SAR Reduction in 7T C-Spine Imaging Using a “Dark
Modes” Transmit Array Strategy
Yigitcan Eryaman,1,2,3* Bastien Guerin,2Boris Keil,2,10Azma Mareyam,2
Joaquin L. Herraiz,1,3Robert K. Kosior,3,9Adrian Martin,3,8Angel Torrado-Carvajal,3,7
Norberto Malpica,3,7Juan A. Hernandez-Tamames,3,7Emanuele Schiavi,3,8
Elfar Adalsteinsson,3,4,5,6and Lawrence L. Wald2,5
Purpose: Local specific absorption rate (SAR) limits many
applications of parallel transmit (pTx) in ultra high-field imag-
ing. In this Note, we introduce the use of an array element,
which is intentionally inefficient at generating spin excitation (a
“dark mode”) to attempt a partial cancellation of the electric
field from those elements that do generate excitation. We
show that adding dipole elements oriented orthogonal to their
conventional orientation to a linear array of conventional loop
elements can lower the local SAR hotspot in a C-spine array
at 7 T.
Methods: We model electromagnetic fields in a head=torso
model to calculate SAR and excitation B1þpatterns generated
by conventional loop arrays and loop arrays with added elec-
tric dipole elements. We utilize the dark modes that are gener-
ated by the intentional and inefficient orientation of dipole
elements in order to reduce peak 10g local SAR while main-
taining excitation fidelity.
Results: For B1þshimming in the spine, the addition of dipole
elements did not significantly alter the B1þspatial pattern but
reduced local SAR by 36%.
Conclusion: The dipole elements provide a sufficiently compli-
mentary B1þand electric field pattern to the loop array that
can be exploited by the radiofrequency shimming algorithm to
reduce local SAR.
Magn Reson Med 000:000–000, 2014.
C 2014 Wiley Periodicals, Inc.
Key words: parallel transmit; local SAR; global SAR; radiative
dipole; loop–dipole arrays; excitation fidelity
Parallel transmit (pTx) arrays are currently in investiga-
tional use to alleviate radio frequency (RF) field inhomo-
geneity problems in high-field MRI (1–5) and offer the
potential to optimize specific absorption rate (SAR) as
part of the pulse design process (6–9). The geometry of
the individual coils is an important design parameter
that can be optimized in order to improve MRI excita-
tion. The coil elements used in the transmit array can
have diverse geometries, including microstrip coils (1,5),
conventional loop coils (2,3,6–8), and radiative dipole
antenna (10). The latter was recently introduced as a
transmit element for high-field transmit arrays (10) but
was shown to have a higher peak local SAR at 7T com-
pared to a loop element producing identical B1þin the
middle of a uniform phantom. In a comparison of these
three types of transmit elements, the loop antenna had
the smallest local SAR. Nonetheless, the dipole’s B1þ
field penetrated longer distances in a phantom, likely
due to the lack of cancellation of currents compared to
micro-strip coils or conventional loop elements (10).
The B1þfield pattern generated by any transmit element
depends on the orientation of the element with respect to
B0. For the dipole array, previous uses have sensibly ori-
ented it to produce the maximum B1þfield at the center of
the body. In this study, we use dipole elements with their
conductive element aligned orthogonal to the direction of
the static magnetic field (z- axis), as shown in Figure 1. In
this arrangement, the dipoles produce RF magnetic fields
mostly in the z-direction—and with little Bxor Bycompo-
nent that can give rise to the desired B1þcomponent.
Thus, the B1þcomponent generated by these elements is
small compared to that generated by a loop or a conven-
tionally oriented dipole. This property of the dipole ele-
ments enables us to energize these elements without
generating spin excitation. This situation is similar to that
previously shown for the “dark modes” of the degenerately
tuned birdcage coil—those modes that generate the wrong
circular polarization for spin excitation (11). We have
hypothesized that, although not useful for spin excitation,
these dark modes or dark elements are potentially useful
for generating electric (E-) fields that partially cancel the E-
1Research Laboratory of Electronics, Massachusetts Institute of Technol-
ogy, Cambridge, Massachusetts, USA.
2A. A. Martinos Center for Biomedical Imaging, Department of Radiology,
Massachusetts General Hospital, Charlestown, Massachusetts, USA.
