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Fast calculation software for modified Look-Locker inversion recovery (MOLLI) T1 mapping


Abstract and Figures

Background The purpose of this study was to develop a software tool and evaluate different T1 map calculation methods in terms of computation time in cardiac magnetic resonance imaging. Methods The modified Look-Locker inversion recovery (MOLLI) sequence was used to acquire multiple inversion time (TI) images for pre- and post-contrast T1 mapping. The T1 map calculation involved pixel-wise curve fitting based on the T1 relaxation model. A variety of methods were evaluated using data from 30 subjects for computational efficiency: MRmap, python Levenberg–Marquardt (LM), python reduced-dimension (RD) non-linear least square, C++ single- and multi-core LM, and C++ single- and multi-core RD. Results Median (interquartile range) computation time was 126 s (98–141) for the publicly available software MRmap, 261 s (249–282) for python LM, 77 s (74–80) for python RD, 3.4 s (3.1–3.6) for C++ multi-core LM, and 1.9 s (1.9–2.0) for C++ multi-core RD. The fastest C++ multi-core RD and the publicly available MRmap showed good agreement of myocardial T1 values, resulting in 95% Bland–Altman limits of agreement of (− 0.83 to 0.58 ms) and (− 6.57 to 7.36 ms) with mean differences of − 0.13 ms and 0.39 ms, for the pre- and post-contrast, respectively. Conclusion The C++ multi-core RD was the fastest method on a regular eight-core personal computer for pre- or post-contrast T1 map calculation. The presented software tool (fT1fit) facilitated rapid T1 map and extracellular volume fraction map calculations.
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Kimetal. BMC Med Imaging (2021) 21:26
Fast calculation software formodied
Look-Locker inversion recovery (MOLLI) T1
Yoon‑Chul Kim1, Khu Rai Kim2, Hyelee Lee3 and Yeon Hyeon Choe4*
Background: The purpose of this study was to develop a software tool and evaluate different T1 map calculation
methods in terms of computation time in cardiac magnetic resonance imaging.
Methods: The modified Look‑Locker inversion recovery (MOLLI) sequence was used to acquire multiple inversion
time (TI) images for pre‑ and post‑contrast T1 mapping. The T1 map calculation involved pixel‑wise curve fitting based
on the T1 relaxation model. A variety of methods were evaluated using data from 30 subjects for computational
efficiency: MRmap, python Levenberg–Marquardt (LM), python reduced‑dimension (RD) non‑linear least square, C++
single‑ and multi‑core LM, and C++ single‑ and multi‑core RD.
Results: Median (interquartile range) computation time was 126 s (98–141) for the publicly available software
MRmap, 261 s (249–282) for python LM, 77 s (74–80) for python RD, 3.4 s (3.1–3.6) for C++ multi‑core LM, and 1.9 s
(1.9–2.0) for C++ multi‑core RD. The fastest C++ multi‑core RD and the publicly available MRmap showed good
agreement of myocardial T1 values, resulting in 95% Bland–Altman limits of agreement of ( 0.83 to 0.58 ms) and
( 6.57 to 7.36 ms) with mean differences of 0.13 ms and 0.39 ms, for the pre‑ and post‑contrast, respectively.
Conclusion: The C++ multi‑core RD was the fastest method on a regular eight‑core personal computer for pre‑ or
post‑contrast T1 map calculation. The presented software tool (fT1fit) facilitated rapid T1 map and extracellular vol‑
ume fraction map calculations.
Keywords: MRI, Heart, T1 mapping, Parameter estimation
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Cardiac T1 mapping in magnetic resonance imaging
(MRI) is a non-invasive and quantitative method for the
characterization of the myocardial tissue [14] and is
particularly useful for the evaluation of diffuse myocar-
dial fibrosis [5]. It typically involves two separate image
acquisitions: native T1 mapping (a.k.a. pre-contrast T1
mapping) and post-contrast T1 mapping. Extracellular
volume fraction (ECV), which is a biomarker for myo-
cardial fibrosis, can be attained in a pixel-wise manner
from the pre- and post-contrast T1 maps [6, 7]. Due to
its quantitative nature, cardiac T1 mapping is advanta-
geous over late gadolinium enhanced imaging, in which
the accurate nulling of the healthy myocardial signals in
an inversion recovery sequence is challenging in patients
with diffuse myocardial fibrosis. e pattern of diffuse
myocardial fibrosis is typically observed in patients with
non-ischemic heart disease, such as hypertrophic cardio-
myopathy (HCM), cardiac amyloidosis, and dilated car-
diomyopathy [5].
