Basic Physics for the Anaesthetist

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Basic Physics for the Anaesthetist

K nowledge of some physics is required in order to understand the function of many items of apparatus for anaesthesia delivery and physiological monitoring. This chapter emphasizes the more elementary aspects of physical principles and it is hoped that the reader may be stimulated to study some of the books written specifically for anaesthetists and which examine this topic in greater detail (see ‘Further reading’). Sophisticated measurement techniques may be required for more complex types of anaesthesia, in the intensive care unit and during anaesthesia for severely ill patients, and an understanding of the principles involved in performing such measurements is required in the later stages of the anaesthetist’s training.

This chapter concentrates on the more common applications, including pressure and flow in gases and liquids, electricity and electrical safety. However, it is necessary first to consider some basic definitions.

BASIC DEFINITIONS

It is now customary in medical practice to employ the International System (Système Internationale; SI) of units. Common exceptions to the use of the SI system include measurement of arterial pressure and, to a lesser extent, gas pressure. The mercury column is used commonly to calibrate electronic arterial pressure measuring devices and so ‘mmHg’ is retained. Pressures in gas cylinders are also referred to frequently in terms of the ‘normal’ atmospheric pressure of 760 mmHg; this is equal to 1.013 bar (or approximately 1 bar). Low pressures are expressed usually in the SI unit of kilopascals (kPa) whilst higher pressures are referred to in bar (100 kPa = 1 bar). The basic and derived units of the SI system are shown in Table 14.1.

TABLE 14.1

Physical Quantities

The fundamental quantities in physics are mass, length and time.

Mass (m) is defined as the amount of matter in a body. The unit of mass is the kilogram (kg), for which the standard is a block of platinum held in a Physics Reference Laboratory.

Length (l) is defined as the distance between two points. The SI unit is the metre (m), which is defined as the distance occupied by a specified number of wavelengths of light.

Time (t) is measured in seconds. The reference standard for time is based on the frequency of resonation of the caesium atom.

From these basic definitions, several units of measurement may be derived:

Volume has units of m³.

Density is defined as mass per unit volume:

Velocity is defined as the distance travelled per unit time:

Acceleration is defined as the rate of change of velocity:

Force is that which is required to give a mass acceleration:

The SI unit of force is the newton (N). One newton is the force required to give a mass of 1 kg an acceleration of 1 m s^–1:

1 N = 1 kg m s^–2

Weight is the force of the earth’s attraction for a body. When a body falls freely under the influence of gravity, it accelerates at a rate of 9.81 m s^–2 (g):

Momentum is defined as mass multiplied by velocity:

momentum = m × v

Work is undertaken when a force moves an object:

work = force × distance

= F × l N m (or joules, J)

Energy is the capacity for undertaking work. Thus it has the same units as those of work. Energy can exist in several forms, such as mechanical (kinetic energy [KE] or potential energy [PE]), thermal or electrical and all have the same units.

Power (P) is the rate of doing work. The SI unit of power is the watt, which is equal to 1 J s^− 1:

power = work per unit time

= joules per second = watt (W)

Pressure is defined as force per unit area:

= pascal (Pa)

As 1 Pa is a rather small unit, it is more common in medical practice to use the kilopascal (kPa): 1 kPa ≈ 7.5 mmHg.

FLUIDS

Substances may exist in solid, liquid or gaseous form. These forms or phases differ from each other according to the random movement of their constituent atoms or molecules. In solids, molecules oscillate about a fixed point, whereas in liquids the molecules possess higher velocities and therefore higher kinetic energy; they move more freely and thus do not bear a constant relationship in space to other molecules. The molecules of gases possess even higher kinetic energy and move freely to an even greater extent.

Both gases and liquids are termed fluids. Liquids are incompressible and at constant temperature occupy a fixed volume, conforming to the shape of a container; gases have no fixed volume but expand to occupy the total space of a container. Nevertheless the techniques for analysing the behaviour of liquids and gases (or fluids in general) in terms of their hydraulic and thermodynamic properties are very similar.

In the process of vaporization, random loss of liquid molecules with higher kinetic (thermal) energies from the liquid occurs while vapour molecules randomly lose thermal (kinetic) energy and return to the liquid state. Heating a liquid increases the kinetic energy of its molecules, permitting a higher proportion to escape from the surface into the vapour phase. The acquisition by these molecules of higher kinetic energy requires an energy source and this usually comes from the thermal energy of the liquid itself, which leads to a reduction in its thermal energy as vaporization occurs and hence the liquid cools.

