04-Bio-A8 · Undated paper
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format: National Exams — 04-Bio-A8 Biophysical Measurements. Three hours, open book, any non-communicating calculator. Seven questions of equal value (20 marks each); five constitute a complete paper and only the first five appearing in the answer book are marked. All seven are solved here, because this set is a study resource rather than an examination script. Every question is qualitative/descriptive — there is no numerical data to compute — so each answer follows flowing prose with instrumentation block diagrams where the question explicitly asks for one.
Reference texts (the books an open-book candidate should have on the desk for this subject):
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.
Pulse oximetry rests on two physical facts. First, oxygenated haemoglobin (HbO$_2$) and deoxygenated (reduced) haemoglobin (Hb) have markedly different optical absorption spectra: at a red wavelength around 660 nm, deoxyhaemoglobin absorbs considerably more than oxyhaemoglobin, while at an infrared wavelength around 940 nm this relationship reverses and oxyhaemoglobin absorbs somewhat more — so the ratio of absorption at these two wavelengths is a direct, monotonic indicator of the fraction of haemoglobin that is oxygenated, per the Beer–Lambert law of light absorption through an absorbing medium. Second, arterial blood is distinguished from all the other tissue the light passes through (skin, bone, venous blood, tissue fluid) by the fact that it alone pulsates with each heartbeat: as arterial volume rises and falls with the cardiac cycle, the optical path length of light through arterial blood, and hence the transmitted light intensity, varies at the pulse rate. A photoplethysmographic signal therefore decomposes into a large, slowly varying DC component (light attenuated by the constant tissue bed — skin, bone, venous blood, non-pulsatile arterial blood) and a small, pulse-synchronous AC component attributable specifically to the pulsatile arterial blood volume change. By measuring the AC/DC ratio at both wavelengths and forming the ratio-of-ratios $R=(AC/DC)_{660}/(AC/DC)_{940}$, the confounding effects of tissue thickness, skin pigmentation, and light-source intensity — all of which affect AC and DC proportionally and so cancel in the ratio — are largely removed (to first order only — see part (iii)), leaving $R$ dependent essentially only on oxygen saturation. Because multiple scattering in tissue means the Beer–Lambert law is not exactly obeyed, $R$ is mapped to $SpO_2$ using an empirical calibration curve derived from controlled human or animal desaturation studies rather than from theory alone.
The dual LEDs (660 nm red and 940 nm infrared) are switched on and off in rapid, time-multiplexed sequence (with a brief both-off interval to sample ambient light), so a single photodetector on the opposite side of the tissue can distinguish the two wavelengths in time rather than needing two separate detectors. Light passes through the fingertip or earlobe (a site chosen for a thin, well-perfused, pulsatile vascular bed) and the transmitted fraction is captured by a photodiode with a transimpedance amplifier, converting the photocurrent to a voltage. A sample-and-hold demultiplexer, synchronized to the LED switching sequence, separates this single composite signal back into its red and infrared channels (and subtracts the ambient-light sample from each). Each channel is then processed by an AC/DC separation stage (high-pass/low-pass filtering) to extract the pulsatile and baseline components and form the ratio $R$. Finally, a stored empirical calibration curve converts $R$ into a displayed $SpO_2$ percentage, typically alongside a plethysmographic waveform display and a heart rate derived from the pulsatile signal's periodicity.
Both increase the fixed (non-pulsatile) optical attenuation the light must overcome, reducing the DC signal level and, with it, the absolute size of the AC signal available to measure — and because $SpO_2$ is derived from the ratio $R$ rather than absolute intensities, this is cancelled to first order, provided the detected signal remains large enough to measure accurately above the noise floor. For pigmentation it cancels only partly: melanin absorbs more strongly at 660 nm than at 940 nm, LED emission spectra are broad, and many devices were calibrated on predominantly lightly pigmented volunteers, so clinical studies (e.g. Sjoding et al., NEJM 2020) found occult hypoxaemia missed about three times as often in Black patients. Accommodation therefore has two parts: recovering enough signal, and calibrating across the full range of skin pigmentation. The instrument compensates by using automatic gain control on the LED drive current (increasing optical output power) and on the photodiode amplifier gain, together with a wide-dynamic-range analogue-to-digital converter, so that adequate signal amplitude is recovered even through heavily pigmented or thick tissue. If the signal still cannot be made adequate, the practical remedy is to relocate the sensor to a thinner, better-perfused site (e.g. earlobe rather than a thick finger) or to use a reflectance-mode probe instead of a transmission probe. On the calibration side, the $R$-to-$SpO_2$ curve should be validated in controlled desaturation studies that include volunteers across the full range of skin pigmentation, and a doubtful reading in a darkly pigmented patient should be confirmed by arterial blood-gas analysis.
Motion artifact is the dominant source: patient or limb movement changes the optical path length and can also cause venous blood to pulsate, mimicking or corrupting the true arterial pulsatile signal and producing erroneous readings or signal dropout. Ambient light interference from room lighting, surgical lamps, or other equipment operating at overlapping wavelengths can add directly to the photodetector signal; this is why the instrumentation includes a brief both-LEDs-off sampling interval to measure and subtract the ambient contribution from each reading.
An anaesthetized patient with a heavily pigmented finger and cold, poorly perfused peripheries would have the sensor moved to the earlobe (thinner tissue, often better perfused under anaesthesia) and the oximeter's automatic gain control would raise LED drive current to recover adequate AC amplitude, while continuous ambient-light subtraction protects the reading from the operating-room lighting.
