Fellowship of the Royal College of Anaesthetists (FRCA) Physics, Clinical Measurement and Statistics Syllabus

State Ohm's law and the equations relating power, current, voltage and resistance.

Ohm's law: $V = IR$. Power: $P = VI = I^{2}R = \frac{V^{2}}{R}$, where $V$ = voltage (volts), $I$ = current (amperes), $R$ = resistance (ohms), $P$ = power (watts).

Define capacitance, inductance and impedance.

Capacitance: ability to store charge, $C = \frac{Q}{V}$, unit farad. Inductance: a changing current induces an opposing EMF, unit henry. Impedance ($Z$): total opposition to alternating current, combining resistance and reactance; unit ohm.

What current magnitudes (at 50 Hz, mains) cause tingling, the 'can't let go' threshold, and ventricular fibrillation?

~1 mA: tingling/perception threshold. ~5 mA: pain. ~15 mA: tetanic muscle contraction ('can't let go'). ~50-100 mA: ventricular fibrillation. ~>5 A: sustained myocardial contraction/burns.

Define microshock and macroshock and the threshold current for microshock VF.

Macroshock: current applied to intact skin. Microshock: small current delivered directly to the myocardium via an intracardiac conductor (e.g. pacing wire, CVC). As little as $100\ \mu\text{A}$ (0.1 mA) applied directly to the heart can cause ventricular fibrillation.

Classify electrical equipment into Class I, II and III, and define Type B, BF and CF applied parts.

Class I: protected by earthing of the casing. Class II: double/reinforced insulation, no earth needed. Class III: uses safety extra-low voltage (<24 V AC). Type B: earthed, no isolated part. Type BF: floating (isolated) applied part. Type CF: floating part safe for direct cardiac connection (lowest leakage).

What is a floating (isolated) circuit and how does it improve electrical safety?

An isolated circuit uses an isolating transformer so the patient circuit is not referenced to earth. A fault to earth then does not allow current to flow back through the patient/operator to complete a circuit, reducing shock risk. Type F (floating) applied parts use this principle.

Explain the principle of diathermy and contrast monopolar with bipolar diathermy.

Diathermy uses high-frequency AC (0.3-3 MHz) to heat tissue; high frequency avoids stimulating excitable membranes. Monopolar: current passes from a small active electrode through the patient to a large return plate — high current density at tip cuts/coagulates. Bipolar: current passes only between the two limbs of forceps — safer, no return plate needed, used in pacemaker patients/extremities.

Why does diathermy use high frequency AC, and what cutting versus coagulation waveforms are used?

High frequency (>50 kHz, typically 0.3-3 MHz) is above the frequency that depolarises nerve/cardiac cells, so it heats tissue without causing electrocution/VF. Cutting uses a continuous low-voltage sine wave; coagulation uses a pulsed/interrupted higher-voltage waveform.

What precautions are taken with diathermy in a patient with a pacemaker?

Use bipolar diathermy if possible; if monopolar is essential use short bursts at lowest power, place the return plate so current does not cross the pacemaker/heart, keep diathermy away from the device, have a magnet/external defibrillator and pacing available, and consult cardiology to reprogram to fixed-rate mode if needed.

What does LASER stand for and what are the main hazards and protective measures in theatre?

Light Amplification by Stimulated Emission of Radiation. Hazards: eye injury (retinal/corneal burns), skin burns, airway fire, and plume (smoke) inhalation. Protection: wavelength-specific goggles, matt instruments, warning signs, eye protection for patient, fire precautions (saline-soaked swabs, low FiO2, laser-resistant tubes), and smoke evacuation.

Explain the principle of fibreoptic transmission of light.

Light is transmitted along a glass/plastic fibre by total internal reflection: the core has a higher refractive index than the cladding, so light striking the boundary above the critical angle is reflected back internally, allowing transmission around bends with minimal loss.

Compare monophasic and biphasic defibrillator waveforms and typical energies.

Monophasic: current flows in one direction; typical shock 360 J. Biphasic: current reverses direction mid-shock, achieving defibrillation at lower energy (120-200 J) with less myocardial damage and higher first-shock success. Energy delivered $= \frac{1}{2}CV^{2}$ from a charged capacitor.

State the energy stored in a defibrillator capacitor and the role of the inductor.

Energy stored $E = \frac{1}{2}CV^{2}$ where $C$ is capacitance and $V$ the charging voltage. The inductor in series prolongs and smooths the current pulse (lengthening it to several milliseconds) and prevents an excessively sharp spike that would damage the myocardium.

