Phasor representation of oxy- and deoxyhemoglobin concentrations: what is the meaning of out-of-phase oscillations as measured by near-infrared spectroscopy?

We propose a phasor representation for oscillations at a given frequency (or relatively narrow frequency band) of hemoglobin concentrations in tissue, as well as hemoglobin concentrations measured by near-infrared spectroscopy. This representation provides a straightforward visualization of the phase relationships between oscillations of oxy-, deoxy-, and total hemoglobin concentrations ([HbO], [Hb], and [HbT], respectively). We observe that measured oscillations of [Hb] and [HbO] with a phase difference that is neither 0 nor pi must result from the combination of different physiological processes that are out of phase (or time shifted) with respect to each other. Finally, we propose the use of cross-correlation phasors to map phase relationships and correlation levels among hemoglobin oscillations measured at spatially distinct locations at a given frequency. Such a representation may find a natural application in the study of functional connectivity networks in the brain.