Open Access
4 Department of Radiology and HVSI Imaging Center, Heart Vascular
Stroke Institute, Samsung Medical Center, Sungkyunkwan University
School of Medicine, 81 Ilwon‑ro, Gangnam‑gu, Seoul 06351, South Korea
Full list of author information is available at the end of the article
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Kimetal. BMC Med Imaging (2021) 21:26
T1 map calculation involves curve fitting for the quan-
tification of T1 longitudinal relaxation time on a pixel-
wise basis. e curve fitting process is time-consuming in
general, and low-level programming languages such as C
and C++ are desirable for improved computational effi-
ciency. T1 parameters are estimated via non-linear least
squares, and Levenberg–Marquardt (LM) optimization
is typically utilized with good initial values of the param-
eters in the T1 fitting model. Alternatively, to overcome
the issue of initialization of the parameters and to reduce
the search space, Barral etal. presented a reduced dimen-
sion non-linear least squares (RD-NLS) approach, which
resulted in initialization-free optimization and accelera-
tion in T1 map calculation [8]. In other studies, T1 map
calculation was reported to take longer than a minute per
image [9, 10]. Recent related studies of software develop-
ment in parameter mapping focused on magnetization
transfer imaging [11] and neuroimage processing [12],
and they lack the comparison of computational efficiency
among different calculation methods.
e existence of a variety of methods for T1 map calcu-
lation motivated us to develop a software tool for evalu-
ating the performance of the methods. In particular, we
sought to develop a Python-based user interface that
can also test a C++ implementation with pybind11 [13].
e interface setup facilitates the comparison between
Python-based and C++-based methods. Moreover, the
Python language serves as a framework for deep learn-
ing libraries [1416] and is commonly adopted for the
development of deep learning algorithms, which may
have potential for improving the performance in cardiac
T1 mapping [17]. In an earlier study, we demonstrated
fast T1 map calculation using the LM-based method
implemented in C++, as a module for a comprehensive
quantitative cardiac MRI analysis tool [18]. In the present
study, we focus on evaluating the performance of differ-
ent T1 map calculation methods with an emphasis on the
comparison between the LM method and the RD-NLS
method implemented in C++ as well as an emphasis on
the comparison between the RD-NLS method and the
publicly available MRmap for T1 estimation accuracy in
the myocardium.
We describe the T1 mapping sequence parameters, T1
map calculation methods, and their implementations
and evaluations. Figure 1 shows a custom user inter-
face tool for the study, which is available at https ://sites
.googl kim1/softw are/t1_map_compa re.
Fig. 1 A screenshot of the user interface for the calculation of pre‑ and post‑T1 maps as well as an ECV map. The interface allows a user to select a
T1 map calculation method for the comparison of computation time and accuracy. It also provides ECV map calculation as well as T1 fitting result in
a user interactive way
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Kimetal. BMC Med Imaging (2021) 21:26
Source code is available at https ://githu 52/
fT1fi t.
Data acquisition
Cardiac MRI scans were performed on a 1.5 T scan-
ner (Siemens Avanto, Erlangen, Germany). Clinical MR
examinations were approved by our institutional review
board, and informed consent was obtained from the sub-
jects prior to MRI scans. Subjects with suspected car-
diovascular diseases were enrolled between May 2014
and May 2015. Subjects who took cardiac pre- and post-
contrast T1 mapping scan exams were included for the
present study. Subjects with inadequate image quality
due to severe motion were excluded. A total of 30 sub-
jects were considered for our study. ey consisted of 9
HCM patients, 10 cardiac amyloidosis patients, 7 coro-
nary artery disease patients, and 4 healthy volunteers.
e modified Look-Locker inversion recovery
(MOLLI) sequence was used for cardiac T1 map-
ping [19, 20]. Imaging parameters were slice thick-
ness = 8 mm, echo time (TE) = 1.01 ms, spacing
between slices = 20 mm, the number of phase encod-
ing steps = 104, pixel bandwidth = 1085 Hz, acquisi-
tion matrix = 192 × 120, image matrix = 384 × 288, pixel
spacing = 0.9375 mm × 0.9375 mm, and field of view
(FOV) = 360mm × 270mm. e MOLLI protocols used
were different for the pre-contrast and post-contrast
T1 mapping. e MOLLI 5(3)3 protocol used for pre-
contrast T1 mapping consisted of 5 inversion time (TI)
image acquisitions after the first inversion pulse, a three-
heartbeat pause for the recovery of the longitudinal mag-
netization, and 3 TI image acquisitions after the second
inversion pulse. e MOLLI 4(1)3(1)2 protocol used for
post-contrast T1 mapping consisted of 4 TI image acqui-
sitions after the first inversion pulse, a one-heartbeat
pause, 3 TI image acquisitions after the second inversion,
a one-heartbeat pause, and 2 TI image acquisitions after
the third inversion. Since the post-contrast T1 relaxation
time is approximately less than 500ms, which is much
shorter than the pre-contrast T1 (~ 950ms for myocar-
dium and ~ 1500 ms for blood), the 3 inversion pulses
used in the 4(1)3(1)2 protocol enables more adequate
sampling of the early part of T1 relaxation than the 2
inversion pulses used in the 5(3)3 protocol. Instead of 5
images after the first inversion, 4 images were acquired
in the post-contrast T1 mapping because for the short
T1 (< 500ms) relaxation the image from the fifth heart-
beat appears similar to the image from the fourth heart
beat due to fast T1 recovery and thus is unnecessary [21].
e TI images were acquired in a diastolic cardiac phase.
