Signal nonlinearity in fMRI: a comparison between BOLD and MION

In this paper, we introduce a methodology for comparing the nonlinearities present in sets of time series using four different nonlinearity measures, one of which, the "delay vector variance" method, is a novel approach to the characterization of a time series. It is then applied to examine the difference in nonlinearity between functional magnetic resonance imaging (fMRI) signals that have been recorded using different contrast agents. Recently, an exogenous contrast agent, monocrystalline iron oxide particle (MION), has been introduced for fMRI, which has been shown to increase the functional sensitivity compared with the traditional blood oxygen level dependent (BOLD) technique. The resulting fMRI signals are influenced by cerebral blood volume, whereas the more traditionally recorded BOLD signals are influenced not only by cerebral blood volume, but also by the cerebral blood flow and the metabolic rate of oxygen. The proposed methodology is applied to address the question whether this difference in the number of physiological variables is reflected in a difference in the degree of nonlinearity. We therefore analyze two sets of fMRI signals, one from a BOLD and the other from a MION monkey study with similar experimental designs. In the neuroimaging context, the proposed nonlinearity analyses are different from those described in the literature, since no a priori model is assumed: rather than pinpointing the source(s) of nonlinearity, nonparametric analyses are performed on BOLD and MION fMRI signals. Furthermore, we introduce a strategy for analyzing a population of fMRI signals, rather than focusing the analysis on one signal, as is traditionally done in the domain of nonlinear signal processing. Our results show that, overall, the BOLD signals are more nonlinear in nature than the MION ones, which is in agreement with current hypotheses.