04-Bio-A8 · May 2015
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format: National Exams, May 2015 — 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. Questions 2 and 4 cover nerve-fibre stimulate/record instrumentation and the Einthoven-triangle/Lead I ECG.
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.
An ultrasound beam directed at an artery is scattered by the moving red blood cells within it; because the scatterers are moving relative to the (stationary) transducer, the frequency of the backscattered echo is shifted from the transmitted frequency by an amount proportional to the blood velocity component along the beam. For a beam making angle $\theta$ with the vessel axis, the Doppler shift is $f_d = 2f_0v\cos\theta/c$, where $f_0$ is the transmitted frequency, $v$ the blood velocity, and $c$ the speed of sound in tissue. Measuring $f_d$ therefore yields the blood velocity directly, and because the shift is proportional to velocity, systole (peak forward flow) and diastole are readily distinguished in the recovered Doppler signal — the basis for non-invasively assessing flow in a superficial vessel such as the carotid artery. Doppler itself gives velocity; to estimate volumetric flow the mean velocity across the lumen (from the intensity-weighted mean Doppler frequency of the spectrum, $\bar v=c\,\bar f_d/(2f_0\cos\theta)$) is multiplied by the vessel cross-sectional area, $Q=\bar v\,\pi d^2/4$, with the diameter $d$ measured by B-mode imaging or estimated, and the result averaged over whole cardiac cycles. For example, an 8 MHz beam at $\theta=60^\circ$ on a peak velocity of 0.5 m/s gives $f_d=2(8\times10^6)(0.5)(0.5)/1540\approx2.6$ kHz (audible), and a time-averaged mean velocity of 0.25 m/s in a 6 mm carotid gives $Q\approx0.42$ L/min. The accuracy therefore depends on knowing $\theta$, on the whole lumen being insonated uniformly, and on the diameter estimate, since the diameter enters squared.
A CW system uses two separate piezoelectric crystals in one probe: a transmit crystal, continuously driven by a CW oscillator at a fixed frequency (no pulsing, so transmission and reception happen simultaneously and continuously), and a receive crystal that continuously picks up backscattered echo from everything within the overlapping transmit/receive beam. The mixer/demodulator compares the received signal against the reference oscillator signal, and the difference frequency this produces is exactly the Doppler shift $f_d$, which for physiological velocities and MHz-range transmit frequencies falls conveniently in the audible range. This audio-frequency Doppler signal is fed to an audio amplifier and speaker, letting the operator hear the characteristic pulsatile "whoosh" of arterial flow directly, and in parallel to a zero-crossing detector or spectral (FFT) analyzer, which converts the Doppler audio into a quantitative velocity-versus-time trace or spectral display for objective measurement and recording.
Depth of penetration is governed primarily by attenuation, which increases with both distance travelled and, importantly, with frequency: attenuation in soft tissue is approximately $\alpha \approx 0.5\ \text{dB}/(\text{cm}\cdot\text{MHz})$, so attenuation in decibels is roughly $A \approx \alpha \, f \, d$ for depth $d$ and frequency $f$ — doubling the frequency roughly doubles the dB loss for the same depth, which is why higher frequencies reach shallower maximum depths before the returning echo becomes too weak to detect. Beam spread (divergence) is governed by the transducer's aperture diameter $D$ relative to the wavelength $\lambda = c/f$: the beam remains roughly collimated out to the near-field (Fresnel-zone) length $N \approx D^2/(4\lambda)$, beyond which it diverges in the far field at an angle $\theta \approx 1.22\,\lambda/D$ (the diffraction/Rayleigh limit). A larger aperture or a higher frequency (shorter $\lambda$) both narrow the beam and extend the near field, improving lateral resolution, but higher frequency simultaneously worsens penetration through the attenuation relation above — the fundamental resolution-versus-penetration trade-off in ultrasound.
Because the carotid artery lies only a few centimetres beneath the skin surface, penetration depth is not the limiting concern, so a relatively high frequency, typically in the 5–10 MHz range (commonly about 8 MHz), is chosen. This favours a narrower, better-focused beam and a larger, more easily resolved Doppler shift for a given velocity (since $f_d\propto f_0$), improving both spatial and velocity resolution, without incurring an excessive attenuation penalty over the short path length involved.
A vascular technologist screening for carotid stenosis places an 8 MHz CW Doppler probe over the neck at roughly 45–60° to the vessel, listens for the characteristic high-pitched, turbulent "musical" sound that indicates a jet through a narrowed segment, and confirms it quantitatively from the spectral analyzer's peak systolic velocity trace, which rises sharply at the site of a significant stenosis.
