# Model Mathematics

### Component: model_parameters

$t$$t=time$$delta_t= 1.0$

### Component: R_A

$R_A t + delta_t =epsilon t ⁢ⅇ gamma ⁢ H_A$

### Component: P_G

$P_G t + delta_t =P_V+P_A⁢R_E t R_A t ⁢C_A t C_E t 1.0 +R_E t R_A t ⁢C_A t C_E t$

### Component: phi

$phi t + delta_t = epsilon_max - psi 1.0 +ⅇ kappa ⁢Na_M t - D_TGF - Na_half$

### Component: epsilon

$epsilon t + delta_t =phi t + epsilon t ⁢ 2.0 ⁢ zeta omega ⁢ delta + 2.0 omega ⁢ delta 2.0 -⁢epsilon t - delta omega ⁢ delta 2.0 1.0 + 2.0 ⁢ zeta omega ⁢ delta + 1.0 omega ⁢ delta 2.0$

### Component: pi_G

$pi_G= pi ⁢ C_A + C_E 2.0$

### Component: pi

$pi C = a ⁢ C + b ⁢ C 2.0$

### Component: SNGFR

$SNGFR= Kf ⁢ P_G - P_BC + pi_G$

### Component: Na_I

$Na_I t =Na_R t 0.67$

### Component: H2O_I

$H2O_I t =H2O_R t 0.67$

### Component: H2O_D_M

$H2O_D_M t =H2O_D_M t + delta_t$

### Component: Na_D_M

$Na_D_M t =Na_D_M t + delta_t$

### Component: Na_D

$Na_D t =Na_M t H2O_M t + delta_t ⁢H2O_D t + delta_t$

### Component: Na_M

$Na_M t + delta_t =H2O_M t ⁢Na_A t + delta_t H2O_A t + Na_G$

### Component: H2O_D

$H2O_D t + delta_t =Na_D t Na_D_M t ⁢H2O_D_M t$

### Component: H2O_M

$H2O_M t + delta_t =Na_M t Na_D_M t ⁢H2O_D_M t$

### Component: Na_A

$Na_A t + delta_t =H2O_A t H2O_M_A t + delta_t ⁢Na_M_A t -Na_G t ⁢H2O_M t$

### Component: Na_G

$Na_G = Na_M - Na_A$

### Component: Na_M_A

$Na_M_A = Na_M + Na_A$

### Component: H2O_M_A

$H2O_M_A = H2O_M + H2O_A$

$R_ADH=log10⁡ ADH_I ⁢ 1e12 2.0$

### Component: R_ALD

$R_ALD=log10⁡ ALD_I ⁢ 1e11 3.0$

### Component: H2O_R

$H2O_R=R_ADH⁢H2O_I- Na_I ⁢H2O_I_IFNa_I_IF$

### Component: Na_R

$Na_R = R_ALD ⁢ Na_max ⁢ Na_I$
Source
Derived from workspace Moss, Kazmierczak, Kirley, Harris, 2009 at changeset 5c2c881f7263.
Collaboration
To begin collaborating on this work, please use your git client and issue this command: