04-Bio-A8 · May 2014
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format: National Exams, May 2014 — 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.
Blood is a substantially better electrical conductor (lower resistivity, $\rho\approx150\,\Omega\cdot\text{cm}$) than the surrounding lung, muscle, and fat tissue of the thorax, because its high electrolyte and cellular (erythrocyte) content gives it a much lower bulk resistivity than air-filled lung or fatty tissue. During each cardiac cycle the volume of blood in the thoracic aorta and great vessels rises sharply as the left ventricle ejects its stroke volume, and this transient increase in the highly conductive blood volume lowers the electrical impedance measured across the thorax. Impedance cardiography exploits this: the thoracic impedance $Z(t)$ has a large, nearly constant baseline component $Z_0$ (set by the static geometry and composition of the thorax) and a small, rapidly time-varying component $\Delta Z(t)$ synchronous with the cardiac cycle, whose rate of change $dZ/dt$ during systole is proportional to the rate of volume change of blood in the aorta. Kubicek's formula relates the peak of $dZ/dt$, the ventricular ejection time (from the ECG and the impedance waveform), the baseline impedance $Z_0$, blood resistivity, and the distance between the inner sensing electrodes to a computed stroke volume, from which cardiac output follows as stroke volume × heart rate. Because the technique is continuous and completely non-invasive, it is used for beat-to-beat haemodynamic monitoring where an invasive thermodilution catheter would be undesirable.
A pair of outer (current-injecting) band electrodes is placed around the base of the neck and around the lower thorax/xiphoid level, and a pair of inner (voltage-sensing) electrodes is placed just inside them on the thorax. The four-electrode arrangement is used specifically because it decouples current injection from voltage sensing: the high-input-impedance sensing amplifier draws essentially no current through the inner electrodes, so the poorly-controlled and highly variable skin–electrode contact impedance at those electrodes drops no measurable voltage and does not corrupt the measurement — a two-electrode method would instead measure the contact impedance in series with the tissue impedance of interest, which swamps the small cardiac signal. The constant-current oscillator generates a safe, high-frequency (typically 50–100 kHz, chosen to be well above the frequency range that would stimulate excitable tissue) sinusoidal current of about 1–4 mA, injected through the outer electrodes. The voltage sense and demodulator block picks up the resulting high-frequency voltage between the inner electrodes (proportional to the thoracic impedance by Ohm's law) and demodulates it back to baseband, recovering $Z(t)$. The baseline/pulsatile separator splits this into the slowly varying $Z_0$ and the small pulsatile $\Delta Z(t)$, and differentiates the latter to give $dZ/dt$. Finally, the amplifier, filter, and display/recorder block conditions these signals (often alongside a simultaneous ECG channel for timing reference) for display, storage, and the stroke-volume calculation.
An ICU monitor combining impedance cardiography with a standard ECG lead would derive continuous, beat-to-beat cardiac output for a haemodynamically unstable patient without inserting a pulmonary-artery catheter, flagging a falling $dZ/dt_{max}$ as an early sign of deteriorating contractility or worsening hypovolaemia before blood pressure itself trends down.