All of the TI images were aligned using the motion cor-
rection algorithm [22]. e TI images were exported
as digital imaging and communications in medicine
(DICOM) files for T1 map calculation.
T1 Map calculation
T1 map calculation was performed pixel-by-pixel. In
general, the TI images can be available as either complex-
valued or magnitude-valued. In the present study, the
DICOM dataset was available as magnitude TI images,
and most cardiac MRI scanner systems in hospitals save
the DICOM dataset in the magnitude scale by default. At
each voxel’s location (x, y), the signal intensity
can be
modeled as the following T1 relaxation curve.
For a set of inversion times t = [
TI 1
TI 2
, …,
] and a set
of corresponding signals [
S(TI 1),S(TI 2),...,S(TI N)
there are N equations and 3 unknowns, which are
, b,
and c. In the present study, N was 8 for the pre-contrast
data, while N was 9 for the post-contrast data. Notably, b
is the reciprocal of T1* (i.e., the apparent T1). e objec-
tive function
to be minimized was then given as the
sum of squares of the difference between the relaxation
model and the data.
is is a nonlinear least squares problem, and the Lev-
enberg–Marquardt (LM) algorithm [23] can be used to
iteratively estimate the parameters
, b, and c. We empiri-
cally selected the initial values for the parameter set (
b, c) = (350, 0.001, 150) for the pre-contrast data and
(350, 0.005, 150) for the post-contrast data. Since our
dataset was in the magnitude scale and
of Eq.(1) can
cover the negative-value range, we incrementally flipped
the polarity of
S(TI i)
to find the best fit of Eq.(1) [24].
Notably, the estimated T1* does not incorporate the
effect of the tip down of the spin magnetization for every
repetition time. Hence, the Look-Locker correction was
applied in the following way to arrive at the corrected T1
Meanwhile, the RD-NLS (or RD) method expands the
objective function Eq.(2) and finds the optimal estimates
of the parameters separately (refer to Appendix B in Bar-
ral etal. [8] for detailed mathematical derivations). e
function to be optimized for T1 is independent of the
other two parameters. Hence, the decoupling leads to a
one-dimensional search problem for T1 estimation.
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Kimetal. BMC Med Imaging (2021) 21:26
Python andC++ implementation
For the LM method, we implemented the T1 map
calculation in Python. To solve the non-linear least
squares problem, we used the scipy.optimize.curve_fit()
function, which is based on the Levenberg–Marquardt
algorithm. e method is referred to as LM_python.
For the RD method, we converted the original MAT-
LAB script written by Barral et al. (code available at
http://www-mrsrl .stanf al/t1map .html)
to Python. We noted that the original RD algorithm
failed to work in some cases where the two candidate
TIs produced unsatisfactory fitting results. Hence, we
modified the RD algorithm by introducing three candi-
date TIs. is helped remove the unsatisfactory fitting
and improved the accuracy (Fig. 2). e method is
referred to as RD_python.
We also implemented both the LM- and RD-based
T1 map calculations in C++ and used pybind11 [13]
to make the compiled C++ code compatible with the
Python environment. e C++ implementation was
performed on a Windows OS, Microsoft Visual Studio
2017 platform. For the LM-based T1 parameter estima-
tion, we used the solve_least_squares_lm function of the
Dlib library [25]. In addition, for the multi-core imple-
mentation, we used the OpenMP library [26] for the
parallelization of the ‘for’ loop in the pixel-wise T1 map
calculation. We chose the static schedule option for par-
allelization. For evaluation, the methods are referred to
Fig. 2 An example of improved fitting result after modification of the original RD‑NLS method. The unsatisfactory performance of the original
RD‑NLS occurred when some inversion time (TI) values were very close such that the choice of minimal TI closest to 0 can be sensitive to noise.
a A poor fitting result when the RD‑NLS method was applied without any modification of the script. b A correction after the modification, which
considered three candidate samples for polarity restorations (see arrows)
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Kimetal. BMC Med Imaging (2021) 21:26
as LM_C++_single-core, RD_C++_single-core, LM_
C++_multi-core, and RD_C++_multi-core.
To ensure that the curve fitting is correctly performed
at each pixel location and the samples are placed close to
the T1 relaxation curve, we developed a graphical user
interface (GUI) that enables a user to load the DICOM
TI image data, select a method for T1 map calculation,
and mouse-click a pixel location for displaying its curve
fitting result. e GUI also performs the calculation and
display of the pre- and post-contrast T1 maps as well as
the ECV map (Fig.1). e GUI was implemented using
the PyQT library [27] on a 64-bit Windows PC.
