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

 

List:

·       Intro

·       Heterogeneity

·       Resistance

·       Compliance

 

Intro:

Time constant

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

Equation

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

Graph

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:

Causes

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

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

Effects

·  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)

Quantification

·  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)

Representation

 

Resistance:

Definition

·  Resistance = pressure drop / flow rate

Normal

·  Adult: 2cmH2O/L/s

·  Neonate at 48 hours: 25cmH2O/L/s

Equations

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

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

Determinants

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):

Definition

·  ∆volume/∆transpulmonary pressure

Normal

·  Adult 200mL/cmH2O

·  Neonate 1.5-6mL/cmH2O

Determinants

·  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 ↑Alveolar number, ↑alveolar size (↑radius -> ↓pressure – LaPlace)

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

o N.B. compliance constant when indexed to size (i.e. compliance/FRC)

·  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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