3Madrid-MIT Mþ Vision Consortium, Madrid, Spain.
4Department of Electrical Engineering and Computer Science, Massachu-
setts Institute of Technology, Cambridge, Massachusetts, USA.
5Harvard-MIT Health Sciences and Technology, Massachusetts Institute of
Technology, Cambridge, Massachusetts, USA.
6Institute of Medical Engineering and Science, Massachusetts Institute of
Technology, Cambridge, Massachusetts, USA.
7Departmentof Electronic Technology,
M? ostoles, Madrid, Spain.
8Department ofApplied Mathematics,
M? ostoles, Madrid, Spain.
9Faculty of Medicine, University of Calgary, Calgary, Canada.
10Harvard Medical School, Boston, Massachusetts, USA.
Grant sponsor: National Institutes of Health NIBIB; grant numbers:
R01EB006847; R01EB007942; Grant sponsor: Comunidad de Madrid,
Madrid-MIT M1Vision Consortium.
*Correspondence to: Yigitcan Eryaman, Ph.D., Research Laboratory of
Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139.
Additional Supporting Information may be found in the online version of
Received 16 October 2013; revised 17 March 2014; accepted 17 March
Published online 00 Month 2014 in Wiley Online Library (wileyonlinelibrary.
Magnetic Resonance in Medicine 00:00–00 (2014)
C 2014 Wiley Periodicals, Inc.
fields associated with spin excitation resulting from con-
ventional elements. In the case of the combined loop and
dipole array described here, the loop elements are expected
to generate spin excitation (along with unwanted E-fields),
and the dipoles are used to attempt to partially cancel
these E-fields and thus reduce local SAR. We validated
this concept in a simulation study of a C-spine excitation
array at 7 T.
We performed electromagnetic (EM) simulations of an
array with dimensions similar to a previously con-
structed four-channel loop array (12) and compared it to
an array of identical loops with “dark” dipole elements
added, as shown in Figure 1. The width and height of
the loop element were chosen as 69 mm and 155 mm,
respectively. Four capacitors were distributed around the
loops for matching and tuning. The length of the dipoles
were chosen as 118 mm. All transmit element models
were constructed by using a 10-mm wide copper stri-
pline. The lower part of the array was located approxi-
mately 40 mm away from the lower body; and the upper
part of the array was located approximately 80 mm away
from the head. Simulations were performed with SEM-
CAD X EM Solver (Speag, Zurich, Switzerland) using the
virtual family model “Duke” (IT’IS Foundation, Zurich,
Switzerland). The calculation was done on a grid size
chosen by the software that varied between 1 mm and
4.5 mm; however, the larger grid size was mainly in
areas of free space. After the fields were calculated on
the nonuniform grid, we interpolated the results onto a
uniform 3-mm grid. Uniaxial perfectly matched layer
(UPML) boundaries were placed 500 mm from the field
sensor area (400 mm ? 220 mm ? 340 mm), which was
the area over which the fields are calculated (Fig. 1),
leading to a total simulation volume of 1400 mm ? 1220
mm ? 1340 mm. UPML boundaries were placed at a suf-
ficient distance to the RF coil and body model. Loops
and dipole antennas were matched and tuned to the Lar-
mor frequency for 7 T (298 MHz). The reflection coeffi-
cient seen from the excitation ports of all elements were
adjusted to a value less than ?17 dB. First, the structure
is modeled in SEMCAD (e.g., the loop of the loop coil
with no capacitors). Next, using the simulated imped-
ance of this structure—as determined by SEMCAD at the
Larmor frequency—we calculated the needed capacitor
values to match and tune the loop to 50 Ohms at 297.2
MHz using MATLAB (Mathworks, Inc., Natick, MA).
Then we placed these values into the SEMCAD model
and repeated the procedure until it converged (after
about 2 or 3 iterations). Starting from the drive port and
working counterclockwise, the calculated C values (in
pF) are as follows: loop 1 ¼ 35, 3.52, 3.52, 3.52; loop 2 ¼
35, 3.52, 3.52, 3.52; loop 3 ¼ 34, 3.51, 3.51, 3.51; and
loop 4 ¼ 30, 3.57, 3.57, 3.57. Similarly for the four
dipoles (circuit diagram shown in Fig. 1), simulated L
and C were: dipole 1 ¼ 144.4 nH, 34.0 pF; dipole 2 ¼
144.6 nH, 35.5 pF; dipole 3 ¼ 143.9 nH, 35.1 pF; and
dipole 4 ¼ 143.3 nH, 32.5 pF. The copper traces were
modeled as perfect conductors. No additional dielectric
material was placed between the RF coil and the body.
