24 April 2002 Simple mathematical model for functional magnetic resonance imaging data
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The objective of this study is to introduce a simple mathematical model for the brain image under both resting and activated states to facilitate both the understanding of the underlying neurophysiology and the realization of data sets. Two data sets were composed to simulate fMRI data. First set consists of a small spot that simulates the activated region superimposed on real baseline data. To simulate the signal enhancement, the hemodynamic response vector multiplies all pixels in the activated spot. Therefore, the resultant spots were added sequentially to the baseline images to create the first data set. The second set was formed by using the proposed model. The model took into account both random and physiological noise that are found in fMRI data. The random noise was assumed to vary from one frame to another while the physiological pattern was assumed of similar pattern throughout the brain with smooth spatial variations. A threshold cross-correlation technique was used on both data sets to compare the resultant activation maps. A falsehood measure was proposed and used as to test the accuracy of the activation detection. Finally, the results between the two data sets are compared to demonstrate the accuracy of the model.
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Bassem K. Ouda, Bassem K. Ouda, Bassel S. Tawfik, Bassel S. Tawfik, Abou-Bakr M. Youssef, Abou-Bakr M. Youssef, } "Simple mathematical model for functional magnetic resonance imaging data", Proc. SPIE 4683, Medical Imaging 2002: Physiology and Function from Multidimensional Images, (24 April 2002); doi: 10.1117/12.463605; https://doi.org/10.1117/12.463605

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