/* * Simulation of nutrient digestion, absorption and outflow in * the rumen: model description * * Model Status * * This CellML model runs in both OpenCell and COR. The units have * been checked and they are consistent. In order to balance the * units in a couple of equations a "balancing factor" had to be * introduced (eqs 4.13 and 14.36). Also note there are two typographical * errors in the published paper: eq 1.1 should be C_Pd = Q_Pd/V_Ru * (not C_Pd = Q_Pd*V_Ru) and eq 8.2 P_Fu_InFu = Y_Fu_InFu*D_Fu * (not P_Fu_InFu = U_Fu_InFu*D_Fu). Finally there are quite a * few variables with undefined values. To complete the CellML * model, where parameter values were missing, a value of 1.000 * has been used. Note that there are some genuine values of 1. * These have been entered as just 1 or 1.0. The model simulation * output looks reasonable, but with no results figures in the * published paper it is hard to say whether or not the CellML * model accurately recreates the published results. * * Model Structure * * ABSTRACT: A mathematical model is described that stimulates * the digestion, absorption and outflow of nutrients in the rumen. * The model consists of 17 state variables, representing nitrogen, * carbohydrate, lipid, microbial and volatile fatty acid pools. * The flux equations are described by Michaelis-Menten or mass * action forms with model_parameters calculated from the literature. * Several specific areas of improvement in representation of rumen * processes were reconsidered during model development. These * included microbial substrate preference, differential outflow * and chemical composition of rumen microbes, recycling of microbial * matter within the rumen, uncoupling of fermentation with respect * to nitrogen availability, reduced microbial activity at reduced * rumen pH and pH-dependent absorption of volatile fatty acids * and ammonia. The model was used to examine the effects of the * diet on the profile of nutrients available for absorption and * was shown to respond appropriately to different intake and nitrogen * levels. The validity of the improvements and the predictions * of nutrient supply on a variety of dietary inputs are tested * in a companion paper. * * The original paper reference is cited below: * * Simulation of nutrient digestion, absorption and outflow in * the rumen: model description, Dijkstra J, Neal HD, Beever DE, * and France J, 1992, The Journal of Nutrition, 122, 2239-2256. * PubMed ID: 1331382 * * [[Image file: dijkstra_1992.png]] * * Diagrammatic representation of the rumen model. Purple boxes * indicate state variables and arrows indicate fluxes. */ import nsrunit; unit conversion on; // unit molar predefined unit gram_per_litre=1 kilogram^1*meter^(-3); unit day=86400 second^1; unit mole_per_day=1.1574074E-5 second^(-1)*mole^1; unit mole_per_litre_day=.01157407 meter^(-3)*second^(-1)*mole^1; unit gram_per_day=1.1574074E-8 kilogram^1*second^(-1); unit gram_per_mole=.001 kilogram^1*mole^(-1); unit mole_per_gram_day=.01157407 kilogram^(-1)*second^(-1)*mole^1; unit mole_per_gram=1E3 kilogram^(-1)*mole^1; unit gram_per_litre_day=1.1574074E-5 kilogram^1*meter^(-3)*second^(-1); unit litre_per_day=1.1574074E-8 meter^3*second^(-1); unit first_order_rate_constant=1.1574074E-5 second^(-1); math main { realDomain time day; time.min=0; extern time.max; extern time.delta; real U_Pd_PdPs(time) mole_per_day; real Q_Pd(time) mole; when(time=time.min) Q_Pd=1.000; real C_Pd(time) molar; real U_Pd_PdEx(time) mole_per_day; real P_Pd_InPd mole_per_day; real v_PdPs(time) mole_per_day; real v_PdPs_star mole_per_gram_day; v_PdPs_star=0.0576; real M_Pd_PdPs molar; real M_Pd_PdPs_star molar; M_Pd_PdPs_star=0.264; real Y_Pd_InPd molar; Y_Pd_InPd=0.0091; real D_Pd