SI units, dimensions and measurement in anaesthesia

Why this matters to the anaesthetist

Anaesthesia is the most quantitative of the clinical specialities. Every minute of a case the anaesthetist reads and sets numbers — a blood pressure, an end-tidal carbon dioxide, a flow of oxygen, a dose of adrenaline, a partial pressure of sevoflurane — and every one of those numbers is meaningless without its unit. The number 0.4 is a fraction of a millilitre if it is a CVP, four-tenths of a millimole per litre of carbon dioxide if it is a PaCO2, forty per cent of a minimum alveolar concentration if it is an age-adjusted MAC, and four-tenths of a milligram per kilogram per hour if it is a ketamine infusion. Get the unit wrong and the number kills the patient: a microgram mistaken for a milligram is a thousand-fold overdose, a kilopascal misread as a millimetre of mercury is a clinically important pressure error, and a transducer zeroed to the wrong height gives a reproducibly wrong central venous pressure that is then treated with intravenous fluid [4][5].

The fellowship examination therefore treats units and measurement as foundational. The ANZCA Primary asks the candidate to list the seven SI base units and the dimensions of the derived units, to write the pressure conversions, to convert a dose between mcg per kg per min and mg per kg per h, and to distinguish accuracy from precision. The Final and the viva extend this to the measurement chain (transducer, amplifier, analogue-to-digital converter, display) and to the analysis of error in every device the anaesthetist uses. This topic rebuilds the whole framework: the base units and their modern definitions, the derived units and their base-unit combinations, dimensions and dimensional analysis, prefixes, the three coexisting unit systems, significant figures, the pressure conversions, the dose and flow conversions, the anaesthesia-specific units (MAC, blood-to-gas coefficient, partial pressure), the mcg-versus-mg medication-safety problem, and accuracy, precision and error [1][3].

The seven SI base units

The International System of Units is built on seven independent base units. A base unit is one that cannot be expressed in terms of the others; every other unit in the system is a coherent combination of these seven. Since the revision of 20 May 2019, each base unit is defined not by a physical artefact but by fixing the numerical value of an invariant constant of nature, so the definitions are universal, stable and independent of time and place [3].

Three points the examiner probes. First, the dimension symbols are conventionally a single roman letter: M (mass), L (length), T (time), I (electric current), theta (thermodynamic temperature), N (amount of substance) and J (luminous intensity). Second, the kilogram is the only base unit whose name carries a prefix (kilo-); the unit is the kilogram, not the gram, and the gram is a derived unit equal to 10 to the minus 3 kg. Third, the mole is a count — one mole is exactly 6.022 140 76 times 10 to the 23 entities — and is dimensionally the amount of substance N, not a mass; a mole of different substances has different masses but always the same number of particles. [1]

SI derived units

Every other unit in the SI is a coherent combination of the seven base units — coherent meaning no numerical factors other than one are needed. The derived units the anaesthetist must know, with their base-unit decompositions: [1]

The chain to memorise runs from force upward: a force (newton, kg m per s squared) acting over a distance does work and stores energy (joule, N m); energy delivered per unit time is power (watt, J per s); power dissipated in driving a current against a resistance is voltage times current, defining the volt (W per A) and the ohm (V per A); and charge delivered over time is current (coulomb is A s). Two non-obvious ones the examiner loves: the pascal is the newton per square metre (so pressure is force per area, with dimensions M L to the minus one per T squared), and the hertz is per second (a heart rate of 72 beats per minute is 1.2 Hz). The radiological units — becquerel, gray and sievert — share the same base dimensions but differ in what they count: the becquerel counts disintegrations per second (activity), the gray counts energy absorbed per kilogram of tissue (absorbed dose), and the sievert multiplies the gray by a dimensionless quality factor to weight the biological damage of different radiations [3].

