Source: docs/evidence_review/smith2004_variable_dictionary.md @ e3d560e · Source SHA-256 2890ea9a9f52eb55ff1cbd610bd5c3810da7ee6b9735d61c7383ccc52e77e1d6 · Markdown source

Smith 2004 canonical CellML: variable and equation dictionary

evidence review draft 2026-11-01; equations transcribed mechanically from MathML; interpretation fields are ours and marked; nothing here changes the model

Counts: 76 variables, 32 equations, 14 components. Source files: docs/evidence/a_smith_2004_canonical.cellml (equations, units, values) and docs/evidence/a_smith_2004.cellml (SemSim composite annotations, PMR workspace 267). Machine-readable version: smith2004_variable_dictionary.json.

Units declared in the CellML

name definition
kPa [['pascal', 'kilo', None]]
mL [['liter', 'milli', None]]
per_mL [['liter', 'milli', '-1']]
kPa_per_mL [['kPa', None, None], ['per_mL', None, None]]
kPa_second_per_mL [['pascal', 'kilo', None], ['second', None, None], ['mL', None, '-1']]
mL_per_second [['mL', None, None], ['second', None, '-1']]
mL_per_second2 [['mL', None, None], ['second', None, '-2']]
per_second2 [['second', None, '-2']]
kPa_second2_per_mL [['pascal', 'kilo', None], ['second', None, '2'], ['mL', None, '-1']]

Equations (mechanical MathML transcription)

id component defines equation
E1 driver_function tau (tau = piecewise{ time if time<=period ; time-period if time<=2*period ; ... ; time-12*period if time<=13*period }) [14-beat explicit remainder, see CellML]
E2 driver_function e_t (e_t = (A * exp(((-B) * ((tau - C) ^ 2[dimensionless])))))
E3 pericardium V_pcd (V_pcd = (V_lv + V_rv))
E4 pericardium P_pcd (P_pcd = (P_0_pcd * (exp((lambda_pcd * (V_pcd - V_0_pcd))) - 1[dimensionless])))
E5 pericardium P_peri (P_peri = (P_pcd + P_th))
E6 left_ventricle V_lvf (V_lvf = (V_lv - V_spt))
E7 left_ventricle P_lvf (P_lvf = ((e_t * P_es_lvf) + ((1[dimensionless] - e_t) * P_ed_lvf)))
E8 left_ventricle P_lv (P_lv = (P_lvf + P_peri))
E9 left_ventricle V_lv (ODE) (d(V_lv)/dtime = piecewise{ 0[mL_per_second] if ((Q_mt < 0[mL_per_second]) and (Q_av < 0[mL_per_second])) ; (-Q_av) if (Q_mt < 0[mL_per_second]) ; Q_mt if (Q_av < 0[mL_per_second]) ; (Q_mt - Q_av) otherwise })
E10 lvf_calculator P_es_lvf (P_es_lvf = (E_es_lvf * (V_lvf - V_d_lvf)))
E11 lvf_calculator P_ed_lvf (P_ed_lvf = (P_0_lvf * (exp((lambda_lvf * (V_lvf - V_0_lvf))) - 1[dimensionless])))
E12 right_ventricle V_rvf (V_rvf = (V_rv + V_spt))
E13 right_ventricle P_rvf (P_rvf = ((e_t * P_es_rvf) + ((1[dimensionless] - e_t) * P_ed_rvf)))
E14 right_ventricle P_rv (P_rv = (P_rvf + P_peri))
E15 right_ventricle V_rv (ODE) (d(V_rv)/dtime = piecewise{ 0[mL_per_second] if ((Q_tc < 0[mL_per_second]) and (Q_pv < 0[mL_per_second])) ; (-Q_pv) if (Q_tc < 0[mL_per_second]) ; Q_tc if (Q_pv < 0[mL_per_second]) ; (Q_tc - Q_pv) otherwise })