All elements were assumed perfectly decoupled in order
to simplify EM simulations. In practice, we previously
showed that the loop array could be constructed with a
maximum S12 of ?14 dB (12).
We constructed a loop and two dipoles and performed
S parameter measurements. The loop and the dipoles
were matched and tuned at 297.2 MHz. The coupling
between the loop and the dipoles at different locations
(S12) were measured using a network analyzer. We also
acquired B1þmaps of the loop and the dipoles (in dark
mode and regular operation mode) individually using a
uniform phantom, as shown in Supporting Figures S1
and S2. B1þmaps were obtained using a uniform phan-
tom with a 3.3 g=L NiCl2.6H2O, 2.4 g=L NaCl solution.
The dimensions of the phantom (rectangular box) were
150 ? 150 ? 380 mm. The conductivity and relative per-
mittivity of the solution were measured as 0.7 S=m and
80, respectively. A standard gradient recalled echo
sequence (pulse repetition time ¼ 600 msec) was used to
acquire the B1þmaps with a resolution of 3.1 ? 3.1 ? 5
mm. MRI images are obtained using excitation voltages
varying from 0V to 200V for each element. The measured
image intensities were fitted to sinusoids to calculate the
B1þvariation of each transmit element in the imaging
plane. A Tx=Rx switch was used to receive the MRI sig-
nal with the same coil. The EM simulations were also
performed to calculate the B1þmaps in the same uni-
Using loop elements alone, we calculated simulated
B1þpatterns from two different sets of excitation cur-
rents. First, we used a simple linear phase increment to
the loops (0?, 30?, 60?, 90?) with constant magnitude.
Secondly, we used particle swarm optimization (PSO)
(13) to optimize the amplitude and phase of each port’s
excitation (RF shimming) to minimize the magnitude
least square (MLS) flip-angle error over the spinal region
of interest (ROI). The ROI was drawn manually in only
one image plane (thus, it has only 1 pixel depth in the
patient L–R direction).
The local SAR distribution of these two methods is
calculated for a mean B1þfield of 1 mT at the spinal
cord ROI. A home-written region growing algorithm was
used. For each voxel in the body, a neighborhood of
voxels that approximates 10g tissue is chosen. Inside
the body, growth in this region is roughly isotropic.
Near the edge of the body, it stops growing at the sur-
face and only grows inwardly. The 10g SAR is then
averaged over this region. After establishing the opti-
mum excitation and resulting SAR pattern from the
loop elements alone, we energized the dipole elements
to ascertaintheir effect.
expected to generate small transverse B1þfield at the
location of the spinal cord due to their orientation.
However, the electric fields generated by the dipoles are
comparable in magnitude to the loop elements. We opti-
mized the currents on the dipole elements to reduce the
overall peak local SAR using PSO. For the optimization,
SAR matrices were compressed to a smaller set of 141
virtual observation points (14) to enable fast evaluation
of peak 10g local SAR. The optimization was con-
strained to maximally cancel the local SAR while
achieving the same B1þto within 3% at each point in
The dipole elementsare
2 Eryaman et al.
the spinal cord ROI as the loops alone. Supporting
Table S1 shows the magnitudes (root means square volt-
age [Vrms]) and the phases of the voltages on all array
elements. In addition to the comparison described
above, we calculated optimum RF shimming solutions
between the magnitude of the simulated and desired
flip-angle profile while explicitly constraining both
global and local SAR (7). This was performed for both
the loop array and the loop þ dipole array. The target
pattern was a uniform 25?flip angle excitation on the
spinal ROI. The algorithm was free to adjust the phase
and amplitude of all elements within the power and
global SAR constraints. Each pulse consisted of a sinc
profile (3 lobes; 0.8 ms second duration; duty cycle of
10%). Calculating the pulse several times with different
local SAR constraints results in an L-curve that shows
the trade-off between local SAR and the flip-angle target
fidelity [% root-mean-square error (RMSE)] for the mag-
nitude image. The global SAR, maximum peak RF
power, and average RF power were explicitly con-
strained (to 3.2 W=kg, 5 kW and 500 W, respectively).
