Functional magnetic resonance imaging (fMRI) data analysis has been carried out recently in the framework of information theory, by means of the Shannon entropy. As a natural extension, a method based on the generalized Tsallis entropy was developed to the analysis event-related (ER-fMRI), where a brief stimulus is presented, followed by a long period of rest. The new technique aims for spatial localization neuronal activity due to a specific task. This method does not require a priori hypothesis of the hemodynamic response function (HRF) shape and the linear relation between BOLD responses with the presented task. Numerical simulations were performed so as to determine the optimal values of the Tsallis q parameter and the number of levels, L. In order to avoid undesirable divergences of the Tsallis entropy, only positive q values were studied. Results from simulated data (with L = 3) indicated that, for q = 0.8, the active brain areas are detected with the highest performance. Moreover, the method was tested for an in vivo experiment and demonstrated the ability to discriminate active brain regions that selectively responded to a bilateral motor task.
The Kullback-Leibler distance (or relative entropy) is applied in the analysis of functional magnetic resonance (fMRI) data series. Our study is designed for event-related (ER) experiments, where a brief stimulus is presented and a long period of rest is followed. In particular, this relative entropy is used as a measure of the "distance" between the probability distributions p 1 and p 2 of the signal levels related to stimulus and non-stimulus. In order to avoid undesirable divergences of the Kullback-Leibler distance, a small positive parameter δ is introduced in the definition of the probability functions in such a way that it does not bias the comparison between both distributions. Numerical simulations are performed so as to determine the probability densities of the mean Kullback-Leibler distance D (throughout the N epochs of the whole experiment). For small values of N (N < 30), such probability densities f (D) are found to be fitted very well by Gamma distributions (χ 2 < 0.0009). The sensitivity and specificity of the method are evaluated by construction of the receiver operating characteristic (ROC) curves for some values of signal-to-noise ratio (SNR). The functional maps corresponding to real data series from an asymptomatic volunteer submitted to an ER motor stimulus is obtained by using the proposed technique. The maps present activation in primary and secondary motor brain areas. Both simulated and real data analyses indicate that the relative entropy can be useful for fMRI analysis in the information measure scenario.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.