Quantitative MRI by nonlinear inversion of the Bloch equations.
Bloch equations
model-based reconstruction
nonlinear inversion
quantitative MRI
sensitivity analysis
state-transition matrix
Journal
Magnetic resonance in medicine
ISSN: 1522-2594
Titre abrégé: Magn Reson Med
Pays: United States
ID NLM: 8505245
Informations de publication
Date de publication:
08 2023
08 2023
Historique:
revised:
16
02
2023
received:
15
09
2022
accepted:
20
03
2023
medline:
29
5
2023
pubmed:
24
4
2023
entrez:
24
04
2023
Statut:
ppublish
Résumé
Development of a generic model-based reconstruction framework for multiparametric quantitative MRI that can be used with data from different pulse sequences. Generic nonlinear model-based reconstruction for quantitative MRI estimates parametric maps directly from the acquired k-space by numerical optimization. This requires numerically accurate and efficient methods to solve the Bloch equations and their partial derivatives. In this work, we combine direct sensitivity analysis and pre-computed state-transition matrices into a generic framework for calibrationless model-based reconstruction that can be applied to different pulse sequences. As a proof-of-concept, the method is implemented and validated for quantitative The direct sensitivity analysis enables a highly accurate and numerically stable calculation of the derivatives. The state-transition matrices efficiently exploit repeating patterns in pulse sequences, speeding up the calculation by a factor of 10 for the examples considered in this work, while preserving the accuracy of native ordinary differential equations solvers. The generic model-based method reproduces quantitative results of previous model-based reconstructions based on the known analytical solutions for radial IR FLASH. For IR bSFFP it produces accurate By developing efficient tools for numerical optimizations using the Bloch equations as forward model, this work enables generic model-based reconstruction for quantitative MRI.
Types de publication
Journal Article
Research Support, N.I.H., Extramural
Research Support, Non-U.S. Gov't
Langues
eng
Sous-ensembles de citation
IM
Pagination
520-538Subventions
Organisme : NIH HHS
ID : U24EB029240
Pays : United States
Informations de copyright
© 2023 The Authors. Magnetic Resonance in Medicine published by Wiley Periodicals LLC on behalf of International Society for Magnetic Resonance in Medicine.
Références
Graff C, Li Z, Bilgin A, Altbach MI, Gmitro AF, Clarkson EW. Iterative T2 estimation from highly undersampled radial fast spin-echo data. Proc Int Soc Mag Reson Med. 2006;14:925.
Olafsson VT, Noll DC, Fessler JA. Fast joint reconstruction of dynamic R2*$$ {R}_2^{\ast } $$ and field maps in functional MRI. IEEE Trans Med Imaging. 2008;27:1177-1188.
Block KT, Uecker M, Frahm J. Model-based iterative reconstruction for radial fast spin-echo MRI. IEEE Trans Med Imaging. 2009;28:1759-1769.
Sumpf TJ, Uecker M, Boretius S, Frahm J. Model-based nonlinear inverse reconstruction for T2-mapping using highly undersampled spin-echo MRI. J Magn Reson Imaging. 2011;34:420-428.
Wang X, Tan Z, Scholand N, Roeloffs V, Uecker M. Physics-based reconstruction methods for magnetic resonance imaging. Philos Trans R Soc A. 2021;379.
Ma D, Gulani V, Seiberlich N, et al. Magnetic resonance fingerprinting. Nature. 2013;495:187-192.
Petzschner FH, Ponce IP, Blaimer M, Jakob PM, Breuer FA. Fast MR parameter mapping using k-t principal component analysis. Magn Reson Med. 2011;66:706-716.
Huang C, Graff CG, Clarkson EW, Bilgin A, Altbach MI. T2 mapping from highly undersampled data by reconstruction of principal component coefficient maps using compressed sensing. Magn Reson Med. 2012;67:1355-1366.
Zhao B, Lu W, Hitchens TK, Lam F, Ho C, Liang Z-P. Accelerated MR parameter mapping with low-rank and sparsity constraints. Magn Reson Med. 2015;74:489-498.
Tamir JI, Uecker M, Chen W, et al. T2 shuffling: sharp, multicontrast, volumetric fast spin-echo imaging. Magn Reson Med. 2017;77:180-195.
Assländer J, Cloos MA, Knoll F, Sodickson DK, Hennig J, Lattanzi R. Low rank alternating direction method of multipliers reconstruction for MR fingerprinting. Magn Reson Med. 2018;79:83-96.
