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Magnetic Resonance Materials in Physics, Biology and Medicine (2023) 36:257–277
https://doi.org/10.1007/s10334-023-01075-1
RESEARCH ARTICLE
Radiofrequency antenna concepts forhuman cardiac MR at14.0T
BilguunNurzed1 · AndreKuehne2 · ChristophStefanAigner3 · SebastianSchmitter3 · ThoralfNiendorf1,2,4 ·
ThomasWilhelmEigentler1,5
Received: 31 October 2022 / Revised: 23 February 2023 / Accepted: 27 February 2023 / Published online: 15 March 2023
© The Author(s) 2023
Abstract
Objective To examine the feasibility of human cardiac MR (CMR) at 14.0T using high-density radiofrequency (RF) dipole
transceiver arrays in conjunction with static and dynamic parallel transmission (pTx).
Materials and methods RF arrays comprised of self-grounded bow-tie (SGBT) antennas, bow-tie (BT) antennas, or fraction-
ated dipole (FD) antennas were used in this simulation study. Static and dynamic pTx were applied to enhance transmission
field (B1+) uniformity and efficiency in the heart of the human voxel model. B1+ distribution and maximum specific absorp-
tion rate averaged over 10g tissue (SAR10g) were examined at 7.0T and 14.0T.
Results At 14.0T static pTx revealed a minimum B1+ROI efficiency of 0.91μT/√kW (SGBT), 0.73μT/√kW (BT), and
0.56μT/√kW (FD) and maximum SAR10g of 4.24W/kg, 1.45W/kg, and 2.04W/kg. Dynamic pTx with 8 kT points indicate
a balance between B1+ROI homogeneity (coefficient of variation < 14%) and efficiency (minimum B1+ROI > 1.11µT/√kW)
at 14.0T with a maximum SAR10g < 5.25 W/kg.
Discussion MRI of the human heart at 14.0T is feasible from an electrodynamic and theoretical standpoint, provided that
multi-channel high-density antennas are arranged accordingly. These findings provide a technical foundation for further
explorations into CMR at 14.0T.
Keywords Electrodynamics· Ultrahigh field MR· Electrical dipole· Parallel transmission· Cardiovascular MRI
Introduction
The progress of ultrahigh field magnetic resonance (UHF-
MR) provides meaningful technologies for advancing bio-
medical and diagnostic magnetic resonance imaging (MRI).
With 7.0T human MRI now widely used in clinical research,
there is increasing interest in exploring even higher magnetic
field strengths [1, 2]. This includes pioneering reports on
MRI technology at 9.4T, 10.5T and 11.7T, and corre-
sponding invivo applications [312]. The MR research and
superconductor science community have already taken even
more ambitious steps towards the future, envisioning human
MR at 14.0T [1316]. Recently, the Dutch National 14Tesla
Initiative in Medical Science (DYNAMIC) received funding
for the implementation of the first 14.0T class human MR
instrument as part of the large-scale research infrastructure
national roadmap of the Netherlands [17]. Joint efforts of the
nuclear magnetic resonance (NMR) and MRI communities
have identified the scientific questions that drive these ambi-
tions, together with the technological challenges and pros-
pects for achieving human MRI at 20.0T [1416, 1821].
Thoralf Niendorf and Thomas Wilhelm Eigentler have an equal
contribution.
* Thoralf Niendorf
thoralf.niendor[email protected]
1 Max-Delbrück-Center forMolecular Medicine
intheHelmholtz Association (MDC), Berlin Ultrahigh Field
Facility (B.U.F.F.), Robert Rössle Strasse 10, 13125Berlin,
Germany
2 MRI.TOOLS GmbH, Berlin, Germany
3 Physikalisch-Technische Bundesanstalt (PTB),
Braunschweig, Berlin, Germany
4 Experimental andClinical Research Center (ECRC),
ajoint cooperation betweentheCharité Medical Faculty
andtheMax-Delbrück-Center forMolecular Medicine
intheHelmholtz Association, Berlin, Germany
5 Chair ofMedical Engineering, Technische Universität Berlin,
Berlin, Germany
258 Magnetic Resonance Materials in Physics, Biology and Medicine (2023) 36:257–277
1 3
These bold steps will require rigorous technical develop-
ments, assessment of physiological constraints, and invivo
evaluation studies that have to be tested and validated by
those who adopt the technology. Recent experience at 7.0T
offers insights into how such efforts can lead to valuable
results [2227].
Advances in body and cardiovascular magnetic resonance
(CMR) imaging at 7.0T offer a perspective into what we
might expect as the technology moves to even higher mag-
neticfield strengths [28, 29]. CMR applications at 7.0T
include imaging and spectroscopy of the heart and large
vessels [30, 31]. The spectrum of applications includes
high spatial resolution imaging of cardiac morphology and
cardiac chamber quantification [32, 33], blood oxygenation
level-dependent, susceptibility or iron imaging of the heart
[3437], non-invasive tissue characterization and phenotyp-
ing [38], analysis of hemodynamics and heart valve planime-
try [39, 40], probing of cardiac energetics [41], computation
of myocardial pH [42], and the assessment of myocardial
tissue ion concentration including sodium and potassium
MRI [4345]. Clinical CMR at UHF strengths is already
conceivable [4650], though practical and technical issues
still need to be resolved before UHF-CMR can move into
routine clinical settings [28].
Studies on UHF-CMR are making progress with novel
radiofrequency (RF) technologies and MR methodologies
to address electrodynamic constraints and transmission field
(B1+) non-uniformities [5153]. This research includes the
implementation of a local transceiver (Tx/Rx) arrays and
multi-channel transmission (Tx) arrays in conjunction with
multi-channel local receive (Rx) arrays. Surface RF transmit
arrays tailored for CMR take advantage of loops [5457],
stripline-configurations [58], stripline waveguide-like ele-
ments, slot-antennas [59], dipoles [60], loop-dipoles [61,
62], and building blocks of bow-tie antenna variants [63,
64]. Dipole antenna configurations have received increased
attention for UHF-CMR. Dipole antennas provide a sym-
metrical B1+ transmission perpendicular to the dipole, which
simplifies the optimization of the resulting B1+ in static pTx
[60]. Their linear current patterns help to improve the signal-
to-noise ratio (SNR) performance en route to ultimate intrin-
sic SNR [65]. Current dipole antenna array configurations
commonly rely on geometric decoupling, which limits the
number of Tx elements placed on the torso [6062].
Multi-channel Tx/Rx RF coil designs tailored for UHF-
CMR involve rigid, flexible and modular configurations.
The development process has shown a trend towards
increasing numbers of transmit and receive elements to
improve anatomical coverage. A higher number of RF ele-
ments is conceptually appealing to increase the degrees
of freedom for B1+ shaping and uniform B1+ distribution
[66]. A higher channel count benefits signal reception and
supports higher acceleration in parallel imaging (PI) [67,
68]. To further highlight Tx array configurations, pioneer-
ing work has demonstrated a path towards body coil con-
cepts suited for MR of the torso at 7.0T [6973].
Moving to even higher magnetic field strengths, 14.0T
class instruments will facilitate sharper spatiotemporal
details of the heart, enable enhanced blood-dependent
and tissue contrast mechanisms, and will allow for better
and faster visualization of substances relevant to cardiac
metabolism.
These opportunities are motivating research into
electrodynamics at UHF and are driving innovations in
RF antenna design tailored for CMR at frequencies of
600MHz. Recognizing this, in the current simulation
study we present RF coil concepts for human CMR at
14.0T, and explore the feasibility of multi-element dipole
antenna-based RF array configurations. In addition, elec-
tromagnetic field (EMF) simulations were conducted in
human voxel models to detail B1+ efficiency (B1+/√1kW)
and distributions, specific absorption rate (SAR), and PI
performance.
