Model Mathematics

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Component: input_values

Component: state_variables

Component: parameter_values

Component: environment

Component: kidney

Component: perfusion_pressure

\frac{d}{d time} (PAR1) = \frac{100 + (PA - 100) RCDFPC - PAR1}{RCDFDP} PAR = \{\begin{matrix} RAPRSP if RAPRSP > 0 \land RFCDFT ≦ 0 \\ PAR1 if RFCDFT > 0 \\ PA - GBL otherwise \end{matrix}

Component: renal_autoregulatory_feedback_factor

RNAUG1T = (MDFLW - 1) RNAUGN + 1 RNAUG1 = \{\begin{matrix} RNAULL if RNAUG1T < RNAULL \\ RNAUUL if RNAUG1T > RNAUUL \\ RNAUG1T otherwise \end{matrix} RNAUG2 = RNAUG1 - RNAUG3 \frac{d}{d time} (RNAUG3) = (RNAUG2 - 1) RNAUAD

Component: afferent_arterial_resistance

Component: autonomic_effect_on_AAR

AUMKT = (AUM - 1) ARF + 1 AUMK = \{\begin{matrix} 0.8 if AUMKT < 0.8 \\ AUMKT otherwise \end{matrix}

Component: angiotensin_effect_on_AAR

ANMAR1 = (ANM - 1) ANMAM + 1 ANMAR = \{\begin{matrix} ANMARL if ANMAR1 < ANMARL \\ ANMAR1 otherwise \end{matrix}

Component: AAR_calculation

AAR1 = AARK PAMKRN AUMK RNAUG2 ANMAR 40 MYOGRS

Component: atrial_natriuretic_peptide_effect_on_AAR

AART = (AAR1 - (ANPX ANPXAF)) + ANPXAF AAR = \{\begin{matrix} AARLL if AART < AARLL \\ AART otherwise \end{matrix}

Component: efferent_arterial_resistance

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 AUMK2 EAR = \{\begin{matrix} EARLL if EAR1 < EARLL \\ EAR1 otherwise \end{matrix}

Component: total_renal_resistance

RR = AAR + EAR

Component: normal_renal_blood_flow

RFN = \frac{PAR}{RR}

Component: actual_renal_blood_flow

RBF = REK RFN

Component: glomerular_capillaries

Component: glomerular_colloid_osmotic_pressure

EFAFPR1 = \frac{RFN (1 - HM1)}{RFN (1 - HM1) - GFN} EFAFPR = \{\begin{matrix} 1 if EFAFPR1 < 1 \\ EFAFPR1 otherwise \end{matrix} GLPC = \{\begin{matrix} {EFAFPR}^{1.35} PPC 0.98 if GLPCA > 0 \\ PPC + 4 otherwise \end{matrix}

Component: glomerular_pressure

APD = AAR RFN GLP = PAR - APD

Component: glomerular_filtration_rate

PFL = GLP - GLPC - PXTP GFN1 = PFL GFLC GFN = \{\begin{matrix} GFNLL if GFN1 < GFNLL \\ GFN1 otherwise \end{matrix} GFR = GFN REK

Component: proximal_tubular_and_macula_densa_flow

PTFL = GFN 8 MDFLWT = (PTFL - 1) MDFL1 + 1 MDFLW = \{\begin{matrix} 0 if MDFLWT < 0 \\ MDFLWT otherwise \end{matrix}

Component: renal_tissue_osmotic_pressure

RTSPPC1 = GLPC RTPPR - RTPPRS RTSPPC = \{\begin{matrix} 1 if RTSPPC1 < 1 \\ RTSPPC1 otherwise \end{matrix}

Component: urea_handling

Component: glomerular_urea_concentration

\frac{d}{d time} (PLUR) = URFORM - UROD

Component: plasma_urea_concentration

PLURC = \frac{PLUR}{VTW}

Component: renal_peritubular_capillaries

Component: peritubular_capillary_pressure

RCPRS = ((RFN - 1.2) RFABX + 1.2) RVRS

Component: peritubular_capillary_reabsorption_factor

RABSPR = GLPC + RTSPRS - RCPRS - RTSPPC RFAB1 = RABSPR RABSC RFAB = RFAB1 RFABD1 = (RFAB - 1) RFABDM + 1 RFABD = \{\begin{matrix} 0.0001 if RFABD1 < 0.0001 \\ RFABD1 otherwise \end{matrix}

Component: sodium_and_potassium_handling

Component: distal_tubular_Na_delivery

DTNAI = MDFLW CNA 0.0061619

Component: Na_reabsorption_into_distal_tubules

DTNARA1 = \frac{AMNA RFABD DTNAR}{DIURET} ((ADHMK - 1) AHMNAR + 1) DTNARA = \{\begin{matrix} DTNARL if DTNARA1 < DTNARL \\ DTNARA1 otherwise \end{matrix}

Component: angiotensin_induced_Na_reabsorption_into_distal_tubules

DTNANG1 = ((ANM - 1) ANMNAM + 1) 0.1 DTNANG = \{\begin{matrix} 0 if DTNANG1 < 0 \\ DTNANG1 otherwise \end{matrix}

Component: distal_tubular_K_delivery

DTKI = \frac{DTNAI CKE}{CNA}

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 + 1 MDFLK = \{\begin{matrix} 0.1 if MDFLK1 < 0.1 \\ MDFLK1 otherwise \end{matrix}

Component: K_reabsorption_into_distal_tubules

\frac{d}{d time} (DTKA) = (\frac{KODN}{VUDN} 0.0004518 - DTKA) 1.0

Component: K_secretion_from_distal_tubules

ANMKE1 = (ANM - 1) ANMKEM + 1 ANMKE = \{\begin{matrix} ANMKEL if ANMKE1 < ANMKEL \\ ANMKE1 otherwise \end{matrix} DTKSC = \frac{{(\frac{CKE}{4.4})}^{CKEEX} AMK 0.08 MDFLK}{ANMKE}

Component: urinary_excretion

Component: normal_Na_excretion

NODN1 = DTNAI - DTNARA - DTNANG NODN = \{\begin{matrix} 0.00000001 if NODN1 < 0.00000001 \\ NODN1 otherwise \end{matrix}

Component: normal_K_excretion

KODN1 = DTKI + DTKSC - DTKA - RFABK KODN = \{\begin{matrix} 0 if KODN1 < 0 \\ KODN1 otherwise \end{matrix}

Component: normal_urea_excretion

DTURI = {GFN}^{2} PLURC 3.84

Component: normal_osmolar_and_water_excretion

OSMOPN1 = DTURI + 2 (NODN + KODN) OSMOPN = \{\begin{matrix} 0.6 if OSMOPN1 > 0.6 \\ OSMOPN1 otherwise \end{matrix}

Component: normal_urine_volume

OSMOP1T = OSMOPN1 - 0.6 OSMOP1 = \{\begin{matrix} 0 if OSMOP1T < 0 \\ OSMOP1T otherwise \end{matrix} VUDN = \frac{OSMOPN}{600 ADHMK} + \frac{OSMOP1}{360}

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