Abstract
Blocked designs in functional magnetic resonance imaging (fMRI) are useful to localize functional brain areas. A blocked design consists of different blocks of trials of the same stimulus type and is characterized by three factors: the length of blocks, i.e., number of trials per blocks, the ordering of task and rest blocks, and the time between trials within one block. Optimal design theory was applied to find the optimal combination of these three design factors. Furthermore, different error structures were used within a general linear model for the analysis of fMRI data, and the maximin criterion was applied to find designs which are robust against misspecification of model parameters.
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Aguirre, G.K., & D’Esposito, M. (1999). Experimental design for brain fMRI. In C.T.W. Moonen, & P.A. Bandettini (Eds.), Functional MRI (pp. 369–380). Berlin: Springer.
Atkinson, A.C., & Donev, A.N. (1996). Optimum experimental designs. Oxford: Clarendon.
Berger, M.P.F., & Tan, F.E.S. (2004). Robust designs for linear mixed effects model. Applied Statistics, 53(4), 569–581.
Binder, J.R., Rao, S.M., Hammeke, T.A., Frost, J.A., Bandettini, P.A., & Hyde, J.S. (1994). Effects of stimulus rate on signal response during functional magnetic resonance imaging of auditory cortex. Cognitive Brain Research, 2, 31–38.
Birn, R.M., Cox, R.W., & Bandettini, P.A. (2002). Detection versus estimation in event-related fMRI: choosing the optimal stimulus timing. NeuroImage, 15, 252–264.
Boynton, G.M., Engel, S.A., Glover, G.H., & Heeger, D.J. (1996). Linear systems analysis of functional magnetic resonance imaging in human V1. The Journal of Neuroscience, 16(13), 4207–4221.
Buckner, R.L., Bandettini, P.A., O’Craven, K.M., Savoy, R.L., Petersen, S.E., Raichle, M.E., & Rosen, B.R. (1996). Detection of cortical activation during averaged single trials of a cognitive task using functional magnetic resonance imaging. Proceedings of the National Academy of Sciences of the United States of America, 93, 14878–14883.
Bullmore, E., Brammer, M., Williams, S.C.R., Rabe-Hesketh, S., Janot, N., David, A., Mellers, J., Howard, R., & Sham, P. (1996). Statistical methods of estimation and inference for functional MR image analysis. Magnetic Resonance in Medicine, 35, 261–277.
Buračas, G.T., & Boynton, G.M. (2002). Efficient design of event-related fMRI experiments using M-sequences. NeuroImage, 16, 801–813.
Burock, M.A., & Dale, A.M. (2000). Estimation and detection of event-related fMRI signals with temporally correlated noise: a statistically efficient and unbiased approach. Human Brain Mapping, 11, 249–260.
Chaloner, K., & Verdinelli, I. (1995). Bayesian experimental design: a review. Statistical Science, 10(3), 273–304.
Chatfield, C. (2003). The Analysis of Time Series: An Introduction (6th ed.). London/Boca Raton: Chapman and Hall/CRC Press.
Chein, J.M., & Schneider, W. (2003). Designing effective fMRI experiments. In J. Grafman, & I. Robertson (Eds.), The handbook of neuropsychology. Amsterdam: Elsevier.
Cohen, M.S. (1997). Parametric analysis of fMRI data using linear systems methods. NeuroImage, 6, 93–103.
Conlisk, J., & Watts, H. (1979). A model for optimizing experimental designs for estimating response surfaces. Journal of Econometrics, 11, 27–42.
Culham, J.C. (2006). Functional neuroimaging: Experimental design and analysis. In R. Cabeza, & A. Kingstone (Eds.), Handbook of functional neuroimaging of cognition (pp. 53–82). Cambridge: MIT Press.
Dale, A.M. (1999). Optimal experimental design for event-related fMRI. Human Brain Mapping, 8, 109–114.
Dale, A.M., & Buckner, R.L. (1997). Selective averaging of rapidly presented individual trials using fMRI. Human Brain Mapping, 5, 329–340.
Dette, H., Martinez Lopez, I., Ortiz Rodriguez, I.M., & Pepelyshev, A. (2006). Maximin efficient design of experiment for exponential regression models. Journal of Statistical Planning and Inference, 136, 4397–4418.
