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Annotated references
Every formula and constant in the model, traced to source
This mirrors the citations already sitting in the model's own code
comments (the Live monitor tab's The math panel shows the live-substituted formulas
themselves). Sources tagged loaded in this chat are
documents Kyle supplied directly; sources tagged web-verified
were located and checked against the model's constants during grounding passes on
2026-08-28 and 2026-09-10 — the full record is in the project's
frc-ppl-pra-grounding.md and lagged-cvp-model-notes.md notes.
Sources
- [1]Kenny JE. An Approach to Mechanical Heart-Lung Interaction, 1st ed.loaded in this chat
The model's primary textbook. Grounds the Campbell-diagram/FRC concept (ch.1); the mmHg↔cmH₂O conversion 1 mmHg = 1.36 cmH₂O (ch.2,
PPL_TO_MMHG); the Eq.12 transmission fractionfPpl=CL/(CL+CCW)andCrs=CL·CCW/(CL+CCW)(ch.1); the end-expiration CVP-measurement rationale (ch.7) and the three-simultaneous-effects passage on inspiration and Pra (ch.7); the Starling-resistor venous-return floor, ≈atmospheric (ch.2/ch.10); the "cardiac-function curve's x-intercept tracks intrathoracic pressure" mechanism behindshiftAndSeptalAt()(ch.8, citing Guyton and Marini); mean pulmonary artery pressure ≈14 mmHg at rest, citing ref [329] (ch.10, used forPA0); the ventricular-interdependence/septal-bowing mechanism, citing Jardin's status-asthmaticus study (ch.5–6); and the "pulmonary" vs. "extra-pulmonary" ARDS distinction (ch.9 p.289: in pulmonary ARDS the lung accounts for ≈80% of total respiratory-system stiffness, chest wall essentially preserved), used to setards's chest-wall compliance equal to the model's own normal baseline (ccw:150as of the 2026-09-16 Kenny-calibrated rescale — see the constants index below). - [2]Enfield KB. "Pulses Paradoxus — An Introduction to Heart-Lung Interactions" (talk), slide 17.Kyle's own talk
"Actual vs. relative pressure" framing at FRC: 760 mmHg/0 cmH₂O at the airway opening vs. 756 mmHg/−4 cmH₂O in the pleural space. This is the model's own Ppl-at-FRC anchor in both breathing modes (
respState()) and the diagram's initial Ppl/Pmsf placeholder labels — the 2026-09-10 recalibration moved the model from −5 to this exact number. - [3]Del Rio-Pertuz G, Nugent K, Argueta-Sosa E. "Right heart catheterization in clinical practice: a review of basic physiology and important issues relevant to interpretation." Am J Cardiovasc Dis 2023;13(3):122–137.loaded in this chat
Table 2: clinical normal ranges — RAP 0–6 mmHg, PCWP 6–12 mmHg, mPAP 10–20 mmHg (via [PASP+2·PADP]/3). Grounds
PA0=15,PCWP0=9, and thecvp0=7Normal-preset baseline (sits at the top of this RAP range). - [4]Fujimoto N, Shibata S, Hastings JL, Carrick-Ranson G, Bhella PS, Palmer D, Fu Q, Levine BD. "Effects of pericardial constraint and ventricular interaction on left ventricular hemodynamics in the unloaded heart." Am J Physiol Heart Circ Physiol 2011;300:H1688–H1695.loaded in this chat
Table 1: measured baseline RAP = 8.0±1.9 mmHg, PCWP = 11.4±2.3 mmHg in 50 healthy supine volunteers — real measured data, not an illustrative diagram value. Grounds
PCWP0=9and thecvp0=7Normal-preset baseline (just under this measured mean). Also defines LVTMP = PCWP−RAP, an independent pericardial-constraint parallel to the deck's own Ppl/Pra,tm transmural-pressure argument (discussed infrc-ppl-pra-grounding.md§5, not yet a modeled constant). - [5]Whelton PK, et al. "2017 ACC/AHA/AAPA/ABC/ACPM/AGS/APhA/ASH/ASPC/NMA/PCNA Guideline for the Prevention, Detection, Evaluation, and Management of High Blood Pressure in Adults." Hypertension 2018;71:e13–e115.web-verified
Normal blood pressure defined as <120/<80 mmHg. Grounds
SBP0=118,DBP0=76. - [6]Kussmaul A. "Ueber schwielige Mediastino-pericarditis und den paradoxen Puls." 1873.web-verified
Original description of pulsus paradoxus in constrictive/effusive pericardial disease — "pulse simultaneously slight and irregular, disappearing during inspiration and returning upon expiration." Source of the classic >10 mmHg pulsus-paradoxus flag threshold in the readouts panel.
