Introduction

Gas measurements

Important variables characterising a gas mixture are pressure, flow (volume) and concentration. Each desired variable has a separate transducer being able to selectively measure the variable. Probe is perhaps the broadest concept; sensor is a little more specific comprising the transducer and its protective housing perhaps with a sampling part bringing the transducer in correct position with respect to the gas to be measured. Sensor considerations include biocompatibility/disinfection/sterility. Transducer is the part which converts the energy correlated to the variable into (usually) electric form.

Sensor response time

A response time better than 0.1 – 0.2 s is needed in order to obtain in-vivo undistorted real time curves during patient respiration.

Sensor selectivity

A measuring instrument is constructed to be maximum sensitive to the intended (desired) variable(s). By selectivity we mean the degree of reduced sensitivity to other variables. Important unintended variables interfering with the measurement may be temperature, ambient pressure, water vapour, alcohol etc. Medical gas measurements are usually done in multigas systems, and interfering variables may then be all other possible gases than the intended. Example: The sensitivity of a paramagnetic oxygen analyzer to nitrous oxide (NO) (unintended) in an oxygen (intended) gas mixture. Selectivity is dependent on the measuring principle and whether the sensor is directly sensitive to the intended variable or the measured variable is recalculated to the desired variable. Example: Oxygen sensor sensitive to partial pressure [kPa], result to be given as oxygen saturation [%].

A special case is water, as vapor or condensed water droplets. There are two problems: the sensor may be sensible to water vapor in an unintended way interfering with he results. Or the sensor function is disturbed by being covered by liquid water. Some instruments dry the sampled gas before it is measured. The concentration of the intended gas may then be too high relative to what it is in the patient airway. In many cases the sensor is heated to cancel water condensation.

Sensor calibration

Single point calibration, for instance a zero point calibration with an oxygen sensor placed in pure nitrogen. Two-point calibration with the oxygen sensor placed in pure nitrogen and then in pure oxygen; three-point calibration (checking linearity) adding measurement in air. NB! The measurements may be disturbed by interfering variables such as ambient pressure, electromagnetic radiation, relative humidity, mechanical position etc.

Calibration intervals are dependent on sensor stability and needed accuracy.

Gas sampling

Usually we are interested in the variables (flow, pressure, concentration) as near (proximal) to the patient as possible. The choice of sampling position is of interest, from proximal somewhere near the Y-piece to distal inside the ventilator. In the ventilator a sensor is well protected, at the Y-piece it must stand rough handling and the cables are a source of annoyance. These factors are well illustrated in the sidestream and mainstream sampling systems.

Sidestream sampling

Figure 11 Sidestream sampling to a multigas analyzer

A constant gas flow is aspired through a thin tube from the breathing system as shown in Fig.11. The choice of internal diameter and sampling (aspiration) flow rate must be carefully considered and be based on a compromise (See problem 12). The sampling flow rate [mL/min] should of course be small in comparison with the respiration flow rate. Even with a small sampling flow rate the gas velocity should be high so that the delay between the sampling and display instants is small. The gas concentration is a function of time at the sampling position on the respiration tube, but a function of position along the length of the sampling tube. The sampling flow is continuous, and along the tube length there will be gradients according to the concentration variation. A longitudinal diffusion process will occur, smearing the peaks out, but leaving the area under the curve unchanged. The curve will be softened, and the high frequency components reduced (low pass (LP) filtering).To reduce this LP filter effect the gas velocity in the sampling tube should be as high as possible.

A HME (Heat & Moisture Exchange) filter is often used to reduce patient water and heat loss. Such a filter also reduces mucus (slime) in the distal part of the breathing system, so the sampling position should be at the distal part of the HME filter. The minimum internal sampling tube diameter is related to the trouble with tube obstruction. Sampling directly from the inspiration tube will be much easier, but expiration data is not obtained.