Methods
RF antenna building blocks
This simulation study builds on dipole variants established
for CMR at 7.0T and MRI of the torso at 10.5T, includ-
ing self-grounded bow-tie (SGBT) building blocks [63],
bow-tie (BT) building blocks [64] and fractionated dipole
(FD) antennas [6062]. The dimensions of the RF building
blocks were adapted to the 1H resonance frequency at 14.0T
(f = 600MHz) and the corresponding wavelength in tissue
(~ 5–6cm). The SGBT has a size of 24.3 × 48.0 × 89.3 mm3
at 7.0T and 12.2 × 24.0 × 44.7 mm3 at 14.0T. For each SGBT
a parallel capacitor and a serial inductor were used for tuning
and matching. The BT uses a size of 53.0 × 76.0 × 156.0 mm3
at 7.0T and 26.5 × 38.0 × 78.0 mm3 at 14.0T. The tun-
ing and matching circuit consist of a serial and a paral-
lel capacitor. The FD consists of a dipole antenna (7.0T:
304.0 × 10.0 × 1.6 mm3, 14.0T: 152.0 × 5.0 × 0.8 mm3),
where low loss optimized meander elements are modeled
as lumped elements (7.0T: L = 33.5nH, Q = 258.2 at 7.0T,
14.0T: L = 17.9nH, Q = 88.0) between the three segments
of the antenna legs. The inductivity was set to minimize the
imaginary part of the antennas’ impedance and as a trade-
off between superficial SAR and B1+ [60]. For improved
geometric conformity to the upper torso of the human voxel
model, a 160° angled FD configuration was used [61]. The
tuning and matching circuit consists of a parallel inductor
and a serial capacitor, whereas no housing was included for
these antenna configurations.
259Magnetic Resonance Materials in Physics, Biology and Medicine (2023) 36:257–277
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Cardiac RF arrays
Three cardiac RF arrays were examined for each building
block (BB) (Fig.1):
At 7.0T the BBs were arranged so that each RF array
provided ample upper torso coverage (Fig.1). The
BBs were placed with the highest density, resulting in
Sij −8.6dB for human voxel Duke and Sij ≤ −8.3dB
for human voxel model Ella. This setup is referred to as
baseline (BL).
At 14.0T the BBs were assembled into RF arrays with
the number of BBs, the center position of the BBs and
the anatomical coverage identical to the setup used at
7.0T (Fig.1). This setup is referred to as the same chan-
nel count (SCC).
At 14.0T the number of BBs was doubled from the 7.0T
setup (Fig.1). The BBs provided ample upper torso cov-
erage as the 7.0T BL and 14.0T SCC setups. This setup
is referred to as double channel count (DCC).
At 7.0T BL, a 5–6–5 matrix (anterior and posterior sec-
tion) of SGBT was used to form a 32-channel parallel trans-
mission (pTx)/Rx RF array (Fig.1a). No extra space was
added between BBs. A 16-channel pTx/Rx RF array (4 × 2
matrix for the anterior and posterior section) was set up for
the BT (Fig.1b). The nearest-neighbor distance was 10mm.
For the FD, an 8-channel pTx/Rx RF array (4 × 1 matrix for
the anterior and the posterior section) was used together with
a nearest-neighbor distance of 60mm (Fig.1c).
At 14.0T, the SCC setup used the same center posi-
tion for each BB as implemented at 7.0T (Fig.1). The
left–right distance between elements was 24.0mm for the
SGBT-based 32-channel pTx/Rx array, 48.0mm for the
BT based 16-channel pTx/Rx array, and 80.0mm for the
FD based 8-channel pTx/Rx array. For the DCC setup at
14.0T, a 64-channel pTx/Rx SGBT array (7–9–9–7 matrix
for the anterior and the posterior section, no additional space
between BBs) was used. A 32-channel pTx/Rx array (matrix:
5–6–5 for the anterior and the posterior section, nearest
neighbor distance = 10mm) was examined for the BT. A
16-channel pTx/Rx array (8 × 1 matrix for the anterior and
the posterior section, nearest neighbor distance = 25mm)
Fig. 1 Anterior and posterior views of the cardiac RF arrays using
a self-grounded bow-tie antenna building blocks; b bow-tie antenna
building blocks; and c fractionated dipole antennas placed on the
human voxel model Duke. Duke was truncated at the neck and the
hips. For the baseline setups at 7.0 T 32-channel pTx/Rx SGBT,
16-channel pTx/Rx BT, and 8-channel pTx/Rx FD array configura-
tions were used. At 14.0T the building blocks were assembled into
RF arrays with the same numbers, center position and anatomical
coverage as the 7.0 T BL setups. These setups are referred as the
same channel count setups. For the double channel count setups at
14.0T the number of building blocks was increased to 64-channel
pTx/Rx SGBT, 32-channel pTx/Rx BT, and 16-channel pTx/Rx FD
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260 Magnetic Resonance Materials in Physics, Biology and Medicine (2023) 36:257–277
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was investigated for the FD. A dielectric pad consisting of
D2O was placed between the SGBT RF arrays and the sub-
ject to enhance EMF coupling [63]. To conform to the upper
torso, the bend FD [61] RF arrays were used for channels
2 and 3 for the BL and the SCC setup, as well as channels
3–6 for the DCC setup. At 14.0T the FD array was shifted
10mm towards the feet (z-direction) to ensure full heart
coverage (Fig.1).
Electromagnetic field simulations
Numerical EMF simulations of the RF arrays were per-
formed using the finite difference time domain solver
[74] of CST Studio Suite 2020 (CST Studio Suite 2020,
Dassault Systèmes, Vélizy-Villacoublay Cedex, France).
Broadband excitation (bandwidth: Δfex = ± 50.0MHz)
was applied for a center frequency of fex = 297.2MHz and
fex = 600MHz. The human voxel models Duke (body mass
index [BMI] = 23.1kg/m2) and Ella (BMI = 22.7kg/m2) of
the Virtual Family (resolution: 1.0 × 1.0 × 1.0 mm3) were
used [75]. Duke and Ella were truncated at the neck and the
hips and placed at the isocenter of an RF shield model of
the 7.0T and 14.0T MRI bore. For the EMF simulations,
the electrical material parameters of the antennas and the
tissue parameters provided by the IT ‘IS Foundation [76]
were adapted to 297.2MHz and 600MHz conditions.
Co‑simulation
For each magnetic field strength, a co-simulation was per-
formed in Matlab 2019b (Mathworks, Natick, MA) for
channel-wise tuning and matching with a lossy capacitor
and/or a lossy inductor. The estimated losses were evalu-
ated by the equivalent series resistance of the capacitors
based on the datasets of non-magnetic ceramic capacitors
(atc100c, American Technical Ceramics, NY). The losses of
the inductors are considered through the Q-factor according
to the database for non-magnetic air-coil inductors (1512sp,
Coilcraft Inc., Cary, IL). The results of the EMF simula-
tions and the material/tissue properties were used for the
post-processing (Matlab 2019b) to calculate B1+ and maxi-
mum SAR10g distributions at an isotropic resolution of
4.0 × 4.0 × 4.0 mm3.