E16 rvf_calculator P_es_rvf (P_es_rvf = (E_es_rvf * (V_rvf - V_d_rvf)))
E17 rvf_calculator P_ed_rvf (P_ed_rvf = (P_0_rvf * (exp((lambda_rvf * (V_rvf - V_0_rvf))) - 1[dimensionless])))
E18 septum 0[kPa] (0[kPa] = (((((e_t * E_es_spt * (V_spt - V_d_spt)) + ((one - e_t) * P_0_spt * (exp((lambda_spt * (V_spt - V_0_spt))) - one))) - (e_t * E_es_lvf * (V_lv - V_spt))) - ((1[dimensionless] - e_t) * P_0_lvf * (exp((lambda_lvf * (V_lv - V_spt))) - 1[dimensionless]))) + (e_t * E_es_rvf * (V_rv + V_spt)) + ((1[dimensionless] - e_t) * P_0_rvf * (exp((lambda_rvf * (V_rv + V_spt))) - 1[dimensionless]))))
E19 pulmonary_artery P_pa (P_pa = ((E_es_pa * (V_pa - V_d_pa)) + P_th))
E20 pulmonary_artery V_pa (ODE) (d(V_pa)/dtime = piecewise{ (-Q_pul) if (Q_pv < 0[mL_per_second]) ; (Q_pv - Q_pul) otherwise })
E21 pulmonary_vein P_pu (P_pu = ((E_es_pu * (V_pu - V_d_pu)) + P_th))
E22 pulmonary_vein V_pu (ODE) (d(V_pu)/dtime = piecewise{ Q_pul if (Q_mt < 0[mL_per_second]) ; (Q_pul - Q_mt) otherwise })
E23 aorta P_ao (P_ao = (E_es_ao * (V_ao - V_d_ao)))
E24 aorta V_ao (ODE) (d(V_ao)/dtime = piecewise{ (-Q_sys) if (Q_av < 0[mL_per_second]) ; (Q_av - Q_sys) otherwise })
E25 vena_cava P_vc (P_vc = (E_es_vc * (V_vc - V_d_vc)))
E26 vena_cava V_vc (ODE) (d(V_vc)/dtime = piecewise{ Q_sys if (Q_tc < 0[mL_per_second]) ; (Q_sys - Q_tc) otherwise })
E27 flow Q_sys (Q_sys = ((P_ao - P_vc) / R_sys))
E28 flow Q_pul (Q_pul = ((P_pa - P_pu) / R_pul))
E29 flow Q_mt (ODE) (d(Q_mt)/dtime = piecewise{ 0[mL_per_second2] if (((P_pu - P_lv) < 0[kPa]) and (Q_mt < 0[mL_per_second])) ; (((P_pu - P_lv) - (Q_mt * R_mt)) / L_mt) otherwise })
E30 flow Q_av (ODE) (d(Q_av)/dtime = piecewise{ 0[mL_per_second2] if (((P_lv - P_ao) < 0[kPa]) and (Q_av < 0[mL_per_second])) ; (((P_lv - P_ao) - (Q_av * R_av)) / L_av) otherwise })
E31 flow Q_tc (ODE) (d(Q_tc)/dtime = piecewise{ 0[mL_per_second2] if (((P_vc - P_rv) < 0[kPa]) and (Q_tc < 0[mL_per_second])) ; (((P_vc - P_rv) - (Q_tc * R_tc)) / L_tc) otherwise })
E32 flow Q_pv (ODE) (d(Q_pv)/dtime = piecewise{ 0[mL_per_second2] if (((P_rv - P_pa) < 0[kPa]) and (Q_pv < 0[mL_per_second])) ; (((P_rv - P_pa) - (Q_pv * R_pv)) / L_pv) otherwise })

Variables

Columns: unit as declared in the CellML; unit as read under the C1 decision of 2026-11-01 (decisions.md); role; defining equation; SemSim workspace-267 annotation (free text / OPB property / entity or process); definition in the 2004 manuscript; reference point and external pressure (our reading of the equations); direction; unit status; values and units in the literature. UNKNOWN means no retained source settles it; CONFLICT Cn points to evidence_review.md.

