# Signal Detection in Functional MRI

**Benali H. ^{1}, Kruggel F.^{2}, Pelegrini M.^{1}, Svensen M.^{3}**

*1 Faculte de Medicine Pitie-Salpetriere, 2 University of California, Irvine, 3 Max-Planck-Institute of Cognitive Neuroscience, Leipzig*

The detection of significantly activated areas is commonly achieved by applying a test statistic. A statistical parameter map (or z-score map) is calculated, which represents for each voxel the amount of correlation of the time-series data with a given stimulus function. Multiple linear regression has been adopted as the most sensitive and versatile approach here.

However, with increasing temporal resolution of recent scanning protocols and more elaborate data preprocessing schemes, data independence in space and time is no longer a valid assumption. Revising the statistical background of the linear regression in the presence of autocorrelations, an equation for correcting the effective number of degrees of freedom (DOF) was derived. The effective DOF was found to depend on the regressor matrix and on the correlation matrix of the residuals. The advantage of this interpretation is given by the fact that is data-driven, independent of any specific preprocessing method, and not linked to properties of a pre-defined smoothing matrix. For data from blocked designs, an AR(1) model was found as the most parsimonious model. For data from event-related experiments preprocessed by filters commonly applied for fMRI time-series, we proposed a "damped oscillator" function to model the correlation structure. Approximations were derived which avoid complex matrix calculations and dramatically reduced computation time. Efficient analytical expressions exist for both correlation models, so processing times were only slightly higher in comparison with the uncorrected linear regression method.

Left: Estimated autocorrelation coefficients (crosses), fitted autocorrelation functions (AR(1) model: dashed, damped oscillator model: continuous line) for a sample background voxel of a lowpass-filtered data set. Right: Two z-score maps, overlaid onto the corresponding anatomical slices, from an event-related fMRI experiment in language comprehension are shown. In the top row, z-scores were uncorrected, in the bottom row corrected by the correlation-based approach, using the "damped oscillator" function.

**Read more...**

Benali H., Pelegrini M., Kruggel F. (2001) **Spatio-Temporal Covariance Model for Medical Images Sequences: Application to Functional MRI Data.** In: Leahy R., Insana M. (eds.), *Information Processing in Medical Imaging 2001, Lecture Notes in Computer Science 2082, pp. 197-203.* Springer, Berlin.

Kruggel F., Pelegrini-Issac N., Benali H. (2002) **Estimating the Effective Degrees of Freedom in Univariate Multiple Regression Analysis.** *Medical Image Analysis 6, 63-75*.

Svensen M., Kruggel F., von Cramon D.Y. (2000) **ICA of fMRI Group Study Data.** In: Gedeon T., Wong P., Halgamuge S., Kasabov N., Nauck D., Fukushima K. (eds.), *7 ^{th} International Conference on Neural Information Processing (Taejon), pp. 88-93.*

Svensen M., Kruggel F., Benali H. (2002) **ICA of fMRI Group Study Data.** *NeuroImage 15, 551-563.*