Hilbert T, Sumpf TJ, Weiland E, et al. Accelerated T2 mapping combining parallel MRI and model-based reconstruction: GRAPPATINI. J Magn Reson Imaging. 2018;48:359-368.
Wang X, Roeloffs V, Klosowski J, et al. Model-based T1 mapping with sparsity constraints using single-shot inversion-recovery radial FLASH. Magn Reson Med. 2018;79:730-740.
Tan Z, Voit D, Kollmeier JM, Uecker M, Frahm J. Dynamic water/fat separation and inhomogeneity mapping adjoint estimation using undersampled triple-echo multi-spoke radial FLASH. Magn Reson Med. 2019;82:1000-1011.
Lee PK, Watkins LE, Anderson TI, Buonincontri G, Hargreaves BA. Flexible and efficient optimization of quantitative sequences using automatic differentiation of Bloch simulations. Magn Reson Med. 2019;82:1438-1451.
Dong G, Hintermüller M, Papafitsoros K. Quantitative magnetic resonance imaging: from fingerprinting to integrated physics-based models. SIAM J Imag Sci. 2019;12:927-971.
Ben-Eliezer N, Sodickson DK, Shepherd T, Wiggins GC, Block KT. Accelerated and motion-robust in vivo T2 mapping from radially undersampled data using bloch-simulation-based iterative reconstruction. Magn Reson Med. 2016;75:1346-1354.
Sbrizzi A, Heide O, Cloos M, et al. Fast quantitative MRI as a nonlinear tomography problem. Magn Reson Imaging. 2018;46:56-63.
Dickinson RP, Gelinas RJ. Sensitivity analysis of ordinary differential equation systems-a direct method. J Comput Phys. 1976;21:123-143.
Scholand N, Wang X, Rosenzweig S, Uecker M. Generalized model-based reconstruction for quantitative MRI using the Bloch-equations. Magn Reson Mater Phy. 2019;36:235.
Scholand N, Wang X, Rosenzweig S, Holme HCM, Uecker M. Generic quantitative MRI using model-based reconstruction with the Bloch equations. Proc Int Soc Mag Reson Med. 2020;28:5694.
Scholand N, Graf C, Uecker M. Efficient Bloch simulation based on precomputed state-transition matrices. Proc Int Soc Mag Reson Med. 2022;30:0748.
Scholand N, Uecker M. Sensitivity analysis of the Bloch equations. Proc Int Soc Mag Reson Med. 2022;30:1700.
Moler C, Loan C. Nineteen dubious ways to compute the exponential of a matrix. SIAM Rev. 1978;20:4.
Moler C, Loan CV. Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later*. SIAM Rev. 2003;45:3.
Assländer J, Novikov DS, Lattanzi R, Sodickson DK, Cloos MA. Hybrid-state free precession in nuclear magnetic resonance. Commun Phys. 2019;2:73.
Malik SJ, Teixeira RPAG, West DJ, Wood TC, Hajnal JV. Steady-state imaging with inhomogeneous magnetization transfer contrast using multiband radiofrequency pulses. Magn Reson Med. 2020;83:935-949.
Uecker M, Hohage T, Block KT, Frahm J. Image reconstruction by regularized nonlinear inversion-joint estimation of coil sensitivities and image content. Magn Reson Med. 2008;60:674-682.
Vasanawala S, Murphy M, Alley M, et al. Practical parallel imaging compressed sensing MRI: summary of two years of experience in accelerating body MRI of pediatric patients. Proc IEEE Int Symp Biomed Imaging. 2011;2011:1039-1043.
Beck A, Teboulle M. A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J Img Sci. 2009;2:183-202.
Uecker M, Virtue P, Ong F, et al. Software toolbox and programming library for compressed sensing and parallel imaging. Paper presented at: ISMRM Scientific Workshop; 2013; Sedona, AZ.
Blumenthal M, Luo G, Schilling M, Holme HCM, Uecker M. Deep, deep learning with BART. Magn Reson Med. 2023;89:678-693.
Dormand J, Prince P. A family of embedded Runge-Kutta formulae. J Comput Appl Math. 1980;6:19-26.
Schmitt P, Griswold MA, Jakob PM, et al. Inversion recovery TrueFISP: quantification of T1, T2, and spin density. Magn Reson Med. 2004;51:661-667.
