Model Mathematics

Component based math viewer is available

Component: environment

Component: temp_myogrs_and_pamk

Component: aldosterone

Component: angiotensin_control_of_aldosterone_secretion

ANMAL = (ANM - 1) ANMALD + 1

Component: osmotic_control_of_aldosterone_secretion

OSMAL = \frac{CKE - 3.3}{1.0}

Component: aldosterone_secretion

AMRBSC = ANMAL 0.909 OSMAL AMRT = (AMRBSC - 1) AMKMUL + 1 AMR = \{\begin{matrix} 0 if AMRT < 0 \\ AMRT otherwise \end{matrix} AMR1 = \{\begin{matrix} ALDKNS if ALDKNS > 0 \\ AMR + ALDINF otherwise \end{matrix}

Component: aldosterone_concentration

\frac{d}{d time} (AMC) = \frac{AMR1 - AMC}{AMT}

Component: general_aldosterone_multiplier

AM1 = AM1UL - (\frac{AM1UL - 1}{\frac{AM1LL - 1}{AM1LL - AM1UL} (AMC - 1) AMCSNS + 1}) AM = (AM1 - 1) ALDMM + 1

Component: aldosterone_effect_on_cell_membrane_K_transport

AMKT = (AM - 1) AMKM + 1 AMK = \{\begin{matrix} 0.2 if AMKT < 0.2 \\ AMKT otherwise \end{matrix}

Component: aldosterone_effect_on_cell_membrane_Na_transport

AMNAT = (AM - 1) AMNAM + 1 AMNA = \{\begin{matrix} AMNALL if AMNAT < AMNALL \\ AMNAUL if AMNAT > AMNAUL \\ AMNAT otherwise \end{matrix}

Component: aldosterone_parameter_values

Component: angiotensin

Component: instantaneous_angiotensin_formation

MDFLW3 = MDFLW ANGSCR = \{\begin{matrix} \frac{1}{1 + (MDFLW3 - 1) 72} if MDFLW3 > 1 \\ 10 - (\frac{9}{1 + (1 - MDFLW3) 8}) otherwise \end{matrix}

Component: time_delayed_angiotensin_formation

ANX = (ANGSCR - 1) ANXM \frac{d}{d time} (ANX1) = \frac{ANX - ANX1}{ANV}

Component: total_angiotensin_formation

ANPRT = (ANGSCR + ANX1) REK ANPR = \{\begin{matrix} 0.00001 if ANPRT < 0.00001 \\ ANPRT otherwise \end{matrix}

Component: artificial_angiotensin_formation

ANPR1 = \{\begin{matrix} ANGKNS if ANGKNS > 0 \\ ANPR + ANGINF otherwise \end{matrix}

Component: angiotensin_concentration

\frac{d}{d time} (ANC) = \frac{ANPR1 - ANC}{ANT}

Component: general_angiotensin_multiplier

ANM = ANMUL - (\frac{ANMUL - 1}{\frac{ANMLL - 1}{ANMLL - ANMUL} (ANC - 1) ANCSNS + 1})

Component: angiotensin_effect_on_circulation

ANU1 = (ANM - 1) ANUM + 1 ANU = \{\begin{matrix} ANULL if ANU1 < ANULL \\ ANU1 otherwise \end{matrix}

Component: angiotensin_effect_on_venous_constriction

ANUVN = (ANU - 1) ANUVM + 1

Component: angiotensin_parameter_values

Component: antidiuretic_hormone

Component: osmotic_control_of_ADH_secretion

ADHNA1 = \frac{CNA - CNR}{142 - CNR} ADHNA = \{\begin{matrix} 0 if ADHNA1 < 0 \\ ADHNA1 otherwise \end{matrix}

Component: pressure_control_of_ADH_secretion

ADHPA = \{\begin{matrix} ADHPUL if PA1 > ADHPUL \\ PA1 otherwise \end{matrix} ADHPR = {(ADHPUL - ADHPA)}^{2} ADHPAM

Component: total_ADH_secretion

ADH1 = ADHNA + ADHPR + ADHINF ADH = \{\begin{matrix} 0 if ADH1 < 0 \\ ADH1 otherwise \end{matrix}

Component: ADH_in_blood

\frac{d}{d time} (ADHC) = \frac{ADH - ADHC}{ADHTC}

Component: ADH_effect_on_nonrenal_vascular_resistance

ADHMV1 = ADHVUL - (\frac{ADHVUL - 1}{\frac{ADHVLL - 1}{ADHVLL - ADHVUL} (ADHC - 1) + 1}) ADHMV = \{\begin{matrix} ADHVLL if ADHMV1 < ADHVLL \\ ADHMV1 otherwise \end{matrix}

