Optimal design of multi-subject blocked fMRI experiments

The design of a multi-subject fMRI experiment needs specification of the number of subjects and scanning time per subject. For example, for a blocked design with conditions A or B, fixed block length and block order ABN, where N denotes a null block, the optimal number of cycles of ABN and the optimal number of subjects have to be determined. This paper presents a method to determine the optimal number of subjects and optimal number of cycles for a blocked design based on the A-optimality criterion and a linear cost function by which the number of cycles and the number of subjects are restricted. Estimation of individual stimulus effects and estimation of contrasts between stimulus effects are both considered. The mixed-effects model is applied and analytical results for the A-optimal number of subjects and A-optimal number of cycles are obtained under the assumption of uncorrelated errors. For correlated errors with a first-order autoregressive (AR1) error structure, numerical results are presented. Our results show how the optimal number of cycles and subjects depend on the within- to between-subject variance ratio. Our method is a new approach to determine the optimal scanning time and optimal number of subjects for a multi-subject fMRI experiment. In contrast to previous results based on power analyses, the optimal number of cycles and subjects can be described analytically and costs are considered.

[1]  Kevin Murphy,et al.  An empirical investigation into the number of subjects required for an event-related fMRI study , 2004, NeuroImage.

[2]  Ming-Hung Kao,et al.  Multi-Objective Optimal Experimental Designs for ER-fMRI Using MATLAB , 2009 .

[3]  Mark W. Woolrich,et al.  Advances in functional and structural MR image analysis and implementation as FSL , 2004, NeuroImage.

[4]  Toshiharu Nakai,et al.  The effect of task block arrangement on the detectability of activation in fMRI. , 2003, Magnetic resonance imaging.

[5]  R. Turner,et al.  Event-Related fMRI: Characterizing Differential Responses , 1998, NeuroImage.

[6]  Marc M. Van Hulle,et al.  Estimating the global order of the fMRI noise model , 2005, NeuroImage.

[7]  D. Harville.  Matrix Algebra From a Statistician's Perspective , 1998 .

[8]  Nikos K Logothetis,et al.  Interpreting the BOLD signal. , 2004, Annual review of physiology.

[9]  B Maus,et al.  Optimization of Blocked Designs in fMRI Studies , 2009, NeuroImage.

[10]  E. Bullmore,et al.  Statistical methods of estimation and inference for functional MR image analysis , 1996, Magnetic resonance in medicine.

[11]  Gary H Glover,et al.  Estimating sample size in functional MRI (fMRI) neuroimaging studies: Statistical power analyses , 2002, Journal of Neuroscience Methods.

[12]  Thomas T. Liu,et al.  Efficiency, power, and entropy in event-related FMRI with multiple trial types Part I: theory , 2004, NeuroImage.

[13]  R. Buxton,et al.  Detection Power, Estimation Efficiency, and Predictability in Event-Related fMRI , 2001, NeuroImage.

[14]  Karl J. Friston,et al.  Convolution Models for fMRI , 2007 .

[15]  M. Bianciardi,et al.  Evaluation of mixed effects in event-related fMRI studies: impact of first-level design and filtering , 2004, NeuroImage.

[16]  Thomas E. Nichols,et al.  Optimization of experimental design in fMRI: a general framework using a genetic algorithm , 2003, NeuroImage.

[17]  S. Faro,et al.  Investigation of Alternating and Continuous Experimental Task Designs During Single Finger Opposition fMRI: A Comparative Study , 2000, Journal of computer assisted tomography.

[18]  H. Schouten,et al.  Sample size formula with a continuous outcome for unequal group sizes and unequal variances. , 1999, Statistics in medicine.

[19]  Thomas E. Nichols,et al.  Power calculation for group fMRI studies accounting for arbitrary design and temporal autocorrelation , 2008, NeuroImage.

[20]  W. D. Penny,et al.  Random-Effects Analysis , 2002 .

[21]  Abhyuday Mandal,et al.  Multi-objective optimal experimental designs for event-related fMRI studies , 2009, NeuroImage.

[22]  A M Dale,et al.  Optimal experimental design for event‐related fMRI , 1999, Human brain mapping.

[23]  S. Hayasaka,et al.  Power and sample size calculation for neuroimaging studies by non-central random field theory , 2007, NeuroImage.

[24]  G. McCarthy,et al.  Evidence for a Refractory Period in the Hemodynamic Response to Visual Stimuli as Measured by MRI , 2000, NeuroImage.

[25]  Chris Chatfield,et al.  The Analysis of Time Series: An Introduction , 1981 .

[26]  Anthony C. Atkinson,et al.  Optimum Experimental Designs, with SAS , 2007 .

[27]  Karl J. Friston,et al.  Statistical parametric mapping , 2013 .

[28]  W. Penny,et al.  Random-Effects Analysis , 2002 .

[29]  Guillaume P. Dehaene,et al.  Functional segregation of cortical language areas by sentence repetition , 2006, Human brain mapping.

[30]  M. Lovell.  Seasonal Adjustment of Economic Time Series and Multiple Regression Analysis , 1963 .

[31]  R. Goebel,et al.  Exploring brain function with magnetic resonance imaging. , 1999, European journal of radiology.

[32]  Martijn P. F. Berger,et al.  Optimal Designs for Multilevel Studies , 2008 .

[33]  Karl J. Friston,et al.  Stochastic Designs in Event-Related fMRI , 1999, NeuroImage.

[34]  J.A. Mumford,et al.  Modeling and inference of multisubject fMRI data , 2006, IEEE Engineering in Medicine and Biology Magazine.

[35]  D. Heeger,et al.  Linear Systems Analysis of Functional Magnetic Resonance Imaging in Human V1 , 1996, The Journal of Neuroscience.

[36]  Peter A. Bandettini,et al.  Detection versus Estimation in Event-Related fMRI: Choosing the Optimal Stimulus Timing , 2002, NeuroImage.

[37]  Mark W. Woolrich,et al.  Bayesian analysis of neuroimaging data in FSL , 2009, NeuroImage.

[38]  M. D’Esposito,et al.  Experimental Design for Brain fMRI , 2000 .

[39]  M. Lindquist.  The Statistical Analysis of fMRI Data. , 2008, 0906.3662.

[40]  George A. F. Seber,et al.  Linear regression analysis , 1977 .

[41]  Rainer Goebel,et al.  Robustness of optimal design of fMRI experiments with application of a genetic algorithm , 2010, NeuroImage.

[42]  John Suckling,et al.  Components of variance in a multicentre functional MRI study and implications for calculation of statistical power , 2008, Human brain mapping.

[43]  Karl J. Friston,et al.  Human Brain Function , 1997 .

[44]  Harvey Goldstein,et al.  Handbook of multilevel analysis , 2008 .

[45]  Alan C. Evans,et al.  A general statistical analysis for fMRI data , 2000, NeuroImage.