2008B13 Explain the concept of time constants and relate these to “fast” and “slow” alveoli.



·         Intro

·         Heterogeneity

·         Resistance

·         Compliance



Time constant

·   Time taken for completion of an exponential process (e.g. alveolar filling) had the initial rate of change continued


·   Alveolar time constant (τ) = resistance to filling (R) x compliance of alveolus (C)


Vt = Vf x (1-e-1/τ)

Normal values

·   ‘R’ 2cmH2O/L/s

·   ‘C’ 100mL/cmH2O (0.1L/cmH2O)

·   ‘τ’ 0.2 seconds (and 95% completion in 0.6 seconds)

Types of alveoli

·   Fast: ↓ τ hence ↓R, ↓C

·   Slow: ↑ τ hence ↑R, ↑C


Heterogeneity of lung unit filling:


·   Variation in time constants (e.g. COPD)

·   Inspiratory time insufficient for filling of slow lung units (i.e. high RR, high I:E ratio)


·   Fast alveoli well ventilated

·   Slow alveoli relatively hypoventilated; ↓ PAO2 and ↑PACO2

·   Contributes to difference between dynamic compliance (lower) and static compliance (higher)

·   Pendelluft (distribution of air from fast to slow units at end inspiration and early expiration)


·   Capnography:

o Slope of plateau (phase 3) heterogeneity

o Slow units with ↑PACO2 empty late

·   Airway pressure:

o Peak to plateau pressure drop heterogeneity

o (Pendelluft -> ↓ average surface tension -> drop in airway pressure)




·   Resistance = pressure drop / flow rate


·   Adult: 2cmH2O/L/s

·   Neonate at 48 hours: 25cmH2O/L/s


·   Laminar: R = (8 x length x viscosity)/(π x radius4)

·   Turbulent: (P1-P2) length x density / (radius5)


Factors ↑resistance:

·   ↓Airway radius:

o ↓Absolute lung size (e.g. neonate cf. adult)

o ↓Relative lung volume (e.g. diaphragm displacement in pregnancy)

o Intraluminal obstruction (e.g. mucus)

o Luminal obstruction (bronchoconstriction, swelling)

o Extraluminal obstruction (e.g. dynamic airways compression)

o *most important factor since raised to power of 4 or 5*

·   ↑Density: e.g. reduced with heliox

·   ↑Viscosity: e.g. ↑ with ↑temp

·   ↑Length: not under control


Lung compliance (LC):


·   ∆volume/∆transpulmonary pressure


·   Adult 200mL/cmH2O

·   Neonate 1.5-6mL/cmH2O


·   Intrinsic elasticity:

o Elderly/smoking -> emphysema-> ↑LC

o Fibrosis -> ↓LC

o Pulmonary oedema -> ↓LC

·   Surfactant:

o Deficiency -> ↓LC (prematurity, SP-B or SP-C deficiency)

·   Absolute lung size:

o LaPlace’s law: Surface tension (ST) = pressure x radius / 4

o ↑size -> ↑alveolar radius -> ↓ ST -> ↑LC

o Adult LC: 100mL/cmH2O > Neonate LC: 1.5-6mL/cmH2O

o Male > female

o Taller > shorter

·   Relative lung volume

o High: surfactant spread out -> ↑ST -> ↓ LC

o Low: ↓ radius -> ↑ST, alveolar collapse -> ↓LC

o Max compliance at FRC

o (note lung volumes reduced in pregnancy, obesity, supine position)

·   Gravity:

o Basal compression -> ↓alveolar volume at FRC -> ↑basal LC

o Apical traction -> ↑alveolar volume at FRC -> ↓apical LC

·   Pulmonary blood volume

o Congestion -> ↓ LC

o (e.g. heart failure, supine posture)



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