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Dimensions and dimensional analysis

Every physical quantity carries dimensions written as a product of powers of the seven base dimensions M, L, T, I, theta, N and J. The dimensions of the common quantities: [1]

• Area L squared; volume L cubed; density M per L cubed; velocity L per T; acceleration L per T squared.
• Force M L per T squared; pressure M L to the minus one per T squared; energy M L squared per T squared; power M L squared per T cubed.
• Dynamic viscosity M per L per T; flow rate (volume per time) L cubed per T; surface tension M per T squared.
• Electric charge I T; voltage M L squared per T cubed per I; resistance M L squared per T cubed per I squared. [1]

Dimensional analysis is the requirement that both sides of any physical equation share identical dimensions. It is the most powerful single check on a formula, because an algebraic error almost always breaks the dimensions. Three worked examples for the fellowship. [1]

Force equals mass times acceleration. Newton's second law is F equals m a. Mass has dimension M, acceleration has dimension L per T squared, so force has dimension M L per T squared — the newton. The check: a one-kilogram mass accelerating at one metre per second squared needs exactly one newton. Dimensional consistency is satisfied. [1]

Pressure is force per area. Force is M L per T squared, area is L squared, so pressure is M L per T squared divided by L squared equals M L to the minus one per T squared — the pascal, kg per m per s squared. A pressure of one pascal is one newton spread over one square metre, which is tiny (atmospheric pressure is 101 325 pascals), which is why the kilopascal and millimetre of mercury are the practical units. [1]

Poiseuille's law is dimensionally a flow. The Hagen-Poiseuille equation for laminar flow through a tube is Q equals pi r to the fourth times delta P divided by 8 eta L. Checking dimensions: r to the fourth is L to the fourth; delta P is M L to the minus one per T squared; the numerator is M L cubed per T squared. The denominator has eta (M per L per T) times L, which is M per T. Dividing, the viscosity and mass cancel and one is left with L cubed per T — a volume per unit time, exactly what a flow must be [1]. If a candidate writes Poiseuille with r squared instead of r to the fourth, the dimensions still come out as a flow (because r to the second is L squared, giving L cubed per T), so dimensional analysis alone does not catch the famous r-to-the-fourth error — but it catches almost every other slip.

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Unit prefixes

Prefixes scale the base unit by powers of ten, so a single unit spans many orders of magnitude. The clinically important prefixes: [1]

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A misplaced prefix is among the commonest causes of medication error in the operating theatre. Confusing milli (10 to the minus 3) with micro (10 to the minus 6) is a thousand-fold difference: one milligram is one thousand micrograms. A milligram of a catecholamine mistaken for a microgram is a thousand-fold overdose and an immediate arrest; a microgram mistaken for a milligram in a paediatric patient can be a dose that is simply not delivered. The microgram is the dangerous one, because its symbol is ambiguous — the Greek mu is poorly handwritten, and "mcg" looks unlike "mg" but can still be misread at the end of a long shift [4][5][6].

The three coexisting unit systems: SI, CGS and imperial

Three systems of units have historical currency, and medicine still uses all three. [1]

The SI (Systeme International) is the modern metric system, built on the metre, kilogram, second and ampere (the MKSA base). It is coherent: the derived units are products of the base units with no extra factors. It is the global standard for science and the system every anaesthesia textbook uses for physics. [1]

The CGS system (centimetre-gram-second) is the older metric system. Its derived units are the dyne for force (g cm per s squared, equal to 10 to the minus 5 newton), the erg for energy (dyne cm, equal to 10 to the minus 7 joule) and the barye for pressure (dyne per cm squared, equal to 0.1 pascal). CGS appears in older physiology and pharmacology texts (the dyne is still seen in cardiac-output literature) and in some surface-tension and viscosity work, but it is otherwise obsolete in anaesthesia. [1]

The imperial / US customary system uses the foot, pound and second. Its pressure unit is the pound per square inch (psi), equal to 6895 pascals or 6.895 kPa or 51.7 mmHg; cylinder pressures in the United States are quoted in psi (a full oxygen cylinder is about 2200 psi or 150 bar). One inch is 25.4 millimetres, one pound (mass) is 0.4536 kilograms, and one fluid ounce is 29.57 millilitres. [1]

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The reason medicine is a mixture is historical. Blood pressure was first measured with a mercury column (Torricelli, then Riva-Rocci), so it is reported in millimetres of mercury; central venous and airway pressures were measured with water columns, so they are in centimetres of water; chemistry standardised on the mole and the litre; respiratory gases drifted between millimetres of mercury and kilopascals depending on the country. The ANZCA convention is to report blood gases in kilopascals and haemodynamics in millimetres of mercury, but the candidate must move fluently between the two. [1]

Significant figures and scientific notation

A measurement is reported with significant figures that reflect its precision. The rules: [1]

