You are here: Home / Exposures / Salem, Saidel, Stanley, Cabrera, 2002 / Mechanistic Model of Myocardial Energy Metabolism Under Normal and Ischemic Conditions

Model Mathematics

Component based math viewer is available

Component: environment

Component: v1

v1 = Vmax \frac{GL}{Km + GL}

Component: v2

v2 = Vmax \frac{O2}{Km + O2}

Component: v3

v3 = k3 FA

k3 = Vmax \frac{{PS}^{-1}}{{PS0}^{-1} + {PS}^{-1}}

Component: v4

v4 = k4 FA

k4 = Vmax (epsilon \frac{{AF}^{-1}}{{AF0}^{-1} + {AF}^{-1}} + (1 - epsilon) \frac{{RS}^{-1}}{{RS0}^{-1} + {RS}^{-1}})

Component: v5

v5 = k5 GP

k5 = Vmax (epsilon \frac{PS}{PS0 + PS} + (1 - epsilon) \frac{{RS}^{-1}}{{RS0}^{-1} + {RS}^{-1}})

Component: v6

v6 = k6 GP

k6 = Vmax (epsilon \frac{{PS}^{-1}}{{PS0}^{-1} + {PS}^{-1}} + (1 - epsilon) {(\frac{{CS}^{-1}}{{CS0}^{-1} + {CS}^{-1}})}^{2})

Component: v7

v7 = k7 GY

k7 = Vmax (epsilon \frac{PS}{PS0 + PS} + (1 - epsilon) {(\frac{CS}{CS0 + CS})}^{2})

Component: v8

v8 = k8 TG

k8 = Vmax

Component: v9

v9 = k9 PY

k9 = Vmax \frac{RS}{RS0 + RS}

Component: v10

v10 = k10 PY

k10 = Vmax (epsilon \frac{{RS}^{-1}}{{RS0}^{-1} + {RS}^{-1}} + (1 - epsilon) \frac{{AF}^{-1}}{{AF0}^{-1} + {AF}^{-1}})

Component: v11

v11 = k11 LA

k11 = Vmax \frac{{RS}^{-1}}{{RS0}^{-1} + {RS}^{-1}}

Component: v12

v12 = k12 AC

k12 = Vmax (epsilon \frac{{RS}^{-1}}{{RS0}^{-1} + {RS}^{-1}} + (1 - epsilon) \frac{PS}{PS0 + PS})

Component: v13

v13 = k13 CR

k13 = Vmax \frac{{PS}^{-1}}{{PS0}^{-1} + {PS}^{-1}}

Component: v14

v14 = k14 PC

k14 = Vmax \frac{PS}{PS0 + PS}

Component: v15

v15 = k15 CoA_pool

k15 = Vmax (epsilon \frac{{RS}^{-1}}{{RS0}^{-1} + {RS}^{-1}} + (1 - epsilon) \frac{{FC}^{-1}}{{FC0}^{-1} + {FC}^{-1}})

Component: v16

v16 = k16 AC

k16 = Vmax (epsilon \frac{{RS}^{-1}}{{RS0}^{-1} + {RS}^{-1}} + (1 - epsilon) \frac{{FC}^{-1}}{{FC0}^{-1} + {FC}^{-1}})

Component: v17

v17 = k17 ATP

k17 = Vmax

Component: GL

\frac{d}{d time} (GL) = F (aGL - (sigmaGL GL)) - v1

Component: FA

\frac{d}{d time} (FA) = 3 v8 + F (aFA - (sigmaFA FA)) - (v3 + v4)

Component: GP

\frac{d}{d time} (GP) = v1 + v7 - (v5 + v6)

Component: GY

\frac{d}{d time} (GY) = v6 - v7

Component: TG

\frac{d}{d time} (TG) = \frac{1}{3} v3 - v8

Component: PY

\frac{d}{d time} (PY) = 2 v5 + v11 - (v9 + v10)

Component: LA

\frac{d}{d time} (LA) = v9 + F (aLA - (sigmaLA LA)) - v11

Component: AC

\frac{d}{d time} (AC) = v10 + v4 - (v12 + v16)

Component: FC

\frac{d}{d time} (FC) = v12 + v15 + v16 - (v10 + v4)

Component: CoA_pool

\frac{d}{d time} (CoA_pool) = v16 - v15

Component: O2

\frac{d}{d time} (O2) = F (aO2 - (sigmaO2 O2)) - v2

Component: CO2

\frac{d}{d time} (CO2) = v10 + 2 v12 + F (aCO2 - (sigmaCO2 CO2))

Component: NAD

\frac{d}{d time} (NAD) = v9 + 2 v2 - (2 v5 + v10 + v11 + \frac{11}{3} v12 + \frac{35}{3} v4)

Component: ADP

\frac{d}{d time} (ADP) = v1 + v6 + 2 v4 + 2 v3 + v13 + v17 - (3 v5 + v12 + 6 v2 + v14)

Component: PC

\frac{d}{d time} (PC) = v13 - v14

Component: CR

\frac{d}{d time} (CR) = v14 - v13

Component: ATP

Component: NADH

Component: CS0

Component: PS0

Component: RS0

Component: AF0

Component: FC0

Component: CS

CS = \frac{CR}{PC}

Component: RS

RS = \frac{NADH}{NAD}

Component: PS

PS = \frac{ADP}{ATP}

Component: AF

AF = \frac{AC}{FC}

Component: model_parameters

F = \{\begin{matrix} 1.0 if time > 0.0 \land time < 5.0 \\ 0.4 otherwise \end{matrix}

Source: Derived from workspace Salem, Saidel, Stanley, Cabrera, 2002 at changeset e0281b3b5e99.

Collaboration: To begin collaborating on this work, please use your git client and issue this command:

Downloads

Views Available

Tools

License: This work is licensed under a Creative Commons Attribution 3.0 Unported License.

Mechanistic Model of Myocardial Energy Metabolism Under Normal and Ischemic Conditions