What do the first three letters of the NBG/NASPE pacemaker code denote?

Position I = chamber Paced; II = chamber Sensed; III = Response to sensing. Letters: O=none, A=atrium, V=ventricle, D=dual. E.g. DDD = dual paced, dual sensed, dual (triggered+inhibited) response. Position IV = rate modulation (R), V = multisite pacing.

Compare the operating principles of resistance strain gauge versus piezoelectric transducers.

Resistance strain gauge: applied force stretches a wire/semiconductor, changing its resistance (used in a Wheatstone bridge) — used in invasive BP transducers. Piezoelectric: deformation of a crystal generates a voltage proportional to applied pressure — used in ultrasound and some rapidly changing pressure measurements.

Describe the Wheatstone bridge and its use in pressure measurement.

A Wheatstone bridge is a circuit of four resistors arranged in two parallel branches with a galvanometer/measuring device across the midpoints. When a strain gauge resistor changes, the bridge becomes unbalanced and the output voltage is proportional to the change, allowing sensitive measurement of small resistance changes from pressure transducers.

What are the requirements for accurate invasive arterial pressure measurement (damping and natural frequency)?

The system should have a high natural frequency (>20-40 Hz, well above the highest pulse harmonic) and an optimal damping coefficient of ~0.64-0.7. Over-damping underestimates systolic and overestimates diastolic; under-damping overshoots (resonance) exaggerating systolic. The transducer must be zeroed at the level of the right atrium (mid-axillary line).

Explain the principle of infrared absorption spectroscopy for gas analysis and which gases it can measure.

Gases with two or more dissimilar atoms absorb infrared radiation at characteristic wavelengths (Beer-Lambert law). The amount absorbed is proportional to concentration. It measures $\ce{CO2}$, $\ce{N2O}$ and volatile agents. It cannot measure oxygen, nitrogen or helium (these molecules are non-polar/symmetrical or monatomic and do not absorb IR).

How is oxygen concentration measured? Name and describe two methods.

Paramagnetic analysis: $\ce{O2}$ is paramagnetic (attracted to a magnetic field), and the degree of attraction is proportional to concentration — fast, accurate. Fuel cell/galvanic cell: $\ce{O2}$ diffuses to a cathode generating a current proportional to $\ce{O2}$ (slow, consumable). Also the Clark polarographic electrode (with a polarising voltage).

State the Beer-Lambert law and its relevance to gas/blood analysis.

$$A = \varepsilon \cdot c \cdot l$$ Absorbance $A$ equals the molar absorptivity $\varepsilon$ times concentration $c$ times path length $l$. It underpins infrared gas analysis and pulse oximetry, where light absorption is proportional to the concentration of the absorbing substance.

Explain the principle of pulse oximetry and the two wavelengths used.

Pulse oximetry uses two LEDs at 660 nm (red) and 940 nm (infrared). Oxyhaemoglobin absorbs more infrared, deoxyhaemoglobin more red. The device measures the pulsatile (arterial) component of absorption and calculates the ratio of red to infrared absorption to derive $\text{SpO}_2$ from a stored calibration curve.

List the main sources of error/inaccuracy in pulse oximetry.

Carboxyhaemoglobin (reads falsely high), methaemoglobin (tends toward 85%), motion artefact, poor perfusion/hypotension, nail varnish, ambient/surgical light, venous pulsation, methylene blue dye (false low), and reduced accuracy below 70-80% saturation. It does not detect hyperoxia or hypoventilation if oxygen is supplied.

What is co-oximetry and how does it differ from pulse oximetry?

A co-oximeter is a benchtop device using 4 or more wavelengths of light on a blood sample to measure the fractions of oxyhaemoglobin, deoxyhaemoglobin, carboxyhaemoglobin and methaemoglobin separately. Unlike pulse oximetry (2 wavelengths, only functional $\text{SaO}_2$), it gives true fractional saturation and detects dyshaemoglobins.

Compare resistance thermometers, thermistors and thermocouples for temperature measurement.

Resistance thermometer (platinum wire): resistance rises linearly with temperature. Thermistor: a semiconductor bead whose resistance falls non-linearly (exponentially) as temperature rises — small, fast, cheap. Thermocouple: two dissimilar metals joined; the junction generates a voltage proportional to temperature (Seebeck effect) — small and fast.