variable unit declared unit as read value role eq. SemSim free text SemSim OPB property SemSim entity / process definition in source paper reference point / external pressure direction unit status literature value (unit)
A dimensionless dimensionless 1 parameter (constant) or ODE initial condition Gaussian Curve Magnitude - - n/a n/a consistent
B per_second2 per_second2 80 parameter (constant) or ODE initial condition Gaussian Curve Width - - n/a n/a consistent
C second second 0.375 parameter (constant) or ODE initial condition Gaussian Curve Delay - - n/a n/a consistent Paeme 2011 eq (4): C_1 = 0.27 s, D_1 = 1 s, citing Smith 2005 Control Eng Pract (not Smith 2004); CellML C = 0.375 s, period 0.75 s; Smith 2004 author manuscript (card S6P): Eq. (5): C=0.27 for the single-chamber profile of Figure 3; closed-loop C not stated (C7)
E_es_ao kPa_per_mL mmHg/mL 0.6913 parameter (constant) or ODE initial condition Aortic end systolic elastance - - n/a n/a C1 decided Paeme 2011 Tables 1-3 (CC BY, docs/evidence/d_fulltext_PMC3271239_paeme2011.xml): 0.0 mmHg/ml (sic; CellML 0.6913)
E_es_lvf kPa_per_mL mmHg/mL 2.8798 parameter (constant) or ODE initial condition Left ventricular free wall end systolic elastance; Left ventricular free wall end systolic pressure - - n/a n/a C1 decided Paeme 2011 Tables 1-3 (CC BY, docs/evidence/d_fulltext_PMC3271239_paeme2011.xml): 2.8798 mmHg/ml
E_es_pa kPa_per_mL mmHg/mL 0.369 parameter (constant) or ODE initial condition Pulmonary arterial end systolic elastance - - n/a n/a C1 decided Paeme 2011 Tables 1-3 (CC BY, docs/evidence/d_fulltext_PMC3271239_paeme2011.xml): 0.3690 mmHg/ml
E_es_pu kPa_per_mL mmHg/mL 0.0073 parameter (constant) or ODE initial condition End systolic pulmonary vein elastance - - n/a n/a C1 decided Paeme 2011 Tables 1-3 (CC BY, docs/evidence/d_fulltext_PMC3271239_paeme2011.xml): 0.0073 mmHg/ml
E_es_rvf kPa_per_mL mmHg/mL 0.585 parameter (constant) or ODE initial condition Right ventricular free wall end systolic elastance - - n/a n/a C1 decided Paeme 2011 Tables 1-3 (CC BY, docs/evidence/d_fulltext_PMC3271239_paeme2011.xml): 0.5850 mmHg/ml
E_es_spt kPa_per_mL mmHg/mL 48.754 parameter (constant) or ODE initial condition Septal end systolic elastance - - n/a n/a C1 decided Paeme 2011 Tables 1-3 (CC BY, docs/evidence/d_fulltext_PMC3271239_paeme2011.xml): 48.7540 mmHg/ml
E_es_vc kPa_per_mL mmHg/mL 0.0059 parameter (constant) or ODE initial condition Vena cava end systolic elastance - - n/a n/a C1 decided Paeme 2011 Tables 1-3 (CC BY, docs/evidence/d_fulltext_PMC3271239_paeme2011.xml): 0.0059 mmHg/ml
L_av kPa_second2_per_mL mmHg·s²/mL 1.2189e-4 parameter (constant) or ODE initial condition Atrial valve fluid inertance - - n/a n/a C1 decided Paeme 2011 Tables 1-3 (CC BY, docs/evidence/d_fulltext_PMC3271239_paeme2011.xml): 1.2189e-4 mmHg s^2/ml; Smith 2004 author manuscript (card S6P): inertance at this valve is in the manuscript (p. 9, Figure 1); unit system mmHg s^2/ml (p. 17); value not given
L_mt kPa_second2_per_mL mmHg·s²/mL 7.6968e-5 parameter (constant) or ODE initial condition Mitrial valve fluid inertance - - n/a n/a C1 decided Paeme 2011 Tables 1-3 (CC BY, docs/evidence/d_fulltext_PMC3271239_paeme2011.xml): 7.6968e-5 mmHg s^2/ml; Smith 2004 author manuscript (card S6P): CONFLICT C9: the manuscript includes inertia only at the aortic and pulmonary outflow (p. 9, p. 13, Figure 1); no source located for a mitral/tricuspid inertance
