20-Bio-A6 Biomedical Signal Processing · Undated paper
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
National Exams May 2019 — 04-Bio-A6, 3 hours, closed book (one of two calculators permitted — any Casio or Sharp approved model). Six questions are printed; the first five as they appear in the answer book are marked, each of equal value; most require an essay-format answer. All six are answered here.
Reference texts: Guyton & Hall, Textbook of Medical Physiology (13th ed.); Junqueira & Mescher, Basic Histology: Text and Atlas (14th ed.); Robbins & Cotran, Pathologic Basis of Disease (9th ed., for the Q2 autopsy case).
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.
For a single tube, the Hagen–Poiseuille relation $R = 8\eta L/(\pi r^4)$ makes an individual capillary's own resistance enormous — its radius is far smaller than an arteriole's, and resistance scales with the fourth power of radius. But no single capillary carries the circulation's blood alone: capillaries are connected in a vast parallel network, with each arteriole feeding tens to hundreds of capillaries side by side, and the total cross–sectional area of the capillary bed (the sum of every individual capillary's lumen) is roughly 500–1000 times that of the aorta — far larger than the combined cross-sectional area of the (much less numerous) arterioles that feed it. For resistors in parallel, $1/R_{total} = \sum_i 1/R_i$, so the combined resistance falls as the number of parallel paths rises, even though each individual path's own resistance is high. Because the capillary bed adds so many more parallel elements than the arteriolar segment upstream of it, its aggregate resistance is actually lower than the arterioles', despite each single capillary being narrower than each single arteriole. The arterioles remain the site of greatest resistance in the systemic circulation precisely because they are few enough, and can actively vary their own smooth-muscle tone, to dominate total peripheral resistance — not because any one arteriole is individually more resistive than any one capillary.
This is also why blood velocity is lowest in the capillaries (continuity: velocity $\propto$ 1/total cross-sectional area) even though flow resistance there is collectively low — the two facts are not contradictory, since velocity depends on total lumen area while resistance to the whole bed depends on both the number of parallel paths and each path's own (high) individual resistance.
The Frank–Starling law states that, within physiological limits, the heart pumps whatever volume of blood returns to it (venous return) — the greater the volume of blood that fills the ventricle during diastole (end-diastolic volume, i.e. preload), the greater the force of the subsequent contraction and the greater the stroke volume ejected, without needing any change in heart rate or extrinsic nervous/hormonal input. This intrinsic property lets the two ventricles automatically pump equal outputs and adapt output to changing venous return beat-to-beat.
The property responsible is the length–tension relationship of cardiac muscle: stretching the ventricular wall by a greater diastolic filling volume lengthens individual sarcomeres (toward, but normally not beyond, their optimal length, ≈2.0–2.2 µm), which increases the number of effective actin–myosin cross-bridge interactions and increases the myofilaments’ sensitivity to calcium (length-dependent activation) — both raising the force the fibre can generate for the same level of activator calcium. Unlike skeletal muscle, whose operating sarcomere length rarely departs far from optimal, the heart normally operates on the ascending limb of this curve, so it can meaningfully increase contractile force purely by being stretched more.
Each valve opens or closes purely according to which side of it has the higher pressure at that instant — a valve opens when upstream pressure exceeds downstream pressure, and closes when that pressure difference reverses.
| Phase | Atrial pressure | Ventricular pressure | Aortic pressure | Valve event |
|---|---|---|---|---|
| Diastole, rapid/slow filling | Low, rising slightly (≈2–10 mmHg) | Low, rising slowly with filling | Falling slowly from the prior systolic peak toward the diastolic minimum (≈120→80 mmHg) | Mitral open (Patrium > Pventricle); aortic closed |
| Atrial systole (“a” wave) | Small extra rise as atrium contracts | Tops up to end-diastolic volume/pressure | ≈80 mmHg (diastolic minimum) | Both valves still as in diastole |
| Isovolumic contraction | Small “c” wave (AV valve bulges back) | Rises steeply, no volume change | ≈80 mmHg, unchanged | Mitral closes when Pvent > Patrium (S1); aortic still closed |
| Ejection | “v” wave builds (filling behind closed mitral valve) | Rises then falls, peak ≈120 mmHg | Rises with ventricle to ≈120 mmHg, then falls | Aortic opens when Pvent > Paorta |
| Isovolumic relaxation | Peaks (“v” wave) then falls as mitral opens | Falls steeply, no volume change | Dicrotic notch, then falls slowly | Aortic closes when Paorta > Pvent (S2); mitral still closed until Pvent < Patrium |
In short: the atrial pressure trace is a low, gently oscillating baseline (a, c, v waves) that sets when the mitral valve can open; ventricular pressure swings the widest, from near-zero in diastole to the systolic peak, and its crossing points with atrial and aortic pressure are exactly what open and close the mitral and aortic valves respectively; aortic pressure rises and falls over a much narrower systolic–diastolic range (≈80–120 mmHg), because the elastic aortic wall stores energy during ejection and releases it (recoil) to sustain forward flow through diastole, with the dicrotic notch marking the instant of aortic valve closure.
Exercising muscle needs a large increase in its own blood flow (to deliver O$_2$/substrate and remove metabolic heat and CO$_2$/lactate), which requires local vasodilation; at the same time, the heat generated by contracting muscle raises core temperature, which drives reflex cutaneous vasodilation and sweating to dissipate that heat — and in a hot environment this thermal load is compounded by high ambient temperature reducing (or reversing) the normal skin-to-environment temperature gradient, so an even larger fraction of cardiac output must be diverted to the skin to maintain heat loss. Cardiac output, however, is finite, so muscle and skin vasodilation are competing for the same limited flow, and both compete with maintaining adequate venous return and total peripheral resistance (via reflex vasoconstriction elsewhere, e.g. splanchnic bed) to hold mean arterial pressure. Prolonged sweating in the heat also depletes plasma volume, lowering central venous pressure and cardiac preload/stroke volume (Frank–Starling law working in reverse), which forces heart rate to rise further just to sustain cardiac output (“cardiovascular drift”). The result is that the cardiovascular system is asked simultaneously to perfuse active muscle, dissipate heat through the skin, and defend arterial pressure, from a blood volume that is itself shrinking — three competing demands on one limited resource, which is why combined heat-plus-exercise stress, more than either alone, risks a fall in blood pressure (orthostatic/exertional syncope) and a rise in core temperature (heat exhaustion/heat stroke) at the same time.
