Optimal control theory for applications in Magnetic Resonance Imaging

Aigner, CS, Clason, C, Rund, A, Stollberger, R: Efficient high resolution rf pulse design applied to simultaneous multi-slice excitation. J. Magn. Reson. 263, 33 (2016). Assémat, E, Lapert, M, Zhang, Y, Braun, M, Glaser, SJ, Sugny, D: Simultaneous time-optimal control of the inversion of two spin-\(\frac {1}{2}\) particles. Phys. Rev. A. 82(1), 013415 (2010). Bernstein, MA, King, KF, Zhou: Handbook of MRI Pulse Sequences. Elsevier, Burlington-San Diego-London, London (2004). Black, S, Gao, F, Bilbao, J: Understanding white matter disease. Stroke. 40(3 suppl 1), 48–52 (2009). Bonnard, B, Chyba, M: Singular Trajectories and Their Role in Control Theory, Mathematics and applications, vol. 40 edn. Springer, Berlin (2003). Bonnard, B, Chyba, M, Marriott, J: Singular trajectories and the contrast imaging problem in nuclear magnetic resonance. SIAM J. Control. Optim. 51(2), 1325–1349 (2013). Bonnard, B, Chyba, M, Sugny, D: Time-minimal control of dissipative two-level quantum systems: The generic case. IEEE Trans. Automat. Control. 54(11), 2598–2610 (2009). Bonnard, B, Claeys, M, Cots, O, Martinon, P: Geometric and numerical methods in the contrast imaging problem in nuclear magnetic resonance. Acta Applicandae Math. 135(1), 5–45 (2014). Bonnard, B, Cots, O: Geometric numerical methods and results in the contrast imaging problem in nuclear magnetic resonance. Math. Model. Methods Appl. Sci. 24(01), 187–212 (2014). Bonnard, B, Cots, O, Glaser, SJ, Lapert, M, Sugny, D, Zhang, Y: Geometric optimal control of the contrast imaging problem in nuclear magnetic resonance. IEEE IEEE Trans. Autom. Control. 57(8), 1957–1969 (2012). Bonnard, B, Sugny, D: Time-minimal control of dissipative two-level quantum systems: The integrable case. SIAM J. Control Optim. 48(3), 1289–1308 (2009). Bonnard, B, Sugny, D: Optimal Control with Applications in Space and Quantum Dynamics vol. 5. AIMS: Applied mathematics, New York (2012). Boscain, U, Mason, P: Time minimal trajectories for a spin 1/2 particle in a magnetic field. J. Math. Phys. 47(6), 062101 (2006). Boscain, U, Picolli, B: Optimal Syntheses for Control Systems on 2-D Manifolds vol. 43. 29 B. Springer, Berlin (2004). Brif, C, Chakrabarti, R, Rabitz, H: Control of quantum phenomena: Past, present and future. New J. Phys. 12(7), 075008 (2010). Bryson, AJ, Ho, Y-C: Applied Optimal Control. Hemisphere, Washington, DC (1975). Conolly, S, Nishimura, D, Macovski, A: Optimal control methods in NMR spectroscopy. IEEE Trans. Med. Imaging. MI-5, 106–115 (1986). D’Alessandro, D: Introduction to Quantum Control and Dynamics, Applied mathematics and nonlinear science series edn. Chapman and Hall, Boca Raton (2008). D’Alessandro, D, Dahled, M: Optimal control of two-level quantum systems. IEEE Trans. Automat. Control. 46(6), 866–876 (2001). Daems, D, Ruschhaupt, A, Sugny, D, Guérin, S: Robust quantum control by a single-shot shaped pulse. Phys. Rev. Lett. 111, 050404 (2013). de Fouquiere, P, Schirmer, SG, Glaser, SJ, Kuprov, I: Second order gradient ascent pulse engineering. J. Magn. Reson. 212, 412 (2011). de Graaf, RA, Brown, PB, McIntyre, S, Nixon, TW, Behar, KL, Rothman, DL: High magnetic field water and metabolite proton T1 and T2 relaxation in rat brain in vivo. Magn. Reson. Med. 56(2), 386–394 (2006). Dong, D, Petersen, IA: Quantum control theory and applications: A survey. IET Control Theory A. 4(12), 2651–2671 (2010). Ernst, RR, Anderson, WA. Rev. Sci. Instrum. 