litre_per_day; D_Pd=1.000; real k_PdEx first_order_rate_constant; real T_Pd day; T_Pd=1.000; real T_Pd_star day; T_Pd_star=0.66; real Q_Ma(time) gram; when(time=time.min) Q_Ma=1.000; real Q_Mc(time) gram; when(time=time.min) Q_Mc=1.000; real V_Ru litre; V_Ru=1.000; real k_SoEx first_order_rate_constant; k_SoEx=1.000; real C_Ps(time) molar; real U_McPs_PsAm(time) mole_per_day; real U_Ps_PsMa(time) mole_per_day; real U_Ps_PsMc(time) mole_per_day; real U_MaPs_PsAm(time) mole_per_day; real M_Ha_McMa molar; M_Ha_McMa=0.0248; real Q_Ps(time) mole; when(time=time.min) Q_Ps=1.000; real P_Ps_InPs mole_per_day; real P_Ps_SaPs mole_per_day; real P_Ps_PdPs(time) mole_per_day; real P_Ps_MaMd(time) mole_per_day; real P_Ps_McPs(time) mole_per_day; real U_Ps_PsEx(time) mole_per_day; real U_Mc_McPs(time) mole_per_day; real v_Ma_PsAm(time) mole_per_day; real v_Mc_PsAm(time) mole_per_day; real v_PsMa(time) mole_per_day; real v_PsMc(time) mole_per_day; real v_PsAm_star mole_per_gram_day; v_PsAm_star=0.0144; real v_PsMa_star mole_per_gram_day; v_PsMa_star=0.0576; real v_PsMc_star mole_per_gram_day; v_PsMc_star=0.0576; real k_PsEx first_order_rate_constant; real Y_Ps_InPs molar; Y_Ps_InPs=0.0091; real Y_Ps_SaPs molar; Y_Ps_SaPs=0.0010; real Y_Ps_PdPs dimensionless; Y_Ps_PdPs=1.0; real Y_Ps_MaMd mole_per_gram; Y_Ps_MaMd=0.0067; real Y_Ps_McPs dimensionless; Y_Ps_McPs=0.0067; real D_Ps litre_per_day; D_Ps=1.000; real M_Ps_PsAm molar; M_Ps_PsAm=0.0289; real M_Ps_PsMa molar; M_Ps_PsMa=0.0224; real M_Ps_PsMc molar; M_Ps_PsMc=0.0224; real M_Ha_PsMa molar; M_Ha_PsMa=0.0248; real M_Hc_PsMc molar; M_Hc_PsMc=0.0248; real J_Ha_PsAm molar; J_Ha_PsAm=0.0165; real J_Hc_PsAm molar; J_Hc_PsAm=0.0165; real U_Mc_McEg(time) gram_per_day; real U_Ma_MaMd(time) gram_per_day; real U_Hc_PsMc(time) mole_per_day; real U_Ha_McMa(time) mole_per_day; real C_Ha(time) molar; real C_Hc(time) molar; real k_FlEx first_order_rate_constant; k_FlEx=1.000; real J_Ha_McAm molar; J_Ha_McAm=0.0165; real Q_Pu(time) mole; when(time=time.min) Q_Pu=1.000; real C_Pu(time) molar; real P_Pu_InPu mole_per_day; real U_Pu_PuEx(time) mole_per_day; real Y_Pu_InPu molar; Y_Pu_InPu=0.0091; real D_Pu litre_per_day; D_Pu=1.000; real k_PuEx first_order_rate_constant; real C_Am(time) molar; real U_Am_AmMc(time) mole_per_day; real U_Am_AmMa(time) mole_per_day; real U_Mc_McAm(time) mole_per_day; real Q_Am(time) mole; when(time=time.min) Q_Am=1.000; real P_Am_InAm mole_per_day; real P_Am_UeAm(time) mole_per_day; real P_MaAm_PsAm(time) mole_per_day; real P_McAm_PsAm(time) mole_per_day; real P_Am_McAm(time) mole_per_day; real U_Am_AmAb(time) mole_per_day; real U_Am_AmEx(time) mole_per_day; real v_UeAm(time) mole_per_day; real v_AmAb mole_per_day; real v_AmMa(time) mole_per_day; real v_AmMc(time) mole_per_day; real v_UeAm_star mole_per_litre_day; v_UeAm_star=0.00165; real v_AmAb_star mole_per_litre_day; v_AmAb_star=1.10; real v_AmMa_star mole_per_gram_day; v_AmMa_star=0.0528; real v_AmMc_star mole_per_gram_day; v_AmMc_star=0.0528; real k_AmEx first_order_rate_constant; real Y_Am_InAm molar; Y_Am_InAm=0.0588; real Y_Am_UeAm dimensionless; Y_Am_UeAm=2.0; real Y_Am_PsAm dimensionless; Y_Am_PsAm=1.257; real Y_Am_McAm dimensionless; Y_Am_McAm=0.0084; real M_Am_AmMa molar; M_Am_AmMa=0.00135; real M_Am_AmMc molar; M_Am_AmMc=0.00135; real M_Am_AmAb molar; M_Am_AmAb=0.0132; real M_pH_AmAb dimensionless; M_pH_AmAb=7.5; real phi_pH_AmAb dimensionless; phi_pH_AmAb=7.85; real M_Ha_AmMa molar; M_Ha_AmMa=0.0159; real M_Hc_AmMc molar; M_Hc_AmMc=0.0159; real J_Am_UeAm molar; J_Am_UeAm=0.00621; real D_Am litre_per_day; D_Am=1.000; real pH dimensionless; pH=7.000; real f_Po_Ma dimensionless; f_Po_Ma=0.35; real f_Ni_Fe dimensionless; f_Ni_Fe=1.000; real Q_Li(time) mole; when(time=time.min) Q_Li=1.000; real