- [7]Jardin F, et al. Circulation 1982;66(4):887.web-verified
Status-asthmaticus septal-shift data — already Kenny's own reference [280]. Grounds the ventricular-interdependence/
septalShiftmechanism (interdep, tamponade and asthma presets). - [8]Yang F, et al. Front Physiol 2021. DOI: 10.3389/fphys.2021.639761.web-verified
Echocardiographic cohort, 99 healthy adults measured at 500 m and again ~15 h after ascent to 4100 m: mPAP 14.4→18.1 mmHg (Δ3.7), PCWP 9.9→8.9 (Δ−1.0), brachial SBP/DBP 117/73→121/81. Grounds
HPV_PA_BUMP=3.7,HPV_PCWP_DROP=1.0,HPV_SBP_BUMP=4,HPV_DBP_BUMP=8— the hpvGain=1 anchor for the High-altitude preset. - [9]"Clinical review: Guyton — the role of mean circulatory filling pressure and right atrial pressure in controlling cardiac output." Critical Care 2010. DOI: 10.1186/cc9247.web-verified
Notes that Guyton's theoretical zero RA-pressure intercept "had not been measured in a functioning cardiovascular system in humans," and that measured mean systemic filling pressure (Maas et al., 18.8 mmHg euvolemic supine) runs well above the classic teaching value. Context/caveat for the
cvp0recalibration decision, not a specific-constant citation. - [10]"Physiology, Central Venous Pressure." StatPearls (NBK519493).web-verified
Clinically-cited normal CVP ≈8–12 mmHg — corroborates Fujimoto's [4] measured value. Supporting source for
cvp0=7. - [11]Forbes LM, Bull TM, Lahm T, et al. "Right ventricular performance during acute hypoxic exercise." J Physiol 2024;602(21):5523–5537. DOI: 10.1113/JP284943.loaded in this chat
Invasive haemodynamics in 10 healthy adults at rest and exercise under acute hypoxia (FiO₂=0.12): mPAP rose to 20 [15–33] mmHg and RVSP to 54 [49–59] mmHg at hypoxic exercise, with RV contractility rising appropriately in step (afterload rises, contractile reserve is not the limiting factor). Citing Maggiorini et al. 2001, Forbes also reports mean PA pressures spanning "high teens to low 30s" in healthy adults at this same FiO₂. Supporting source for the HAPE preset's
hpvGain=3.5target of mean PA in the low-30s. - [12]Müller J, Mayer L, Schneider SR, et al. "Pulmonary haemodynamics and right heart function during exercise at high versus low altitude in patients with pulmonary vascular disease: a randomised crossover trial." Heart 2026;112:28–36. DOI: 10.1136/heartjnl-2024-325605.loaded in this chat
27 patients with PAH/CTEPH at high (2500 m) vs. low (470 m) altitude: resting systolic PAP significantly higher at altitude, total pulmonary resistance significantly higher at altitude (rest through peak exercise), and RV-arterial coupling lower at rest. A diseased population, distinct from the healthy-ascent physiology [8] the altitude preset is calibrated to — used here as qualitative support for the HAPE preset's "frankly pulmonary-hypertensive, afterload-stressed RV" framing at
hpvGain=3.5, not as a direct calibration anchor. - [13]Michard F, Boussat S, Chemla D, et al. "Relation between respiratory changes in arterial pulse pressure and fluid responsiveness in septic patients with acute circulatory failure." Am J Respir Crit Care Med 2000;162(1):134–138.web-verified
Cited by name in the deck's own walkthrough text as one source for the ≈12–13% SPV/PPV fluid-responsiveness threshold used to flag the readouts panel's SPV%.
- [14]Marik PE, Cavallazzi R, Vasu T, Hirani A. "Dynamic changes in arterial waveform derived variables and fluid responsiveness in mechanically ventilated patients: a systematic review of the literature." Crit Care Med 2009;37(9):2642–2647.web-verified
Cited alongside [13] for the same ≈12–13% SPV/PPV threshold.
- [15]Behazin N, Jones SB, Cohen RI, Loring SH. "Respiratory restriction and elevated pleural and esophageal pressures in morbid obesity." J Appl Physiol 2009;108(1):212–218.web-verified
51 obese vs. 10 nonobese anesthetized, paralyzed subjects: Crs and CL lower in obese, principally from lower lung volume, not lower chest-wall compliance (Ccw not significantly different); pleural pressure at relaxation volume higher in obese (12.5±3.9 vs. 6.9±3.1 cmH₂O). Grounds the Respiratory & Circulatory Curves tool's "Restrictive load" mechanism (positional shift of the chest-wall curve, not its slope) and slide s14's obesity discussion.