Explain the Seebeck effect used in a thermocouple.

When two wires of dissimilar metals are joined at two junctions held at different temperatures, a small voltage (electromotive force) is generated that is proportional to the temperature difference between the junctions. One junction is kept at a reference temperature to measure the unknown.

Name three depth-of-anaesthesia / neuromuscular monitoring modalities and what each assesses.

Depth of anaesthesia: processed EEG (e.g. Bispectral Index, BIS, 0-100, target 40-60) and entropy. Neuromuscular: peripheral nerve stimulator with train-of-four (TOF), giving the TOF ratio (T4/T1) and TOF count; double-burst and post-tetanic count for deeper block.

Define the train-of-four ratio and the TOF count thresholds for clinical recovery.

Train-of-four (TOF) delivers four stimuli at 2 Hz; the TOF ratio is the amplitude of the 4th twitch divided by the 1st ($T_4/T_1$). Fade indicates non-depolarising block. Adequate clinical recovery requires a TOF ratio $\geq 0.9$. TOF count of 0 = deep block; the first twitch typically returns when ~90-95% of receptors are blocked.

Compare thermodilution cardiac output measurement (PAC) with the principle behind it (Stewart-Hamilton equation).

A known volume of cold saline is injected into the right atrium and temperature change is measured downstream in the pulmonary artery. Cardiac output is inversely proportional to the area under the temperature-time curve, per the Stewart-Hamilton equation: $$Q = \frac{V(T_{b}-T_{i})K}{\int \Delta T_{b}\,dt}$$ Smaller area = higher cardiac output.

Name three less-invasive cardiac output monitoring technologies and their principles.

Oesophageal Doppler: measures aortic blood flow velocity by Doppler shift. Pulse contour analysis (e.g. LiDCO, PiCCO): derives stroke volume from the arterial waveform, often calibrated by lithium or thermodilution. Thoracic bioimpedance/bioreactance: detects changes in thoracic electrical impedance with each stroke volume. Also Fick principle methods.

State the Fick principle for cardiac output measurement.

$$\text{CO} = \frac{\dot{V}\ce{O2}}{Ca\ce{O2} - Cv\ce{O2}}$$ Cardiac output equals oxygen consumption divided by the arteriovenous oxygen content difference. It states that the uptake of a substance by an organ equals the blood flow times the arteriovenous concentration difference.

State the pin-index safety system positions and colour codes for oxygen and nitrous oxide cylinders (UK).

The pin index system uses a unique pin configuration so the wrong cylinder cannot fit a yoke. Oxygen pins at positions 2 and 5, cylinder body white with white shoulders. Nitrous oxide pins at positions 3 and 5, cylinder French blue. Entonox: pins 7, blue with white shoulders. (Colours per ISO/UK convention.)

State the filling pressures and contents of a size E oxygen cylinder versus nitrous oxide cylinder.

Oxygen (E): stored as compressed gas at ~137 bar, contains ~680 L; gauge pressure falls linearly with contents (obeys Boyle's law). Nitrous oxide (E): stored as liquid + vapour at ~44 bar (4400 kPa), contains ~1800 L; gauge pressure stays constant until liquid is exhausted, so the filling ratio (0.75 in UK) indicates contents, not the gauge.

What pipeline pressures are supplied to the anaesthetic machine, and what is the role of pressure regulators?

Pipeline (and machine) working pressure is ~4 bar (400 kPa); cylinders supply at high pressure (e.g. oxygen 137 bar) reduced by regulators to ~4 bar before entering the machine. Regulators reduce high variable cylinder pressure to a constant safe working pressure and protect downstream components.

List the key safety features of a modern anaesthetic machine.

Pin index system, non-interchangeable gas-specific connections (NIST/Schrader), oxygen failure alarm (e.g. Ritchie whistle), hypoxic guard linking O2 and N2O flows (minimum ~25% O2), oxygen flush, anti-hypoxia mixture device, pressure relief valves, vaporiser interlock, and the oxygen analyser as ultimate guarantee of delivered O2.

Explain the function of the oxygen failure (Ritchie) whistle and the anti-hypoxia link.

The oxygen failure warning device sounds (whistle powered by the failing O2 supply) when oxygen supply pressure falls below a threshold (~200 kPa / 2 bar), and simultaneously cuts off other gases / opens the room air entrainment. The hypoxic guard (e.g. chain link) mechanically/pneumatically links N2O and O2 flowmeters to ensure delivered O2 cannot fall below ~25%.