C_Li(time) molar; real P_Li_InLi mole_per_day; real P_Li_MaMd(time) mole_per_day; real U_Li_LiEx(time) mole_per_day; real Y_Li_InLi molar; Y_Li_InLi=0.0015; real Y_Li_MaMd mole_per_gram; Y_Li_MaMd=0.00021; real D_Li litre_per_day; D_Li=1.000; real k_LiEx first_order_rate_constant; real U_Sd_SdHa(time) mole_per_day; real Q_Sd(time) mole; when(time=time.min) Q_Sd=1.000; real C_Sd(time) molar; real P_Sd_InSd mole_per_day; real U_Sd_SdEx(time) mole_per_day; real Y_Sd_InSd molar; Y_Sd_InSd=0.0062; real D_Sd litre_per_day; D_Sd=1.000; real k_SdEx first_order_rate_constant; real v_SdHa(time) mole_per_day; real v_SdHa_star mole_per_gram_day; v_SdHa_star=0.2179; real M_Sd_SdHa molar; real M_Sd_SdHa_star molar; M_Sd_SdHa_star=0.416; real T_Sd day; T_Sd=1.000; real T_Sd_star day; T_Sd_star=1.04; real U_Fd_FdHc(time) mole_per_day; real Q_Fd(time) mole; when(time=time.min) Q_Fd=1.000; real C_Fd(time) molar; real P_Fd_InFd mole_per_day; real U_Fd_FdEx(time) mole_per_day; real Y_Fd_InFd molar; Y_Fd_InFd=0.0062; real D_Fd litre_per_day; D_Fd=1.000; real k_FdEx first_order_rate_constant; real v_FdHc(time) mole_per_day; real v_FdHc_star mole_per_gram_day; v_FdHc_star=0.1646; real M_Fd_FdHc molar; real M_Fd_FdHc_star molar; M_Fd_FdHc_star=0.332; real T_Fd day; T_Fd=1.000; real T_Fd_star day; T_Fd_star=0.83; real phi_pH_FdHc dimensionless; phi_pH_FdHc=22.9; real M_pH_FdHc dimensionless; M_pH_FdHc=5.97; real pm dimensionless; pm=1.000; real f dimensionless; f=1.000; real Q_Fu(time) mole; when(time=time.min) Q_Fu=1.000; real C_Fu(time) molar; real P_Fu_InFu mole_per_day; real U_Fu_FuEx(time) mole_per_day; real Y_Fu_InFu molar; Y_Fu_InFu=0.0062; real D_Fu litre_per_day; D_Fu=1.000; real k_FuEx first_order_rate_constant; real U_Ha_HaAs(time) mole_per_day; real U_Ha_AmMa(time) mole_per_day; real U_Ha_PsMa(time) mole_per_day; real U_Ha_HaVa(time) mole_per_day; real P_Ha_WrHa mole_per_day; real P_Ha_LaHa mole_per_day; real P_Ha_SrHa mole_per_day; real P_Ha_SdHa(time) mole_per_day; real P_Ha_MaMd(time) mole_per_day; real Q_Ha(time) mole; when(time=time.min) Q_Ha=1.000; real U_Ha_HaEx(time) mole_per_day; real R_Ha_AmMa dimensionless; R_Ha_AmMa=1.793; real R_Ha_PsMa dimensionless; R_Ha_PsMa=1.291; real R_Ha_McMa mole_per_gram; R_Ha_McMa=0.0086; real M_Ha_HaAs molar; M_Ha_HaAs=0.0268; real M_Ha_HaVa molar; M_Ha_HaVa=0.055; real v_HaAs(time) mole_per_day; real v_HaVa(time) mole_per_day; real v_HaAs_star mole_per_gram_day; v_HaAs_star=0.053; real v_HaVa_star mole_per_gram_day; v_HaVa_star=0.1646; real k_HaEx first_order_rate_constant; real Y_Ha_WrHa molar; Y_Ha_WrHa=0.0062; real Y_Ha_SrHa molar; Y_Ha_SrHa=0.0062; real Y_Ha_LaHa molar; Y_Ha_LaHa=0.0025; real Y_Ha_SdHa dimensionless; Y_Ha_SdHa=1.0; real Y_Ha_MaMd mole_per_gram; Y_Ha_MaMd=0.0062; real D_Wr litre_per_day; D_Wr=1.000; real D_Sr litre_per_day; D_Sr=1.000; real D_La litre_per_day; D_La=1.000; real J_Am_HaVa molar; J_Am_HaVa=0.00861; real J_Ps_HaVa molar; J_Ps_HaVa=0.01465; real U_As_MaMd(time) gram_per_day; real U_Mc_McMa(time) gram_per_day; real U_Hc_AmMc(time) mole_per_day; real U_Hc_HcVa(time) mole_per_day; real Q_Hc(time) mole; when(time=time.min) Q_Hc=1.000; real P_Hc_FdHc(time) mole_per_day; real U_Hc_HcEx(time) mole_per_day; real R_Hc_AmMc dimensionless; R_Hc_AmMc=1.793; real R_Hc_PsMc dimensionless; R_Hc_PsMc=1.291; real v_HcVa(time) mole_per_day; real v_HcVa_star mole_per_gram_day; v_HcVa_star=0.1646; real k_HcEx first_order_rate_constant; real Y_Hc_FdHc dimensionless; Y_Hc_FdHc=1.0; real M_Hc_HcVa molar; M_Hc_HcVa=0.055; real J_Am_HcVa molar; J_Am_HcVa=0.00861; real J_Ps_HcVa molar; J_Ps_HcVa=0.01465; real C_Ma(time) gram_per_litre; real P_Ma_AmMa(time) gram_per_day; real P_Ma_PsMa(time) gram_per_day; real P_Ma_McMa(time) gram_per_day; real