The physical principle
Why some gases absorb infrared and others cannot
What you should already have
About 80 minutes
Plus the time it takes to redraw this lesson’s figures from memory, which is the fastest way to find out what you have not understood.
Where this shows up
Capnography is the monitor that confirms the tube is in the trachea, and there is no substitute for it in that moment. This lesson covers how the measurement is actually made, every way the reading can be wrong, and what each shape of the trace means.
Learning outcomes
By the end of this lesson you should be able to:
- State which gases absorb infrared and which cannot, and explain the molecular property that decides it.
- State the Beer–Lambert relationship with every symbol defined, and separate its two component laws.
- Describe how a capnometer measures carbon dioxide, and distinguish that from how gas is delivered to the analyser.
- Compare sidestream with mainstream sampling on delay, water handling, dead space and which gases can be measured.
- Describe zeroing and calibration, and give each source of error with its mechanism, the direction of the error and its remedy.
- Draw a normal capnogram with labelled and scaled axes, four numbered phases, the end-tidal point and the α and β angles.
- Interpret abnormal traces, and quote the normal end-tidal value and the arterial to end-tidal gradient in both units.
- Describe paramagnetic, fuel cell and polarographic oxygen analysis, and the physiological effects of hypercarbia.
Together these settle 5 syllabus objectives: Infrared absorption and the Beer–Lambert law; Capnometer design, sampling, calibration and error; The capnogram, and the arterial to end-tidal gradient; Paramagnetic, fuel cell and polarographic oxygen analysis and Hypoxia, hyperoxia, hypercapnia, respiratory inadequacy and failure. Tick them on the Clinical measurement objective list once you can do all of the above without notes.
A molecule absorbs infrared radiation only if its vibration changes its dipole moment — that is, only if the distribution of charge across the molecule is asymmetrical or becomes asymmetrical as the bonds stretch and bend. Carbon dioxide, nitrous oxide, water vapour and the halogenated volatile agents all satisfy this. Oxygen, nitrogen and helium do not: they are elementary or symmetrical, have no dipole moment, and are effectively transparent to infrared.
Where each gas absorbs
| Gas | Absorbs infrared at | Band used clinically | Why it matters |
|---|---|---|---|
| Carbon dioxide | 4.26 µm | Narrow band, 4.2–4.3 µm | The working wavelength of every theatre capnometer |
| Nitrous oxide | 4.5 µm (also absorbs near 4.3 µm) | Separate band | Spectral overlap and collision broadening both cause CO₂ over-reading |
| Volatile agents | 3.3 µm (C–H bond stretching) | 3.3 µm, with several bands used for agent identification | All the modern agents share this band, so identification needs more than one wavelength |
| Water vapour | Broad absorption across the infrared | Removed rather than measured | Condensation and vapour are a source of error, not a signal |
| Oxygen, nitrogen, helium | None | Not measurable by infrared | Elementary and symmetrical: no dipole moment, so no infrared absorption |
The Beer–Lambert law
Infrared light of the chosen wavelength is passed through a chamber of known path length containing the sample. The transmitted intensity falls exponentially with both the concentration of the absorbing gas and the distance the light travels through it.
- I — transmitted intensity reaching the detector
- I₀ — incident intensity leaving the source
- ε — the extinction coefficient (molar absorptivity): how strongly one mole of this particular gas absorbs at this particular wavelength, in L·mol⁻¹·cm⁻¹. It is a fixed property of the molecule, not of the sample or the instrument, and it is the term that makes the method gas-specific — carbon dioxide has a large ε at 4.26 µm and a negligible one elsewhere, which is exactly why a narrow optical filter can pick it out of a mixture. A gas with ε = 0 at the chosen wavelength, such as oxygen, cannot be measured this way at all.
- c — concentration of the absorbing gas, the quantity being measured
- l — path length through the sample chamber, fixed by the design
The two component laws are worth separating, because each states something different. Beer's law states that absorption is proportional to the concentration of the absorbing substance. Lambert's law states that absorption is proportional to the path length. Combined, the energy absorbed from the narrow infrared band passing through the chamber is proportional to the number of absorbing carbon dioxide molecules present. Concentration is then obtained by comparing the measured absorbance with that of a known calibration standard.
Instrument design
Inside the capnometer, and where you attach it
Components of the optical bench
- Infrared source — a heated element emitting a broad infrared spectrum.
- Optical filter, or a rotating filter wheel, selecting the narrow 4.2–4.3 µm band. Selectivity here determines how much nitrous oxide interference gets through.
- Sample chamber of fixed path length, with sapphire windows. Ordinary glass cannot be used because glass itself absorbs infrared.
- Reference path or reference cell, containing a gas that does not absorb at the chosen wavelength, so the analyser measures a ratio rather than an absolute intensity and is insensitive to drift in the source.
- Photodetector and processor, converting transmitted intensity to a displayed concentration or partial pressure.
Sidestream against mainstream
| Sidestream | Mainstream | |
|---|---|---|
| Where the analyser sits | Remote from the patient; gas is aspirated to it | In the breathing system at the airway |
| Sampling | 50–200 mL/min drawn through fine-bore tubing | No gas removed; the chamber is part of the circuit |
| Delay | Transit delay of roughly 2–4 s, plus the analyser rise time | Effectively real time |
| Weight at the airway | Light — only the sampling line | Heavier cuvette, with drag and disconnection risk |
| Water and secretions | Water trap and filter required; the line can block or kink | Cuvette heated to about 40 °C to prevent condensation; windows can be soiled |
| Dead space | Negligible added dead space | Adds apparatus dead space, which matters in neonates |
| Other gases | The same sample can be analysed for O₂, N₂O and volatile agents | Usually carbon dioxide alone |
| Non-intubated patient | Usable through nasal cannulae or an oxygen mask | Not usable without an airway device |
| Main drawback | Delay, blockage, gas removal from the circuit in low-flow or paediatric use | Bulk at the airway, cost of the cuvette, cleaning |
Performance and error
Calibration, response time and the ways the reading goes wrong
Zeroing and calibration
The analyser is zeroed against a carbon dioxide-free gas, usually room air, which sets the value of I₀ and compensates for gradual soiling of the windows and ageing of the source. It is calibrated against a gas mixture of known carbon dioxide concentration, which sets the scale. Zeroing corrects the offset; calibration corrects the gain. Both are needed.
Response time
The total delay between gas leaving the alveolus and the number changing on the screen is the transit time along the sampling line plus the rise time of the analyser itself, conventionally the time to move from 10% to 90% of a step change. If that total approaches the duration of expiration, the plateau is never reached and end-tidal carbon dioxide is under-read. This is why neonatal and high-respiratory-rate monitoring is the setting where sidestream sampling most often fails.
Sources of error
| Source | Mechanism | Effect on the reading | Remedy |
|---|---|---|---|
| Collision (pressure) broadening | Nitrous oxide and oxygen broaden the CO₂ absorption peak, so more infrared is absorbed than the CO₂ concentration alone would explain | Over-reading of carbon dioxide | Modern analysers correct automatically once the gas mixture is entered or measured |
| Overlapping absorption spectra | Nitrous oxide also absorbs close to the CO₂ band | Over-reading | Narrow, well-selected optical filters; multi-wavelength correction |
| Water vapour and condensation | Water absorbs infrared broadly and droplets scatter it | Unpredictable error; blocked sampling line | Water trap, hydrophobic filter, heated cuvette, Nafion tubing |
| Soiled or scratched windows | Reduced transmitted intensity is read as absorption | Over-reading and drift | Cleaning and regular zeroing |
| Leak or kink in the sampling line | Entrained room air dilutes the sample | Under-reading and a damped, blunted waveform | Inspect the line and the connections; check the water trap |
| Excessive sampling rate | Fresh gas is entrained during expiration, particularly at small tidal volumes | Under-reading, loss of the plateau | Reduce the sample flow in paediatric and low-flow use |
| Slow response or long transit time | Rise time plus transit time exceeds the duration of expiration | Plateau never reached; under-reading at high respiratory rates | Short, wide-bore sampling line; mainstream sampling in neonates |
| Barometric pressure | The analyser measures partial pressure but may display volumes per cent | Apparent discrepancy at altitude or under hyperbaric conditions | State which quantity is displayed; pressure compensation |
Interactive figure
The capnogram
Select a phase to see what gas is being sampled and why the trace has that shape, then switch to the abnormal traces and read each one as a deviation from the normal waveform held behind it.
Four phases, two angles, one end-tidal point
Select a phase above. The marks in this question are labelling marks, so practise naming each part in order: phase I dead-space gas, phase II mixing upstroke, phase III alveolar plateau, the end-tidal point at the end of that plateau, and phase IV the inspiratory downstroke.
Reading the waveform
The normal capnogram, phase by phase
| Phase | What it is | Gas being sampled | Shape |
|---|---|---|---|
| Phase I | Start of expiration | Carbon dioxide-free gas from the conducting airways — the anatomical dead space | Flat, on a zero baseline |
| Phase II | Mixing upstroke | Dead-space gas mixing with arriving alveolar gas | Rapid S-shaped rise |
| Phase III | Alveolar plateau | Carbon dioxide-rich gas from the alveoli | Near-horizontal with a slight upslope; end-tidal carbon dioxide is the value at its end |
| Phase IV | Inspiratory downstroke | Fresh gas washing the sampling point | Turns through almost a right angle and falls rapidly to baseline |
The slight upslope of phase III is real and is worth explaining rather than drawing flat: alveoli with longer time constants and lower ventilation–perfusion ratios empty later in expiration and carry more carbon dioxide, so the concentration creeps upward across the plateau.
The two angles
- α angle — between phases II and III, normally about 100–110°. It increases with obstruction to expiratory flow and with ventilation–perfusion mismatch.
- β angle — between phase III and the inspiratory downstroke, normally about 90°. It increases with rebreathing.
Normal values
| Quantity | kPa | mmHg | Comment |
|---|---|---|---|
| PaCO₂ | 4.7–6.0 kPa | 35–45 mmHg | Arterial partial pressure |
| PETCO₂ | 4.0–5.3 kPa | 30–40 mmHg | End of the alveolar plateau |
| Pa–ETCO₂ gradient | 0.3–0.7 kPa | 2–5 mmHg | Widens with alveolar dead space |
| Mixed venous PCO₂ | 6.1 kPa | 46 mmHg | Reference point on the CO₂ dissociation curve |
| CO₂ production | ≈ 200 mL/min | — | Resting adult; rises with metabolic rate |
Why end-tidal carbon dioxide is lower than arterial
The arterial to end-tidal difference exists because alveolar dead space — alveoli that are ventilated but not perfused — contributes carbon dioxide-free gas to the expirate and dilutes the alveolar sample. In a healthy anaesthetised adult the gradient is small and reasonably stable, which is what makes end-tidal carbon dioxide a useful surrogate for arterial carbon dioxide.
It becomes unreliable exactly when the gradient changes. It widens with hypovolaemia, reduced cardiac output, pulmonary embolism, high airway pressures or excessive positive end-expiratory pressure, chronic lung disease, increasing age and the upright posture. In those situations a falling end-tidal value does not mean a falling arterial value — it may mean the opposite.
Pattern to mechanism
Abnormal traces, and what capnography is actually for
A diagnostic sequence that works under pressure
- Is there a waveform at all? No waveform is an airway or circulatory emergency: disconnection, oesophageal intubation, total obstruction, apnoea or cardiac arrest.
- Does the baseline reach zero? A raised baseline is rebreathing — exhausted absorbent, an incompetent valve or inadequate fresh gas flow.
- Is there a true plateau? An upsloping, shark-fin expiratory limb with a widened α angle is obstruction to expiratory flow.
- Is the height right? Normal shape with a changed height is a ventilation, circulation or production problem — and the direction and speed of change separate them.
- Is anything superimposed? A single notch is patient effort; small regular ripples at the cardiac rate are cardiogenic oscillations.
Causes of a raised end-tidal carbon dioxide
Organise these by mechanism rather than listing them at random. The three-way split is what makes the list explanatory, and it stops a single category standing in for the whole.
| Mechanism | Causes |
|---|---|
| Increased endogenous production | Malignant hyperthermia · thyroid storm · phaeochromocytoma · neuroleptic malignant syndrome · sepsis · fever · shivering · seizures · light anaesthesia · overfeeding, particularly a high carbohydrate load · release of a limb tourniquet or reperfusion of an ischaemic bed · a rise in cardiac output delivering more carbon dioxide to the lungs, including return of spontaneous circulation |
| Exogenous carbon dioxide load | Carbon dioxide insufflation during laparoscopy, worse with extraperitoneal insufflation · sodium bicarbonate administration · transfusion of stored blood |
| Reduced elimination | Hypoventilation from opioids, volatile agents, residual block, inadequate set minute ventilation, high spinal or neuromuscular disease · increased physiological or apparatus dead space · rebreathing from an exhausted absorber, an incompetent valve or inadequate fresh gas flow · airway obstruction and bronchospasm · reduced functional residual capacity from pneumoperitoneum or head-down positioning · chronic obstructive pulmonary disease |
| Artefact | Collision broadening by nitrous oxide · an uncalibrated or unzeroed analyser · soiled windows |
The clinical roles of capnography
| Role | What the waveform gives you |
|---|---|
| Confirming tracheal intubation | A sustained waveform over six breaths. The most important single use, and the standard of care. |
| Continuous airway monitoring | Detects disconnection, extubation, obstruction and circuit failure earlier than any other monitor. |
| Adequacy of ventilation | Continuous trend of hypo- and hyperventilation between blood gases. |
| Adequacy of circulation | A fall in end-tidal carbon dioxide with an unchanged ventilation reflects reduced pulmonary blood flow. |
| Cardiopulmonary resuscitation | Guides compression quality and signals return of spontaneous circulation. |
| Diagnosis of the breathing system | A raised baseline identifies rebreathing; a shark fin identifies obstruction. |
| Metabolic monitoring | A progressive unexplained rise is the earliest sign of malignant hyperthermia. |
| Depth of block and patient effort | A curare cleft signals returning spontaneous respiratory effort. |
| Sedation and recovery | Nasal capnography detects apnoea and airway obstruction earlier than pulse oximetry. |
Alternatives and their place
Other ways to measure carbon dioxide
- Severinghaus electrode. Carbon dioxide diffuses across a carbon dioxide-permeable membrane into a thin film of bicarbonate solution, where it forms carbonic acid and dissociates. The resulting change in hydrogen ion concentration is measured by a glass pH electrode; a tenfold change in carbon dioxide partial pressure produces approximately one unit of pH change. This is how a blood gas analyser measures PCO₂ in blood, not in gas.
- Colorimetric detector. A pH-sensitive dye — classically metacresol purple — changes from purple to yellow in the presence of carbon dioxide. It is a disposable qualitative device for confirming tracheal placement when no capnograph is available. It gives no waveform, no number and no trend, and it is unreliable after gastric insufflation or contamination with gastric contents.
- Mass spectrometry. Sample gas is ionised and the ions are separated by mass-to-charge ratio in a magnetic field. It can identify and quantify every gas in the mixture, is highly accurate, but is expensive and bulky and has largely disappeared from clinical use.
- Raman spectroscopy. A laser illuminates the sample and a small proportion of scattered light is shifted in wavelength by an amount characteristic of each molecule. It can measure oxygen and nitrogen as well, but the equipment is large and no longer in routine theatre use.
- Photoacoustic spectroscopy. Pulsed infrared radiation is absorbed by the gas, causing cyclical heating, expansion and a pressure wave that a microphone detects as sound. It is fast, stable and needs no optical detector, and it appears in some multi-gas analysers.
The gas infrared cannot see
Oxygen analysis
| Method | Principle | Strengths | Limitations |
|---|---|---|---|
| Paramagnetic analysis | Oxygen has two unpaired electrons in its outer shell and is attracted into a magnetic field. In a differential paramagnetic cell, a rapidly switched magnetic field acting on the sample and a reference gas produces a pressure difference across a transducer, proportional to the difference in oxygen partial pressure. | Fast, accurate, no consumable element, continuous breath-by-breath display | Water vapour must be removed; nitric oxide is also paramagnetic and interferes |
| Fuel cell (galvanic cell) | Oxygen diffuses through a membrane to a gold cathode and is reduced; a lead anode is oxidised in potassium hydroxide. The current generated is proportional to the oxygen partial pressure. No external polarising voltage is required. | Simple, self-powered, cheap; widely used as a circuit oxygen monitor | Consumed in use with a finite life; slow response of roughly 20–30 s; temperature dependent |
| Polarographic (Clark) electrode | A platinum cathode and a silver/silver chloride anode in potassium chloride, behind an oxygen-permeable membrane, with an external polarising voltage of about 0.6 V. Oxygen is reduced at the cathode (O₂ + 2H₂O + 4e⁻ → 4OH⁻) and the current is proportional to the oxygen partial pressure. | Measures PO₂ in blood as well as in gas; the reference method in a blood gas analyser | Needs a polarising voltage and regular calibration; membrane and electrolyte deteriorate; temperature dependent |
| Pulse oximetry | Measures oxygen saturation of haemoglobin, not partial pressure, from the differential absorption of red and infrared light by oxyhaemoglobin and deoxyhaemoglobin in pulsatile blood. | Non-invasive and continuous | Not a measure of oxygen tension, content or delivery; unreliable with poor perfusion, dyshaemoglobins and motion |
Completing the multi-gas analyser
Volatile agent analysis
| Method | Principle | Current status |
|---|---|---|
| Infrared absorption | All modern volatile agents contain C–H bonds and absorb strongly near 3.3 µm. Measuring at several wavelengths allows the analyser both to quantify the agent and to identify which agent is present. | The standard method in current anaesthetic machines |
| Refractometry | The agent alters the refractive index of the gas mixture, producing an interference pattern. | Historically used for calibrating vaporisers rather than for monitoring |
| Ultraviolet absorption | Halothane absorbs ultraviolet light; other agents do so weakly. | Effectively obsolete |
| Piezoelectric quartz crystal | A lipophilic coating on an oscillating quartz crystal absorbs the agent; the added mass lowers the resonant frequency. | Cannot distinguish between agents |
| Mass spectrometry and Raman spectroscopy | Ionised or scattered light gives a spectrum from which every gas in the mixture can be identified and quantified. | Accurate but expensive, bulky and no longer used in routine theatre practice |
All the agents in current use are halogenated hydrocarbons or ethers containing C–H bonds, so they all absorb near 3.3 µm. A single-wavelength analyser can therefore tell you how much agent is present but not which agent it is — and since the minimum alveolar concentration of desflurane is roughly fifteen times that of isoflurane, an analyser that misidentifies the agent will report a dangerously misleading depth. Modern analysers sample several wavelengths and match the resulting absorption pattern against known spectra to identify the agent before quantifying it.
From measurement to physiology
The physiological effects of hypercarbia
The chemistry underneath
Carbon dioxide raises hydrogen ion concentration by spontaneous and carbonic anhydrase-catalysed hydration:
Carbon dioxide also reacts with free amine groups in proteins to form carbamate compounds. At cellular level it diffuses readily across cell membranes and generates carbonic acid and hydrogen ions inside the cell, but intracellular buffering is rapid, reaching about 90% completion within three hours of the onset of hypercarbia. The resulting pH follows the Henderson–Hasselbalch relationship:
As rules of thumb for the exam: in acute respiratory acidosis pH falls by approximately 0.08 for every 10 mmHg (1.33 kPa) rise in PaCO₂, and bicarbonate rises by about 1 mmol/L. With chronic hypercarbia, renal compensation raises bicarbonate by about 4 mmol/L for each 10 mmHg, over two to three days.
System by system
| System | Mechanism | Effect | Qualifier worth stating |
|---|---|---|---|
| Cardiovascular | Increased sympathetic discharge with raised plasma adrenaline and noradrenaline | Increased contractility, cardiac output, heart rate and blood pressure; increased risk of arrhythmias; systemic vasodilatation with warm flushed peripheries and a bounding pulse | Direct effects of carbon dioxide and acidaemia on the myocardium and vascular smooth muscle are depressant and vasodilatory. At severe levels the direct depression dominates and cardiac output falls. |
| Central nervous system | Cerebral vasodilatation; direct narcotic effect at high tensions | Increased cerebral blood flow and intracranial pressure, lowered seizure threshold, headache, confusion, drowsiness and eventually carbon dioxide narcosis | Carbon dioxide crosses the blood–brain barrier freely whereas bicarbonate does not, so acute changes act rapidly on the central chemoreceptors. |
| Respiratory | Stimulation of central and peripheral chemoreceptors | Increased minute ventilation, mainly through tidal volume; bronchodilatation; enhanced hypoxic pulmonary vasoconstriction with improved ventilation–perfusion matching; increased pulmonary vascular resistance | Volatile agents flatten the ventilatory response to carbon dioxide and shift the apnoeic threshold, which is why hypercarbia is common under anaesthesia. |
| Oxygen transport | Bohr effect | Rightward shift of the oxyhaemoglobin dissociation curve, reducing haemoglobin affinity and favouring tissue unloading; the Haldane effect assists carbon dioxide offloading in the lung | If the inspired oxygen fraction is fixed, a rising PaCO₂ lowers alveolar PO₂ through the alveolar gas equation. |
| Metabolic and renal | H⁺/K⁺ exchange; renal compensation over days | Hyperkalaemia; increased ionised calcium; increased renal bicarbonate reabsorption and hydrogen ion excretion over two to three days | Intracellular buffering is rapid, reaching about 90% completion within three hours of the onset of hypercarbia. |
| Other | Immunomodulatory effects of hypercapnic acidosis | Dampening of neutrophil and cytokine-mediated lung injury; sweating, agitation and muscle twitching; increased uterine blood flow | These protective effects are part of the rationale for permissive hypercapnia in acute respiratory distress syndrome. |
And the mirror image: hypocarbia
- Cerebral vasoconstriction with reduced cerebral blood flow — useful briefly to reduce intracranial pressure, harmful if sustained because it risks cerebral ischaemia. This is why routine prolonged hyperventilation is no longer recommended after head injury.
- Leftward shift of the oxyhaemoglobin dissociation curve, increasing haemoglobin affinity and impairing tissue unloading.
- Hypokalaemia and reduced ionised calcium, with paraesthesiae, tetany and a positive Chvostek sign in the awake patient.
- Reduced cardiac output at extremes, coronary vasoconstriction and arrhythmias.
- Apnoea in the anaesthetised patient once PaCO₂ falls below the apnoeic threshold.
- Inhibition of hypoxic pulmonary vasoconstriction, worsening ventilation–perfusion matching.
Reading the trace
Drawing a capnogram, and what has to be on it
The drawing checklist
- y-axis: PCO₂ in mmHg or kPa, with the unit written
- x-axis: time in seconds
- Baseline sitting on zero
- All four phases numbered
- End-tidal point marked at the end of phase III
- Expiration and inspiration indicated
- α and β angles labelled with their normal values
- What gas each phase represents
- Why phase III slopes slightly upward
- Normal ETCO₂ in both units
- The arterial to end-tidal gradient, and what widens it
- One sentence on what each angle indicates
The three past questions this topic has been set from, with their answers worked in full, are in the question bank: defining and measuring end-tidal carbon dioxide, how a capnometer measures it and the types of capnography and their role in practice.