L_pv kPa_second2_per_mL mmHg·s²/mL 1.4868e-4 parameter (constant) or ODE initial condition Pulmonary valve fluid inertance - - n/a n/a C1 decided Paeme 2011 Tables 1-3 (CC BY, docs/evidence/d_fulltext_PMC3271239_paeme2011.xml): 1.4868e-4 mmHg s^2/ml; Smith 2004 author manuscript (card S6P): inertance at this valve is in the manuscript (p. 9, Figure 1); unit system mmHg s^2/ml (p. 17); value not given
L_tc kPa_second2_per_mL mmHg·s²/mL 8.0093e-5 parameter (constant) or ODE initial condition Tricuspid valve fluid inertance - - n/a n/a C1 decided Paeme 2011 Tables 1-3 (CC BY, docs/evidence/d_fulltext_PMC3271239_paeme2011.xml): 8.0093e-5 mmHg s^2/ml; Smith 2004 author manuscript (card S6P): CONFLICT C9: the manuscript includes inertia only at the aortic and pulmonary outflow (p. 9, p. 13, Figure 1); no source located for a mitral/tricuspid inertance
P_0_lvf kPa mmHg 0.1203 parameter (constant) or ODE initial condition End diastolic pressure across the left ventricular wall - - EDPVR scale parameter n/a C1 decided Paeme 2011 Tables 1-3 (CC BY, docs/evidence/d_fulltext_PMC3271239_paeme2011.xml): 0.1203 mmHg
P_0_pcd kPa mmHg 0.5003 parameter (constant) or ODE initial condition End diastolic pressure across the pericardium - - pericardium EDPVR scale parameter n/a C1 decided Paeme 2011 Tables 1-3 (CC BY, docs/evidence/d_fulltext_PMC3271239_paeme2011.xml): 0.5003 mmHg
P_0_rvf kPa mmHg 0.2157 parameter (constant) or ODE initial condition Right ventricular free wall end diastolic pressure - - EDPVR scale parameter n/a C1 decided Paeme 2011 Tables 1-3 (CC BY, docs/evidence/d_fulltext_PMC3271239_paeme2011.xml): 0.2157 mmHg
P_0_spt kPa mmHg 1.1101 parameter (constant) or ODE initial condition Septal wall end diastolic pressure - - EDPVR scale parameter (septum) n/a C1 decided Paeme 2011 Tables 1-3 (CC BY, docs/evidence/d_fulltext_PMC3271239_paeme2011.xml): 1.1101 mmHg
P_ao kPa mmHg algebraic (explicitly computed) E23 Pressure in systemic arteries OPB_00509 (Fluid pressure) physicalPropertyOf: FMA_9670 (Portion of blood) --part_of--> FMA_12239 (Lumen of aorta) P_ao = E_es_ao*(V_ao-V_d_ao); NO P_th term (E23) n/a C1 decided
P_ed_lvf kPa mmHg algebraic (explicitly computed) E11 End diastolic pressure across the left ventricular free wall - - EDPVR pressure of LV free wall (E11) n/a C1 decided
P_ed_rvf kPa mmHg algebraic (explicitly computed) E17 Right ventricular free wall end diastolic pressure - - EDPVR pressure of RV free wall (E17) n/a C1 decided
P_es_lvf kPa mmHg algebraic (explicitly computed) E10 Left ventricular freewall end systolic blood pressure - - ESPVR pressure of LV free wall (E10) n/a C1 decided
P_es_rvf kPa mmHg algebraic (explicitly computed) E16 Right ventricular free wall end systolic pressure - - ESPVR pressure of RV free wall (E16) n/a C1 decided
P_lv kPa mmHg algebraic (explicitly computed) E8 Left ventricular blood pressure OPB_00509 (Fluid pressure) physicalPropertyOf: FMA_9670 (Portion of blood) --part_of--> FMA_9466 (Cavity of left ventricle) Pressure in the left ventricle (Smith 2004 author manuscript (card S6P), Table 1 / pp. 10-11) P_lv = P_lvf + P_peri; P_peri = P_pcd + P_th, so P_lv includes thoracic pressure (E8,E5) n/a C1 decided
P_lvf kPa mmHg algebraic (explicitly computed) E7 Pressure across the left ventricular freewall - - Pressure across the left ventricular free wall (Smith 2004 author manuscript (card S6P), Table 1 / pp. 10-11) transmural-type pressure across LV free wall; excludes P_peri (E7) n/a C1 decided
P_pa kPa mmHg algebraic (explicitly computed) E19 Blood pressure in the pulmonary artery OPB_00509 (Fluid pressure) physicalPropertyOf: FMA_9670 (Portion of blood) --part_of--> FMA_14167 (Lumen of pulmonary trunk) P_pa = E_es_pa*(V_pa-V_d_pa) + P_th; includes P_th (E19); CONFLICT C3: the manuscript adds P_th only via P_peri (Eq. 14); no peripheral P_th term n/a C1 decided