B1 superposition
To benchmark the RF array performance we evaluated the
optimal transmit and receive efficiency for each voxel indi-
vidually. This metric provides a theoretical electromagnetic
performance limit [77, 78]. Assessing the RF array trans-
mit efficiency (TXE) and intrinsic SNR (iSNR) requires the
B1+ and B1 amplitudes and the power correlation matrix
of each RF channel [77]. The loss terms for the RF arrays
were evaluated using a framework for calculating the power
correlation matrices [79]. The optimal TXE and iSNR are
defined by the ratio of the NMR signal (B1+, B1) to the dis-
sipated RF power of the sample. The problem of finding the
maximum ratio can be treated as a generalized eigenvalue
problem, where the largest eigenvalue corresponds to the
maximum TXE and iSNR [77, 78]. For the intrinsic optimal
magnitude superposition of the B1+ and B1 fields only the
sample losses are considered, and for the realistic superposi-
tion sample, coil and coupling losses are taken into account.
The ratio between intrinsic and realistic B1+ and B1 super-
position is defined as the performance ratio (%). The calcu-
lated TXE and iSNR maps are assessed and compared within
the region of interest (ROI) covering the entire 3D heart.
Field shaping forstatic parallel transmission
The optimization was based on the magnitude of the sum
of the complex B1+ maps in the ROI covering the entire 3D
heart, with a channel-specific normalized complex excita-
tion vector excch (excch/abs(excch)) [80]. Field shaping was
first performed for static pTx to determine an optimal excch
using channel-wise RF phase optimization or channel-wise
RF phase and RF amplitude optimization. The transmission
field-shaping was performed using an unconstrained genetic
algorithm (GA) in combination with an unconstrained mini-
mization(fminunc) implemented in the global optimization
toolbox of Matlab 2019b [81, 82]. The total RF power for the
excitation vectors (Pfwd) obtained from the pTx field shaping
can be calculated following the equation:
where superscript H denotes conjugate transpose, exc the
complex excitation vector for Nch channels, Ich the identity
matrix for Nch channels, with R = 50 and U≈316V if we
consider 2kW at each port without losses. The obtained
B1+ maps of the optimization were scaled to the root mean
square of 1kW as a total incident power PIn (power flow into
ports) which is referred to as B1+ efficiency (B1+ /√1kW).
Minimum B1+ optimization
To avoid signal dropouts the minimum of the superposed
B1+ of the individual channels (Eq.2) across the ROI cov-
ering the entire 3D heart was maximized using the target
function:
(1)
P
fwd =excH(Ich
U
2
R
)
exc
(2)
Maximize
Φtarget
(
excch
)
= min
(||||
Nch
ch=1B+
1ch
excch
||||ROI )
261Magnetic Resonance Materials in Physics, Biology and Medicine (2023) 36:257–277
1 3
with Nch being the number of channels, B1+ch the channel-
wise complex transmission field inside the 3D ROI, and
excch the complex excitation vector for Nch channels.
Coefficient ofvariation optimization
To minimize the coefficient of variation (CoV = standard
deviation/mean) across 3D ROI covering the entire heart,
the following target function was used:
The coefficient of variation indicates the (non)uniformity
of the B1+ distribution.
SAR optimization
A multiobjective optimizer (MOO) is used to perform a
trade-off between two objectives using the GA [82]. The
resulting Pareto-front of the MOO finds a solution in which
one objective is improved and one objective degraded. For
better SAR management at higher static magnetic field
strength, SAR is included as one of the objectives, and mini-
mum B1+ROI as the other objective in the MOO approach.
SAR10g distribution was compressed using virtual observa-
tion points (VOP) [83]. The overestimation factor for the
VOP calculation was iteratively reduced until reaching a
mean overestimation of 15%. The VOP with a mean overes-
timation of 15% was only used in the optimization process.
The number of VOP was at 7.0T < 1493 and at 14.0T with
double the channel count < 23,579.
The target function
Φtotat
=(
Φtarget,ΦSAR)
is given by:
where superscript H denotes conjugate transpose. To maxi-
mize the minimum B1+ROI in this minimization approach
a minus sign was added for the target function. From the
results of the MOO, the non-compressed SAR matrix
was used for each excitation vector of the solution. Based
on the results an excitation vector maximizing (mini-
mum B1+ROI/√SAR10g) was evaluated.
Field shaping withdynamic parallel transmission
Dynamic pTx was performed with tailored kT-points, a
series of RF sub-pulses and gradient blips, with the goal of
3D flip angle (FA) homogenization (CoV(FA)) targeting the
(3)
Minimize
Φtargetexcch=(
SD
Nch
ch=1B+
1ch
excch
ROI
mean
Nch
ch=1B+
1ch
excch
ROI )
(4)
MinimizeΦtotal
(
excch
)
= (−min
(||||
Nch
ch=1B+
1ch
excch
||||
ROI
),
max(excch
H
VOP excch))
whole heart [84]. The pulse design problem [52] was solved
in Matlab 2019b using the small-tip-angle approximation
(STA) for a nominal FA distribution of 10° across the whole
heart with an interleaved greedy + local method [52, 85,
86]. The computation of the solution included a global RF
power regularization but no local SAR constraints. 4 and 8
kT point pTx pulses were optimized with rectangular-shaped
RF sub-pulses and a total pulse duration of τtotal = 0.96ms
(4 × τsub-pulse = 100µs, 4 × τblips 140µs) and τtotal = 1.92ms
(8 × τsub-pulse = 100µs, 8 × τblips 140µs), respectively.
where γ denotes the gyromagnetic ratio, Pfwd the forward
power and k the power scaling factor. The pulse duration of
the kT point pTx pulses was scaled to 1ms for an inserted
power (PIn) of 1kW to compare dynamic and static pTx
approaches. The obtained FA maps (FA = γ B1+ τ) were
scaled into B1+ efficiency maps where the forward power
(Pfwd) of the kT points was scaled to 1ms (
𝜏
total
1ms
) and only the
time of the sub-pulses (
𝜏
subpulse
+
𝜏blip
𝜏
subpulse
)
was considered. The
maximum SAR10g (PIn = 1W) of the kT points was evaluated
from the sum of the SAR10g distribution for each
sub-pulse.
(5)
+
1eff =FA
2𝜋𝛾𝜏subpulse
PIn
Pfwd
=
𝜏total
1ms
𝜏subpulse +𝜏blip
𝜏
Table 1 Simulated maximum reflection (Sii) and coupling (Sij) values
after tuning and matching for the 7.0T baseline (BL), 14.0T same
channel count (SCC), and double channel count (DCC) setups using
self-grounded bow-tie (SGBT) antenna building blocks, bow-tie
(BT) antenna building blocks, and fractionated dipole (FD) antennas
placed on the human voxel models Duke and Ella
Antenna max dB 7.0T BL 14.0T SCC 14.0T DCC
Simulated maximum reflection (Sii) and coupling (Sij) for Duke
SGBT Reflection Sii −27.5 −63.5 −18.9
Coupling Sij −9.4 −20.0 −10.6
BT Reflection Sii −21.2 −44.9 −24.4
Coupling Sij −8.6 −14.5 −9.8
FD Reflection Sii −21.4 −47.2 −25.4
Coupling Sij −15.3 −15.7 −10.3
Simulated maximum reflection (Sii) and coupling (Sij) for Ella
SGBT Reflection Sii −17.7 −23.5 −12.7
Coupling Sij −8.5 −13.7 −10.2
BT Reflection Sii −22.2 −45.2 −25.4
Coupling Sij −8.3 −15.1 −9.7
FD Reflection Sii −29.9 −15.3 −21.1
Coupling Sij −13.0 −14.9 −8.4
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262 Magnetic Resonance Materials in Physics, Biology and Medicine (2023) 36:257–277
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263Magnetic Resonance Materials in Physics, Biology and Medicine (2023) 36:257–277
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Assessment ofnoise amplification (G‑factor)
A post-processing framework was used to assess the parallel
imaging (PI) performance through SENSE geometry (g) fac-
tor maps [67, 68]. The maps were calculated using reduction
factors of R = 2 to R = 4. The phase encoding (PE) direction
was placed along the main left–right (L–R, y-axis) and along
the semi-minor anterior–posterior (A–P, x-axis) direction.
