Parallel Circulation Oxygen Explorer

Compare oxygen budgets

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Paper laboratory

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Model & validation

Steady state, complete mixing, bound oxygen only and prescribed oxygen consumption. Conservation checks and cross-runtime agreement verify the numerical implementation; they do not establish clinical validity.

What the equations assume

A common mixed arterial content supplies pulmonary and systemic paths. Pulmonary venous saturation Spv is an explicit endpoint. Qt = Qp + Qs; oxygen capacity B = κ × Hb or an explicit direct capacity. In consistent volume units, Ca = B × Spv − M/Qp, Cv = Ca − M/Qs, and systemic oxygen delivery is Qs × Ca. Pulmonary net oxygen uptake equals the prescribed consumption M; gross pulmonary oxygen flux is a different quantity.

The implementation includes the 100 mL/dL and 1,000 mL/L conversions explicitly. Per-kg flows use mL blood/kg/min and oxygen fluxes mL O₂/kg/min. Per-m² flow uses L blood/min/m² and oxygen flux mL O₂/min/m². Resistance experiments use L blood/min, mmHg and mmHg·min/L; normalized source indices have units L/min × saturation, not physical mL O₂/min.

Negative venous content is masked as no admissible steady state at the requested consumption. The Cv = 0 boundary remains a distinct status. Undefined zero-demand ratios remain null. Sa/Sv criteria are separately selected strict inequalities; equality is not above a criterion. No saturation clipping or automatic demand adjustment occurs.

Source equations and explicit extensions

• Barnea et al., Circulation 1998: parallel oxygen balances and excess/ratio equations. Both B = 22 and Hb15 × κ1.38 = 20.7 conventions are retained. Reconstructed curves explicitly assume Spv = .96; reported landmark discrepancies remain visible.
• Ahmed et al., JTCVS 2023: abstract-supported Hb/CI examples and strict Sa > 70%, Sv > 40% criteria. Full-text constants and figures are unavailable; exact source replication is disabled. Spv = .98 and κ = 1.34 are teaching assumptions.
• Savorgnan et al., JCDD 2026: source-compatible nominal output law and source table audit. Table 1 and perturbation-scope discrepancies remain unresolved. Table 3 arithmetic agreement does not verify physiology. Original author-code/Monte Carlo replication remains unavailable.

Analytical boundaries, Hb gains, optima, nonlinear shunt resistance, circuit-secant output closure and declared-distribution paired ensembles are explicit derivations or sensitivity extensions. Resistance profiles describe assumptions; they are not drug doses or clinical efficacy rankings. The output-law anchor and shunt calibration are frozen according to each experiment's declared reference policy.

Excluded physiology and use

No patient-specific prediction, treatment target or dosing recommendation is produced. The model excludes pulsatility and time dynamics, ventricular mechanics, oxygen dissociation and dissolved oxygen, viscosity feedback, autoregulation, collateral flows and supply-dependent consumption. A caval sample is not necessarily ideal mixed venous blood. Hb changes here hold the displayed flows and demand fixed.

Inspect the last selected state's balances

The record below comes from the same engine result displayed in Explore or Compare. It retains units through its requested state, raw balance residuals and status; masked oxygen outputs do not erase valid circuit outputs.

Build and verification provenance

Machine-readable application gate evidence · Source-access status · Third-party notices · Citations and discrepancies · Derivation and unit contract