P_pcd kPa mmHg algebraic (explicitly computed) E4 Pressure across the pericardial wall OPB_00509 (Fluid pressure) - Pressure across the pericardium wall (Smith 2004 author manuscript (card S6P), Table 1 / pp. 10-11) pressure generated by pericardium as function of V_pcd (E4) n/a C1 decided
P_peri kPa mmHg algebraic (explicitly computed) E5 Pericardial blood volume OPB_00509 (Fluid pressure) physicalPropertyOf: FMA_9887 (Portion of pericardial fluid) Pressure in the pericardium (Smith 2004 author manuscript (card S6P), Table 1 / pp. 10-11) P_pcd + P_th (E5) n/a C1 decided
P_pu kPa mmHg algebraic (explicitly computed) E21 Pulmonary venous blood pressure OPB_00509 (Fluid pressure) physicalPropertyOf: FMA_9670 (Portion of blood) --part_of--> FMA_52455 (Lumen of pulmonary venous tree organ) P_pu = E_es_pu*(V_pu-V_d_pu) + P_th; includes P_th (E21); CONFLICT C3: the manuscript adds P_th only via P_peri (Eq. 14); no peripheral P_th term n/a C1 decided
P_rv kPa mmHg algebraic (explicitly computed) E14 Right ventricular blood pressure OPB_00509 (Fluid pressure) physicalPropertyOf: FMA_9670 (Portion of blood) --part_of--> FMA_9291 (Cavity of right ventricle) Pressure in the right ventricle (Smith 2004 author manuscript (card S6P), Table 1 / pp. 10-11) P_rv = P_rvf + P_peri; includes P_th (E14,E5) n/a C1 decided
P_rvf kPa mmHg algebraic (explicitly computed) E13 Pressure across the right ventricular free wall - - Pressure across the right ventricular free wall (Smith 2004 author manuscript (card S6P), Table 1 / pp. 10-11) transmural-type pressure across RV free wall; excludes P_peri (E13) n/a C1 decided
P_th kPa mmHg -4 parameter (constant) or ODE initial condition Thoracic cavity pressure - - Pressure in the thoracic cavity (Smith 2004 author manuscript (card S6P), Table 1 / pp. 10-11) constant parameter; external (thoracic) pressure, value -4 labelled kPa n/a C1 decided Paeme 2011 Tables 1-3 (CC BY, docs/evidence/d_fulltext_PMC3271239_paeme2011.xml): -4 mmHg
P_vc kPa mmHg algebraic (explicitly computed) E25 Blood Pressure in the Vena Cava OPB_00509 (Fluid pressure) physicalPropertyOf: FMA_9670 (Portion of blood) --part_of--> FMA_280059 (Set of lumens of vena cava trunks) P_vc = E_es_vc*(V_vc-V_d_vc); NO P_th term (E25); CONFLICT C3: Revie 2013 (A.3) writes P_vc = E_vc(V_vc - V_d,vc) + P_th n/a C1 decided
Q_av mL_per_second mL_per_second 0 ODE state variable E30 Blood flow through atrial valve OPB_00299 (Fluid flow rate) physicalPropertyOf: custom:Blood flow through aortic valve --hasSinkParticipant--> sink_5 --hasPhysicalEntityReference--> FMA_9670 (Portion of blood) --part_of--> FMA_12239 (Lumen of aorta) --hasSourceParticipant--> source_5 --hasPhysicalEntityReference--> FMA_9670 (Portion of blood) --part_of--> FMA_9466 (Cavity of left ventricle) n/a from P_lv side to P_ao side: LV -> aorta through aortic valve (E30); positive = forward; process occursIn Aortic valve UBERON:0002137 (FMA:7236) consistent
Q_mt mL_per_second mL_per_second 245.5813 ODE state variable E29 Blood flow through mitrial valve OPB_00299 (Fluid flow rate) physicalPropertyOf: custom:Blood flow through mitral valve --hasSinkParticipant--> sink_3 --hasPhysicalEntityReference--> FMA_9670 (Portion of blood) --part_of--> FMA_9466 (Cavity of left ventricle) --hasSourceParticipant--> source_3 --hasPhysicalEntityReference--> FMA_9670 (Portion of blood) --part_of--> FMA_52455 (Lumen of pulmonary venous tree organ) n/a from P_pu side to P_lv side: pulmonary vein -> LV through mitral valve (E29); positive = forward; process occursIn Mitral valve UBERON:0002135 (FMA:7235) consistent
