Quantitative relations between BOLD responses, cortical energetics, and impulse firing

The blood oxygen level-dependent (BOLD) functional magnetic resonance imaging signal arises as a consequence of changes in blood flow and oxygen usage 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 nonzero baseline activity in a completely consistent way and is thus able to account for both sustained 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 positive BOLD signal arising from deeper cortical laminae in response to an increase in neural firing is shown to arise as a consequence of the larger baseline activity in deeper laminae. Finally, we provide quantitative relations integrating BOLD responses, energetics, and impulse firing, which among other predictions give the same results as existing theories when the baseline activity is zero. NEW & NOTEWORTHY We use a recently established relation between energetics and neural activity to give a quantitative account of BOLD dependence on neural activity. The incorporation of a nonzero baseline neural activity accounts for positive and negative BOLD signals, shows that changes in neural activity give BOLD changes that are smaller the larger the baseline, and provides a basis for the observed inverse relation between BOLD responses and the depth of cortical laminae giving rise to them.