# 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 |  |

## Open items carried into the evidence review

- C1 decided 2026-11-01: CellML numerals read as mmHg-based, no conversion; R13 lifted (decisions.md)
- C2 resolved: V_tot is an unused, mislabelled total blood volume; the simulated stressed volume is the 1500 mL sum of initial volumes
- C3 peripheral P_th terms (E19, E21; Revie also on P_vc) are not in the manuscript; source UNKNOWN
- C7 period 0.75 s confirmed (80 bpm); closed-loop delay C = 0.375 s has no located source
- C9 L_mt, L_tc (E29, E31) not in the manuscript, which has inertia only at aortic and pulmonary outflow
- C10 E18 omits V_d/V_0 offsets present in manuscript Eq. 20 (no effect at current zero values)
- C11 valve law: manuscript removes Q from the state vector; CellML holds dQ/dt = 0, so a negative Q is frozen (matches Hermes run C)
- V_spt implicit equation E18 solved by NLA; V_spt initial value absent
- Driver function E1 covers only 13 periods explicitly (14 beats per PMR note)
- SemSim ws267 annotates V_lvf/V_rvf/V_spt with OPB_01061 (van't Hoff law), a dependency class, not a property: reference-annotation defect
- SemSim ws267 free text for P_peri reads "Pericardial blood volume" while the property is Fluid pressure of Portion of pericardial fluid: text/annotation conflict
- SemSim ws267 free text for Q_av/R_av/L_av says "atrial valve" while the process is named "Blood flow through aortic valve": naming defect
- C3 P_vc thoracic-pressure term: CellML E25 has none; Revie 2013 (A.3) includes +P_th on P_vc (and on P_pu, P_pa, not P_ao)