Figure 2 shows the simulated B1þmap of the individual
loop and dipole elements. The spinal cord B1þof the
loops were significantly larger than the B1þof the
dipoles reflecting the choice of orientation of the dipoles,
which are arranged to generate magnetic fields mainly in
the z-direction (Fig. 2; bottom row). Because of their
weak contribution to B1þ, the dipole elements can be
excited without affecting the B1þof the loop array. Fig-
ure 3 shows the simulation results for the B1þdistribu-
tion of two separate excitation patterns: 1) linear-phased
current pattern with loops carrying currents with con-
stant magnitude but with linear phase changing in the z-
direction. 2) Currents optimized with PSO to minimize
MLS with RF shimming. Figure 3 (3a, 3d) shows B1þ
due to four loops only. Figure 3 (3b, 3e) shows B1þdue
to the loop–dipole array (4 loops, plus 4 dipole ele-
ments), whereas the dipoles produce the “dark modes,”
as explained above. Figure 3 (3c, 3f) shows the B1þon
the spinal ROI. As can be seen from both the sagittal B1þ
maps and the B1þplots, the excitation of the dark modes
with the dipole elements did not change the B1þpattern
of the loops significantly.
Although the dipoles have minimal effect on the B1þ
pattern, the peak 10g local SAR was reduced when the
dipoles were energized. SAR reduction is demonstrated
for both the linear phased current pattern (Fig. 4) and
the uniform B1þpattern obtained with RF shimming
(Fig. 5). Figure 4 and Figure 5 show the 10g local SAR
distribution of two arrays in three planes chosen so that
the axial plane always contains the peak local SAR hot-
spot. Energizing the dipole elements reduced the peak
local SAR by 16% and 36%, respectively, for the linear
phase and full RF shimming cases.
The global SAR values for the loop-only and loop þ
dipole array were 1.21 W=kg and 1.29 W=kg for the lin-
ear phase excitation. For the MLS RF shimming, the
global SAR were calculated as 1.40 W=kg and 1.44 W=kg
for the loop-only and loop þ dipole array, respectively.
Figure 6 shows the local SAR tradeoff of the loop array
and the loop þ dipole array as L curves. The addition of
the dipoles-reduced local SAR for all of the excitations
studied. SAR reduction was 28% for the approximate
optimal operating point on the L-curve (an RMSE excita-
tion fidelity of 5% over the spinal cord ROI).
One loop and two dipole elements were constructed
with the same dimensions discussed in the methods sec-
tion. Supporting Figure S1 shows the matching-tuning
(S11) and the decoupling (S12) behavior of the loop and
the dipoles at different locations. Data in row 1 of the
table in Supporting Figure S1 was obtained using a sin-
gle loop and a single dipole. The position of the dipole
was changed whereas the position of the loop was kept
constant. When the dipole was located symmetrically in
the middle of the loop, decoupling value (S12) of ?22.6
dB was obtained. It is also shown that the loop couples
strongly with the neighboring dipole (S12 ¼ ?5.4 dB.)
The coupling between the loop and the next nearest
dipole and the farthest dipole was weaker (?14.1 dB and
?18.2 dB, respectively). Row 2 of the table in Supporting
Figure S1 shows the coupling between the two dipole
FIG. 1. B1þfield of the loop was larger than the z component of
the loop’s magnetic field. B1þof the dipole in the above orienta-
tion was smaller than the z component of the dipole’s field.
Alignment of the dipoles in this orientation enables generating
“dark modes” (a, b). Loop array and the loop–dipole array (c)
were designed for spine imaging. Red and blue cones show the
voltage sources and lump elements, respectively. Relative dis-
tance of the arrays to the body is shown from side view (d). [Color
figure can be viewed in the online issue, which is available at
SAR Reduction Using a “Dark Modes” Strategy3
elements: in the nearest-neighbor positions and in the
next two most distant positions. Supporting Figure S2
shows the simulated and the measured B1þof the loop
and the dipole in the two orthogonal orientations of the
dipole. In general, we have a good qualitative agreement
between the simulated and measured B1þfor both ele-
ments. Note that the transmit efficiency (B1þ) of the
dipole is reduced in the dark element orientation when
compared to the regular orientation.