Component: ADH_effect_on_kidney

ADHMK1 = ADHKUL - (\frac{ADHKUL - 1}{\frac{ADHKLL - 1}{ADHKLL - ADHKUL} (ADHC - 1) + 1}) ADHMK = \{\begin{matrix} ADHKLL if ADHMK1 < ADHKLL \\ ADHMK1 otherwise \end{matrix}

Component: antidiuretic_hormone_parameter_values

Component: atrial_natriuretic_peptide

Component: total_ANP_secreted

ANPL = \{\begin{matrix} 0 if (PLA - 1) 1 < 0 \\ (PLA - 1) 1 otherwise \end{matrix} ANPR2 = \{\begin{matrix} 0 if (PRA + 1) 2 < 0 \\ (PRA + 1) 2 otherwise \end{matrix} ANP = \frac{ANPL + ANPR2}{3}

Component: ANP_into_circulation

ANP1 = \{\begin{matrix} ANPKNS if ANPKNS > 0 \\ ANP + ANPINF otherwise \end{matrix}

Component: ANP_in_plasma

\frac{d}{d time} (ANPC) = \frac{ANP1 - ANPC}{ANPTC}

Component: ANP_effect_on_renal_afferent_arteriolar_resistance

ANPX1 = ANPXUL - (\frac{ANPXUL}{0.5555556 (1 + ANPC)}) ANPX = \{\begin{matrix} - 1 if ANPX1 < - 1 \\ ANPX1 otherwise \end{matrix}

Component: atrial_natriuretic_peptide_parameter_values

Component: autonomics

Component: pressure_driving_autonomic_receptors

PA1 = \{\begin{matrix} CRRFLX if CRRFLX > 0.0000001 \\ PA - EXE otherwise \end{matrix}

Component: chemoreceptors_effect_of_PA

AUC = \{\begin{matrix} 0.005 (80 - PA1) AUC1 if PA1 < 80 \land PA1 \geq 40 \\ 0.2 AUC1 if PA1 < 40 \\ 0 otherwise \end{matrix}

Component: chemoreceptors_effect_of_art_PO2

AUC2 = \{\begin{matrix} O2CHMO (80 - PO2ART) if PO2ART < 80 \land PO2ART \geq 40 \\ O2CHMO 40 if PO2ART < 40 \\ 0 otherwise \end{matrix} AUC3 = AUC + AUC2

Component: arterial_baroreceptor_reflex

AUB = \{\begin{matrix} 0.016667 (160 - PA1) if PA1 < 160 \land PA1 \geq 80 \\ 1.3336 if PA1 < 80 \\ 0 otherwise \end{matrix} A1B = (AUB - 1) AUX + 1 AU6A = A1B - AU4 \frac{d}{d time} (AU6) = \frac{AU6A - AU6}{BAROTC} AU6C = AU6

Component: CNS_ischemic_reflex

AUN = \{\begin{matrix} 0.04 (40 - PA1) AUN1 if PA1 < 40 \\ 0 otherwise \end{matrix}

Component: autonomic_response_to_vasculature_pressure

AULP = (\frac{15}{PLA + PRA + PPA} - 1) AULPM + 1

Component: autonomic_response_to_exercise

AUEX = {EXC}^{EXCXP}

Component: total_autonomic_stimulation

AUTTL1 = (AUEX AULP (AUC3 + AU6C + AUN) - 1) EXCML + 1 AUTTL = \{\begin{matrix} 0 if AUTTL1 < 0 \\ AUTTL1 otherwise \end{matrix}

Component: actual_autonomic_stimulation

DAU = \frac{AUTTL - AU1}{AUDMP} \frac{d}{d time} (AU1) = DAU AUT = AUMAX - (\frac{AUMAX - 1}{ⅇ^{AUSLP (AU1 - 1)}}) AU = \{\begin{matrix} AUMIN if AUT < AUMIN \\ AUT otherwise \end{matrix}

Component: autonomic_drive_on_target_organs_and_tissues

VVR = (VV9 - (AU AUL)) + AUL AUO = AU - 1 AUH = AUO AUV + 1 AUR = AUO AUS + 1 AOM = AUO O2A + 1 AUM = {(AUO AUM1 + 1)}^{AUM2} AVE = AUO AUY + 1

