Physics for anaesthesia

Learning objectives.

By reading this article you should be able to:

• •Describe the physical principles of magnetic resonance imaging
• •Discuss the principles of depth of anaesthesia monitoring, in particular bispectral index and evoked potentials
• •Explain the principles of LASERs and apply these to their safe use in the surgical environment
• •Compare the different uses of light spectroscopy in patient monitoring

Key points.

• •Magnetic resonance imaging is a powerful diagnostic technique but the powerful magnetic fields used can be hazardous to the patient, the anaesthetist, and anaesthetic equipment.
• •Lasers have a number of surgical applications and associated potential risks to patients and operating room staff.
• •The algorithm of bispectral (BIS) depth of anaesthesia monitors analyse the phase relationships (bispectral index), burst suppression ratio, and power spectrum in different wavebands.
• •Light spectroscopy has several applications in anaesthesia, including pulse oximetry and gas and vapour analysis, but has some limitations.

This article will discuss the applied physics relevant to anaesthetic practice in four areas, some of which are of relatively recent application in anaesthesia and medicine: these are magnetism and magnetic resonance; lasers; depth of anaesthesia monitoring; and light spectroscopy.

Magnetism and magnetic resonance

Applications of magnetism in anaesthetic practice

Traditionally we think of magnetic fields in a macroscopic sense, as a phenomenon, which links electricity and mechanical movement. A magnetic field can be used to provide mechanical force from electric current in a motor, or vice versa in a generator. It induces an opposing voltage in a current carrying wire, proportional to the rate of change of the current; this is the basis of an electrical inductance, which is thus relevant only in AC. Magnetic flux density in such a field can be intensified if the wire is wrapped into a coil, the core of which can be air or iron. Two such coils of wire wrapped on opposite sides of the same enclosed metallic core make a transformer, used for changing voltages, and as a way of isolating two electrical circuits from each other. In a mass spectrometer, molecules in a gas mixture are ionised and separated in a magnetic field according to their molecular mass, and this is used to identify components in a gas mixture. Separation of components assumes the same degree of ionisation, which does not always occur; identification depends on gas species not having the same molecular masses, although this problem can be overcome by looking more widely within the mass spectrum for those that do (e.g. CO₂ and N₂O: 44 Da; O₂ and CO: 28 Da).

However, magnetic fields can be thought of in a microscopic way too. Most molecules are repelled by a magnetic field (diamagnetic), but two gaseous molecules, oxygen and nitric oxide, are attracted into the field (paramagnetic), because of the presence of an unpaired electron in the outer molecular shell; typically this enables oxygen concentrations to be analysed in anaesthesia. Using the electromagnetic properties of atoms within a magnetic field and achieving nuclear magnetic resonance forms the basis of the magnetic resonance imaging (MRI) scanner.

MRI

All atoms spin about an axis, and if they have an associated electrical charge, this spin causes a magnetic field around the atom, as if the atom itself were a bar magnet. Macroscopically, the directions of axes of spin are randomly directed, so there is usually no overall associated magnetic field, unless for example, a small magnetic field is applied to a ferromagnetic body; or if a magnetised body is put into an even smaller magnetic field, such as the Earth's 50 μT field, when it aligns itself with the field.

The hydrogen atom, the proton, is ubiquitous in the body, for example in molecules of water, and is a very simple atom, so it is used to form an image in MRI scanners. If a very large external magnetic field, B₀, usually between 1 and 3 Tesla in an MRI scanner, is applied to a substance, the individual, spinning, magnetised atoms orientate themselves parallel to that field. Most of the atoms line up parallel to the field, with the ‘north pole’ pointing in the same direction as the field. A smaller number is lined up in the opposite direction, with the north pole of the atom facing against the field, anti-parallel to it; this latter orientation is less stable, being associated with a higher energy level. These spinning atoms are also precessing (Fig. 1), that is, their axis of spin is wobbling about the axis vector of the applied magnetic field, much as a top spinning within a gravitational field precesses until it falls over, or as the earth itself precesses as it spins on its own axis. The frequency of precession has a value, the Larmor frequency, which is characteristic of the atom and proportional to the strength of the applied magnetic field; for example, the proton has a Larmor frequency of 42.6 MHz, when a field of 1 Tesla is applied. In addition, each atom is precessing independently, out of phase with neighbouring atoms. Therefore, any signal detectable from the precession is overwhelmed by the larger field B₀, as it is nearly parallel to it and orders of magnitude smaller than it.

