Model Mathematics

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Component: SAmembrane

ISAout = \{\begin{matrix} - 0.5 if Total_current < - 20 \\ 0 otherwise \end{matrix} ISAout_atrium = \{\begin{matrix} - 0.5 if Total_current < - 2 \land Total_current > - 3 \land V < 0 \\ 0 otherwise \end{matrix} Total_current = i_Na + i_K1 + i_to + i_Kur + i_Kr + i_Ks + i_B_Na + i_B_Ca + i_NaK + i_CaP + i_NaCa + i_Ca_L + i_Ca_T + i_f + i_KACh \frac{d}{d time} (V) = \frac{- Total_current}{Cm}

Component: fast_sodium_current

i_Na = Cm g_Na m^{3} h j (V - E_Na) E_Na = \frac{R T}{F} \ln (\frac{Na_o}{Na_i})

Component: fast_sodium_current_m_gate

alpha_m = \{\begin{matrix} 3.2 if V = - 47.13 \\ \frac{0.32 (V + 47.13)}{1 - (ⅇ^{(- 0.1) (V + 47.13)})} otherwise \end{matrix} beta_m = 0.08 ⅇ^{\frac{- V}{11}} m_inf = \frac{alpha_m}{alpha_m + beta_m} tau_m = \frac{1}{alpha_m + beta_m} \frac{d}{d time} (m) = \frac{m_inf - m}{tau_m}

Component: fast_sodium_current_h_gate

alpha_h = \{\begin{matrix} 0.135 ⅇ^{\frac{V + 80}{- 6.8}} if V < - 40 \\ 0 otherwise \end{matrix} beta_h = \{\begin{matrix} 3.56 ⅇ^{0.079 V} + 3.1 e 5 ⅇ^{0.35 V} if V < - 40 \\ \frac{1}{0.13 (1 + ⅇ^{\frac{V + 10.66}{- 11.1}})} otherwise \end{matrix} h_inf = \frac{alpha_h}{alpha_h + beta_h} tau_h = \frac{1}{alpha_h + beta_h} \frac{d}{d time} (h) = \frac{h_inf - h}{tau_h}

Component: fast_sodium_current_j_gate

alpha_j = \{\begin{matrix} \frac{((- 1.2714 e 5) ⅇ^{0.2444 V} - (3.474 e -5 ⅇ^{(- 0.04391) V})) (V + 37.78)}{1 + ⅇ^{0.311 (V + 79.23)}} if V < - 40 \\ 0 otherwise \end{matrix} beta_j = \{\begin{matrix} \frac{0.1212 ⅇ^{(- 0.01052) V}}{1 + ⅇ^{(- 0.1378) (V + 40.14)}} if V < - 40 \\ \frac{0.3 ⅇ^{(- 2.535 e -7) V}}{1 + ⅇ^{(- 0.1) (V + 32)}} otherwise \end{matrix} j_inf = \frac{alpha_j}{alpha_j + beta_j} tau_j = \frac{1}{alpha_j + beta_j} \frac{d}{d time} (j) = \frac{j_inf - j}{tau_j}

Component: time_independent_potassium_current

E_K = \frac{R T}{F} \ln (\frac{K_o}{K_i}) i_K1 = \frac{Cm g_K1 (V - E_K)}{1 + ⅇ^{0.07 (V + 80)}}

Component: transient_outward_K_current

i_to = Cm g_to {oa}^{3} oi (V - E_K)

Component: transient_outward_K_current_oa_gate

alpha_oa = 0.65 {(ⅇ^{\frac{V - (- 10)}{- 8.5}} + ⅇ^{\frac{V - (- 10) - 40}{- 59}})}^{- 1} beta_oa = 0.65 {(2.5 + ⅇ^{\frac{(V - (- 10)) + 72}{17}})}^{- 1} tau_oa = \frac{{(alpha_oa + beta_oa)}^{- 1}}{K_Q10} oa_infinity = {(1 + ⅇ^{\frac{(V - (- 10)) + 10.47}{- 17.54}})}^{- 1} \frac{d}{d time} (oa) = \frac{oa_infinity - oa}{tau_oa}

Component: transient_outward_K_current_oi_gate

alpha_oi = {(18.53 + 1 ⅇ^{\frac{(V - (- 10)) + 103.7}{10.95}})}^{- 1} beta_oi = {(35.56 + 1 ⅇ^{\frac{V - (- 10) - 8.74}{- 7.44}})}^{- 1} tau_oi = \frac{{(alpha_oi + beta_oi)}^{- 1}}{K_Q10} oi_infinity = {(1 + ⅇ^{\frac{(V - (- 10)) + 33.1}{5.3}})}^{- 1} \frac{d}{d time} (oi) = \frac{oi_infinity - oi}{tau_oi}

Component: ultrarapid_delayed_rectifier_K_current

g_Kur = (0.005 + \frac{0.05}{1 + ⅇ^{\frac{V - 15}{- 13}}}) 0.13 i_Kur = Cm g_Kur {ua}^{3} ui (V - E_K)

Component: ultrarapid_delayed_rectifier_K_current_ua_gate

alpha_ua = 0.65 {(ⅇ^{\frac{V - (- 10)}{- 8.5}} + ⅇ^{\frac{V - (- 10) - 40}{- 59}})}^{- 1} beta_ua = 0.65 {(2.5 + ⅇ^{\frac{(V - (- 10)) + 72}{17}})}^{- 1} tau_ua = \frac{{(alpha_ua + beta_ua)}^{- 1}}{K_Q10} ua_infinity = {(1 + ⅇ^{\frac{(V - (- 10)) + 20.3}{- 9.6}})}^{- 1} \frac{d}{d time} (ua) = \frac{ua_infinity - ua}{tau_ua}

Component: ultrarapid_delayed_rectifier_K_current_ui_gate

alpha_ui = {(21 + 1 ⅇ^{\frac{V - (- 10) - 195}{- 28}})}^{- 1} beta_ui = \frac{1}{ⅇ^{\frac{V - (- 10) - 168}{- 16}}} tau_ui = \frac{{(alpha_ui + beta_ui)}^{- 1}}{K_Q10} ui_infinity = {(1 + ⅇ^{\frac{V - (- 10) - 109.45}{27.48}})}^{- 1} \frac{d}{d time} (ui) = \frac{ui_infinity - ui}{tau_ui}

Component: rapid_delayed_rectifier_K_current

i_Kr = \frac{Cm g_Kr xr (V - E_K)}{1 + ⅇ^{\frac{V + 15}{22.4}}}

Component: rapid_delayed_rectifier_K_current_xr_gate

alpha_xr = \{\begin{matrix} 0.0015 if | V + 14.1 | < 1 e -10 \\ \frac{0.0003 (V + 14.1)}{1 - (ⅇ^{\frac{V + 14.1}{- 5}})} otherwise \end{matrix} beta_xr = \{\begin{matrix} 3.7836118 e -4 if | V - 3.3328 | < 1 e -10 \\ \frac{0.000073898 (V - 3.3328)}{ⅇ^{\frac{V - 3.3328}{5.1237}} - 1} otherwise \end{matrix} tau_xr = {(alpha_xr + beta_xr)}^{- 1} xr_infinity = {(1 + ⅇ^{\frac{V + 14.1}{- 6.5}})}^{- 1} \frac{d}{d time} (xr) = \frac{xr_infinity - xr}{tau_xr}