Component: autonomics_parameter_values

Component: capillary_dynamics

Component: capillary_membrane_dynamics

Component: capillary_pressure

PC = RVS 1.7 BFN + PVS

Component: rate_of_fluid_out_of_capillaries

VTC = ((PC - PPC - PGH) + PTC) CFC + VTCPL

Component: plasma_volume_and_protein

Component: plasma_volume

VPD = (VTL - VTC - DFP) + TRPL \frac{d}{d time} (VP) = VPD

Component: plasma_protein_concentration

CPP = \frac{PRP}{VP}

Component: protein_destruction_and_formation

CPPD = \{\begin{matrix} 0 if CPP - CPR < 0 \\ CPP - CPR otherwise \end{matrix} DLP = LPPR - ({CPPD}^{LPDE} LPK)

Component: plasma_leakage

PRCD = \{\begin{matrix} 0 if PC - PCR < 0 \\ PC - PCR otherwise \end{matrix} VTCPL = {(PRCD CPK)}^{PCE}

Component: protein_influx_into_interstitium

DPC = VTCPL CPP + (CPP - CPI) 0.00104

Component: total_plasma_protein

DPP = (DLP + DPL - DPC - PPD) + TRPL 72 \frac{d}{d time} (PRP) = DPP

Component: plasma_colloid_osmotic_pressure

PPC = 0.28 CPP + 0.0019 {CPP}^{2}

Component: systemic_tissue_fluid_volume_and_protein

Component: total_systemic_fluid_volume

VTS = VEC - VP - VPF

Component: interstitial_fluid_volume

\frac{d}{d time} (VTS2) = ((VTS - 12) TSSLML - VTS2) TSSLTC VTS1 = VTS - VTS2

Component: total_interstitial_protein

DPI = DPC - DPL \frac{d}{d time} (TSP) = DPI

Component: interstitial_protein_concentration

CPI = \frac{TSP}{VTS}

Component: interstitial_colloid_osmotic_pressure

PTCPR = 0.28 CPI + 0.0019 {CPI}^{2}

Component: lymph_protein_flow

DPL = CPI VTL

Component: tissue_gel_and_fluid_and_lymph_flow

Component: hydrostatic_pressure_of_tissue_gel

CHY = {(\frac{\frac{HYL}{VTS}}{5})}^{CMPTSS} PGH = CHY PGHF + PTT

Component: total_osmotic_pressure_of_tissue_gel

POSHYL = CHY 2 PTC = POSHYL PTCPR GCOPF

Component: total_tissue_pressure

PTT = {(\frac{VTS1 - VTSF}{VTSF})}^{2} 1

Component: interstial_free_fluid_pressure

PIF = PGH - POSHYL

Component: interstitial_solid_tissue_pressure

PTS = PTT - PIF

Component: lymph_flow

PLD1 = PIF + PLDF - PTT PLD = \{\begin{matrix} 7 if PLD1 > 7 \\ PLD1 otherwise \end{matrix} VTL = \{\begin{matrix} 0 if PLD < 0 \\ PLD 0.02 otherwise \end{matrix}

Component: interstitial_gel_volume

VG = \{\begin{matrix} 0 if VTS ≦ 0 \\ 0 + \frac{(11.4 - 0) (VTS - 0)}{12 - 0} if VTS > 0 \land VTS ≦ 12 \\ 11.4 + \frac{(14 - 11.4) (VTS - 12)}{15 - 12} if VTS > 12 \land VTS ≦ 15 \\ 14 + \frac{(16 - 14) (VTS - 15)}{18 - 15} if VTS > 15 \land VTS ≦ 18 \\ 16 + \frac{(17.3 - 16) (VTS - 18)}{21 - 18} if VTS > 18 \land VTS ≦ 21 \\ 17.3 + \frac{(18 - 17.3) (VTS - 21)}{24 - 21} if VTS > 21 \land VTS ≦ 24 \\ 18 otherwise \end{matrix}