We evaluated the following methods in terms of speed
on a Windows PC (AMD Ryzen 7 1800X Eight-Core Pro-
cessor and 16.0 GB RAM): MRmap, LM_python, RD_
python, LM_C++_single-core, RD_C++_single-core,
LM_C++_multi-core, and RD_C++_multi-core.
For the evaluation, we used the MRmap software
[9], which is publicly available for download at https ://
sourc eforg cts/mrmap /. We chose the follow-
ing options for T1 map calculation: Limits of T1, T2,
and Noise for pre-contrast were set to 3000, 350, and 0,
respectively. Limits of T1, T2, and Noise for post-con-
trast were set to 1500, 350, and 0, respectively. Specifi-
cally, the setting of the Noise value had to be consistent,
since the choice of the value significantly affected the
computation speed. Registration was set to None. Pro-
cess was set to “T1 mapping—MOLLI,” and Correction
was set to “Look-Locker.
For the evaluation of accuracy in T1 value, we manu-
ally drew a region of interest (ROI) in the myocardium
in either a pre- or a post-contrast T1 map of each subject
and used the same ROI mask for the T1 maps estimated
using MRmap and the RD_C++_multi-core method.
Mean T1 values were calculated within the myocardial
ROIs. Bland–Altman analysis was performed by com-
puting the mean difference and 95% limits of agreement
between the two T1 measurements.
Table 1 lists the computation time for MRmap,
LM_python, RD_python, LM_C++_single-core,
RD_C++_single-core, LM_C++_multi-core, and RD_
C++_multi-core for pre- and post-contrast TI image
sets in 30 subjects. e RD method was superior to the
LM method in computation time for all three different
ways of implementation: python, single-core C++, and
multi-core C++. e RD_C++_multi-core method
took approximately 2s for T1 map generation in both
pre- and post-contrast T1 maps. ere were statistically
significant differences in computation time between
RD_C++_multi-core and LM_C++_multi-core: 1.9s
vs. 3.4s (p < 0.001) for pre-contrast and 2.1s vs. 3.3s
(p < 0.001) for post-contrast. e distributions of com-
putation time clearly exhibit the superior performance
of RD_C++_multi-core (Fig.3).
Qualitative comparisons of the methods in pre-
and post-contrast T1 measurements are shown in an
HCM patient (Fig. 4), and all the methods produced
similar T1 measurements in the myocardium and
blood regions of interest. ese similarities were also
observed in other subjects’ T1 map data. Curve fit-
ting examples for the pre-contrast and post-contrast
MOLLI protocols are shown for the blood and myocar-
dium in a normal volunteer (Fig.5). In particular, the
post-contrast MOLLI 4(1)3(1)2 protocol, which uses
three inversion pulses, is advantageous in estimating a
short T1 value by fitting three samples in early TIs, over
the pre-contrast MOLLI 5(3)3 protocol, which uses two
inversion pulses.
T1 measurements in the myocardium for the four
methods (i.e., LM_python, RD_python, LM_C++, RD_
C++) are shown in Fig.6 for the pre-contrast (top row)
and post-contrast (bottom row) cases. e Bland–Alt-
man plots show good agreement between each of the
four methods and the reference MRmap in all subjects
except for a few outliers. Most of the T1 difference val-
ues lie within 2ms. Table2 shows Bland–Altman sta-
tistics for the four methods. For all the methods, the
absolute mean difference was small (< 1ms) for the pre-
and post-contrast cases. e 95% limit of agreement
was wider for the post-contrast than for the pre-con-
trast, but this is likely due to the outlier whose differ-
ence value was approximately 18ms (see the plots in
the bottom row of Fig.6). As expected, the amyloidosis
group (AMYL) shows high pre-contrast T1 values in
the myocardium (see the plots in the top row of Fig.6).
Table 1 Comparison of computation time in the pre-
and post-contrast T1 map calculations (n = 30).
The measurements in the columns indicate median
(interquartile range) expressed inseconds
* Eight cores were simultaneously used for the calculation
Method Pre-contrast Post-contrast
MRmap 126.0 (98.3–140.6) 111.8 (93.7–140.6)
LM_python 261.3 (249.3–282.4) 249.6 (242.6–262.1)
RD_python 77.0 (74.0–80.1) 77.8 (75.9–81.4)
LM_C++_single‑core 28.6 (27.3–29.8) 28.0 (26.9–29.9)
RD_C++_single‑core 15.2 (15.0–15.9) 16.2 (16.1–16.8)
LM_C++_multi‑core* 3.4 (3.1–3.6) 3.3 (3.0–3.5)
RD_C++_multi‑core* 1.9 (1.9–2.0) 2.1 (2.0–2.2)
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Kimetal. BMC Med Imaging (2021) 21:26
We demonstrated a rapid T1 map calculation method,
which only took approximately 2s for 384 × 288 × 8 or
384 × 288 × 9 images on a personal desktop computer
equipped with an eight-core processor. is is a signifi-
cant improvement over other methods demonstrated in
the literature. For comparison, we measured computa-
tion time on MRmap, which was 126s in pre-contrast
and 112 s in post-contrast. In the literature, MRmap
was reported to take 113 s for a set of 128 × 128 × 8
images with a noise level of 0 [9]. e MRmap code was
written in Interactive Data Language (IDL), which is a
high-level language so that it is computationally slow.
