Hemodynamic Models

Richard Buxton
University of California at San Diego

Neural activity in the brain is accompanied by changes in cerebral blood flow (CBF) and
blood oxygenation that are detectable with functional magnetic resonance imaging
(fMRI) techniques. In this talk, recent mathematical models of this hemodynamic
response are reviewed and integrated. Models are described for: 1) the blood
oxygenation level dependent (BOLD) signal as a function of changes in cerebral oxygen
extraction fraction (E) and cerebral blood volume (CBV); 2) the balloon model, proposed
to describe the transient dynamics of CBV and deoxy-hemoglobin and how they affect
the BOLD signal; 3) neurovascular coupling, relating the responses in CBF and cerebral
metabolic rate of oxygen (CMRO2) to the neural activity response; and 4) a simple model
for the temporal nonlinearity of the neural response itself. These models are integrated
into a combined model for the steps linking a stimulus to the measured BOLD and CBF
responses. Experimental results examining transient features of the BOLD response
(post-stimulus undershoot and initial dip), nonlinearities of the hemodynamic response,
and the role of the physiologic baseline state in altering the BOLD signal are discussed
in the context of the proposed models. Quantitative modeling of the hemodynamic
response, when combined with experimental data measuring both the BOLD and CBF
responses, makes possible a more specific and quantitative assessment of brain
physiology than is possible with standard BOLD imaging alone. This approach has the
potential to enhance numerous studies of brain function in development, health and

Acknowledgements: The author is supported by NIH grants NS-36722 and NS-042069.

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