1. All non-zero digits are significant (123.4 has four).
2. Leading zeros are not significant (0.0045 has two — the 4 and the 5).
3. Captive zeros (between non-zero digits) are significant (1002 has four).
4. Trailing zeros are significant only if a decimal point is shown (100. has three, 100 has one, 0.0100 has three).
5. In multiplication and division the result carries the number of significant figures of the least precise operand (1.234 times 2.0 equals 2.5, not 2.468).
6. In addition and subtraction the result carries the decimal places of the least precise operand (12.3 plus 0.456 equals 12.8). [1]

Scientific notation expresses a number as a times 10 to the n, where a is between 1 (inclusive) and 10 (exclusive) and n is an integer. It removes the ambiguity of trailing zeros: 1.00 times 10 to the 3 has three significant figures, 1 times 10 to the 3 has one. In anaesthesia it tames the range of magnitudes — the Boltzmann constant is 1.380 649 times 10 to the minus 23 J per K, an arterial pH is about 7.40, an inspired oxygen fraction is 0.21, and a body mass is about 70 kg — all expressible in the same notation. [1]

The clinical rule that follows is simple: do not report a measurement with more precision than the instrument delivers. An oscillometric cuff measures blood pressure to perhaps plus or minus 5 mmHg, so reporting 124 over 78 mmHg to the single millimetre overstates the precision; a cardiac output measured by thermodilution is reproducible to about plus or minus 10 per cent, so a value of 4.97 L per min should be reported as 5.0 L per min. Reporting inflated precision is a form of error because it implies a confidence the measurement does not have. [1]

Pressure units and clinical conversions

Pressure is the quantity the anaesthetist measures most often and in the greatest variety of units. The SI unit is the pascal (Pa), one newton per square metre; the practical units are the kilopascal, the millimetre of mercury (mmHg, also called the torr), the centimetre of water (cmH2O), the bar and the atmosphere (atm). A pressure can also be expressed as pounds per square inch (psi) in North America. [1]

The unit conversions are all derived from the hydrostatic pressure of a column of fluid, P equals rho g h (density times gravity times height). A column of mercury 1 millimetre tall exerts a pressure of the density of mercury (13 595 kg per m cubed) times gravity (9.80665 m per s squared) times 0.001 m, which is 133.322 pascals — so 1 mmHg equals 133.3 Pa equals 0.133 kPa. A column of water 1 centimetre tall exerts 98.07 Pa — so 1 cmH2O equals 98.07 Pa equals 0.098 kPa, and 1 mmHg equals 1.36 cmH2O. [1]

The single conversion to memorise, and the one the examiner wants: [1]

From this master conversion the useful working factors fall out: [1]

• kPa to mmHg: multiply by 7.5 (1 kPa equals 7.5 mmHg). A PaCO2 of 5.3 kPa is about 40 mmHg; a PaO2 of 13 kPa is about 98 mmHg.
• mmHg to kPa: multiply by 0.133 (divide by 7.5). A blood pressure of 120 over 80 mmHg is 16 over 10.7 kPa.
• mmHg to cmH2O: multiply by 1.36. An airway plateau pressure of 20 cmH2O is about 14.7 mmHg; a CVP of 8 mmHg is about 11 cmH2O.
• bar to kPa: multiply by 100. A full oxygen cylinder at 137 bar is 13 700 kPa, about 135 atmospheres. [1]

Two distinctions the viva probes. Absolute pressure is measured against a vacuum; gauge pressure is measured against atmospheric pressure and is what a cylinder gauge or a tyre pressure reads. A cylinder gauge reading 137 bar is at 138 bar absolute (137 plus the roughly 1 bar of atmosphere). Gauge pressure is zero when the pressure inside equals the atmosphere; absolute pressure is zero only in a vacuum. The ventilator and the vapouriser work in gauge pressure relative to the atmosphere, which is why a small leak drops the reading to zero rather than to minus one bar. [1]

The partial pressure of a gas in a mixture is its fraction times the total pressure (Dalton's law), and it is reported in the same pressure units — kPa or mmHg. The inspired partial pressure of oxygen at sea level breathing air is 0.21 times 101.3 equals 21.2 kPa equals 159 mmHg. Partial pressure is what drives diffusion and what the alveolus and the mitochondrion actually "see"; the fraction (per cent) is the convenient scaled version. [1]

