Goodness of Fit to the Convolution Model of fMRI Data and Determination of the Regularization Parameter

In the analysis of fMRI data, the time when the event of interest occurred in the experiment is usually used for analysis. However, in recent years, measurement of fMRI data which is not necessarily related to a certain simple event, such as measurement in resting state, is often performed. In this paper, we propose a method to analyze fMRI data without using time when events of interest occurred. In the proposed method, we fit a generation model of convolution form to fMRI data and obtain values of goodness of fit to the generation model. If the goodness of fit is sufficiently large for data from a voxel, the data can be considered to include a time course from neural activities. We suggest that this goodness of fit can be used to know whether the MR time series from a certain voxel contains a signal induced by neural activities or not. We propose a method to decide the value of the regularization parameter of the generation model using difference between data from voxels in gray matter and white matter. We compare the analysis result using the measure we proposed, the result by the fractional amplitude of low-frequency fluctuation (fALFF) and the result by generalized linear model using time course of events in the experiment. To evaluate analysis methods, we analyzed event related fMRI data. Both the index we proposed and the fALFF measure were similar to the result of analysis with generalized linear model, that is, usual analysis of variance. However, the measure we proposed showed higher correlation coefficient because of constant linear relation including range with large neural activities.