Supplement 1:
THEORY
The golden angle radial acquisitions for Look-Locker based T1 mapping [1; 2] guarantee
optimal profile distribution and offer high flexibility in temporal resolution and profile selection
[3]. The principle of golden angle Look-Locker based T1 mapping and the contrast enhancing kspace filter [4] is schematically illustrated in Figure 1. After an inversion pulse radial profiles are
acquired in a golden angle order during the complete T1 relaxation time of the magnetization
(Figure 1A). As already mentioned the golden angle profile order allows us to choose any
number of profiles at any given time point during the T1 relaxation and always obtain a nearly
uniformly filled k-space. In order to produce the desired contrast at a specific moment all
acquired profiles may be used for image reconstruction, however, the undesired low frequency
contrast content of time distant profiles has to be filtered out. In this way we can freely choose
the number of images (i.e. Look-Locker phase images) that we want to reconstruct and their
placement on a T1 relaxation curve (Figure 1B). Density correction and regridding is applied to
the filtered radially ordered k-space allowing the reconstruction of these images by standard
Fourier transformation. From such a series of reconstructed T1 weighted images of varying T1
contrast (Figure 1B), a T1 map is computed by pixel-wise exponential fitting (Figure 1C and D).
IMAGING SEQUENCE AND IMAGE RECONSTRUCTION
Acquisition
The above described method was expanded for multi-slice acquisition to allow volume coverage
of the entire abdomen. An adiabatic, slice selective inversion pre-pulse was implemented to
ensure uniform signal inversion across the selected slice and to minimize B1 inhomogeneities. A
repetition time (TR) of 12 ms and a flip angle (FA) of 6° were chosen to minimize the loss of
magnetization during the Look-Locker experiment. This choice of a relatively long TR and low
FA allows for a straightforward conversion of the measured “apparent” T1 relaxation time (T1*)
into the “true” T1 [5]. The acquisition time for each slice was set to 8016 ms, i.e. 668 radial
profiles, for an optimal mapping of T1 values into the range from 200 ms to 1600 ms.
The GOLD sequence parameters for in vivo, 2D multi-slice, abdominal T1 mapping during free
breathing were as follows: single-inversion T1 weighted turbo field echo (TFE), with slice
selective adiabatic inversion pre-pulse, 18-20 slices, slice thickness = 6 mm, FOV=360x360
mm2, 8 s sequence acquisition time, TR=12 ms, FA=6°, 668 radial profiles with golden angle
view order, reconstruction matrix 256x256. These parameters were used for all in vivo
experiments. For in vitro experiments a smaller FOV (160x160 mm2) was used due to small
sample sizes. Full in vitro parameters were: 2D multi-slice, single-inversion T1 weighted turbo
field echo (TFE), with slice selective adiabatic inversion pre-pulse, 1-6 slices, slice thickness = 6
mm, FOV=160x160 mm2, 8 s sequence acquisition time, TR=12 ms, FA=6°, 668 radial profiles
with golden angle view order, reconstruction matrix 256x256. In order to maintain the sequence
acquisition time (8 s) optimal for T1 mapping of the range between 200 and 1600 ms angle
density was increased to 835% (compare to in vivo 371%). To maintain the spatial in plane
resolution (2x2 mm2) the acquisition matrix was reduced to 80 x 80 (compare in vivo 180 x 180).
Reconstruction
The contrast enhancing k-space filter was optimized as follows: 5 radial profiles closest to each
Look-Locker phase time point Ti were used to fill the center of k-space (Figure 1A). A time shift
Ti = 35.7 ms was added to account for gradient delays and the merging of 5 center profiles for
reconstruction of one Look-Locker image. The number of radial profiles used to reconstruct one
Look-Locker image was optimized in a way that the effect of time distant profiles on the image
contrast was minimized. Thus, when the Nyquist criterion was fulfilled in the outermost parts of
k-space, no more profiles were added to the reconstruction (even if available). A non-equidistant
distribution of Look-Locker images was chosen along the T1 relaxation curve which was based
on the Fibonacci series (Ti with i = 0, 1, 1, 2, 3, 5, 8, 13...). The final number of Look-Locker
images was automatically computed based on the total number of acquired profiles.
Consequently, Look-Locker phases were densely packed during the initial slope of the T1
relaxation curve and spread out more widely during the equilibrium part of the T1 relaxation
curve. This resulted in overall fewer Look-Locker phases and thus faster reconstruction process.
To allow for an immediate T1 map quality control, the described image and T1 map
reconstruction was implemented on the MRI scanner console using the dedicated software
package ReconFrame (GyroTools, Zurich, Switzerland).
Figure 1: (A) An adiabatic, slice selective, inversion pre-pulse is followed by a train of N radial,
low flip angle data acquisitions with golden angle order. The T1 relaxation curve of the
magnetization is schematically represented with i=1-9 representative Look-Locker phase images
as black dots on the curve. For the reconstruction of one Look-Locker phase image at time point
Ti=TR*i along the relaxation curve, the 5 profiles closest to Ti are used to fill the k-space center
and thus determine the contrast, i.e. T1 weighting, in the image. The characteristic radial k-space
trajectories together with the contrast enhancing k-space filter cut offs (circles) are shown for the
first 34 acquired profiles. Accordingly, the rest of k-space is filled using the remaining profiles.
(B) The corresponding nine Look-Locker phase images of different T1 weighting reconstructed
using the k-space contrast enhancing filter. (C) Pixel wise fitting of the T1 relaxation curve yields
the “apparent” T1 relaxation time (T1*) for each pixel in the T1 map. The example shows the
varying image pixel intensity and the respective fitted T1 relaxation curve for the intragastric
pixel indicated in (B). (D) The resulting T1 map computed from the all Look-Locker images by
pixel wise fitting.
REFERENCES:
1
Look DC, Locker DR (1970) Time saving in measurement of NMR and EPR relaxation
times. journal article 41:250-251
2
Hinson WH, Sobol WT (1988) A new method of computing spin-lattice relaxation maps in
magnetic resonance imaging using fast scanning protocols. Med Phys 15:551-561
3
Winkelmann S, Schaeffter T, Koehler T, Eggers H, Doessel O (2007) An optimal radial
profile order based on the Golden Ratio for time-resolved MRI. IEEE Trans Med Imaging
26:68-76
4
Song HK, Dougherty L (2000) k-Space weighted image contrast (KWIC) for contrast
manipulation in projection reconstruction MRI. Magnetic Resonance in Medicine 44:825832
5
Deichmann R, Haase A (1992) Quantification of T1 values by SNAPSHOT-FLASH NMR
imaging. Journal of Magnetic Resonance (1969) 96:608-612