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.
The experiment isolates a single unmyelinated fibre (e.g. a dissected invertebrate giant axon or a fine mammalian C-fibre) in a temperature-controlled physiological saline bath. Two electrode pairs are needed on the same preparation: an extracellular stimulating pair, placed some distance along the fibre, that injects current to depolarize the membrane past threshold; and an intracellular recording microelectrode, placed downstream of the stimulus site, that measures the propagated transmembrane action potential this triggers — the same membrane circuit analysed in Question 1, now driven externally rather than left to settle at rest.
A pair of fine bipolar hook or suction electrodes (platinum or Ag/AgCl) straddles the fibre at a point well upstream of the recording site, spaced a few millimetres apart along the fibre with the cathode nearer the recording electrode: outward membrane current under the cathode depolarizes the fibre and launches the spike there, while placing the anode on the far side keeps the local hyperpolarization under it from blocking the impulse on its way to the recording site. The fibre is lifted into air or oil at the stimulating site (or the electrodes are closely applied) so the current passes through the fibre rather than being shunted by the bath. They are driven by a constant-current stimulus isolator: an isolated (floating, non-earth-referenced) current source delivering a brief rectangular pulse, typically 0.1–0.5 ms wide, because floating the stimulus output prevents stimulus current from returning through the bath's ground path and appearing as an artifact at the recording electrode, and is also a basic electrical-safety requirement for any instrument coupled to living tissue. The stimulus amplitude is set well above the fibre's measured threshold — a "supramaximal" stimulus, commonly twice threshold — because the threshold current of an extracellularly stimulated fibre depends on electrode–fibre distance, bath shunting, electrode polarization and the fibre's own condition, all of which drift during an experiment, and a comfortable safety margin ensures the fibre fires reliably on every sweep despite small trial-to-trial variation. The isolator's trigger output is also sent to the computer, marking time-zero for each sweep so the recorded trace can be aligned and, if desired, averaged across repeats.
The transmembrane potential itself requires an intracellular glass micropipette microelectrode (tip diameter well under 1 μm, filled with a concentrated electrolyte such as 3 M KCl to keep its own resistance manageable) impaled directly through the membrane into the axoplasm, paired with an Ag/AgCl reference electrode in the bath outside the fibre; the potential difference between the two is, by definition, the transmembrane potential $V_m(t)$. Because such a microelectrode is a very high impedance source (tens of megohms), it must feed a dedicated electrometer headstage — a unity-gain, ultra-high-input-impedance (typically FET-input) buffer mounted physically right at the electrode — before any cable run; connecting the bare microelectrode straight to a distant amplifier would load the electrode against its own resistance and add cable capacitance, both of which slow and attenuate the recorded spike. The headstage normally also includes capacitance-compensation ("negative capacitance") circuitry that cancels the electrode's own RC filtering so the recorded rise time reflects the membrane, not the pipette. From the headstage the signal passes to a differential amplifier and bandpass filter stage, referenced against the bath electrode, DC-coupled, with a passband wide enough (DC to several kHz) to preserve both the steady resting level and the fast sodium-driven upstroke of the spike. Finally an ADC/data-acquisition card, hardware-triggered by the stimulus pulse, samples the amplified waveform at a rate well above Nyquist for the action potential's rise time (tens of kHz is typical) and hands the digitized sweep to the computer for display, storage and measurement (spike amplitude, duration, and — from the known stimulus-to-recording-electrode distance and the latency between the trigger and the spike — conduction velocity).
Several noise sources must be controlled. Mains (60 Hz) interference picked up by the long, high-impedance microelectrode lead is the dominant environmental noise; it is rejected by the differential amplifier's common-mode rejection and by shielding the headstage and bath in a grounded Faraday enclosure. Stimulus artifact — the much larger stimulating pulse bleeding electrically or capacitively into the recording path — is minimized by the stimulus isolator's floating output and by physically separating the stimulating and recording electrode sites; a short blanking interval around the stimulus can also be applied before the spike itself arrives. Microelectrode (thermal/Johnson) noise grows with the electrode's own resistance, so a well-fabricated, no-higher-than-necessary resistance pipette and a low-noise FET headstage input keep this contribution below the spike amplitude. Mechanical vibration can dislodge or damage the intracellular seal; the preparation is normally mounted on a vibration-isolation table. Finally, bath temperature drift changes both the resting potential and the kinetics of the voltage-gated conductances (Question 1), so the bath is temperature-controlled to keep the recorded spike shape and threshold repeatable from sweep to sweep.
A classic squid-giant-axon-style preparation uses exactly this arrangement — extracellular bipolar stimulation at one end of the isolated axon, an intracellular glass microelectrode with FET headstage some distance downstream, and a computer DAQ triggered on the stimulus — to measure the propagated action potential's amplitude, duration and conduction velocity, the same measurement approach used clinically (in a very different, surface-electrode form) for the nerve-conduction studies referenced again in the practice set below.
