Quantitative relations between BOLD responses, cortical energetics and impulse firing

The blood oxygen level dependent (BOLD) functional magnetic resonance imaging (fMRI) signal arises as a consequence of changes in blood flow (CBF) and oxygen usage (CMR$_{O_2}$) that in turn are modulated by changes in neural activity. Much attention has been given to both theoretical and experimental aspects of the energetics but not to the neural activity. Here we identify the best energetic theory for the steady-state BOLD signal on the basis of correct predictions of experimental observations. This theory is then used, together with the recently determined relationship between energetics and neural activity, to predict how the BOLD signal changes with activity. Unlike existing treatments, this new theory incorporates a non-zero baseline activity in a completely consistent way, and is thus able to account for both positive and negative BOLD signals. We also show that the increase in BOLD signal for a given increase in activity is significantly smaller the larger the baseline activity, as is experimentally observed. Furthermore, the decline of the BOLD signal arising from deeper cortical lamina in response to an increase in neural firing is shown to arise as a consequence of the larger baseline activity in deeper lamina. Finally, we provide quantitative relations integrating BOLD responses, energetics and impulse firing, which amongst other predictions, provides the same results as existing theories when the baseline activity is zero.

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