You are here: Home / Exposures / Phillips, Robinson, 2008 / Sleep deprivation in a quantitative physiologically based model of the ascending arousal system (Sleep Deprivation Model)

Model Mathematics

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Component: environment

Component: v

Qv = \frac{Qmax}{1 + ⅇ^{\frac{- (Vv - theta)}{sigma}}}

\frac{d}{d time} (Vv) = \{\begin{matrix} 0.0 if time \geq awake_start \land time < awake_end \\ \frac{v_vm Qm + D - Vv}{\frac{tau_v}{3600}} otherwise \end{matrix}

Component: m

Qm = \frac{Qmax}{1 + ⅇ^{\frac{- (Vm - theta)}{sigma}}}

\frac{d}{d time} (Vm) = \{\begin{matrix} 0.0 if time \geq awake_start \land time < awake_end \\ \frac{A + v_mv Qv - Vm}{\frac{tau_m}{3600}} otherwise \end{matrix}

Component: H

\frac{d}{d time} (H) = \frac{mu Qm - H}{chi}

Component: D

D = v_vc C + v_vh H

C = c0 + \cos (omega (time - alpha))

omega = \frac{2 π}{24}

Component: model_parameters

Source: Derived from workspace Phillips 2008 at changeset 8aa3ccf088d8.; This exposure was expired. A more up-to-date exposure is available, or view related resources.

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