Principles of Measurement in Anaesthesia
Study notes for the ANZCA Primary Examination by James Mitchell
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Integrating with respect to time gives the exponential function:
This situation is analogous to the elimination of a drug which demonstrates first-order kinetics, such as the washout curve of an inhaled anaesthetic. It is also analogous to the natural expiration from the lungs where -k equals the rate constant of expiration, the reciprocal of the time constant (compliance times resistance).
Integration is the derivation of a function which expresses the area under a function y = f (x) from x = 0 to any value of x.
Differentiation is the reverse process: deriving a function which expresses the rate of change of f (x).
2. Explain electrical concepts such as current, potential difference, resistance, impedance and capacitance as they relate to biomedical apparatus.
Current is the flow of charged particles resulting from a potential difference or changing magnetic field. Most commonly this is a flow of electrons through a metal or other conductor (such as graphite) which has freely mobile electrons. A current can also flow through solutions containing charged particles. All body fluids contain ions and so are capable of conducting current. The unit of current is the Ampere (1 Coulomb/second). Many quantities in monitoring devices are measured indirectly as electrical current. Nerve stimulators are calibrated to deliver a determined current through the tissue between the electrodes.
Solids which do not contain many unbound electrons and solutions with few ions are poor conductors and are known as insulators.
Seimconductors contain electrons which are loosely bound and may conduct a current if electrons are given enough energy to become unbound. This effect is seen in thermistors and photodetectors used in monitoring equipment. It is also the basis for transistors and silicon-based integrated circuits which are universally present in electronic equipment.
Potential difference is the difference in electrical energy between two points. Its unit is the Volt (1 Joule/Coulomb) and it generates a electromotive force which drives a current of charged particles.
Resistance is a measure of the electromotive force required to drive a current through a material. Its unit is the Ohm (1 Volt/Ampere). Thermistors display a change in resistance over a range of temperature and so with calibration the current flow for a specified voltage can be measured and used to determine temperature. Similarly some materials display an increase in resistance as they are stretched, allowing for tension or pressure to be measured indirectly.
When a small change in resistance is to be measured, a Wheatstone Bridge circuit is commonly employed.
Impedance is the resistance of a component or circuit with a specified characteristic current flowing. Resistance of many components (capacitors and inductors) varies with frequency of alternating current. In a surgical diathermy device, a capacitor is part of the circuit, providing low impedance at the high frequency typically used (1 MHz), but high impedance to low frequency currents likely to cause arrhythmias (50 Hz).
Capacitance is a measure of the charge a device can hold. Its unit is the Farad (1 Coulomb/Volt). Defibrillators are based on a capacitor which is charged with a calibrated voltage to provide a determined energy output for DC reversion. The energy stored in a capacitor is 0.5 x charge x potential. A typical output of 360 J is usually produced by about 5000 V across about 150 mC. An inductor is used to slow the discharge of the defibrillator.
3. Explain the SI system of units.
Seven basic SI units from which all other units are derived
Mass kg Time s Distance m Current A Temperature K Luminous intensity cd Amount of substance mol
Derived SI units (some of them)
Temperature °C K - 273.15 Force N kg m s-2 Pressure Pa N m-2 Energy J N m Power W J s-1 Frequency Hz s-1 Volume l 10-3 m3 Charge C A s Potential V W A-1 or J C-1 Capacitance F C V-1 Resistance W V A-1 Magnetic flux Wb V s Radiation dose Gy J kg-1 water Radiation exposure Sievert Gy·tissue factor ·radiation type factor
Prefixes (multipliers)
atto a 10-18 femto f 10-15 pico p 10-12 nano n 10-9 micro µ 10-6 milli m 10-3 kilo k 103 mega M 106 giga G 109 tera T 1012 peta P 1015 exa E 1018
Some non-SI units with conversions
4. Describe the laws governing the behaviour of fluids.
Pressure mmHg 132 Pa cmH2O 98 Pa atm 101.325 kPa psi 6.89 kPa Energy calorie 4.18 J Resistance dyne s cm-5 80 mmHg l-1 min Catheter size French external circumference in mm Gauge 20 (1 - log external diameter in mm) Glucose mg/dl mmol/l x 18
Flow is characterized as laminar or turbulent. In laminar flow, fluid moves without eddies and flow is equal to pressure (P) over resistance (R):
In a cylindrical tube, resistance to flow is related to radius (r) and length (l) of the tube and viscosity (η) of the fluid, yielding the Hagen-Poiseuille equation:
Above a critical speed, laminar flow changes to turbulent flow. For a smooth cylindrical tube, the transition occurs when Reynolds number is approximately 2000. For rough or bent tubes, the transition occurs at lower numbers. Reynolds number (RN) is defined in terms of speed (n), density (ρ) and viscosity (η) of the fluid and diameter (d) of the tube:
For turbulent flow, the relationship determining flow is described empirically:
The relationship with tube diameter is complex and roughly related to slightly greater than diameter to the power four.