Q_pul mL_per_second mL_per_second algebraic (explicitly computed) E28 Pulmonary blood flow OPB_00299 (Fluid flow rate) physicalPropertyOf: custom:Pulmonary circulatory blood flow --hasSinkParticipant--> sink_2 --hasPhysicalEntityReference--> FMA_9670 (Portion of blood) --part_of--> FMA_52455 (Lumen of pulmonary venous tree organ) --hasSourceParticipant--> source_2 --hasPhysicalEntityReference--> FMA_9670 (Portion of blood) --part_of--> FMA_14167 (Lumen of pulmonary trunk) n/a from P_pa side to P_pu side: pulmonary artery -> pulmonary vein (E28); positive = forward consistent
Q_pv mL_per_second mL_per_second 0 ODE state variable E32 Blood flow through pulmonary valve OPB_00299 (Fluid flow rate) physicalPropertyOf: custom:Blood flow through pulmonary valve --hasSinkParticipant--> sink_4 --hasPhysicalEntityReference--> FMA_9670 (Portion of blood) --part_of--> FMA_14167 (Lumen of pulmonary trunk) --hasSourceParticipant--> source_4 --hasPhysicalEntityReference--> FMA_9670 (Portion of blood) --part_of--> FMA_9291 (Cavity of right ventricle) n/a from P_rv side to P_pa side: RV -> pulmonary artery through pulmonary valve (E32); positive = forward; process occursIn Pulmonary valve UBERON:0002146 (FMA:7246) consistent
Q_sys mL_per_second mL_per_second algebraic (explicitly computed) E27 Systemic circulatory blood flow OPB_00299 (Fluid flow rate) physicalPropertyOf: custom:Systemic circulatory blood flow --hasSinkParticipant--> sink_1 --hasPhysicalEntityReference--> FMA_9670 (Portion of blood) --part_of--> FMA_280059 (Set of lumens of vena cava trunks) --hasSourceParticipant--> source_1 --hasPhysicalEntityReference--> FMA_9670 (Portion of blood) --part_of--> FMA_12239 (Lumen of aorta) n/a from P_ao side to P_vc side: aorta -> vena cava (E27); positive = forward consistent
Q_tc mL_per_second mL_per_second 190.0661 ODE state variable E31 Blood flow across tricuspid valve OPB_00299 (Fluid flow rate) physicalPropertyOf: custom:Blood flow through tricuspid valve --hasSinkParticipant--> sink_0 --hasPhysicalEntityReference--> FMA_9670 (Portion of blood) --part_of--> FMA_9291 (Cavity of right ventricle) --hasSourceParticipant--> source_0 --hasPhysicalEntityReference--> FMA_9670 (Portion of blood) --part_of--> FMA_280059 (Set of lumens of vena cava trunks) n/a from P_vc side to P_rv side: vena cava -> RV through tricuspid valve (E31); positive = forward; process occursIn Tricuspid valve UBERON:0002134 (FMA:7234) consistent
R_av kPa_second_per_mL mmHg·s/mL 0.0180 parameter (constant) or ODE initial condition Atrial valve fluid resistance - - n/a n/a C1 decided Paeme 2011 Tables 1-3 (CC BY, docs/evidence/d_fulltext_PMC3271239_paeme2011.xml): 0.0180 mmHg s/ml
R_mt kPa_second_per_mL mmHg·s/mL 0.0158 parameter (constant) or ODE initial condition Mitrial valve fluid resistance - - n/a n/a C1 decided Paeme 2011 Tables 1-3 (CC BY, docs/evidence/d_fulltext_PMC3271239_paeme2011.xml): 0.0158 mmHg s/ml
R_pul kPa_second_per_mL mmHg·s/mL 0.1552 parameter (constant) or ODE initial condition Pulmonary circulatory fluid resistance - - n/a n/a C1 decided note: not tabulated in Paeme 2011 or Revie 2013; Pironet 2013 gives re-identified canine values only
R_pv kPa_second_per_mL mmHg·s/mL 0.0055 parameter (constant) or ODE initial condition Pulmonary valve fluid resistance - - n/a n/a C1 decided Paeme 2011 Tables 1-3 (CC BY, docs/evidence/d_fulltext_PMC3271239_paeme2011.xml): 0.0055 mmHg s/ml