Component: slow_delayed_rectifier_K_current

i_Ks = Cm g_Ks {xs}^{2} (V - E_K)

Component: slow_delayed_rectifier_K_current_xs_gate

alpha_xs = \{\begin{matrix} 0.00068 if | V - 19.9 | < 1 e -10 \\ \frac{0.00004 (V - 19.9)}{1 - (ⅇ^{\frac{V - 19.9}{- 17}})} otherwise \end{matrix} beta_xs = \{\begin{matrix} 0.000315 if | V - 19.9 | < 1 e -10 \\ \frac{0.000035 (V - 19.9)}{ⅇ^{\frac{V - 19.9}{9}} - 1} otherwise \end{matrix} tau_xs = 0.5 {(alpha_xs + beta_xs)}^{- 1} xs_infinity = {(1 + ⅇ^{\frac{V - 19.9}{- 12.7}})}^{- 0.5} \frac{d}{d time} (xs) = \frac{xs_infinity - xs}{tau_xs}

Component: L_type_Ca_channel

i_Ca_L = Cm g_Ca_L d f f_Ca (V - 65)

Component: L_type_Ca_channel_d_gate

d_infinity = {(1 + ⅇ^{\frac{V + 10}{- 8}})}^{- 1} tau_d = \{\begin{matrix} \frac{4.579}{1 + ⅇ^{\frac{V + 10}{- 6.24}}} if | V + 10 | < 1 e -10 \\ \frac{1 - (ⅇ^{\frac{V + 10}{- 6.24}})}{0.035 (V + 10) (1 + ⅇ^{\frac{V + 10}{- 6.24}})} otherwise \end{matrix} \frac{d}{d time} (d) = \frac{d_infinity - d}{tau_d}

Component: L_type_Ca_channel_f_gate

f_infinity = \frac{ⅇ^{\frac{- (V + 28)}{6.9}}}{1 + ⅇ^{\frac{- (V + 28)}{6.9}}} tau_f = 9 {(0.0197 ⅇ^{(- ({0.0337}^{2})) {(V + 10)}^{2}} + 0.02)}^{- 1} \frac{d}{d time} (f) = \frac{f_infinity - f}{tau_f}

Component: L_type_Ca_channel_f_Ca_gate

f_Ca_infinity = {(1 + \frac{Ca_i}{0.00035})}^{- 1} tau_f_Ca = 2 \frac{d}{d time} (f_Ca) = \frac{f_Ca_infinity - f_Ca}{tau_f_Ca}

Component: sodium_potassium_pump

sigma = \frac{1}{7} (ⅇ^{\frac{Na_o}{67.3}} - 1) f_NaK = {(1 + 0.1245 ⅇ^{\frac{(- 0.1) F V}{R T}} + 0.0365 sigma ⅇ^{\frac{(- F) V}{R T}})}^{- 1} i_NaK = \frac{\frac{Cm i_NaK_max f_NaK 1}{1 + {(\frac{Km_Na_i}{Na_i})}^{1.5}} K_o}{K_o + Km_K_o}

Component: background_currents

E_Ca = \frac{R T}{2 F} \ln (\frac{Ca_o}{Ca_i}) i_B_Na = Cm g_B_Na (V - E_Na) i_B_Ca = Cm g_B_Ca (V - E_Ca) i_B_K = Cm g_B_K (V - E_K)

Component: Na_Ca_exchanger_current

i_NaCa = \frac{Cm I_NaCa_max (ⅇ^{\frac{gamma F V}{R T}} {Na_i}^{3} Ca_o - (ⅇ^{\frac{(gamma - 1) F V}{R T}} {Na_o}^{3} Ca_i))}{({K_mNa}^{3} + {Na_o}^{3}) (K_mCa + Ca_o) (1 + K_sat ⅇ^{\frac{(gamma - 1) V F}{R T}})}

Component: sarcolemmal_calcium_pump_current

i_CaP = \frac{Cm i_CaP_max Ca_i}{0.0005 + Ca_i}

Component: Ca_release_current_from_JSR

Fn = 1 e 3 (1 e -15 V_rel i_rel - (\frac{1 e -15}{2 F} (0.5 i_Ca_L - (0.2 i_NaCa)))) i_rel = K_rel u^{2} v w (Ca_rel - Ca_i)

Component: Ca_release_current_from_JSR_u_gate

tau_u = 8 u_infinity = {(1 + ⅇ^{\frac{- (Fn - 3.4175 e -13)}{13.67 e -16}})}^{- 1} \frac{d}{d time} (u) = \frac{u_infinity - u}{tau_u}

Component: Ca_release_current_from_JSR_v_gate

tau_v = 1.91 + 2.09 {(1 + ⅇ^{\frac{- (Fn - 3.4175 e -13)}{13.67 e -16}})}^{- 1} v_infinity = 1 - ({(1 + ⅇ^{\frac{- (Fn - 6.835 e -14)}{13.67 e -16}})}^{- 1}) \frac{d}{d time} (v) = \frac{v_infinity - v}{tau_v}

Component: Ca_release_current_from_JSR_w_gate

tau_w = \{\begin{matrix} \frac{6 0.2}{1.3} if | V - 7.9 | < 1 e -10 \\ \frac{6 (1 - (ⅇ^{\frac{- (V - 7.9)}{5}}))}{(1 + 0.3 ⅇ^{\frac{- (V - 7.9)}{5}}) 1 (V - 7.9)} otherwise \end{matrix} w_infinity = 1 - ({(1 + ⅇ^{\frac{- (V - 40)}{17}})}^{- 1}) \frac{d}{d time} (w) = \frac{w_infinity - w}{tau_w}

Component: transfer_current_from_NSR_to_JSR

i_tr = \frac{Ca_up - Ca_rel}{tau_tr}

Component: Ca_uptake_current_by_the_NSR

i_up = \frac{I_up_max}{1 + \frac{K_up}{Ca_i}}

Component: Ca_leak_current_by_the_NSR

i_up_leak = \frac{I_up_max Ca_up}{Ca_up_max}

Component: Ca_buffers

Ca_CMDN = \frac{CMDN_max Ca_i}{Ca_i + Km_CMDN} Ca_TRPN = \frac{TRPN_max Ca_i}{Ca_i + Km_TRPN} Ca_CSQN = \frac{CSQN_max Ca_rel}{Ca_rel + Km_CSQN}