Classify the Mapleson breathing systems and state the most efficient for spontaneous versus controlled ventilation.

Mapleson A, B, C, D, E, F. For spontaneous ventilation the Mapleson A (Magill) is most efficient (fresh gas flow ~equal to minute ventilation). For controlled ventilation the Mapleson D (and its Bain coaxial modification) is most efficient. Mapleson E/F (Ayre's T-piece/Jackson-Rees) are used in paediatrics.

What fresh gas flow is required for a Mapleson A during spontaneous breathing and a Mapleson D during controlled ventilation?

Mapleson A (spontaneous): FGF ~70-100 mL/kg/min, approximately equal to alveolar minute ventilation. Mapleson D/Bain (controlled): FGF ~70 mL/kg/min (some quote 100 mL/kg/min) to prevent rebreathing. The Bain is a coaxial D system.

Describe how a circle breathing system works and the function of soda lime.

A circle system recirculates gas through inspiratory and expiratory limbs with unidirectional valves, a reservoir bag, APL valve and a $\ce{CO2}$ absorber, allowing low fresh gas flows. Soda lime (~94% $\ce{Ca(OH)2}$, with $\ce{NaOH}$ and indicator) absorbs $\ce{CO2}$: $\ce{CO2 + Ca(OH)2 -> CaCO3 + H2O + heat}$, and the indicator changes colour when exhausted.

Classify ventilators by their cycling mechanism.

Ventilators are classified by the variable that ends inspiration (cycling): volume-cycled (stops at set volume), pressure-cycled (stops at set pressure), time-cycled (stops after set time), and flow-cycled (stops when flow falls to a threshold, e.g. pressure support). They are also classed by power source and by minute volume divider vs bag-in-bottle design.

What are the hazards of theatre pollution by anaesthetic gases and how does active scavenging work?

Chronic exposure concerns: possible teratogenicity, fertility effects, and N2O's effect on vitamin B12/methionine synthase; environmental greenhouse effect. Active scavenging uses a collecting valve, transfer tubing, a receiving system with positive and negative pressure relief, and a disposal route (e.g. vacuum) to remove waste gas. UK COSHH limits: N2O 100 ppm, isoflurane 50 ppm, sevoflurane 20 ppm (8-hr TWA).

Compare cleaning, disinfection and sterilisation.

Cleaning: physical removal of visible contamination/organic matter (prerequisite). Disinfection: reduction of microorganisms to a safe level but not all spores (e.g. chemical, pasteurisation). Sterilisation: complete destruction of all microorganisms including spores and prions (e.g. autoclave, ethylene oxide, gamma irradiation).

Describe autoclave sterilisation parameters and when ethylene oxide or single-use devices are preferred.

Autoclave (steam under pressure): e.g. $134\,^{\circ}\text{C}$ at 2 bar for 3 min, or $121\,^{\circ}\text{C}$ at 1 bar for 15 min. Ethylene oxide or low-temperature methods (e.g. gas plasma) are used for heat-sensitive equipment. Single-use devices are used where reprocessing is unreliable or to prevent prion (vCJD) transmission, since prions resist standard autoclaving.

Classify types of data: nominal, ordinal, interval and ratio.

Nominal: categories with no order (e.g. blood group). Ordinal: ordered categories without consistent intervals (e.g. ASA grade, pain score). Interval: ordered with equal intervals but no true zero (e.g. °C). Ratio: equal intervals with an absolute zero (e.g. kelvin, weight, height).

Define mean, median and mode and state which is best for skewed data.

Mean: arithmetic average (sum/n). Median: middle value when data are ranked. Mode: most frequent value. For skewed (non-normal) data the median is the most representative measure of central tendency because the mean is distorted by outliers.

Define standard deviation, variance and standard error of the mean, including the SEM formula.

Variance: mean of the squared deviations from the mean ($\sigma^{2}$). Standard deviation: $\sigma = \sqrt{\text{variance}}$, describing spread of the data. Standard error of the mean: $$SEM = \frac{\sigma}{\sqrt{n}}$$ describing the precision of the estimate of the population mean.

Describe the properties of a normal (Gaussian) distribution including the empirical rule.

Symmetrical bell shape where mean = median = mode. ~68% of values lie within $\pm 1$ SD, ~95% within $\pm 1.96$ SD (commonly stated $\pm 2$ SD), and ~99.7% within $\pm 3$ SD of the mean.

