Respiratory Physiology III (Mechanics II) - Josh Pillemer
1. Airways resistance
•
Physics of gas flow
•
Factors affecting
•
Measurement of
3. Work of breathing
•
Description
•
Components of
2. Closing capacity
•
Definition
•
Relationship to airway closure
•
Clinical significance
•
Measurement
4. Pathological states
•
Altered lung mechanics in common disease
1. AIRWAYS RESISTANCE
Physics of gas flow
Laminar flow:
Turbulent flow:
[Nunn]
- "Advancing cone" - parabolic
- Note linear relationship between driving pressure and
flow rate [i.e. ܲ = ݇. ܸሶ]
Where:
ܸሶ = Flow rate
ܲ = Pressure gradient
‫ = ݎ‬radius of tube
ߟ = viscosity of gas
݈ = length of tube
Hagen-Poiseuille:
ܸሶ =
௉.గ.௥ ర
଼.ఎ.௟
[Nunn]
- Square front vs. cone
- Note the square relationship between driving pressure
and flow rate [i.e. ܲ = ݇. ܸሶ ଶ ]
• Driving pressure ∝ gas density
• Driving pressure independent of gas viscosity
ଵ
• Driving pressure ∝ ௥ఱ (Fanning eqn)
௉
But then we also know:
- Quantifying resistance is a bit harder [ܴ = ௏ሶ]
- Can consider Pressure gradient in a few ways:
ܲ = ܸሶ . ܴ [effectively Ohm's]
a) ܲ = ݇ଵ . ܸሶ + ݇ଶ . ܸሶ ଶ
Thus:
ࡾ =
ૡ.࢒.ࣁ
࣊.࢘૝
݇ଵ = H-P coefficient
݇ଶ = turbulent equivalent
[Studies yield: ܲ (݇ܲܽ) = 0.24 ܸሶ + 0.03. ܸሶ 2 ]
௡
b) ܲ = ‫ܭ‬. ൫ܸሶ ൯
݊ = 1 ⟹ laminar flow
ଵ.ଷ
[Studies yield: ܲ (݇ܲܽ) = 0.24 ൫ܸሶ ൯
]
݊ = 2 ⟹ turbulent flow
Reynolds' number
•
•
•
Gives an indication of the likelihood of laminar (<2000) vs turbulent (>4000) flow
Effectively a ratio between the density and viscosity of a gas
Note that there is not much variation in viscosities of inhalable gases, but densities may vary widely
ܴ݁ =
•
ଶ௥.௩.ௗ
ఎ
‫ = ݎ‬radius of tube
݀ = density of gas
ߟ = viscosity of gas
Also concept of entrance length - which is the distance required to attain laminar flow
Entrance length = 0.03 x tube diameter x Reynolds' number
Factors affecting airways resistance: *** PRIMARY QUESTION *** (Anaes 2003, 1999, 1998)
- Define: Resistance = Driving pressure / Flow [Where driving pressure = mouth - alv pressure]
- Airways resistance is ~ 0.5 - 2.5 cmH2O / L/s [During slow tidal volume breathing]
[Check: Driving pressure usually ~1 cm H2O, Flow usually ~ 0.5 L/s --> Resistance ~ 2 cmH2O / L/s]
- Hagen-Posieuille tells us that airway size is likely to be the most influential factor in airways resistance
- Even though the diameter of the small airways is very small,
their total cross sectional area is so large that they make very
little contribution to overall resistance. The vast majority of
airways resistance occurs in the medium-sized bronchi (up
to ~gen 5). [Only ~20% resistance attributed to airways <2mm diam]
--> See diagram from West
- Lung volume is one of the major determinants of airways
resistance. As lung volume increases, the airways are pulled
open [by radial traction of lung parenchyma] with fall in R.
Conversely, as lung volume falls, R dramatically rises.
Furthermore, fall in volume predisposes to small airway
collapse [smaller airway calibre along with higher intrapleural pressure], which will increase R if enough of the small
airways are affected.
-The other major determinants of airway resistance are the other factors that determine airway size by means of
bronchial smooth muscle contraction/relaxation:
Bronchoconstriction:
Irritants (smoke), parasympathetic activity, ACh use, low
alveolar pCO2
Bronchodilation:
β2 agonists, Adrenaline, Isoprenaline
- And last of all, the density and (less so) viscosity of inhaled gas will have an impact on resistance.
