In event-related (ER) BOLD-fMRI brain activation studies, understanding the relationship between the elicited BOLD signal and its underlying neuronal activity is essential for any quantitative interpretation of the neural events from the BOLD measurements. This requires a better understanding of the dynamic BOLD response. Besides the neuronal activity-induced positive BOLD response, the dynamic response is also characterized by a profound post-stimulus undershoot. The relationship between the positive response and the post-stimulus undershoot, however, remains poorly understood. Earlier studies using block-design paradigms with long stimulation durations (>10s) do not suggest a quantitative relationship. Using an ER paradigm, this study revealed a linear coupling between the positive BOLD response and the post-stimulus undershoot across the human visual cortex. The voxelwise linear coupling across the visual cortex strongly supports a homogeneous hemodynamic response in ER paradigms, though the BOLD response magnitude varies substantially over a wide range across the visual cortex. Although underlying neuronal activity is responsible for a BOLD response, the blood volume fraction affects the magnitude of the BOLD response; the larger the blood volume fraction, the larger the magnitude. This effect needs to be accounted for in any quantitative interpretation of the BOLD measurements. In the absence of nonlinear neuronal activities, the nonlinear vascular response renders the estimated BOLD responses smaller in rapid presentation (RP) ER paradigms compared to that in ER paradigms, and this reduction effect also needs to be considered when interpreting the estimated BOLD responses in RP-ER paradigms. Interestingly, this nonlinear effect might be simply accounted for by a scaling factor across the visual cortex.