PHYSICS

© 2005 The Medicine Publishing Company Ltd405ANAESTHESIA AND INTENSIVE CARE MEDICINE 6:12

Most clinical measurements require a measuring device and a human operator, either of which can give rise to errors. The device may be wrongly calibrated or malfunctioning; the operator may select an inappropriate device or take the reading incorrectly. Set-up or calibration errors are common to many devices, whereas other errors depend on the type of measurement being made.

Generic sources of error Calibration error – to calibrate a device, the measured value is compared with a known standard. Any discrepancy between the measured and actual values may require adjustment of the device to bring the two into agreement. A calibration error occurs when an incorrect standard is used. For example, a fuel cell oxygen sensor generates a voltage proportional to the partial pressure of oxygen present. This voltage is electronically converted to give a percentage concentration of oxygen. As the voltage also depends on the age of the cell, the ambient temperature and pressure, it is customary to calibrate the sensor every 24 hours. The sensor is removed from the breathing system and exposed to room air. The analyser then fine-tunes the voltage conversion so that 21% is displayed. If the sensor is exposed to a higher concentration of oxygen during calibration, for example if it is left connected to the breathing system, it will subsequently under-read. To prevent such calibration errors, most analysers display an error message if the output voltage of the cell falls outside preset limits. This example illustrates one-point calibration where the sensor is calibrated at a single reference point of 21% oxygen. A one-point calibration assumes a straight-line relationship between the measured quantity (oxygen partial pressure) and sensor response (voltage). It also relies on the line having the same gradient regard-less of external factors such as temperature changes (Figure 1). For greater accuracy, a two-point calibration can be performed, when the sensor is calibrated using 21% and 100% oxygen. Using a second point verifies the first calibration and allows the analyser to compensate for gradient changes in the calibration plot. A two-

point calibration is sometimes called a span because it increases the accuracy of measurements in the range spanned by the two reference points. Offset error – an offset or zero error occurs when a device is zeroed against an incorrect value. For example, an arterial line transducer is usually zeroed by opening the three-way tap to air because it is designed to indicate the difference between the measured and atmospheric pressures. If the transducer is zeroed as illustrated in Figure 2, it will be calibrated against the hydrostatic pressure of fluid in the tubing. The transducer will read zero when the actual pressure difference is (for example) 30 mm of mercury, therefore it will under-read when used for patient monitoring. Drift can be defined as a gradual change in the reading from a measurement device even though the measured value has not changed. It can be caused by temperature fluctuations, chemical changes within the analyser (such as depletion of reactants) or contamination of the sensor. Precision and accuracy – precision defines the spread between repeated measurements of the same quantity. Accuracy defines how well the mean of repeated measurements corresponds to that quantity. Imagine archers shooting at a target (Figure 3). Archer A’s arrows land nowhere near the target and are spread widely. His attempts are inaccurate and imprecise. Archer B’s arrows are much closer to the target (accurate), but not close to each other (imprecise). Archer C’s arrows miss the target (inaccurate) but land close to each other (precise). Archer D fares best because his arrows all hit the target (accurate and precise). In the context of blood pressure measurement, A could represent estimating pressure by palpation while B could represent non-invasive measurement. C and D could both represent invasive measurement; the difference being that C has not been correctly calibrated.

Device-specific errorsNon-invasive blood pressure: the most common source of error is using an incorrectly sized pneumatic cuff. The maximal occlusion

Ian Dyer is Consultant Anaesthetist at Princess of Wales Hospital,

Bridgend, UK. He qualified from the University of Newcastle upon Tyne

and trained in anaesthesia in Newcastle, Leicester and South Wales.

His interests are regional anaesthesia, orthopaedic anaesthesia and

teaching. David J Williams is Consultant Anaesthetist at Morriston Hospital,

Swansea, UK. He graduated from Birmingham University Medical School,

and trained in anaesthesia in South Wales. His interests include diving

medicine and anaesthesia for developing countries.

Common errors in clinical measurementIan Dyer

David J Williams

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Oxygen sensor calibration plots

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The green line represents a correctly calibrated oxygen sensor, giving appropriate readings at 21% and 100% oxygen. If the gradient of the calibration plot is constant then a one-point calibration is adequate to correct any offset error (red line). If the gradient may change then a two-point calibration is required (blue line).

Actual percentage oxygen

PHYSICS

© 2005 The Medicine Publishing Company Ltd406ANAESTHESIA AND INTENSIVE CARE MEDICINE 6:12

Invasive pressure measurement: errors can arise if the pressure transducer is incorrectly zeroed, as discussed above. A common misconception is that the transducer needs to be level with the patient when zeroing. Atmospheric pressure does not change significantly between floor and ceiling, so the transducer can be zeroed in any position. When making measurements, the trans-ducer should be level with the patient’s heart, otherwise hydro-static pressure in the connecting tubing affects the reading. Damping of the pressure waveform due to poor positioning of the cannula, or the use of overly compliant tubing, underestimates systolic pressure and overestimates diastolic pressure. The mean pressure is still reasonably accurate. Some invasive monitoring systems can drift if the electrical connections are short-circuited. This can happen if saline from the connecting tubing leaks onto the connections when the system is set up.