G-factor assessment was performed for 1D SENSE accelera-
tion using field of view (FOV) = 324 × 232mm (matrix size:
81 × 58, voxel size 4.0 × 4.0 × 4.0 mm3) for an axial (x–y)
plane through the center of the heart of the voxel model.
Results
Co‑simulation
The worst-case reflection and coupling for Duke and Ella
after tuning and matching can be found in Table1. The
SGBT tuning and matching network was model specific,
and showed a high deviation between Duke and Ella for
the given setup. For all setups, C values (min.-max.) of
0.2pF–31.7pF (Duke) and 0.2pF–19.0pF (Ella) were
found. The L values (min.-max.) were 2.5nH–20.2nH
(Duke) and 2.5nH–18.4nH (Ella). The BT tuning and
matching network was robust against different models
and showed minor deviation between Duke and Ella. The
serial C values were between 1.8pF–7.7pF (Duke) and
1.9pF–6.6pF (Ella) whereas the parallel C values were
between 2.8pF–14.8pF (Duke) and 3.3pF–14.3pF (Ella).
The FD tuning and matching network was model specific,
with a high deviation between Duke and Ella for a given
setup. L values of (min.–max.) of 12.2nH–61.4nH (Duke)
and 16.8nH–62.0nH (Ella) were found and C values
(min.–max.) of 3.8pF–9.7nF (Duke) and 3.1pF–1.60nF
(Ella) were found.
B1 superposition
The sum of the magnitude of the superposed B1+ (Fig.2)
revealed a lower TXE (realistic) for Duke at 14.0T with
the SCC setups compared to the 7.0T BL setups, where the
BT array showed the largest decrease in the mean value of
−43% and the SGBT showed the smallest decrease in the
mean value of −16%. Increasing the channel count for the
DCC setups at 14.0T revealed in the best-case 113% higher
mean and 130% higher minimum TXE (realistic) for the
BT array, and in the worst-case 26% higher mean and 13%
higher minimum TXE (realistic) for the FD array, compared
to the SCC setups. The DCC setups had the largest standard
deviation of the RF array configurations investigated. The
DCC setups had increased mean TXE for the BT (+ 21%)
and SGBT (+ 19%), relative to the 7.0T BL setups, but
decreased mean TXE for the FD (−5%) as well as decreased
minimum values. The iSNR values for reception are shown
in Fig.2. Similar behavior could be obtained for Ella with
only higher TXE/iSNR for a given setup (data not shown).
Field shaping using static pTx
PTx using an excitation vector with equal phase (0°)
and amplitude (1) for all channels was used as a baseline
(Table2). The baseline pTx provided for Duke a minimum
B1+ROI < 0.05µT/√kW, a CoV < 56% for an ROI covering
the entire heart, and a maximum SAR10g < 0.67W/kg for
all RF arrays at 7.0T (BL) and 14.0T (SCC and DCC)
(Table2). The baseline pTx results for Ella are shown in
Table2.
Minimum B1+ optimization
For Duke, phase and amplitude optimized pTx had higher
minimum B1+ROI > 1.59µT/√kW for the 7.0T BL setups
(Fig.3). At 14.0T, the SCC setups had ~ 72% lower mini-
mum B1+ROI compared to the 7.0T BL setups (Table3).
Increasing the channel count for the DCC setups at 14.0T
resulted in a 46% increased minimum B1+ROI only for the
BT setup, but with a higher SAR level. The SGBT and FD
showed 10–15% lower minimum B1+ROI whereas only the
SGBT showed a lower SAR level. The phase and amplitude
optimized pTx approach resulted in elevated CoV values.
The corresponding results for Ella can be obtained at the
bottom in Table3.
Coefficient ofvariation optimization
For Duke, phase and amplitude optimized pTx showed
at least a two-fold decrease in the CoV for mini-
mized CoV(B1+ROI) (Fig.4) with an elevated minimum
B1+ROI > 0.37µT/√kW for the 7.0T BL setups compared
to the baseline pTx with equal excitation. The 14.0T
SCC setups had a CoV < 35% with a lower minimum
Fig. 2 Axial and sagittal views through the center of the heart ROI
showing realistic ac B1+ (TXE) and df B1 (iSNR) superposition
maps (accounting for sample, coil, and coupling losses). Annotations
highlight the mean ± SD (minimum) TXE and iSNR values and the
mean performance ratio in % over the whole 3D cardiac ROI using
the a, d) self-grounded bow-tie antenna building block; b, e) bow-tie
antenna building block; and c,f) the fractionated dipole antenna RF
arrays at 7.0T (baseline) and 14.0T (same channel count and double
channel count). The cardiac ROI is depicted in red
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264 Magnetic Resonance Materials in Physics, Biology and Medicine (2023) 36:257–277
1 3
B1+ROI < 0.01µT/√kW and a high SAR level < 7.09W/kg
(Table4). The DCC setups demonstrated a further decreased
CoV < 29% with a minimum B1+ROI < 0.02µT/√kW and a
SAR level < 2.71W/kg. The corresponding results for Ella
are shown in Table4.
SAR optimization
Moving towards 14.0T revealed an increased SAR level
which was addressed by the phase and amplitude pTx
optimized MOO approach (Fig.5). For Duke, the 14.0T
SCC setups were capable of 63–85% reduction in maximum
SAR10g with only 6–11% reduction in minimum B1+ROI
(Table5) compared to the static pTx approach with maxi-
mized minimum B1+ROI (Table3, SCC setups). The DCC
setups with increased channel count had 79–88% reduced
maximum SAR10g with only 0–29% reduced minimum
B1+ROI (Table5) compared to the static pTx approach with
maximized minimum B1+ROI (Table3, DCC setups). The
MOO revealed a CoV above 54% at 14.0T for both setups.
The corresponding results for Ella are shown in Table5.
Field shaping using dynamic pTx
Performing dynamic pTx (Fig.6) with 4 kT points for
Duke revealed for the 14.0T SCC setups a worst-case
CoV < 28% with minimum B1+ROI < 0.56µT/√kW, and
maximum SAR10g < 3.26W/kg. The DCC setups with 4
kT points had lower CoV with enhanced minimum B1+ROI
and reduced SAR level (Table6). Increasing to 8 kT points
revealed a worst-case CoV < 20% at 14.0T for the SCC set-
ups, with minimum B1+ROI < 0.59µT/√kW and maximum
SAR10g < 8.15W/kg (Table6). The DCC setups with 8 kT
points had lower CoV with enhanced minimum B1+ROI and
reduced SAR level (Table6). The corresponding results for
Ella are shown in Table6.
Assessment ofnoise amplification (G‑factor)
The assessment of the noise amplification due to PI for Duke
is summarized in Table7, which shows the mean and maxi-
mum g-factors of the RF arrays under investigation. Two-
fold acceleration Ry along the main axis of the RF arrays
(phase encoding along the L-R direction) revealed a maxi-
mum noise amplification of gmax = 1.04 and gmax < 2.79 with
Ry = 4 for all RF arrays at 7.0T BL. At 14.0T, the SCC set-
ups had gmax < 1.29 for two-fold acceleration, and for Ry = 4
a gmax < 3.28 was found. The DCC setup with increased
channel count had reduced gmax < 1.06 for two-fold accel-
eration and Ry = 4 a gmax < 1.60 at 14.0T. The corresponding
noise amplification values along the A-P phase encoding
direction (Rx) are shown in Table7.