Fig 1.

Precession of the proton.

If another electromagnetic field is applied perpendicular to the first, and if its frequency corresponds to the precessing frequency, all the atoms precess together, and ‘nuclear magnetic resonance’ is said to have occurred. This transverse field is in the radiofrequency range, corresponding to the Larmor frequency of protons. The radiofrequency field is applied for just long enough, usually 1 ms, to allow all the atoms to realign themselves into the higher energy, anti-parallel orientation, and the precessing atoms, resonating together, give an amplified magnetic vector signal, perpendicular to the precession axis, which, because of its resonant strength and its direction, is now detectable by the radiofrequency receiver.

The magnetic signal is detectable after the radiofrequency field is removed, when two sorts of relaxation phase begin as most of the atoms realign themselves back to the original, parallel, low energy state, and in doing so release energy, which is detectable; moreover, they now begin to precess out of phase again. Different tissues have different characteristic relaxation times, which is what allows the MRI scanner to distinguish different tissues and give visual contrast. The T1, or spin-lattice relaxation time is because of atoms realigning to the low energy direction and giving energy to the surrounding atomic lattice; the T2, or spin-spin relaxation time is because of the precessing atoms giving spin energy to neighbouring atoms, which causes precession to de-resonate, or go out of phase. The relaxation times are measured in seconds or minutes.

The final mechanism within an MRI scanner is an additional magnetic field gradient along the axis of the patient, so that the precession (Larmor) frequencies also vary with location along this axis. In this way, the transverse radiofrequency field can be tuned to allow resonance to occur at slightly different frequencies for different ‘slices’ of the body, allowing better resolution of an image. These gradients can be applied in orthogonal directions (mutually perpendicular), allowing accurate three-dimensional representation of the tissue block. The reason a MRI scan takes so long is that, as the radiofrequency field is moved along the body part being examined, its frequency has to be changed to correspond to the local longitudinal magnetic field, in order to cause magnetic resonance. In order to allow a large field value B₀ of 1–3 Tesla to be developed in the main magnet, it has to be cooled to a very low temperature of −268.8°C, to make it superconducting, and allow electric current to flow through it with very low resistance. The orthogonal field gradient magnets are designed to be in the range of about 10⁻³ B₀ in each direction; this gives a very small gradient, but enough to provide localisation of tissues in magnetic resonance terms. The radiofrequency coils transmit the transverse resonating frequency, and receive the transverse signal from the resonating precessing atoms. Figure 2 shows the three sets of magnetic fields in an MRI scanner.

Fig 2.

Magnetic coils in MRI scanner.

The advantages of MRI scanning are that no ionising radiation is used and the technique is non-invasive, so it is relatively safe. It gives better imaging resolution of most tissues in three dimensions than, for example, computerised tomographic scanning. However, it cannot image tissues such as bone, where the protons are fixed in bone tissue, rather than being allowed to precess and resonate. It cannot be used in the presence of pacemakers, the function of which would be interfered with by the magnetic field. Unsecured metallic objects anywhere near the field become projectiles, and all anaesthetic and monitoring equipment needs to be made of non-ferromagnetic materials.

Lasers

Electrons can be considered as distributed in a number of concentric shells around the nucleus that have different energies. If electrons move from one level or shell to another, energy is consumed or liberated in steps or quanta; quanta of light are called photons.

If external energy in the form of a photon, above a certain threshold, is applied to the atoms of suitable gases, liquids or solids, the atoms absorb the photon of energy and leave the ‘ground state’ energy level (resting level) and achieve an ‘excited’ (higher energy) level (Fig. 3a). The level of excitation depends on the amount of applied energy being supplied by, for example, heat, light or electricity. In the excited state, the electrons move to higher energy orbits, further away from the nucleus. Once an electron moves to a higher energy orbit, its tendency is to eventually spontaneously lose energy and return to the ground state (Fig. 3b). When this happens, it releases a photon of light energy. This process is spontaneous emission, and the light emitted from such a material may be of narrow bandwidth, but not necessarily of single wavelength, and the energy released from different atoms in the material is not in phase. This process forms the basis of fluorescence.

