Advertisement

Control and Optimization Problems in Hyperpolarized Carbon-13 MRI

  • John Maidens
  • Murat Arcak
Chapter
Part of the Lecture Notes in Control and Information Sciences - Proceedings book series (LNCOINSPRO)

Abstract

Hyperpolarized carbon-13 magnetic resonance imaging (MRI) is an emerging technology for probing metabolic activity in living subjects, which promises to provide clinicians new insights into diseases such as cancer and heart failure. These experiments involve an injection of a hyperpolarized substrate, often pyruvate labeled with carbon-13, which is imaged over time as it spreads throughout the subject’s body and is transformed into various metabolic products. Designing these dynamic experiments and processing the resulting data requires the integration of noisy information across temporal, spatial, and chemical dimensions, and thus provides a wealth of interesting problems from an optimization and control perspective. In this work, we provide an introduction to the field of hyperpolarized carbon-13 MRI targeted toward researchers in control and optimization theory. We then describe three challenge problems that arise in metabolic imaging with hyperpolarized substrates: the design of optimal substrate injection profiles, the design of optimal flip angle sequences, and the constrained estimation of metabolism maps from experimental data. We describe the current state of research on each of these problems, and comment on aspects that remain open. We hope that these challenge problems will serve to direct future research in control.

References

  1. 1.
    Ardenkjær-Larsen, J.H., Fridlund, B., Gram, A., Hansson, G., Hansson, L., Lerche, M.H., Servin, R., Thaning, M., Golman, K.: Increase in signal-to-noise ratio of \(>\)10,000 times in liquid-state NMR. Proc. Nat. Acad. Sci. 100(18), 10,158–10,163 (2003)Google Scholar
  2. 2.
    Bernstein, M.A., King, K.F., Zhou, X.J.: Basic pulse sequences. In: Handbook of MRI Pulse Sequences, pp. 579–647. Academic Press (2004)Google Scholar
  3. 3.
    Boyd, S., Parikh, N., Chu, E., Peleato, B., Eckstein, J.: Distributed optimization and statistical learning via the alternating direction method of multipliers. Found. Trends Mach. Learn. 3(1), 1–122 (2011)CrossRefzbMATHGoogle Scholar
  4. 4.
    Brindle, K.M.: NMR methods for measuring enzyme kinetics in vivo. Prog. Nucl. Magn. Reson. Spectrosc. 20(3), 257–293 (1988)CrossRefGoogle Scholar
  5. 5.
    Gevers, M., Bombois, X., Hildebrand, R., Solari, G.: Optimal experiment design for open and closed-loop system identification. Commun. Inf. Syst. 11(3), 197–224 (2011)MathSciNetzbMATHGoogle Scholar
  6. 6.
    Goodwin, G., Payne, R.: Dynamic System Identification: Experiment Design and Data Analysis. Academic Press (1977)Google Scholar
  7. 7.
    Gudbjartsson, H., Patz, S.: The rician distribution of noisy MRI data. Magn. Reson. Med. 34(6), 910–914 (1995)CrossRefGoogle Scholar
  8. 8.
    Harrison, C., Yang, C., Jindal, A., Deberardinis, R., Hooshyar, M., Merritt, M., Dean Sherry, A., Malloy, C.: Comparison of kinetic models for analysis of pyruvate-to-lactate exchange by hyperpolarized \(^{13}\)C NMR. NMR Biomed. 25(11), 1286–1294 (2012)CrossRefGoogle Scholar
  9. 9.
    Kazan, S.M., Reynolds, S., Kennerley, A., Wholey, E., Bluff, J.E., Berwick, J., Cunningham, V.J., Paley, M.N., Tozer, G.M.: Kinetic modeling of hyperpolarized \(^{13}\)C pyruvate metabolism in tumors using a measured arterial input function. Magn. Reson. Med. 70(4), 943–953 (2013)CrossRefGoogle Scholar
  10. 10.
    Larson, P.E., Kerr, A.B., Chen, A.P., Lustig, M.S., Zierhut, M.L., Hu, S., Cunningham, C.H., Pauly, J.M., Kurhanewicz, J., Vigneron, D.B.: Multiband excitation pulses for hyperpolarized \(^{13}\)C dynamic chemical-shift imaging. J. Magn. Reson. 194(1), 121–127 (2008)CrossRefGoogle Scholar
  11. 11.
    Ljung, L.: System Identification: Theory for the User. Pearson Education (1999)Google Scholar
  12. 12.
    Maidens, J., Arcak, M.: Semidefinite relaxations in optimal experiment design with application to substrate injection for hyperpolarized MRI. In: Proceedings of the American Control Conference (ACC), pp. 2023–2028 (2016)Google Scholar
  13. 13.
    Maidens, J., Gordon, J.W., Arcak, M., Larson, P.E.Z.: Optimizing flip angles for metabolic rate estimation in hyperpolarized carbon-13 MRI. IEEE Trans. Med. Imaging 35(11), 2403–2412 (2016)CrossRefGoogle Scholar
  14. 14.
    Maidens, J., Gordon, J.W., Arcak, M., Chen, H.Y., Park, I., Criekinge, M.V., Milshteyn, E., Bok, R., Aggarwal, R., Ferrone, M., Slater, J.B., Kurhanewicz, J., Vigneron, D.B., Larson, P.E.Z.: Spatio-temporally constrained reconstruction for hyperpolarized carbon-13 MRI using kinetic models. In: Proceedings of the ISMRM Annual Meeting. http://submissions.mirasmart.com/ISMRM2017/ViewSubmissionPublic.aspx?sei=GH0eaFQTF (2017)
  15. 15.
    Nelson, S.J., Kurhanewicz, J., Vigneron, D.B., Larson, P.E.Z., Harzstark, A.L., Ferrone, M., van Criekinge, M., Chang, J.W., Bok, R., Park, I., Reed, G., Carvajal, L., Small, E.J., Munster, P., Weinberg, V.K., Ardenkjaer-Larsen, J.H., Chen, A.P., Hurd, R.E., Odegardstuen, L.I., Robb, F.J., Tropp, J., Murray, J.A.: Metabolic imaging of patients with prostate cancer using hyperpolarized [1-\(^{13}\)C]pyruvate. Sci. Transl. Med. 5(198), 198ra108 (2013)Google Scholar
  16. 16.
    Nishimura, D.G.: Principles of Magnetic Resonance Imaging. Lulu (2010)Google Scholar
  17. 17.
    Pukelsheim, F.: Optimal Design of Experiments. Probability and mathematical statistics. Wiley, New York (1993)Google Scholar
  18. 18.
    Søgaard, L.V., Schilling, F., Janich, M.A., Menzel, M.I., Ardenkjaer-Larsen, J.H.: In vivo measurement of apparent diffusion coefficients of hyperpolarized \(^{13}\)C-labeled metabolites. NMR Biomed. 27(5), 561–569 (2014)CrossRefGoogle Scholar
  19. 19.
    Walter, É., Pronzato, L.: Identification of Parametric Models from Experimental Data. Communications and Control Engineering. Springer (1997)Google Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Department of Electrical Engineering and Computer SciencesUniversity of CaliforniaBerkeleyUSA

Personalised recommendations