At the entrance of the instrument the sampled gas must pass a trap to take away mucus and water. The measuring chambers are accordingly spared for contamination. If the sampling point is chosen to be on the right (patient) side of the HME filter the risk of sampling tube and instrument contamination is larger.
Due to the suction pump there will be an increasing negative pressure in the sampling and measuring system from the Y-tube along the sampling tube, the trap, and the measuring chambers to the pump. (see problem 12.). The aspired gas can be brought back to the breathing system, or sent to a scavenging system. Paramagnetic oxygen instruments mixes the unknown gas with a reference gas (room air), and the returned gas to the breathing tube is therefore not the same as the aspired gas. By sampling just a small gas volume pr min the unknown gas is not very disturbed.
Some characteristic properties of sidestream sampling:

Different measuring chambers may be mounted in series to form a multigas analyzer.

Sampling gas is aspirated from the breathing system, this poses problems in paediatric anaesthesia particularly.

Sample gas flow rate must be small and the tube thin to obtain sufficient high gas velocity so that concentration gradients along the sampling tubes are not smeared out.

Measuring results not in real time but delayed e.g. 0,2s.

Thin sampling tube can easily be obstructed. Humidity and mucus must be filtered out in a special trap before the gas can be allowed into the measuring chambers.

The transducers are well protected inside the instrument.

Mainstream sampling

The sensor is situated in the mainstream as shown on Fig.12. Even if there are no thin sampling tube there may also here be problems with humidity, poor transparency and mucus build up. The sensor must be heated to avoid water condensation. Characteristic properties of a mainstream sampling system are:

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  Measurement in real time.
  
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  Difficult to realize multigas analysis in one sensor head.
  
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  No thin tube which can be obstructed.
  
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  Sensor head optics must be cleaned frequently.
  
• 
  Sensor head increases dead space.
  
• 
  Sensor head heavy, fragile and warm (anti condensation precaution).
  

Figure 12 Mainstream sampling

Sampling inside the ventilator

Sidestream and mainstream sampling are parts of the breathing system proximal to the patient. However, the sampling position may be moved to inside the ventilator/ anaesthesia machine avoiding extra cables/tubing outside the box. But then the results do not necessarily reflect true patient data. In a test procedure before use on the patient the Y-tube may be connected to a special connector on the machine so that the machine can apply gas a short moment and measure volumes and compliances of the breathing system. In this way the machine to a certain extent can calculate the true patient data continuously during use. In such a system the tubing must not be changed during use.

Gas concentration measurements

Three different measuring principles in widespread use are shown in Table 4.
Table 4 Three measuring principles

	Measuring principle	medium	variables	time const	comments
1a	Spectrophotometric	gas	CO2, H2O, agent vapors	0.1s	capnography included
1b	Spectrophotometric puls­oximetry	blood	O2	1-10s	also in-vitro cuvette-oximetry and in blood gas analyzers
2a	Paramagnetic, contin.	gas	O2	10s	sample gas unchanged
2b	Paramagnetisk, pulsed	gas	O2	0.2s	sample gas changed
3a	El.chem. fuel cell, membrane covered	gas or liquid	O2	30s	limited lifetime, drifts and frequent calibration, single use
3b	El.chem. polarographic membrane covered (Clark)	gas or liquid	O2	0.1-20s	membrane & el.lyte change and reuse, used in blood gas machine
3c	El.chem. membrane covered (Severinghaus)	gas or liquid	CO2	30s	used in blood gas machine

Table 4 shows different in-vivo and in-vitro principles for blood gases. This is of interest for quality control, but also raises questions with respect to which result is the most correct one. There are e.g. often discrepancies for the same patient between the oxygen results obtained with pulsoximeter (in-vivo), the sidestream paramagnetic analyzer (in-vivo) and blood samples analyzed on a stationary blood gas analyzer (in vitro). There are many reasons for these differences: the handling of the in vitro samples from the patient to the measuring instrument perhaps in a remote laboratory, different calibration, recalculation of data obtained with different measuring principles. In order to assess such problems it is important to know the different measuring principles and their characteristic properties. In this chapter a survey is therefore given of the different measuring principles and a more detailed description of gas analyzers. The non-gas instrumentation is more detailed described under clinical chemistry and intensive care.