U_Ma_PoEx(time) gram_per_day; real U_Ma_MaEx(time) gram_per_day; real k_MaMd first_order_rate_constant; real Y_Ma_AmMa gram_per_mole; Y_Ma_AmMa=118.91; real Y_Ma_PsMa gram_per_mole; Y_Ma_PsMa=149.48; real Y_Ma_McMa dimensionless; Y_Ma_McMa=149.48; real k_MaEx first_order_rate_constant; real k_PoEx first_order_rate_constant; real Q_As(time) gram; when(time=time.min) Q_As=1.000; real C_As(time) gram_per_litre; real P_As_HaAs(time) gram_per_day; real U_As_PoEx(time) gram_per_day; real U_As_AsEx(time) gram_per_day; real k_AsEx first_order_rate_constant; real k_AsMd first_order_rate_constant; real Y_As_HaAs gram_per_mole; Y_As_HaAs=112.5; real C_Mc(time) gram_per_litre; real P_Mc_AmMc(time) gram_per_day; real P_Mc_PsMc(time) gram_per_day; real U_Mc_McEx(time) gram_per_day; real k_McEx first_order_rate_constant; real Y_Mc_AmMc gram_per_mole; Y_Mc_AmMc=118.91; real Y_Mc_PsMc gram_per_mole; Y_Mc_PsMc=149.48; real v_McEg(time) gram_per_day; real v_McEg_star first_order_rate_constant; v_McEg_star=15.439; real M_Mc_McEg gram_per_litre; M_Mc_McEg=34.694; real Q_Ac(time) mole; when(time=time.min) Q_Ac=1.000; real C_Ac(time) molar; real P_Ac_InAc mole_per_day; real P_Ac_AmMa(time) mole_per_day; real P_Ac_AmMc(time) mole_per_day; real P_Ac_PsMa(time) mole_per_day; real P_Ac_PsMc(time) mole_per_day; real P_Ac_HaAs(time) mole_per_day; real P_Ac_HaVa(time) mole_per_day; real P_Ac_HcVa(time) mole_per_day; real P_MaAc_PsAm(time) mole_per_day; real P_McAc_PsAm(time) mole_per_day; real P_Ac_McMa(time) mole_per_day; real P_Ac_McAm(time) mole_per_day; real U_Ac_AcAb(time) mole_per_day; real U_Ac_AcEx(time) mole_per_day; real Q_Ac.U_Hf_AmMa(time) mole_per_day; real Q_Ac.U_Hf_AmMc(time) mole_per_day; real Q_Ac.U_Hf_PsMa(time) mole_per_day; real Q_Ac.U_Hf_PsMc(time) mole_per_day; real Q_Ac.U_Hf_HaAs(time) mole_per_day; real Q_Ac.U_Hf_McMa(time) mole_per_day; real M_Ac_AcAb molar; M_Ac_AcAb=0.338; real v_AcAb mole_per_day; real v_AcAb_star mole_per_litre_day; v_AcAb_star=7.86; real Y_Ac_LaAc dimensionless; real Y_Ac_HaVa(time) dimensionless; real Y_Ac_PsVa dimensionless; real Y_Ac_AmMa(time) dimensionless; real Y_Ac_AmMc dimensionless; real Y_Ac_PsMa(time) dimensionless; real Y_Ac_PsMc dimensionless; real Y_Ac_HaAs(time) dimensionless; real Y_Ac_McMa dimensionless; real Y_Ac_PsAm dimensionless; real Y_Ac_McAm dimensionless; real Y_Ac_WrAc dimensionless; Y_Ac_WrAc=1.000; real Y_Ac_InAc molar; Y_Ac_InAc=0.0167; real Y_Ac_StAc dimensionless; Y_Ac_StAc=1.000; real Y_Ac_CeAc dimensionless; Y_Ac_CeAc=1.000; real Y_Ac_HeAc dimensionless; Y_Ac_HeAc=1.000; real Y_Ac_PsAc dimensionless; Y_Ac_PsAc=1.000; real Y_Ac_HcVa dimensionless; real k_AcEx first_order_rate_constant; real D_Ac litre_per_day; D_Ac=1.000; real J_pH_AcAb dimensionless; J_pH_AcAb=6.45; real phi_pH_AcAb dimensionless; phi_pH_AcAb=6.48; real f_Hf_AmMa dimensionless; f_Hf_AmMa=0.526; real f_Hf_AmMc dimensionless; f_Hf_AmMc=0.526; real f_Hf_PsMa dimensionless; f_Hf_PsMa=0.711; real f_Hf_PsMc dimensionless; f_Hf_PsMc=0.711; real f_Hf_HaAs dimensionless; f_Hf_HaAs=0.306; real f_Hf_McMa dimensionless; f_Hf_McMa=0.711; real f_Lc_Le dimensionless; f_Lc_Le=2.250; real f_Ce_Fd dimensionless; f_Ce_Fd=1.000; real Q_Pr(time) mole; when(time=time.min) Q_Pr=1.000; real C_Pr(time) molar; real P_Pr_InPr mole_per_day; real P_Pr_AmMa(time) mole_per_day; real P_Pr_AmMc(time) mole_per_day; real P_Pr_PsMa(time) mole_per_day; real P_Pr_PsMc(time) mole_per_day; real P_Pr_HaAs(time) mole_per_day; real P_Pr_HaVa(time) mole_per_day; real P_Pr_HcVa(time) mole_per_day; real P_MaPr_PsAm(time) mole_per_day; real P_McPr_PsAm(time) mole_per_day; real P_Pr_McMa(time) mole_per_day; real P_Pr_McAm(time) mole_per_day; real U_Pr_PrAb(time) mole_per_day; real U_Pr_PrEx(time) mole_per_day; real