
was powered by the PA through a single port (resulting in linear polarization). A RF eld probe
(consisting of a diode soldered to the end of a coaxial cable) was axed to the supporting bench
of the coil. The PA was fed by the RF generator, and the frequency was swept across a spectrum
(20 MHz to 300 MHz) to determine at which frequency the largest signal amplitude occured on
the oscilloscope display. As predicted by the VNA (160 MHz), the largest signal amplitude was
observed at approximately 156 MHz.
6.2 Impedance Matching
In order to minimise reected power from the birdcage coil, variable capacitors were added in
parallel across each input port. These capacitors were tuned using a Smith chart on the VNA to
set the input impedance of the ports to approximately 50 Ω (gure 11). Small variations between
the port Smith charts were observable, and were possibly inunced by environmental interference
(such as metallic objects within the vicinity of the test).
23

24. (a) Port 1 input impedance.
(b) Port 2 input impedance.
Figure 11: VNA-generated Smith chart of birdcage coil input impedances. The green arrows
(center of charts) denote the impedance match at 156 MHz.
24

25. 6.3 RF Heating Experiment
An experiment was conducted to observe the RF heating capabilities of the designed coil. Due to
the unexpected resonant frequency of the coil (156 MHz, as opposed to 128 MHz), the quadrature
divider designed to operate at 128 MHz was unusable during heating tests. The coil was instead
fed power through a single port, resulting in linear polarization.
A 20 cm insulated copper wire was placed within a saline-lled phantom, and aligned with the
long axis of the coil. A ber optic temperature probe was used to measure temperature changes at
the tip of the wire (gure 12). The temperature of the experimentation room was decreased from
22◦
C to 18◦
C approximately one hour before testing (for the duration of the experiment, the room
temperature was decreasing). The temperature probe measured 19.3◦
C for approximately ve
minutes before testing, and so was taken as a baseline temperature. Temperatures were recorded
every minute during the test (duration of 21 minutes). The RF generator was set to 156.5 MHz, and
the PA was turned on (drawing 2 amps). The wire tip increased in temperature by approximately
0.7◦
C over a period of 10 minutes. At the end of this time, RF power was turned o and the wire
was left to cool for a further 11 minutes (gure 13).
Figure 12: 20 cm insulated copper wire mounted inside the phantom (before insertion of saline
gel). A ber optic thermometer was mounted coincident with the tip of the wire.
25

26. Figure 13: RF Heating experiment in saline phantom using 20 cm insulated copper wire. The
birdcage coil was fed a 156.5 MHz signal via a single port (linear polarization).
6.4 Post-Experiment Analysis
During the test, the SWR meter of the power amplifer was measured to determine the amount
of power reected and absorbed by the birdcage coil. Forward (Vf ) and reverse (Vr) voltages for
the SWR meter were approximately 2.06 V and 1.09 V respectively. The reection coecient
was calculated as Γ = Vr
Vf
= 0.53, and the SWR was calculated as
1+Γ
1−Γ
= 3.25. This SWR value
indicates that approximately 25-30% of the power fed to the birdcage coil was reected back to
the amplier, despite the previous VNA Smith chart analyses indicating a suitable 50 Ω input
impedance match for both of the coil ports. The large magnitude of the reected power could be
due to coil impedance changes caused by the saline-lled phantom.
The temperature of the wire tip increased by approximately 0.7◦
C during the experiment. It
may be possible to increase the amount of heating by changing the wire length or orientation. A
circularly polarized eld (created by feeding the coil in quadrature, as opposed to a single-port
feed) may also cause signicant dierences in the magnitude of heating. Further analysis and
testing would be required to conrm these hypotheses.
6.5 Post-Design Analysis
The designed birdcage coil demonstrated the ability to induce RF heating through the same mech-
anisms as those found in a MRI machine. However, due to the unexpected resonant frequency of
the coil, it fails to meet all of the requirements specied for this project. The resonant frequency
could be modied to be 128 MHz by changing the values of the end ring capacitors, but this may
be a trial-and-error process.
Later research found that for birdcage coils created using conductive elements with maximum
dimension greater than λ/20 (as is the case with the coil designed in this project), it is necessary
to use EM eld simulation software to calculate and predict the resonant frequency of the coil.
In these situations, the electromagnetic eld of the coil is strongly inuenced by the presence
26