Discussion
This work examines the electromagnetic challenges of CMR
at 14.0T, and provides RF coil concepts that address the
electrodynamic constraints of imaging the human heart
at 14.0T based on EMF simulations. Our numerical find-
ings indicate that CMR at 14.0T is feasible with realistic
RF antenna systems, and provides a foundation for further
exploration and real-world implementation. This simulation
Table 2 Summary of the mean B1+, minimum B1+, coefficient of var-
iation (CoV(B1+ROI)) across the entire 3D heart of the human voxel
models Duke and Ella, and the maximum SAR10g for an excitation
vector with equal phase (0°) and amplitude (1V) for all channels
using self-grounded bow-tie (SGBT) antenna building block, bow-tie
(BT) antenna building block, and fractionated dipole (FD) antenna
RF arrays at 7.0T (baseline, BL) and 14.0T (same channel count,
SCC, double channel count, DCC). The total RF power for the exci-
tation vectors (Pfwd) is presented for a lossless 2kW power at each
channel
Excitation with equal phase (0°) and amplitude (1)
mean
B1+ROI
[µT/√kW]
min.
B1+ROI
[µT/√kW]
max.
SAR10g
[W/kg]
CoV
[%] Pfwd [kW]
Duke
7.0T BL
SGBT 5.21 0.02 0.30 45 64
BT 3.40 0.03 0.23 44 32
FD 5.05 0.01 0.25 39 16
14.0T
SCC
SGBT 3.37 0.05 0.62 52 64
BT 1.96 0.01 0.67 55 32
FD 3.38 0.04 0.57 48 16
14.0T
DCC
SGBT 4.58 0.03 0.45 56 128
BT 2.80 0.03 0.25 46 64
FD 2.51 0.03 0.41 48 32
Ella
7.0T BL
SGBT 5.41 0.06 0.29 39 64
BT 4.31 0.04 0.19 41 32
FD 6.17 0.06 0.28 39 16
14.0T
SCC
SGBT 3.70 0.01 1.08 51 64
BT 2.44 0.02 0.50 44 32
FD 3.51 0.02 0.40 41 16
14.0T
DCC
SGBT 4.85 0.03 0.49 52 128
BT 3.21 0.04 0.22 39 64
FD 2.79 0.03 0.27 42 32
265Magnetic Resonance Materials in Physics, Biology and Medicine (2023) 36:257–277
1 3
study presents results derived from the human voxel models
Duke and Ella. The larger upper torso and cardiac ROI of
Duke as compared to the female human voxel model Ella
makes the male model more challenging for CMR, with
lower B1+ efficiency and homogeneity. Here we focus on the
male voxel model Duke, given the more challenging appli-
cation and for the reason that both voxel models showed
similar behavior at 14.0T CMR. Furthermore, the anten-
nas were designed for 7.0T MR application and are not
optimized antenna designs for 14.0T CMR. For simplicity
the antenna dimensions were scaled linearly to the magnetic
field strength, resulting in undesired losses in the antenna.
However, it has been shown that electrodynamic scaling is
a feasible approach for investigating RF behavior at varying
static magnetic field strengths [87]. Furthermore, losses in
the signal chain, or resulting from cardiac motion were not
considered in this study.
From the co-simulation sufficient tuning and match-
ing were obtained with neglectable losses. The SGBT and
FD arrays revealed a model-specific tuning and matching
Fig. 3 Axial and sagittal views through the center of the heart show-
ing B1+ efficiency maps (B1+/√1kW) obtained for static pTx phase
and amplitude shimming using the a self-grounded bow-tie antenna
building block; b bow-tie antenna building block; and c the fraction-
ated dipole antenna RF array configurations at 7.0T (baseline, BL)
and 14.0T (same channel count, SCC, double channel count, DCC).
The cardiac ROI is depicted in red. The superposed minimum B1+
of all channels within the whole 3D cardiac ROI was maximized in
the optimization process. The spider diagrams illustrate the relative
changes of the mean B1+ROI, minimum B1+ROI, maximum SAR10g,
CoV(B1+ROI), TXE, and intrinsic SNR values for the 14.0 T SCC
(orange) and DCC (grey) with respect to the 7.0T baseline (black)
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266 Magnetic Resonance Materials in Physics, Biology and Medicine (2023) 36:257–277
1 3
network, whereas the BT array showed a robust network
against different body models. Such a model-specific tuning
and matching network would indeed make a real-life appli-
cation more challenging, and a trade-off between the tuning
and matching network of the different body types would be
necessary and would result in higher worst-case reflection
and coupling. This would lead to increased losses.
The shortened antennas of the SCC setups resulted
in a narrower FOV of the antenna. The narrow FOV and
the larger distance between the BBs at 14.0T caused
less interference of the individual EMFs. Along with the
higher losses at 14.0T, this resulted in a lower TXE and
iSNR compared to the 7.0T BL setups. The wavelength
and antenna shortening at 14.0T improved the antenna
density per unit area, allowing for twice the number of
BBs for the DCC setups. The enhanced channel density of
the DCC setup is beneficial to offset the reduction of B1+
and B1 superposition. The enhanced density of the DCC
setups and the closer-positioned antennas allowed better
control of the EMFs. The intrinsic B1+ and B1 superpo-
sition yielded higher mean TXE and iSNR for the DCC
setups (14.0T) compared to the SCC setups (14.0T) and
the 7.0T baseline setups. This is because the higher chan-
nel count enabled a greater degree of freedom. However,
a TXE and iSNR gradient between the periphery and the
center of the body was obtained. For the latter, minimum
TXE and iSNR remained below the minimum obtained for
the 7.0T BL setups. This behavior was already reported
at lower field strength [88] and remains a major constraint
and challenge of CMR. At 14.0T the performance ratio
of the three RF array concepts showed an increase of < 8%
losses in the antenna and coupling compared to the 7.0T
baseline setups. This difference suggests that the electro-
dynamic scaling of the antennas is feasible, with only a
minor impact on the transmit/receive performance. The
SGBT array at 14.0T had values almost twice as high
for TXE and iSNR compared to the BT (high losses) and
compared to the FD (4 × lower channel count). To achieve
the enhanced TXE and iSNR values, the SGBT array with
enhanced channel count will require more total RF power.
This is also reflected in the total RF power obtained from
the static and dynamic pTx optimization.
Enlarging the number of BBs is conceptually appealing to
increase the degrees of freedom for B1+ shaping and uniform
B1+ distribution, as seen for the optimal B1 superposition.
At 7.0T, phase-optimized pTx provided sufficient perfor-
mance to reduce B1+ efficiency (Eq.2) and inhomogeneity
(Eq.3) across the whole 3D heart. At 14.0T phase opti-
mized pTx targeting the whole 3D heart showed limitations,
while phase and amplitude optimized pTx showed promising
results with maximized minimum B1+ROI < 1.01µT/√kW
(Duke) for the SGBT SCC setup, which was approximately
twice the minimum B1+ROI of the BT and FD RF arrays. The
higher minimum B1+ROI of the SGBT array is reflected on
the B1+ superposition. The higher minimum B1+ROI of the
SGBT comes with an elevated SAR level (7.01W/kg), which
resulted in the lowest SAR efficiency (mean B1+/√SAR) of
the three concepts, while the FD showed the highest SAR
efficiency. The increased channel count of the DCC setups
resulted in greater B1+ efficiency and reduced maximum
Table 3 Summary of the mean B1+, minimum B1+, coefficient of var-
iation (CoV(B1+ROI)) across the entire 3D heart of the human voxel
models Duke and Ella, and the maximum SAR10g for a phase and
amplitude pTx approach with optimized minimum B1+ in the ROI
using self-grounded bow-tie (SGBT) antenna building block, bow-tie
(BT) antenna building block, and fractionated dipole (FD) antenna
RF arrays at 7.0T (baseline, BL) and 14.0T (same channel count,
SCC, double channel count, DCC). The total RF power for the exci-
tation vectors (Pfwd) is presented for a lossless 2kW power at each
channel
Minimum B1+ optimization
mean
B1+ROI
[µT/√kW]
min.