The behaviour of gases is described by the gas laws. Because gases are composed of small molecules or atoms widely spaced, their physical properties are very similar regardless of the identity of the molecules or atoms.
Boyle's Law states that for a constant quantity of gas at a constant temperature, the absolute pressure is inversely proportional to the volume. Charles's Law states that for a constant quantity of gas at a constant pressure, the absolute temperature of the gas is proportional to its volume. Avogadro's Hypothesis states that equal volumes of gas at the same temperature and pressure contain the same number of molecules. One mole of gas occupies 22.4 dm3 at s.t.p. (273.15 K, 101.325 kPa). These laws combine to give the relation:
Where R is the universal gas constant.
Real gases all have a temperature at which they condense into liquids (boiling point at standard pressure). Over a range of pressures, the temperature at which a gas will condense varies below the critical temperature (the temperature at which the gas will condense at critical pressure and above which it will not condense). At a temperature well below critical temperature, a gas will start to condense with decreasing volume, maintaining a constant pressure over a range of volume until it is entirely condensed.
With gas mixtures, separation of the constituents by condensation of one into the liquid phase may occur below the "pseudo-critical" temperature over a range of pressures.
5. Describe the principles of measurement employed by apparatus in clinical use, including transducers and describe their calibration.
For the measurement of continuous flows, an alternating bellows device is used in gas and water supplies, with the direction of flow into the bellows alternating as it is filled. In anaesthesia, the Wright respirometer connects in series with the circuit and records tidal volume with each breath. A set of slits generates a circular flow inside the meter which spins a vane connected directly to a rotating dial via a gearing system. It is not accurate for continuous flow.
Most commonly in anaesthesia, tidal volume and flow is measured using an electronic flow meter. Sets of blades cause the flow of gas to spin a mounted vane which interrupts a light beam shone through the housing of the device. Electronic processing of the frequency and duration of the interruption of the light beam allows calculation of flow (Ohmeda). Alternatively the cooling of a fine heated wire across the gas flow can be used to calculate flow (Dräger). These devices all measure gas flows at ambient temperature and pressure.
Measurement of continuous flow also occurs in the flowmeters of the anaesthetic machine. These consist of a calibrated glass tube of variable internal diameter in which a grooved bobbin is suspended by the flow of gas. The flow through a flowmeter tube is complex and dependent on the characteristics of the particular gas being measured, so they are calibrated empirically for a specific gas or mixture at a specific temperature and pressure. The pressure drop across the bobbin is constant and determined by the weight of the bobbin. The size of the orifice around the bobbin increases as it moves up the glass tube, allowing more gas flow for the fixed pressure drop. This is a "fixed pressure, variable orifice" flowmeter.
Highly variable flows may be measured with specific devices such as the peak flow meter. In this a ratcheted marker is moved against a variable resistance as the patient breathes out forcefully. The maximum displacement of the marker is calibrated to show the peak flow rate. This measurement is highly effort-dependent.
For constant measurement of respiratory flows, a pneumotachograph may be used. In this device a heated gauze screen maintains a region of laminar flow which provides a fixed resistance which results in a pressure drop across the gauze proportional to flow. By electronically integrating this pressure drop against time, the device can calculate the flow continuously.
Measurement of flow in liquids is simpler than gases because the variations in volume with temperature and pressure are much less. In IV giving sets, flow may be measured using a calibrated drop chamber in which the drop rate is counted either manually or electronically. The accuracy of this method depends on the composition of the fluid.
More common in slow infusions is the use of volumetric pumps. These incorporate an electric pump in the infusion line which is calibrated to deliver a controlled volume and operated at a rate programmed into the pump.
For small volumes, a mechanical syringe-driver operated by a stepper motor is used. Combined with calibrated syringes, this can deliver very accurate flows of small volumes over extended periods, such as in subcutaneous infusion of narcotics by portable battery-driven devices.
Measurement of liquid flow in the body is generally by indirect methods with the exception of dialysis and bypass devices where mechanical or electromagnetic methods can be used. Dilution of a marker such as fluorescent dye, radioactive tracer or thermal dilution with cold crystalloid produces a washout curve when introduced into a fluid flow. The curve can be integrated to calculate flow rate. This technique is used to measure cardiac output.
Flow can also be deduced from concentration changes in a marker across an organ if the rate of excretion or absorption of the marker can be separately measured. This is the Fick principle and is used in the calculation of cardiac output from the rate of oxygen uptake from the lungs and the change from mixed venous to arterial oxygen concentration. It is also used in the calculation of GFR from creatinine output.
An approximation of flow can be determined from ultrasound Doppler studies of fluid velocity and vessel area. This is used to estimate flows across heart valves.
7. Describe and compare the methods of measuring temperature.
Most gases are diamagnetic, being repelled by a magnetic field, because of the characteristics of their outer shell electrons. Oxygen is paramagnetic because of its unpaired outer shell electrons and so is attracted by a magnetic field. This effect is used to produce a paramagnetic analyzer to determine oxygen concentration.