Other software tools also deserve to be mentioned. e
T1 map calculation of Altabella etal. was reported to
take 66s for the magnitude fitting on 31,080 fitted vox-
els from a set of 218 × 256 × 8 images [10]. e T1 map
calculation of Liu et al., referred to as the vectorized
Levenberg–Marquardt fitting, was reported to take
60s on average in MATLAB for a set of 256 × 256 × 8
images. It is undeniable that the C++ nature of the
proposed method was the main cause of the speed
improvement. However, it is important to note that
the way of implementation via the Python wrapper
Fig. 3 Comparison of computation time. RD_C++_multi‑core took shorter computation time than LM_C++_multi‑core in both pre‑ and
post‑contrast cases. The outliers (i.e., the lowest value in all four methods) took the shortest computation time due to the smallest image
dimensions (256 × 218), while most of the images are of the dimensions (384 × 288)
Fig. 4 Qualitative comparison of T1 mapping accuracy in a subject with hypertrophic cardiomyopathy. a Pre‑contrast T1 maps. b Post‑contrast T1
maps. All the methods resulted in similar T1 measurements in the myocardium and blood
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Kimetal. BMC Med Imaging (2021) 21:26
facilitated code readability and maintenance. It is
noted that a C++ implementation for T1 mapping was
recently demonstrated by Werys etal. [28], although we
did not compare their method with our methods.
ere may be room for improvement in computa-
tional speed in the proposed method. First, the noise
level (or the threshold level) can be applied to the
images as was demonstrated in [9, 10]. By increasing
the threshold up to an acceptable level, one can exclude
a fairly large number of pixels whose intensity is not
sufficiently high (e.g., the background air region) from
the curve fitting process, and this could help reduce
the computation time. Second, loop scheduling can be
optimized when using the OpenMP library. In general,
OpenMP provides three kinds of scheduling: static,
dynamic, and guided. ere may be an opportunity
for speed improvement by, for example, trying these
scheduling methods with different choices of chunk
size in dynamic mode and finding the optimal one.
Python provides a convenient environment for devel-
opers in terms of code readability and thus facilitates the
debugging process. is was especially true in the design
of a T1 map calculation algorithm and a graphical user
interface in the present study. We first implemented a
Python version of the T1 map calculation and translated
it to a C++ version. For the verification of the C++
implementation in terms of accuracy, we compared the
T1 maps generated by the Python implementation and
the C++ method within the graphical user interface.
is was helpful in evaluating the accuracy of the C++
In this study, different MOLLI sequence protocols
were used in the acquisitions of pre-contrast and post-
contrast T1 data: MOLLI 5(3)3 for the pre-contrast and
MOLLI 4(1)3(1)2 for the post-contrast. ere are other
Fig. 5 Curve fitting examples when the RD_C++_multi‑core method was used. (Top row) curve fits of the samples acquired using the
pre‑contrast MOLLI 5(3)3 protocol. (Bottom row) curve fits of the samples acquired using the post‑contrast MOLLI 4(1)3(1)2 protocol. The left
plots represent curve fitting on a voxel corresponding to the left ventricular blood pool, while the right plots represent curve fitting on a voxel
corresponding to the myocardium. The solid blue line denotes the estimated T1 relaxation curve after fitting. Note that the nulling time typically
ranges 200–400 ms for the post‑contrast, and acquiring three samples instead of two in early TIs in post MOLLI is helpful in estimating short T1
values, which are typical in post‑contrast tissue
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Kimetal. BMC Med Imaging (2021) 21:26
MOLLI sequence variants reported in the literature
(Table2 of Kellman and Hansen[20]). Intra-individual
comparisons among the MOLLI sampling schemes may
be worth investigating because the curve fitting on dif-
ferent sampling schemes may affect the T1 map results
as well as the ECV map results. However, implementing
the intra-individual comparisons would be challenging
due to patient discomfort as a result of repeated use of
contrast agent and repeated breath-holds.
e rapid computation framework based on pybind11
and multicore C++ has the potential to be applied
to three-dimensional (3D) T1 mapping [29], which
has larger dimensions than 2D T1 mapping, as well
as to other pixel-wise parameter estimation of T2,
T2*, tissue perfusion, and permeability. For example,
deconvolution process in model-based tissue perfusion
quantification [30] can be accelerated using C++ and
parallel processors.
e current study has several limitations. First,
this was a single-center study conducted using data
acquired on the Siemens 1.5T scanner, with a small
number of subjects (n = 30) for evaluation. Second, the
tool supported only the magnitude data rather than
both magnitude and complex-valued data. ird, the
computation time was assessed on a single desktop
computer only. Evaluation on other types of computers
(e.g., mobile phone with a restricted capacity for cen-
tral processing unit (CPU) and memory, workstation
computer with a higher capacity for CPU and memory)
would be worth investigating.