Collision of randomly moving molecules in the gaseous phase with the walls of a container is responsible for the pressure exerted by a gas. The difference between a gas and a vapour will be discussed later.

Behaviour of Gases

The Gas Laws

There are three gas laws which determine the behaviour of gases and which are important to anaesthetists. These are derived from the kinetic theory of gases; they depend on the assumption that the substances concerned are perfect gases (rather than vapours), and they assume a fixed mass of gas.

Boyle’s law states that, at constant temperature, the volume (V) of a given mass of gas varies inversely with its absolute pressure (P):

PV = k₁

Charles’ law states that, at constant pressure, the volume of a given mass of gas varies directly with its absolute temperature (T):

V = k₂T

The third gas law (sometimes known as Gay-Lussac’s law) states that, at constant volume, the absolute pressure of a given mass of gas varies directly with its absolute temperature:

P = k₃T

Combining these three gas laws:

PV = kT

where suffixes 1 and 2 represent two conditions different in P, V and T of the gas. Note that where a change of conditions occurs slowly enough for T₁ = T₂, conditions are said to be isothermal, and the combined gas law could be thought of as another form of Boyle’s law.

The behaviour of a mixture of gases in a container is described by Dalton’s law of partial pressures. This states that, in a mixture of gases, the pressure exerted by each gas is the same as that which it would exert if it alone occupied the container. Dalton’s law can be used to compare volumetric fractions (concentrations) to calculate partial pressures, which are an important concept in anaesthesia. Thus, in a cylinder of compressed air at a pressure of 100 bar, the pressure exerted by nitrogen is equal to 79 bar, as the fractional concentration of nitrogen is 0.79.

GAS REGULATORS

Pressure Relief Valves

The Heidbrink valve is a common component of many anaesthesia breathing systems. In the Magill breathing system, the anaesthetist may vary the force in the spring(s), thereby controlling the pressure within the breathing system (Fig. 14.2). At equilibrium, the force exerted by the spring is equal to the force exerted by gas within the system:

FIGURE 14.2 A pressure relief valve.

force (F) = gas pressure (P) × disc area (A)

Modern anaesthesia systems contain a variety of pressure relief valves, in each of which the force is fixed so as to provide a gas escape mechanism when pressure reaches a preset level. Thus, an anaesthetic machine may contain a pressure relief valve operating at 35 kPa, situated on the back bar of the machine between the vaporizers and the breathing system to protect the flowmeters and vaporizers from excessive pressures. Modern ventilators contain a pressure relief valve set at 7 kPa to protect the patient from barotrauma. A much lower pressure is set in relief valves which form part of anaesthetic scavenging systems and these may operate at pressures of 0.2–0.3 kPa to protect the patient from negative pressure applied to the lungs.

Pressure-Reducing Valves (Pressure Regulators)

Pressure regulators have two important functions in anaesthetic machines:

They reduce high pressures of compressed gases to manageable levels (acting as pressure-reducing valves).

They minimize fluctuations in the pressure within an anaesthetic machine, which would necessitate frequent manipulations of flowmeter controls.

Modern anaesthetic machines are designed to operate with an inlet gas supply at a pressure of 3–4 bar (usually 4 bar in the UK). Hospital pipeline supplies also operate at a pressure of 4 bar and therefore pressure regulators are not required between a hospital pipeline supply and an anaesthetic machine. In contrast, the contents of cylinders of all medical gases (i.e. oxygen, nitrous oxide, air and Entonox) are at much higher pressures. Thus, cylinders of these gases require a pressure-reducing valve between the cylinder and the flowmeter.

The principle on which the simplest type of pressure-reducing valve operates is shown in Figure 14.3. High-pressure gas enters through the valve and forces the flexible diaphragm upwards, tending to close the valve and prevent further ingress of gas from the high-pressure source.

FIGURE 14.3 A simple pressure-reducing valve.

If there is no tension in the spring, the relationship between the reduced pressure (p) and the high pressure (P) is very approximately equal to the ratio of the areas of the valve seating (a) and the diaphragm (A):

p.A = P.a

By tensing the spring, a force F is produced which offsets the closing effect of the valve. Thus, p may be increased by increasing the force in the spring.

