Nonlinear Coupling between Evoked rCBF and BOLD Signals: A Simulation Study of Hemodynamic Responses

Abstract

The aim of this work was to investigate the dependence of BOLD responses on different patterns of stimulus input/neuronal changes. In an earlier report, we described an input-state-output model that combined (i) the Balloon/Windkessel model of nonlinear coupling between rCBF and BOLD signals, and (ii) a linear model of how regional flow changes with synaptic activity. In the present investigation, the input-state-output model was used to explore the dependence of simulated PET (rCBF) and fMRI (BOLD) signals on various parameters pertaining to experimental design. Biophysical simulations were used to estimate rCBF and BOLD responses as functions of (a) a prior stimulus, (b) epoch length (for a fixed SOA), (c) SOA (for a fixed number of events), and (d) stimulus amplitude. We also addressed the notion that a single neuronal response may differ, in terms of the relative contributions of early and late neural components, and investigated the effect of (e) the relative size of the late or “endogenous” neural component. We were interested in the estimated average rCBF and BOLD responses per stimulus or event, not in the statistical efficiency with which these responses are detected. The BOLD response was underestimated relative to rCBF with a preceding stimulus, increasing epoch length, and increasing SOA. Furthermore, the BOLD response showed some highly nonlinear behaviour when varying stimulus amplitude, suggesting some form of hemodynamic “rectification.” Finally, the BOLD response was underestimated in the context of large late neuronal components. The difference between rCBF and BOLD is attributed to the nonlinear transduction of rCBF to BOLD signal. Our simulations support the idea that varying parameters that specify the experimental design may have differential effects in PET and fMRI. Moreover, they show that fMRI can be asymmetric in its ability to detect deactivations relative to activations when an absolute baseline is stipulated. Finally, our simulations suggest that relative insensitivity to BOLD signal in specific regions, such as the temporal lobe, may be partly explained by higher cognitive functions eliciting a relatively large late endogenous neuronal component.