37, 93 (1966). Ernst, RR, Bodenhausen, G, Wokaun, A: Principles of Nuclear Magnetic Resonance in One and Two Dimensions vol. 14. Clarendon Press, Oxford (1987). Garon, A, Glaser, SJ, Sugny, D: Time-optimal control of SU(2) quantum operations. Phys. Rev. A. 88, 043422 (2013). Glaser, SJ, Boscain, U, Calarco, T, Koch, CP, Kockenberger, W, Kosloff, R, Kuprov, I, Luy, B, Schirmer, S, Schulte-Herbrüggen, T, Sugny, D, Wilhelm, FK: Training schrödinger’s cat: Quantum optimal control. Eur. Phys. J. D. 69, 279 (2015). Gershenzon, NI, Kobzar, K, Luy, B, Glaser, SJ, Skinner, TE: Optimal control design of excitation pulses that accomodate relaxation. J. Magn. Reson. 188, 330 (2007). Jurdjevic, V: Geometric Control Theory. Cambridge University Press, Cambridge, Cambridge (1997). Khaneja, N, Brockett, R, Glaser, SJ: Time optimal control in spin systems. Phys. Rev. A. 63, 032308 (2001). Khaneja, N, Glaser, SJ, Brockett, R: Sub-Riemannian geometry and time optimal control of three spin systems: Quantum gates and coherence transfer. Phys. Rev. A. 65, 032301 (2002). Khaneja, N, Reiss, T, Kehlet, C, Schulte-Herbrüggen, T, Glaser, SJ: Optimal control of coupled spin dynamics: design of NMR pulse sequences by gradient ascent algorithms. J. Magn. Reson. 172(2), 296–305 (2005). Kobzar, K, Skinner, TE, Khaneja, N, Glaser, SJ, Luy, B: Exploring the limits of broadband excitation and inversion pulses. J. Magn. Reson. 170, 236 (2004). Kobzar, K, Skinner, TE, Khaneja, N, Glaser, SJ, Luy, B: Exploring the limits of excitation and inversion pulses ii: Rf-power optimized pulses. J. Magn. Reson. 194, 58 (2008). Kobzar, K, Ehni, S, Skinner, TE, Glaser, SJ, Luy, B: Exploring the limits of broadband 90 and 180 universal rotation pulses. J. Magn. Reson. 225, 142 (2012). Krotov, VF: Global Methods in Optimal Control. Marcel Dekker, New-York (1996). Lapert, M, Assémat, E, Glaser, SJ, Sugny, D: Understanding the global structure of two-level quantum systems with relaxation: Vector fields organized through the magic plane and the steady-state ellipsoid. Phys. Rev. A. 88, 033407 (2013). Lapert, M, Assémat, E, Glaser, SJ, Sugny, D: Optimal control of the signal-to-noise ratio per unit time for a spin-1/2 particle. Phys. Rev. A. 90, 023411 (2014). Lapert, M, Assémat, E, Glaser, SJ, Sugny, D: Optimal control of the signal-to-noise ratio per unit time of a spin 1/2 particle: The crusher gradient and the radiation damping cases. J. Chem. Phys. 142, 044202–19 (2015). Lapert, M, Salomon, J, Sugny, D: Time-optimal monotonically convergent algorithm with an application to the control of spin systems. Phys. Rev. A. 85, 033406 (2012). Lapert, M, Zhang, Y, Braun, M, Glaser, SJ, Sugny, D: Singular extremals for the time-optimal control of dissipative spin \(\frac {1}{2}\) particles. Phys. Rev. Lett. 104, 083001 (2010). Lapert, M, Zhang, Y, Glaser, SJ, Sugny, D: Towards the time-optimal control of dissipative spin 1/2 particles in nuclear magnetic resonance. J. Phys. B: At., Mol. Opt. Phys. 44, 154014 (2011). Lapert, M, Zhang, Y, Janich, M, Glaser, SJ, Sugny, D: Exploring the physical limits of saturation contrast in magnetic resonance imaging. Sci. Rep. 2, 589 (2012). Lefebvre, PM, Van Reeth, E, Ratiney, H, Beuf, O, Brusseau, E, Lambert, SA, Glaser, SJ, Sugny, D, Grenier, D, Tse Ve Koon, K: Active Control of the Spatial MRI Phase Distribution with Optimal Control Theory. J. Magn. Reson. 