Without the spring, the simple pressure regulator has the disadvantage that reduced pressure decreases proportionally with the decrease in cylinder pressure. The addition of a force from the spring considerably reduces but does not eliminate this problem, and in order to overcome it, newer pressure regulators contain an extra closing spring. During high flows, the input to the valve may not be able to keep pace with the output. This can cause the regulated pressure to fall. A two-stage regulator can be employed in order to overcome this. Simple one-stage regulators are often designed for use with a specific gas. A universal regulator, in which the body is used for all gases but has different seatings and springs fitted for each specific gas, is now available.

Pressure Demand Regulators

These are regulators in which gas flow occurs when an inspiratory effort is applied to the outlet port. The Entonox valve is a two-stage regulator and its mode of action is demonstrated in Figure 14.4. The first stage is identical to the reducing valve described above. The second-stage valve contains a diaphragm. Movement of this diaphragm tilts a rod, which controls the flow of gas from the first-stage valve. The second stage is adjusted so that gas flows only when pressure is below atmospheric.

FIGURE 14.4 The Entonox two-stage pressure demand regulator.

Flow of Fluids

Viscosity (η) is the constant of proportionality relating the stress (τ) between layers of flowing fluid (or between the fluid and the vessel wall), and the velocity gradient across the vessel, dv/dr.

Hence:

In this context, velocity gradient is equal to the difference between velocities of different fluid layers divided by the distance between layers (Fig. 14.5B). The units of the coefficient of viscosity are Pascal seconds (Pa s).

Fluids for which η is constant are referred to as Newtonian fluids. However, some biological fluids are non-Newtonian, an example of which is blood; viscosity changes with the rate of flow of blood (as a result of change in distribution of cells) and, in stored blood, with time (blood thickens on storage).

Viscosity of liquids diminishes with increase in temperature, whereas viscosity of a gas increases with increase in temperature. An increase in temperature is due to an increase of kinetic energy of fluid molecules. This can be thought of as causing a freeing up of intermolecular bonds in liquids, and an increase in intermolecular collisions in gas.

Laminar Flow

Laminar flow through a tube is illustrated in Figure 14.5A. In this situation, there is a smooth, orderly flow of fluid such that molecules travel with the greatest velocity in the axial stream, whilst the velocity of those in contact with the wall of the tube may be virtually zero. The linear velocity of axial flow is twice the average linear velocity of flow.

In a tube in which laminar flow occurs, the relationship between flow and pressure is given by the Hagen–Poiseuille formula:

where is the flow, ∆P is the pressure gradient along the tube, r is the radius of the tube, η is the viscosity of fluid and l is the length of the tube.

The Hagen–Poiseuille formula applies only to Newtonian fluids and to laminar flow. In non-Newtonian fluids such as blood, increase in velocity of flow may alter viscosity because of variation in the dispersion of cells within plasma.

Turbulent Flow: Flow of Fluids Through Orifices

In turbulent flow, fluid no longer moves in orderly planes but swirls and eddies around in a haphazard manner as illustrated in Figure 14.6. Essentially, turbulent flow is less efficient in the transport of fluids because energy is wasted in the eddies, in friction and in noise (bruits). Although viscosity is the important physical variable in relation to the behaviour of fluids in laminar flow, turbulent flow is more markedly affected by changes in fluid density.

FIGURE 14.5 (A) Diagrammatic illustration of laminar flow. (B) Velocity gradient.

FIGURE 14.6 Diagrammatic illustration of turbulent flow.

It may be seen from Figure 14.7 that the relationship between pressure and flow is linear within certain limits. However, as velocity increases, a point is reached (the critical point or critical velocity) at which the characteristics of flow change from laminar to turbulent. The critical point is dependent upon several factors, which were investigated by the physicist Osborne Reynolds. These factors are related by the formula used for calculation of Reynolds’ number:

FIGURE 14.7 The relationship between pressure and flow in a fluid is linear up to the critical point, above which flow becomes turbulent.

where v is the fluid linear velocity, r is the radius of the tube, ρ is the fluid density and η is its viscosity.

Studies with cylindrical tubes have shown that if Reynolds’ number exceeds 2000, flow is likely to be turbulent, whereas a Reynolds’ number of less than 2000 is usually associated with laminar flow. However, localized areas of turbulent flow can occur at lower Reynolds’ numbers (i.e. at lower velocities) when there are changes in fluid direction, such as at bends, or changes in cross sectional area of the tube.

