calcNomParams <- function(){ #Constants and Unit conversions nL_mL=1e+06 dl_ml=0.01 L_dL=10 L_mL=1000 L_m3=0.001 g_mg=0.001 ng_mg=1e-06 secs_mins=60 min_hr=60 hr_day=24 min_day=1440 MW_creatinine=113.12 Pi=3.1416 viscosity_length_constant=1.5e-09 gamma = 1.16667e-5; #Scaling parameters - can be used to parameterize model for other species ECF_scale_species = 1 BV_scale_species=1 water_intake_species_scale = 1 CO_scale_species = 1 ######################################################################################## #Parameters of normal human physiology based on literature and commmon medical knowledge ######################################################################################## ####Systemic parameters nominal_map_setpoint=85 #mmHg CO_nom= 5 #L/min ECF_nom = 15 Na_intake_rate=.07 #mEq/min - 100mmol/day or 2300 mg/day nom_water_intake = 2 #L/day ref_Na_concentration=140 #mEq/L plasma_protein_concentration = 7 #g/dl plasma_albumin_concentration= 3.5 #g/dl glucose_concentration = 5.5 #mmol/L plasma_urea = 5 #mmol/L equilibrium_serum_creatinine=0.8 #mg/dl potassium_concentration=5 #mEq/L P_venous=4 #mmHg R_venous=3.4 #mmHg nom_right_atrial_pressure=0.87 #mmHg reference_BV_mean_filling_pressure=30.18 #mmHg ####Renal parameters nom_renal_blood_flow_L_min = 1 #L/min baseline_nephrons=2e6 nom_Kf=3.9 #nl/min*mmHg nom_oncotic_pressure_difference = 28.2 #mmHg P_renal_vein=4 #mmHg RIHP0 = 6 nom_oncotic_pressure_peritubular= 28.2 #mmHg interstitial_oncotic_pressure = 5 #mmHg #Renal Vasculature nom_preafferent_arteriole_resistance= 14 ##15 #mmHg nom_afferent_diameter=1.65e-5 ###1.5e-05 #mmHg nom_efferent_diameter=1.1e-05 #mmHg #Renal Tubules Dc_pt_nom = 27e-6 #m Dc_lh = 17e-6 #m Dc_dt = 17e-6 #m Dc_cd = 17e-6 L_pt_s1_nom = 0.005 L_pt_s2_nom = 0.005 #m L_pt_s3_nom =0.004 #m L_lh_des = 0.01 ###0.003 #m L_lh_asc = 0.01 ###0.003 #m L_dct = 0.005 #m L_cd = L_lh_des tubular_compliance = 0.2 Pc_pt_s1_mmHg = 20.2#19.4#13.2 #15 #mmHg Pc_pt_s2_mmHg = 15 Pc_pt_s3_mmHg = 11 #mmHg Pc_lh_des_mmHg = 8 #mmHg Pc_lh_asc_mmHg = 7 #mmHg Pc_dt_mmHg = 6 #mmHg Pc_cd_mmHg = 5 #mmHg nominal_pt_na_reabsorption=0.7# 0.75 #fraction nominal_loh_na_reabsorption = 0.88 #0.65 #fraction nominal_dt_na_reabsorption=0.5 #fraction LoH_flow_dependence = 0.85 DCT_flow_dependence = 0.85 CD_flow_dependence = 0.85 nom_DCT_Na_Reabs_amt = 3.7e-7 nom_CD_Na_Reabs_amt = 2.5e-7 ###Renal Glucose reabsorption nom_glucose_reabs_per_unit_length_s1 = 0.0002 nom_glucose_reabs_per_unit_length_s2 = 0 nom_glucose_reabs_per_unit_length_s3 = 0.000025 diabetic_adaptation = 1 SGLT2_inhibition = 1 SGLT1_inhibition = 1 CA_inhibitor = 1 ###Renal urea reabsorption urea_permeability_PT = 0.5 ####Renal albumin seiving nom_glomerular_albumin_sieving_coefficient = 0.0001 #% max_albumin_reabsorption_fraction=0.98448 #% maximum_reabsorption_capacity = 5.5e-7 #mg/min ####RAAS Pathway parameters concentration_to_renin_activity_conversion_plasma = 61 nominal_equilibrium_PRA = 1000 #937 #fmol/ml/hr nominal_equilibrium_AngI = 7.5 #fmol/ml nominal_equilibrium_AngII = 4.75 #fmol/ml nominal_renin_half_life = 0.1733 # (hr) nominal_AngI_half_life = 0.5/60 #(hr) nominal_AngII_half_life = 0.66/60 #(hr) nominal_AT1_bound_AngII_half_life = 12/60 #hr nominal_AT2_bound_AngII_half_life = 12/60 #hr ACE_chymase_fraction = 0.95 #% of AngI converted by ACE. The rest is converted by chymase fraction_AT1_bound_AngII = 0.75 #assume AngII preferentially binds to AT1 vs AT2 ######################################################################################## #The following parameters are calculated at equilibrium using the parameters above ######################################################################################## #This pressure is the setpoint that determines the myogenic response of the preafferent vasculature nom_preafferent_pressure = nominal_map_setpoint - nom_renal_blood_flow_L_min*nom_preafferent_arteriole_resistance; #This pressure is the setpoint that determines the myogenic response of the afferent vasculature nom_glomerular_pressure = nom_preafferent_pressure - nom_renal_blood_flow_L_min*(L_m3*viscosity_length_constant/(nom_afferent_diameter^4)/baseline_nephrons); #This pressure is the setpoint that determines the tubular pressure-natriuresis response nom_postglomerular_pressure = nom_preafferent_pressure - nom_renal_blood_flow_L_min*(L_m3*viscosity_length_constant*(1/(nom_afferent_diameter^4)+1/(nom_efferent_diameter^4))/baseline_nephrons); # The rate of sodium excretion must equal the rate of sodium intake. Sodium reabsorption rates vary along the tubule, but based on literature # measurements we have a good, and literature data provides estimates for these rates. However, there is a precise # rate of sodium reabsorption required to achieve the equilibrium defined by the parameters above. # Assuming that reabsorption rates are known in all but one segment of the tubule, the exact rate # of reabsorption of the remaining segment can be calculated. We chose to calculate the CD rate of reabsorpion based on estimates for # PT, LoH, and DT reabsorption. nom_GFR = nom_Kf*(nom_glomerular_pressure - nom_oncotic_pressure_difference - Pc_pt_s1_mmHg)/nL_mL*baseline_nephrons; nom_filtered_sodium_load = nom_GFR/L_mL*ref_Na_concentration; nom_PT_Na_outflow = nom_filtered_sodium_load*(1-nominal_pt_na_reabsorption); nom_Na_in_AscLoH = nom_PT_Na_outflow/baseline_nephrons; AscLoH_Reab_Rate =(2*nominal_loh_na_reabsorption*nom_Na_in_AscLoH)/L_lh_des; #osmoles reabsorbed per unit length per minute. factor of 2 because osmoles = 2 nom_LoH_Na_outflow = nom_PT_Na_outflow*(1-nominal_loh_na_reabsorption); nom_Na_in_DCT = nom_LoH_Na_outflow/baseline_nephrons; nom_DT_Na_outflow = nom_LoH_Na_outflow*(1-nominal_dt_na_reabsorption); nominal_cd_na_reabsorption = 1-Na_intake_rate/nom_DT_Na_outflow; nom_Na_in_CD = nom_DT_Na_outflow/baseline_nephrons; #RBF = (MAP - P_venous)/RVR. Given MAP, P_venous, RBF, and preafferent, afferent, and efferent resistances, the remaining peritubular resistance at steady state can be determined nom_RVR = (nominal_map_setpoint - P_venous)/nom_renal_blood_flow_L_min nom_peritubular_resistance = nom_RVR - (nom_preafferent_arteriole_resistance + L_m3*viscosity_length_constant*(1/nom_afferent_diameter^4+1/nom_efferent_diameter^4)/baseline_nephrons); #Calculate the normal amount of sodium reabsorbed per unit surface area of the PT PT_Na_reab_perUnitSA_0 = (nom_filtered_sodium_load/baseline_nephrons)* nominal_pt_na_reabsorption/(3.14*Dc_pt_nom*(L_pt_s1_nom+L_pt_s2_nom+L_pt_s3_nom)) #Given the values for baseline MAP and CO above, the baseline TPR required to maintain this MAP and CO can be calculated. Since TPR includes renal vascular resistance, the baseline systemic (non-renal) resistance #can be calculated from this TPR and the values for baseline renal resistances defined above. nom_TPR = nominal_map_setpoint/CO_nom #nom_systemic_arterial_resistance= (nom_TPR-R_venous)*nom_RVR/(nom_RVR - nom_TPR-R_venous) nom_systemic_arterial_resistance= nom_TPR-R_venous tubular_reabsorption = nom_GFR/1000 - nom_water_intake*water_intake_species_scale/60/24 #at SS, water excretion equals water intake RIHP0 = 6 #Both RIHP and Kf are unknown, so we can either assume RIHP and calculate Kf, or vice versa. Since RIHP has been measured experimentally, #it seems better to assume a normal value for RIHP and calculate Kf nom_peritubular_cap_Kf = - tubular_reabsorption/(nom_postglomerular_pressure - RIHP0 - (nom_oncotic_pressure_peritubular - interstitial_oncotic_pressure)) ####RAAS Pathway parameters #Values for half lives and equilibrium concentrations of RAAS peptides available in the literature and # defined above to calculate nominal values for other RAAS