Coupling of neural activation to blood flow in the somatosensory cortex of rats is time-intensity separable, but not linear

Changes in cerebral blood flow (CBF) because of functional activation are used as a surrogate for neural activity in many functional neuroimaging studies. In these studies, it is often assumed that the CBF response is a linear-time invariant (LTI) transform of the underlying neural activity. By using a previously developed animal model system of electrical forepaw stimulation in rats (n = 11), laser Doppler measurements of CBF, and somatosensory evoked potentials, measurements of neural activity were obtained when the stimulus duration and intensity were separately varied. These two sets of time series data were used to assess the LTI assumption. The CBF data were modeled as a transform of neural activity (N₁-P₂ amplitude of the somatosensory evoked potential) by using first-order (linear) and second-order (nonlinear) components. Although a pure LTI model explained a large amount of the variance in the data for changes in stimulus duration, our results demonstrated that the second-order kernel (i.e., a nonlinear component) contributed an explanatory component that is both statistically significant and appreciable in magnitude. For variations in stimulus intensity, a pure LTI model explained almost all of the variance in the CBF data. In particular, the shape of the CBF response did not depend on intensity of neural activity when duration was held constant (time-intensity separability). These results have important implications for the analysis and interpretation of neuroimaging data.