While the behaviour of fluids in laminar flow can be described by the Hagen–Poiseuille equation, the characteristics of turbulent flow are dependent on:

the square root of the pressure difference driving the flow

the square of the diameter of the vessel

the square root of density (ρ) of the fluid, i.e.:

A tube can be thought of as having a length many times its diameter. In an orifice by contrast, the diameter of the fluid pathway exceeds the length. The flow rate of a fluid through an orifice is much more likely to be turbulent and is described by the factors discussed above.

Applications of Turbulence in Anaesthetic Practice:

In upper respiratory tract obstruction of any severity, flow is inevitably turbulent downstream of the obstruction; thus for the same respiratory effort (driving pressure), a lower tidal volume is achieved than when flow is laminar. The extent of turbulent flow may be reduced by reducing gas density; clinically, it is common practice to administer oxygen-enriched helium rather than oxygen alone (the density of oxygen is 1360 kg m^− 3 and that of helium is 160 kg m^− 3). This reduces the likelihood of turbulent flow and reduces the respiratory effort required by the patient.

In anaesthetic breathing systems, a sudden change in diameter of tubing or irregularity of the wall may be responsible for a change from laminar to turbulent flow. Thus, tracheal and other breathing tubes should possess smooth internal surfaces, gradual bends and no constrictions.

Resistance to breathing is much greater when a tracheal tube of small diameter is used (Fig. 14.8). Tubes should be of as large a diameter and as short as possible.

FIGURE 14.8 Resistance to gas flow through tracheal tubes of different internal diameter (ID).

In a variable orifice flowmeter, gas flow at low flow rates is predominantly laminar. Flow depends on viscosity. At higher flow rates, because the flowmeter behaves as an orifice, turbulent flow dominates and density is more important than viscosity.

THE VENTURI, THE INJECTOR AND BERNOULLI

A venturi is a tube with a section of smaller diameter than either the upstream or the downstream parts of the tube. The principles governing the behaviour of fluid flow through a venturi were formulated by Bernoulli in 1778, some 60 years earlier than Venturi himself. In any continuum, the energy of the fluid may be decribed by the Bernoulli equation, which suggests that the sum of energies possessed by the fluid is constant, i.e.:

assuming that the predominant fluid flow is horizontal such that gravitational potential energy can be ignored.

In a venturi, in order that the fluid flow be continuous, its velocity must increase through its narrowed throat (v₂ > v₁). This is associated with an increase in kinetic energy and Bernoulli’s equation shows that where this occurs, there is an associated reduction in potential energy and therefore in pressure. Beyond the constriction, velocity decreases back to the initial value and the pressure rises again. The principle is illustrated in Figure 14.9. At point A, the energy in the fluid consists of potential (pressure) and kinetic (velocity), but at point B the amount of kinetic energy has increased because of the increased velocity. As the total energy state must remain constant, pressure is reduced at point B. A venturi has a number of uses, including that of a flow measurement device. For optimum performance of a venturi, it is desirable for fluid flow to remain laminar and this is achieved by gradual opening of the tube beyond the constriction. In this way, if a U tube manometer is placed with one limb sampling the pressure at point A and the other at point B, then if the flow remains laminar, Hagen–Poiseuille’s equation suggests a linear relationship between the pressure difference and the flow; this makes calibration of such a flowmeter relatively easy. This contrasts with an orifice, at the outflow of which the flow is usually turbulent. Although an orifice can be used as a flowmeter, the relationship between pressure difference and flow is non-linear. Another use of a venturi is as a device for entraining fluid from without. If a flow of oxygen is fed into a venturi through a nozzle, the low pressure induced at the throat may be used to entrain air, thus giving a metered supply of oxygen-enriched air, or acting as an injector by multiplying the amount of air flowing through the venturi towards the patient’s lungs. If, instead, a hole is made in the side of the venturi at the throat, then the low pressure at that point may form the basis of a suction device (Fig. 14.10).

FIGURE 14.9 The Bernoulli principle. See text for full details.

FIGURE 14.10 Fluid entrainment by a venturi injector.

The injector principle may be seen in anaesthetic practice in the following situations:

Oxygen therapy. Several types of venturi oxygen masks are available which provide oxygen-enriched air. With an appropriate flow of oxygen (usually exceeding 4 L min^–1), there is a large degree of entrainment of air. This results in a total gas flow that exceeds the patient’s peak inspiratory flow rate, thus ensuring that the inspired oxygen concentration remains constant, and it prevents an increase in apparatus dead space which always accompanies the use of low-flow oxygen devices.

