Model Mathematics

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Component: environment

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}

Model Mathematics

Component: environment

Component: circulatory_dynamics

Component: total_blood_volume_change

Component: right_atrium

Component: right_atrial_blood_volume

Component: right_atrial_pressure

Component: autonomic_stimulation_effect_on_right_atrial_pressure

Component: right_ventricle

Component: pressure_effect_on_right_ventricular_pumping

Component: pumping_effectiveness_of_right_ventricle

Component: right_ventricular_output

Component: pulmonary_vasculature

Component: pulmonary_vasculature_blood_volume

Component: pulmonary_vasculature_pressure

Component: pulmonary_arterial_resistance

Component: pulmonary_venous_resistance

Component: total_pulmonary_vascular_resistance

Component: pressure_gradient_through_the_lungs

Component: rate_of_blood_flow_from_pulmonary_veins_to_left_atrium

Component: left_atrium

Component: left_atrial_blood_volume

Component: left_atrial_pressure

Component: autonomic_stimulation_effect_on_left_atrial_pressure

Component: left_ventricle

Component: pumping_effectiveness_of_left_ventricle

Component: left_ventricular_output

Component: systemic_venous_system

Component: venous_blood_volume

Component: angiotensin_induced_venous_constriction

Component: venous_excess_volume

Component: venous_average_pressure

Component: venous_outflow_pressure_into_heart

Component: resistance_from_veins_to_right_atrium

Component: rate_of_blood_flow_from_veins_to_right_atrium

Component: venous_resistance

Component: NM_NR_venous_resistance

Component: systemic_arterial_system

Component: arterial_blood_volume

Component: arterial_pressure_and_pressure_gradient

Component: pressure_effect_on_arterial_distention

Component: non_renal_systemic_arterial_resistance_multiplier

Component: NM_NR_arterial_resistance

Component: pressure_gradient_from_arteries_to_veins

Component: M_systemic_resistance

Component: total_NM_NR_systemic_resistance

Component: blood_flow_through_M_tissues

Component: blood_flow_through_NM_NR_tissues

Component: blood_flow_through_AV_fistulas

Component: systemic_blood_flow

Component: total_peripheral_resistance

Component: parameter_values