Component: intracellular_ion_concentrations

V_i = V_cell 0.68 V_rel = 0.0048 V_cell V_up = 0.0552 V_cell \frac{d}{d time} (Na_i) = \frac{(- 3) i_NaK - (3 i_NaCa + i_B_Na + i_Na)}{V_i F} \frac{d}{d time} (K_i) = \frac{2 i_NaK - (i_K1 + i_to + i_Kur + i_Kr + i_Ks + i_B_K)}{V_i F} \frac{d}{d time} (Ca_i) = \frac{B1}{B2} B1 = \frac{2 i_NaCa - (i_CaP + i_Ca_L + i_B_Ca)}{2 V_i F} + \frac{V_up (i_up_leak - i_up) + i_rel V_rel}{V_i} B2 = 1 + \frac{TRPN_max Km_TRPN}{{(Ca_i + Km_TRPN)}^{2}} + \frac{CMDN_max Km_CMDN}{{(Ca_i + Km_CMDN)}^{2}} \frac{d}{d time} (Ca_up) = i_up - (i_up_leak + \frac{i_tr V_rel}{V_up}) \frac{d}{d time} (Ca_rel) = (i_tr - i_rel) {(1 + \frac{CSQN_max Km_CSQN}{{(Ca_rel + Km_CSQN)}^{2}})}^{- 1}

Component: funny_current

alpha_d_f = \frac{0.36 (V + 148.8)}{ⅇ^{0.066 (V + 148.8)} - 1} beta_d_f = \frac{0.1 (V + 87.3)}{1 - (ⅇ^{(- 0.21) (V + 87.3)})} tau_d_f = \frac{1}{alpha_d_f + beta_d_f} - 0.054 d_f_infinity = \frac{1}{alpha_d_f + beta_d_f} \frac{d}{d time} (d_f) = \frac{d_f_infinity - d_f}{tau_d_f} i_f = g_f d_f (V - E_f)

Component: T_type_Ca_channel

i_Ca_T = g_Ca_T d_T f_T (V - E_Ca_T)

Component: T_type_Ca_channel_d_gate

alpha_d_T = 1068 ⅇ^{\frac{V + 26.3}{30}} beta_d_T = 1068 ⅇ^{\frac{V + 26.3}{- 30}} tau_d_T = \frac{1}{alpha_d_T + beta_d_T} d_T_infinity = \frac{1}{1 + ⅇ^{\frac{V + 26.3}{- 6}}} \frac{d}{d time} (d_T) = \frac{d_T_infinity - d_T}{tau_d_T}

Component: T_type_Ca_channel_f_gate

alpha_f_T = 15.3 ⅇ^{\frac{V + 61.7}{- 83.3}} beta_f_T = 15 ⅇ^{\frac{V + 61.7}{15.38}} tau_f_T = \frac{1}{alpha_f_T + beta_f_T} f_T_infinity = \frac{1}{1 + ⅇ^{\frac{V + 61.7}{5.6}}} \frac{d}{d time} (f_T) = \frac{f_T_infinity - f_T}{tau_f_T}

Component: standard_ionic_concentrations

Component: ACh_dependent_potassium_current

i_KACh = \frac{g_ACh (Vm - E_K)}{1 + ⅇ^{\frac{Vm + 20}{20}}} y

Component: ACh_dependent_potassium_current_y_gate

alpha_y = \{\begin{matrix} 0.0002475 if ACh = 0 \\ \frac{0.01232}{1 + \frac{Km_ACh}{ACh}} + 0.0002475 otherwise \end{matrix} beta_y = 0.01 ⅇ^{0.0133 (Vm + 40)} \frac{d}{d time} (y) = alpha_y (1 - y) - (beta_y y)

Component: environment

hrf = \frac{1000}{\frac{HR}{60}}

Component: LATiming

start = \{\begin{matrix} realtime if ISAin < 0 \end{matrix} beattime = \frac{realtime - start - (⌊ \frac{realtime - start}{hrf} ⌋ hrf)}{1000}

Component: LAElastanceFunction

Ts = TsK \sqrt{\frac{hrf}{1000}} E_LA = \{\begin{matrix} Edia + \frac{(Esys - Edia) (1 - (\cos (\frac{π time}{Ts})))}{2} if time \geq 0 \land time ≦ Ts \\ Edia + \frac{(Esys - Edia) (1 + \cos (\frac{2 π (time - Ts)}{Ts}))}{2} if time < 1.5 Ts \land time \geq Ts \\ Edia otherwise \end{matrix}

Component: LeftAtrium

\frac{d}{d time} (sub_X_LA) = \frac{conc_X_PV F_LA - (conc_X_LA F_LV)}{1000} conc_X_LA = \frac{sub_X_LA}{V_LA} P_LA = E_LA (V_LA - V_LA_0) + P_LA_ext F_LA = \frac{P_PV - P_LA}{R_LA} \frac{d}{d time} (V_LA) = \frac{F_LA - F_LV}{1000}

Component: LeftVentricle

P_LV = P_LVin + P_LA_ext \frac{d}{d time} (sub_X_LV) = \frac{conc_X_LA F_LV - (conc_X_LV (F_AO + F_CO))}{1000} conc_X_LV = \frac{sub_X_LV}{V_LV} F_LV = \{\begin{matrix} \frac{P_LA - P_LV}{R_LV} if P_LA > P_LV \\ 0 otherwise \end{matrix} \frac{d}{d time} (V_LV) = \frac{F_LV - F_AO - F_CO}{1000}

Component: Aorta

\frac{d}{d time} (sub_X_AO) = \frac{conc_X_LV F_AO - (conc_X_AO (F_CR + F_AR))}{1000} conc_X_AO = \frac{sub_X_AO}{V_AO} \frac{d}{d time} (F_AOalways) = \frac{\frac{1}{L_AO} (P_LV - P_AO) - (\frac{R_AO}{L_AO} F_AOalways)}{1000} F_AO = \{\begin{matrix} F_AOalways if P_LV > P_AO \\ 0 otherwise \end{matrix} \frac{d}{d time} (V_AO) = \frac{F_AO - F_AR - F_CR}{1000} P_AO = \frac{1}{C_AO} (V_AO - V_AO_0)

Component: CoronaryCirc

\frac{d}{d time} (sub_X_CO) = \frac{conc_X_LV F_CO - (conc_X_CO F_COV)}{1000} conc_X_CO = \frac{sub_X_CO}{V_CO} \frac{d}{d time} (V_CO) = \frac{F_CO - F_COV}{1000} P_CO = \frac{1}{C_CO} (V_CO - V_CO_0) F_CO = \{\begin{matrix} \frac{P_LV - P_CO}{R_CO} if P_LV > P_CO \\ 0 otherwise \end{matrix} F_COV = \frac{P_CO - P_RA}{R_COV}

Component: CarotidCirc

conc_X_CRtissue = \frac{sub_X_CRtissue}{V_CRtissue} \frac{d}{d time} (sub_X_CRtissue) = \frac{(conc_X_CR - conc_X_CRtissue) D_CRtissue}{1000} \frac{d}{d time} (sub_X_CR) = \frac{conc_X_AO F_CR - (conc_X_CR F_CRV) - ((conc_X_CR - conc_X_CRtissue) D_CRtissue)}{1000} conc_X_CR = \frac{sub_X_CR}{V_CR} \frac{d}{d time} (V_CR) = \frac{F_CR - F_CRV}{1000} P_CR = \frac{1}{C_CR} (V_CR - V_CR_0) F_CR = \frac{P_AO - P_CR}{R_CR} F_CRV = \frac{P_CR - P_VC}{R_CRV}

