Model Mathematics

Met = \{\begin{matrix} 45 if time \geq 0 \land time < 5 \\ 52 if time \geq 5 \land time < 15 \\ 55 if time \geq 15 \land time < 60 \\ 52 if time \geq 60 \land time < 75 \\ 45 if time \geq 75 \end{matrix}

Hcy = \frac{AdoHcy K_AHC}{Ado}

\frac{d}{d time} (AdoMet) = V_MATI + V_MATIII - (V_MET + V_GNMT)

\frac{d}{d time} (AdoHcy) = \frac{V_MET + V_GNMT - V_D}{1 + \frac{K_AHC}{Ado}}

V_MATI = \frac{V_MATImax}{1 + \frac{Km_MATI}{Met} (1 + \frac{AdoMet}{Ki_MATI})}

V_MATIII = \frac{V_MATIIImax}{1 + \frac{Km1_MATIII Km2_MATIII}{{Met}^{2} + Met Km2_MATIII}} Km1_MATIII = \frac{20000}{1 + 5.7 {(\frac{AdoMet}{AdoMet + 600})}^{2}}

V_MET = \frac{V_METmax}{1 + \frac{Km1_MET}{AdoMet} + Km2_MET_A + \frac{Km2_MET_A Km1_MET}{AdoMet}} Km1_MET = 10 (1 + \frac{AdoHcy}{4})

V_GNMT = \frac{\frac{V_GNMTmax}{1 + {(\frac{Km_GNMT}{AdoMet})}^{2.3}} 1}{1 + \frac{AdoHcy}{Ki_GNMT}}

V_D = alpha_d Hcy