Maximin Designs for Ultra-Fast Functional Brain Imaging

  • R. Alghamdi
  • A. Alrumayh
  • M.-H. KaoEmail author
Part of the ICSA Book Series in Statistics book series (ICSABSS)


Functional brain imaging experiments allow researchers to study the inner workings of the human brain, and are widely conducted in many fields. An important experimental design issue for such an experiment is the selection of a sequence of mental stimuli that allows us to collect informative data for making precise and valid statistical inferences. However, obtaining a good stimulus sequence can be challenging, especially when brain mapping technology with a high temporal resolution is employed. In this work, we focus on such ultra-fast functional brain imaging studies, and propose an efficient approach for obtaining high-quality stimulus sequences by taking the uncertainty of the autocorrelation of the response into account. The performance of our proposed approach is demonstrated via case studies.



The research of Ming-Hung Kao was in part supported by the National Science Foundation grants DMS-13-52213, and CMMI-17-26445.


  1. Aguirre, G.K., Mattar, M.G., Magis-Weinberg, L.: De Bruijn cycles for neural decoding. Neuroimage 56(3), 1293–1300 (2011)CrossRefGoogle Scholar
  2. Buračas, G.T., Boynton, G.M.: Efficient design of event-related fMRI experiments using m-sequences. NeuroImage 16(3), 801–813 (2002)CrossRefGoogle Scholar
  3. Cheng, C.-S., Kao, M.-H.: Optimal experimental designs for fMRI via circulant biased weighing designs. Ann. Stat. 43(6), 2565–2587 (2015)MathSciNetCrossRefGoogle Scholar
  4. Chernoff, H.: Locally optimal designs for estimating parameters. Ann. Math. Stat. 24(4), 586–602 (1953)MathSciNetCrossRefGoogle Scholar
  5. Dale, A.M.: Optimal experimental design for event-related fMRI. Hum. Brain Mapp. 8(2–3), 109–114 (1999)CrossRefGoogle Scholar
  6. Friston, K.J., Zarahn, E., Josephs, O., Henson, R.N.A., Dale, A.M.: Stochastic designs in event-related fMRI. NeuroImage 10(5), 607–619 (1999)CrossRefGoogle Scholar
  7. Friston, K.J. Ashburner J.T., Kiebel, S.J., Nichols, T.E., Penny, W.D.: Statistical Parametric Mapping: The Analysis of Functional Brain Images. Amsterdam, Elsevier/Academic Press (2007)CrossRefGoogle Scholar
  8. Kao, M.H.: Multi-objective optimal experimental designs for ER-fMRI using MATLAB. J. Stat. Softw. 30(11), 1–13 (2009)CrossRefGoogle Scholar
  9. Kao, M.-H.: A new type of experimental designs for event-related fMRI via Hadamard matrices. Stat. Prob. Lett. 84(0), 108–112 (2014)MathSciNetCrossRefGoogle Scholar
  10. Kao, M.-H., Mittelmann, H.D.: A fast algorithm for constructing efficient event-related functional magnetic resonance imaging designs. J. Stat. Comput. Simul. 84(11), 2391–2407 (2014)MathSciNetCrossRefGoogle Scholar
  11. Kao, M.-H., Stufken, J.: Optimal design for event-related fMRI studies. In: Dean, A., Morris M., Stufken, J., Bingham, D. (eds.) Handbook of Design and Analysis of Experiments, pp. 895–924 CRC Press, Boca Raton (2015)Google Scholar
  12. Kao, M.-H., Mandal, A., Lazar, N., Stufken, J.: Multi-objective optimal experimental designs for event-related fMRI studies. NeuroImage 44(3), 849–856 (2009)CrossRefGoogle Scholar
  13. Kao, M.-H., Mandal, A., Stufken, J.: Constrained multi-objective designs for functional MRI experiments via a modified nondominated sorting genetic algorithm. J. R. Stat. Soc. Ser. C (Appl. Stat.) 61(4), 515–534 (2012)Google Scholar
  14. Kao, M.-H., Majumdar, D., Mandal, A., Stufken, J.: Maximin and maximin-efficient event-related fMRI designs under a nonlinear model. Ann. Appl. Stat. 7(4), 1940–1959 (2013)MathSciNetCrossRefGoogle Scholar
  15. Kiefer, J.: Optimum experimental designs. J. R. Stat. Soc. Ser. B (Methodol.) 21(2), 272–319 (1959)MathSciNetzbMATHGoogle Scholar
  16. Liu, T.T.: Efficiency, power, and entropy in event-related fMRI with multiple trial types: part II: design of experiments. NeuroImage 21(1), 401–413 (2004)CrossRefGoogle Scholar
  17. Liu, T.T., Frank, L.R.: Efficiency, power, and entropy in event-related fMRI with multiple trial types: part I: theory. NeuroImage 21(1), 387–400 (2004)CrossRefGoogle Scholar
  18. Maus, B., van Breukelen, G.J.P., Goebel, R., Berger, M.P.F.: Robustness of optimal design of fMRI experiments with application of a genetic algorithm. Neuroimage 49(3), 2433–2443 (2010)CrossRefGoogle Scholar
  19. Niederreiter, H.: Low-discrepancy and low-dispersion sequences. J. Number Theory 30(1), 51–70 (1988)MathSciNetCrossRefGoogle Scholar
  20. Proulx, S., Safi-Harb, M., Levan, P., An, D., Watanabe, S., Gotman, J.: Increased sensitivity of fast bold fMRI with a subject-specific hemodynamic response function and application to epilepsy. NeuroImage 93(1), 59–73 (2014)CrossRefGoogle Scholar
  21. Saleh, M., Kao, M.-H., Pan, R.: Design D-optimal event-related functional magnetic resonance imaging experiments. J. R. Stat. Soc. Ser. C (Appl. Stat.) 66(1), 73–91 (2017)CrossRefGoogle Scholar
  22. Santner, T.J., Williams, B.J., Notz, W.: The Design and Analysis of Computer Experiments. Springer, New York (2003)CrossRefGoogle Scholar
  23. Scholkmann, F., Kleiser, S., Metz, A.J., Zimmermann, R., Mata Pavia, J., Wolf, U., Wolf, M.: A review on continuous wave functional near-infrared spectroscopy and imaging instrumentation and methodology. NeuroImage 85, Part 1(0), 6–27 (2014)CrossRefGoogle Scholar
  24. Wager, T.D., Nichols, T.E.: Optimization of experimental design in fMRI: a general framework using a genetic algorithm. NeuroImage 18(2), 293–309 (2003)CrossRefGoogle Scholar
  25. Worsley, K.J., Liao, C.H., Aston, J., Petre, V., Duncan, G.H., Morales, F., Evans, A.C.: A general statistical analysis for fMRI data. NeuroImage 15(1), 1–15 (2002)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of Mathematical and Statistical SciencesArizona State UniversityTempeUSA

Personalised recommendations