20-Bio-A6 Biomedical Signal Processing · December 2013
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
National Exams December 2013 — 04-Bio-A6, 3 hours, closed book (approved Casio/Sharp calculator only). 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.
The respiratory quotient, $RQ = \dot V_{CO_2}/\dot V_{O_2}$, reflects which substrate is being metabolised (carbohydrate, $RQ\approx1.0$; mixed diet, $RQ\approx0.8$; fat, $RQ\approx0.7$) and sets the ratio in which the body adds CO$_2$ to, and removes O$_2$ from, the alveolar gas with each breath. Because the moles of O$_2$ consumed and CO$_2$ produced are not equal whenever $RQ\neq1$, the alveolar gas equation carries an explicit $R$ term, $P_{AO_2}=P_{IO_2}-P_{ACO_2}/R\;(+$ a small correction$)$: for the same alveolar $P_{CO_2}$ and inspired $P_{O_2}$, a lower $RQ$ (fat metabolism) means more O$_2$ is withdrawn from the alveolus for each CO$_2$ molecule returned to it, so alveolar (and hence arterial) $P_{O_2}$ runs slightly lower than it would on a purely carbohydrate diet at the same ventilation. Physiologically, $RQ$ therefore shifts the exact proportion of O$_2$ and CO$_2$ in alveolar gas (and the small net change in total alveolar gas volume per breath) for a given level of ventilation and metabolic rate, even though total ventilation is what ultimately sets the absolute levels of $P_{ACO_2}$ and $P_{AO_2}$.
Oxygen is carried in two forms: bound to haemoglobin and physically dissolved in plasma. Dissolved O$_2$ is negligible under normal conditions (≈0.003 mL O$_2$/dL blood per mmHg $P_{O_2}$). The dominant determinant is therefore the blood's haemoglobin concentration: each gram of fully saturated haemoglobin carries ≈1.34–1.39 mL O$_2$ (Hüfner's constant), so $O_2\text{ capacity} = [\text{Hb}]\ (\text{g/dL})\times1.34\ \text{mL O}_2/\text{g}$, achieved when percentage saturation ($S_aO_2$, set by arterial $P_{O_2}$ via the sigmoid dissociation curve) is 100%. Consequently, oxygen-carrying capacity falls in anaemia (low [Hb], even with normal $P_{O_2}$ and normal saturation) and rises in polycythaemia (high [Hb]), while conditions that reduce functional hameoglobin without changing total [Hb] — carboxyhaemoglobin from CO poisoning, methaemoglobin — likewise reduce effective carrying capacity because that fraction of haemoglobin can no longer bind O$_2$.
Myoglobin has a single O$_2$-binding haem group and no subunit–subunit cooperativity, so its dissociation curve is a simple rectangular hyperbola with very high O$_2$ affinity (low $P_{50}$, ≈1–5 mmHg): it is already almost fully saturated at the low $P_{O_2}$ found inside resting muscle, and releases essentially none of its O$_2$ until local $P_{O_2}$ falls very low (as in intense exercise/relative ischaemia). This makes myoglobin a poor transporter across a range of pressures but an excellent local O$_2$ store and short-range diffusion facilitator within the muscle fibre. Haemoglobin's four subunits bind O$_2$ cooperatively (sequential T→R quaternary transitions raise each successive subunit's affinity), giving a sigmoidal curve with a much lower affinity ($P_{50}\approx26$–27 mmHg): the flat upper plateau lets it load to near-full saturation at alveolar/arterial $P_{O_2}$ (≈100 mmHg) even if arterial $P_{O_2}$ falls somewhat, while the steep middle portion lets it unload a large fraction of that O$_2$ over the range of $P_{O_2}$ actually found in resting-to-working tissue. The two curves are thus matched to two different jobs: haemoglobin's sigmoid shape is what makes it an efficient bulk transporter between lungs and tissue, while myoglobin's high-affinity hyperbola is what makes it an efficient local O$_2$ reservoir, releasing its store only when intracellular $P_{O_2}$ drops well below what haemoglobin itself would still be unloading at.
CO$_2$ produced by tissue metabolism diffuses down its partial-pressure gradient from the cell, through the interstitial fluid, into the capillary plasma. From plasma it diffuses into the red cell, where the enzyme carbonic anhydrase rapidly converts it (with water) to carbonic acid, which dissociates to bicarbonate and a hydrogen ion; the H$^+$ is buffered chiefly by deoxyhaemoglobin (the Haldane effect: deoxygenated Hb is a better H$^+$ buffer and also binds CO$_2$ directly as carbamino compounds more readily), while HCO$_3^-$ largely exits the red cell into plasma in exchange for Cl$^-$ (the chloride shift). Venous blood therefore carries CO$_2$ in three forms — as bicarbonate (≈70%), as carbamino compounds mainly on hameoglobin (≈23%), and simply dissolved (≈7%). At the pulmonary capillaries, the falling $P_{CO_2}$ (as CO$_2$ diffuses into the alveolar gas, which has a lower $P_{CO_2}$) reverses every step: HCO$_3^-$ re-enters the red cell (reverse chloride shift), carbonic anhydrase reforms CO$_2$ from H$_2$CO$_3$, carbamino-CO$_2$ is released as haemoglobin becomes oxygenated (the same Haldane effect operating in reverse), and the regenerated dissolved CO$_2$ diffuses from red cell to plasma to alveolar gas, from which it is exhaled.
