A quantitative physiologic model of blood oxygenation for functional magnetic resonance imaging

Abstract

Rationale and objectives: Variations in venous deoxyhemoglobin levels in response to neuronal activation represent a complex interplay between focal changes in cerebral blood flow (CBF), cerebral blood volume (CBV), and regional metabolism. The authors present a mathematic model that characterizes the response of venous oxygenation to changes in these variables.

Methods: Using a mass balance approach, the equations for a simple input-output model are derived and solved using Matlab. Changes in blood oxygenation are related to available results from functional magnetic resonance imaging experiments.

Results: Increases in CBF produce declines in oxygen extraction fraction and venous deoxyhemoglobin according to Fick's law, and are quantitatively in agreement with available magnetic resonance and positron-emission tomography data. A flow-volume envelope defines the changes in CBF relative to CBV.

Conclusions: It is possible to obtain a quantitative understanding of changes in blood oxygenation and to relate these changes to the observed dynamics of magnetic resonance signal change in the setting of functional stimulation.