parameters not available in the literature: #ACE activity #Chymase activity #AT1 receptor binding rate #AT2 receptor binding rate #equilibrium AT1_bound_AngII #These values are then assumed to be fixed unless specified otherwise. #Calculating these nominal parameter values initially in a separate file is required so that these parameters can then be varied independently in the main model nominal_equilibrium_PRC = nominal_equilibrium_PRA/concentration_to_renin_activity_conversion_plasma nominal_AngI_degradation_rate = log(2)/nominal_AngI_half_life #/hr nominal_AngII_degradation_rate = log(2)/nominal_AngII_half_life #/hr nominal_AT1_bound_AngII_degradation_rate = log(2)/nominal_AT1_bound_AngII_half_life nominal_AT2_bound_AngII_degradation_rate = log(2)/nominal_AT2_bound_AngII_half_life #ACE converts 95% of AngI, chymase converts the rest nominal_ACE_activity = (ACE_chymase_fraction*(nominal_equilibrium_PRA - nominal_AngI_degradation_rate*nominal_equilibrium_AngI)/nominal_equilibrium_AngI)#Therapy_effect_on_ACE nominal_chymase_activity = (1-ACE_chymase_fraction)*(nominal_equilibrium_PRA - nominal_AngI_degradation_rate*nominal_equilibrium_AngI)/nominal_equilibrium_AngI #75% of bound AngII is AT1, the rest is AT2 nominal_AT1_receptor_binding_rate = fraction_AT1_bound_AngII*(nominal_equilibrium_AngI*(nominal_ACE_activity+nominal_chymase_activity)-nominal_AngII_degradation_rate*nominal_equilibrium_AngII)/nominal_equilibrium_AngII nominal_AT2_receptor_binding_rate = (1-fraction_AT1_bound_AngII)*(nominal_equilibrium_AngI*(nominal_ACE_activity+nominal_chymase_activity)-nominal_AngII_degradation_rate*nominal_equilibrium_AngII)/nominal_equilibrium_AngII nominal_equilibrium_AT1_bound_AngII = nominal_equilibrium_AngII*nominal_AT1_receptor_binding_rate/nominal_AT1_bound_AngII_degradation_rate nominal_equilibrium_AT2_bound_AngII = nominal_equilibrium_AngII*nominal_AT2_receptor_binding_rate/nominal_AT2_bound_AngII_degradation_rate ######################################################################################## #The following parameters were determined indirectly from many different literature studies on the response #various changes in the system (e.g. drug treatments, infusions of peptide, fluid, sodium, etc.....) ######################################################################################## #Effects of AT1-bound AngII on preafferent, afferent, and efferent resistance, and aldosterone secretion AT1_svr_slope = 0 AT1_preaff_slope = 0 AT1_aff_slope=0.005 AT1_eff_slope = 0.01 AT1_PT_slope = 0.002 #0.00065 AT1_aldo_slope = 0.02 #Effects of Aldosterone on distal and collecting duct sodium reabsorption nominal_aldosterone_concentration=85 hill_aldo_DT=0.1 scale_aldo_DT=1 hill_aldo_CD=0.02 scale_aldo_CD=1 #Effects of Atrial Natriuretic Peptide (ANP)preafferent, afferent, and efferent resistance and collectin duct sodium reabsorption nom_ANP=1 rap_anp_slope=1 anp_aff_resistance_slope=0.4125 anp_eff_resistance_slope=0.0825 anp_preaff_resistance_slope=0.4125 anp_cd_slope =0.055 #Effects of Renal Sympathetic Nerve Activity on preafferent resistance, renin secretion, and PT sodium reabsorption nom_rsna = 1 map_rsna_slope=5 rap_rsna_slope=0.008 rsna_preaff_vmax=0 #1.5, rsna_preaff_EC50 = 1 rsna_preaff_hill = 4 rsna_renin_slope=0.36 pt_rsna_scale=1 pt_rsna_slope=1 #Osmolarity control of vasopressin secretion Na_controller_gain=2 Kp_VP = 0.1 Ki_VP = 0.01 nom_ADH_urea_permeability = .94 nom_ADH_water_permeability = .94 #Effects of Vasopressin on water intake and reabsorption nominal_vasopressin_conc=4 water_intake_vasopressin_scale = 1.5 water_intake_vasopressin_slope = -0.5 #Magnitude and Steepness of tubuloglomerular feedback S_tubulo_glomerular_feedback=0.6 F_md_scale_tubulo_glomerular_feedback=6 MD_Na_concentration_setpoint = 83 #Effect of macula densa sodium flow on renin secretion #md_renin_low_slope = 5 #md_renin_high_slope = -0.2 md_renin_A = 1 md_renin_tau = 1.25 #Responsiveness of renal vasculature to regulatory signals preaff_diameter_range=0.25 afferent_diameter_range=1.2e-05 efferent_diameter_range=3e-06 preaff_signal_nonlin_scale=3 afferent_signal_nonlin_scale=3 efferent_signal_nonlin_scale=3 #Limit on PT sodium reabsorption renal_threshold_Na_reabs = 16e-6 #Empirical relationship between blood volume and cardiac filling pressure - from Guyton BV_filling_pressure_slope=7.436 #RAAS pathway (these parameters can be set to different values than used to calculate the equilibrium state above) AngI_half_life=0.008333 AngII_half_life=0.011 AT1_bound_AngII_half_life=0.2 AT1_PRC_slope=-1.2 AT1_PRC_yint=0 AT2_bound_AngII_half_life=0.2 concentration_to_renin_activity_conversion_plasma=61 fraction_AT1_bound_AngII=0.75 nominal_ACE_activity=48.9 nominal_AT1_receptor_binding_rate=12.1 nominal_AT2_receptor_binding_rate=4.0 nominal_chymase_activity=1.25 nominal_equilibrium_AT1_bound_AngII=16.6315288606173 nominal_equilibrium_PRC=16.4 renin_half_life=0.1733 #Transfer constants for ODEs - determine speed of processes C_aldo_secretion=1000 C_prerenal_blood_pressure=1000 C_P_bowmans = 1000 C_P_oncotic = 1000 C_rbf=1000 C_pt_water=1000 C_tgf_reset=0 C_cardiac_output_delayed=.001 C_co_error=0.00001 C_rihp = 0.1#0.01 #time delay between peritubular pressure and RIHP C_tgf=1#/30 #1000 C_na_excretion_na_amount=-1/2#/30#/60 C_na_intake_na_amount=1/2#/30#/60 C_urine_flow_ecf_volume=-1/2#/30#/60 C_water_intake_ecf_volume=1/2#/30#/60 C_Na_error=1#/6#0 C_serum_creatinine = 1#/60 #Therapy effects HCTZ_effect_on_DT_Na_reabs = 1 HCTZ_effect_on_renin_secretion = 1 DRI_effect_on_PRA = 1 CCB_effect_on_preafferent_resistance = 1 CCB_effect_on_afferent_resistance = 1 CCB_effect_on_efferent_resistance = 1 MR_antagonist_effect_on_aldo_MR = 1 #################################################################### #These parameters are by default set to ensure strong autoregulation of cardiac output, RBF, glomerular pressure, and MAP #However, reducing these parameters reduces the ability of the system to autoregulate, and is necessary for modeling the development of hypertension, etc. #################################################################### #Metabololic tissue autoregulation of cardiac output tissue_autoreg_scale=1 Kp_CO=1.5 Ki_CO=30 #Renal autoregulation of glomerular pressure gp_autoreg_scale=2 preaff_autoreg_scale = 2 myogenic_steepness=2 #Renal autoregulation of renal blood flow RBF_autoreg_scale = 0#3 RBF_autoreg_steepness=0.001 #Pressure natiuresis effect through collecting duct sodium reabsorption #Parameters selected based on Isaksson 2014: #For a 10X increase in salt intake:MAP increases by 5mmHg, Renin decreases by 45% #GFR increases by 1.4ml/min #Strong CD effect required to minimize BP rise #PT effect + LoH effect required to produce renin response #If PT effect is too big, GFR will decrease instead of increase. #So LoH must make up for the rest pressure_natriuresis_CD_scale = 2 pressure_natriuresis_CD_slope=5 pressure_natriuresis_PT_scale = 0.2 pressure_natriuresis_PT_slope = 5 pressure_natriuresis_LoH_scale = 1 pressure_natriuresis_LoH_slope = 5 pressure_natriuresis_DCT_scale = 0 pressure_natriuresis_DCT_slope = 5 #Glomerular pressure effect on glomerular hypertrophy maximal_glom_surface_area_increase = 0#.5 T_glomerular_pressure_increases_Kf = 1e10 #PT sodium reabsorption effects on tubular hypertrophy maximal_tubule_length_increase = 0#.5 maximal_tubule_diameter_increase = 0#.25 T_PT_Na_reabs_PT_length = 1e10 T_PT_Na_reabs_PT_diameter = 1e10 #Rate at which the tubular pressure natriuresis mechanism is lost in diabetes (should be zero or negative number) CD_PN_loss_rate = 0 t=sort(ls()) param=sapply(t,names) for (i in 1:length(t)){ param[i]=get(t[i]) } param$param=NULL return(param) }