Model Mathematics

Component: input_values

Component: state_variables

Component: parameter_values

Component: environment

Component: kidney

Component: perfusion_pressure

ddtimePAR1=100+PA-100RCDFPC-PAR1RCDFDP PAR=RAPRSPifRAPRSP>0RFCDFT0PAR1ifRFCDFT>0PA-GBLotherwise

Component: renal_autoregulatory_feedback_factor

RNAUG1T=MDFLW-1RNAUGN+1 RNAUG1=RNAULLifRNAUG1T<RNAULLRNAUULifRNAUG1T>RNAUULRNAUG1Totherwise RNAUG2=RNAUG1-RNAUG3 ddtimeRNAUG3=RNAUG2-1RNAUAD

Component: afferent_arterial_resistance

Component: autonomic_effect_on_AAR

AUMKT=AUM-1ARF+1 AUMK=0.8ifAUMKT<0.8AUMKTotherwise

Component: angiotensin_effect_on_AAR

ANMAR1=ANM-1ANMAM+1 ANMAR=ANMARLifANMAR1<ANMARLANMAR1otherwise

Component: AAR_calculation

AAR1=AARKPAMKRNAUMKRNAUG2ANMAR40MYOGRS

Component: atrial_natriuretic_peptide_effect_on_AAR

AART=AAR1-ANPXANPXAF+ANPXAF AAR=AARLLifAART<AARLLAARTotherwise

Component: efferent_arterial_resistance

Component: autonomic_effect_on_EAR

AUMK2=AUMK-1AUMK1+1

Component: angiotensin_effect_on_EAR

ANMER=ANM-1ANMEM+1

Component: effect_of_renal_autoregulatory_feedback_on_EAR

RNAUG4=RNAUG2-1EFAFR+1

Component: EAR_calculation

EAR1=43.333EARKANMERRNAUG4MYOGRSAUMK2 EAR=EARLLifEAR1<EARLLEAR1otherwise

Component: total_renal_resistance

RR=AAR+EAR

Component: normal_renal_blood_flow

RFN=PARRR

Component: actual_renal_blood_flow

RBF=REKRFN

Component: glomerular_capillaries

Component: glomerular_colloid_osmotic_pressure

EFAFPR1=RFN1-HM1RFN1-HM1-GFN EFAFPR=1ifEFAFPR1<1EFAFPR1otherwise GLPC=EFAFPR1.35PPC0.98ifGLPCA>0PPC+4otherwise

Component: glomerular_pressure

APD=AARRFN GLP=PAR-APD

Component: glomerular_filtration_rate

PFL=GLP-GLPC-PXTP GFN1=PFLGFLC GFN=GFNLLifGFN1<GFNLLGFN1otherwise GFR=GFNREK

Component: proximal_tubular_and_macula_densa_flow

PTFL=GFN8 MDFLWT=PTFL-1MDFL1+1 MDFLW=0ifMDFLWT<0MDFLWTotherwise

Component: renal_tissue_osmotic_pressure

RTSPPC1=GLPCRTPPR-RTPPRS RTSPPC=1ifRTSPPC1<1RTSPPC1otherwise

Component: urea_handling

Component: glomerular_urea_concentration

ddtimePLUR=URFORM-UROD

Component: plasma_urea_concentration

PLURC=PLURVTW

Component: renal_peritubular_capillaries

Component: peritubular_capillary_pressure

RCPRS=RFN-1.2RFABX+1.2RVRS

Component: peritubular_capillary_reabsorption_factor

RABSPR=GLPC+RTSPRS-RCPRS-RTSPPC RFAB1=RABSPRRABSC RFAB=RFAB1 RFABD1=RFAB-1RFABDM+1 RFABD=0.0001ifRFABD1<0.0001RFABD1otherwise

Component: sodium_and_potassium_handling

Component: distal_tubular_Na_delivery

DTNAI=MDFLWCNA0.0061619

Component: Na_reabsorption_into_distal_tubules

DTNARA1=AMNARFABDDTNARDIURETADHMK-1AHMNAR+1 DTNARA=DTNARLifDTNARA1<DTNARLDTNARA1otherwise

Component: angiotensin_induced_Na_reabsorption_into_distal_tubules

DTNANG1=ANM-1ANMNAM+10.1 DTNANG=0ifDTNANG1<0DTNANG1otherwise

Component: distal_tubular_K_delivery

DTKI=DTNAICKECNA

Component: effect_of_physical_forces_on_distal_K_reabsorption

RFABK=RFABD-1RFABKM

Component: effect_of_fluid_flow_on_distal_K_reabsorption

MDFLK1=MDFLW-1MDFLKM+1 MDFLK=0.1ifMDFLK1<0.1MDFLK1otherwise

Component: K_reabsorption_into_distal_tubules

ddtimeDTKA=KODNVUDN0.0004518-DTKA1.0

Component: K_secretion_from_distal_tubules

ANMKE1=ANM-1ANMKEM+1 ANMKE=ANMKELifANMKE1<ANMKELANMKE1otherwise DTKSC=CKE4.4CKEEXAMK0.08MDFLKANMKE

Component: urinary_excretion

Component: normal_Na_excretion

NODN1=DTNAI-DTNARA-DTNANG NODN=0.00000001ifNODN1<0.00000001NODN1otherwise

Component: normal_K_excretion

KODN1=DTKI+DTKSC-DTKA-RFABK KODN=0ifKODN1<0KODN1otherwise

Component: normal_urea_excretion

DTURI=GFN2PLURC3.84

Component: normal_osmolar_and_water_excretion

OSMOPN1=DTURI+2NODN+KODN OSMOPN=0.6ifOSMOPN1>0.6OSMOPN1otherwise

Component: normal_urine_volume

OSMOP1T=OSMOPN1-0.6 OSMOP1=0ifOSMOP1T<0OSMOP1Totherwise VUDN=OSMOPN600ADHMK+OSMOP1360

Component: actual_Na_excretion_rate

NOD=NODNREK

Component: actual_K_excretion_rate

KOD=KODNREK

Component: actual_urea_excretion_rate

UROD=DTURIREK

Component: actual_urine_volume

VUD=VUDNREK

Component: state_variables

Component: parameter_values