R_sys kPa_second_per_mL mmHg·s/mL 1.0889 parameter (constant) or ODE initial condition Systemic circulatory fluid resistance - - n/a n/a C1 decided note: not tabulated in Paeme 2011 or Revie 2013; Pironet 2013 gives re-identified canine values only
R_tc kPa_second_per_mL mmHg·s/mL 0.0237 parameter (constant) or ODE initial condition Tricuspid valve fluid resistance - - n/a n/a C1 decided Paeme 2011 Tables 1-3 (CC BY, docs/evidence/d_fulltext_PMC3271239_paeme2011.xml): 0.0237 mmHg s/ml
V_0_lvf mL mL 0 parameter (constant) or ODE initial condition Left ventricular free wall volume at end diastolic pressure - - n/a n/a consistent
V_0_pcd mL mL 200 parameter (constant) or ODE initial condition Pericardial volume at end diastolic pressure - - n/a n/a consistent Paeme 2011 Tables 1-3 (CC BY, docs/evidence/d_fulltext_PMC3271239_paeme2011.xml): 200.00 ml
V_0_rvf mL mL 0 parameter (constant) or ODE initial condition Right ventricular free wall volume at end diastolic pressure - - n/a n/a consistent
V_0_spt mL mL 2 parameter (constant) or ODE initial condition Septal wall volume at end diastolic pressure OPB_00154 (Fluid volume) - n/a n/a consistent Paeme 2011 Tables 1-3 (CC BY, docs/evidence/d_fulltext_PMC3271239_paeme2011.xml): 2.00 ml
V_ao mL mL 133.3381 ODE state variable E24 Volume of blood contained in aorta OPB_00154 (Fluid volume) physicalPropertyOf: FMA_9670 (Portion of blood) --part_of--> FMA_12239 (Lumen of aorta) n/a n/a consistent
V_d_ao mL mL 0 parameter (constant) or ODE initial condition Aortic blood volume at zero pressure - - n/a n/a consistent
V_d_lvf mL mL 0 parameter (constant) or ODE initial condition Left ventricular free wall volume at end zero pressure - - n/a n/a consistent
V_d_pa mL mL 0 parameter (constant) or ODE initial condition Pulmonary arterial blood volume at zero pressure OPB_00154 (Fluid volume) - n/a n/a consistent
V_d_pu mL mL 0 parameter (constant) or ODE initial condition - - - n/a n/a consistent
V_d_rvf mL mL 0 parameter (constant) or ODE initial condition Right ventricular free wall volume at zero pressure - - n/a n/a consistent
V_d_spt mL mL 2 parameter (constant) or ODE initial condition Septal wall volume at zero pressure OPB_00154 (Fluid volume) - n/a n/a consistent Paeme 2011 Tables 1-3 (CC BY, docs/evidence/d_fulltext_PMC3271239_paeme2011.xml): 2.00 ml
V_d_vc mL mL 0 parameter (constant) or ODE initial condition Vena cava volume at zero pressure - - n/a n/a consistent
V_lv mL mL 94.6812 ODE state variable E9 Volume of blood contained in left ventricle OPB_00154 (Fluid volume) physicalPropertyOf: FMA_9670 (Portion of blood) --part_of--> FMA_9466 (Cavity of left ventricle) Left ventricle volume (Smith 2004 author manuscript (card S6P), Table 1 / pp. 10-11) n/a n/a consistent
V_lvf mL mL algebraic (explicitly computed) E6 Volume of the free wall of the left ventricle OPB_01061 (van't Hoff law of osmosis (master) / van't Hoff law (v1.07)) physicalPropertyOf: FMA_9556 (Wall of left ventricle) Left ventricular free wall volume; "not physical volumes" (Smith 2004 author manuscript (card S6P), Table 1 / pp. 10-11) n/a n/a consistent
V_pa mL mL 43.0123 ODE state variable E20 Pulmonary arterial blood volume OPB_00154 (Fluid volume) physicalPropertyOf: FMA_9670 (Portion of blood) --part_of--> FMA_52449 (Lumen of pulmonary arterial tree) n/a n/a consistent
V_pcd mL mL algebraic (explicitly computed) E3 Volume of the pericardium OPB_00154 (Fluid volume) physicalPropertyOf: FMA_9869 (Pericardium) Pericardium volume; excludes the volume of the atria and the myocardium (Smith 2004 author manuscript (card S6P), Table 1 / pp. 10-11) n/a n/a consistent