Component: Arteries

\frac{d}{d time} (sub_X_AR) = \frac{conc_X_AO F_AR - (conc_X_AR (F_SK + F_AD + F_MU + F_GI + F_LI + F_KI + F_OT))}{1000} conc_X_AR = \frac{sub_X_AR}{V_AR} \frac{d}{d time} (V_AR) = \frac{F_AR - F_AD - F_MU - F_GI - F_LI - F_KI - F_OT - F_SK}{1000} P_AR = \frac{1}{C_AR} (V_AR - V_AR_0) F_AR = \frac{P_AO - P_AR}{R_AR}

Component: Adipose

\frac{d}{d time} (sub_X_AD) = \frac{conc_X_AR F_AD - (conc_X_AD F_ADV)}{1000} conc_X_AD = \frac{sub_X_AD}{V_AD} \frac{d}{d time} (V_AD) = \frac{F_AD - F_ADV}{1000} F_ADV = \frac{P_AD - P_VE}{R_ADV} P_AD = \frac{1}{C_AD} (V_AD - V_AD_0) F_AD = \frac{P_AR - P_AD}{R_AD}

Component: Muscle

\frac{d}{d time} (sub_X_MU) = \frac{conc_X_AR F_MU - (conc_X_MU F_MUV)}{1000} conc_X_MU = \frac{sub_X_MU}{V_MU} \frac{d}{d time} (V_MU) = \frac{F_MU - F_MUV}{1000} F_MUV = \frac{P_MU - P_VE}{R_MUV} P_MU = \frac{1}{C_MU} (V_MU - V_MU_0) F_MU = \frac{P_AR - P_MU}{R_MU}

Component: GutIntestine

\frac{d}{d time} (sub_X_GI) = \frac{conc_X_AR F_GI - (conc_X_GI F_GIV)}{1000} conc_X_GI = \frac{sub_X_GI}{V_GI} \frac{d}{d time} (V_GI) = \frac{F_GI - F_GIV}{1000} F_GIV = \frac{P_GI - P_LI}{R_GIV} P_GI = \frac{1}{C_GI} (V_GI - V_GI_0) F_GI = \frac{P_AR - P_GI}{R_GI}

Component: Liver

\frac{d}{d time} (sub_X_LI) = \frac{(conc_X_GI F_GIV + conc_X_AR F_LI - (conc_X_LI F_LIV)) + conc_X_LI metabolism}{1000} conc_X_LI = \frac{sub_X_LI}{V_LI} \frac{d}{d time} (V_LI) = \frac{F_GIV + F_LI - F_LIV}{1000} F_LIV = \frac{P_LI - P_VE}{R_LIV} P_LI = \frac{1}{C_LI} (V_LI - V_LI_0) F_LI = \frac{P_AR - P_LI}{R_LI}

Component: Kidney

\frac{d}{d time} (sub_X_KI) = \frac{conc_X_AR F_KI - (conc_X_KI F_KIV)}{1000} conc_X_KI = \frac{sub_X_KI}{V_KI} \frac{d}{d time} (V_KI) = \frac{F_KI - F_KIV}{1000} F_KIV = \frac{P_KI - P_VE}{R_KIV} P_KI = \frac{1}{C_KI} (V_KI - V_KI_0) F_KI = \frac{P_AR - P_KI}{R_KI}

Component: Skin

\frac{d}{d time} (sub_X_SK) = \frac{conc_X_AR F_SK - (conc_X_SK F_SKV)}{1000} conc_X_SK = \frac{sub_X_SK}{V_SK} \frac{d}{d time} (V_SK) = \frac{F_SK - F_SKV}{1000} F_SKV = \frac{P_SK - P_VE}{R_SKV} P_SK = \frac{1}{C_SK} (V_SK - V_SK_0) F_SK = \frac{P_AR - P_SK}{R_SK}

Component: OtherTissue

\frac{d}{d time} (sub_X_OT) = \frac{conc_X_AR F_OT - (conc_X_OT F_OTV)}{1000} conc_X_OT = \frac{sub_X_OT}{V_OT} \frac{d}{d time} (V_OT) = \frac{F_OT - F_OTV}{1000} F_OTV = \frac{P_OT - P_VE}{R_OTV} P_OT = \frac{1}{C_OT} (V_OT - V_OT_0) F_OT = \frac{P_AR - P_OT}{R_OT}

Component: Veins

\frac{d}{d time} (sub_X_VE) = \frac{conc_X_SK F_SKV + conc_X_AD F_ADV + conc_X_MU F_MUV + conc_X_LI F_LIV + conc_X_KI F_KIV + conc_X_OT F_OTV - (conc_X_VE F_VEV)}{1000} conc_X_VE = \frac{sub_X_VE}{V_VE} F_VE = F_SKV + F_ADV + F_MUV + F_LIV + F_KIV + F_OTV \frac{d}{d time} (V_VE) = \frac{F_VE - F_VEV}{1000} P_VE = \frac{1}{C_VE} (V_VE - V_VE_0) F_VEV = \frac{P_VE - P_VC}{R_VEV}

Component: VenaCava

\frac{d}{d time} (sub_X_VC) = \frac{conc_X_VE F_VEV + conc_X_CR F_CRV - (conc_X_VC F_VCV)}{1000} conc_X_VC = \frac{sub_X_VC}{V_VC} F_VC = F_CRV + F_VEV F_VCV = \frac{P_VC - P_RA}{R_VCV} \frac{d}{d time} (V_VC) = \frac{F_VC - F_VCV}{1000} P_VC = \frac{1}{C_VC} (V_VC - V_VC_0)

Component: RATiming

start = \{\begin{matrix} realtime if ISAin < 0 \end{matrix} beattime = \frac{realtime - start - (⌊ \frac{realtime - start}{hrf} ⌋ hrf)}{1000}

Component: RAElastanceFunction

Ts = TsK \sqrt{\frac{hrf}{1000}} E_RA = \{\begin{matrix} Edia + \frac{(Esys - Edia) (1 - (\cos (\frac{π time}{Ts})))}{2} if time \geq 0 \land time ≦ Ts \\ Edia + \frac{(Esys - Edia) (1 + \cos (\frac{2 π (time - Ts)}{Ts}))}{2} if time < 1.5 Ts \land time \geq Ts \\ Edia otherwise \end{matrix}

Component: RightAtrium

\frac{d}{d time} (sub_X_RA) = \frac{conc_X_VC F_VCV + conc_X_CO F_COV - (conc_X_RA F_RV)}{1000} conc_X_RA = \frac{sub_X_RA}{V_RA} P_RA = E_RA (V_RA - V_RA_0) + P_RA_ext F_RA = F_VCV + F_COV \frac{d}{d time} (V_RA) = \frac{F_RA - F_RV}{1000}