Fig. 6 Bland–Altman plots for the four T1 calculation methods when compared with MRmap as reference. (Top row) pre‑contrast T1 measurements
in the myocardium. (Bottom row) post‑contrast T1 measurements in the myocardium. From left to right, (1) LM_python, (2) RD_python, (3) LM_
C++_multi‑core, and (4) RD_C++_multi‑core
Table 2 Bland–Altman statistics forthemyocardial T1 measurements withMRmap asthereference method
* T1 measurements between multi-core and single-core were the same
Pre-contrast Post-contrast
Mean Dierence, ms 95% Limits ofAgreement, ms Mean Dierence, ms 95% Limits
LM_python 0.24 5.11 to 4.63 0.72 5.81 to 7.25
RD_python 0.13 0.83 to 0.58 0.60 5.95 to 7.14
LM_C++_multi‑core* 0.04 1.34 to 1.25 0.63 5.96 to 7.22
RD_C++_multi‑core* 0.13 0.83 to 0.58 0.39 6.57 to 7.36
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Kimetal. BMC Med Imaging (2021) 21:26
We evaluated the performance of the RD-NLS in terms
of speed and accuracy compared with that of the LM
method. e RD-NLS implemented with C++ and paral-
lel processing library was the fastest, taking < 3s in both
pre- and post-contrast T1 map calculation on a regular
desktop computer. e Python wrapper has the potential
to improve workflow in the implementation of rapid pix-
elwise parametric mapping, not merely of T1 estimation
but also of tissue perfusion- and permeability-related
parameter estimation. e implementation details avail-
able as open source may be helpful resources for other
researchers’ investigations and validation of new meth-
ods in parameter mapping.
MRI: Magnetic resonance imaging; ECV: Extracellular volume fraction; LM:
Levenberg–Marquardt; RD‑NLS: Reduced dimension non‑linear least squares;
MOLLI: Modified Look‑Locker inversion recovery; TE: Echo time; FOV: Field of
view; TI: Inversion time; DICOM: Digital imaging and communications in medi‑
cine; GUI: Graphical user interface; ROI: Region of interest; HCM: Hypertrophic
cardiomyopathy; AMYL: Amyloidosis; CAD: Coronary artery disease; VOL:
Healthy volunteer; CPU: Central processing unit.
Not applicable.
Author contributions
YK, KRK, HL implemented the methods. YK analyzed the results of the meth‑
ods. YK was a main contributor in writing the manuscript. YHC designed the
study and drafted the manuscript. All authors have read and approved the
This work was supported by the National Research Foundation of Korea (grant
number 2018R1D1A1B07042692) and the DongKook Life Science. Co., Ltd.,
Republic of Korea. The funding sources had no role in the study design, data
collection, and data analysis or in the writing of the manuscript.
Availability of data and materials
Data in the present study are not publicly available since they include private
patient information. The de‑identified data are available from the correspond‑
ing author upon request after the approval of the institutional review board
of Samsung Medical Center. The code is available at https ://githu
52/fT1fi t.
Ethics approval and consent to participate
This study was approved by the institutional review board at Samsung Medi‑
cal Center, and the requirement for informed consent for the use of patient
data was waived.
Consent for publication
Not applicable.
Competing interests
The authors declare that they have no competing interests.
Author details
1 Clinical Research Institute, Samsung Medical Center, Sungkyunkwan Univer‑
sity School of Medicine, Seoul, South Korea. 2 Department of Electronic Engi‑
neering, Sogang University, Seoul, South Korea. 3 Department of Mathematics,
Sogang University, Seoul, South Korea. 4 Department of Radiology and HVSI
Imaging Center, Heart Vascular Stroke Institute, Samsung Medical Center,
Sungkyunkwan University School of Medicine, 81 Ilwon‑ro, Gangnam‑gu,
Seoul 06351, South Korea.
