Zhibo Zhu1, Yannick Bliesener1, R. Marc Lebel2,3, and Krishna Shrinivas Nayak1
1Electrical and Computer Engineering, University of Southern California, Los Angeles, CA, United States, 2Global MR Applications & Workflow, GE Healthcare, Calgary, AB, Canada, 3Radiology, University of Calgary, Calgary, AB, Canada
Synopsis
Quantitative
DCE-MRI requires pre-contrast T1 mapping with matching resolution
and coverage. Recent studies have shown that sparse sampling and constrained
reconstruction can be applied to both DCE-MRI and pre-contrast T1
mapping with the variable flip angle (VFA) approach. Here, we demonstrate and
evaluate direct estimation of T1 from sparsely sampled VFA raw data. In
healthy subjects, we demonstrate superior T1 estimation compared with
prior methods at subsampling factors >10.
Purpose
To develop and
evaluate efficient pre-contrast T1 mapping compatible with the
workflow requirements of high-resolution whole-brain DCE-MRI.Introduction
Dynamic contrast enhancement (DCE)-MRI is a powerful tool that can reveal the spatial distribution of vascular parameters, including permeability and plasma volume. Recent studies have overcome traditional limitations such as poor spatial resolution and poor spatial coverage, using compressed sensing and constrained reconstruction 1-4. Quantitative DCE-MRI requires pre-contrast T1 and M0 maps with matching spatial resolution and coverage 5,6, which would require prohibitively long scan time. However, recently demonstrated sparse sampling with model-based T1 estimation could make this possible 7,8. Sparse variable flip angle (VFA) T1 mapping has even been efficiently integrated into the pre-contrast phase of a DCE-MRI scan 3. The conventional reconstruction that combines parallel imaging and DESPOT1 modeling has thus far been unsuccessful at high undersampling factors (>10). Here, we demonstrate a framework for direct estimation of pre-contrast T1 and M0 that is inspired by recent direct estimation of tracer-kinetic parameter maps 9,10.Methods
VFA T1/M0 mapping is
performed by solving the following model constrained inverse problem:
$$p=\min_p \| U F S D (p) - k \|^2_{\ell_2}$$
where $$$p$$$ concatenates
T1 and M0 into a vector, $$$U$$$ is the subsampling
operator, $$$F$$$ is the Fourier
transform, $$$S$$$ is the coil
sensitivity, $$$D$$$ is the SPGR
signal operator, and $$$k$$$ is measured $$$k$$$-space data. This problem is solved using nonlinear conjugate gradient (NLCG).
Fully sampled VFA data were acquired on one healthy
male volunteer, using a GE MR750 scanner with a 12-channel head coil. The flip
angles were logarithmically spaced from 1.5° to 15° 3. Parameters: 5
ms TR, 1.9 ms TE, 240×240×240 mm3 FOV, 2 mm slice thickness, and
256×240×120 matrix size.
This data was subsampled to evaluate T1 and
M0 mapping accuracy as a function of subsampling factor . Subsampling followed the randomized Golden-Angle (RGA) pattern 11 shown in Figure 1. Due to the elliptical footprint, we used a
weighted sampling operator $$$U$$$ with small assigned weight (0.1)
to $$$k$$$-space corners and set $$$k$$$ values in those locations to be
zero. We report error and convergence speed within tissue regions of interest (ROI)
for gray matter, white matter, and cerebrospinal fluid.Results
Figure 2 contains direct estimation results as a function of
subsampling factor. Error was computed as percent difference with respect to the
reference (fully sampled direct reconstruction). Error smoothly increases with subsampling
factor, and direct estimation provides better performance than the conventional
approach at all subsampling factors. This is especially true for R>10, where
direct estimation has far fewer regions with errors larger than 20%.
Figure 3 illustrates the
algorithm convergence for WM, GM and CSF ROI’s for three subsampling factors. As
expected, we observe that CSF, which has the longest T1 values, takes
longest to converge and had the largest residual errors. RMSE in CSF decreased non-monotonically during the iterations of the optimizer.
Figure 4 shows T1 mean, standard deviation and RMSE for the proposed
approach from different subsampling factor. As expected, T1 mean,
std and RMSE increase as subsampling factor increases. We also observed non-monotonic decrease of RMSE as a function of scan time.
Figure 5 shows Fourier Radial Error Spectrum Plots (ESP) 12,13 for the conventional approach and proposed approach. The proposed approach provides
superior performance in low to mid-range of spatial frequencies for all
subsampling factors.Discussion
Direct T1 and M0 estimation can be applied to sparse
pre-contrast VFA mapping, and it provides several improvements over
conventional indirect approaches. In stark contrast to conventional approaches that
use two separate steps, direct estimation integrates image reconstruction and T1
mapping in a single step. This simplification allows the algorithm to exploit
rich data redundancy along the flip angle dimension. This is expected to allow
even faster data acquisition, and a superior trade-off between scan time and
performance.