Temperature scales

Temperature is measured in three scales. The SI unit is the kelvin (K), an absolute scale whose zero is absolute zero; the degree Celsius (deg C) shares the same increment but is offset so that 0 deg C is the freezing point of water; and the degree Fahrenheit (deg F) is the imperial scale. [1]

• Kelvin to Celsius: deg C equals K minus 273.15. A change of 1 K is identical to a change of 1 deg C; only the zero differs. Normal body temperature 37 deg C is 310.15 K.
• Celsius to Fahrenheit: deg F equals 9/5 times deg C plus 32. Body temperature 37 deg C is 98.6 deg F.
• Absolute zero is 0 K equals minus 273.15 deg C equals minus 459.67 deg F — the temperature at which all thermal motion ceases. [1]

Clinical temperature is always in degrees Celsius (the body, the theatre, the warmed fluid); thermodynamic calculations in the gas laws use kelvin. The common error is to plug a Celsius temperature into the universal gas equation — it must be kelvin, because the equation PV equals nRT is derived from absolute temperature. A 20 deg C error (using 310 instead of 310 K is fine, but using 37 instead of 310 K) gives a 16 per cent error in any calculated volume. [1]

Concentration units

Concentration — the amount or mass of a substance in a given volume or mass of solvent — appears in several forms in anaesthesia, and the candidate must choose the right one for each context. [1]

• Amount per volume (molarity), mol per L or mmol per L: the SI-compatible measure, used for electrolytes (sodium 140 mmol per L, potassium 4.5 mmol per L) and for blood gases (bicarbonate, base excess). One mole per litre is 1000 mmol per L.
• Mass per volume, mg per L, g per dL, mg per mL: used for haemoglobin (g per dL or g per L), albumin, drug plasma levels. Haemoglobin of 15 g per dL is 150 g per L.
• Partial pressure, kPa or mmHg: for arterial and alveolar gases (PaO2, PaCO2). A partial pressure is not a concentration but it determines the dissolved concentration through Henry's law (content equals solubility times partial pressure).
• Fraction or per cent (parts per hundred): for the inspired oxygen fraction (FiO2 0.21 or 21 per cent) and the volatile-agent concentration (sevoflurane 2 per cent). Per cent in a gas mixture is a volume per volume measure.
• Parts per million (ppm) and parts per billion (ppb): for trace gases — carbon monoxide in the circle system, atmospheric nitrous oxide pollution, theatre volatile pollution. One ppm is one part in 10 to the 6, equivalent to 0.0001 per cent.
• Molality, mol per kg: moles per kilogram of solvent (not per litre of solution), used in physical chemistry; equals molarity only for dilute aqueous solutions.
• Mass per mass or international units per mL: heparin is dosed in units, insulin in units per mL, vitamin preparations in international units. [1]

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Gas-volume conventions: STP, ATPS, BTPS and STPD

Because a gas volume depends on the temperature and pressure at which it is measured, respiratory volumes are reported under standardised conditions, and the candidate must know which convention each measurement uses. [1]

• STP (standard temperature and pressure): 0 deg C (273.15 K) and 101.325 kPa (1 atm), dry. The molar volume of an ideal gas at STP is 22.414 L per mol (and 22.71 L per mol at SATP, standard ambient temperature and pressure, 25 deg C and 100 kPa).
• ATPS (ambient temperature and pressure, saturated): the conditions at which a spirometer actually measures — room temperature, ambient pressure, fully saturated with water vapour.
• BTPS (body temperature and pressure, saturated): 37 deg C, ambient pressure, saturated. Lung volumes measured by spirometry (tidal volume, vital capacity) are conventionally reported in BTPS, because the gas is in the body when it is breathed.
• STPD (standard temperature and pressure, dry): 0 deg C, 101.325 kPa, dry. Metabolic gas exchange — oxygen consumption (VO2 about 250 mL per min) and carbon dioxide production (VCO2 about 200 mL per min) — is reported in STPD, so that volumes from different altitudes and pressures are comparable. [1]

The conversion between conditions uses the combined gas law (P1 V1 over T1 equals P2 V2 over T2), corrected for the water-vapour pressure at the source temperature (47 mmHg at 37 deg C, about 18 mmHg at 20 deg C). A spirometer volume measured ATPS at 20 deg C is converted to BTPS by a factor of about 1.1 — a measured 400 mL tidal volume becomes about 440 mL in the body. [1]