B1+ROI
[µT/√kW]
max.
SAR10g
[W/kg]
CoV
[%] Pfwd [kW]
Duke
7.0T BL
SGBT 6.82 3.32 0.71 41 16
BT 3.50 1.59 0.23 36 14
FD 7.44 2.81 0.57 42 5
14.0T
SCC
SGBT 5.37 1.01 7.01 90 3
BT 2.25 0.50 0.62 66 5
FD 4.61 0.66 1.44 62 5
14.0T
DCC
SGBT 5.01 0.91 4.24 90 8
BT 3.85 0.73 1.45 70 5
FD 5.05 0.56 2.04 78 4
Ella
7.0T BL
SGBT 7.50 4.59 0.67 34 13
BT 4.48 2.31 0.17 31 8
FD 8.81 4.55 0.63 37 5
14.0T
SCC
SGBT 6.71 1.43 5.73 89 3
BT 2.26 0.63 0.65 44 5
FD 5.41 0.96 2.44 74 2
14.0T
DCC
SGBT 6.49 1.64 3.61 74 8
BT 4.45 1.30 1.05 65 7
FD 5.41 1.00 1.44 71 4
267Magnetic Resonance Materials in Physics, Biology and Medicine (2023) 36:257–277
1 3
SAR10g, with optimized minimum B1+ROI compared to the
SCC setups, resulting in greater SAR efficiency (< + 20%).
The higher SAR efficiency yielded less RF input power con-
sumption to achieve an equivalent FA while staying within
the safety limits [89].
To more closely examine RF power deposition with
respect to safety requirements [89], we included the objec-
tive of SAR10g in our optimizations. MOO offers options for
a trade-off between the objective of minimum B1+ROI and
the objective of maximum SAR10g. Phase-optimized pTx
showed limited performance with respect to an optimized
SAR efficiency (< −3%). Phase and amplitude-optimized
pTx MOO enabled a decreased SAR level (< −88%) with
only a minor reduction in minimum B1+ROI (< −29%),
resulting in enhanced SAR efficiency (< + 117%), which
underlines the value of the MOO approach at 14.0T. The
results for Ella showed similar behavior with only higher B1+
efficiency values for the static pTx approach.
The static pTx approach provided limited performance
at 14.0T where no signal dropouts were obtained, but the
Fig. 4 Axial and sagittal views through the center of the heart show-
ing B1+ efficiency maps (B1+/√1kW) obtained for static pTx phase
and amplitude shimming using the a self-grounded bow-tie antenna
building block; b bow-tie antenna building block; and c the fraction-
ated dipole antenna RF array configurations at 7.0T (baseline, BL)
and 14.0T (same channel count, SCC, double channel count, DCC).
The cardiac ROI is depicted in red. The CoV (B1+) within the whole
3D cardiac ROI was minimized in the optimization process. The spi-
der diagrams illustrate the relative changes of the mean B1+ROI, mini-
mum B1+ROI, maximum SAR10g, CoV(B1+ROI), TXE, and intrinsic
SNR values for the 14.0T SCC (orange) and DCC (grey) with respect
to the 7.0T baseline (black)
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268 Magnetic Resonance Materials in Physics, Biology and Medicine (2023) 36:257–277
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269Magnetic Resonance Materials in Physics, Biology and Medicine (2023) 36:257–277
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challenges of transmission inhomogeneity could not be fully
addressed. Approaching this obstacle, we performed the
CoV optimization (Eq.3) but the results were not promis-
ing. Including Eq.3 as one of the objectives in the MOO
yielded insufficient results where the DCC setups had
CoV > 29% with a SAR level < 0.63W/kg and a minimum
B1+ROI < 0.27µT/√kW. To tackle these challenges, the
dynamic pTx using kT-points was performed. The scaled B1+
maps with dynamic pTx revealed a more uniform B1+ distri-
bution compared to the static pTx approach with optimized
CoV. However, the improved CoV was associated with
reduced B1+ efficiency. Increasing the number of sub-RF-
pulses showed an improved CoV, but with a more enhanced
SAR level which is a major safety concern. Increasing the
channel count for the DCC setups could address this obsta-
cle with lower CoV as well as lower SAR level compared
to the SCC setups. Dynamic pTx with 8 kT points in con-
junction with the increased channel density of the DCC set-
ups showed the best results for the SGBT RF array, with
improved CoV (10%) compared to the static pTx (26%) at
14.0T, while achieving a minimum B1+ROI = 1.79µT/√kW
and a maximum SAR10g < 3.18W/kg. The higher degrees
of freedom of the dynamic pTx approach will require more
total RF power than the static pTx approach. These results
obtained from the dynamic pTx using the DCC setups at
14.0T are competitive when benchmarked against previous
reports on CMR at 3.0T and 7.0T. For CMR at 3.0T a CoV
of 31% was reported for cardiac ROI covering the whole
heart [88, 90, 91]. Dynamic pTx at 7.0T using 4 kT points
yielded a CoV of ~ 10% [52].
Our assessment of the parallel imaging performance of
CMR at 7.0T and 14.0T confirmed previous reports that
showed reduced noise amplification at higher magnetic field
strengths for an elliptic cylinder or a sphere, using magnetic
field strengths up to 11.5T [67]. Parallel acquisition of the
upper torso and the use of higher magnetic field strengths
are synergistic because with the wavelength shortening PI
becomes more effective in large objects. This advantage
facilitates higher acceleration factors for CMR at 14.0T
compared to 7.0T. This PI gain would benefit CMR in the
presence of physiological motion, and further real-time
imaging of the heart. By doubling the Rx channel count,
the DCC setups at 14.0T led to a reduction in the mean and
maximum g-factors compared to the SCC configurations
and the 7.0T baseline setups. The DCC setup of the SGBT
Table 4 Summary of the mean B1+, minimum B1+, coefficient of
variation (CoV(B1+ROI)) across the entire heart of the human voxel
models Duke and Ella, and the maximum SAR10g for a phase and
amplitude pTx approach with optimized CoV(B1+) in the ROI using
self-grounded bow-tie (SGBT) antenna building block, bow-tie (BT)
antenna building block, and fractionated dipole (FD) antenna RF
arrays at 7.0T (baseline, BL) and 14.0T (same channel count, SCC,
double channel count, DCC). The total RF power for the excitation
vectors (Pfwd) is presented for a lossless 2kW power at each channel
CoV optimization
mean
B1+ROI
[µT/√kW]
min.
B1+ROI
[µT/√kW]
max.
