Boyle's Law:
- For a fixed mass of gas at constant temperature, the pressure (P) and volume (V) are inversely proportional, such that P ×V = k, where k is a constant.
Charles' Law:
- The volume occupied by a fixed mass of gas at constant pressure is directly proportional to its absolute temperature (V/T = k).
Third gas law (Gay-Lussac's Law):
- The pressure of a fixed mass of gas at constant volume is directly proportional to its absolute temperature (P/T = k).
Avogadro's Law:
- Equal volumes of gases at the same temperature and pressure contain the same number of molecules (6.023 × 1023, Avogadro’s number).
Universal (Ideal) Gas Law:
- The state of a fixed mass of gas is determined by its pressure, volume and temperature(PV = nRT)
Henry's Law
- The amount of a given gas dissolved in a given liquid is directly proportional to the partial pressure of the gas in contact with the liquid:
P = Hv × M
Where
- P is pressure
- M is the molar concentration of gas
- Hv is Henry's Proportionality Constant
Flow = volume / time
Volume = flow × time
Pressure = flow × resistance
Resistance = change in pressure / flow
Compliance = volume / change in pressure
Work of breathing = pressure × volume
The Bohr equation for measuring dead space:
VD/VT = (FACO2 - FECO2) / FACO2
Where:
- VD = dead space volume
- VT = tidal volume
- FECO2 = fraction of expired CO2
- FACO2 = fraction of alveolar CO2
Diffusing capacity = Net rate of gas transfer / Partial pressure gradient
Alveolar gas equation
PAO2 = (FiO2 × (Patm - PH2O) - (PaCO2 / RQ)Where
- PAO2 = Partial pressure of alveolar oxygen
- FiO2 = fraction of inspired oxygen
- Patm = Atmospheric pressure (usually 760 mmHg)
- PH2O = partial pressure of water vapour at the alveolus (usually 47 mmHg)
- PaCO2 = Partial pressure of arterial carbon dioxide
- RQ = respiratory quotient, usually 0.8
Oxygen content of whole blood
= (sO2 × ceHb × BO2 ) + (PaO2 × 0.03), where:
- ceHb = the effective haemoglobin concentration
- i.e. concentration of haemoglobin species capable of carrying and releasing oxygen appropriately
- PaO2 = the partial pressure of oxygen in arterial gas
- 0.03 = the content, in ml/L/mmHg, of dissolved oxygen in blood
- Henry's law states that the amount of dissolved gas in a liquid is proportional to its partial pressure above the liquid;
- Ergo the amount of oxygen dissolved in is proportional to its partial pressure, e.g for a PaO2 of 100 mmHg the oxygen content is 0.03 × 100 = 3ml/L
- BO2 = the maximum amount of Hb-bound O2 per unit volume of blood
- normally 1.39 of dry Hb, or closer to 1.30 in "real" conditions
- sO2 = oxygen saturation:
- determined by the sigmoid oxygen-haemoglobin dissociation curve
- Sigmoid shape of the curve comes from the positive cooperativityof oxygen binding
- Once an oxygen molecule is bound to it, the oxygenated subunit increases the oxygen affinity of the three remaining subunits
- This is because of a conformational change produced by each subunit binding oxygen, which mediates the transition from the T (tense, deoxygenated) state to the R (relaxed, oxygenated) state
The shunt equation
Qs/Qt = (CcO2 - CaO2) / (CcO2 - CvO2)
where
- Qs/Qt = shunt fraction (shunt flow divided by total cardiac output)
- CcO2 = pulmonary end-capillary O2 content, same as alveolar O2 content
- CaO2 = arterial O2 content
- CvO2 = mixed venous O2 content
Maury, Bertrand. The respiratory system in equations. Springer Science & Business Media, 2013.