281, 82–93 (2017). Levitt, MH: Spin Dynamics: Basics of Nuclear Magnetic Resonance. Wiley, New York (2008). Machnes, S, Sander, U, Glaser, SJ, de Fouquieres, P, Gruslys, A, Schirmer, S, Schulte-Herbrüggen, T: Comparing, optimising and benchmarking quantum control algorithms in a unifying programming framework. Phys. Rev. A. 84, 022305 (2011). Massire, A, Cloos, MA, Vignaud, A, Bihan, DL, Amadon, A, Boulant, N: Design of non-selective refocusing pulses with phase-free rotation axis by gradient ascent pulse engineering algorithm in parallel transmission at 7 t. J. Magn. Reson. 230, 76 (2013). Mukherjee, V, Carlini, A, Mari, A, Caneva, TSM, Carlarco, T, Fazio, R, Giovannetti, V: Speeding up and slowing down the relaxation of a qubit by optimal control. Phys. Rev. A. 88, 062326 (2013). Nielsen, NC, Kehlet, C, Glaser, SJ, Khaneja, N: Optimal control methods in NMR spectroscopy. Encycl. Nucl. Magn. Reson. 9, 100 (2010). Pontryagin, LS, Boltyanskii, VG, Gamkrelidze, RV, Mishchenko, EF: The Mathematical Theory of the Optimal Process. Wiley-Interscience, New-York (1962). Reich, D, Ndong, M, Koch, CP: Monotonically convergent optimization in quantum control using Krotov’s method. J. Chem. Phys. 136, 104103 (2012). Ruschhaupt, A, Chen, X, Alonso, D, Muga, JG: Optimally robust shortcuts to population inversion in two-level quantum systems. New J. Phys. 14(9), 093040 (2012). Sbrizzi, A, Hoogduin, H, Hajnal, JV, van der Berg, CA, Luijten, PR: Optimal control design of turbo spin-echo sequences with applications to parallel-transmit systems. Magn. Reson. Med. 77, 361 (2017). Skinner, TE, Reiss, TO, Luy, B, Khaneja, N, Glaser, SJ: Application of optimal control theory to the design of broadband excitation pulses for high resolution nmr. J. Magn. Reson. 163, 8 (2003). Skinner, TE, Reiss, TO, Luy, B, Khaneja, N, Glaser, SJ: Reducing the duration of broadband excitation pulses using optimal control with limited rf amplitude. J. Magn. Reson. 167, 68 (2004). Skinner, TE, Reiss, O, Luy, B, Khaneja, N, Glaser, SJ: Tailoring the optimal control cost function to a desired output: Application to minimizing phase errors in short broadband excitation pulses. J. Magn. Reson. 172, 17 (2005). Skinner, TE, Kobzar, K, Luy, B, Bendall, R, Bermel, W, Khaneja, N, Glaser, SJ: Optimal control design of constant amplitude phase-modulated pulses: Application to calibration-free broadband excitation. J. Magn. Reson. 179, 241 (2006). Tosner, Z, Vosegaard, T, Kehlet, CT, Khaneja, N, Glaser, SJ, Nielsen, NC: Optimal control in nmr spectroscopy: Numerical implementation in simpson. J. Magn. Reson. 197, 120 (2009). Van Reeth, E, Ratiney, H, Tesch, M, Grenier, D, Beuf, O, Glaser, SJ, Sugny, D: Optimal control design of preparation pulses for contrast optimization in mri. J. Magn. Reson. 279, 39–50 (2017). Vinding, MS, Maximov, II, Tošner, Z, Nielsen, NC: Fast numerical design of spatial-selective rf pulses in mri using krotov and quasi-newton based optimal control methods. J. Chem. Phys. 137, 054203 (2012). Xu, D, King, KF, Zhu, Y, McKinnon, GC, Liang, Z-P: Designing multichannel, multidimensional, arbitrary flip angle rf pulses using an optimal control approach. Magn. Reson. Med. 59, 547 (2008). Zhang, Y, Lapert, M, Sugny, D, Braun, M, Glaser, SJ: Time-optimal control of spin 1/2 particles in the presence of radiation damping and relaxation. J. Chem. Phys. 134, 054103 (2011).