Component: RightVentricle

lva = EmaxLV 10 rva = EmaxRV 10 lvb = P0lv (ⅇ^{kelv V_LV} - 1) rvb = P0rv (ⅇ^{kerv V_RV} - 1) P_RV = \frac{(P_LV - lvb) rva}{lva - lvb} + \frac{(lva - P_LV) rvb}{lva - lvb} \frac{d}{d time} (sub_X_RV) = \frac{conc_X_RA F_RV - (conc_X_RV F_PA)}{1000} conc_X_RV = \frac{sub_X_RV}{V_RV} F_RV = \{\begin{matrix} \frac{P_RA - P_RV}{R_RV} if P_RA > P_RV \\ 0 otherwise \end{matrix} \frac{d}{d time} (V_RV) = \frac{F_RV - F_PA}{1000}

Component: PulmonaryArtery

\frac{d}{d time} (sub_X_PA) = \frac{conc_X_RV F_PA - (conc_X_PA F_Pa)}{1000} conc_X_PA = \frac{sub_X_PA}{V_PA} F_PA = \{\begin{matrix} \frac{P_RV - P_PA}{R_PA} if P_RV > P_PA \\ 0 otherwise \end{matrix} \frac{d}{d time} (V_PA) = \frac{F_PA - F_Pa}{1000} P_PA = \frac{1}{C_PA} (V_PA - V_PA_0)

Component: PulmonaryArteries

\frac{d}{d time} (sub_X_Pa) = \frac{conc_X_PA F_Pa - (conc_X_Pa (F_PC + F_SH))}{1000} conc_X_Pa = \frac{sub_X_Pa}{V_Pa} \frac{d}{d time} (V_Pa) = \frac{F_Pa - F_PC - F_SH}{1000} P_Pa = \frac{1}{C_Pa} (V_Pa - V_Pa_0) F_Pa = \frac{P_PA - P_Pa}{R_Pa}

Component: Shunt

F_SH = \frac{P_Pa - P_PC}{R_SH}

Component: PulmonaryCapillaries

\frac{d}{d time} (sub_X_PC) = \frac{conc_X_Pa F_PC - (conc_X_PC F_PCV)}{1000} conc_X_PC = \frac{sub_X_PC}{V_PC} \frac{d}{d time} (V_PC) = \frac{F_PC - F_PCV}{1000} P_PC = \frac{1}{C_PC} (V_PC - V_PC_0) F_PC = \frac{P_Pa - P_PC}{R_PC} F_PCV = \frac{P_PC - P_PV}{R_PCV}

Component: PulmonaryVein

\frac{d}{d time} (sub_X_PV) = \frac{conc_X_PC F_PCV + conc_X_Pa F_SH - (conc_X_PV F_LA)}{1000} conc_X_PV = \frac{sub_X_PV}{V_PV} F_PV = F_PCV + F_SH \frac{d}{d time} (V_PV) = \frac{F_PV - F_LA}{1000} P_PV = \frac{1}{C_PV} (V_PV - V_PV_0)

Component: additional_currents

ICa_additional = topOUt - Cai IK_additional = - Istim

Component: default_parameters

Component: default_initial_conditions

Component: membrane_potential

\frac{d}{d time} (V) = \frac{- Itotal}{Cm}

Component: total_membrane_current

Itotal = ISAstim + ICa_additional + INa_additional + IK_additional + INa + IK1 + Ito + IKr + IKs + ICaL + INaCa + INaK + IbNa + IbCa + IpCa + IpK

Component: K_flux

K_flux = \frac{Am}{vC F} (IK_additional + IK1 + Ito + IKr + IKs + IpK - (INaK 2))

Component: Na_flux

Na_flux = \frac{Am}{vC F} (INa + INa_additional + IbNa + INaK 3 + INaCa 3)

Component: Ca_flux

Ca_flux = \frac{Am}{2 vC F} (2 INaCa - (ICa_additional + ICaL + IbCa + IpCa))

Component: Ca_SR_flux

Ca_SR_flux = Jleak + Jrel + JCaSR_additional - Jup

Component: INa

INa = g_Na m^{3} h j (V - E_Na)

Component: IK1

IK1 = g_K1 \sqrt{\frac{Ko}{5.4}} K1_infinity (V - E_K)

Component: Ito

Ito = g_to r s (V - E_K)

Component: IKr

IKr = g_Kr \sqrt{\frac{Ko}{5.4}} Xr1 Xr2 (V - E_K)

Component: IKs

IKs = g_Ks {Xs}^{2} (V - E_Ks)

Component: INaK

INaK = \frac{P_NaK Ko Nai}{(Ko + K_mK) (Nai + K_mNa) (1 + 0.1245 ⅇ^{\frac{(- 0.1) V F}{R T}} + 0.0353 ⅇ^{\frac{(- V) F}{R T}})}

Component: IpK

IpK = \frac{g_pK (V - E_K)}{1 + ⅇ^{\frac{25 - V}{5.98}}}

Component: IbNa

IbNa = g_bNa (V - E_Na)

Component: ICaL

ICaL = \frac{\frac{g_CaL d f fCa 4 V F^{2}}{R T} (Cai ⅇ^{\frac{2 V F}{R T}} - (0.341 Cao))}{ⅇ^{\frac{2 V F}{R T}} - 1}

Component: IpCa

IpCa = \frac{g_pCa Cai}{K_pCa + Cai}

Component: INaCa

INaCa = \frac{k_NaCa (ⅇ^{\frac{gamma V F}{R T}} {Nai}^{3} Cao - (ⅇ^{\frac{(gamma - 1) V F}{R T}} {Nao}^{3} Cai alpha))}{({K_mNai}^{3} + {Nao}^{3}) (K_mCa + Cao) (1 + k_sat ⅇ^{\frac{(gamma - 1) V F}{R T}})}

Component: IbCa

IbCa = g_bCa (V - E_Ca)

Component: ENa

reversal_potential = \frac{R T}{z F} \ln (\frac{extracellular_concentration}{intracellular_concentration})

Component: EK

reversal_potential = \frac{R T}{z F} \ln (\frac{extracellular_concentration}{intracellular_concentration})

Component: ECa

reversal_potential = \frac{R T}{z F} \ln (\frac{extracellular_concentration}{intracellular_concentration})

Component: EKs

reversal_potential = \frac{R T}{z F} \ln (\frac{multiplier_1 extracellular_concentration_1 + multiplier_2 extracellular_concentration_2}{multiplier_1 intracellular_concentration_1 + multiplier_2 intracellular_concentration_2})