Fig 3.

Photons and atoms: (a) photon absorption; (b) spontaneous emission of photon; (c) stimulated emission of photons.

To achieve ‘stimulated emission’, energised electrons act as energy sources for neighbouring atoms to achieve the same state. If a photon of energy from a stimulated atom in a homogeneous medium interacts with an identical neighbouring stimulated atom, then when the latter relaxes, it releases two identical photons of energy as light of a wavelength specific to that medium, and in phase with each other (Fig. 3c). When a sufficient number of atoms are energised and there is a majority of atoms with electrons in the higher energy state, ‘population inversion’ is said to have occurred. Laser light, created from stimulated emission, has the following properties:

• (i)the light is monochromatic—it contains one specific wavelength;
• (ii)the light released is coherent—all the wavelengths are in phase;
• (iii)the light is highly directional, collimated.

Laser is an acronym: Light Amplification by Stimulated Emission of Radiation. The laser is a device which amplifies the way the energised atoms release photons. In any type of laser, the lasing medium, which gives the laser its wavelength or colour, is ‘pumped’ with energy to get the atoms into an excited state. Typically, intense flashes of light or electrical discharges pump the lasing medium and energise a large number of atoms to put their electrons in the excited state to cause stimulated emission as described above. To further amplify the amount of energy available, and to allow resonance to occur to achieve stimulated emission, the laser device has a pair of mirrors, one at each end of the lasing medium. The photons reflect off the mirrors to travel back and forth through the lasing medium, constantly stimulating other electrons to make the downward energy jump to release photons, and a cascade effect occurs. One of the mirrors is not completely silvered, so that at the appropriate density of light, the laser light will be allowed through the mirror. To give an example, Figure 4 illustrates how a ruby laser works. An energy source (pump), such as from a high intensity flash from a mercury vapour discharge lamp, emits radiation into the ruby rod. The light excites atoms in the ruby and some of these atoms emit photons of energy as they fall back to the lower shell. Some of these photons run in a direction parallel to the ruby's axis, as they are reflected by the mirrors. As they pass through the crystal, they stimulate emissions in other atoms and a cascade effect occurs.

Fig 4.

LASER.

There are many types of laser and the medium can be solid, liquid, gas, or semiconductor. Examples are:

• (i)solid state lasers, for example, ruby with a wavelength of 694.3 nm;
• (ii)gas lasers, for example, CO₂ [far infrared (IR)] 10 600 nm;
• (iii)dye lasers; complex organic dyes in liquid solution; they are tunable between 570 and 630 nm;
• (iv)semiconductor lasers; low power, current through PN (semiconductor) junction.

The laser can be classified into four groups of energy output:

• (i)Class 1: these lasers cannot emit laser radiation at known hazard levels;
• (ii)Class 2: these are low-power visible lasers, at a radiant power not above 1 mW;
• (iii)Class 3: these are intermediate and moderate power lasers, and are hazardous only if the beam itself is directly viewed;
• (iv)Class 4: these are high power lasers (>500 mW, continuous), which are hazardous to view and are also a skin hazard.

All biomedical applications of laser energy depend on tissue absorption. However, the particular response depends on where the absorption occurs. There are three ranges of radiant energy (IR, visible, and ultraviolet), which produce different tissue responses. IR induces molecular vibration, leading to heat effects. Visible light produces photochemical effects. Ultraviolet radiation can produce molecular bond dissociation and skin burns. CO₂ lasers are normally used for surgical applications, such as in gynaecology, and argon-ion gas lasers can be used for ophthalmology. Solid state lasers such as neodymium:yttrium-aluminium garnet (YAG) can be used for dermatology.

