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Model Mathematics

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Component: environment

Component: cAMP

\frac{d}{d time} (cAMP) = \frac{Vmsm Ko (1.0 + Kb ACTH)}{1.0 + Ka ACTH + Ko (1.0 + Kb ACTH)} - (\frac{Vdsm cAMP}{Kdsm + cAMP}) ACTH = \{\begin{matrix} 12 e -6 if time \geq 0.0 \land time < 10.0 \\ 16 e -6 if time \geq 10.0 \land time < 20.0 \\ 12 e -6 if time \geq 20.0 \land time < 35.0 \\ 16 e -6 if time \geq 35.0 \land time < 45.0 \\ 12 e -6 otherwise \end{matrix}

Component: IS

IS = \frac{K Crpt {cAMP}^{n}}{{Kd}^{n} + {cAMP}^{n}}

Component: V

\frac{d}{d time} (V) = P IS - (Q V)

Component: W

\frac{d}{d time} (W) = T {CHOC}^{-1.0} - (U W)

Component: CHOC

\frac{d}{d time} (CHOC) = V + W + Lmtr CHOM - (Kmtr CHOC)

Component: CHOM

\frac{d}{d time} (CHOM) = Kmtr CHOC + Kbac CHON + Kcf CHOL - (Lmtr CHOM + Kcb CHOM + Kfor CHOM)

Component: CHOL

\frac{d}{d time} (CHOL) = Kcb CHOM - (Kcf CHOL)

Component: Kmtr

\frac{d}{d time} (Kmtr) = C IS - (D Kmtr)

Component: Kfor

\frac{d}{d time} (Kfor) = R IS - (S Kfor)

Component: CHON

\frac{d}{d time} (CHON) = Kfor CHOM - (Kbac CHON + \frac{Vm CHON}{Km + CHON})

Component: PREG

\frac{d}{d time} (PREG) = \frac{Vm CHON}{Km + CHON} - (\frac{Vmptr PREG}{Kmptr + PREG})

Component: PRO

\frac{d}{d time} (PRO) = HA \frac{Vmptr PREG}{Kmptr + PREG} - (AH PRO)

Component: HYPR

\frac{d}{d time} (HYPR) = AH PRO - (HY HYPR)

Component: CORT

\frac{d}{d time} (CORT) = HY HYPR - (LH CORT)

Component: model_parameters

Source: Derived from workspace Dempsher, Gann, Phair, 1984 at changeset 2ca6eff5a2f3.

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A mechanistic model of ACTH-stimulated cortisol secretion