A dynamical model of the laminar BOLD response

High-resolution functional magnetic resonance imaging (fMRI) using blood oxygenation dependent level-dependent (BOLD) signal is an increasingly popular tool to non-invasively examine neuronal processes at the mesoscopic level. However, as the BOLD signal stems from hemodynamic changes, its temporal and spatial properties do not match those of the underlying neuronal activity. In particular, the laminar BOLD response (LBR), commonly measured with gradient-echo (GE) MRI sequence, is confounded by non-local changes in deoxygenated hemoglobin and cerebral blood volume propagated within intracortical ascending veins, leading to unidirectional blurring of the neuronal activity distribution towards the cortical surface. Here, we present a new cortical depth-dependent model of the BOLD response based on principle of mass conservation, which takes the effect of ascending (and pial) veins on the cortical BOLD responses explicitly into account. It can be used to model cortical depth-dependence of BOLD signal amplitudes during steady state, and to model the dependencies of transient features (i.e. early-overshoot, post-stimulus undershoot or initial dip) on various baseline and activity-related physiological parameters for any spatiotemporal distribution of neuronal changes. We demonstrate that the commonly-observed spatial increase of LBR is mainly due to baseline blood volume increase towards the surface. In contrast, an occasionally observed local maximum in the LBR (i.e. the so-called “bump”) is mainly due to spatially inhomogeneous neuronal changes rather than locally higher baseline blood volume. In addition, we show that the GE-BOLD signal laminar point-spread functions, representing the signal leakage towards the surface, depend on several physiological parameters and on the level of neuronal activity. Furthermore, even in the case of simultaneous neuronal changes at each depth, inter-laminar delays of LBR transients are present due to ascending vein. In summary, the model provides a conceptual framework for the biophysical interpretation of common experimental observations in high-resolution fMRI data. Finally, using Bayesian model inversion, the model will allow deconvolution of the spatiotemporal hemodynamic bias of the LBR and provide estimate of the underlying laminar excitatory and inhibitory neuronal activity.