Component: interstitial_free_fluid_volume

VIF = VTS - VG

Component: capillary_dynamics_parameter_values

Component: circulatory_dynamics

Component: total_blood_volume_change

VBD = \frac{VP + VRC - VVS1 - VAS1 - VLA1 - VPA1 - VRA1}{2}

Component: right_atrium

Component: right_atrial_blood_volume

DRA = QVO - QRO \frac{d}{d time} (VRA1) = DRA VRA = VRA1 + VBD 0.0574

Component: right_atrial_pressure

VRE = VRA - 0.1 PRA = \frac{VRE}{0.005}

Component: autonomic_stimulation_effect_on_right_atrial_pressure

PRA1 = (PRA + 8) (HTAUML (AU - 1) + 1) - 8

Component: right_ventricle

Component: pressure_effect_on_right_ventricular_pumping

PP2 = \frac{\frac{PPA}{AUH}}{OSA} RVM = \{\begin{matrix} 1.06 if PP2 ≦ 0 \\ 1.06 + \frac{(0.97 - 1.06) (PP2 - 0)}{32 - 0} if PP2 > 0 \land PP2 ≦ 32 \\ 0.97 + \frac{(0.93 - 0.97) (PP2 - 32)}{38.4 - 32} if PP2 > 32 \land PP2 ≦ 38.4 \\ 0.93 + \frac{(0.8 - 0.93) (PP2 - 38.4)}{48 - 38.4} if PP2 > 38.4 \land PP2 ≦ 48 \\ 0.8 + \frac{(0.46 - 0.8) (PP2 - 48)}{60.8 - 48} if PP2 > 48 \land PP2 ≦ 60.8 \\ 0.46 + \frac{(0 - 0.46) (PP2 - 60.8)}{72 - 60.8} if PP2 > 60.8 \land PP2 ≦ 72 \\ 0 otherwise \end{matrix}

Component: pumping_effectiveness_of_right_ventricle

HPEF = (1 - QRF) AUH RVM HSR HMD HPR + \frac{QRF QLO}{QLN}

Component: right_ventricular_output

QRN = \{\begin{matrix} 0 if PRA1 ≦ - 8 \\ 0 + \frac{(0.75 - 0) (PRA1 - (- 8))}{- 6 - (- 8)} if PRA1 > - 8 \land PRA1 ≦ - 6 \\ 0.75 + \frac{(2.6 - 0.75) (PRA1 - (- 6))}{- 2 - (- 6)} if PRA1 > - 6 \land PRA1 ≦ - 2 \\ 2.6 + \frac{(9.8 - 2.6) (PRA1 - (- 2))}{4 - (- 2)} if PRA1 > - 2 \land PRA1 ≦ 4 \\ 9.8 + \frac{(13.5 - 9.8) (PRA1 - 4)}{12 - 4} if PRA1 > 4 \land PRA1 ≦ 12 \\ 13.5 otherwise \end{matrix} QRO = QRN HPEF

Component: pulmonary_vasculature

Component: pulmonary_vasculature_blood_volume

DPA = QRO - QPO \frac{d}{d time} (VPA1) = DPA VPA = VPA1 + VBD 0.155

Component: pulmonary_vasculature_pressure

VPE = VPA - 0.30625 PPA = \frac{VPE}{0.0048}

Component: pulmonary_arterial_resistance

PP1T = 0.026 PPA PP1 = \{\begin{matrix} 0.00001 if PP1T < 0.00001 \\ PP1T otherwise \end{matrix} CPA = {PP1}^{0.5} RPA = \frac{1}{CPA}

Component: pulmonary_venous_resistance

PL1 = PLA + 18 RPV = \frac{1}{PL1 0.0357}

Component: total_pulmonary_vascular_resistance

RPT = RPV + RPA

Component: pressure_gradient_through_the_lungs

PGL = PPA - PLA

Component: rate_of_blood_flow_from_pulmonary_veins_to_left_atrium

QPO = \frac{PGL}{RPT}

Component: left_atrium

Component: left_atrial_blood_volume

DLA = QPO - QLO \frac{d}{d time} (VLA1) = DLA VLA = VLA1 + VBD 0.128

Component: left_atrial_pressure

VLE = VLA - 0.38 PLA = \frac{VLE}{0.01}

Component: autonomic_stimulation_effect_on_left_atrial_pressure

PLA1 = (PLA + 4) (HTAUML (AU - 1) + 1) - 4

Component: left_ventricle

Component: pumping_effectiveness_of_left_ventricle

PA2 = \frac{PA}{AUH OSA} LVM = \{\begin{matrix} 1.04 if PA2 ≦ 0 \\ 1.04 + \frac{(1.025 - 1.04) (PA2 - 0)}{60 - 0} if PA2 > 0 \land PA2 ≦ 60 \\ 1.025 + \frac{(0.97 - 1.025) (PA2 - 60)}{125 - 60} if PA2 > 60 \land PA2 ≦ 125 \\ 0.97 + \frac{(0.88 - 0.97) (PA2 - 125)}{160 - 125} if PA2 > 125 \land PA2 ≦ 160 \\ 0.88 + \frac{(0.59 - 0.88) (PA2 - 160)}{200 - 160} if PA2 > 160 \land PA2 ≦ 200 \\ 0.59 + \frac{(0 - 0.59) (PA2 - 200)}{240 - 200} if PA2 > 200 \land PA2 ≦ 240 \\ 0 otherwise \end{matrix}