Pulse oximeters estimate oxyhaemoglobin concentrations by measuring the absorption of light. Wavelengths of 660 and 940 nm are used. The absorption ratio is compared with an inbuilt table of known values, to give the percentage of oxyhaemoglobin present. Other substances that absorb light at these wavelengths can lead to errors. Carboxyhaemoglobin has an absorption spectrum similar to oxyhaemoglobin at 660 nm. High levels of carboxyhaemoglobin, for example in patients suffering from smoke inhalation, cause the pulse oximeter to over-read. Methaemoglobin absorbs equally at 660 and 940 nm and as the concentration increases, the absorption ratio tends towards unity, corresponding to a saturation reading of 85%. Dyes, such as methylene blue and indocyanine green, cause a fall in measured oxygen saturations. Blue nail varnish causes a slight fall in the reading; other colours seem to have no significant effect. The oximeter reading is unaffected by bilirubin or skin pigmentation. Poor peripheral perfusion, due to cold or compression of the limb, may cause local hypoxia and underestimate the true satu-ration. Hypoperfusion also reduces the signal (pulsatile absorb-ance) to noise (tissue absorbance) ratio making the reading more susceptible to artefacts. Movement at the probe site can alter the distance between the light emitter and detector and cause errors. Radiofrequency interference from diathermy equipment can also affect the reading.

Fuel-cell oxygen analysers may exhibit drift if the ambient temperature changes, because the voltage produced by the

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pressure under the cuff is proportional to the inflation pressure and cuff width. A cuff that is too narrow generates lower tissue pres-sures than indicated and thus overestimates blood pressure. Con-versely, a very wide cuff slightly underestimates blood pressure. A correctly fitted cuff should cover two-thirds of the upper arm or should be roughly 20% wider than the diameter of the limb. Pressure exerted on the cuff from an external source, for example a surgeon leaning on it during surgery, causes blood pressure to be overestimated. Movement of the limb due to shivering or while positioning the patient can cause pressure fluctuations in the cuff and incorrect readings. Cardiac arrhythmias and leaks in the cuff or connecting tubing can also lead to errors.

Transducer offset error

If the transducer is zeroed when the three-way tap is open to A and closed to B, the pressure at the transducer is atmospheric plus P1, resulting in an offset error when zeroing.(P1 represents the hydrostatic pressure in the manometer tubing)

Saline bag

Manometer tubing

Three-way tap

Transducer

P1

A

B

Precision and accuracy

See text for explanation

AInaccurate and imprecise

BAccurate but imprecise

CInaccurate but precise

DAccurate and precise

PHYSICS

© 2005 The Medicine Publishing Company Ltd407ANAESTHESIA AND INTENSIVE CARE MEDICINE 6:12

electrochemical reaction increases with temperature. Some fuel-cell analysers contain a thermistor to provide temperature compen-sation. Drift can also occur as the cell ages, because the output voltage falls as the reactants are consumed. Fuel cells measure the partial pressure of oxygen, therefore any back-pressure applied to the analyser overestimates the oxygen percentage.

Infrared gas analysers sample gases from the anaesthetic breath-ing system via a narrow-bore sampling tube. They can be used to measure the volatile anaesthetics, carbon dioxide and nitrous oxide. Errors due to entrainment of room air can occur if there are leaks in any of the connections, causing the analyser to under-read. A partial obstruction in the sampling line may also cause the analyser to under-read. If the sampling chamber inflow is partially blocked, the pressure in the chamber may fall. This reduces the density of gas in the chamber causing an artificially low reading. Water vapour causes carbon dioxide measurements to be slightly overestimated; with sidestream analysers this effect is minimal because most water vapour condenses in the sample tubing and water trap. Some older gas analysers use only a single wavelength of light and cannot automatically differentiate volatile anaesthetic agents. If the wrong agent is selected, the displayed concentration can be out by a factor of 2–6. Ethanol or acetone, sometimes found in expired air, absorb infrared light and may significantly increase halothane readings. Mixtures of volatiles, such as sevoflurane and isoflurane in a circle system, may be incorrectly detected as another agent, such as halothane.

Electrocardiogram: the ECG provides useful information regarding the patient’s heart rate, rhythm and ST-segment analysis. However, the displayed heart rate figure is not always accurate. To measure heart rate, most systems count the QRS complexes, because their size makes them the easiest feature to recognize. However, T waves of abnormally high amplitude, as in hyperkalaemia, can be mistaken for QRS complexes, leading to ‘double counting’, particularly if the QRS complex is of low amplitude. Pacemaker spikes can also cause this problem. Poor electrode positioning, baseline drift due to poor electrode contact and electrical interference from diathermy or 50 Hz mains hum can render the ECG signal unreadable by the monitor. This leads to the display of erroneous alarms, such as ‘asystole’, when in fact a recognizable ECG trace is being displayed.

Blood gas analysis: blood gas electrodes are susceptible to drift and most machines self-calibrate every hour or so, using cylinders of reference gases. Poor sampling or processing techniques are the most common sources of error. Samples taken from arterial lines may contain high levels of heparin unless a sufficient volume of blood is first withdrawn and discarded. Heparin is an acidic molecule and samples containing high levels have an artificially low pH. Sometimes the sample contains air bubbles, which may be inadvertently injected into the analyser. If the gas electrodes are in contact with air rather than the fluid sample, the analysis will be incorrect. To allow detection of this error, most analysers have a window for inspection of the sample as it passes through the machine.