Nebulizers. These are used to entrain water from a reservoir. If the water inlet is suitably positioned, the entrained water may be broken up into a fine mist by the high gas velocity.

Portable suction apparatus.

Oxygen tents.

As a driving gas in a ventilator (Fig. 14.11).

FIGURE 14.11 A simple injector.

The Coanda Effect

The Coanda effect describes a phenomenon whereby when gas flows through a tube and enters a Y-junction, gas tends to cling either to one side of the tube or to the other. This is because a Y-junction usually implies a reduction in downstream tube diameter, and thus an increase in velocity with a reduction in pressure adjacent to the wall. The gas is often not divided equally between the two outlets. The principle has been used in anaesthetic ventilators (termed fluidic ventilators), as the application of a small pressure distal to the restriction may enable gas flow to be switched (using an external cross flow of gas) from one side to another (Fig. 14.12).

FIGURE 14.12 The Coanda effect.

HEAT

Heat is the energy which may be transferred from a body at a hotter temperature to one at a colder temperature. Its units are therefore Joules. As alluded to earlier, energy takes a number of forms and, if account is taken of energy losses, they are interchangeable. For example, if heat energy is applied to an engine, mechanical energy is the output. In a refrigeration cycle, mechanical energy is put in and heat is extracted from the cold compartment to the environment. Temperature is a measure of the tendency of an object to gain or lose heat.

Temperature and its Measurement

The Kelvin scale was adopted as an international temperature scale. The triple point of water is chosen as one reference point for the temperature scale; this is the point at which all three phases of water (ice, water, steam) are in equilibrium with each other, and although the pressure at which this occurs is very low (0.006 bar), the temperature at which this occurs is only fractionally greater than that of the ice point at atmospheric pressure (1.013 bar). The internationally agreed temperature ‘number’ of the triple point of water is 273.16, because it is this number of units above the recognized absolute zero of temperature, which was deduced from extrapolations of the relationships between pressure, volume and temperature of gases. Hence the unit of thermodynamic temperature (the Kelvin; K) is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water. The difference in temperature between the ice point for water and the steam point remains 100 units, which makes the range almost identical to the earlier, empirically derived, Celsius scale. It is not precisely the same, because this scale has its datum at 273.15 K, i.e. 0.01 K below the triple point. Although the unit on the thermodynamic Celsius scale is identical to that on the Kelvin scale, it is usual to denote 273.15 K as 0 °C.

Consequently, the intervals on the Celsius scale are identical to those on the Kelvin scale and the relationship between the two scales is as follows:

temperature (K) = temperature (°C) + 273.15

Temperature is measured in clinical practice by one of the following techniques:

Liquid expansion thermometer. Mercury and alcohol are the more commonly used liquids.

Thermistor. This is a semiconductor, which exhibits a reduction in electrical resistance with increase in temperature.

Thermocouple. This relies on the Seebeck effect. When two metal conductors are joined together to form a circuit, a potential difference is produced which is proportional to the difference in the temperatures of the two junctions. In order to measure temperature, one junction has to be kept at a constant temperature.

Chemical thermometers. These thermometers are described in more detail in Chapter 16.

Specific Heat Capacity

The specific heat capacity of a substance is the energy required to raise the temperature of 1 kg of the substance by 1 K, i.e.:

heat energy required = mass × specific heat capacity × temperature rise

Its units are J kg^− 1 K^− 1. For gases, there are slight differences in specific heat capacities depending on whether the thermodynamic process being undergone is at constant pressure or at constant volume. The specific heat capacity of different substances is of interest because anaesthetists are frequently concerned with maintenance of body temperature in unconscious patients.

Heat is lost from patients by the processes of:

conduction

convection

radiation, which is the most common mode of heat loss

evaporation.

The specific heat capacity of gases is up to 1000 times smaller than that of liquids. Consequently, humidification of inspired gases is a more important method of conserving heat than warming dry gases; in addition, the use of humidified gases minimizes the very large energy loss produced by evaporation of fluid from the respiratory tract.

The skin acts as an almost perfect radiator; radiant losses in susceptible patients may be reduced by the use of reflective aluminium foil (‘space blanket’).

