Skip to main content
. Author manuscript; available in PMC: 2011 Jan 3.
Published in final edited form as: Wiley Interdiscip Rev Cogn Sci. 2010 Jun;1(3):446–459. doi: 10.1002/wcs.58

Figure 2.

Figure 2

Schematic summary of the neural state equation and the hemodynamic forward model in DCM; reproduced, with permission, from Figure 1 in [33]. Experimentally controlled input functions u evoke neural responses x, modeled by a bilinear differential state equation, which trigger a hemodynamic cascade, modeled by 4 state equations with 5 parameters. These hemodynamic parameters comprise the rate constant of the vasodilatory signal decay (κ), the rate constant for auto-regulatory feedback by blood flow (γ), transit time (τ), Grubb's vessel stiffness exponent (α), and capillary resting net oxygen extraction (ρ). The so-called Balloon model consists of the two equations describing the dynamics of blood volume (v) and deoxyhemoglobin content (q) (light grey boxes). Integrating the state equations for a given set of inputs and parameters produces predicted time-series for v and q which enter a BOLD signal equation λ (dark grey box) to give a predicted BOLD response.