For spine imaging, the local SAR reduction is achieved
by energizing “dark” elements—the dipoles which do
not change significant B1þprofiles, but which do pro-
vide additional degrees of freedom to cancel E-fields
(and thus reduce SAR). For RF shimming excitation, the
maximal local SAR hot spot occurred in the inferior C-
spine where the loops are closest to the body. For the
linear phased current excitation, the maximal local SAR
hot spot occurred in the neck. In both cases, adjuvant
excitation with dipoles enabled overall peak SAR reduc-
tion. The position of the hot spot did not change for
these examples. However, the addition of the dipoles
increased the local SAR hot spot at the neck by 3.1% for
the RF shimming excitation pattern. Global SAR did not
increase significantly when the dipoles are energized.
The peak 10g local SAR remained as the limiting RF
safety factor in these examples. Hard constraints can be
added to the optimization problem in order control
global SAR properly while reducing local SAR.
We refer to the dipoles as “dark” in the sense that they
produced little effect on B1þdue to their orientation.
However, they do not generate the ideal null B1þfields
in space. In order to ensure that no or little B1þdistor-
tion was caused by the dipoles, the dipole currents were
constrained in the optimization process. By constraining
B1þperturbation levels in the optimization, a prior B1þ
pattern obtained by loops on the whole spinal ROI was
preserved with no significant change due to the excita-
tion of the dipoles. An alternative approach would be to
simply include the dipole fields in a general pulse-
optimization process that explicitly constrains local
SAR, such as that demonstrated by Gu? erin et al. (7).
Although inclusion of the dipole B1þfields would have
little effect on the B1þdistribution of the studied config-
uration, the extra computational time would likely be
acceptable for an array with elements that were not truly
The length of the dipoles used in this study was
smaller than the quarter wavelength. In contrast to Raaij-
makers et al. (10), the purpose of our study was not to
maximize transmit efficiency. Our goal was to provide
an E-field for cancelling local SAR without perturbing
the excitation (B1þ¼ 0 ideally). Thus, although perhaps
the shortened structure is less than optimal for transmit
applications, it was successful for the purpose for which
it was employed.
FIG. 2. B1þdistribution due to 1 root means square voltage excitation of individual loop and dipole elements are shown. B1þof loop
elements were larger than B1þof dipole elements (oriented as in Fig. 1) in the spine ROI. Bzdistribution due to 1 V excitation of dipole
elements is also shown. In comparison, dipoles (oriented as in Fig. 1) generate magnetic fields mostly in z-direction, which makes them
dark elements for MR excitation. Rectangles show the location of the coil elements.
4 Eryaman et al.
In this Note, an array of four loop and four dipole ele-
ments is compared to four loop elements in terms of
excitation fidelity and peak local SAR tradeoff. Alterna-
tively, the loop–dipole array could have been compared
to an array of equal number of elements, for example, an
eight-loop array. We chose not to pursue this comparison
FIG. 3. B1þdistribution (sagittal
plane) due to linear-phased cur-
rent pattern (top row) and MLS
RF shimming (bottom row) for
loop array and loop-dipole arrays
are shown. Supporting Table S1
showsthe magnitudes (Vrms)
and the phases of the voltages
on all array elements. Position of
the spinal cord is marked with
“white dots” in the map. (a,d)
dipole array (4 loops plus 4
dipole elements). (c,f) The B1þ
on the spinal ROI. The addition
of the dipole elements does not
change the B1þpattern of the
FIG. 4. Local SAR (10 g) distribution in axial, coronal, and sagittal planes for the loop array and loop þ dipole arrays. The four loops
were excited with a linear-phased current pattern (as in Fig. 3 a, 3b, 3c) and an optimized MLS RF shimming pattern (as in Fig. 3d, 3e,
3f). Row 1 and row 3 show the SAR distribution due to loops alone. In the loop þ dipole case, the dipole currents were chosen with
PSO to minimize peak local SAR. Row 2 and row 4 show the SAR distribution due to loops þ dipoles. The axial plane through the larg-
est hot spot is shown. Adding the dipoles allowed the same B1þpattern to be achieved with 36% reduction in 10g SAR.
