Bleeding, blood flow, tourniquet pressure and triage decisions
Educational model, not medical advice. Take a certified first-aid course. Numbers are textbook-level and simplified.
Strap tension T (Laplace: p = T/(w r)) sets the skin pressure; the strip-load model gives the smaller pressure that reaches the artery. Occlusion needs the artery line above systolic.
Wound leak vs pressure at the artery: a half-tight tourniquet that only squeezes the veins makes bleeding worse.
Skin pressure needed for arterial occlusion vs strap width (narrow bands need much more, and cut in).
Abstract patient cards: only the four START observations are shown. Walking? Breathing rate? Perfusion (capillary refill / radial pulse)? Obeys simple commands?
Illustrative survival probability vs delay to hospital for each category (the model assumption, not data).
Laminar flow of a Newtonian fluid in a rigid tube. Flow scales with the fourth power of the radius: a vessel with twice the radius carries (and leaks) 16 times as much at the same pressure drop. Blood is shear-thinning and vessels are elastic, so this is the textbook scaling, not an exact law. The absolute scale of the leak (1 L/min for a fully open 3.5 mm artery at 93 mmHg) is a calibration of the model, not a measurement.
The two-element Windkessel treats the arteries as one elastic chamber (compliance C) draining through the peripheral resistance R. The heart ejects the stroke volume SV in about a third of each beat (half-sine inflow), so P rises and then decays exponentially with time constant RC. Cardiac output about 5 L/min; blood volume about 70 mL/kg (about 5 L for 70 kg, approximate). The 1/3 rule for MAP is an approximation; the simulated time-average is shown as well.
Blood volume falls with the leak and is slowly refilled by fluid shifts from the tissues. A simple reflex controller raises heart rate, resistance and venous tone as the mean pressure falls. The widely taught ATLS classes of haemorrhage (Class I under 15 %, II 15-30 %, III 30-40 %, IV over 40 % of blood volume) are shown as bands; the model reproduces the trend (heart rate rising, pulse pressure narrowing, pressure falling late) but it is a teaching simplification: real patients vary a lot (age, fitness, medication). Time-to-critical estimates show why stopping the bleeding early matters.
A vessel collapses when the external pressure exceeds the internal one, so flow stops once P_ext exceeds about the systolic pressure (120 mmHg is about 16 kPa). The pressure of the hand spreads with depth in the tissue (elastic half-space, Boussinesq/Love, bone ignored): a small fingertip contact loses pressure fast with depth, a broad palm and firm push reaches the vessel. This is why published first-aid guidance asks for firm, sustained, direct pressure on the wound. Wound packing fills the cavity and adds local pressure (illustrative).
A strap under tension presses on a cylinder with pressure T/(w r). A wide strap transmits that pressure deeper (strip load), so wide cuffs occlude an artery at lower skin pressure, a documented effect in surgical tourniquet literature; a narrow band concentrates force and damages tissue. The windlass is a lever: each turn takes up strap length, the strap (a spring with stiffness EA) and the tissue (compressible) then settle at the pressure where their lengths agree. Hand force at the handle F = T x rod radius / handle length.
Veins are thin-walled and collapse at lower pressures than arteries. A tourniquet that is too loose stops the venous outflow but still lets arterial blood in, so the limb fills and a wound beyond it can bleed more. In the model the wound sits in a small lumped network (artery in, vein out, wound leak) and the leak peaks at a pressure between venous and diastolic, then falls to zero when the artery is occluded. A tourniquet must be tight enough to stop the artery; commonly taught practice is to note the time and that tissue tolerates about two hours.
The START algorithm (Simple Triage And Rapid Treatment, widely taught; Newport Beach, 1983) sorts patients using Walking, Respirations (over 30/min), Perfusion (capillary refill over 2 s or no radial pulse) and Mental status (cannot follow simple commands) into Immediate, Delayed, Minor and Expectant/deceased. The simulation is a discrete-event queue: patients arrive at the collection point, ambulances take one patient per trip. Survival is S(t) = s0 exp(-t/tau) with category-dependent s0 and tau (illustrative assumptions). With limited transport the order matters: serving time-critical patients first raises the expected number of survivors. Triage is practised by medical teams; this is a numerical teaching model, not a field guide.
Principles referenced as publicly known: Stop the Bleed (direct pressure, wound packing, tourniquet), START triage, ATLS haemorrhage classes, Poiseuille, Windkessel (Frank 1899), Laplace's law. No text is copied. This page is not affiliated with any organisation. Educational model, not medical advice - take a certified first-aid course.
The model gives the trend; real bleeding patients can look very different.