Q_Pr.U_Hf_AmMa(time) mole_per_day; real Q_Pr.U_Hf_AmMc(time) mole_per_day; real Q_Pr.U_Hf_PsMa(time) mole_per_day; real Q_Pr.U_Hf_PsMc(time) mole_per_day; real Q_Pr.U_Hf_HaAs(time) mole_per_day; real Q_Pr.U_Hf_McMa(time) mole_per_day; real M_Pr_PrAb molar; M_Pr_PrAb=0.338; real v_PrAb mole_per_day; real v_PrAb_star mole_per_litre_day; v_PrAb_star=7.86; real Y_Pr_LaPr dimensionless; real Y_Pr_HaVa(time) dimensionless; real Y_Pr_PsVa dimensionless; real Y_Pr_AmMa(time) dimensionless; real Y_Pr_AmMc dimensionless; real Y_Pr_PsMa(time) dimensionless; real Y_Pr_PsMc dimensionless; real Y_Pr_HaAs(time) dimensionless; real Y_Pr_McMa dimensionless; real Y_Pr_PsAm dimensionless; real Y_Pr_McAm dimensionless; real Y_Pr_WrPr dimensionless; Y_Pr_WrPr=1.000; real Y_Pr_InPr molar; Y_Pr_InPr=0.0135; real Y_Pr_HcVa dimensionless; real Y_Pr_StPr dimensionless; Y_Pr_StPr=1.000; real Y_Pr_CePr dimensionless; Y_Pr_CePr=1.000; real Y_Pr_HePr dimensionless; Y_Pr_HePr=1.000; real Y_Pr_PsPr dimensionless; Y_Pr_PsPr=1.000; real k_PrEx first_order_rate_constant; real D_Pr litre_per_day; D_Pr=1.000; real phi_pH_PrAb dimensionless; phi_pH_PrAb=6.48; real J_pH_PrAb dimensionless; J_pH_PrAb=6.45; real Q_Bu(time) mole; when(time=time.min) Q_Bu=1.000; real C_Bu(time) molar; real P_Bu_InBu mole_per_day; real P_Bu_AmMa(time) mole_per_day; real P_Bu_AmMc(time) mole_per_day; real P_Bu_PsMa(time) mole_per_day; real P_Bu_PsMc(time) mole_per_day; real P_Bu_HaAs(time) mole_per_day; real P_Bu_HaVa(time) mole_per_day; real P_Bu_HcVa(time) mole_per_day; real P_MaBu_PsAm(time) mole_per_day; real P_McBu_PsAm(time) mole_per_day; real P_Bu_McMa(time) mole_per_day; real P_Bu_McAm(time) mole_per_day; real U_Bu_BuAb(time) mole_per_day; real U_Bu_BuEx(time) mole_per_day; real Q_Bu.U_Hf_AmMa(time) mole_per_day; real Q_Bu.U_Hf_AmMc(time) mole_per_day; real Q_Bu.U_Hf_PsMa(time) mole_per_day; real Q_Bu.U_Hf_PsMc(time) mole_per_day; real Q_Bu.U_Hf_HaAs(time) mole_per_day; real Q_Bu.U_Hf_McMa(time) mole_per_day; real M_Bu_BuAb molar; M_Bu_BuAb=0.338; real v_BuAb mole_per_day; real v_BuAb_star mole_per_litre_day; v_BuAb_star=7.86; real Y_Bu_LaBu dimensionless; real Y_Bu_HaVa(time) dimensionless; real Y_Bu_PsVa dimensionless; real Y_Bu_AmMa(time) dimensionless; real Y_Bu_AmMc dimensionless; real Y_Bu_PsMa(time) dimensionless; real Y_Bu_PsMc dimensionless; real Y_Bu_HaAs(time) dimensionless; real Y_Bu_McMa dimensionless; real Y_Bu_PsAm dimensionless; real Y_Bu_McAm dimensionless; real Y_Bu_WrBu dimensionless; Y_Bu_WrBu=1.000; real Y_Bu_InBu molar; Y_Bu_InBu=0.0114; real Y_Bu_HcVa dimensionless; real Y_Bu_StBu dimensionless; Y_Bu_StBu=1.000; real Y_Bu_CeBu dimensionless; Y_Bu_CeBu=1.000; real Y_Bu_HeBu dimensionless; Y_Bu_HeBu=1.000; real Y_Bu_PsBu dimensionless; Y_Bu_PsBu=1.000; real k_BuEx first_order_rate_constant; real D_Bu litre_per_day; D_Bu=1.000; real phi_pH_BuAb dimensionless; phi_pH_BuAb=6.48; real J_pH_BuAb dimensionless; J_pH_BuAb=6.45; real Q_Vl(time) mole; when(time=time.min) Q_Vl=1.000; real C_Vl(time) molar; real P_Vl_InVl mole_per_day; real P_Vl_AmMa(time) mole_per_day; real P_Vl_AmMc(time) mole_per_day; real P_Vl_PsMa(time) mole_per_day; real P_Vl_PsMc(time) mole_per_day; real P_Vl_HaAs(time) mole_per_day; real P_Vl_HaVa(time) mole_per_day; real P_Vl_HcVa(time) mole_per_day; real P_MaVl_PsAm(time) mole_per_day; real P_McVl_PsAm(time) mole_per_day; real P_Vl_McMa(time) mole_per_day; real P_Vl_McAm(time) mole_per_day; real U_Vl_VlAb(time) mole_per_day; real U_Vl_VlEx(time) mole_per_day; real Q_Vl.U_Hf_AmMa(time) mole_per_day; real Q_Vl.U_Hf_AmMc(time) mole_per_day; real Q_Vl.U_Hf_PsMa(time) mole_per_day; real Q_Vl.U_Hf_PsMc(time) mole_per_day; real Q_Vl.U_Hf_HaAs(time) mole_per_day; real Q_Vl.U_Hf_McMa(time) mole_per_day; real M_Vl_VlAb