PDA and PH Physiology Simulator Experimental

Circulation model

Closed-loop model with time-varying elastance atria and ventricles, systemic (intrathoracic and extrathoracic arteries, extrathoracic and intrathoracic veins) and pulmonary (arteries, veins) compartments, valves that allow no backward flow, and atrial inflow tracts that resist backward flow ten times more than forward flow. Parameters for a healthy 1-week-old term neonate (3500 g, total blood volume 310 mL, heart rate 130/min): Sá Couto 2006, Appendix and Table WA2; compartment equations: Goodwin 2004, Appendix 1; activation curves and timing: Sá Couto 2006 Eq 1–3. The PDA heart (dilated, more contractile LV: ELVMAX 106, ELVMIN 1.75, Table WA3) is the “LV adapted” option. The baroreflex is left out.

Check against the published model (base circulation only). With the published linear duct (resistance 0.5, inertia 0.0018) and the Table WA3 LV, at 130/min, this implementation gives aorta 69/20 mmHg (mean 37), PA 51/18 (mean 30), LV 71/4, RV 52/3, systemic flow 315 and pulmonary flow 1122 mL/min; the corrected published values are 70/20 (37), 51/18 (30), 72/4, 52/3, 316 and 1123 (Zijlmans 2009 Table 2). Without a duct: aorta 68/40, PA 29/10, output 454 mL/min (published 68/40, 29/10, 455). This checks the base model only, not the duct geometry, the rescaling, other heart rates or the Doppler read-outs below. The published model itself missed some of its textbook targets for a PDA (PA diastolic 18 vs 28, aortic diastolic 20 vs 30 mmHg; Sá Couto 2006 Table 2).

HeartCalc additions (assumptions, not from the model papers)

• Duct geometry. A cone narrowest at the pulmonary end, with the aortic end 1.45 times the minimum diameter [derived: the ratio of the group means of the aortic and pulmonary ends, 4.5 and 3.1 mm, in Paudel 2021, abstract; Sathanandam 2020’s minimal and maximal diameters in infants ≤2 kg, 2.8 and 4.1 mm, give the same ratio, though it calls most of those ducts long and tubular]. Default length 10 mm (Sathanandam 2020: 10.6 ± 2.2 mm). Both series are persistent ducts weeks after birth.
• Duct pressure loss. Convective loss at the narrowest point (½ρv², the simplified Bernoulli relation) plus blood inertia over the cone (ρ·length/(π·r_min·r_aortic)); blood density 1.055 g/cm³ as in Colebank 2026 (no neonatal source found). Friction and a discharge (vena contracta) coefficient are left out, so the slider diameter acts as an effective orifice and small ducts are less restrictive than real ones (a larger shunt for a given diameter). The close Doppler–catheter agreement for left-to-right ducts (Musewe 1987: slopes 1.03 to 1.12, narrowest diameters 1.5–9 mm, ages not given in the abstract (indexed infant to adolescent), abstract) comes from larger ducts; in vitro, for a 0.06 cm² tunnel (about 2.8 mm across [derived]), Doppler underestimated the true pressure drop by 12% at 1 cm and 42% at 4 cm long; no tunnel as small as a 1–2 mm duct was tested (Teirstein 1985, abstract). No source gives neonatal whole-blood viscosity. For comparison: at 1 kg, 150/min and normal PVR (rescaled profile), the model’s descending aortic end-diastolic flow is absent from about 0.9 mm and reversed from about 1.3 mm, whereas in ventilated preterm infants post-ductal aortic diastolic flow was invariably antegrade with a ductal diameter of 1.5 mm or less (Evans & Iyer 1995, 48 infants <1500 g, abstract).
• Weight. Volumes and compliances scale with weight, resistances inversely, so pressures and flow per kg do not depend on weight.
• Rescaled option. An exact rescaling of the term model (flows ×1.71, pressures ×0.86) so that, with the duct closed and at the model heart rate of 130/min, systemic flow is 222 mL/kg/min (Groves 2011, phase-contrast MRI, 28 stable infants with an echo-proven closed duct, birth gestation 28–41 weeks, scan gestation 34 weeks, postnatal day 10) and SVR 173.5 mmHg/(L/min/kg) (the midpoint of 163 and 184, the values of two groups of ventilated preterm infants of median 28 weeks at 7–31 h split at mean BP 30 mmHg, Kluckow & Evans 1996, abstract; ductal diameter was 1.6 and 0.7 mm in those groups, so many ducts were likely open [inferred] and this is not a closed-duct SVR). Waveform shapes and timing are unchanged, and blood volume per kg rises with the rescaling (not physiological). A single-point comparison: a 2.0 mm duct at 1 kg, 150/min, LV not adapted gives LVO 432 mL/kg/min, the MRI mean in preterm infants with a PDA (Broadhouse 2014: 432, and 260 without; duct sizes not reported); at 130/min it gives 382, and 489–545 with the LV adapted.
• Sliders. SVR and PVR multiply every resistance the model’s SVR and PVR are spread over. Heart rate goes beyond the published model, which was run only at 130/min (135 in Zijlmans 2009); at 200/min diastole is very short.
• Descending aortic flow. The model’s flow from intrathoracic to extrathoracic arteries stands in for the abdominal aorta; the model has one systemic arterial bed, with no separate pre-ductal circulation. Our rule: absent if end-diastolic flow lies within ±3% of its systolic peak, reversed below −3%, otherwise forward. Only absent or reversed is sent to part 2 as the AAP 2025 criterion; forward flow is left blank there, because “decreased” has no number. The simulator shows the end-diastolic share beside the same circulation with the duct closed.
• Doppler. Duct velocity = flow / minimum area; velocities within 0.05 m/s of zero do not count as right-to-left flow. TR and PR velocities = √(ΔP/4) from the simulated RV–RA and PA–RV pressures, with jets assumed present and too small to change the circulation.