Component: Nai

\frac{d}{d time} (Nai) = - Na_flux

Component: Ki

\frac{d}{d time} (Ki) = - K_flux

Component: Cai

aCai = - 1 bCai = Cai_total + Kbufc + Bufc cCai = (- Bufc) Cai_total Cai_buf = \frac{\sqrt{{bCai}^{2} - (4 aCai cCai)} - bCai}{2 aCai} Cai = Cai_total - Cai_buf \frac{d}{d time} (Cai_total) = Ca_flux + Ca_SR_flux aCaSR = - 1 bCaSR = CaSR_total + Kbufsr + Bufsr cCaSR = (- Bufsr) CaSR_total CaSR_buf = \frac{\sqrt{{bCaSR}^{2} - (4 aCaSR cCaSR)} - bCaSR}{2 aCaSR} CaSR = CaSR_total - CaSR_buf \frac{d}{d time} (CaSR_total) = \frac{vC}{vSR} (- Ca_SR_flux)

Component: Jleak

Jleak = V_leak (CaSR - Cai)

Component: Jup

Jup = \frac{Vmax_up}{1 + \frac{{K_up}^{2}}{{Cai}^{2}}}

Component: Jrel

Jrel = (\frac{a_rel {CaSR}^{2}}{{b_rel}^{2} + {CaSR}^{2}} + c_rel) d g

Component: m_gate

m_infinity = \frac{1}{{(1 + ⅇ^{\frac{- 56.86 - V}{9.03}})}^{2}} alpha_m = \frac{1}{1 + ⅇ^{\frac{- 60 - V}{5}}} beta_m = \frac{0.1}{1 + ⅇ^{\frac{35 + V}{5}}} + \frac{0.1}{1 + ⅇ^{\frac{V - 50}{200}}} tau_m = 1 alpha_m beta_m \frac{d}{d time} (m) = \frac{m_infinity - m}{tau_m}

Component: h_gate

h_infinity = \frac{1}{{(1 + ⅇ^{\frac{71.55 + V}{7.43}})}^{2}} alpha_h = \{\begin{matrix} 0.057 ⅇ^{\frac{- (80 + V)}{6.8}} if V < - 40 \\ 0 otherwise \end{matrix} beta_h = \{\begin{matrix} 2.7 ⅇ^{0.079 V} + 3.1 e 5 ⅇ^{0.3485 V} if V < - 40 \\ \frac{0.77}{0.13 (1 + ⅇ^{\frac{- (V + 10.66)}{11.1}})} otherwise \end{matrix} tau_h = \frac{1}{alpha_h + beta_h} \frac{d}{d time} (h) = \frac{h_infinity - h}{tau_h}

Component: j_gate

j_infinity = \frac{1}{{(1 + ⅇ^{\frac{71.55 + V}{7.43}})}^{2}} alpha_j = \{\begin{matrix} \frac{((- 2.5428 e 4) ⅇ^{0.2444 V} - (6.948 e -6 ⅇ^{(- 0.04391) V})) (V + 37.78)}{1 + ⅇ^{0.311 (V + 79.23)}} if V < - 40 \\ 0 otherwise \end{matrix} beta_j = \{\begin{matrix} \frac{0.02424 ⅇ^{(- 0.01052) V}}{1 + ⅇ^{(- 0.1378) (V + 40.14)}} if V < - 40 \\ \frac{0.6 ⅇ^{0.057 V}}{1 + ⅇ^{(- 0.1) (V + 32)}} otherwise \end{matrix} tau_j = \frac{1}{alpha_j + beta_j} \frac{d}{d time} (j) = \frac{j_infinity - j}{tau_j}

Component: K1_gate

K1_infinity = \frac{alpha_K1}{alpha_K1 + beta_K1} alpha_K1 = \frac{0.1}{1 + ⅇ^{0.06 (V - (E_K + 200))}} beta_K1 = \frac{3 ⅇ^{0.0002 ((V - E_K) + 100)} + ⅇ^{0.1 (V - (E_K + 10))}}{1 + ⅇ^{(- 0.5) (V - E_K)}}

Component: r_gate

\frac{d}{d time} (r) = \frac{r_infinity - r}{tau_r} r_infinity = \frac{1}{1 + ⅇ^{\frac{20 - V}{6}}} tau_r = 9.5 ⅇ^{\frac{- ({(V + 40)}^{2})}{1800}} + 0.8

Component: s_gate

\frac{d}{d time} (s) = \frac{s_infinity - s}{tau_s} s_infinity = \frac{1}{1 + ⅇ^{\frac{20 + V}{5}}} tau_s = 85 ⅇ^{\frac{- ({(V + 45)}^{2})}{320}} + \frac{5}{1 + ⅇ^{\frac{V - 20}{5}}} + 3

Component: Xr1_gate

\frac{d}{d time} (Xr1) = \frac{Xr1_infinity - Xr1}{tau_Xr1} Xr1_infinity = \frac{1}{1 + ⅇ^{\frac{- 26 - V}{7}}} alpha_Xr1 = \frac{450}{1 + ⅇ^{\frac{- 45 - V}{10}}} beta_Xr1 = \frac{6}{1 + ⅇ^{\frac{V + 30}{11.5}}} tau_Xr1 = 1 alpha_Xr1 beta_Xr1

Component: Xr2_gate

\frac{d}{d time} (Xr2) = \frac{Xr2_infinity - Xr2}{tau_Xr2} Xr2_infinity = \frac{1}{1 + ⅇ^{\frac{88 + V}{24}}} alpha_Xr2 = \frac{3}{1 + ⅇ^{\frac{- 60 - V}{20}}} beta_Xr2 = \frac{1.12}{1 + ⅇ^{\frac{V - 60}{20}}} tau_Xr2 = 1 alpha_Xr2 beta_Xr2

Component: Xs_gate

\frac{d}{d time} (Xs) = \frac{Xs_infinity - Xs}{tau_Xs} Xs_infinity = \frac{1}{1 + ⅇ^{\frac{- 5 - V}{14}}} alpha_Xs = \frac{1100}{\sqrt{1 + ⅇ^{\frac{- 10 - V}{6}}}} beta_Xs = \frac{1}{1 + ⅇ^{\frac{V - 60}{20}}} tau_Xs = 1 alpha_Xs beta_Xs

Component: d_gate

d_infinity = \frac{1}{1 + ⅇ^{\frac{- 5 - V}{7.5}}} alpha_d = \frac{1.4}{1 + ⅇ^{\frac{- 35 - V}{13}}} + 0.25 beta_d = \frac{1.4}{1 + ⅇ^{\frac{5 + V}{5}}} gamma_d = \frac{1}{1 + ⅇ^{\frac{50 - V}{20}}} tau_d = 1 alpha_d beta_d + gamma_d \frac{d}{d time} (d) = \frac{d_infinity - d}{tau_d}

Component: f_gate

f_infinity = \frac{1}{1 + ⅇ^{\frac{20 + V}{7}}} tau_f = 1125 ⅇ^{\frac{- ({(V + 27)}^{2})}{240}} + \frac{165}{1 + ⅇ^{\frac{25 - V}{10}}} + 80 \frac{d}{d time} (f) = \frac{f_infinity - f}{tau_f}