Interestingly, we noticed
a small T1 bias as R increases. For white matter, the bias was always
less than 60 ms, and for R<10 it was less than 20 ms. This is an important consideration that
requires further investigation. We also observed slow convergence in long T1 tissues,
partially due to the VFA angles being
optimized for T1 values closer to white matter. This warrants further investigation if tracer
kinetic maps are being used in long T1 regions. We further observed non-monotonic behavior of RMSE with respect to iterations during optimization and scan time. We will investigate reasons for this non-monotonic behavior and suitable stopping criteria in future research.
This study has several practical
limitations. We utilized only one fully
sampled volunteer dataset. This would
need to be repeated in several subjects, preferably patients receiving
clinically indicated DCE-MRI.
Fully-sampled VFA data were subsampled in this study. Findings would need to be tested with
prospective undersampling, and ideally integrated into a comprehensive
high-resolution whole-brain DCE-MRI protocol3.Conclusion
Direct estimation of
pre-contrast T1 and M0
for high resolution DCE-MRI is feasible.
The proposed approach provides superior performance especially for subsampling
factors >10.Acknowledgements
We acknowledge National Institute of Health
grant support (#R33-CA225400).References
[1] R. M.
Lebel, J. Jones, J. C. Ferre, M. Law, K. S. Nayak. Highly accelerated
dynamic contrast enhanced imaging. Magnetic Resonance in Medicine.
71(2):635-644. February 2014.
[2] Y. Guo, R. M.
Lebel, Y. Zhu, S. G. Lingala, M. S. Shiroishi, M. Law, K. S.
Nayak. High-resolution Whole-brain DCE-MRI Using Constrained Reconstruction:
Prospective Clinical Evaluation in Brain Tumor Patients. Medical Physics
43:2013. April 2016.
[3] R. M. Lebel, Y.
Guo, S. G. Lingala, R. Frayne, K. S. Nayak. "Highly Accelerated
DCE imaging with integrated T1 mapping." Proc. ISMRM 25th Scientific
Sessions, Honolulu, April 2017, p138.
[4] J. S. Park, E. Lim, S.
H. Choi, C. H. Sohn, J. Lee, J. Park, Model-Based High-Definition Dynamic Contrast
Enhanced MRI for Concurrent Estimation of Perfusion and Microvascular Permeability, Medical Image Analysis 59 (2020) 101566.
[5] C. Lavini, Simulating
the effect of input errors on the accuracy of Tofts’ pharmacokinetic model
parameters. Magn. Reson. Imaging 2015;33:222–235.
[6] Di Giovanni P., Azlan
CA, Ahearn T. S., Semple S. I., Gilbert F. J., Redpath T. W.. The accuracy of
pharmacokinetic parameter measurement in DCE-MRI of the breast at 3 T. Phys.
Med. Biol. 2010;55:121–132.
[7] Zhao B., Lam F., Liang Z., Model-based MR parameter mapping with sparsity
constraints Parameter estimation and performance bound, IEEE Trans Med Imaging.
2014 Sep; 33(9): 1832-1844.
[8] Maier O., Schoormans
J., Schloegl M., et al. Rapid T1 quantification from high resolution 3D data
with model‐based reconstruction.
Magn Reson Med. 2019;81:2072-2089.
[9] Dikaios N., Arridge S.,
Hamy V., Punwani S., Atkinson D. Direct parametric reconstruction from
undersampled (k, t)-space data in dynamic contrast enhanced MRI. Med Image Anal
2014;18:989–1001.
[10] Y. Guo, S. G.
Lingala, Y. Zhu, R. M. Lebel, K. S. Nayak. Direct Estimation of
Tracer-Kinetic Parameter Maps from Highly Undersampled Brain
DCE-MRI. Magnetic Resonance in Medicine. 78(4):1566-1578. October 2017.
[11] Y. Zhu, Y. Guo, S. G. Lingala,
R. M. Lebel, M. Law, K. S. Nayak. GOCART: GOlden-angle CArtesian
Randomized Time-resolved 3D MRI. Magnetic Resonance Imaging. 34: 940-950.
September 2016.
[12] T. H. Kim, J.
P. Haldar. The Fourier Radial Error Spectrum Plot: A more nuanced quantitative
evaluation of image reconstruction quality. IEEE International Symposium on
Biomedical Imaging, Washington, DC, 2018.
[13] T. H.
Kim, J. P. Haldar. Assessing MR image reconstruction quality using the
Fourier Radial Error Spectrum plot. Joint Annual Meeting ISMRM-ESMRMB, Paris,
2018.