V_pu mL mL 808.4579 ODE state variable E22 Pulmonary venous blood volume OPB_00154 (Fluid volume) physicalPropertyOf: FMA_9670 (Portion of blood) --part_of--> FMA_52455 (Lumen of pulmonary venous tree organ) n/a n/a consistent
V_rv mL mL 90.7302 ODE state variable E15 Right ventricle blood volume OPB_00154 (Fluid volume) physicalPropertyOf: FMA_9670 (Portion of blood) --part_of--> FMA_9291 (Cavity of right ventricle) Right ventricle volume (Smith 2004 author manuscript (card S6P), Table 1 / pp. 10-11) n/a n/a consistent
V_rvf mL mL algebraic (explicitly computed) E12 Right ventricular free wall volume OPB_01061 (van't Hoff law of osmosis (master) / van't Hoff law (v1.07)) physicalPropertyOf: FMA_9533 (Wall of right ventricle) Right ventricular free wall volume; "not physical volumes" (Smith 2004 author manuscript (card S6P), Table 1 / pp. 10-11) n/a n/a consistent
V_spt mL mL algebraic state solved from implicit equation E18 (nonlinear algebraic, needs NLA solver) (manuscript Eq. 20: "zero finding solutions") Septal wall volume OPB_01061 (van't Hoff law of osmosis (master) / van't Hoff law (v1.07)) physicalPropertyOf: FMA_7180 (Cardiac septum) Septum free wall volume; "not physical volumes" (Smith 2004 author manuscript (card S6P), Table 1 / pp. 10-11) n/a n/a consistent
V_tot mL UNKNOWN (5.5; fits litres; unused by E1-E32) 5.5 parameter (constant) or ODE initial condition Total blood volume in the body - - n/a n/a CONFLICT C2 resolved as annotation defect Paeme 2011 Tables 1-3 (CC BY, docs/evidence/d_fulltext_PMC3271239_paeme2011.xml): 5.5 l
V_vc mL mL 329.7803 ODE state variable E26 Vena cava blood volume OPB_00154 (Fluid volume) physicalPropertyOf: FMA_9670 (Portion of blood) --part_of--> FMA_280059 (Set of lumens of vena cava trunks) n/a n/a consistent
e_t dimensionless dimensionless algebraic (explicitly computed) E2 Heart beat driver function - - n/a n/a consistent
lambda_lvf per_mL per_mL 0.033 parameter (constant) or ODE initial condition Left Ventricular Freewall Diastolic Exponential Parameter - - n/a n/a consistent Paeme 2011 Tables 1-3 (CC BY, docs/evidence/d_fulltext_PMC3271239_paeme2011.xml): 0.033 1/ml
lambda_pcd per_mL per_mL 0.03 parameter (constant) or ODE initial condition Pericardial Diastolic Exponential Parameter - - n/a n/a consistent Paeme 2011 Tables 1-3 (CC BY, docs/evidence/d_fulltext_PMC3271239_paeme2011.xml): 0.030 1/ml
lambda_rvf per_mL per_mL 0.023 parameter (constant) or ODE initial condition Right Ventricular Freewall Diastolic Exponential Parameter - - n/a n/a consistent Paeme 2011 Tables 1-3 (CC BY, docs/evidence/d_fulltext_PMC3271239_paeme2011.xml): 0.023 1/ml
lambda_spt per_mL per_mL 0.435 parameter (constant) or ODE initial condition Septal Wall Diastolic Exponential Parameter - - n/a n/a consistent Paeme 2011 Tables 1-3 (CC BY, docs/evidence/d_fulltext_PMC3271239_paeme2011.xml): 0.435 1/ml
one dimensionless dimensionless 1 parameter (constant) or ODE initial condition - - - n/a n/a consistent
period second second 0.75 parameter (constant) or ODE initial condition Length of Heart Contraction - - n/a n/a consistent Smith 2004 author manuscript (card S6P): "a fixed heart rate of 80 beats/minute" (p. 17) = 0.75 s, matching the CellML
tau second second algebraic (explicitly computed) E1 Contraction Time Elapsed - - n/a n/a consistent
time second second free variable (independent) - OPB_01023 - n/a n/a consistent

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