SAR10g
[W/kg]
CoV
[%] Pfwd [kW]
Duke
7.0T BL
SGBT 1.64 0.88 1.65 10 9
BT 0.96 0.37 0.30 18 6
FD 2.48 1.17 1.45 20 3
14.0T
SCC
SGBT 0.92 0.01 7.09 25 6
BT 0.41 0.00 0.62 32 6
FD 1.32 0.01 1.76 35 5
14.0T
DCC
SGBT 0.85 0.02 2.71 26 11
BT 0.49 0.01 0.58 27 7
FD 0.65 0.00 2.03 29 5
Ella
7.0T BL
SGBT 1.89 1.01 3.09 14 5
BT 1.71 0.88 0.64 15 5
FD 3.27 1.63 1.19 16 4
14.0T
SCC
SGBT 1.34 0.05 2.45 21 13
BT 0.59 0.03 1.45 27 7
FD 1.51 0.07 2.95 28 3
14.0T
DCC
SGBT 1.10 0.10 2.50 22 16
BT 1.27 0.01 0.61 24 19
FD 1.24 0.03 1.36 24 8
Fig. 5 ac Pareto front derived from the static phase and amplitude
optimized pTx MOO approach using the a self-grounded bow-tie
antenna building block; b bow-tie antenna building block; and c the
fractionated dipole antenna RF array configurations at 7.0T (base-
line, BL) and 14.0 T (same channel count, SCC, double channel
count, DCC). Each point of the solution represents one optimized
excitation vector where a trade-off between the minimum B1+ROI and
the maximum SAR10g was found. The green circles indicate the high-
est minimum B1+ROI/√SAR10g ratio. df Axial and sagittal views
through the center of the heart (depicted in red) illustrating B1+ effi-
ciency maps (B1+/√1kW) obtained for the excitation vectors with
the highest minimum B1+ROI/√SAR10g ratio (indicated by the green
circles in a-c). The spider diagrams illustrate the relative changes of
the mean B1+ROI, minimum B1+ROI, maximum SAR10g, CoV(B1+ROI),
TXE, and intrinsic SNR values for the 14.0T SCC (orange) and DCC
(grey) with respect to the 7.0T baseline (black)
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270 Magnetic Resonance Materials in Physics, Biology and Medicine (2023) 36:257–277
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271Magnetic Resonance Materials in Physics, Biology and Medicine (2023) 36:257–277
1 3
RF array showed the best PI performance. The improved PI
performance at higher magnetic field strengths can be fur-
ther enhanced by increasing the channel count, as previously
demonstrated for accelerated cardiac MRI at 3.0T [92, 93].
Our results indicate that a multi-transmit system beyond
the current state-of-the-art 8 or 16 Tx channels will be
essential for CMR at 14.0T. The literature shows that pTx
systems with > 16 Tx channels are very feasible [71, 94].
Increasing the Tx channel count would further improve B1+
efficiency, homogeneity, and SAR efficiency. The limiting
factors for enhanced channel density are the dimensions of
the Tx elements, as well as the coupling because the ana-
tomical coverage is limited on the upper torso. The low cou-
pling and compact size of the SGBT BB allowed up to 64
elements (14.0T) on the upper torso in the current study.
To summarize, of the three RF array configurations
investigated, the SGBT array had the highest TXE and
iSNR. The superior performance of the SGBT RF array
configuration is due to the greater channel count per unit
area compared to the BT (2x) and FD (4x) RF arrays, as
well as the improved coupling of the EMF afforded by the
dielectric pad. The higher channel count will require more
total RF power in order the achieve the results presented.
Nevertheless, the higher B1+ efficiency comes with an
increased SAR level which might constitute an RF power
deposition concern. This constraint of the SGBT array con-
figuration was addressed by including SAR in the MOO.
Using this approach, the SAR level obtained for phase and
amplitude optimized pTx strategy of the SGBT was reduced
by a factor of ~ 5.5 (0.77W/kg versus 4.24 W/kg) while a
minimum B1+ROI of 0.73µT/√kW (before 0.91µT/√kW)
was achieved. The dynamic pTx approach using kT points
showed promising results where a uniform B1+ distribution
could be achieved with increased kT points. This will also
require more total RF power compared to the static pTx
approach. The merits of the SGBT array configuration are
not limited to the transmission side, but also yield enhanced
coil sensitivity for reception versus the BT and the FD array
configurations [95]. The 14.0T DCC setup and the SGBT
RF array were synergistic, and showed the best parallel
imaging performance of the three RF coil configurations
investigated.
Conclusions
While the number of reports on experimental and clinical
research for cardiac and body UHF-MR at 7.0T continues to
grow, the first steps into the exploration of even higher mag-
netic field strengths are already being taken. While novel
magnet technology will surely support MR at B0 > 11.7T in
the future, its use for cardiac MRI might be constrained by
technical challenges, physiological limitations, and practical
Table 5 Summary of the mean B1+, minimum B1+, coefficient of var-
iation (CoV(B1+ROI)) across the entire heart of the human voxel mod-
els Duke and Ella, and the maximum SAR10g for the multiobjective
phase and amplitude optimizer, with a trade-off between minimum
B1+ in the heart and maximum SAR10g using self-grounded bow-tie
(SGBT) antenna building block, bow-tie (BT) antenna building block,
and fractionated dipole (FD) antenna RF arrays at 7.0T (baseline,
BL) and 14.0T (same channel count, SCC, double channel count,
DCC). The total RF power for the excitation vectors (Pfwd) is pre-
sented for a lossless 2kW power at each channel
Multiobjective optimization
mean
B1+ROI
[µT/√kW]
min.
B1+ROI
[µT/√kW]
max.
SAR10g
[W/kg]
CoV
[%] Pfwd [kW]
Duke
7.0T BL
SGBT 6.76 2.84 0.36 38 21
BT 2.53 1.16 0.04 32 8
FD 6.18 2.76 0.28 33 9
14.0T
SCC
SGBT 4.32 0.91 1.02 55 21
BT 1.80 0.47 0.23 54 13
FD 4.39 0.59 0.52 56 8
14.0T
DCC
SGBT 4.63 0.73 0.77 57 27
BT 2.54 0.52 0.17 55 13
FD 3.86 0.56 0.43 59 8
Ella
7.0T BL
SGBT 6.96 4.29 0.28 26 20
BT 3.80 1.95 0.10 28 8
FD 7.34 3.88 0.24 27 8
14.0T
SCC
SGBT 5.60 1.44 1.85 65 8
BT 2.38 0.48 0.21 41 7
FD 4.82 0.98 0.53 54 6
14.0T
DCC
SGBT 5.71 1.51 0.81 58 20
BT 3.04 0.94 0.22 48 11
FD 3.79 0.88 0.39 59 8
Fig. 6 Axial and sagittal views through the center of the heart
(depicted in red) showing the B1+ efficiency maps (B1+/√1 kW)
using the a self-grounded bow-tie antenna building block; b bow-tie
antenna building block; and c) the fractionated dipole antenna RF
array configurations at 7.0T (baseline, BL) and 14.0T (same chan-
nel count, SCC, double channel count, DCC). Dynamic pTx was per-
formed with tailored kT-points, using a series of RF sub-pulses and
gradient blips to achieve a homogeneous flip angle (FA) within the
3D ROI targeting the heart. For the optimization, a nominal FA of
10° was targeted in the heart ROI by using 4 and 8 kT-points, with
a total pulse duration of 0.96ms and 1.92ms, respectively. The FA
maps of the pulse design were scaled into B1+ efficiency maps