Gas spectrophotometry

It is well known that he colour of oxygen-rich blood is reddish, of oxygen-poor blood bluish. When the photon absorption is within the visible spectrum such colour changes illustrates the spectrophotometric principle based upon the selective absorbance of light. Spectrophotometry is measurement of colour (colorimetry) and it may be used both in liquids and gases. Many gases are transparent and colourless in the visible spectrum (e.g. nitrogen, oxygen, water, argon) meaning that there is no photon absorption in that range. In the infrared (IR) spectrum however many of the gases of interest do absorb. Each gas absorbes in a characteristic way (Fig. 13), so that selective measurements are possible.
The following gases show selective absorption in the IR spectrum: CO₂, N₂O, water, anesthetic agent vapours. IR gas monitors measure the absorption at several wavelengths in the 3.3 or 8–12 µm areas and then solve a series of simultaneous equations to calculate the concentration. Multiple wavelengths are required in order to identify the anesthetic

Figure 13 IR absorption spectra for some anaesthetic agent vapours.

Datex Ohmeda Division, Instrumentarium Corporation
gases used, and the 8–12 µm range is preferred as this represents the area of the infrared spectrum where anesthetic gases show maximum absorbance (Fig.13). Automated anesthetic agent identification is then possible. But often the instrument must be told which gas is the intended; it is only the concentration which is unknown. The absorption may follow the Lambert-Beers law:

Equation 5 I = I₀ e^-Lμ or ln(I₀/I)=Lμ

if the molecules are much smaller than the wavelength. Referring to Eq.5, I is the measured photon flux, I₀ the input flux to the sampled gas, L absorption length in the gas and μ the linear attenuation coefficient (the product Lμ is the absorbance and must be dimensionless). If there are larger particles in the sample other attenuation mechanisms related to scattering will take place, not necessarily obeying Eq.5.

The linear attenuation coefficient μ is dependent on the gas, wavelength and concentration [mol/L]. Concentration is the measured variable, but the displayed variable may be percentage [%] of the total volume. If the total pressure in the measuring chamber changes because of the suction sampling system or the barometric pressure, the concentration or partial pressure is proportional to the total pressure, but the percentage is independent.

Oxygen and nitrogen gas can not be measured spectrophotometrically because these gases do not have characteristic absorption bands in the optical spectrum.
Fig.14 shows how multiple wavelength measurements are possible. The sampled gas is aspired into the measuring chamber, where some photons from a filtered IR source are absorbed by the gas and others reach the IR detector on the other side. A rotating filter wheel inserts 6 different filters corresponding to different gases in rapid succession. The IR detector must be fast enough to discriminate between each filter. Each rotation also involves a reference filter and a stop filter. Partly overlaying spectra can be separated by using multivariat analysis on the different wavelengths measured data.

Figure 14 Multigas spectrophotometric gas analyzer with rotating filter wheel

The better the optical systems with filters and lenses, the better the selectivity. Filters in the 10 μm range do not look very transparent to the human eye!

Paramagnetic oxygen gas analyzer

Oxygen is one of the few gases which are paramagnetic. Paramagnetism and diamagnetism are the weak magnetic forces in contrast to ferromagnetism. Most substances are diamagnetic, meaning that the substance is repelled by the magnetic poles. Oxygen however is paramagnetic and will be attracted to the magnet poles. Around the poles of a permanent magnet the oxygen concentration is therefore higher than elsewhere in the room. Unpaired electrons in the outer shell give the atom magnetic properties; this is the case for oxygen. Table 5 gives the magnetic susceptibility (intensity of magnetization) of some respiratory gases and shows that the selectivity for oxygen gas is due not to the gas being paramagnetic (+ sign), but that it has a more than 100 times higher magnetic susceptibility than many (not all!) of the other gases. As Eq.6 shows, the force will be proportional to the magnetic moment, which will be proportional to the oxygen concentration [mol/L] or partial pressure [kPa], and therefore also to the chamber total pressure.