Wansapura JP, Holland SK, Dunn RS, Ball WS Jr. NMR relaxation times in the human brain at 3.0 tesla. J Magn Reson Imaging. 1999;9:531-538.
Deimling M, Heid O. Magnetization prepared trueFISP imaging. Paper presented at: Proceedings of the 2nd Annual Meeting of ISMRM; 1994; San Francisco, CA:495.
Deshpande VS, Chung Y-C, Zhang Q, Shea SM, Li D. Reduction of transient signal oscillations in true-FISP using a linear flip angle series magnetization preparation. Magn Reson Med. 2003;49:151-157.
Chung S, Kim D, Breton E, Axel L. Rapid B1+ mapping using a preconditioning RF pulse with TurboFLASH readout. Magn Reson Med. 2010;64:439-446.
Wang X, Rosenzweig S, Scholand N, Holme HCM, Uecker M. Model-based reconstruction for simultaneous multi-slice T1 mapping using single-shot inversion-recovery radial FLASH. Magn Reson Med. 2021;85:1258-1271.
Wang X, Rosenzweig S, Scholand N, Holme HCM, Uecker M. Data for: Model-based reconstruction for simultaneous multi-slice T1 mapping using single-shot inversion-recovery radial FLASH [Data set]. Zenodo. 2020.
Sumpf TJ, Petrovic A, Uecker M, Knoll F, Frahm J. Fast T2 mapping with improved accuracy using Undersampled spin-Echo MRI and model-based reconstructions with a generating function. IEEE Trans Med Imaging. 2014;33:2213-2222.
Stupic KF, Ainslie M, Boss MA, et al. A standard system phantom for magnetic resonance imaging. Magn Reson Med. 2021;86:1194-1211.
Deichmann R. Fast high-resolution T1 mapping of the human brain. Magn Reson Med. 2005;54:20-27.
Uecker M, Lai P, Murphy MJ, et al. ESPIRiT-an eigenvalue approach to autocalibrating parallel MRI: where SENSE meets GRAPPA. Magn Reson Med. 2014;71:990-1001.
Bieri O, Scheffler K. On the origin of apparent low tissue signals in balanced SSFP. Magn Reson Med. 2006;56:1067-1074.
Graham SJ, Henkelman RM. Understanding pulsed magnetization transfer. J Magn Reson Imaging. 1997;7:903-912.
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.
Tan Z, Hohage T, Kalentev O, et al. An eigenvalue approach for the automatic scaling of unknowns in model-based reconstructions: applications to real-time phase-contrast flow MRI. NMR Biomed. 2017;30:e3835.
Assländer J, Lattanzi R, Sodickson DK, Cloos MA. Optimized quantification of spin relaxation times in the hybrid state. Magn Reson Med. 2019;82:1385-1397.
Feng L, Liu F, Soultanidis G, et al. Magnetization-prepared GRASP MRI for rapid 3D T1 mapping and fat/water-separated T1 mapping. Magn Reson Med. 2021; 86: 97-114.
Look DC, Locker DR. Time saving in measurement of NMR and EPR relaxation times. Rev Sci Instrum. 1970;41:250-251.
Deichmann R, Haase A. Quantification of T1 values by SNAPSHOT-FLASH NMR imaging. J Magn Reson. 1992;96:608-612.
Roeloffs V, Wang X, Sumpf TJ, Untenberger M, Voit D, Frahm J. Model-based reconstruction for T1 mapping using single-shot inversion-recovery radial FLASH. Int J Imag Syst Tech. 2016;26:254-263.
Clare S, Jezzard P. Rapid T1 mapping using multislice echo planar imaging. Magn Reson Med. 2001;45:630-634.
Scheffler K, Lehnhardt S. Principles and applications of balanced SSFP techniques. Eur Radiol. 2003;13:2409-2418.
Ehses P, Seiberlich N, Ma D, et al. IR TrueFISP with a golden-ratio-based radial readout: fast quantification of T1, T2, and proton density. Magn Reson Med. 2013;69:71-81.
Pfister J, Blaimer M, Kullmann WH, Bartsch AJ, Jakob PM, Breuer FA. Simultaneous T1 and T2 measurements using inversion recovery TrueFISP with principle component-based reconstruction, off-resonance correction, and multicomponent analysis. Magn Reson Med. 2019;81:3488-3502.