Measurement of airways resistance:
- ܴ݁‫= ݁ܿ݊ܽݐݏ݅ݏ‬
ெ௢௨௧௛ ௣௥௘௦௦௨௥௘ି஺௟௩௘௢௟௔௥ ௣௥௘௦௦௨௥௘
ி௟௢௪ ௥௔௧௘
- All of these are easy to measure except Alveolar pressure. This is done with a body plethysmograph
- Also possible to do using oesophageal balloon recordings of intrapleural pressure, but this will include both airways
resistance and the elastic tissue resistance.
2. CLOSING CAPACITY
- Closing capacity is the lung volume at which dependent airways begin to close.
- This is different to the closing volume by virtue of the fact that it includes the RV (i.e. CC - RV = CV)
- Closing capacity increases with age (= FRC supine @ 44yo, = FRC erect @ 66yo) - likely a result of the loss of elastic
recoil of the lung (resulting in the same situation as described in the lower right diagram on p. 2)
- When FRC < CC, then there will be substantial airway closure during normal respiration, with resultant shunt.
- Measurement is achieved by means of performing a single-breath N2 washout.
•
•
A vital capacity breath of 100% O2 is taken [noting that the apical alveoli will preferentially uptake the N2rich dead space]
A slow exhalation in then performed down to RV, with detection of expired N2
There are clearly 4 phases:
I: Expiration of dead space gas full of O2 but no N2
II: Expiration of a mix of dead space + alveolar gas
III: Pure alveolar gas expiration
IV: Closure of some alveoli with exaggerated output from the
initially-N2-saturated and less-O2-diluted apical alveoli. This is
the Closing Capacity.
3. WORK OF BREATHING
- In thermodynamics, pressure-volume work occurs when the volume of a system changes.
- Work is given by:
[i.e. the area under the curve of pressure vs. volume]
- It can more simply be thought of as the product of the mean pressure and the change in volume.
- This diagram is adapted from West
- Using the "area under the curve" approach, the total work of inspiration can be
seen to be OABCGO.
- The trapezoid OAECGO is described as the work to overcome elastic resistance,
with the shaded area ABCEA giving the non-elastic resistance (the viscous
resistance, from airways and tissues)
- It is likely that there is a bunch of stored elastic energy in the thoracic cage that
helps with a lot of the work in overcoming the elastic resistance. As such, it is more
accurate to think of ABCDA as the work of inspiration, with AECDA being the
elastic component.
- Note that increasing airways resistance or increasing respiratory rate (and thus
flow rate) will bulge the shaded area out to the right (increasing the viscous work
area)
- Also note that increasing the TV will expand the trapezoid OACDGO (increasing
the elastic work area)
- On expiration, the area AECFA is the work to overcome the viscous forces. There is
already enough stored energy to account for this in the expanded elastic structures.
The area difference between AECDA and AECFA is work lost as heat.
- West also describes calculating work of breathing by looking at O2 cost of breathing and using the formula:
‫( ݕ݂݂ܿ݊݁݅ܿ݅ܧ‬%) =
ܷ‫݇ݎ݋ݓ ݈ݑ݂݁ݏ‬
× 100
ܶ‫ܱ ݎ݋( ݀݁݀݊݁݌ݔ݁ ݕ݃ݎ݁݊݁ ݈ܽݐ݋‬2 ܿ‫)ݐݏ݋‬
where efficiency is usually 5-10%, and O2 cost of breathing found to be <5% of total resting O2 consumption.
*** PRIMARY QUESTION *** (CICM Nov 2010)
Describe the physiological consequences of decreasing the FRC by one litre in an adult.
- FRC = Volume of gas in the lungs following a normal/tidal expiration. At this point, the elastic recoil forces of the lung
and chest wall are equal.
- Normal value: ~1.8 L (female), ~2.2 L (male)
- Consequences of lowering FRC by ~50% (down close to RV!):
1. Brings FVC below closing capacity --> significant airway closure --> significant shunt. [As in notes above]
2. Leads to dramatic increase in airways resistance, thereby increasing the work of breathing. [As in notes above]
3. Leads to much lower lung compliance (by looking at the pressure-volume curve at low volumes). As such, we can
imagine a "stiff lung" which needs extra work to fill normally. [Just need to plot gradient of P-V curve at low vol's]
4. Leads to decrease in extra-alveolar vessel calibre,
resulting in high pulmonary vascular resistance,
in turn increasing R heart pressures [See diagram from West]