Depth of anaesthesia monitoring

Bispectral index monitoring

The EEG is a complex waveform, comprising many different frequencies and amplitudes, making analysis for useful monitoring purposes rather challenging. Most analysis techniques examine specific time periods, or epochs of EEG, usually in the range of 2–16 s, and the analysis can be presented in the time domain or the frequency domain. The epochs are converted by Fourier analysis into multiple individual sine waves. From quantification of the frequency spectrum in anaesthesia are obtained single indices, such as the median power frequency (MPF) and the spectral edge frequency (SEF); the MPF is the frequency value where 50% of the power spectrum is below (and above) that value and the SEF is where 95% of the power spectrum is below (Fig. 5). The MPF and SEF have been shown to have different values with different drugs and also to exhibit a biphasic effect, so their value on their own for depth of anaesthesia monitoring is limited.

Fig 5.

Power/frequency spectrum of EEG, showing median power frequency (MPF) and spectral edge frequency (SEF).

One measure, that attempts to eliminate this biphasic effect and get around the fact that different anaesthetic agents affect the EEG in different ways, is the bispectral index (BIS). This is a complex algorithm which produces an index between 0 (very unconscious) and 100 (very awake), and the BIS number is designed to be drug independent. The analysis involved in the algorithm is based on the measures already described, that is, frequency analysis and time-domain analysis, but is dominated by bispectral analysis. Bispectral analysis is a higher-order spectral analysis, that is to say, more complex than simple Fourier transformation, and is based on the phase relationships of individual frequency components to each other. Information hidden in the frequency spectrum can be brought out in the bispectral analysis, and identical frequency spectra can be produced by different brain processes, such as being awake or being anaesthetised. This is demonstrated in Figure 6, which shows a power spectrum which could have been produced by two different EEG processes. On the one hand, the spectrum can be considered to be produced by the summation of four dominant frequencies, 4 Hz, 6 Hz, 10 Hz, and 14 Hz, that is from four electrical generators having independent origins and phases (i.e. they are not coupled together). In contrast, it can be considered to be produced by the coupling of as few as two different frequency generators, say a 3 Hz and a 7 Hz generator. The effect of coupling will be to produce a spectrum consisting of the frequency sum of the two generators, the frequency difference, and the frequency doubled of each generator. The phases of these frequencies will be coupled together, and this is detectable by a BIS monitor. The spectra from the two different EEGs, which are apparently identical, will have been produced by different brain processes (e.g. awake and anaesthetised), but if the bispectra of both EEGs were calculated, they would be very different because of the very different phase relationships.

Fig 6.

Power/frequency spectrum of EEG, showing either uncoupled spectra from four independent frequency sources, or four phase coupled spectra from two sources.

In fact, because of the complexity of the EEG, the BIS monitor algorithm analyses a number of its features, not just the BIS spectrum itself. These include in the time domain, calculation of the ‘burst suppression ratio’, which represents periods of suppressed or isoelectric EEG activity during deep anaesthesia; in the frequency domain, these include the log ratio of the BIS described above of the 0.5–47 Hz and 40–47 Hz bandwidths, and the log ratio power of the 30–47 Hz and 11–20 Hz bandwidths.

Evoked potential monitoring

The cortical potentials so far described (EEG) are spontaneous, but another group of cortical potentials can be considered as evoked. A short external stimulus is enacted, which can be auditory, visual or somatosensory (electric shock or mechanical), and the EEG response is recorded. It is normally lower amplitude than the background EEG, and therefore submerged in it. This auditory evoked response consists of a number of characteristic waves, and it is the latency and amplitude of each wave that is of interest in terms of depth of anaesthesia.

Different waves in the evoked response come from different parts of the brain. For example, the first 10 ms of the auditory response come from the brainstem and the 10–50 ms period come from the auditory cortex. All three modalities, visual, auditory, and somatosensory, are affected by anaesthesia, but the auditory responses seem to be the best modality for anaesthesia monitoring—the brainstem part of the response is robust to anaesthesia, but the 10–50 ms period seem to change in a dose related manner.

Spectroscopy

Light spectroscopy is used in several monitoring techniques in anaesthesia.

