Extended Data Table 4 Details of the Balloon–Windkessel model

From: Simulation and assimilation of the digital human brain

  1. The table gives the formulas of the hemodynamical model that generates the BOLD signals from neural activities. More details can be found in Ref. 19 of the main text. The right column presents the notations of the variables of these equations. Besides, we present the notations and values of the parameters. \({\kappa }_{i}=1.25\) is the inverse of the decay time constant of vasodilatory signal \({s}_{i}\). \({\gamma }_{i}=2.5\) is the inverse of the time constant of the inflow \({f}_{i}\). \({\tau }_{i}=1\) is the time constant of the blood volume \({v}_{i}\), which is the same with that of the deoxyhemoglobin content \({q}_{i}\). A stiffness exponent \(\alpha =0.2\) specifies the flow–volume relationship of the venous balloon. \({\rho }_{i}=0.8\) is the resting oxygen extraction fraction, and hence \(E\left({f}_{i},{\rho }_{i}\right)\) gives the fraction of oxygen extracted from the inflowing blood. \({V}_{0}=0.02\) is the resting blood volume fraction. We take \({k}_{1}=7{\rho }_{i}\), \({k}_{2}=2\), and \({k}_{3}=2{\rho }_{i}-0.2\).
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