VAPORIZATION AND VAPORIZERS

In a liquid, molecules are in a state of continuous motion due to their kinetic energy, and are held in the liquid state because of intermolecular attraction by van der Waal’s forces. Some molecules may develop velocities sufficient to escape from these forces, and if they are close to the surface of a liquid, these molecules may escape to enter the vapour phase. Increasing the temperature of a liquid increases its kinetic energy and a greater number of molecules escape. As the faster moving molecules escape into the vapour phase, the net velocity of the remaining molecules reduces; thus the energy state and therefore temperature of the liquid phase are reduced. The amount of heat required to convert a unit mass of liquid into a vapour without a change in temperature of the liquid is termed the ‘latent heat of vaporization’.

In a closed vessel containing liquid and gas, a state of equilibrium is reached when the number of molecules escaping from the liquid is equal to the number of molecules re-entering the liquid phase. The vapour concentration is then said to be saturated at the specified temperature. Saturated vapour pressure of liquids is independent of the ambient pressure, but increases with increasing temperature.

The boiling point of a liquid is the temperature at which its saturated vapour pressure becomes equal to the ambient pressure. Thus, on the graph in Figure 14.13, the boiling point of each liquid at 1 atmosphere is the temperature at which its saturated vapour pressure is 101.3 kPa.

FIGURE 14.13 Relationship between vapour pressure and temperature for different anaesthetic agents.

Vaporizers

Vaporizers may be classified into two types:

drawover vaporizers

plenum vaporizers.

In the former type, gas is pulled through the vaporizer when the patient inspires, creating a subatmospheric pressure. In the latter type, gas is forced through the vaporizer by the pressure of the fresh gas supply. Consequently, the resistance to gas flow through a drawover vaporizer must be extremely small; the resistance of a plenum vaporizer may be high enough to prevent its use as a drawover vaporizer, although this is not necessarily so.

The principles of both devices are similar. If we consider the simplest form of vaporizer (Fig. 14.14), the concentration (C) of anaesthetic in the gas mixture emerging from the outlet port is dependent upon:

FIGURE 14.14 A simple type of vaporizer.

The saturated vapour pressure of the anaesthetic liquid in the vaporizer. A highly volatile agent such as diethyl ether or desflurane is present in a much higher concentration than a less volatile agent (i.e. with a lower saturated vapour pressure) such as halothane or isoflurane.

The temperature of the liquid anaesthetic agent, as this determines its saturated vapour pressure.

The splitting ratio, i.e. the flow rate of gas through the vaporizing chamber (F_v) in comparison with that through the bypass (F – F_v). Regulation of the splitting ratio is the usual mechanism whereby the anaesthetist controls the output concentration from a vaporizer.

The surface area of the anaesthetic agent in the vaporizer. If the surface area is relatively small during use, the flow of gas through the vaporizing chamber may be too rapid to achieve complete saturation with anaesthetic molecules of the gas above the liquid.

Duration of use. As the liquid in the vaporizing chamber evaporates, its temperature, and thus its saturated vapour pressure, decreases. This leads to a reduction in concentration of anaesthetic in the mixture leaving the exit port.

The flow characteristics through the vaporizing chamber. In the simple vaporizer illustrated, gas passing through the vaporizing chamber may fail to mix completely with vapour as a result of streaming because of poor design. This lack of mixing is flow-dependent.

Modern anaesthetic vaporizers overcome many of the problems described above. Maintenance of full saturation may be achieved by making available a large surface area for vaporization. In the TEC series of vaporizers, this is achieved by the use of wicks which draw up liquid anaesthetic by capillary pressure and provide a very large surface area. Efficient vaporization and prevention of streaming of gas through the vaporizing chamber are achieved by ensuring that gas travels through a concentric helix, which is bounded by the fabric wicks. Another method of ensuring full saturation is to bubble gas through liquid anaesthetic via a sintered disc; the final concentration is determined by mixing a known flow of fresh gas with a measured flow of fully saturated vapour.

Temperature Compensation

Temperature-compensated vaporizers possess a mechanism which produces an increase in flow through the vaporizing chamber (i.e. an increased splitting ratio) as the temperature of liquid anaesthetic decreases. In the TEC vaporizers, a bimetallic strip controls (by bending) a valve which alters flow through the exit port of the vaporizing chamber. In the EMO and Ohio vaporizers, a bellows mechanism is used to regulate the valve (by shortening with decreased temperature), whilst in the Drager Vapor 19 vaporizers, a metal rod acts in a similar fashion.