Component: left_ventricular_output

QLN = \{\begin{matrix} 0.01 if PLA1 ≦ - 2 \\ 0.01 + \frac{(3.6 - 0.01) (PLA1 - (- 2))}{1 - (- 2)} if PLA1 > - 2 \land PLA1 ≦ 1 \\ 3.6 + \frac{(9.4 - 3.6) (PLA1 - 1)}{5 - 1} if PLA1 > 1 \land PLA1 ≦ 5 \\ 9.4 + \frac{(11.6 - 9.4) (PLA1 - 5)}{8 - 5} if PLA1 > 5 \land PLA1 ≦ 8 \\ 11.6 + \frac{(13.5 - 11.6) (PLA1 - 8)}{12 - 8} if PLA1 > 8 \land PLA1 ≦ 12 \\ 13.5 otherwise \end{matrix} QLOT = LVM QLN AUH HSL HMD HPL QLO1 = \frac{PLA - PA}{3} QLO = \{\begin{matrix} QLOT + QLO1 if QLO1 > 0 \\ QLOT otherwise \end{matrix}

Component: systemic_venous_system

Component: venous_blood_volume

DVS = QAO - QVO \frac{d}{d time} (VVS1) = DVS VVS = VVS1 + VBD 0.3986

Component: angiotensin_induced_venous_constriction

VVA = (ANU - 1) ANY

Component: venous_excess_volume

VVE1 = VVS - VVR - VVA - VV7 - VV6 - ATRVFB VVE = \{\begin{matrix} 0.0001 if VVE1 < 0.0001 \\ VVE1 otherwise \end{matrix}

Component: venous_average_pressure

PVS1 = 3.7 + \frac{VVE - 0.74}{CV} PVS = \{\begin{matrix} 0.0001 if PVS1 < 0.0001 \\ PVS1 otherwise \end{matrix}

Component: venous_outflow_pressure_into_heart

PR1 = \{\begin{matrix} PR1LL if PRA < PR1LL \\ PRA otherwise \end{matrix}

Component: resistance_from_veins_to_right_atrium

RVG = \frac{0.74}{{(\frac{PVS}{VIM 3.7})}^{0.5}}

Component: rate_of_blood_flow_from_veins_to_right_atrium

PGV = PVS - PR1 QVO = \frac{PGV}{RVG}

Component: venous_resistance

CN3 = ((PC - 17) CN7 + 17) CN2 RV1 = \frac{RVSM}{CN3} RVS = AVE RV1 VIM ANUVN

Component: NM_NR_venous_resistance

NNRVR = RVS 1.79

Component: systemic_arterial_system

Component: arterial_blood_volume

DAS = QLO - QAO \frac{d}{d time} (VAS1) = DAS VAS = VAS1 + VBD 0.261

Component: arterial_pressure_and_pressure_gradient

VAE = VAS - 0.495 PA = \frac{VAE}{0.00355} PAG = PA - PRA

Component: pressure_effect_on_arterial_distention

PAM = {(\frac{PA}{100})}^{PAEX}

Component: non_renal_systemic_arterial_resistance_multiplier

R1 = \frac{\frac{ANU ADHMV AUM VIM PAMK}{PAM}}{ATRRFB}

Component: NM_NR_arterial_resistance

NNRAR = RAR ARM R1 MYOGRS RMULT1

Component: pressure_gradient_from_arteries_to_veins

PGS = PA - PVS

Component: M_systemic_resistance

RSM = RAM AMM R1 MYOGRS RMULT1

Component: total_NM_NR_systemic_resistance

RSN = NNRAR + NNRVR

Component: blood_flow_through_M_tissues

BFM = \frac{PGS}{RSM}

Component: blood_flow_through_NM_NR_tissues

BFN = \frac{PGS}{RSN}

Component: blood_flow_through_AV_fistulas

FISFLO = PAG FIS

Component: systemic_blood_flow

SYSFLO = BFM + BFN + RBF QAO = SYSFLO + FISFLO

Component: total_peripheral_resistance

RTP = \frac{PAG}{QAO}

Component: circulatory_dynamics_parameter_values

Component: electrolytes

Component: extracellular_Na_concentration

NED = (NID STH - NOD) + TRPL 142 \frac{d}{d time} (NAE) = NED CNA = \frac{NAE}{VEC}

