fMRI Signal Analysis Using Empirical Mean Curve Decomposition Fan Deng Computer Science Department The University of Georgia Introduction fMRI time series is non-linear, non-stationary and is composed of components at multiple temporal scales, which presents significant challenges to its analysis. In the literature, significant effort has been devoted into model-based fMRI signal analysis, while much less attention has been directed to data- driven fMRI signal analysis. In this work we present a novel data-driven multi- scale signal decomposition framework named Empirical Mean Curve Decomposition (EMCD). Targeted on functional brain mapping, EMCD iteratively extracts and optimizes mean envelope components from fMRI signals. The EMCD framework was applied to infer meaningful low-frequency information from BOLD signals from resting state fMRI, task-based fMRI, and natural stimulus fMRI. Background /Related Work The characteristics of non-linear, non-stationary, and composition of components at multiple scales of fMRI signals are challenging to traditional methods include Generalized Linear Models, wavelet algorithms, Markov Random Field models, mixture models, and autoregressive spatial models. The complex intrinsic structures of fMRI signals lay down the fundamental need for data-driven multi-scale decomposition methods. Empirical mode decomposition (EMD) has been recognized as an effective data-driven decomposition approach. Despite its superiority over model-based methods, however, EMD suffers from its finer-to-coarser extraction strategy and its constraints brought by the intrinsic mode functions which limits its applications in fMRI signal analysis. Approach The algorithm decomposes a time series in a multi-scale, data-driven manner. Briefly, the maxima (2) and minima (3) are extracted from the input time series(1). They are optimized (4, 5) by a local scale control algorithm and are interpolated to form superior envelope (6) and inferior envelope (7), respectively. The local scale control algorithm moderately controls the scale to which the time series is decomposed. The mean curve (8) as the output is calculated by averaging both envelopes. This decomposition algorithm is iteratively applied to the input time series (first iteration) and the residues (subsequent iterations). Discussion We presented a novel fMRI signal decomposition algorithm which iteratively extracts the mean curves of time series signals. EMCD extracts coarser-to-finer scale signals, in comparison to EMD which extracts finer-to-coarser scale signals. Our experimental results demonstrate that the extracted low-frequency mean envelope signals by our EMCD method are more meaningful and useful than the residue curves. The applications of EMCD in resting state, task-based, and natural stimulus fMRI data have shown interesting results. Our future work will be more extensive evaluation of this EMCD framework and further comparisons of EMCD and other fMRI signal processing approaches. Acknowledgments Thanks to Author’s advisor: Tianming Liu Collaborators: Kaiming Li, Dajiang Zhu, Xi Jiang, Hanbo Chen, Degang Zhang NIH NIBIB Career Award EB Computer Science Department, The University of Georgia the mode of a time series as the number of complete cycles (a maximum- minimum couple). Comparisons of concepts between EWF and Fourier Analysis are listed in the table below: The main goal of EMCD is to decompose the time series at different scale levels, yielding a composition of riding-wave-free components which are called pure empirical wave forms (EWFs). (EWFs). These EWFs are modeled by a series of alternating maxima and minima only. Define ConceptEmpirical Wave FormFourier Analysis Formx[n], max i, min j y[n], sin(wn) PeriodN/M(x[n])2π/w FrequencyM(x[n])/Nw/2π A full decomposition example of resting state fMRI time series EMCD naturally forms band-pass filters in resting state fMRI data EMCD on task- based fMRI data. The first component resembles the intrinsic BOLD model well. Multimedia feature component extracted from feature series of very high sampling rate. in which M(x[n]) is the mode of the time series, and N is the number of time points. The algorithm controls the local scale of the extrema. By local scale we refer to the period length of a certain cycle. Furthermore, as cycles are determined by extrema, we control the local scale by inserting extrema time points, since the extracted extrema are data-dependent and are not to be modified. Basically, the local scale controls how much alike we want the extracted mean curve and the input time series to be. More details are covered in the author’s submissions to IPMI 2011 and TMI. A pilot result on visual motion saliency features (left), from which we can see that much stronger correlation appears in some brain regions for motion perception including right middle temporal (MT) region and left middle superior temporal (MST) region (black arrows), when we compared the EMCD C1 components of fMRI BOLD signals and the visual saliency feature curve. As a comparison, we calculated Pearson correlation as well and it turns out that most correlation values are close to zero, indicating that Pearson correlation is unable to infer meaningful information. Interestingly, our EMCD-based method shows strong anti-correlation between the visual saliency feature and the fMRI signals of the insular and precuneus regions (red arrows), while Pearson correlation does not. The validity of our results on anti-correlation of insular and precuneus regions is strongly supported by a variety of literature studies that reported the deactivation of vestibular cortex (including insular and precuneus regions) in response to visual motion.