The force F [newton] on a magnetic moment m [Am²] in a magnetic field of flux density B [tesla=weber/m²]:

Equation 6 F = grad (m  B)

Accordingly, if the magnetic field B is strong but constant there is no force on m.

Table 5 Magnetic molar susceptibility _m of respiratory gases. SI unit: [m³/mol], but according to customary practice, cgs units are used and given here as _m/10^-6cm³mol^-1 (CRC Handbook of Chemistry and Physics).

gas	m	m relative
oxygen O2	+3449	+100
nitrogen N2	-12	-0.35
nitric oxide NO	+1461	+42
nitrous oxide N2O	-18.9	-0.55
nitrogen dioxide NO2	+150	+4.3
water vapour H2O	-13.1	-0.38
carbon dioxide CO2	-21	-0,61
argon	-19.3	-0.56

The measuring principle is shown in Fig.15, it was invented by Nobel laureate Linius Pauling in 1946; The Beckman Oxygen Analyser. A diamagnetic gas (e.g. nitrogen) is enclosed in two spheres fixed to the end of an arm which is fixed to a suspended metal wire so that the arm can rotate. The rotation is read by a light beam reflected from a mirror fixed to the arm. The magnetic field is from permanent magnets.

Increased oxygen concentration disturbs the magnetic balance and the spheres are driven out of the magnetic field. The time response is slow, e.g. 5-15s, because of the large chamber volume and the mass of the dumbbell. A somewhat quicker version is made by fixing a magnetic coil to the arm. The coil is supplied with an electric current from a servo system so that the bell positions are virtually unchanged under different oxygen concentrations. The measurement result is read from the coil current.

Figure 15 Paramagnetic oxygen analyzer. The construction is enclosed in a tight box with inlet and outlet for the gas to be examined, the reference gas is enclosed in the two spheres.

Fig.16 shows a more rapid system using a pulsed magnetic field. It is a differential measuring principle, using a differential pressure transducer (microphone) to detect the difference in magnetic action on the unknown gas and a known reference gas, usually room air. Increased concentration of oxygen leads to increased suction of the oxygen molecules into the magnetic gradient field zone, and therefore reduced pressure outside the zone. In order to have a response time < 0.1s, the magnetic field is switched at a frequency of a few hundred hertz. The differential measuring principle implies that the gas output is not the same as the aspired unknown gas.

An important advantage with the paramagnetic measuring principle is long term stability and minimal need of maintenance (if the measuring chamber is kept clean). The differential principle of the pulsed type may also be advantageous. However, the measuring chamber is heavy (the magnet) and must therefore be mounted in a sidestream sampling system.

Figure 16 Paramagnetic oxygen analyzer using pulsed magnetic field. Gray lines are tubes.

Multigas analyzers

Fig.11 showed a multigas analyzer in a sidestream sampling system. The gas first arrives to the spesctrophotometer where CO₂, N₂O, water and anesthetic agent vapors are measured. Then the gas sample is mixed with the reference gas and oxygen concentration is measured.

Problems with such instrumentation are the risk of contamination of the measuring chambers. Water condensation in the chambers must be avoided, by warming the chamber and/or filtering the aspired gas before it enters the chambers. This filtering system is an important part of the construction and determines to a large extent the robustness of the system. If mucus and other contaminations still reach the measuring chambers, special rinsing liquids plus days of dry gas flushing may bring the instrument alive again.