In a paramagnetic analyzer, a dried gas sample flows through a chamber in which a nitrogen-filled dumbbell is balanced in a magnetic field. The dumbbell is displaced by the paramagnetic force on the oxygen in the sample and either its displacement against a torsion spring or else the force required to keep it in position is measured.
By calibrating the device with 100% nitrogen and 100% oxygen, a very accurate measurement of the oxygen concentration in a gas sample may be made.
A more modern design of paramagnetic analyzer uses an alternating magnetic field at the junction of two gas streams (sample and reference). A pressure wave is induced by the change in magnetic field and a pressure transducer between the gas streams can detect differential pressure and allows calculation of the oxygen concentration of the sample rapidly and continuously.Gas chromatography
Chromatography relies on the separation of compounds by their different affinities for a stationary and mobile phase in a chromatography column. In the case of gas chromatography, the mobile phase is usually an unreactive gas such as nitrogen or argon and the stationary phase is a fine crystalline material such as silica coated in polyethylene glycol or silicone oil. The column is kept at a constant temperature and the sample to be analyzed is injected into the gas flow before the column.
At the end of the column a detector records the appearance of the components of the sample against the time since injection. The detector may be a flame ionization detector, a thermal conductivity detector (suitable for inorganic gases) or an electron capture detector (best for halogenated compounds).
Control samples are used to determine the chromatographic characteristics of known gases. These are compared with the unknown sample's trace to determine its constituents. The detector can also be calibrated for quantitative analysis of the sample. Gas chromatography is suitable for analysis of all gases and many compounds which can be made to yield volatile products.Mass spectrometry
Mass spectrometry separates molecules or atoms according to their mass and charge after stripping their outer electrons. A sample is allowed to leak very slowly into an ionization chamber in which an electron beam is used to ionize the sample. The ions are accelerated and focussed through an electric field and then deflected either using a strong magnetic field or an oscillating electric field between four rods ("quadrupole mass spectrometer").
The ions are separated according to their mass and charge and so the components of the sample can be determined quantitatively by analyzing the composition of the ionized sample which will include breakdown products of the components of the sample. This analysis is simple for small molecules and difficult for mixtures of several larger molecules because of the wide variety of breakdown products.
Mass spectrometry can measure very small concentrations in very small samples and can be made to have a response time as little as 0.1 s, but it remains a complex and expensive analysis tool.Raman scattering
The Raman effect occurs when gas molecules absorb energy from photons resulting in quantized changes in vibrational or rotational states. Light is re-emitted with further changes in state producing a spectrum of wavelengths characteristic of the molecules involved. Spectral analysis allows identification of known compounds by comparison with their Raman spectra. This is a technique of similar accuracy to mass spectrometry.Oxygen electrodes
The Clarke oxygen electrode is a polarographic electrode. Oxygen from the sample fluid equilibrates across a membrane with a buffered KCl solution surrounding a glass electrode. The electrode has a platinum cathode and a Ag/AgCl anode. With between 0.5 V and 0.9 V applied across the electrode, the consumption of O2 at the cathode and hence the current in the circuit is dependent on the O2 concentration in the solution which rapidly equilibrates with the sample. In practice, 0.68 V is used. Performance is affected by N2O and halothane.
The fuel cell detector operates on the same principle as the Clarke electrode, but using a lead anode which is oxidized in the operation of the cell. It is oxygen-powered with a voltage output proportional to the oxygen concentration in the electrolyte. In this case the electrolyte is KOH solution.
Both these devices require temperature and pH compensation and have limited lifespans.Blood gas electrodes
Capnographs measure the CO2 content of gas by infrared spectrophotometry. CO2 molecules absorb infrared light at a 4.28 µm by altering their vibration and rotation. Infrared radiation is shone through the sample chamber containing a continuous flow of sampled gas at a controlled pressure. The absorbance at the specified wavelength may be compared with that in a calibration cell containing no CO2 and must also be calibrated periodically to zero. The absolute amount of absorbance may be increased by using a reflected beam which passes through the sample chamber many times.
Some capnographs use multiple light wavelengths and so are able to measure the concentration of volatile anaesthetics and other gases such as NO2.
There are several potential problems with capnography. Side stream capnography has an increased response time as gas from the circuit must be drawn through the sampling line. There is potential for leakage at each connection of the sample line, reducing the CO2 concentration. The gas drawn from the circuit is not a true end-tidal sample even at the end of expiration because of the dead-space in the large airways and circuit, and so there is always an underestimate of PACO2. Mixing within the sample chamber will "blunt" changes in the CO2 trace. Pressure changes in the sample chamber either as a result of airway pressure changes or constriction of the sample line will alter the absolute CO2 concentration in the chamber. Physiological derangements such as V/Q mismatch may result in a wide disparity between PETCO2 and PaCO2 (an increased A-a gradient), reducing the usefulness of capnography.
Main stream capnographs avoid the problems associated with the sample line but are more prone to pressure changes and as the sample chamber windows are made of sapphire, they are very expensive if damaged in handling or cleaning.
12. Measurement of cardiac output