molar; M_Vl_VlAb=0.338; real v_VlAb mole_per_day; real v_VlAb_star mole_per_litre_day; v_VlAb_star=7.86; real Y_Vl_LaVl dimensionless; real Y_Vl_HaVa(time) dimensionless; real Y_Vl_PsVa dimensionless; real Y_Vl_AmMa(time) dimensionless; real Y_Vl_AmMc dimensionless; real Y_Vl_PsMa(time) dimensionless; real Y_Vl_PsMc dimensionless; real Y_Vl_HaAs(time) dimensionless; real Y_Vl_McMa dimensionless; real Y_Vl_PsAm dimensionless; real Y_Vl_McAm dimensionless; real Y_Vl_WrVl dimensionless; Y_Vl_WrVl=1.000; real Y_Vl_InVl molar; Y_Vl_InVl=0.0098; real Y_Vl_HcVa dimensionless; real Y_Vl_StVl dimensionless; Y_Vl_StVl=1.000; real Y_Vl_CeVl dimensionless; Y_Vl_CeVl=1.000; real Y_Vl_HeVl dimensionless; Y_Vl_HeVl=1.000; real Y_Vl_PsVl dimensionless; Y_Vl_PsVl=1.000; real k_VlEx first_order_rate_constant; real D_Vl litre_per_day; D_Vl=1.000; real phi_pH_VlAb dimensionless; phi_pH_VlAb=6.48; real J_pH_VlAb dimensionless; J_pH_VlAb=6.45; // // C_Pd=(Q_Pd/V_Ru); P_Pd_InPd=(Y_Pd_InPd*D_Pd); U_Pd_PdPs=(v_PdPs/(1+M_Pd_PdPs/C_Pd)); U_Pd_PdEx=(k_PdEx*Q_Pd); Q_Pd:time=(P_Pd_InPd-(U_Pd_PdPs+U_Pd_PdEx)); k_PdEx=k_SoEx; M_Pd_PdPs=(M_Pd_PdPs_star*(T_Pd/T_Pd_star)); v_PdPs=(v_PdPs_star*(Q_Ma+Q_Mc)); // C_Ps=(Q_Ps/V_Ru); P_Ps_InPs=(Y_Ps_InPs*D_Ps); P_Ps_SaPs=(Y_Ps_SaPs*D_Ps); P_Ps_PdPs=(Y_Ps_PdPs*U_Pd_PdPs); P_Ps_MaMd=(Y_Ps_MaMd*U_Ma_MaMd); P_Ps_McPs=(Y_Ps_McPs*U_Mc_McPs); U_MaPs_PsAm=(v_Ma_PsAm/(1+M_Ps_PsAm/C_Ps+C_Ha/J_Ha_PsAm)); U_McPs_PsAm=(v_Mc_PsAm/(1+M_Ps_PsAm/C_Ps+C_Hc/J_Hc_PsAm)); U_Ps_PsMa=(v_PsMa/(1+M_Ps_PsMa/C_Ps+M_Ha_PsMa/C_Ha)); U_Ps_PsMc=(v_PsMc/(1+M_Ps_PsMc/C_Ps+M_Hc_PsMc/C_Hc)); U_Ps_PsEx=(k_PsEx*Q_Ps); Q_Ps:time=(P_Ps_InPs+P_Ps_PdPs+P_Ps_MaMd+P_Ps_SaPs+P_Ps_McPs-(U_MaPs_PsAm+U_McPs_PsAm+U_Ps_PsMa+U_Ps_PsMc+U_Ps_PsEx)); U_Mc_McPs=(U_Mc_McEg*((1 mole_per_gram)-((1 mole_per_gram)/(1+C_Ha/J_Ha_McAm)+(1 mole_per_gram)/(1+M_Ha_McMa/C_Ha)))); v_Ma_PsAm=(v_PsAm_star*Q_Ma); v_Mc_PsAm=(v_PsAm_star*Q_Mc); v_PsMa=(v_PsMa_star*Q_Ma); v_PsMc=(v_PsMc_star*Q_Mc); k_PsEx=k_FlEx; // C_Pu=(Q_Pu/V_Ru); P_Pu_InPu=(Y_Pu_InPu*D_Pu); U_Pu_PuEx=(k_PuEx*Q_Pu); Q_Pu:time=(P_Pu_InPu-U_Pu_PuEx); k_PuEx=k_SoEx; // C_Am=(Q_Am/V_Ru); P_Am_InAm=(Y_Am_InAm*D_Am); P_Am_UeAm=(Y_Am_UeAm*v_UeAm); P_MaAm_PsAm=(Y_Am_PsAm*U_MaPs_PsAm); P_McAm_PsAm=(Y_Am_PsAm*U_McPs_PsAm); P_Am_McAm=(Y_Am_McAm*U_Mc_McAm); U_Am_AmMa=(v_AmMa/(1+M_Am_AmMa/C_Am+M_Ha_AmMa/C_Ha)); U_Am_AmMc=(v_AmMc/(1+M_Am_AmMc/C_Am+M_Hc_AmMc/C_Hc)); U_Am_AmAb=(v_AmAb/(1+M_Am_AmAb/C_Am)); U_Am_AmEx=(k_AmEx*Q_Am); Q_Am:time=(P_Am_InAm+P_MaAm_PsAm+P_McAm_PsAm+P_Am_UeAm+P_Am_McAm-(U_Am_AmAb+U_Am_AmMa+U_Am_AmMc+U_Am_AmEx)); v_UeAm=(v_UeAm_star*V_Ru*(f_Ni_Fe/(1+C_Am/J_Am_UeAm))); v_AmAb=(v_AmAb_star*(1 litre)^.25*V_Ru^.75*(1+(M_pH_AmAb/pH)^phi_pH_AmAb)); v_AmMa=(v_AmMa_star*Q_Ma*(1-f_Po_Ma)); v_AmMc=(v_AmMc_star*Q_Mc); U_Mc_McAm=((1 mole_per_gram)*U_Mc_McEg/(1+C_Ha/J_Ha_McAm)); k_AmEx=k_FlEx; // C_Li=(Q_Li/V_Ru); P_Li_InLi=(Y_Li_InLi*D_Li); P_Li_MaMd=(Y_Li_MaMd*U_Ma_MaMd); U_Li_LiEx=(k_LiEx*Q_Li); Q_Li:time=(P_Li_InLi+P_Li_MaMd-U_Li_LiEx); k_LiEx=k_FlEx; // C_Sd=(Q_Sd/V_Ru); P_Sd_InSd=(Y_Sd_InSd*D_Sd); U_Sd_SdHa=(v_SdHa/(1+M_Sd_SdHa/C_Sd)); U_Sd_SdEx=(k_SdEx*Q_Sd); Q_Sd:time=(P_Sd_InSd-(U_Sd_SdHa+U_Sd_SdEx)); v_SdHa=(v_SdHa_star*Q_Ma); M_Sd_SdHa=(M_Sd_SdHa_star*(T_Sd/T_Sd_star)); k_SdEx=k_SoEx; // C_Fd=(Q_Fd/V_Ru); P_Fd_InFd=(Y_Fd_InFd*D_Fd); U_Fd_FdHc=(v_FdHc/(1+M_Fd_FdHc/C_Fd)); U_Fd_FdEx=(k_FdEx*Q_Fd); Q_Fd:time=(P_Fd_InFd-(U_Fd_FdHc+U_Fd_FdEx)); v_FdHc=(v_FdHc_star*Q_Mc*(1-time*f/(1 day)+time*f/(1 