Component: aldosterone_effect_on_cellular_K_distribution

AMK1 = (AMK - 1) ALCLK + 1

Component: extracellular_K_concentration

KTOTD = KID - KOD \frac{d}{d time} (KTOT) = KTOTD KE = \frac{KTOT - 3000}{AMK1 9.3333} CKE = \frac{KE}{VEC}

Component: intracellular_K_concentration

KI = KTOT - KE CKI = \frac{KI}{VIC}

Component: intracellular_fluid_volume

CCD = CKI - CNA VID = CCD VIDML \frac{d}{d time} (VIC) = VID

Component: total_body_water

\frac{d}{d time} (VTW) = TVD - VUD

Component: extracellular_fluid_volume

VEC = VTW - VIC

Component: electrolytes_parameter_values

Component: heart_hypertrophy_or_deterioration

Component: left_ventricular_hypertrophy

\frac{d}{d time} (HPL) = \frac{{(\frac{PA QAO}{500 HSL})}^{Z13} - HPL}{57600}

Component: right_ventricular_hypertrophy

\frac{d}{d time} (HPR) = \frac{{(\frac{PPA QAO}{75 HSR})}^{Z13} - HPR}{57600}

Component: heart_deterioration

DHM = (POT - 10) DHDTR \frac{d}{d time} (HMD1) = DHM HMD = \{\begin{matrix} 1 if HMD1 > 1 \\ HMD1 otherwise \end{matrix}

Component: heart_hypertrophy_or_deterioration_parameter_values

Component: heart_rate_and_stroke_volume

Component: effect_of_autonomic_stimulation_on_HR

AUHR = 72 AUR

Component: effect_of_PRA_on_HR

PRHR = {PR1LL}^{0.5} 5

Component: effect_of_heart_deterioration_on_HR

HDHR = (HMD - 1) 0.5 + 1

Component: heart_rate

HR = (AUHR + PRHR) HDHR

Component: stroke_volume_output

SVO = \frac{QLO}{HR}

Component: HR_and_SV_parameter_values

Component: muscle_autoregulatory_local_blood_flow_control

Component: M_autoregulatory_driving_force

PDO = PMO - 38

Component: M_short_term_autoregulation

Component: M_ST_sensitivity_control

POE = PDO POM + 1

Component: M_ST_time_delay_and_limit

\frac{d}{d time} (AMM1T) = \frac{POE 1 - AMM1T}{A4K} AMM1 = \{\begin{matrix} AMM4 if AMM1T < AMM4 \\ AMM1T otherwise \end{matrix}

Component: M_long_term_autoregulation

Component: M_LT_sensitivity_control

POF = POM2 PDO + 1

Component: M_LT_time_delay

\frac{d}{d time} (AMM2) = \frac{POF 1 - AMM2}{A4K2}

Component: global_M_blood_flow_autoregulation_output

AMM = AMM1 AMM2

Component: M_autoregulatory_local_blood_flow_parameter_values

Component: muscle_O2_delivery

Component: M_O2_blood_supply

O2ARTM = OVA BFM

Component: M_venous_O2_content

OVS = \frac{O2ARTM - RMO}{HM 5.25 BFM} PVO = 57.14 OVS {EXC}^{EXCXP2}

Component: metabolic_O2_consumption_by_M_tissue

P2O = \{\begin{matrix} 38 if PMO > 38 \\ PMO otherwise \end{matrix} MMO = AOM OMM EXC (1 - (\frac{{(38.0001 - P2O)}^{3}}{54872}))

Component: delivery_of_O2_to_M_tissues

RMO = (PVO - PMO) PM5 BFM

Component: volume_of_O2_in_M_tissue

DO2M = RMO - MMO \frac{d}{d time} (QOM1) = DO2M QOM = \{\begin{matrix} 0.0001 if QOM1 < 0.0001 \\ QOM1 otherwise \end{matrix}

Component: pressure_of_O2_in_M_tissue_cells

PMO = PK2 QOM

Component: M_O2_delivery_parameter_values

Component: non_muscle_autoregulatory_local_blood_flow_control

Component: NM_autoregulatory_driving_force

POD = POT - POR

Component: NM_short_term_autoregulation

Component: NM_ST_sensitivity_control

POB = POD POK + 1

Component: NM_ST_time_delay_and_damping

\frac{d}{d time} (AR1T) = \frac{POB 1 - AR1T}{A1K} AR1 = \{\begin{matrix} 0.5 if AR1T < 0.5 \\ AR1T otherwise \end{matrix}

