Systems analysis of functional magnetic resonance imaging data using a physiologic model of venous oxygenation

The authors revisit a simple mathematical model, presented in previous work, that characterizes the response of cerebral venous oxygenation to changes in blood flow and oxygen consumption. This physiologically based model can qualitatively duplicate the results of several recent empirical studies in which other authors have tested the hypothesis of linearity in the functional magnetic resonance imaging (fMRI) response to task activation, in that the experimentally found nearly linear behavior of the system and also its subtle departures from linearity are both predicted by simulations of the model. The model is simple enough that its equations can be explicitly solved. Moreover, an amended model that incorporates a varying cerebral blood volume parameter is found to have similar if not better consistency with the empirical data; indeed, this "extended" model is shown to be solvable by the same differential equation as the authors' simple one, wherein the volume is fixed as a constant. These investigations lend further indirect support to the blood oxygen level-dependent hypothesis of venous deoxyhemoglobin as the primary mechanism for fMRI signal changes during task activation, as well as for the authors' simple system as a useful physiologic model thereof. Although the authors' mathematical model does not formally represent a linear system with respect to the flow input, its underlying linear character may help partially explain the "nearly" linear behavior of the fMRI response.