day)/(1+(M_pH_FdHc/pm)^phi_pH_FdHc))); M_Fd_FdHc=(M_Fd_FdHc_star*(T_Fd/T_Fd_star)); k_FdEx=k_SoEx; // C_Fu=(Q_Fu/V_Ru); P_Fu_InFu=(Y_Fu_InFu*D_Fu); U_Fu_FuEx=(k_FuEx*Q_Fu); Q_Fu:time=(P_Fu_InFu-U_Fu_FuEx); k_FuEx=k_SoEx; // C_Ha=(Q_Ha/V_Ru); P_Ha_WrHa=(Y_Ha_WrHa*D_Wr); P_Ha_SrHa=(Y_Ha_SrHa*D_Sr); P_Ha_LaHa=(Y_Ha_LaHa*D_La); P_Ha_SdHa=(Y_Ha_SdHa*U_Sd_SdHa); P_Ha_MaMd=(Y_Ha_MaMd*U_As_MaMd); U_Ha_AmMa=(R_Ha_AmMa*U_Am_AmMa); U_Ha_PsMa=(R_Ha_PsMa*U_Ps_PsMa); U_Ha_McMa=(R_Ha_McMa*U_Mc_McMa); U_Ha_HaAs=(v_HaAs/(1+M_Ha_HaAs/C_Ha)); U_Ha_HaVa=(v_HaVa*((1-f_Po_Ma)/((1+M_Ha_HaVa/C_Ha)*(1+C_Am/J_Am_HaVa)*(C_Ps/J_Ps_HaVa)))+v_HaVa*f_Po_Ma/(1+M_Ha_HaVa/C_Ha)); U_Ha_HaEx=(k_HaEx*Q_Ha); Q_Ha:time=(P_Ha_WrHa+P_Ha_SrHa+P_Ha_SdHa+P_Ha_MaMd+P_Ha_LaHa-(U_Ha_AmMa+U_Ha_PsMa+U_Ha_McMa+U_Ha_HaAs+U_Ha_HaVa+U_Ha_HaEx)); v_HaAs=(v_HaAs_star*Q_Ma); v_HaVa=(v_HaVa_star*Q_Ma); k_HaEx=k_FlEx; // C_Hc=(Q_Hc/V_Ru); P_Hc_FdHc=(Y_Hc_FdHc*U_Fd_FdHc); U_Hc_AmMc=(R_Hc_AmMc*U_Am_AmMc); U_Hc_PsMc=(R_Hc_PsMc*U_Ps_PsMc); U_Hc_HcVa=(v_HcVa/((1+M_Hc_HcVa/C_Hc)*(1+C_Am/J_Am_HcVa+C_Ps/J_Ps_HcVa))); U_Hc_HcEx=(k_HcEx*Q_Hc); Q_Hc:time=(P_Hc_FdHc-(U_Hc_AmMc+U_Hc_PsMc+U_Hc_HcVa+U_Hc_HcEx)); v_HcVa=(v_HcVa_star*Q_Mc); k_HcEx=k_FlEx; // C_Ma=(Q_Ma/V_Ru); P_Ma_AmMa=(Y_Ma_AmMa*U_Am_AmMa); P_Ma_PsMa=(Y_Ma_PsMa*U_Ps_PsMa); P_Ma_McMa=(Y_Ma_McMa*U_Mc_McMa); U_Ma_MaMd=(k_MaMd*Q_Ma*f_Po_Ma); U_Ma_MaEx=(k_MaEx*Q_Ma*(1-f_Po_Ma)); U_Ma_PoEx=(k_PoEx*Q_Ma*f_Po_Ma); Q_Ma:time=(P_Ma_AmMa+P_Ma_PsMa+P_Ma_McMa-(U_Ma_MaMd+U_Mc_McMa+U_Ma_PoEx)); U_Mc_McMa=(U_Mc_McEg/(1+M_Ha_McMa/C_Ha)); k_MaMd=(k_MaEx-k_PoEx); // C_As=(Q_As/V_Ru); P_As_HaAs=(Y_As_HaAs*U_Ha_HaAs); U_As_MaMd=(k_AsMd*Q_As*f_Po_Ma); U_As_AsEx=(k_AsEx*Q_As*(1-f_Po_Ma)); U_As_PoEx=(k_PoEx*Q_As*f_Po_Ma); Q_As:time=(P_As_HaAs-(U_As_MaMd+U_As_AsEx+U_As_PoEx)); k_AsEx=k_FlEx; k_AsMd=(k_MaEx-k_PoEx); // C_Mc=(Q_Mc/V_Ru); P_Mc_AmMc=(Y_Mc_AmMc*U_Am_AmMc); P_Mc_PsMc=(Y_Mc_PsMc*U_Ps_PsMc); U_Mc_McEg=(v_McEg/(1+M_Mc_McEg/(C_Mc+C_Ma*(1-f_Po_Ma)))); U_Mc_McEx=(k_McEx*Q_Mc); Q_Mc:time=(P_Mc_AmMc+P_Mc_PsMc-(U_Mc_McEg+U_Mc_McEx)); v_McEg=(v_McEg_star*Q_Ma*f_Po_Ma*C_Mc/(C_Mc+C_Ma*(1-f_Po_Ma))); k_McEx=k_SoEx; // C_Ac=(Q_Ac/V_Ru); P_Ac_InAc=(Y_Ac_InAc*D_Ac); P_Ac_AmMa=(Y_Ac_AmMa*Q_Ac.U_Hf_AmMa); P_Ac_AmMc=(Y_Ac_AmMc*Q_Ac.U_Hf_AmMc); P_Ac_PsMa=(Y_Ac_PsMa*Q_Ac.U_Hf_PsMa); P_Ac_PsMc=(Y_Ac_PsMc*Q_Ac.U_Hf_PsMc); P_Ac_HaAs=(Y_Ac_HaAs*Q_Ac.U_Hf_HaAs); P_Ac_HaVa=(Y_Ac_HaVa*U_Ha_HaVa); P_Ac_HcVa=(Y_Ac_HcVa*U_Hc_HcVa); P_MaAc_PsAm=(Y_Ac_PsAm*U_MaPs_PsAm); P_McAc_PsAm=(Y_Ac_PsAm*U_McPs_PsAm); P_Ac_McMa=(Y_Ac_McMa*Q_Ac.U_Hf_McMa); P_Ac_McAm=(Y_Ac_McAm*U_Mc_McAm); U_Ac_AcAb=(v_AcAb/(1+M_Ac_AcAb/C_Ac)); U_Ac_AcEx=(k_AcEx*Q_Ac); Q_Ac:time=(P_Ac_InAc+P_Ac_AmMa+P_Ac_AmMc+P_Ac_PsMa+P_Ac_PsMc+P_Ac_HaAs+P_Ac_HaVa+P_Ac_HcVa+P_MaAc_PsAm+P_McAc_PsAm+P_Ac_McMa+P_Ac_McAm-(U_Ac_AcAb+U_Ac_AcEx)); Q_Ac.U_Hf_AmMa=(f_Hf_AmMa*U_Ha_AmMa); Q_Ac.U_Hf_AmMc=(f_Hf_AmMc*U_Hc_AmMc); Q_Ac.U_Hf_PsMa=(f_Hf_PsMa*U_Ha_PsMa); Q_Ac.U_Hf_PsMc=(f_Hf_PsMc*U_Hc_PsMc); Q_Ac.U_Hf_HaAs=(f_Hf_HaAs*U_Ha_HaAs); Q_Ac.U_Hf_McMa=(f_Hf_McMa*U_Ha_McMa); Y_Ac_LaAc=(f_Lc_Le*Y_Ac_WrAc); Y_Ac_HaVa=((Y_Ac_WrAc*P_Ha_WrHa+Y_Ac_LaAc*P_Ha_LaHa+Y_Ac_StAc*(P_Ha_SrHa+P_Ha_SdHa+P_Ha_MaMd))/(P_Ha_WrHa+P_Ha_LaHa+P_Ha_SrHa+P_Ha_SdHa+P_Ha_MaMd)); Y_Ac_HcVa=(f_Ce_Fd*Y_Ac_CeAc+(1-f_Ce_Fd)*Y_Ac_HeAc); Y_Ac_PsVa=Y_Ac_PsAc; Y_Ac_AmMa=Y_Ac_HaVa; Y_Ac_AmMc=Y_Ac_HcVa; Y_Ac_PsMa=Y_Ac_HaVa; Y_Ac_PsMc=Y_Ac_HcVa; Y_Ac_HaAs=Y_Ac_HaVa; Y_Ac_McMa=Y_Ac_HcVa; Y_Ac_PsAm=Y_Ac_PsVa; Y_Ac_McAm=Y_Ac_PsVa; v_AcAb=(v_AcAb_star*(1 litre)^.25*(V_Ru^.75/(1+(pH/J_pH_AcAb)^phi_pH_AcAb))); k_AcEx=k_FlEx; // C_Pr=(Q_Pr/V_Ru); P_Pr_InPr=(Y_Pr_InPr*D_Pr); P_Pr_AmMa=(Y_Pr_AmMa*Q_Pr.U_Hf_AmMa); P_Pr_AmMc=(Y_Pr_AmMc*Q_Pr.U_Hf_AmMc); P_Pr_PsMa=(Y_Pr_PsMa*Q_Pr.U_Hf_PsMa); P_Pr_PsMc=(Y_Pr_PsMc*Q_Pr.U_Hf_PsMc); P_Pr_HaAs=(Y_Pr_HaAs*Q_Pr.U_Hf_HaAs); P_Pr_HaVa=(Y_Pr_HaVa*U_Ha_HaVa); P_Pr_HcVa=(Y_Pr_HcVa*U_Hc_HcVa); P_MaPr_PsAm=(Y_Pr_PsAm*U_MaPs_PsAm); P_McPr_PsAm=(Y_Pr_PsAm*U_McPs_PsAm); P_Pr_McMa=(Y_Pr_McMa*Q_Pr.U_Hf_McMa); P_Pr_McAm=(Y_Pr_McAm*U_Mc_McAm); U_Pr_PrAb=(v_PrAb/(1+M_Pr_PrAb/C_Pr)); U_Pr_PrEx=(k_PrEx*Q_Pr); Q_Pr:time=(P