This article presents a dynamic model that quantifies the temporal evolution of the concentration and oxygen saturation of hemoglobin in tissue, as determined by time-varying hemodynamic and metabolic parameters: blood volume, flow velocity, and oxygen consumption. This multi-compartment model determines separate contributions from arterioles, capillaries, and venules that comprise the tissue microvasculature, and treats them as a complete network, without making assumptions on the details of the architecture and morphology of the microvascular bed. A key parameter in the model is the effective blood transit time through the capillaries and its associated probability of oxygen release from hemoglobin to tissue, as described by a rate constant for oxygen diffusion. The solution of the model in the time domain predicts the signals measured by hemodynamic-based neuroimaging techniques such as functional near-infrared spectroscopy (fNIRS) and functional magnetic resonance imaging (fMRI) in response to brain activation. In the frequency domain, the model yields an analytical solution based on a phasor representation that provides a framework for quantitative spectroscopy of coherent hemodynamic oscillations. I term this novel technique coherent hemodynamics spectroscopy (CHS), and this article describes how it can be used for the assessment of cerebral autoregulation and the study of hemodynamic oscillations resulting from a variety of periodic physiological challenges, brain activation protocols, or physical maneuvers.
Keywords: Functional magnetic resonance imaging; Hemodynamic model; Hemoglobin concentration; Near-infrared spectroscopy; Phasor; Transfer function analysis.
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