Chris Collins

Tools · medical

Heart, vessels and oxygen

Cardiac output, ejection fraction, MAP and pulse pressure; ΔP = Q × R for the systemic and pulmonary circuits with a pressure cascade; Poiseuille's r⁴ for a vessel, a stenosis or a strap; Dalton, Henry and cylinder arithmetic; and the oxygen–haemoglobin dissociation curve with temperature, CO₂ and pH shifts. Educational simulation only.

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How to use it

Companion to chapters 2, 9 and 11 of Human Biology for the Medical Maker: Circulation, breathing, and the wider body, How disease works and Foundations of chemistry. It covers chapter 9’s exit criterion: calculate MAP, cardiac output and a Poiseuille radius effect, and state the assumptions each makes.

Educational — not a medical device. Not for diagnosis, treatment, monitoring or dosing. Simulation only. The figures are orientation, not reference ranges: nothing here labels a value normal or abnormal, and none of it can be used to judge a person’s numbers.

How to use it

Heart. Cardiac output = heart rate × stroke volume (and stroke volume back from output and rate); ejection fraction = (EDV − ESV) ÷ EDV; mean arterial pressure ≈ Pdia + ⅓(Psys − Pdia) and pulse pressure = Psys − Pdia, with a cartoon pulse showing where the three lines sit. The defaults are chapter 9’s exercise: 118/76 → MAP 90 mmHg and HR 72 × SV 68 mL = 4,896 mL/min ≈ 4.9 L/min; its question (5 L/min at 70 beats/min) gives SV ≈ 71 mL.

ΔP = Q × R. The same cardiac output through the systemic and pulmonary circuits: resistance from each circuit’s driving pressure, in mmHg·min/L (Wood units) and dyn·s·cm⁻⁵. With MAP 90 and a mean pulmonary artery pressure of 15 mmHg the systemic resistance is six times the pulmonary — the book’s "same flow, much lower pressure, therefore much lower resistance". Below it, chapter 9’s orientation pressures around the circuit as ranges, with an optional line for an external interface pressure (chapter 5’s 150 mmHg bench example) to compare with capillary pressure.

Radius (r⁴). How flow at the same driving pressure falls as a radius narrows: for a whole vessel, for a short stenosis in series with the rest (flow holds up until the narrowing is severe, then falls steeply — chapter 11), or for a strap over a short length of artery. A radius 20% narrower gives 0.8⁴ ≈ 41% of the flow; half the radius gives 1/16. This tab is for sensitivity to radius, as chapter 9 insists — not for computing anybody’s flow.

Gas laws. Dalton’s law with water vapour: dry air at 760 mmHg with 20.9% oxygen has a PO₂ of ≈ 159 mmHg; warmed to 37 °C and saturated (≈ 47 mmHg of water vapour) it is (760 − 47) × 0.209 ≈ 149 mmHg, with a partial-pressure table for the other gases. Henry’s law for dissolved oxygen (0.003 mL per 100 mL of blood per mmHg). Cylinder arithmetic: 2 L at 200 bar ≈ 400 L, about 3 h 20 min at 2 L/min.

O₂ dissociation. The sigmoid curve from the Severinghaus equation or the Hill equation, with temperature, PCO₂ and pH moving it. Presets show a right shift (warmer, more CO₂, more acid: working tissue) and a left shift (cooler). P50 and the saturation at any PO₂ are read off for both curves.

Inputs outside each calculator’s range are rejected with a message rather than clamped, and nothing is calculated until they are fixed. Every value carries its unit.

Limits

  • MAP by the ⅓ rule assumes diastole lasts about twice as long as systole; it drifts at fast heart rates.

  • ΔP = Q × R treats each circuit as one steady resistor. Downstream (atrial) pressures default to 0 mmHg; the book gives central venous pressure as ~0–5 mmHg and does not tabulate left atrial or pulmonary capillary pressures, so those are left for you to enter rather than guessed.

  • Poiseuille’s law assumes steady laminar flow of a Newtonian fluid in a rigid tube. Blood is not Newtonian, vessels are compliant, tapered and branched, flow is pulsatile and the network regulates its own radii (chapter 9). The stenosis and strap models ignore turbulent and entrance losses.

  • The dissociation curves describe typical adult haemoglobin; PCO₂ and pH are coupled in the body but independent knobs here; the Severinghaus shift factors are approximations.

  • The cylinder figure is ideal-gas arithmetic; real cylinders are labelled with their actual content.

Sources: chapter 9 (cardiac and pressure figures, from OpenStax Anatomy and Physiology; Poiseuille; dissociation-curve behaviour), chapter 11 (stenosis), chapter 2 (Dalton, Henry, cylinder); J. W. Severinghaus, "Simple, accurate equations for human blood O2 dissociation computations", J Appl Physiol 46:599–602 (1979); A. L. Buck, "New equations for computing vapor pressure and enhancement factor", J Appl Meteorol 20:1527–1532 (1981); dry-air composition from the CRC Handbook of Chemistry and Physics.

Related: test lung and breathing mechanics, diffusion, dialysis and clearance, fluid flow and pipe pressure drop, chemistry: formulas and the periodic table.

Sharing

Share link (under the title) copies a URL that reopens this tool exactly as you have it — every tab’s inputs, with the current tab selected. Opening such a link replaces the inputs this browser had saved for the tool. Link to a tab with its name after #: /tools/circulation/#radius (or #heart, #resistance, #gases, #oxygen).

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