Other gas measuring principles

Membrane covered electrochemical electrodes for oxygen and carbon dioxide are described in chapter 10.2. They can be used for measuring partial pressure both in liquids and gases.
Mass spectrometers (MS) are large and expensive instruments which therefore must use sidestream sampling. A MS consists of a vacuum chamber where the gas is ionized. The ions are accelerated and focused in an electric field by suitable electrodes and then enters a magnetic field zone where they are deflected according to their mass. The selectivity is very good, but molecules with identical mass numbers will interfere with each other, for instance N₂O and CO₂ which both have mass number 44. It can measure several different gases fast enough to measure respiration in real time. The instrumentation maintenance is expensive, and the instrument is best adapted to research or in a central installation serving several patients simultaneously.
More on measured and calculated variables

If the total pressure of a gasmixture e.g. air is increased (Fig.17), the partial pressure of oxygen (pO₂) increases, but the oxygen volume % is constant. Sometimes we are interested in the volume %, sometimes in the pO₂. Let us take the example that oxygen is measured by a partial pressure (pO₂) sensitive sensor, but the result is recalculated to volume %. The volume % will display false values if the total pressure varies. This illustrates that the transducer working principle should always be known.

Figure 17 Closed variable volume

Another example is the one shown in Fig.7, where a water dish is inserted into a dry gas chamber. Then the % oxygen will fall, but not the pO2. In medicine the inspired gas will always have a lower water content than the expired gas.

Gas pressure sensors

Pressure is force per area: P = F/A. The classical measuring device is a liquid filled tube measuring level difference. Often it is formed as an U, if closed in one end it measures absolute pressure, if open it measures relative (gauge) pressure. If it is filled with water cmH₂O may be the preferred unit, if filled with mercury mmHg may be preferred. A mechanical pressure measuring instrument is called a manometer. A pressure sensor alone is not a manometer.

Fig.18 shows two sensors both based upon a precision moulded thin membrane as a part of the sensor house, cf. Fig.2.4 in chapter 2 Webster. The membrane thickness and material properties determine the deflection pr change in pressure level. The thinner the membrane the more sensitive the sensor, but also the more fragile the membrane. The deflection is in principle not a linear function of pressure. The deflection also determines the compliance C of the sensor: C = ΔV /ΔP [mm³/kPa]. ΔV is a volume which implies a transport of inert substance (gas molecules in this case) to and from the membrane according to the variable pressure. Compliance is therefore important for the dynamic response, not for static or slowly varying pressures. A high quality sensor shall have a stiff membrane and low compliance. The membrane deflection may be measured by a piezoelectric beam (left) or an optical reflection system (right). The sensor principles can be operated with the interior volume closed. Then absolute pressure is measured, but if the closed chamber is gas filled this introduces a temperature dependence according to Eq.3. With the interior open to the surrounding air relative (gauge) pressures are measured. With a tube connected to the interior we have a differential transducer which e.g. may be used for flow measurements, see under gas flow sensors. A dome closing the volume above the membrane may be connected to a second tube to adapt it better for differential measurements. The dome can be made of plastic with a soft membrane interfacing the sensor membrane. The complete dome may be sterilized so that it can by used in invasive applications. The whole sensor house may also be sterilized for use as a tissue implant.

Figure 18 Pressure sensors. Left: piezoelectric transducer with an optional dome to be positioned so as to form a closed volume above the membrane. Right: optical transducer

Important specifications for a pressure sensor are: sensitivity, compliance, linearity (membrane property), hysteresis, membrane absolute maximum pressure, size, temperature zero drift, temperature sensitivity drift, temperature range, long term stability, negative pressure properties, sterilizability, biocompatibility.

Gas flow sensors

Rotameter and turbine flow meters, mainstream

A rotameter consists of a slightly conic vertical glass tube with a bobbin at the bottom. With gas flow through the tube the bobbin lifts and starts to rotate. The scale is engraved on the tube external surface so the flow rate can be read. The rotameter is the classical instrument for measuring flow, however it is non-linear, gas viscosity dependent, critically dependent on the conic boring and the bobbin size, and it is a unidirectional device. The calibration is valid only for one gas, and it must be used in a vertical position.

The free bobbin may be replaced by a propeller or turbine with a fixed axis. Such a device is bidirectional, and the rotations pr minute may easily be read by an optical system so that an electronic flow rate signal is available.

