physics related to anaesthesia
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https://aneskey.com/basic-physics-for-the-anaesthetist
Here is a comprehensive overview of the physics principles relevant to anaesthesia, drawn from Miller's Anesthesia (10e), Barash's Clinical Anesthesia (9e), and Morgan & Mikhail's Clinical Anesthesiology (7e).
Physics Related to Anaesthesia
1. PRESSURE
Pressure = Force / Area
- 1 Pascal = 1 Newton per m²
- Clinical pressure units: mmHg (blood pressure, gas partial pressures), cmH₂O (airway pressures), bar/kPa (cylinder pressures)
- Gauge pressure = measured relative to atmospheric pressure (used for blood pressure and airway measurements)
- Absolute pressure = gauge pressure + atmospheric pressure
A full oxygen cylinder contains gas at 137 bar (~2000 lb/in²) gauge pressure. As the cylinder empties at constant temperature, pressure falls linearly (Boyle's law). In practice, temperature also drops due to adiabatic expansion - a process where gas state changes with no heat exchange with surroundings.
2. THE GAS LAWS
Boyle's Law
At constant temperature, volume and pressure of a fixed mass of gas are inversely proportional:
PV = k (constant)
Clinical use: Explains how gas cylinders work; predicts gas volume from cylinder pressure.
Charles' Law
At constant pressure, volume is directly proportional to absolute temperature (in Kelvin):
V = k₂T
Clinical use: Gas expands when warmed (relevant to humidifiers and gas delivery systems).
Gay-Lussac's / Third Gas Law
At constant volume, pressure is directly proportional to absolute temperature:
P = k₃T
Clinical use: Relevant to closed cylinders - if heated, pressure rises dangerously.
Combined (Ideal) Gas Law
PV = nRT
where R = universal gas constant, n = number of moles.
This is the master equation governing the behaviour of anaesthetic gases inside vaporizers, delivery equipment, and the pulmonary alveolus. Key assumption: gas molecules are point masses with perfectly elastic collisions - valid for dilute anaesthetic gases under normal operating conditions. - Miller's Anesthesia, 10e
Dalton's Law of Partial Pressures
P_total = P₁ + P₂ + P₃ + ...
Each gas in a mixture exerts its own partial pressure, equal to its volume fraction × total pressure.
Example: Air is 21% O₂ by volume, so at sea level: P(O₂) = 0.21 × 760 mmHg = ~160 mmHg
Miller's Anesthesia explains this elegantly - when oxygen alone fills a container at 1 atm, 760 mmHg is entirely from oxygen molecules. Replace with air, and nitrogen, oxygen, and trace gases each contribute proportionally.
3. VAPOUR PRESSURE AND VAPORIZATION
Saturated Vapour Pressure (SVP)
When a volatile liquid is in a closed container, molecules enter the vapour phase until equilibrium is reached. These molecules bombard the walls, creating saturated vapour pressure (SVP). SVP:
- Increases with temperature
- Is independent of atmospheric pressure
- Depends only on temperature and the physical properties of the liquid
Latent Heat of Vaporization
Energy must be absorbed from surroundings to vaporize a liquid. This energy comes from the liquid itself in the absence of external heat - causing evaporative cooling, which reduces SVP and vaporizer output. Modern vaporizers are designed to compensate for this (e.g., copper construction has high specific heat and thermal conductivity). - Morgan & Mikhail, 7e
Boiling Point
The temperature at which SVP = atmospheric pressure. Key point: boiling point falls with decreasing atmospheric pressure (relevant at altitude).
| Agent | Boiling Point (°C) | SVP at 20°C (mmHg) | MAC (%) |
|---|---|---|---|
| Halothane | 50.2 | 243 | 0.75 |
| Isoflurane | 48.5 | 238 | 1.15 |
| Sevoflurane | 58.5 | 160 | 1.7 |
| Desflurane | 22.8 | 669 | 6.0-7.25 |
| Enflurane | 56.5 | 175 | 1.68 |
Desflurane's near-room-temperature boiling point and very high SVP (669 mmHg) require a specially heated, pressurized vaporizer (the Tec 6). All other agents use variable bypass vaporizers.
Minimum Alveolar Concentration (MAC)
MAC is expressed in volume percent (v/v%) - the percentage of the alveolar gas that is the anaesthetic. It is the concentration preventing movement in response to surgical stimulus in 50% of subjects. However, it is the partial pressure (mmHg) in the brain that determines anaesthetic depth. The corresponding value is called MAPP (Minimum Alveolar Partial Pressure). - Miller's Anesthesia, 10e
4. FLUID DYNAMICS - FLOW, RESISTANCE, PRESSURE
Ohm's Law Analogy
Flow = Pressure Difference / Resistance
This applies to both electrical circuits and fluid flow (blood, gas). - Morgan & Mikhail, 7e
| Electrical | Fluid/Haemodynamic |
|---|---|
| Voltage (V) | Pressure gradient (ΔP) |
| Current (I) | Flow (F) |
| Resistance (R) | Vascular/airway resistance (R) |
Laminar Flow - Hagen-Poiseuille Equation
In laminar (streamlined) flow:
- Flow is directly proportional to driving pressure
- Resistance:
R = [8 × length × viscosity] / [π × radius⁴]
The 4th power of radius is the most important relationship. Halving the airway radius increases resistance 16-fold. This is why even small amounts of oedema can dramatically increase airway resistance in infants.
Turbulent Flow
- Flow is proportional to the square root of driving pressure
- Occurs at high flow rates, at branch points, and where airway diameter changes suddenly
- Resistance increases with flow rate
- Density (not viscosity) becomes the dominant property
Reynolds Number
Predicts whether flow is laminar or turbulent:
Re = (velocity × diameter × gas density) / gas viscosity
- Re < 2000: laminar flow predominates
- Re > 4000: turbulent flow predominates
- 2000-4000: transitional
Clinical application: Helium has a lower density than air or N₂O, so it decreases Reynolds number and promotes laminar flow. This is why Heliox (helium-oxygen) is useful in upper airway obstruction (croup, subglottic stenosis) - it converts turbulent to laminar flow, reducing the work of breathing. - Barash, 9e
Critical Flow
For anaesthetic gases, the critical flow rate (above which flow becomes turbulent) numerically approximates the airway diameter in mm:
- A 9 mm ETT: critical flow ≈ 9 L/min
- Air (lower density than N₂O) - laminar flow prevails
- Smaller airways: slower flow, so laminar flow predominates peripherally
5. LAW OF LAPLACE
For a cylinder (e.g., blood vessel, lung alveolus):
T = P × r
where T = wall tension, P = transmural pressure, r = radius.
For a sphere:
T = P × r / 2
Clinical applications:
- Aneurysms: As radius increases, tension increases - explaining why aneurysms progressively enlarge and rupture
- Atelectasis: Small alveoli (small r) tend to collapse into adjacent larger alveoli - prevented by surfactant
- LV hypertrophy: Dilated failing ventricles require greater wall tension for the same pressure generation
6. ELECTRICITY AND ELECTRICAL SAFETY
Ohm's Law
V = I × R (Voltage = Current × Resistance)
Power
P = V × I = I² × R
Capacitance and Capacitors
Capacitors store electrical charge. The body itself has capacitance - relevant in understanding why current can flow through a patient to earth even without direct connection.
Electrical Hazards in the OR
- Macroshock: Current passing through intact skin; thresholds - sensation: 1 mA, ventricular fibrillation: >100 mA
- Microshock: Current applied directly to the heart (via central line or pacing wire); VF can occur at just 50-100 µA - 2000× lower threshold
- Isolated (floating) circuits: Used in modern anaesthetic machines to reduce risk; the isolated power system has neither conductor referenced to earth, preventing a single fault from causing current flow through a patient
- Diathermy (electrosurgery): Uses high-frequency AC current (0.5-3 MHz) to cut/coagulate. High frequency bypasses the neuromuscular threshold. The large dispersive electrode means current density at the return pad is too low to cause burns (unlike at the small active electrode).
- Earth leakage current and line isolation monitors protect against inadvertent current paths through patients
7. PHYSICS OF ULTRASOUND
Sound Wave Properties
- Ultrasound: sound waves with frequency >20,000 Hz (20 kHz); clinical US uses 1-20 MHz
- Wavelength (λ) = velocity / frequency
- Higher frequency = better resolution, less penetration
- Lower frequency = poorer resolution, deeper penetration
Reflection and the Doppler Effect
- US reflects at tissue interfaces (impedance mismatch) - the basis of all US imaging
- Doppler principle: Frequency shift in reflected US from moving structures (e.g., red blood cells). Shift is proportional to velocity of movement - used in echo to measure blood flow velocity and cardiac output
Clinical applications
- Regional anaesthesia (nerve blocks)
- Vascular access
- Transoesophageal echocardiography (TOE/TEE) - uses both B-mode imaging and Doppler
- Lung ultrasound, focused cardiac ultrasound (POCUS)
8. HEAT AND TEMPERATURE
| Concept | Anaesthetic relevance |
|---|---|
| Specific heat | Copper's high specific heat stabilises vaporizer temperature |
| Thermal conductivity | Determines how quickly vaporizer re-equilibrates after temperature drop |
| Latent heat | Energy needed to convert liquid anaesthetic to vapour |
| Temperature scales | Kelvin (K) must be used in gas law calculations; K = °C + 273 |
Hypothermia under anaesthesia results from redistribution of heat (core to periphery from vasodilation), radiation, convection, evaporation, and conduction. Forced-air warming blankets counter convective and radiative losses.
9. PRINCIPLES OF PRESSURE GAUGES AND FLOWMETERS
Bourdon Gauge
Used to measure cylinder pressures. A coiled metal tube straightens proportionally to applied pressure, moving a pointer. For oxygen cylinders (gas under pressure), the gauge reading directly reflects remaining contents (Boyle's law applies).
Rotameters (Variable-Orifice Flowmeters)
A bobbin floats in a tapered tube; flow is read from the top of the bobbin. At low flows the annular orifice is narrow (tube-like) and viscosity governs flow. At high flows the orifice is wide (orifice-like) and density governs flow. Rotameters are gas-specific because each gas has unique viscosity and density characteristics.
Oxygen Analyser
Uses a fuel cell (Clark electrode) or paramagnetic properties of oxygen (oxygen is uniquely paramagnetic due to unpaired electrons) to measure O₂ concentration.
Key Summary Table
| Law / Principle | Formula | Anaesthetic Application |
|---|---|---|
| Boyle's Law | PV = k | Cylinder contents, gas compression |
| Charles' Law | V ∝ T | Gas expansion in warm circuits |
| Third Gas Law | P ∝ T | Closed system pressure changes |
| Ideal Gas Law | PV = nRT | Vaporizer & alveolar gas behaviour |
| Dalton's Law | P_total = ΣP_i | Partial pressure of gases/anaesthetics |
| Hagen-Poiseuille | R ∝ 1/r⁴ | Airway resistance; ETT size |
| Reynolds Number | Re = vdρ/η | Laminar vs turbulent flow; Heliox |
| Ohm's Law | V = IR / ΔP = FR | Haemodynamics; electrical safety |
| Laplace's Law | T = Pr | Alveolar stability; vascular wall stress |
| Doppler | Δf ∝ velocity | Echo flow measurement; POCUS |
Sources: Miller's Anesthesia, 2-Volume Set (10e); Barash, Cullen, and Stoelting's Clinical Anesthesia (9e); Morgan and Mikhail's Clinical Anesthesiology (7e); supplemented by Anesthesia Key: Basic Physics for the Anaesthetist and Physics of Anaesthesia Made Easy, Gupta & Gupta, GJAPM 2019.
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