Question 1 of 6

Question 1

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

(a) Resistance to blood flow, and why pressure–flow is non-linear

By the Hagen–Poiseuille relation, $R = 8\eta L / (\pi r^4)$, resistance to flow through any vessel depends on three factors: blood viscosity $\eta$ (set mainly by haematocrit — polycythaemia raises resistance sharply, anaemia lowers it), vessel length $L$, and, dominating both by the fourth-power term, vessel radius $r$. In the intact circulation, total peripheral resistance is further set by how the systemic arterioles are recruited/constricted (sympathetic vasomotor tone, local metabolic autoregulation, circulating vasoactive hormones) and by whether resistances lie in series (whole vascular beds, resistances add) or in parallel (organs sharing the aorta, conductances add).

The pressure–flow relationship in a real vascular bed is non-linear (not a straight line through the origin as simple Ohm’s-law reasoning would predict) for three physiological reasons. First, vascular distensibility: rising pressure passively dilates vessels, which lowers $R$ and makes flow rise faster than pressure once pressure is above the resting level. Second, active autoregulation: tissues (brain, kidney, heart, skeletal muscle) adjust arteriolar tone to hold their own flow roughly constant over a wide pressure range, flattening the curve in the middle. Third, at very low perfusion pressure, vessels approach a critical closing pressure and collapse, so flow falls to zero before pressure reaches zero — the curve does not pass through the origin. The combination of a collapsing lower limb, an autoregulated middle plateau, and a distensible upper limb is what makes the pressure–flow curve for any real vascular bed sigmoid rather than linear.

(b) Quantitative Starling forces at the capillary

Fluid movement across the capillary wall is governed by four forces (the Starling forces), with the classical values quoted for an average systemic capillary:

Net filtration pressure (NFP) $= (P_c + \pi_{if}) - (P_{if} + \pi_p)$. At the arterial end, $NFP = (30+8)-(-3+28) = +13\ \text{mmHg}$ outward (filtration); at the venous end, $NFP = (10+8)-(-3+28) = -7\ \text{mmHg}$, i.e. inward (absorption). The importance is that this near-balance (a small net outward filtration of roughly 0.3 mmHg averaged over the whole capillary bed) keeps plasma volume and interstitial fluid volume within narrow limits: the small excess filtered fluid (about 2–4 L/day) is returned to the circulation by the lymphatics rather than accumulating as oedema. If any one force is deranged — a fall in plasma protein (→ low $\pi_p$), a rise in venous/capillary pressure (→ high $P_c$, e.g. heart failure), or lymphatic obstruction — filtration outstrips absorption and lymphatic return, and interstitial oedema results.

(c) Hydrostatic pressure effects: systemic vs. pulmonary

In the upright systemic circulation, hydrostatic pressure adds to the pressure generated by the heart below heart level and subtracts above it. Standing still, the venous pressure in the feet rises by the full height of the blood column back to the right atrium (≈ 90 mmHg added to the normal ≈0 mmHg central venous pressure), while arterial pressure in the feet rises by the same increment (so mean arterial pressure at the ankle can exceed 180 mmHg standing). Above heart level (e.g. in the head), both arterial and venous pressures fall by the equivalent column height. The skeletal-muscle venous pump and one-way venous valves normally interrupt this column during walking and keep dependent venous pressure low; when the pump fails (prolonged standing, incompetent valves), the sustained high capillary hydrostatic pressure in the legs raises $P_c$ well above the values in the table above, filtration exceeds absorption for the whole limb, and dependent oedema results.

The pulmonary circulation is a low-pressure system (mean pulmonary capillary pressure ≈ 7 mmHg, versus ≈ 17 mmHg average systemic capillary pressure), so gravity-dependent hydrostatic gradients matter proportionally much more there. In the upright normal lung this produces the classical West zones: at the apex, alveolar pressure can exceed pulmonary arterial pressure (zone 1, ventilated but under-perfused, essentially dead space) unless cardiac output is high enough to raise arterial pressure above it; at the base, pulmonary arterial and venous pressures both exceed alveolar pressure (zone 3, fully perfused), and the pressure gradient down the lung raises capillary hydrostatic pressure toward the bases, biasing perfusion (and, in exercise, filtration) preferentially to the lower lobes. In abnormal conditions — left heart failure or mitral stenosis raising pulmonary venous and capillary hydrostatic pressure well above plasma oncotic pressure (≈ 28 mmHg), or hypervolaemia from renal failure — the same Starling balance that normally favours absorption in the lung reverses to net filtration throughout the lung fields, producing pulmonary oedema; this is worsened at the (already higher-pressure) bases first, which is why basal crackles are the classic early sign of left-ventricular failure.