27. of biological tissue, and accurate predictions of resonant spectrum and eld distributions can be
obtained only by full-wave simulation [10]. For birdcage coils using conductive elements with
maximum dimension less than λ/20, a lumped-element analysis can be performed to determine
the resonant behaviours of the coil. The Birdcage Builder software uses lumped-element methods
[17], and thus is likely to be inaccurate for birdcage coils of the size specied for this project.
The designed quadrature splitter appeared to perform as expected, creating an approximate
90◦
phase shift with equal power division between outputs when operated at 128 MHz.
During VNA analysis of the birdcage coil, it was observed that the presence of a person within
the vicinity of the coil caused signicant changes in the magnitude of the measured S11 parameter
(at the resonant frequency, 156 MHz). This is possibly the result of impedance changes caused
through interactions between the coil RF elds and water molecules in the human body. During
pre-experiment testing, it was also observed that a person walking past the birdcage coil aected
the current drawn by the power amplier. This further supports the hypothesis that the presence
of a human body near the coil can modify the coil impedance, as a change in PA current would
occur if the magnitude of the power emitted by the coil was changed.
The sensitivity to external inuences resulting in impedance changes may be mitigated through
use of a RF shield. However, such an addition would cause a signicant change in coil impedance,
resonant frequency, and would decrease the amplitude of transmitted power. A shield was initially
added during construction, but was removed as it appeared to result in inconsistent S11 measure-
ments when using the VNA. Further testing and analysis would be required to determine the cause
of this.
Figure 14: Diagram of systems used to power birdcage coil.
27

28. 7 Conclusion
MRI examinations expose patients to RF elds during examination. Interactions between these
elds and medical implants (such as electrodes, leads, etc) can cause RF heating, inicting damage
to the surrounding tissue. In order to design MRI-safe electrodes, it is necessary to test them under
the same RF conditions as those found in MRI machines. This can be achieved inexpensively
through construction of a birdcage coil designed to emulate the RF exposure of a MRI machine.
The aim of this project was to design and test such a birdcage coil. It was specied that the coil
should resonate at 128 MHz (as is found in 3 T MRI machines) with a quadrature feed (resulting
in circular polarization), be of sucient size to house a full-sized torso phantom, and transmit
enough power to heat prototype electrodes and wires placed within a saline-lled phantom.
The designed bird cage coil met structural and dimensional requirements. Despite designing
for a resonance at 128 MHz, the coil was found to resonate at approximately 156 MHz. The cause
of this disparity is undetermined, but may be the result of unforeseen design parameters. It is
predicted that modications to the values of the end ring 8.2 pF capacitors would resolve this issue.
It was later found that the Birdcage Builder software may be unsuitable for birdcage coils of the size
specied in this project. The resonant behaviour of the coil would be more accurately predicted by
a full-wave EM simulation software, as opposed to a software using only lumped-element analysis
methods (as is used by the Birdcage Builder software)[17].
A quadrature hybrid splitter circuit was designed to divide power and phase-shift an input
signal by 90◦
in order to generate a circularly polarized emission from the coil (as is used in MRI
machines). Performance analysis of the splitter indicated that it functioned satisfactorily, dividing
power equally between both output ports with a phase shift of approximately 85.7◦
. However,
due to the inherent frequency-dependent behaviour of the splitter (operable only at the designed
frequency of 128 MHz), it was found to be incompatible with the 156 MHz resonance of the coil
during testing.
A 100W RF power amplier was constructed and used for testing. Despite tuning of the bird-
cage coil to match input impedance requirements, SWR measurements from the RF PA indicated
that approximately 25-30% of the power fed to the birdcage coil was reected back to the PA
(when fed via a single port only). The cause of this is also undetermined, but may be due to
environmental interactions resulting in modications to the coil impedance.
An experiment was performed to attempt RF heating of a 20 cm insulated copper wire placed
within a saline-lled phantom. The coil was fed a 156 MHz signal via a single port (resulting in
linear polarization). A ber optic thermometer measured a 0.7◦
C temperature rise at the tip of
the wire over a period of ten minutes.
This project has demonstrated that a birdcage coil can be constructed to induce RF heating
via the same mechanisms as those found in MRI machines. The designed coil did not fully match
specied requirements for resonant frequency. Further testing and modications are required to
address these issues.
28

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30. [15] Marta G. Zanchi et al., An Optically Coupled System for Quantitative Monitoring of MRI-
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30