SAR Reduction Using a “Dark Modes” Strategy5
because the linear nature of the spine precludes simply
adding more channels in this array geometry in a way
that preserves the B1þexcitation efficiency in the C-
spine cord. The two possibilities for an eight-loop array
are 1) preserving the loop size and extending the array
well beyond the C-spine (thus, additional elements have
little excitation efficiency at the C-spine) and 2) decreas-
ing the loop size (thus reducing the B1þefficiency at the
depth of the cord).
The loops are located in a coronal plane below the
subject’s back, as shown in Figure 1D. The dipole ele-
ments are in this same plane, centered on the spine, and
are oriented so that the dipole’s conductor points left–
right in the patient’s coordinate system, as shown in Fig-
ure 1c. The high SAR areas of a loop tends to be under
and just beyond the copper strip, with a low SAR region
under the center of the loop (i.e., directly under a
dipole’s conductors). Since we have four loops stacked,
the high SAR regions are likely to be under neighboring
loops=dipoles. The SAR pattern for a dipole is mainly
under the dipole, providing a chance to cancel the field
of neighboring loops. It should be noted, however, that it
is difficult to generalize this description to a body model
because the SAR is shaped by the geometry of the con-
All elements are assumed to be decoupled in order to
simplify EM simulations. Measurements for coupling
parameters can be found in Supporting Figures S1 and
S2. In practice, the addition of dipole elements could
affect the decoupling performance. Decoupling strategies
that have been previously proposed in the literature (15)
can be utilized to overcome these problems.
In order to apply the dark mode concept, the E-field
maps of the dipoles must be known. For this we rely on
simulations. We note that, for all regions, we will have
the simulated B-field and E-field maps, and if we are
proceeding with the calculation, then we trust that the
simulated and measured values are in good agreement.
However, B1þof the dark dipole is difficult to measure
because it is small. Therefore, we could also use the
simulated B1þmaps in these problem areas. We would
then proceed with a pulse calculation providing the best
spatial excitation fidelity subject to regulatory SAR levels
and the amplifiers peak and average power constraints.
We mapped the B1þof the loop and the dipole in a
uniform phantom using a 7 T MR scanner and validated
our EM simulations. SAR reduction using dark elements
was demonstrated with EM simulations only. For an in-
vivo implementation of the loop–dipole array, additional
safety validation experiments should be performed. For
this purpose, E-field=SAR measurements can be made
locally in phantoms by using E-field probes (16) or tem-
perature measurement techniques.
The dark elements actively reduce the local SAR without
significantly changing the flip angle distribution. Thus, trans-
mit failure of any of these elements may lead to elevated
SAR levels in the patient. In practice, such a failure must be
detected by circuitry that either monitors the reflected power
(thus, detected an alteration in the dipole tuning or match-
ing) or detects the RF level with a loop coil immediately
under the dipole coil. Many pTx systems incorporate auto-
matic shutdown using these sorts of detectors (17). Auto-
matic tuning and matching networks can be used to both
properly set the tune=match and actively detect and correct
any loss in the transmit performance (18). In addition, techni-
ques that broaden the bandwidth of the dipoles can also be
used to reduce to RF-loading sensitivities (19).
In this Note, we demonstrated an extension of the conven-
tional array optimization process in which all of the ele-
ments are designed with transmit efficiency in mind. In
the conventional design process, either SAR concerns are
ignored or efficient spin excitation is equated with efficient
B1þfield generation. Although it is certainly true that elec-
tric fields must accompany oscillating magnetic fields, this
generalization ignores the potential for cancellations of
electric fields at discrete locations—and the fact that B1þ
is only one component out of the three ortho-normal com-
ponents (B1þ, B1?, B1z) necessary to completely specify
the magnetic field vector B1 in three-dimensional space.
Our goal was to show that generalizing the design goals of
transmit arrays to include local SAR and utilizing elements
with a wider range of B-field components can be useful for
lowering SAR. Although only shown only for a specific
case, we hope the lessons learned can be broadly applied
to a range of pTx array designs.
FIG. 5. L curves showing the
fidelity (% RMS error) and peak
10g local SAR for the four loops
alone and the loop þ dipole
array. An axial cut through the
peak SAR hotspot is shown for
each array. The MLS RF shim
was optimized using the internal
method. The addition of dipoles
reduced the peak 10 g SAR by
28% at a given excitation fidelity.
6 Eryaman et al.
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