Limitations of the model

• Both ventricles activate together (Sá Couto Eq 1–3) and the aorta has no pulse-transit delay to the duct. With bidirectional flow the model shows a left-to-right spike in early systole before the right-to-left phase; no source we read describes that spike, so the simulator does not send it to part 2.
• The model’s aortic pressure rises earlier and more steeply than its PA pressure. For 2–4 mm ducts at normal PVR (130–150/min), at 1 kg in the rescaled profile or 3.5 kg in the term profile, the left-to-right Vmax is 2.0–2.8 m/s with the LV not adapted and 2.8–3.6 m/s with it adapted: above the 2 m/s that real large ducts often fall below (the AAP 2025 “unrestrictive” marker). The diameter is absolute, so the same duct is relatively larger in a smaller infant: at 0.5 kg in either profile, or 1 kg in the term profile, large ducts at normal PVR can turn bidirectional, with left-to-right peaks of 1.1–2.0 m/s. The ductal-gradient estimate of systolic PA pressure (peak instantaneous gradient) comes out up to 21 mmHg below the model’s PA systolic pressure across these settings, so the simulator’s own values can make part 2 report that the TR and ductal estimates disagree. Compare the two in the simulator.
• No atrial shunting, lung mechanics or oxygenation (lung disease acts here only through PVR), baroreflex, or duct constriction over time.

Part 2: echo relations and HeartCalc rules

• RVSP = 4·TR² + RA pressure; mean PAP = 4·(early PR)² + RV diastolic pressure (here the RA pressure field, default 5); SPAP = 4·(right-to-left ductal V)² + systolic BP, usable only when right-to-left flow lasts ≥30% of the cycle and often unreliable: de Boode 2018, Eq 3–5.
• PA diastolic = 4·(end-diastolic PR)² + RA pressure, RA pressure 5 mmHg in neonates; mean PAP = ⅓ RVSP + ⅔ PADP: McNamara 2024, Fig 14.
• “Ao pressure − gradient = PA pressure” for a ductal gradient: Krishnan 2017 (PPHNet, BPD) Table III. Musewe 1987 (abstract): left-to-right ductal velocities tracked the catheter gradient; in bidirectional ducts the slope was 0.70; right-to-left velocities did not correlate with pressure.
• Neonatal echo indicators of PH: TR >2.8 m/s and/or sPAP more than half systemic; early-diastolic PR >2.3 m/s; right-to-left ductal shunting; continuous left-to-right ductal flow with Vmax <2.0 m/s: Ivy 2024 (WSPH) Table 9.
• Suggested hsPDA echo criteria in preterm infants (any 1 of 4, with 2 of 4 clinical criteria): diameter >1.5 mm; unrestrictive flow, Vmax <2 m/s; ≥moderate LA or LV enlargement; decreased, absent or reversed abdominal aortic end-diastolic flow: AAP 2025 Table 1.
• LVO:RVO bands <1.5 / 1.5–2.5 / >2.5: current Iowa PDA score, Brandt 2026 Table 1.
• HeartCalc rules (our construction, not a published algorithm; Nawaytou 2023 publishes different research rules): the pressure side counts three independent markers (TR jet; left-to-right ductal gradient with systolic BP; early PR) and the shunt-volume side three (LVO:RVO; abdominal aortic diastolic flow; LA/LV size). A side is present if any marker is met and absent only if at least two are assessed and none is met. The pressure side is not decided when the TR and ductal estimates fall on opposite sides of half the systolic BP, or when one pressure marker is met and two are normal; otherwise TR is used and the ductal estimate is listed. A mean PA estimate above the systolic estimate is flagged. The right-to-left estimate, and the left-to-right estimate in bidirectional flow, are listed but never used. Mean BP, when not entered, is DBP + ⅓(SBP − DBP).
• Estimated PVR/SVR = [(mean PAP − LA pressure) / Qp] ÷ [(mean BP − RA pressure) / Qs], with Qp:Qs = LVO/RVO. Not validated against catheter data. LA pressure is rarely known; blank uses the RA pressure, and a large left-to-right shunt raises LA pressure, which makes the estimate too high (the simulator shows this). Shown only when both sides are present. The 0.3 cut-off is a catheter threshold for CHD shunts not repaired by about 1–2 years of age (AHA/ATS 2015; EPPVDN 2019), not derived in preterm infants.

References

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