Flow and volume conversions

Flow is volume per unit time. The SI unit is the cubic metre per second, but clinical practice uses the litre per minute for gas flows and cardiac output, the millilitre per minute for small flows, and the millilitre per second or litre per second for instantaneous airway flows. [1]

• L per min to mL per min: multiply by 1000. A cardiac output of 5 L per min is 5000 mL per min.
• mL per min to mL per s: divide by 60. A coronary blood flow of 250 mL per min is about 4.2 mL per s.
• L per min to mL per s: multiply by 1000 and divide by 60, i.e. divide by 60 and multiply by 1000, giving a factor of 16.67. A cardiac output of 5 L per min is about 83 mL per s.
• Flow to velocity: divide the volumetric flow by the cross-sectional area. A tracheal flow of 500 mL per s through a trachea of cross-section 3 cm squared is a velocity of about 1.7 m per s — the basis for calculating whether flow is laminar or turbulent (Reynolds number). [1]

Peak inspiratory flow is read in L per min on the ventilator (typically 20 to 60 L per min); the vapouriser flow meters and the rotameters are calibrated in L per min; the cardiac output monitor reports L per min. The unit L per min is so ubiquitous that the candidate must be able to convert it instantly to mL per min, mL per s and mL per kg per min (the cardiac index is per square metre, but oxygen delivery per kg uses mL per kg per min). [1]

Dose units and the mcg per kg per min to mg per kg per h conversion

Drug doses are expressed in several forms depending on the drug and the route, and the conversions between them are examined. [1]

• mg per kg — a single bolus dose (propofol 2 to 3 mg per kg, suxamethonium 1 mg per kg, fentanyl 1 to 2 mcg per kg).
• mg per kg per h or mcg per kg per min — an infusion rate (noradrenaline 0.05 to 0.5 mcg per kg per min, propofol 4 to 12 mg per kg per h for sedation, ketamine 0.1 to 0.3 mg per kg per min for analgesia).
• mg per min or units per h — a fixed infusion rate (insulin, oxytocin) not scaled to weight.
• mg per mL or mcg per mL — the concentration of the solution, set by how the drug is diluted. [1]

The single conversion the fellowship demands is mcg per kg per min to mg per kg per h. There are 60 minutes in an hour and 1000 micrograms in a milligram, so 1 mcg per kg per min equals 60 mcg per kg per h equals 0.060 mg per kg per h. To convert a rate from mcg per kg per min to mg per kg per h, multiply by 0.06; to convert back, multiply by 16.7 (which is 60 divided by 3.6, or one over 0.06). Worked example: noradrenaline at 0.1 mcg per kg per min in a 70 kg patient is 0.006 mg per kg per h, which is 0.42 mg per h. [1]

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The full infusion-rate calculation takes the dose, the weight and the concentration and returns the pump speed in mL per h: rate (mL per h) equals dose (mcg per kg per min) times weight (kg) times 60 divided by concentration (mcg per mL). Worked example: noradrenaline 4 mg made up to 50 mL is 80 mcg per mL; at 0.1 mcg per kg per min in a 70 kg patient the rate is 0.1 times 70 times 60 divided by 80, which is 420 divided by 80, which is 5.25 mL per h. Every step is a unit conversion, and dimensional analysis confirms the answer is a volume per time. [1]

Anaesthesia-specific units

Several quantities in anaesthesia have units peculiar to the speciality, and the candidate must know what each one means and why it is reported that way. [1]

MAC is the minimum alveolar concentration of a volatile, in per cent of one atmosphere, that prevents movement in 50 per cent of subjects to a standard surgical stimulus. It is a per cent (a fraction times 100), and at one atmosphere the partial pressure in kPa is approximately the per cent value (sevoflurane MAC 2.0 per cent is about 2.0 kPa partial pressure). The crucial point for the viva: MAC is a CONCENTRATION (per cent) and its anaesthetic effect actually tracks the partial pressure, not the per cent — so at altitude (low atmospheric pressure) a given per cent delivers a lower partial pressure and a weaker effect, and the age-corrected MAC must be interpreted in terms of partial pressure [1].