Component: fCa_gate

fCa_infinity = \frac{alpha_fCa + beta_fCa + gamma_fCa + 0.23}{1.46} alpha_fCa = \frac{1}{1 + {(\frac{Cai}{0.000325})}^{8}} beta_fCa = \frac{0.1}{1 + ⅇ^{\frac{Cai - 0.0005}{0.0001}}} gamma_fCa = \frac{0.2}{1 + ⅇ^{\frac{Cai - 0.00075}{0.0008}}} \frac{d}{d time} (fCa) = \{\begin{matrix} 0 if fCa_infinity > fCa \land V > - 60 \\ \frac{fCa_infinity - fCa}{tau_fCa} otherwise \end{matrix}

Component: g_gate

g_infinity = \{\begin{matrix} \frac{1}{1 + \frac{{Cai}^{6}}{{0.00035}^{6}}} if Cai ≦ 0.00035 \\ \frac{1}{1 + \frac{{Cai}^{16}}{{0.00035}^{16}}} otherwise \end{matrix} \frac{d}{d time} (g) = \{\begin{matrix} 0 if g_infinity > g \land V > - 60 \\ \frac{g_infinity - g}{tau_g} otherwise \end{matrix}

Component: NL_model

Cai = Cai_in radiusLV = {(\frac{\frac{3 V_LV}{2}}{π})}^{\frac{1}{3}} xHalfSL = \frac{10000 2 π radiusLV}{xDen} Tension = ForceExt Fmult P_LV = \frac{\frac{2 Tension}{radiusLV} 1000}{133} - offset \frac{d}{d time} (xInext) = SlidingR (xHalfSL - xInext - xLLimitCB) cTn = 1 - cTnCa - cTnCaCB - cTnCB Q_b = \frac{Y_1 Cai cTn}{1} - (\frac{Z_1 cTnCa}{1}) cTnCaEff = \frac{cTnCa}{ⅇ^{R {(xHalfSL - OptiHSL)}^{2}}} Q_a = \frac{Y_2 cTnCaEff}{1} - (\frac{Z_2 cTnCaCB}{1}) Q_r = \frac{Y_3 cTnCaCB}{1} - (\frac{Z_3 cTnCB Cai}{1}) Q_d1 = \frac{Y_d {(SlidingR (xHalfSL - xInext - xLLimitCB))}^{2} cTnCaCB}{1} Q_d = \frac{Y_4 cTnCB}{1} Q_d2 = \frac{Y_d {(SlidingR (xHalfSL - xInext - xLLimitCB))}^{2} cTnCB}{1} cCaTropC = \frac{trpnbar (Q_r + Q_d2 - Q_b)}{1} \frac{d}{d time} (cTnCa) = Q_b 1 - (Q_a 1) \frac{d}{d time} (cTnCaCB) = Q_a 1 - (Q_r 1) - (Q_d1 1) \frac{d}{d time} (cTnCB) = Q_r 1 - (Q_d 1) - (Q_d2 1) xhhh = xHalfSL - xInext cTRPN = \frac{(cTnCaCB + cTnCB) trpnbar}{1} xNewCBF = \frac{AForceCB (cTnCaCB + cTnCB) trpnbar}{1} ForceP = \{\begin{matrix} xKcoeff {(xHalfSL - 0.97)}^{5} if xHalfSL > 0.97 \\ xKcoeff2 (xHalfSL - 0.97) otherwise \end{matrix} ForceB = xNewCBF xhhh ForceExt = ForceP + ForceB