Di Salle, F., Formisano, E., Linden, D.E.J., Goebel, R., Bonavita, S., Pepino, A., Smaltino, F., & Tedeschi, G. (1999). Exploring brain function with magnetic resonance imaging. European Journal of Radiology, 30, 84–94.
Donaldson, D.I., & Buckner, R.L. (2001). Effective paradigm design. In P. Jezzard, P.M. Matthews, & S.M. Smith (Eds.), Functional MRI: an introduction to methods (pp. 177–196). Oxford: Oxford University Press.
Flaherty, P., Jordan, M.I., & Arkin, A.P. (2006). Robust design of biological experiments. In Y. Weiss, B. Schölkopf, & J. Platt (Eds.), Advances in neural information processing systems (Vol. 18, pp. 363–370). Cambridge: MIT Press.
Formisano, E., Esposito, F., Di Salle, F., & Goebel, R. (2004). Cortex-based independent component analysis of fMRI time series. Magnetic Resonance Imaging, 22, 1493–1504.
Friston, K.J., Fletcher, P., Josephs, O., Holmes, A., Rugg, M.D., & Turner, R. (1998). Event-related fMRI: characterizing differential responses. NeuroImage, 7, 30–40.
Friston, K.J., Holmes, A.P., Poline, J.-B., Grasby, P.J., Williams, S.C.R., Frackowiak, R.S.J., & Turner, R. (1995). Analysis of fMRI time-series revisited. NeuroImage, 2, 45–53.
Friston, K.J., Jezzard, P., & Turner, R. (1994). Analysis of functional MRI time-series. Human Brain Mapping, 1, 153–171.
Friston, K.J., Zarahn, E., Josephs, O., Henson, R.N.A., & Dale, A.M. (1999). Stochastic designs in event-related fMRI. NeuroImage, 10, 607–619.
Gautama, T., & Van Hulle, M.M. (2005). Estimating the global order of the fMRI noise model. NeuroImage, 26, 1211–1217.
Goebel, R., Muckli, L., Zanella, F.E., Singer, W., & Stoerig, P. (2001). Sustained extrastriate cortical activation without visual awareness revealed by fMRI studies of hemianopic patients. Vision Research, 41, 1459–1474.
Hagberg, G.E., Zito, G., Patria, F., & Sanes, J.N. (2001). Improved detection of event-related functional MRI signals using probability functions. NeuroImage, 14, 1193–1205.
Heckman, G.M., Bouvier, S.E., Carr, V.A., Harley, E.M., Cardinal, K.S., & Engel, S.A. (2007). Nonlinearities in rapid event-related fMRI explained by stimulus scaling. NeuroImage, 34, 651–660.
Henson, R.N.A. (2004). Analysis of fMRI time series. In R.S.J. Frackowiak, K.J. Friston, C.D. Frith, R.J. Dolan, C.J. Price, S. Zeki, J. Ashburner, & W. Penny (Eds.), Human brain function (pp. 793–822). Amsterdam: Elsevier.
Honey, G.D., & Bullmore, E.T. (2002). Functional neuroimaging and schizophrenia. Psychiatry, 1, 26–29.
Huettel, S.A., & McCarthy, G. (2000). Evidence for a refractory period in the hemodynamic response to visual stimuli as measured by MRI. NeuroImage, 11, 547–553.
Josephs, O., & Henson, R.N.A. (1999). Event-related functional magnetic resonance imaging: modelling, inference and optimization. Philosophical Transactions of the Royal Society B, 354, 1215–1228.
Kao, M.-H., Mandal, A., Lazar, N., & Stufken, J. (2009). Multi-objective optimal experimental designs for event-related fMRI studies. NeuroImage, 44, 849–856.
Liu, T.T. (2004). Efficiency, power and entropy in event-related fMRI with multiple trial types, part II: design of experiments. Neuroimage, 21, 401–413.
Liu, T.T., & Frank, L.R. (2004). Efficiency, power, and entropy in event-related fMRI with multiple trial types, part I: theory. NeuroImage, 21, 387–400.
Liu, T.T., Frank, L.R., Wong, E.C., & Buxton, R.B. (2001). Detection power, estimation efficiency, and predictability in event-related fMRI. NeuroImage, 13, 759–773.
Logothetis, N.K., & Wandell, B.A. (2004). Interpreting the BOLD signal. Annual Review of Physiology, 66, 735–769.
Maus, B., van Breukelen, G.J.P., Goebel, R., & Berger, M.P.F. (2010). Robustness of optimal design of fMRI experiments with application of a genetic algorithm. NeuroImage, 49, 2433–2443.
Miezin, F.M., Maccotta, L., Ollinger, J.M., Petersen, S.E., & Buckner, R.L. (2000). Characterizing the hemodynamic response: effects of presentation rate, sampling procedure, and the possibility of ordering brain activity based on relative timing. NeuroImage, 11, 735–759.
Mohamed, F.B., Tracy, J.I., Faro, S.H., Emperado, J., Koenigsberg, R., Pinus, A., & Tsai, F.Y. (2000). Investigation of alternating and continuous experimental task designs during single finger opposition fMRI: a comparative study. Journal of Computer Assisted Tomography, 24(6), 935–941.
Nakai, T., Matsumura, A., Nose, T., Kato, C., Glover, G.H., & Matsuo, K. (2003). The effect of task block arrangement on the detectability of activation in fMRI. Magnetic Resonance Imaging, 21, 941–947.
Ouwens, M.J.N.M., Tan, F.E.S., & Berger, M.P.F. (2002). Maximin D-optimal designs for longitudinal mixed effects model. Biometrics, 58, 735–741.
Owen, A.M., Epstein, R., & Johnsrude, I.S. (2003). fMRI: applications to cognitive neuroscience. In P. Jezzard, P.M. Matthews, & S.M. Smith (Eds.), Functional MRI: an introduction to methods (pp. 311–327). Oxford: Oxford University Press.
Pollmann, S., Wiggins, C.J., Norris, D.G., von Cramon, D.Y., & Schubert, T. (1998). Use of short intertrial intervals in single-trial experiments: a 3T fMRI-study. Neuroimage, 8, 327–339.
Pronzato, L., & Walter, E. (1988). Robust experimental design via maximin optimization. Mathematical Biosciences, 89, 161–176.
Purdon, P.L., & Weisskoff, R.M. (1998). Effect of temporal autocorrelation due to physiological noise and stimulus paradigm on voxel-level false-positive rates in fMRI. Human Brain Mapping, 6, 239–249.
Rosen, B.R., Buckner, R.L., & Dale, A.M. (1998). Event-related functional MRI: past, present and future. Proceedings of the National Academy of Sciences, 95, 773–780.
Silvey, S. (1980). Optimal design. London: Chapman & Hall.
Sim, R., & Roy, N. (2005). Global A-optimal robot exploration in SLAM. In Proceedings of the IEEE/RSJ international conference of robotics and automation (ICRA 2005) (pp. 661–666).
Skudlarski, P., Constable, R.T., & Gore, J.C. (1999). ROC analysis of statistical methods used in functional MRI: individual subjects. NeuroImage, 9, 311–329.
Smith, S., Jenkinson, M., Beckmann, C., Miller, K., & Woolrich, M. (2007). Meaningful design and contrast estimability in FMRI. NeuroImage, 34, 127–136.
Wager, T.D., & Nichols, T.E. (2003). Optimization of experimental design in fMRI: a general framework using a genetic algorithm. NeuroImage, 18, 293–309.
Wager, T.D., Vazquez, A., Hernandez, L., & Noll, D.C. (2005). Accounting for nonlinear BOLD effects in fMRI: parameter estimates and a model for prediction in rapid event-related studies. NeuroImage, 25, 206–218.
Worsley, K.J. (2005). Spatial smoothing of autocorrelations to control the degrees of freedom in fMRI analysis. NeuroImage, 26, 635–641.
Worsley, K.J., & Friston, K.J. (1995). Analysis of fMRI time-series revisited-again. NeuroImage, 2, 173–181.
Wüstenberg, T., Giesel, F.L., & Strasburger, H. (2005). Methodische Grundlagen der Optimierung funktioneller MR-Experimente. Radiologe, 45, 99–112.
Zarahn, E., & Friston, K.J. (2002). Some limit results for efficiency in stochastic fMRI designs. Biometrical Journal, 44, 496–509.
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Maus, B., van Breukelen, G.J.P., Goebel, R. et al. Optimization of Blocked Designs in fMRI Studies. Psychometrika 75, 373–390 (2010). https://doi.org/10.1007/s11336-010-9159-3
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DOI: https://doi.org/10.1007/s11336-010-9159-3