Component: NM_intermediate_autoregulation

Component: NM_I_sensitivity_control

POA = PON POD + 1

Component: NM_I_time_delay_and_limit

\frac{d}{d time} (AR2T) = \frac{POA 1 - AR2T}{A2K} AR2 = \{\begin{matrix} 0.5 if AR2T < 0.5 \\ AR2T otherwise \end{matrix}

Component: NM_long_term_autoregulation

Component: NM_LT_sensitivity_control

POC = POZ POD + 1

Component: NM_LT_time_delay_and_limit

\frac{d}{d time} (AR3T) = \frac{POC 1 - AR3T}{A3K} AR3 = \{\begin{matrix} 0.3 if AR3T < 0.3 \\ AR3T otherwise \end{matrix}

Component: total_NM_autoregulation

ARM1 = AR1 AR2 AR3

Component: global_NM_blood_flow_autoregulation_output

ARM = (ARM1 - 1) AUTOSN + 1

Component: NM_autoregulatory_local_blood_flow_parameter_values

Component: non_muscle_O2_delivery

Component: NM_O2_blood_supply

O2ARTN = OVA BFN

Component: NM_venous_O2_content

OSV = \frac{O2ARTN - DOB}{HM 5.25 BFN} POV = OSV 57.14

Component: O2_consumption_by_NM_tissue

P1O = \{\begin{matrix} 35 if POT > 35 \\ POT otherwise \end{matrix} MO2 = AOM O2M (1 - (\frac{{(35.0001 - P1O)}^{3}}{42875}))

Component: delivery_of_O2_to_NM_tissues

DOB = (POV - POT) 12.857 BFN

Component: volume_of_O2_in_NM_tissue

DO2N1 = DOB - MO2 DO2N = \{\begin{matrix} DO2N1 0.1 if QO2 < 6 \land DO2N1 < 0 \\ DO2N1 otherwise \end{matrix} \frac{d}{d time} (QO2T) = DO2N QO2 = \{\begin{matrix} 0 if QO2T < 0 \\ QO2T otherwise \end{matrix}

Component: pressure_of_O2_in_NM_tissue_cells

POT = QO2 0.48611

Component: NM_O2_delivery_parameter_values

Component: pulmonary_fluid_dynamics

Component: pulmonary_capillary_pressure

PCP = \frac{(PPA - PLA) RPV}{RPV + RPA} + PLA

Component: fluid_filtration_into_pulmonary_interstitium

PFI = ((PCP - PPI) + POS - PPC) CPF

Component: pulmonary_interstitial_free_fluid_volume

DFZ = PFI - PLF DFP = DFZ \frac{d}{d time} (VPF1) = DFP VPF = \{\begin{matrix} 0.001 if VPF1 < 0.001 \\ VPF1 otherwise \end{matrix}

Component: pulmonary_interstitial_fluid_pressure

PPI = 2 - (\frac{0.15}{VPF})

Component: concentration_of_protein_in_pulmonary_interstitium

PPZ = PPN - PPO PPD = PPZ \frac{d}{d time} (PPR1) = PPD PPR = \{\begin{matrix} 0.025 if PPR1 < 0.025 \\ PPR1 otherwise \end{matrix} CPN = \frac{PPR}{VPF}

Component: colloid_osmotic_pressure_of_pulmonary_interstitium

POS = CPN 0.4

Component: protein_leakage_into_pulmonary_interstitium

PPN = (CPP - CPN) 0.000225

Component: lung_lymphatic_protein_flow

PLF = (PPI + 11) 0.0003 PPO = PLF CPN

Component: pulmonary_fluid_dynamics_parameter_values

Component: pulmonary_O2_uptake

Component: total_O2_utilization

O2UTIL = DOB + RMO

Component: alveolar_ventilation

ALVENT = O2UTIL VNTSTM 0.026667 O2VTS2 O2VAD2

Component: alveolar_PO2

PO2ALV = PO2AMB - (\frac{\frac{O2UTIL}{ALVENT}}{0.761})

Component: respiratory_O2_diffusion_into_capillaries

RSPDFC = \frac{PL2}{VPTISS + VPF} O2DFS = (PO2ALV - PO2ART) RSPDFC

Component: O2_volume_of_arterial_blood

DOVA = \frac{O2DFS - O2UTIL}{QRO 1.0} \frac{d}{d time} (OVA) = DOVA

Component: arterial_PO2

OSA = \frac{\frac{OVA}{HM}}{5.25} PO2ART = \{\begin{matrix} 114 + (OSA - 1) 6667 if OSA > 1 \\ 74 + (OSA - 0.936) 625 if OSA > 0.936 \land OSA ≦ 1 \\ 46 + (OSA - 0.8) 205.882 if OSA > 0.8 \land OSA ≦ 0.936 \\ OSA 57.5 otherwise \end{matrix}