Pulse oximetry

In oximetry, oxyhaemoglobin (HbO₂), deoxyhaemoglobin (HHb), and other haemoglobin species, have their own absorption spectra in the red to IR bandwidths. Pulse oximeters use light-emitting diodes of two different wavelengths to emit the light in a probe, usually 660 nm (red) and 940 nm (IR), and a photodetector to measure the residual amount of unabsorbed light, in order to compare the spectra of only two species, HbO₂ and HHb. The light is absorbed by all tissues in the light path (e.g. nail, skin, muscle, blood cells), and the software normalises all transmitted signals from non-pulsatile tissue, so that only the signals from pulsatile tissue (i.e. arterial blood) are measured and compared. Errors can occur with pulse oximetry if other haemoglobin species are present, such as COHb and MetHb; the former, which may be significantly present in smokers and patients who have undergone carbon monoxide poisoning, looks like HbO₂ in the red region, giving a higher oxygen saturation than actually exists; MetHb, caused by certain drugs such as methylene blue and nitrites, looks like HHb, and gives a falsely low oxygen saturation; the software will also be misled by pulsatile venous blood.

IR spectroscopy

Molecules, which contain two or more different atom species, absorb IR radiation, because of the nature of the bond between the dissimilar atoms. This property can be used to analyse gases such as carbon dioxide, nitrous oxide, and all anaesthetic vapours, but not oxygen or nitrogen. The absorption, A, of the IR light is related to the intensities of incident light I_i, the transmitted light I_t, the extinction coefficient ε, the path length L, and the concentration C of the absorbing medium by the Beer–Lambert law:

$$\mathrm{A}={\log }_{10}\frac{{\mathrm{I}}_{\mathrm{i}}}{{\mathrm{I}}_{\mathrm{t}}}=\mathrm{\epsilon }\mathrm{LC}$$ (1)

There are a number of sources of error in IR spectroscopy. The majority of absorption of IR for CO₂, N₂O, and CO is in the 4.3, 4.5, and 4.7 μm bands, respectively, although there is considerable overlap in the 3–5 μm range. Therefore, there is significant interference between the spectra of these three gases, particularly between CO₂ and N₂O in the 4.3 μm range. Another source of error is because of the phenomenon of collision broadening, where the absorption spectrum of one gas is actually broadened by the presence of another, because of intermolecular kinetic energy exchanges. Desflurane produces some error in an IR gas analyser, as does cyclopropane and alcohol. A further source of error with this device is related to the fact that its output signal is proportional to the number of molecules present (i.e. the partial pressure of the gas). Therefore, the pressure in the sample and reference cells and the ambient pressure are all important variables against which the device must be calibrated.

Raman spectroscopy

When light falls on an object, it is reflected and scattered by the object. Most of this scattering occurs without any loss of energy or change of wavelength and is known as Rayleigh scattering, which allows us to see the object with scattered waves in the visible spectrum. A small fraction of the incident light, about 10⁻⁶, is scattered with a loss of energy and a change of wavelength characteristic of the molecule off which the light is being reflected; this is Raman scattering, first observed in 1928 by the Indian physicist, after whom the technique is named. Raman spectroscopy has been used in industry for years as a means of identifying solids, liquids, or gases, but has had to await the advent of powerful laser light sources and sensitive photocell detectors to be useful in a clinical setting for breath-by-breath analysis. A Raman spectroscope incorporates an Argon laser source of wavelength 485 nm, high reflectance mirrors to concentrate the laser beam, a gas sampling chamber, appropriate optics, a detection system, and signal processor and display system. There are characteristic wavelength or frequency changes, which identify different gases. If plotted graphically, the amplitudes of the frequency shifted peaks are proportional to the gas concentrations. In Raman spectroscopy, each gas is independently analysed, including CO₂, N₂O, volatile agents, O₂, N₂, and water vapour.

Declaration of interest

None declared.

MCQs

The associated MCQs (to support CME/CPD activity) can be accessed at www.bjaed.org/cme/home by subscribers to BJA Education.

Biography

Patrick Magee PhD, FRCA is a consultant anaesthetist who worked previously at the Royal United Hospital Bath. He initially graduated in Engineering Science and Biomedical Engineering, and maintains these professional links through the British Standards Institute, the Royal Academy of Engineering, the Institute of Mechanical Engineering, and the University of Bath.

Matrix codes: 1A03, 2A04, 3I00