Model Mathematics

\frac{d}{d time} (P_p) = \frac{2 ((Q_Lp R_a - (2 P_p)) + 2 P_a)}{R_a C_p} \frac{d}{d time} (Q_Lp) = \frac{P_ai - P_p - (Q_Lp R_p)}{L_p}

C_p = \frac{3 π {r_p}^{2} {(\frac{r_p}{h_p} + 1)}^{2}}{E_p (\frac{2 r_p}{h_p} + 1)} l_p L_p = \frac{Rho_b}{π {r_p}^{2}} l_p 0.0000075 R_p = \frac{8 Eta_b}{π {r_p}^{4}} l_p

\frac{d}{d time} (r_a) = \frac{r_a0 (P_p (R_a + R_v) r_a + P_v R_a r_a - ((T_ae + T_am + P_ic (r_a + h_a)) (2 R_a + R_v)))}{r_a0 {r_a}^{2} K_Va R_a (R_a + R_v) + Eta_a h_a (2 R_a + R_v)} P_a = \frac{T_a + P_ic (r_a + h_a)}{r_a}

R_a = \frac{K_Ra}{{r_a}^{4}} C_a = \frac{1.0312}{R_a}

Q_a = \frac{2 (P_a - P_v)}{R_a + R_v}

\frac{d}{d time} (P_v) = \frac{2}{C_v} (\frac{P_a - P_v}{R_a + R_v} - (\frac{P_v - P_vo}{R_v}))

T_a = T_ae + T_am + T_av T_ae = h_a (sigma_ae0 (ⅇ^{\frac{K_a_sigma (r_a - r_a0)}{r_a0}} - 1) - sigma_ac) T_am = T_a_max ⅇ^{- ({(| \frac{r_a - r_am}{r_at - r_am} |)}^{n_am})} T_av = \frac{Eta_a}{r_a0} \frac{d}{d time} (r_a) h_a

h_a = \sqrt{{r_a}^{2} + 2 r_a0 h_a0 + {h_a0}^{2}} - r_a T_a_max = T_a_max0 (1 + M_s)

M_s = \frac{ⅇ^{2 M_s1} - 1}{ⅇ^{2 M_s1} + 1} M_s1 = G_myo x_myo + G_shear x_shear + G_neuro x_neuro + G_meta x_meta + x_ini

A_myo = \frac{T_a - T_myo0}{T_myo_s} \frac{d}{d time} (x_myo) = \frac{A_myo - x_myo}{Tau_myo}

A_shear = \frac{K_shear Q_a}{{r_a}^{3}} - 1 \frac{d}{d time} (x_shear) = \frac{A_shear - x_shear}{Tau_shear}

\frac{d}{d time} (x_neuro) = \frac{A_neuro - x_neuro}{Tau_neuro} A_neuro = \{\begin{matrix} 1 if time \geq 1 \\ 0 otherwise \end{matrix}

A_Meta = G_a_Meta (conc_CO2_t - conc_CO2_t_sp) \frac{d}{d time} (x_meta) = \frac{A_Meta - x_meta}{Tau_Meta}

\frac{d}{d time} (conc_CO2_t) = \frac{1}{vol_PVC} (M_CO2 - (Q_a (conc_CO2_v - conc_CO2_a))) conc_CO2_v = alpha_tv conc_CO2_t + beta_tv

M_CO2 = M_CO2_0 (unity + A_neuro \frac{f_Q - unity}{n_QM})