Received: 14 July 2020 Accepted: 2 February 2021
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Full-text available
T1-mapping has proven to be a valuable tool in cardiac imaging. While mainly used in cardiac MRI, it is investigated for usage and application of T1-mapping to imaging of other organs and systems, including abdominal imaging, musculoskeletal imaging or neuroradiology, resulting in potential new prospects for medical imaging. T1-mapping provides numerical data on an inherent, physical property of imaged tissue – enabling quantitative and comparative assessment of tissue characterization f.ex. fibrosis, amyloid contents, fatty transformation, myelinization or contrast enhancement as well as lesion characterization. Reports of application of T1-mapping in assessment of liver, kidney or pancreas fibrosis create perspectives of reducing the number of invasive diagnostic procedures, such as biopsies, as well as monitoring treatment response or disease progression. Furthermore T1-mapping can potentially replace MR elastography in assessment of liver fibrosis or used in thyroid fibrosis to define degree of destruction in AIT or other thyroid diseases. In neuroradiology T1-mapping is promising in the spine imaging, enabling better characterization of spinal cord lesions also has a potential to evaluate effectiveness of conservative or operative treatment. There are also successful reports of employing T1-mapping in orbital imaging, such as in predicting steroid resistant diplopia in Graves’ disease or in evaluation of diabetic cataracts. In musculoskeletal imaging, T1-relaxation could be a possible biomarker of bone quality that could play a role in osteoporotic fracture risk assessment. In conclusion, T1-mapping shows promise as a quantitative method complementary to standard MR imaging beyond cardiac MRI, and needs further research and validation efforts to establish its place in standard diagnostic protocols.
We demonstrate the measurement of the transverse spin relaxation rate of Xe without the influence of the Rb polarization-induced magnetic field gradient. The optical pumping beam and probe beam turn on and off repeatedly during the measurement to reduce the relaxation originating from the Rb polarization-induced magnetic field gradient. During the absence of the optical pumping beam, the nuclear spin of the noble gas atom does not experience the alkali-polarization-induced magnetic field gradient so that the transverse spin relaxation rate (1/T2) decreases. When the duty cycle reaches zero, the measured transverse relaxation time T2 approaches the longitudinal spin relaxation time T1. Our method helps in roughly estimating the longitudinal spin relaxation time with a single measurement of the free induction decay.
Full-text available
TOMATO (Total Mapping Toolbox) is a C++ library for the calculation of parametric maps in cardiac magnetic resonance imaging (MRI). As an open source project, TOMATO allows transparent and standardised cardiac longitudinal relaxation time (T1) mapping in clinical applications. With C++ implementation, TOMATO can easily interface and translate between research software environments and commercial vendors’ closed-source C++ environments on scanners as well as post-processing software. To complement the core library implementation, a ready-to-use command line tool has been provided.
Full-text available
While an enormous number of studies have documented pathological alterations of the myocardial native longitudinal relaxation time (T1) and the fraction of the extracellular myocardial volume (ECV), it has also become clear that continuously evolving T1 mapping sequence, acquisition and evaluation techniques have a substantial impact on quantitative results, making the translation of reported findings into routine clinical use particularly challenging. To provide a basis for the discussion of pathological myocardial T1 and ECV alterations, the present review aims to summarize the methodological aspects of myocardial T1 mapping along with technical and physiological factors influencing results and normal ranges of myocardial native T1 and ECV reported across studies.
Full-text available
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Mapping of the longitudinal relaxation time (T1) and extracellular volume (ECV) offers a means of identifying pathological changes in myocardial tissue, including diffuse changes that may be invisible to existing T1-weighted methods. This technique has recently shown strong clinical utility for pathologies such as Anderson- Fabry disease and amyloidosis and has generated clinical interest as a possible means of detecting small changes in diffuse fibrosis; however, scatter in T1 and ECV estimates offers challenges for detecting these changes, and bias limits comparisons between sites and vendors. There are several technical and physiological pitfalls that influence the accuracy (bias) and precision (repeatability) of T1 and ECV mapping methods. The goal of this review is to describe the most significant of these, and detail current solutions, in order to aid scientists and clinicians to maximise the utility of T1 mapping in their clinical or research setting. A detailed summary of technical and physiological factors, issues relating to contrast agents, and specific disease-related issues is provided, along with some considerations on the future directions of the field.
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Cardiovascular Magnetic Resonance is increasingly used to differentiate the aetiology of cardiomyopathies. Late Gadolinium Enhancement (LGE) is the reference standard for non-invasive imaging of myocardial scar and focal fibrosis and is valuable in the differential diagnosis of ischaemic versus non-ischaemic cardiomyopathy. Diffuse fibrosis may go undetected on LGE imaging. Tissue characterisation with parametric mapping methods has the potential to detect and quantify both focal and diffuse alterations in myocardial structure not assessable by LGE. Native and post-contrast T1 mapping in particular has shown promise as a novel biomarker to support diagnostic, therapeutic and prognostic decision making in ischaemic and non-ischaemic cardiomyopathies as well as in patients with acute chest pain syndromes. Furthermore, changes in the myocardium over time may be assessed longitudinally with this non-invasive tissue characterisation method.
Quantitative mapping of Magnetic Resonance (MR) tissue parameters such as the spin-lattice relaxation time (T1), the spin-spin relaxation time (T2), and the spin-lattice relaxation in the rotating frame (T1ρ), referred to as MR relaxometry in general, has demonstrated improved assessment in a wide range of clinical applications. Compared to conventional contrast-weighted (e.g., T1-, T2-, or T1ρ-weighted) MRI, MR relaxometry provides increased sensitivity to pathologies and delivers important information that can be more specific to tissue composition and microenvironment. The rise of deep learning in the past several years has been revolutionizing many aspects of MRI research, including image reconstruction, image analysis, and disease diagnosis and prognosis. Although deep learning has also shown great potential for MR relaxometry and quantitative MRI in general, this research direction is much less explored to date. The goal of this paper is to discuss the applications of deep learning for rapid MR relaxometry and to review emerging deep learning-based techniques that can be applied to improve MR relaxometry in terms of imaging speed, image quality, and quantification robustness. The paper is comprised of four parts. The first part describes a summary of the imaging models of quantitative MR relaxometry. In the second part, we review existing “classical” methods for accelerating MR relaxometry, including state-of-the-art spatiotemporal acceleration techniques, model-based reconstruction methods, and efficient parameter generation approaches. The third part then presents how deep learning can be used to improve MR relaxometry and how it is linked to conventional techniques. The final part concludes the review by discussing the promises and existing challenges of deep learning for rapid MR relaxometry and potential solutions to address these challenges.
Quantitative evaluation of diseased myocardium in cardiac magnetic resonance imaging (MRI) plays an important role in the diagnosis and prognosis of cardiovascular disease. The development of a user interface with state-of-the-art techniques would be beneficial for the efficient post-processing and analysis of cardiac images. The aim of this study was to develop a custom user interface tool for the quantitative evaluation of the short-axis left ventricle (LV) and myocardium. Modules for cine, perfusion, late gadolinium enhancement (LGE), and T1 mapping data analyses were developed in Python, and a module for three-dimensional (3D) visualization was implemented using PyQtGraph library. The U-net segmentation and manual contour correction in the user interface were effective in generating reference myocardial segmentation masks, which helped obtain labeled data for deep learning model training. The proposed U-net segmentation resulted in a mean Dice score of 0.87 (±0.02) in cine diastolic myocardial segmentation. The LV mass measurement of the proposed method showed good agreement with that of manual segmentation (intraclass correlation coefficient = 0.97, mean difference and 95% Bland-Altman limits of agreement = 4.4 ± 12.2 g). C++ implementation of voxel-wise T1 mapping and its binding via pybind11 led to a significant computational gain in calculating the T1 maps. The 3D visualization enabled fast user interactions in rotating and zooming-in/out of the 3D myocardium and scar transmurality. The custom tool has the potential to provide a fast and comprehensive analysis of the LV and myocardium from multi-parametric MRI data in clinical settings.
Numerical Optimization presents a comprehensive and up-to-date description of the most effective methods in continuous optimization. It responds to the growing interest in optimization in engineering, science, and business by focusing on the methods that are best suited to practical problems. For this new edition the book has been thoroughly updated throughout. There are new chapters on nonlinear interior methods and derivative-free methods for optimization, both of which are used widely in practice and the focus of much current research. Because of the emphasis on practical methods, as well as the extensive illustrations and exercises, the book is accessible to a wide audience. It can be used as a graduate text in engineering, operations research, mathematics, computer science, and business. It also serves as a handbook for researchers and practitioners in the field. The authors have strived to produce a text that is pleasant to read, informative, and rigorous - one that reveals both the beautiful nature of the discipline and its practical side.
Purpose: Cardiac magnetic resonance (CMR) is a useful non-invasive tool for characterizing tissues and detecting myocardial fibrosis and edema. Estimation of extracellular volume fraction (ECV) using T1 sequences is emerging as an accurate biomarker in cardiac diseases associated with diffuse fibrosis. In this study, automatic software for T1 and ECV map generation consisting of an executable file was developed and validated using phantom and human data. Methods: T1 mapping was performed in phantoms and 30 subjects (22 patients and 8 healthy subjects) on a 1.5T MR scanner using the modified Look-Locker inversion-recovery (MOLLI) sequence prototype before and 15 min after contrast agent administration. T1 maps were generated using a Fast Nonlinear Least Squares algorithm. Myocardial ECV maps were generated using both pre- and post-contrast T1 image registration and automatic extraction of blood relaxation rates. Results: Using our software, pre- and post-contrast T1 maps were obtained in phantoms and healthy subjects resulting in a robust and reliable quantification as compared to reference software. Coregistration of pre- and post-contrast images improved the quality of ECV maps. Mean ECV value in healthy subjects was 24.5%±2.5%. Conclusions: This study demonstrated that it is possible to obtain accurate T1 maps and informative ECV maps using our software. Pixel-wise ECV maps obtained with this automatic software made it possible to visualize and evaluate the extent and severity of ECV alterations.