The blood-to-gas partition coefficient (lambda B:G) is the ratio of the concentration of agent dissolved in blood to the concentration in alveolar gas at equilibrium. It is dimensionless (a ratio of two concentrations). A low coefficient (sevoflurane 0.65, desflurane 0.45, nitrous oxide 0.47) means the agent stays in the gas phase, equilibrates fast and has a rapid onset and offset; a high coefficient (halothane 2.4, diethyl ether 12) means it dissolves in blood, slows equilibration and has a slow onset and offset. The oil-to-gas coefficient (also dimensionless) determines potency: a high oil-to-gas means high solubility in the lipid brain and a low MAC (the Meyer-Overton correlation). [1]

Partial pressure of a volatile or a gas is reported in kPa or mmHg and is the fraction times the total pressure. It is what the brain and the alveolus actually respond to. The end-tidal agent concentration on the monitor is a per cent, but the effect is set by its partial pressure. [1]

Specific gravity is the dimensionless ratio of the density of a substance to the density of water (so water is 1.000, local anaesthetic solutions are about 1.0, cerebrospinal fluid is 1.005, blood is about 1.050). It is used to predict baricity — whether a hyperbaric spinal solution (1.080) sinks in the CSF and a hypobaric solution floats. [1]

The Reynolds number (density times velocity times diameter divided by viscosity) is dimensionless and marks the transition from laminar to turbulent flow at a value of about 2000. Because it is dimensionless it is the same in any unit system — a fact that links this topic to the fluid-flow topic. [1]

The mcg versus mg error: a thousand-fold dosing catastrophe

The single most important unit-clinical lesson in anaesthesia is that the prefix error is a thousand-fold error, and it kills patients. Adrenaline labelled "1:1000" is 1 mg per mL (subcutaneous or intramuscular dosing); "1:10 000" is 100 mcg per mL (intravenous cardiac-arrest dosing). Confusing the two — drawing up the 1:1000 concentration for an intravenous bolus — delivers ten times the intended intravenous dose. More dangerous still is the routine confusion of microgram with milligram in infusion programming: an order for "noradrenaline 0.1 mcg per kg per min" programmed into a pump as "0.1 mg per kg per min" delivers a thousand-fold overdose and an immediate hypertensive crisis, stroke or arrest [4][5][6].

The paediatric and perioperative literature documents this repeatedly. Medication errors in paediatric anaesthesia occur at rates of one in every few hundred anaesthetics, and dose errors (wrong dose, wrong concentration, wrong-rate pump programming) are the commonest category, with weight-based calculations and decimal-point and prefix slips the leading mechanism [5][6]. The dose is the most frequent error point in the whole medication chain.

The defences are layered [4][6][7]:

• Write the unit in full. Use "micrograms" (not "mcg" and never the ambiguous Greek mu) and "milligrams" on critical doses; international guidance drops the abbreviation where confusion is possible.
• Always use a leading zero and never a trailing zero. Write 0.1 mg (not .1 mg, which can be misread as 1 mg) and never 1.0 mg (which can be misread as 10 mg).
• Standardise concentrations. A standard noradrenaline concentration (for example 4 mg in 50 mL, that is 80 mcg per mL) across the whole institution removes the per-patient dilution calculation, the commonest source of error.
• Smart-pump drug libraries. The pump holds the concentration and the dose units and warns when a rate exceeds a soft or hard limit; programming in mg per kg per min when the library expects mcg per kg per min is blocked.
• Independent double-check. A second person independently recalculates the dose and the rate for every high-alert infusion; the "independent" is the operative word, because a dependent check inherits the first error.
• Tall Man lettering. Look-alike drug names (NORadrenaline versus NORmabarbital, hydrALAzine versus hydrOXYzine, DOPamine versus DOBUTamine) are capitalised on the middle syllable to distinguish them; the evidence for its effect is real but incomplete [7].
• Forced-function limits. The pump cannot exceed a maximum rate; the syringe cannot exceed a maximum concentration.