Component: chemoreceptor_adaptation_of_alveolar_ventilation

Component: acute_chemoreceptor_adaptation_of_alveolar_ventilation

O2VTST1 = \frac{PO2ART - 67}{30} O2VTST = \{\begin{matrix} 1 if O2VTST1 > 1 \\ 0.6 if O2VTST1 < 0.6 \\ O2VTST1 otherwise \end{matrix} O2VTS2 = \frac{1}{O2VTST}

Component: progressive_chemoreceptor_adaptation_of_alveolar_ventilation

DO2VAD = ((O2VTS2 - 1) 3 - O2VAD1) 0.0005 \frac{d}{d time} (O2VAD1) = DO2VAD O2VAD2 = O2VAD1 + 1

Component: pulmonary_O2_uptake_parameter_values

Component: red_cells_and_viscosity

Component: blood_viscosity_calculations

Component: hematocrit_fraction

VB = VP + VRC HM1 = \frac{VRC}{VB} HM = 100 HM1

Component: viscosity_due_to_RBCs

VIE = \frac{HM}{(HMK - HM) HKM}

Component: blood_viscosity

VIB = VIE + 1.5 VIM = 0.3333 VIB

Component: RBC_formation_and_destruction

Component: oxygen_stimulation

PO2AM1 = \{\begin{matrix} 80 if PO2AMB > 80 \\ PO2AMB otherwise \end{matrix} HM3 = (PO2AM1 - 40) HM HM4 = PO2AMB - 40 HM5 = \{\begin{matrix} 0 if HM3 + HM4 < 0 \\ HM3 + HM4 otherwise \end{matrix} HM7 = HM6 - HM5

Component: RBC_production

RC1 = \{\begin{matrix} 0 if HM7 HM8 REK + 0.000005 < 0 \\ HM7 HM8 REK + 0.000005 otherwise \end{matrix}

Component: RBC_destruction

RC2 = VRC RKC VIM

Component: RBC_volume

RCD = (RC1 - RC2) + TRRBC \frac{d}{d time} (VRC) = RCD

Component: red_cells_and_viscosity_parameter_values

Component: stress_relaxation

Component: short_term_stress_relaxation

\frac{d}{d time} (VV7) = \frac{(VVE - 0.74) SR - VV7}{SRK}

Component: long_term_stress_relaxation

\frac{d}{d time} (VV6) = \frac{(VVE - 0.74) SR2 - VV6}{SRK2}

Component: stress_relaxation_parameter_values

Component: thirst_drinking_and_salt_appetite

Component: effect_of_salt_appetite_stimulation_on_thirst

ANMSML = (ANM - 1) ANMSLT + 1 STH1 = {(Z10 - POT)}^{2} Z11 ANMSML STH = \{\begin{matrix} 0.8 if STH1 < 0.8 \\ 8 if STH1 > 8 \\ STH1 otherwise \end{matrix}

Component: effect_of_antidiuretic_hormone_on_thirst

AHCM = (ADHC - 1) AHTHM + 1

Component: effect_of_angiotensin_on_thirst

ANMTH = (ANM - 1) ANMTM 0.001

Component: rate_of_fluid_intake

AHTH1 = AHCM STH 0.001 AHTH = \{\begin{matrix} 0 if AHTH1 < 0 \\ AHTH1 otherwise \end{matrix} TVZ1 = (ANMTH + AHTH) 1 TVZ = \{\begin{matrix} 0 if TVZ1 < 0 \\ TVZ1 otherwise \end{matrix} \frac{d}{d time} (TVD) = \frac{TVZ + DR - TVD}{TVDDL}

Component: thirst_drinking_and_salt_appetite_parameter_values

Component: volume_receptors

Component: effect_of_pressure_on_volume_receptors

AHZ1 = {(| PRA |)}^{AH10} AH9 AHZ = \{\begin{matrix} - AHZ1 if PRA < 0 \\ AHZ1 otherwise \end{matrix}

Component: time_dependent_volume_receptor_adaptation

\frac{d}{d time} (AHY) = \frac{AHZ - AHY}{AH11}

Component: total_volume_nervous_feedback

AH7 = AHZ - AHY

Component: volume_effect_on_arteries

ATRRFB = AH7 ATRFBM + 1

Component: volume_effect_on_unstressed_venous_volume

ATRVFB = AH7 ATRVM

Component: volume_receptors_parameter_values

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