Component: lung

Fpc = F_PC 0.06 Fsc = F_MU 0.06 Vpc = V_PC Vsc = V_MU DL_CO2 = \sqrt{\frac{Vpc}{Vpcmax}} 16.67 0.0316227766016838 Pao_O2 = (Pao - PH2O) 0.21 Pao_CO2 = (Pao - PH2O) 3 e -4 SHbO2_pc = \frac{{(\frac{PO2_pc}{P50_O2})}^{nH}}{{(\frac{PO2_pc}{P50_O2})}^{nH} + 1} SHbO2_sc = \frac{{(\frac{PO2_sc}{P50_O2})}^{nH}}{{(\frac{PO2_sc}{P50_O2})}^{nH} + 1} dSHbO2dPO2_pc = \frac{nH {PO2_pc}^{- 1} {(\frac{PO2_pc}{P50_O2})}^{nH}}{{({(\frac{PO2_pc}{P50_O2})}^{nH} + 1)}^{2}} dSHbO2dPO2_sc = \frac{nH {PO2_sc}^{- 1} {(\frac{PO2_sc}{P50_O2})}^{nH}}{{({(\frac{PO2_sc}{P50_O2})}^{nH} + 1)}^{2}} CtO2_pc = alphaO2 PO2_pc + CHb SHbO2_pc H CtO2_sc = alphaO2 PO2_sc + CHb SHbO2_sc H DL_O2 = (\sqrt{\frac{Vpc}{Vpcmax}} (0.397 + 0.0085 PO2_pc - (1.3 e -4 {PO2_pc}^{2})) + 5.1 e -7 {PO2_pc}^{3} 31.622776601683782) 0.0316227766016838 V_O2 = \frac{Vcytox alphaO2 PO2_isf}{Kcytox + alphaO2 PO2_isf} O2flux = DL_O2 (PA_O2 - PO2_pc) 22400 0.002678571428571428 SHbCO2_pc = \frac{\frac{PCO2_pc}{P50_CO2}}{\frac{PO2_pc}{P50_CO2} + 1} SHbCO2_sc = \frac{\frac{PCO2_sc}{P50_CO2}}{\frac{PCO2_sc}{P50_CO2} + 1} dSHbCO2dPCO2_pc = \frac{\frac{{PCO2_pc}^{- 1} PCO2_pc}{P50_CO2}}{{(\frac{PCO2_pc}{P50_CO2} + 1)}^{2}} dSHbCO2dPCO2_sc = \frac{\frac{{PCO2_sc}^{- 1} PCO2_sc}{P50_CO2}}{{(\frac{PCO2_sc}{P50_CO2} + 1)}^{2}} CtCO2_pc = alphaCO2 PCO2_pc + CHb SHbCO2_pc H CtCO2_sc = alphaCO2 PCO2_sc + CHb SHbCO2_sc H V_CO2 = RQ V_O2 CO2flux = DL_CO2 (PA_CO2 - PCO2_pc) 22400 0.002678571428571428 Rc = Kc {(\frac{Vcmax}{Vc})}^{2} Rs = As ⅇ^{\frac{Ks (VA - RV)}{Vstar - RV}} + Bs Pl = Al ⅇ^{Kl VA} + Bl Pmus = Amus \sin (6.283185307179586 f time 1.6666666666666667 e -5) + Amus Pc = \{\begin{matrix} Ac - (Bc {(\frac{Vc}{Vcmax} - 0.7)}^{2}) if \frac{Vc}{Vcmax} < 0.5 \\ 5.6 - (Bcp \log_{10} (\frac{Vcmax}{Vc} - 0.999)) otherwise \end{matrix} Pve = \frac{Vve}{Cve} Vcw = VA + VD Pcw = Acw (- 1) + Bcw \log_{10} (\frac{TLC - RV}{Vcw - RV} - 0.999) Ppl = Pcw - Pmus PA = Ppl + Pl + Pve QdotCA = \frac{Pc + Ppl - PA}{Rs} 1000.0000000000001 \frac{d}{d time} (dV) = \frac{Vcw - dV}{tau} 0.001 dVdt = \frac{Vcw - dV}{tau} 0.001 Ru = Au + Ku | dVdt | 1000.0000000000006 \frac{d}{d time} (Vc) = (\frac{Pmus - Pc - Pcw}{Ru + Rs} - (\frac{Pc - Pl - Pve}{Rs})) 0.001 dVcdt = (\frac{Pmus - Pc - Pcw}{Ru + Rs} - (\frac{Pc - Pl - Pve}{Rs})) 0.001 \frac{d}{d time} (VA) = (\frac{Pc - Pl - Pve}{Rs} - (\frac{Pstp Tbody}{(PA + 1030.94) Tstp} (O2flux + CO2flux) 2.2608333333333332 e -5)) 0.001 dVAdt = (\frac{Pc - Pl - Pve}{Rs} - (\frac{Pstp Tbody}{(PA + 1030.94) Tstp} (O2flux + CO2flux) 2.2608333333333332 e -5)) 0.001 PD = Pc + Ppl + Rc (dVcdt + \frac{Pc + Ppl - PA}{Rs} 0.001) 1 e 3 QdotDC = \frac{PD - (Pc + Ppl)}{Rc} 1000.0000000000001 QdotED = QdotDC Pao_N2 = Pao - PH2O - Pao_O2 - Pao_CO2 PplmmHg = Ppl 0.7371913011426465 PC_N2 = (Pc + Ppl + Pao 1.3565 - (PC_O2 1.3565) - (PC_CO2 1.3565)) 0.7371913011426465 PA_N2 = (PA + Pao 1.3565 - (PA_O2 1.3565) - (PA_CO2 1.3565)) 0.7371913011426465 PD_N2 = (PD + Pao 1.3565 - (PD_O2 1.3565) - (PD_CO2 1.3565)) 0.7371913011426465 \frac{d}{d time} (PO2_pc) = \frac{Fpc (CtO2_sc - CtO2_pc) + DL_O2 (PA_O2 - PO2_pc) 0.0026785714285714286}{Vpc (alphaO2 + H CHb dSHbO2dPO2_pc)} 0.01666666666666667 \frac{d}{d time} (PO2_sc) = \frac{Fsc (CtO2_pc - CtO2_sc) + PS alphaO2 (PO2_isf - PO2_sc) 9.999999999999998 e -4}{Vsc (alphaO2 + H CHb dSHbO2dPO2_sc)} 0.01666666666666667 \frac{d}{d time} (PO2_isf) = (\frac{PS (PO2_sc - PO2_isf)}{Visf} - (\frac{V_O2}{alphaO2 Visf} 1 e 3)) 1.666666666666667 e -5 \frac{d}{d time} (PCO2_pc) = \frac{Fpc (CtCO2_sc - CtCO2_pc) + DL_CO2 (PA_CO2 - PCO2_pc) 0.0026785714285714286}{Vpc (alphaCO2 + H CHb dSHbCO2dPCO2_pc)} 0.01666666666666667 \frac{d}{d time} (PCO2_sc) = \frac{Fsc (CtCO2_pc - CtCO2_sc) + PS alphaCO2 (PCO2_isf - PCO2_sc) 9.999999999999998 e -4}{Vsc (alphaCO2 + H CHb dSHbCO2dPCO2_sc)} 0.01666666666666667 \frac{d}{d time} (PCO2_isf) = (\frac{PS (PCO2_sc - PCO2_isf)}{Visf} + \frac{V_CO2}{alphaCO2 Visf} 1 e 3) 1.666666666666667 e -5 \frac{d}{d time} (PD_O2) = \{\begin{matrix} \frac{QdotED Pao_O2 - (QdotDC PD_O2)}{VD} 1.0000000000000002 e -6 if dVAdt > 0 \\ \frac{QdotED PD_O2 - (QdotDC PC_O2)}{VD} 1.0000000000000002 e -6 otherwise \end{matrix} \frac{d}{d time} (PC_O2) = \{\begin{matrix} \frac{QdotDC PD_O2 - (QdotCA PC_O2) - (PC_O2 dVcdt 1000000.0000000001)}{Vc} 1.0000000000000002 e -6 if dVAdt > 0 \\ \frac{QdotDC PC_O2 - (QdotCA PA_O2) - (PC_O2 dVcdt 1000000.0000000001)}{Vc} 1.0000000000000002 e -6 otherwise \end{matrix} \frac{d}{d time} (PA_O2) = \{\begin{matrix} (\frac{QdotCA PC_O2 - (PA_O2 dVAdt 1000000.0000000001)}{VA} - (\frac{\frac{Pstp Tbody}{Tstp} O2flux}{VA} 0.01666666666666667)) 1.0000000000000002 e -6 if dVAdt > 0 \\ (\frac{QdotCA PA_O2 - (PA_O2 dVAdt 1000000.0000000001)}{VA} - (\frac{\frac{Pstp Tbody}{Tstp} O2flux}{VA} 0.01666666666666667)) 1.0000000000000002 e -6 otherwise \end{matrix} \frac{d}{d time} (PD_CO2) = \{\begin{matrix} \frac{QdotED Pao_CO2 - (QdotDC PD_CO2)}{VD} 1.0000000000000002 e -6 if dVAdt > 0 \\ \frac{QdotED PD_CO2 - (QdotDC PC_CO2)}{VD} 1.0000000000000002 e -6 otherwise \end{matrix} \frac{d}{d time} (PC_CO2) = \{\begin{matrix} \frac{QdotDC PD_CO2 - (QdotCA PC_CO2) - (PC_CO2 dVcdt 1000000.0000000001)}{Vc} 1.0000000000000002 e -6 if dVAdt > 0 \\ \frac{QdotDC PC_CO2 - (QdotCA PA_CO2) - (PC_CO2 dVcdt 1000000.0000000001)}{Vc} 1.0000000000000002 e -6 otherwise \end{matrix} \frac{d}{d time} (PA_CO2) = \{\begin{matrix} (\frac{QdotCA PC_CO2 - (PA_CO2 dVAdt 1000000.0000000001)}{VA} - (\frac{\frac{Pstp Tbody}{Tstp} CO2flux}{VA} 0.01666666666666667)) 1.0000000000000002 e -6 if dVAdt > 0 \\ (\frac{QdotCA PA_CO2 - (PA_CO2 dVAdt 1000000.0000000001)}{VA} - (\frac{\frac{Pstp Tbody}{Tstp} CO2flux}{VA} 0.01666666666666667)) 1.0000000000000002 e -6 otherwise \end{matrix}