# Model Mathematics

### Component: perfusion_pressure

$ddtimePAR1=100+PA-100⁢RCDFPC-PAR1RCDFDPPAR=RAPRSPifRAPRSP>0∧RFCDFT≦0PAR1ifRFCDFT>0PA-GBLotherwise$

### Component: renal_autoregulatory_feedback_factor

$RNAUG1T=MDFLW-1⁢RNAUGN+1RNAUG1=RNAULLifRNAUG1TRNAUULRNAUG1TotherwiseRNAUG2=RNAUG1-RNAUG3ddtimeRNAUG3=RNAUG2-1⁢RNAUAD$

### Component: autonomic_effect_on_AAR

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

### Component: angiotensin_effect_on_AAR

$ANMAR1=ANM-1⁢ANMAM+1ANMAR=ANMARLifANMAR1

### Component: AAR_calculation

$AAR1=AARK⁢PAMKRN⁢AUMK⁢RNAUG2⁢ANMAR⁢40⁢MYOGRS$

### Component: atrial_natriuretic_peptide_effect_on_AAR

$AART=AAR1-ANPX⁢ANPXAF+ANPXAFAAR=AARLLifAART

### Component: autonomic_effect_on_EAR

$AUMK2=AUMK-1⁢AUMK1+1$

### Component: angiotensin_effect_on_EAR

$ANMER=ANM-1⁢ANMEM+1$

### Component: effect_of_renal_autoregulatory_feedback_on_EAR

$RNAUG4=RNAUG2-1⁢EFAFR+1$

### Component: EAR_calculation

$EAR1=43.333⁢EARK⁢ANMER⁢RNAUG4⁢MYOGRS⁢AUMK2EAR=EARLLifEAR1

### Component: total_renal_resistance

$RR=AAR+EAR$

### Component: normal_renal_blood_flow

$RFN=PARRR$

### Component: actual_renal_blood_flow

$RBF=REK⁢RFN$

### Component: glomerular_colloid_osmotic_pressure

$EFAFPR1=RFN⁢1-HM1RFN⁢1-HM1-GFNEFAFPR=1ifEFAFPR1<1EFAFPR1otherwiseGLPC=EFAFPR1.35⁢PPC⁢0.98ifGLPCA>0PPC+4otherwise$

### Component: glomerular_pressure

$APD=AAR⁢RFNGLP=PAR-APD$

### Component: glomerular_filtration_rate

$PFL=GLP-GLPC-PXTPGFN1=PFL⁢GFLCGFN=GFNLLifGFN1

### Component: proximal_tubular_and_macula_densa_flow

$PTFL=GFN⁢8MDFLWT=PTFL-1⁢MDFL1+1MDFLW=0ifMDFLWT<0MDFLWTotherwise$

### Component: renal_tissue_osmotic_pressure

$RTSPPC1=GLPC⁢RTPPR-RTPPRSRTSPPC=1ifRTSPPC1<1RTSPPC1otherwise$

### Component: glomerular_urea_concentration

$ddtimePLUR=URFORM-UROD$

### Component: plasma_urea_concentration

$PLURC=PLURVTW$

### Component: peritubular_capillary_pressure

$RCPRS=RFN-1.2⁢RFABX+1.2⁢RVRS$

### Component: peritubular_capillary_reabsorption_factor

$RABSPR=GLPC+RTSPRS-RCPRS-RTSPPCRFAB1=RABSPR⁢RABSCRFAB=RFAB1RFABD1=RFAB-1⁢RFABDM+1RFABD=0.0001ifRFABD1<0.0001RFABD1otherwise$

### Component: distal_tubular_Na_delivery

$DTNAI=MDFLW⁢CNA⁢0.0061619$

### Component: Na_reabsorption_into_distal_tubules

$DTNARA1=AMNA⁢RFABD⁢DTNARDIURET⁢ADHMK-1⁢AHMNAR+1DTNARA=DTNARLifDTNARA1

### Component: angiotensin_induced_Na_reabsorption_into_distal_tubules

$DTNANG1=ANM-1⁢ANMNAM+1⁢0.1DTNANG=0ifDTNANG1<0DTNANG1otherwise$

### Component: distal_tubular_K_delivery

$DTKI=DTNAI⁢CKECNA$

### Component: effect_of_physical_forces_on_distal_K_reabsorption

$RFABK=RFABD-1⁢RFABKM$

### Component: effect_of_fluid_flow_on_distal_K_reabsorption

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

### Component: K_reabsorption_into_distal_tubules

$ddtimeDTKA=KODNVUDN⁢0.0004518-DTKA⁢1.0$

### Component: K_secretion_from_distal_tubules

$ANMKE1=ANM-1⁢ANMKEM+1ANMKE=ANMKELifANMKE1

### Component: normal_Na_excretion

$NODN1=DTNAI-DTNARA-DTNANGNODN=0.00000001ifNODN1<0.00000001NODN1otherwise$

### Component: normal_K_excretion

$KODN1=DTKI+DTKSC-DTKA-RFABKKODN=0ifKODN1<0KODN1otherwise$

### Component: normal_urea_excretion

$DTURI=GFN2⁢PLURC⁢3.84$

### Component: normal_osmolar_and_water_excretion

$OSMOPN1=DTURI+2⁢NODN+KODNOSMOPN=0.6ifOSMOPN1>0.6OSMOPN1otherwise$

### Component: normal_urine_volume

$OSMOP1T=OSMOPN1-0.6OSMOP1=0ifOSMOP1T<0OSMOP1TotherwiseVUDN=OSMOPN600⁢ADHMK+OSMOP1360$

### Component: actual_Na_excretion_rate

$NOD=NODN⁢REK$

### Component: actual_K_excretion_rate

$KOD=KODN⁢REK$

### Component: actual_urea_excretion_rate

$UROD=DTURI⁢REK$

### Component: actual_urine_volume

$VUD=VUDN⁢REK$

### Component: parameter_values

Source
Derived from workspace Guyton, Kidney, 2008 at changeset c88a251a599d.
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