_Pr_InPr+P_Pr_AmMa+P_Pr_AmMc+P_Pr_PsMa+P_Pr_PsMc+P_Pr_HaAs+P_Pr_HaVa+P_Pr_HcVa+P_MaPr_PsAm+P_McPr_PsAm+P_Pr_McMa+P_Pr_McAm-(U_Pr_PrAb+U_Pr_PrEx)); Q_Pr.U_Hf_AmMa=(f_Hf_AmMa*U_Ha_AmMa); Q_Pr.U_Hf_AmMc=(f_Hf_AmMc*U_Hc_AmMc); Q_Pr.U_Hf_PsMa=(f_Hf_PsMa*U_Ha_PsMa); Q_Pr.U_Hf_PsMc=(f_Hf_PsMc*U_Hc_PsMc); Q_Pr.U_Hf_HaAs=(f_Hf_HaAs*U_Ha_HaAs); Q_Pr.U_Hf_McMa=(f_Hf_McMa*U_Ha_McMa); Y_Pr_LaPr=(f_Lc_Le*Y_Pr_WrPr); Y_Pr_HaVa=((Y_Pr_WrPr*P_Ha_WrHa+Y_Pr_LaPr*P_Ha_LaHa+Y_Pr_StPr*(P_Ha_SrHa+P_Ha_SdHa+P_Ha_MaMd))/(P_Ha_WrHa+P_Ha_LaHa+P_Ha_SrHa+P_Ha_SdHa+P_Ha_MaMd)); Y_Pr_HcVa=(f_Ce_Fd*Y_Pr_CePr+(1-f_Ce_Fd)*Y_Pr_HePr); Y_Pr_PsVa=Y_Pr_PsPr; Y_Pr_AmMa=Y_Pr_HaVa; Y_Pr_AmMc=Y_Pr_HcVa; Y_Pr_PsMa=Y_Pr_HaVa; Y_Pr_PsMc=Y_Pr_HcVa; Y_Pr_HaAs=Y_Pr_HaVa; Y_Pr_McMa=Y_Pr_HcVa; Y_Pr_PsAm=Y_Pr_PsVa; Y_Pr_McAm=Y_Pr_PsVa; v_PrAb=(v_PrAb_star*(1 litre)^.25*(V_Ru^.75/(1+(pH/J_pH_PrAb)^phi_pH_PrAb))); k_PrEx=k_FlEx; // C_Bu=(Q_Bu/V_Ru); P_Bu_InBu=(Y_Bu_InBu*D_Bu); P_Bu_AmMa=(Y_Bu_AmMa*Q_Bu.U_Hf_AmMa); P_Bu_AmMc=(Y_Bu_AmMc*Q_Bu.U_Hf_AmMc); P_Bu_PsMa=(Y_Bu_PsMa*Q_Bu.U_Hf_PsMa); P_Bu_PsMc=(Y_Bu_PsMc*Q_Bu.U_Hf_PsMc); P_Bu_HaAs=(Y_Bu_HaAs*Q_Bu.U_Hf_HaAs); P_Bu_HaVa=(Y_Bu_HaVa*U_Ha_HaVa); P_Bu_HcVa=(Y_Bu_HcVa*U_Hc_HcVa); P_MaBu_PsAm=(Y_Bu_PsAm*U_MaPs_PsAm); P_McBu_PsAm=(Y_Bu_PsAm*U_McPs_PsAm); P_Bu_McMa=(Y_Bu_McMa*Q_Bu.U_Hf_McMa); P_Bu_McAm=(Y_Bu_McAm*U_Mc_McAm); U_Bu_BuAb=(v_BuAb/(1+M_Bu_BuAb/C_Bu)); U_Bu_BuEx=(k_BuEx*Q_Bu); Q_Bu:time=(P_Bu_InBu+P_Bu_AmMa+P_Bu_AmMc+P_Bu_PsMa+P_Bu_PsMc+P_Bu_HaAs+P_Bu_HaVa+P_Bu_HcVa+P_MaBu_PsAm+P_McBu_PsAm+P_Bu_McMa+P_Bu_McAm-(U_Bu_BuAb+U_Bu_BuEx)); Q_Bu.U_Hf_AmMa=(f_Hf_AmMa*U_Ha_AmMa); Q_Bu.U_Hf_AmMc=(f_Hf_AmMc*U_Hc_AmMc); Q_Bu.U_Hf_PsMa=(f_Hf_PsMa*U_Ha_PsMa); Q_Bu.U_Hf_PsMc=(f_Hf_PsMc*U_Hc_PsMc); Q_Bu.U_Hf_HaAs=(f_Hf_HaAs*U_Ha_HaAs); Q_Bu.U_Hf_McMa=(f_Hf_McMa*U_Ha_McMa); Y_Bu_LaBu=(f_Lc_Le*Y_Bu_WrBu); Y_Bu_HaVa=((Y_Bu_WrBu*P_Ha_WrHa+Y_Bu_LaBu*P_Ha_LaHa+Y_Bu_StBu*(P_Ha_SrHa+P_Ha_SdHa+P_Ha_MaMd))/(P_Ha_WrHa+P_Ha_LaHa+P_Ha_SrHa+P_Ha_SdHa+P_Ha_MaMd)); Y_Bu_HcVa=(f_Ce_Fd*Y_Bu_CeBu+(1-f_Ce_Fd)*Y_Bu_HeBu); Y_Bu_PsVa=Y_Bu_PsBu; Y_Bu_AmMa=Y_Bu_HaVa; Y_Bu_AmMc=Y_Bu_HcVa; Y_Bu_PsMa=Y_Bu_HaVa; Y_Bu_PsMc=Y_Bu_HcVa; Y_Bu_HaAs=Y_Bu_HaVa; Y_Bu_McMa=Y_Bu_HcVa; Y_Bu_PsAm=Y_Bu_PsVa; Y_Bu_McAm=Y_Bu_PsVa; v_BuAb=(v_BuAb_star*(1 litre)^.25*(V_Ru^.75/(1+(pH/J_pH_BuAb)^phi_pH_BuAb))); k_BuEx=k_FlEx; // C_Vl=(Q_Vl/V_Ru); P_Vl_InVl=(Y_Vl_InVl*D_Vl); P_Vl_AmMa=(Y_Vl_AmMa*Q_Vl.U_Hf_AmMa); P_Vl_AmMc=(Y_Vl_AmMc*Q_Vl.U_Hf_AmMc); P_Vl_PsMa=(Y_Vl_PsMa*Q_Vl.U_Hf_PsMa); P_Vl_PsMc=(Y_Vl_PsMc*Q_Vl.U_Hf_PsMc); P_Vl_HaAs=(Y_Vl_HaAs*Q_Vl.U_Hf_HaAs); P_Vl_HaVa=(Y_Vl_HaVa*U_Ha_HaVa); P_Vl_HcVa=(Y_Vl_HcVa*U_Hc_HcVa); P_MaVl_PsAm=(Y_Vl_PsAm*U_MaPs_PsAm); P_McVl_PsAm=(Y_Vl_PsAm*U_McPs_PsAm); P_Vl_McMa=(Y_Vl_McMa*Q_Vl.U_Hf_McMa); P_Vl_McAm=(Y_Vl_McAm*U_Mc_McAm); U_Vl_VlAb=(v_VlAb/(1+M_Vl_VlAb/C_Vl)); U_Vl_VlEx=(k_VlEx*Q_Vl); Q_Vl:time=(P_Vl_InVl+P_Vl_AmMa+P_Vl_AmMc+P_Vl_PsMa+P_Vl_PsMc+P_Vl_HaAs+P_Vl_HaVa+P_Vl_HcVa+P_MaVl_PsAm+P_McVl_PsAm+P_Vl_McMa+P_Vl_McAm-(U_Vl_VlAb+U_Vl_VlEx)); Q_Vl.U_Hf_AmMa=(f_Hf_AmMa*U_Ha_AmMa); Q_Vl.U_Hf_AmMc=(f_Hf_AmMc*U_Hc_AmMc); Q_Vl.U_Hf_PsMa=(f_Hf_PsMa*U_Ha_PsMa); Q_Vl.U_Hf_PsMc=(f_Hf_PsMc*U_Hc_PsMc); Q_Vl.U_Hf_HaAs=(f_Hf_HaAs*U_Ha_HaAs); Q_Vl.U_Hf_McMa=(f_Hf_McMa*U_Ha_McMa); Y_Vl_LaVl=(f_Lc_Le*Y_Vl_WrVl); Y_Vl_HaVa=((Y_Vl_WrVl*P_Ha_WrHa+Y_Vl_LaVl*P_Ha_LaHa+Y_Vl_StVl*(P_Ha_SrHa+P_Ha_SdHa+P_Ha_MaMd))/(P_Ha_WrHa+P_Ha_LaHa+P_Ha_SrHa+P_Ha_SdHa+P_Ha_MaMd)); Y_Vl_HcVa=(f_Ce_Fd*Y_Vl_CeVl+(1-f_Ce_Fd)*Y_Vl_HeVl); Y_Vl_PsVa=Y_Vl_PsVl; Y_Vl_AmMa=Y_Vl_HaVa; Y_Vl_AmMc=Y_Vl_HcVa; Y_Vl_PsMa=Y_Vl_HaVa; Y_Vl_PsMc=Y_Vl_HcVa; Y_Vl_HaAs=Y_Vl_HaVa; Y_Vl_McMa=Y_Vl_HcVa; Y_Vl_PsAm=Y_Vl_PsVa; Y_Vl_McAm=Y_Vl_PsVa; v_VlAb=(v_VlAb_star*(1 litre)^.25*(V_Ru^.75/(1+(pH/J_pH_VlAb)^phi_pH_VlAb))); k_VlEx=k_FlEx; // k_MaEx=k_FlEx; k_PoEx=(k_SoEx/2); }