Back Pressure (Pumping Effect)

Some gas-driven mechanical ventilators (e.g. the Manley ventilator) produce a considerable increase in pressure in the outlet port and back bar of the anaesthetic machine. This pressure is highest during the inspiratory phase of ventilation. If the simple vaporizer shown in Figure 14.14 is attached to the back bar, the increased pressure during inspiration compresses the gas in the vaporizer; some gas in the region of the inlet port of the vaporizer is forced into the vaporizing chamber, where more vapour is added to it. Subsequently, there is a temporary surge in anaesthetic concentration when the pressure decreases at the end of the inspiratory cycle.

This effect is irrelevant with efficient vaporizers (i.e. those which saturate gas fully in the vaporization chamber) because gas in the outlet port is already saturated with vapour. However, when pressure reduces at the end of inspiration, some saturated gas passes retrogradely out of the inspiratory port and mixes with the bypass gas. Thus, a temporary increase in total vapour concentration may still occur in the gas supplied to the patient. Methods of overcoming this problem include:

incorporation of a one-way valve in the outlet port

construction of a bypass chamber and vaporizing chamber which are of equal volumes so that the gas in each is compressed or expanded equally

construction of a long inlet tube to the vaporizing chamber so that retrograde flow from the vaporizing chamber does not reach the bypass channel (as in the Mark 3 TEC vaporizers).

HUMIDITY AND HUMIDIFICATION

Absolute and Relative Humidity

Absolute humidity (g m^–3 or mg L^− 1) is the mass of water vapour present in a given volume of gas. Relative humidity is the ratio of mass of water vapour in a given volume of gas to the mass required to saturate that volume of gas at the same temperature.

Since a mass of water vapour in a sample of air has an associated temperature-dependent vapour pressure, relative humidity (RH) may also be expressed as:

In normal practice, relative humidity may be measured using:

The hair hygrometer. This operates on the principle that a hair elongates if humidity increases; the hair length controls a pointer. This simple device may be mounted on a wall. It is reasonably accurate only in the range 15–85% relative humidity.

The wet and dry bulb hygrometer. The dry bulb measures the actual temperature, whereas the wet bulb measures a lower temperature as a result of the cooling effect of evaporation of water. The rate of vaporization is related to the humidity of the ambient gas and the difference between the two temperatures is a measure of ambient humidity; the relative humidity is obtained from a set of tables.

Regnault’s hygrometer. This consists of a thin silver tube containing ether and a thermometer to show the temperature of the ether. Air is pumped through the ether to produce evaporation, thereby cooling the silver tube. When gas in contact with the tube is saturated with water vapour, it condenses as a mist on the bright silver. The temperature at which this takes place is known as the dew point, from which relative humidity is obtained from tables.

Humidification of the Respiratory Tract

Air drawn into the respiratory tract becomes fully saturated with water in the trachea at a temperature of 37 °C. Under these conditions, the SVP of water is 6.3 kPa (47 mmHg); this represents a fractional concentration of 6.2%. The concentration of water is 44 mg L^–1. At 21 °C, saturated water vapour contains 2.4% water vapour or 18 mg L^–1. Thus, there is a considerable capacity for patients to lose both water and heat when the lungs are ventilated with dry gases.

There are three means of humidifying inspired gas:

heated humidifier (water vaporizer)

nebulizer

condenser humidifier (also known as heat and moisture exchanging [HME] humidifier).

The hot water bath humidifier is a simple device for heating water to 45–60 °C. These devices have several potential problems, including infection if the water temperature decreases below 45 °C, scalding the patient if the temperature exceeds 60 °C (these high temperatures may be used to prevent growth of bacteria) and condensation of water in the inspiratory anaesthetic tubing. These devices are approximately 80% efficient.

Some nebulizers are based upon a Venturi system; a gas supply entrains water, which is broken up into a large number of droplets. The ultrasonic nebulizer operates by dropping water onto a surface, which is vibrated at a frequency of 2 MHz. This breaks up the water particles into extremely small droplets. The main problem with these nebulizers is the possibility that supersaturation of inspired gas may occur and the patient may be overloaded with water.

The condenser humidifier (or artificial nose) may consist of a simple wire mesh, which is inserted between the tracheal tube and the anaesthetic breathing system. More recently, humidifiers constructed of rolled corrugated paper have been introduced. These devices are approximately 70% efficient.