Define the null hypothesis, Type I and Type II errors.

Null hypothesis ($H_0$): there is no difference/effect. Type I error ($\alpha$): rejecting a true null hypothesis (false positive); conventionally $\alpha = 0.05$. Type II error ($\beta$): failing to reject a false null hypothesis (false negative); conventionally $\beta = 0.2$.

Define statistical power and state how it is calculated and increased.

Power $= 1 - \beta$, the probability of correctly detecting a real effect (rejecting a false null), conventionally $\geq 0.8$ (80%). Power is increased by a larger sample size, a larger effect size, lower variability, and a higher (less strict) $\alpha$.

Define the p-value and the 95% confidence interval.

P-value: the probability of obtaining the observed result (or more extreme) if the null hypothesis were true; $p<0.05$ is conventionally 'significant'. 95% confidence interval: the range within which the true population value lies with 95% certainty; if it crosses the line of no effect (0 for differences, 1 for ratios) the result is non-significant.

Match the correct parametric test to the comparison: two groups, more than two groups, and correlation.

Two independent groups (parametric): unpaired (Student's) t-test. Two paired measurements: paired t-test. Three or more groups: ANOVA (analysis of variance). Linear relationship between two continuous variables: Pearson correlation coefficient and linear regression.

Name the non-parametric equivalents of the unpaired t-test, paired t-test, ANOVA and Pearson correlation.

Unpaired t-test → Mann-Whitney U test. Paired t-test → Wilcoxon signed-rank test. One-way ANOVA → Kruskal-Wallis test. Pearson correlation → Spearman's rank correlation. Use non-parametric tests for ordinal or non-normally distributed data.

When is the chi-squared test used and what does it assess?

The chi-squared ($\chi^2$) test is used for categorical (nominal) data to assess whether observed frequencies differ from expected frequencies, i.e. association between categorical variables in a contingency table. Fisher's exact test is used instead when expected cell counts are small (<5).

Define sensitivity and specificity with their formulas.

Sensitivity = true positives correctly identified $= \frac{TP}{TP+FN}$ (ability to detect disease; rules out when negative — SnNout). Specificity = true negatives correctly identified $= \frac{TN}{TN+FP}$ (ability to exclude disease; rules in when positive — SpPin).

Define positive and negative predictive value and how they relate to prevalence.

Positive predictive value $PPV = \frac{TP}{TP+FP}$ (probability disease is present given a positive test). Negative predictive value $NPV = \frac{TN}{TN+FN}$. Unlike sensitivity/specificity, predictive values depend on disease prevalence: PPV falls as prevalence falls.

Define the likelihood ratio and what an ROC curve represents.

Positive likelihood ratio $LR^{+} = \frac{\text{sensitivity}}{1-\text{specificity}}$; negative $LR^{-} = \frac{1-\text{sensitivity}}{\text{specificity}}$. A ROC (receiver operating characteristic) curve plots sensitivity (true positive rate) against 1 − specificity (false positive rate) at various thresholds; the area under the curve (AUC) reflects overall test accuracy (0.5 = useless, 1.0 = perfect).

Rank the hierarchy of clinical evidence from strongest to weakest.

From strongest: systematic reviews/meta-analyses of RCTs → randomised controlled trials → cohort studies → case-control studies → cross-sectional/case series → case reports → expert opinion. Higher levels have lower risk of bias.

Define randomisation, blinding and allocation concealment in trial design.

Randomisation: assigning participants to groups by chance to balance confounders. Allocation concealment: hiding the upcoming assignment from those enrolling, to prevent selection bias. Blinding: keeping participants (single), and also investigators/assessors (double) unaware of group allocation to prevent performance and detection bias.

Define number needed to treat (NNT), absolute risk reduction and relative risk.

Absolute risk reduction $ARR = \text{risk}_{control} - \text{risk}_{treatment}$. Number needed to treat $NNT = \frac{1}{ARR}$ (patients treated to prevent one event). Relative risk $RR = \frac{\text{risk}_{treatment}}{\text{risk}_{control}}$; relative risk reduction $RRR = 1 - RR$.

Distinguish an odds ratio from a relative risk and state which study design uses each.

Relative risk (RR): ratio of incidence in exposed vs unexposed — used in cohort/RCTs where incidence is known. Odds ratio (OR): ratio of odds of exposure in cases vs controls — used in case-control studies where incidence cannot be calculated. OR approximates RR when the outcome is rare.