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Hemodynamic Balloon Model

Buxton, R.B., Uludağ, K., Dubowitz, D.J., Liu, T.T. (2004). Modeling the hemodynamic response to brain activation. NeuroImage 23, S220–S233. doi:10.1016/j.neuroimage.2004.07.013

The causal chain of the paper's Fig. 1, from stimulus to measured BOLD signal. Every step is drawn with its equation and the 1–2 parameters (Table 1 notation) that shape it. The right-hand panel recreates Fig. 4: how the timing of CBV and CBF relative to CMRO2 produces an initial overshoot, a post-stimulus undershoot or an initial dip. Solid = current settings; dotted gray = Table 1 defaults for the same stimulus.

Stimulus → Neural Response
↙ N(t)
N(t) ↘
CBF Response
(Eq. 12),
CMRO2 Response
(Eq. 3) ;
f(t) ↘
↙ m(t)
Balloon ModelEqs. 10–11
↙ v(t)
q(t) ↘
CBV Response
Deoxy-Hb Response
v(t) ↘
↙ q(t)
BOLD Response
(1.5 T, TE = 40 ms; Obata et al., 2004)