Hot wire flow sensor, mainstream (also Fig.8.13 in chapter 8)

Figure 19 Hot wire flow meter with two termistors, cross section shown to the right

Two temperature dependent resistors (thermistors) are used in a tube, one of them is used for measuring gas inlet temperature (Fig.19). The other is heated by an electric current at the same time as its resistance can be measured (how?). The flowing gas with a lower and known temperature cools the heated thermistor according to the gas velocity and the temperature is followed by monitoring its electrical resistance. It is a spot sensor, and the thermistor transducers can be made very small with thin wires, with just a small disturbance of the flow profile. The construction is robust and lightweight, but the position of the thermistors is critical. In its simplest form as shown it is a unidirectional device. The sensitivity is dependent on the thermal properties, heat capacity in particular, of the gas. It is sensitive to gas pressure.

Vane deflection flow sensor, mainstream

Figure 20 Vane flow sensor in a tube, cross section shown to the right

Vane deflection is dependent on gas velocity and density as well as gas pressure. Non-linearity dependent on the back eddy behind the vane, less pronounced if the vane is soft and deflects. Direction sensitive. Vane disturbs the parabolic flow profile, and it is more a cross sectional area sensor than a spot sensor. Transducer may be of a piezoelectric or straingauge type.

Pitot flow sensor (also with remote transducer)

Figure 21 Pitot flow sensor in a tube, cross section shown to the right
The Pitot tube flow sensor is based upon Eq.8 (Bernoulli) and the so called kinetic part of it: ½ v². The sensitivity is accordingly dependent on gas density  (and therefore gas pressure) and the calibration factor is dependent on gas type and the gas mixture. The output is proportional to the square of gas velocity, and Fig.21 shows two Pitot tubes with the tube opening with and against the velocity direction. The sensitivity is doubled with a kinetic factor v². Actually it is a gas velocity spot sensor, and a velocity profile has to be assumed to obtain flow. The disturbance of the velocity profile, turbulence included is considerable as small diameter Pitot tubes destroy the dynamic properties of the sensor. If the tubes and transducer are low compliance components mainstream sampling with a remote differential transducer is possible. The sensor is direction sensitive. The pressure differential transducer may be based upon light reflection from the sensing membrane, discuss other possible technologies.

Poiseuille flow sensor (also with remote transducer)

This sensor measures differential pressure ΔP across a well defined flow resistance, it is also called a pneumotachometer. Because it is based upon the law of Poiseuille (Eq.2) the sensitivity is gas viscosity dependent. The dimension of R in Eq.2 is [Pa/m³/s]. If the mean pressure in the tube doubles the molar flow [mol/s] doubles, but R is constant because gas viscosity has a surprisingly low pressure dependence. Volume flow [m³/s] is therefore the intended variable of this sensor, not molar flow. The viscosity dependence is a problem if it is a mixture of different gases; each gas will have its own calibration factor.

The pressure difference is proportional to gas flow if the flow pattern is laminar. The pressure difference is measured at the wall where the gas velocity is zero, and the pressure difference represents the whole cross sectional area. Flow direction can be determined. If the sampling tubes and transducer have low compliance the transducer may be remote as a part of a main stream sampling system, it may be then be realised as a very robust system.

Figure 22 Poiseuille gas flow sensor (pneumotachometer)

The flow resistance can be obtained with or without a narrow passage zone as shown on Fig.22. A narrow zone increases sensitivity ΔP/Q (Poiseuille). A so called Fleisch tube is a special resistance with many small gas channels (capillaries) in parallel. Thin capillaries will be vulnerable to accumulation of secretions or other contaminants and from the condensation of water vapor. Therefore the tube must be heated if used on expired gas.

Doppler flow meter, mainstream

A usual ultrasound Doppler flowmeter for blood is not useful for ordinary gas measurements. Blood flow can be measured because the blood cells are sufficiently large (about 5-10 μm), small molecules do not give sufficient reflected signal strength. However, in a gas the flow can be measured in transmission instead of reflective mode. The velocity of sound will be higher if sound direction is in the gas flow direction. The problem is that such transmission mode requires separate transmitting and receiving probes on each side of the organ.