SOLUBILITY OF GASES

Henry’s law states that, at a given temperature, the amount of a gas which dissolves in a liquid is directly proportional to the partial pressure of the gas in equilibrium with the liquid. If a liquid is heated and its temperature rises, the partial pressure of its saturated vapour increases. This will result in gas molecules coming out of solution, and a lesser amount of gas remaining dissolved in the liquid. This is exemplified by the carbon dioxide bubbles in a bottle of tonic water becoming more apparent as time elapses from its removal from the refrigerator.

It is customary to confine the term ‘tension’ to the partial pressure of a gas exerted by gas molecules in solution, but the terms are synonymous. The tension of the gas in solution is in equilibrium with the partial pressure of the gas above it. A relatively insoluble gas will reach equilibrium more quickly than a soluble one.

Solubility Coefficients

The Bunsen solubility coefficient is the volume of gas which dissolves in a unit volume of liquid at a given temperature when the gas in equilibrium with the liquid is at a pressure of 1 atmosphere.

The Ostwald solubility coefficient is the volume of gas which dissolves in a unit volume of liquid at a given temperature. Thus, the Ostwald solubility coefficient is independent of pressure.

The partition coefficient is the ratio of the amount of substance in one phase compared with a second phase, each phase being of equal volume and in equilibrium, e.g. the amount of carbon dioxide in the gas phase compared with the amount of carbon dioxide dissolved in blood. As with the Ostwald coefficient, it is necessary to define the temperature but not the pressure. The partition coefficient may be applied to two liquids, but the Ostwald coefficient applies to partition between gas and liquid. The blood/gas partition coefficient of an anaesthetic agent is an indicator of the speed with which the alveolar gas concentration equilibrates with the inspired concentration, a low coefficient (e.g. desflurane 0.42) leading to rapid equilibration. The oil/gas partition coefficient is a measure of its potency, a high coefficient (e.g. isoflurane 98.5) indicating an agent highly soluble in cerebral tissue, leading to high anaesthetic potency and low MAC. The Overton-Meyer hypothesis shows an inverse relationship between MAC and the logarithm of lipid potency.

Diffusion

If two different gases or liquids are separated in a container by an impermeable partition which is then removed, gradual mixing of the two different substances occurs as a result of the kinetic activity of each species of molecule. This is illustrated in Figure 14.15. The principle governing this process is described by Fick’s law of diffusion, which states that the rate of diffusion of a substance across unit area is proportional to the concentration gradient. Graham’s law (which applies to gases only) states that the rate of diffusion of a gas is inversely proportional to the square root of its molecular weight or density.

FIGURE 14.15 Illustration of diffusion in fluids. (A) Fluids X and Y separated by partition. (B) Mixing of fluids after removal of partition.

In the example shown in Figure 14.15B, the interface between fluids X and Y immediately after removal of the partition would be the interface between the two species of fluid. In biology, however, there is normally a membrane separating gases or separating gas and liquids.

The rate of diffusion of gases may be affected by the nature of the membrane. In the lungs, the alveolar membrane is moist and may be regarded as a water film. Thus, diffusion of gases through the alveolar membrane is dependent not only on the properties of diffusion described above but also on the solubility of gas in the water film. As carbon dioxide is more highly soluble in water than oxygen, it diffuses more rapidly across the alveolar membrane, despite the larger partial pressure gradient for oxygen.

Osmosis

In the examples given above, the membranes are permeable to all substances. However, in biology, membranes are frequently semipermeable, i.e. they allow the passage of some substances but are impermeable to others. This is illustrated in Figure 14.16. In Figure 14.16A, initially equal volumes of water and glucose solution are separated by a semipermeable membrane. Water molecules pass freely through the membrane to dilute the glucose solution (Fig. 14.16B). This process continues until the volume of the diluted glucose solution supports a significantly greater head of fluid pressure than the water volume on the other side of the membrane. This hydrostatic pressure opposes the flow of water molecules through the membrane into the glucose solution, driven by the difference in solution constituents. This driving pressure is termed the osmotic pressure. Note that, depending on the membrane properties, the glucose molecules are probably too large to allow significant flow in the opposite direction. By application of a hydrostatic pressure on the glucose side (Fig. 14.16C), the process of further transfer of water molecules can be prevented or even reversed; this pressure (P) is equal to the osmotic pressure exerted by the glucose solution.