Accuracy, precision, calibration and error

Every measurement carries error, and the candidate must classify and quantify it. [1]

• Random error (imprecision) is the scatter of repeat measurements around their mean, from noise in the instrument and the process. It is reduced by averaging repeat readings; it is quantified by the standard deviation or the coefficient of variation.
• Systematic error (bias) is a consistent offset of the measurement from the true value, from a mis-calibration, a zero offset, or a flawed assumption. It is removed by calibration against a standard; it cannot be reduced by averaging.
• Accuracy is the closeness of a measurement to the true value (it suffers from both random and systematic error).
• Precision is the reproducibility (scatter) of repeat measurements (it suffers only from random error). [1]

The two are independent. A precise but biased instrument gives a tightly clustered but wrong answer (the classic example is a bathroom scale that reads 2 kg high every time — highly precise, badly inaccurate). An accurate-on-average but imprecise instrument scatters widely around the true value. Calibration fixes bias; averaging fixes random scatter; only both together give an accurate and precise measurement. [1]

The measurement chain that every anaesthetic monitor embodies is transducer, signal conditioning, analogue-to-digital conversion, display, and each link contributes error. The transducer converts the physical quantity (pressure, light, temperature) to an electrical signal; the conditioning amplifies and filters it; the analogue-to-digital converter samples it at a finite resolution; the display shows it with a finite number of digits. The total error is the combination of the errors at each link, and the reportable resolution (the number of significant figures) is set by the largest single error source. [1]

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Blood-pressure measurement illustrates the whole framework. The mercury sphygmomanometer, read by a trained observer, is the reference standard (it is a direct hydrostatic column — its accuracy is set by gravity and the density of mercury). The oscillometric cuff estimates the mean arterial pressure from the point of maximum oscillation and derives systolic and diastolic by an algorithm; it is convenient but less accurate at extremes of pressure, in atrial fibrillation, and with movement [1][2]. The intra-arterial line measures pressure directly through a fluid-filled catheter and transducer, and its accuracy depends on correct zeroing (to the mid-axillary line), correct levelling, a correctly damped system (no under- or over-damping) and a patent catheter [1]. Each method has its own accuracy, precision, calibration requirements and characteristic errors.

A worked anaesthetic by the numbers

To anchor the whole topic, trace a single patient through induction and notice the units at every step. [1]

A 70 kg, 37 deg C, 180 cm man. His body mass index is mass (kg) divided by height (m) squared, which is 70 divided by 1.8 squared, which is 21.6 kg per m squared (a mass per area). Pre-oxygenation lifts his alveolar oxygen from 13 kPa to about 90 kPa (a partial pressure); the safe apnoea time extends from about 2 min to about 8 min. Induction is propofol 2 mg per kg, which is 140 mg (a mass), drawn from a 10 mg per mL solution, so 14 mL (a volume). Suxamethonium 1 mg per kg is 100 mg, and the intubating dose reaches the neuromuscular junction in 60 s (a time). [1]

Maintenance is sevoflurane at an age-adjusted MAC of about 1.7 per cent (a volume per volume fraction), delivering an alveolar partial pressure of about 1.7 kPa. The oxygen flow is 2 L per min (a flow) and the fresh-gas flow is set so the agent monitor reads the target end-tidal concentration. His cardiac output is 5 L per min (a flow) at a heart rate of 1.2 Hz (72 beats per min); his blood pressure is 120 over 80 mmHg (a pressure, 16 over 10.7 kPa). The airway plateau pressure is 18 cmH2O (a pressure, about 13 mmHg). A noradrenaline infusion at 0.1 mcg per kg per min — that is 0.006 mg per kg per h, that is 0.42 mg per h, that is 7 mcg per min — runs at 5.25 mL per h from an 80 mcg per mL solution. [1]

Every number is paired with a unit, every unit is a power of a base unit, and every conversion (mg per kg per h to mcg per kg per min, kPa to mmHg, L per min to mL per s) is an exercise in dimensional analysis. The anaesthetist who can do this fluently and safely — and who knows where the thousand-fold error lies in wait — is practising the physics of measurement at the bedside. [1]

Measurement in anaesthesia — the unit reference table

Red flags

References

1. [1]Pickering TG, Hall JE, Appel LJ, Falkner BE, Graves J, Hill MN, Jones DW, Kurtz T, Sheps SG, Roccella EJ Recommendations for blood pressure measurement in humans and experimental animals: part 1: blood pressure measurement in humans: a statement for professionals from the Subcommittee of Professional and Public Education of the American Heart Association Council on High Blood Pressure Research Circulation, 2005.PMID 15699287
2. [2]Alpert BS, Quinn D Oscillometric blood pressure: a review for clinicians J Am Soc Hypertens, 2014.PMID 25492837
3. [3]Saito N [Redefinition of the International System of Units (SI) and Related Quantities in the Field of Ionizing Radiation] Igaku Butsuri, 2021.PMID 33853980
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