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272 Magnetic Resonance Materials in Physics, Biology and Medicine (2023) 36:257–277
1 3
Table 6 Summary of the mean B1+, minimum B1+, coefficient of var-
iation (CoV(B1+ROI)) across the entire heart of the human voxel mod-
els Duke and Ella, and the maximum SAR10g for 4 and 8 kT point
pTx pulses using self-grounded bow-tie (SGBT) antenna building
block, bow-tie (BT) antenna building block, and fractionated dipole
(FD) antenna RF arrays at 7.0T (baseline, BL) and 14.0T (same
channel count, SCC, double channel count, DCC). The total RF
power for the excitation vectors (Pfwd) is presented for a lossless 2kW
power at each channel
Dynamic pTx using kT points on Duke
mean B1+ROI [µT/√kW] min. B1+ROI
[µT/√kW] max. SAR10g [W/kg] CoV
[%] Pfwd [kW]
4 kT points
7.0T BL
SGBT 6.10 4.66 1.36 6 11
BT 3.75 2.39 0.95 11 27
FD 5.56 3.85 0.85 7 13
14.0T SCC
SGBT 3.67 1.44 3.18 14 28
BT 2.03 0.56 3.26 28 66
FD 3.53 0.66 2.80 21 28
14.0T DCC
SGBT 3.76 1.80 1.69 13 52
BT 3.13 0.93 2.71 17 36
FD 3.41 0.63 1.33 22 30
8kT points
7.0T BL
SGBT 5.52 4.47 2.77 5 14
BT 3.59 2.53 1.90 8 31
FD 4.96 3.95 1.90 5 17
14.0T SCC
SGBT 3.27 1.51 6.07 10 36
BT 1.73 0.59 8.15 20 105
FD 3.00 1.17 5.13 15 42
14.0T DCC
SGBT 3.40 1.79 3.18 10 95
BT 2.81 1.23 5.25 12 48
FD 2.90 1.11 2.86 14 45
Dynamic pTx using kT points on Ella
mean B1+ROI [µT/√kW] min. B1+ROI
[µT/√kW] max. SAR10g [W/kg] CoV
[%] Pfwd [kW]
4 kT points
7.0T BL
SGBT 7.30 5.71 1.19 6 8
BT 4.89 3.74 0.73 7 17
FD 7.57 5.85 0.91 9 7
14.0T SCC
SGBT 4.50 2.60 5.94 11 19
BT 2.65 1.04 2.65 23 44
FD 4.00 1.59 2.25 16 23
14.0T DCC
SGBT 4.03 2.18 2.00 11 23
BT 3.94 1.86 2.17 12 24
FD 4.29 1.57 1.69 20 20
8kT points
7.0T BL
273Magnetic Resonance Materials in Physics, Biology and Medicine (2023) 36:257–277
1 3
obstacles. These include the need for a better understanding
of electrodynamic constraints that arise through increased
spin excitation frequency. Power losses due to frequency-
dependent changes in the conductive properties of tissues
will occur, and several legitimate challenges concerning RF
power deposition restrictions, B1+ efficiency constraints,
depth penetration limitations, and radiation losses will need
to be resolved. These challenges notwithstanding, this study
indicates that an MRI of the human heart at 14.0T is feasible
from an electrodynamic and theoretical standpoint. These
findings open the door to further research that might catalyze
a next-generation 14.0T human MR system. Such systems
will undoubtedly unveil new dimensions of the processes of
cardiac health and disease.
Supplementary Information The online version contains supplemen-
tary material available at https:// doi. or g/ 10. 1007/ s10334- 023- 01075-1.
Acknowledgements This project has received funding in part (BN,
TWE, TN,) from the European Research Council (ERC) under the
European Union's Horizon 2020 research and innovation program
under grant agreement No 743077 (ThermalMR). The authors wish
to thank Mostafa Berangi (MRI.TOOLS GmbH, Berlin, Germany)
for fruitful discussions on the B1+ maps scaling of the FA maps and
Jason Millward (Max Delbrueck Center for Molecular Medicine in the
Table 6 (continued)
Dynamic pTx using kT points on Ella
mean B1+ROI [µT/√kW] min. B1+ROI
[µT/√kW] max. SAR10g [W/kg] CoV
[%] Pfwd [kW]
SGBT 6.89 5.75 2.59 4 9
BT 4.46 3.55 1.53 5 20
FD 6.30 5.13 1.88 4 11
14.0T SCC
SGBT 4.12 2.79 9.87 8 24
BT 2.40 1.02 4.45 16 61
FD 3.73 2.01 3.89 12 28
14.0T DCC
SGBT 4.18 2.77 4.40 8 23
BT 3.66 2.05 4.24 10 29
FD 3.76 1.39 3.27 17 27
Table 7 The (a) mean and
(b) maximum g-factors of the
self-grounded bow-tie (SGBT)
antenna building block, bow-tie
(BT) antenna building block,
and the fractionated dipole (FD)
antenna RF array configurations
at 7.0T (baseline, BL) and
14.0T (same channel count,
SCC, double channel count
DCC) in the cardiac ROI
of Duke for SENSE image
reduction for R = 2–4. The
g-factors are given in the
anterior–posterior (Rx) and
left–right (Ry) phase encoding
direction
The DCC setups at 14.0T are indicated with +
Noise amplification
SGBT BT FD
(a) mean 7.0T 14.0T 14.0 T+7.0T 14.0T 14.0 T+7.0T 14.0T 14.0 T+
Ry = 2 1.00 1.00 1.00 1.00 1.02 1.00 1.00 1.00 1.00
Ry = 3 1.02 1.02 1.00 1.06 1.10 1.01 1.02 1.04 1.00
Ry = 4 1.09 1.02 1.02 1.26 1.23 1.06 1.06 1.06 1.02
Rx = 2 1.02 1.01 1.01 1.05 1.02 1.03 1.04 1.04 1.02
Rx = 3 1.26 1.11 1.11 1.85 1.27 1.30 1.53 1.47 1.18
Rx = 4 1.49 1.25 1.27 2.61 1.54 1.65 1.91 1.81 1.35
(b) max 7.0T 14.0T 14.0 T+7.0T 14.0T 14.0 T+7.0T 14.0T 14.0 T+
Ry = 2 1.04 1.05 1.01 1.04 1.29 1.06 1.04 1.09 1.01
Ry = 3 1.21 1.49 1.06 1.39 2.44 1.18 1.15 1.36 1.14
Ry = 4 1.67 1.31 1.11 2.39 3.28 1.60 2.79 2.90 1.39
Rx = 2 1.16 1.17 1.13 1.46 1.59 1.43 1.30 1.66 1.24
Rx = 3 1.87 1.57 1.92 4.22 3.77 2.41 7.99 4.08 1.70
Rx = 4 2.64 2.26 2.58 7.94 4.83 3.70 15.41 5.97 2.19
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274 Magnetic Resonance Materials in Physics, Biology and Medicine (2023) 36:257–277
1 3
Helmholtz Association, Berlin, Germany) for editing and proofreading
the manuscript.
Funding Open Access funding enabled and organized by Projekt
DEAL.
Data availability The antenna models and the cardiac RF arrays on the
human voxel models from CST Studio Suite 2020 can be downloaded
fromhttps:// github. com/ bnurz ed/ Dipole- RF- Arrays- for- cardi ac- MRI-.
The code for the kT point pulse design can be downloaded from https://
github. com/ chaig ner/ UP_ body.
Declarations
Conflict of interest Thoralf Niendorf is founder and CEO of MRI.
TOOLS GmbH, Berlin, Germany. Andre Kuehne is an employee of
MRI.TOOLS GmbH, Berlin, Germany.
Ethical standards Furthermore, this study did not involve human par-
ticipants, their data, or biological material.
Open Access This article is licensed under a Creative Commons Attri-
bution 4.0 International License, which permits use, sharing, adapta-
tion, distribution and reproduction in any medium or format, as long
as you give appropriate credit to the original author(s) and the source,
provide a link to the Creative Commons licence, and indicate if changes
were made. The images or other third party material in this article are
included in the article's Creative Commons licence, unless indicated
otherwise in a credit line to the material. If material is not included in
the article's Creative Commons licence and your intended use is not
permitted by statutory regulation or exceeds the permitted use, you will
need to obtain permission directly from the copyright holder. To view a
copy of this licence, visit http:// creat iveco mmons. org/ licen ses/ by/4. 0/.
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