- [16]Pelosi P, Ravagnan I, Giurati G, et al. "Positive end-expiratory pressure improves respiratory function in obese but not in normal subjects during anesthesia and paralysis." Anesthesiology 1999;91(5):1221–1231.web-verified
PEEP 0 vs. 10 cmH₂O in obese vs. normal postoperative patients: PEEP improved elastance/compliance and oxygenation (r=0.81 with recruitment) in the obese group only — a recruitable, low-lung-volume picture, not fixed tissue stiffening. Supporting citation for slide s14's PEEP-reversibility point (the model itself does not yet make compliance a function of PEEP/operating volume — see the review notes).
- [17]Broseghini C, Brandolese R, Poggi R, et al. "Respiratory mechanics during the first day of mechanical ventilation in patients with pulmonary edema and chronic airway obstruction." Am Rev Respir Dis 1988;138(2):355–361.web-verified
Mean static respiratory-system compliance 35±5 mL/cmH₂O in ARDS patients on day 1 of ventilation. Grounds the ards preset's
cl:46, ccw:150(reproduces this Crs almost exactly — 35.2 vs. the literature's 35 — via the series formula, with chest wall left at the model's Kenny-calibrated normal per Kenny [1] ch.9's "pulmonary ARDS" phenotype).
Constants & formulas, traced to source
Ppl at FRC = −4 cmH₂O[1] [2]
fPpl = CL/(CL+CCW), Crs (Kenny Eq.12)[1]
PPL_TO_MMHG = 1/1.36 (mmHg↔cmH₂O)[1]
STARLING_FLOOR = 0 mmHg[1]
End-expiration CVP measurement rationale[1]
shiftAndSeptalAt() / cardiac-function curve x-intercept tracks ITP[1]
PA0 = 15 mmHg[1] [3]
PCWP0 = 9 mmHg[3] [4]
cvp0 = 7 mmHg (normalSpont, normalVent, altitude, hape)[3] [4] [10]
cvp0 = 9 mmHg (asthma, stiffChest)tuned
Nudged above the cvp0=7 baseline to preserve separation from Normal, not independently literature-set.
SBP0 = 118, DBP0 = 76 mmHg[5]
Pulsus paradoxus >10 mmHg threshold[6]
septalShift / interdep (ventricular interdependence)[1] [7]
HPV_PA_BUMP, HPV_PCWP_DROP, HPV_SBP_BUMP, HPV_DBP_BUMP (hpvGain=1 anchor)[8]
hpvGain=3.5 (HAPE preset — mean PA target low-30s, frankly pulmonary-hypertensive)[11] [12]
SPV/PPV fluid-responsiveness threshold ≈12–13%[13] [14]
Restrictive-load mechanism (Respiratory & Circulatory Curves tool, chest-wall curve position shift)[15] [16]
normal baseline: cl:200, ccw:150 (Crs=85.7 mL/cmH₂O, Kenny's own stated normal)[1]
Rescaled 2026-09-16 from an earlier cl:100/ccw:100 (Crs=50) baseline that sat ~40% below Kenny's own 200/150 mL/cmH₂O figure — every other preset below is rescaled to keep its relationship to this corrected baseline.
ards preset: cl:46, ccw:150 (Crs=35.2 mL/cmH₂O)[1] [17]
stiffChest (Obesity) preset: cl:102, ccw:150[15] [16]
tamponade preset: cl:200, ccw:150 (compliance unchanged, matches normal)n/a
No literature was found connecting tamponade to altered lung or chest-wall compliance; a prior version of this preset cut cl:60 with no citation and no supporting mechanism — removed 2026-09-15.
asthma cl:150, copd cl:460, hape cl:80tuned
Direction (reduced compliance from air-trapping in asthma and HAPE; increased compliance from lost elastic recoil in COPD) is standard, textbook-plausible physiology, and HAPE's direction is corroborated by Clarenbach et al. 2012 (PLoS One 7(7):e41188). No specific magnitude was found in the literature for any of the three to check these numbers against — each is scaled proportionally to the same fraction of normal as before the 2026-09-16 baseline rescale.
CO_MAX, CO_TAU, CO_RA0, C_RA, CO_SHIFT_GAIN, SEPTAL_CO_GAIN, ITP_MODE_GAINtuned
Engineering-tuned gain/shape constants with no single measurable literature value — verified instead against literature-reported output claims ([1] Kenny's own model text, [6] pulsus threshold, [13][14] SPV/PPV threshold).