This chapter is most relevant to Section F3(viii) from the 2017 CICM Primary Syllabus, which expects the exam candidates to "explain the relationship between resistance and respiratory gas flow". This topic has appeared multiple times in the Part One written papers, always as some variation on the theme of "which factors affect airway resistance":

At this stage, judging from the college comments, none of these questions were particularly invested in the minutiae of respiratory resistance physiology. To pass, it appears one merely needs to have a reasonable grasp of what Reynolds' number is, and to be able to discuss laminar and turbulent flow. Extended forays into the subjects of gas compression and tissue deformation would have risked being viewed as immodest displays of intellectual masturbation, bringing the opprobrium of more pragmatic examiners.

In summary:

  • Respiratory system resistance is mainly a combination of resistance to gas flow in the airways and resistance to deformation of tissues of both the lung and chest wall.
  • It is usually expressed as a change in pressure per unit flow, usually in cmH2O per litre per second. 
  • Its reciprocal is conductance. Normally, specific airway conductance is used, which is conductance expressed per unit of lung volume.
  • The total resistance of the respiratory system is composed of several contributing factors:
    • Resistance from deformation of the tissues (important at all flow rates)
      • Tissue resistance from lung parenchyma (~70%)
      • Tissue resistance from chest wall (~30% )
    • Inertance of air and thoracic tissues (important at high respiratory rates) 
    • Compression of intrathoracic gas (important mainly with high respiratory pressures)
    • Resistance from air flow friction, which in turn depends on
      • Reynolds number, which depends on
        • Airway diameter (increases with lung volume)
        • Airway length (increases with lung volume)
        • Flow rate
        • Gas density
        • Gas viscosity
      • Proportion of turbulent flow (at high flow, upper airways)
      • Proportion of laminar flow (low flow rates and in the lower airways)
  • In normal airways, the flow is mainly laminar (turbulent flow is localised to the upper airways)
  • Resistance to laminar flow increases in proportion to flow rate and is described by the Hagen-Poiseuilee equation, being affected by the following factors:
    • Airway length
    • The fourth power of airway diameter
    • Gas viscosity
  • Resistance to turbulent flow increases exponentially with flow rate, and the main determinant of the rate of pressure change is the density of the gas.

 As an overview of this topic, David Kaminsky's 2012 article stands out as one of the best, particularly for a discussion of measurement techniques. Nunn's chapter on respiratory system resistance (p.33-50 of the 8th edition) should probably be viewed as essential, given its status as the Official College-recommended Textbook.

Definition of resistance and conductance

Respiratory system resistance is occasionally described as "non-elastic resistance" to separate it from the concept of "elastic resistance" which is essentially static compliance, related by Nunn's as an "impedance to inflation of the lung" which "occurs when no gas is flowing".  There is a reason for separating the concepts in this way. The main functional difference between elastic and non-elastic resistance is that in elastic resistance, the energy expended on stretching things is stored and recovered, whereas in non-elastic resistance it is wasted on the production of heat. From the summary section of Nunn's, we get this definition:

"Respiratory system resistance is a combination of resistance to gas flow in the airways and resistance to deformation of tissues of both the lung and chest wall."

That is probably good enough for a CICM SAQ answer, even though it omits several minor components of nonelastic resistance. To be fair, it is possible to completely ignore them, because they contribute minimally to the routines of normal breathing,  but they are worth knowing about nonetheless. If one were a completeness Nazi, one would rephrase the definition thus:

"Respiratory system resistance is a combination of resistance to gas flow in the airways, resistance to deformation of tissues of both the lung and chest wall, inertia of those tissues, inertia of the gas, and gas compression"

Resistance is generally expressed as a pressure per unit flow, usually in cmH2O per litre per second. 

Conductance is the reciprocal of resistance, and is defined as

"the instantaneous rate of gas flow in the airway per unit of pressure difference"

and it is usually expressed as specific conductance, or conductance per unit lung volume, which allows a comparison of conductance among lungs of different size (eg. children and adults)

Components which make up respiratory resistance

One way of listing the factors which make up respiratory resistance is to write them in the form of an equation, for example something like the one below, modified from Milic-Emili et al (1990). This is known as Rohrer's equation, after Rohrer (1915):

Rohrer's equation

where

  • Rrs is the resistance of the respiratory system,
  • Rt is the resistance from deformation of the lungs and chest wall,
  • K1 is an empirical constant representing gas viscosity 
  • K2 is an empirical constant representing gas density and airway geometry, and
  • is the flow as volume per unit time

Breaking this down somewhat, we can say that respiratory resistance is a combination of multiple factors, which contribute unequally and which have different importance at different points in the respiratory tract and under different flow conditions:

  • Resistance from deformation of the tissues (important at all flow rates)
    • Tissue resistance from lung parenchyma (~70%)
    • Tissue resistance from chest wall (~30% )
  • Inertance of air and thoracic tissues (important at high respiratory rates) 
  • Compression of intrathoracic gas (important mainly with high respiratory pressures)
  • Airflow pattern, which in turn depends on
    • Reynolds number, which depends on
      • Airway diameter
      • Flow rate
      • Gas density
      • Gas viscosity
    • Proportion of turbulent flow (at high flow, upper airways)
    • Proportion of laminar flow (low flow rates and in the lower airways)

The relative contribution of this component varies depending on which textbook you read. Nunn's splits the relative contributions 50:50 between tissue resistance and airway resistance, whereas Levitzky's Pulmonary Physiology (2007) puts the airway resistance at the top with 80%. The superiority of either claim is difficult to determine considering that neither editor offered any references to support these figures.  Urbankowski & Przybylowski (2016) even give a breakdown of which structures contribute to the resistance the most, again without allusion to any specific experimental source. The numbers they produced are sufficiently authoritative-looking that one would be tempted to reproduce them in some sort of totally unofficial non-peer-reviewed internet resource, in case they were not totally made up.

Components of total airway resistance;
Urbankowski & Przybylowski (2016)
Component Resistance (cmH2O/L/s) Percentage of total
Mouth and pharynx 0.5 19%
Trachea and main bronchi 0.5 19%
Peripheral bronchi 0.2 8%
Lung tissue 0.2 8%
Chest wall 1.2 46%

These components will now be discussed in greater detail, in ascending order of exam importance, such that the most irrelevant content will come first, as if it were a light entrée to the meat and potatos of this topic.

Compression of intrathoracic gas

In expiration, the forces of the chest wall and lung recoil apply a positive pressure on the intrathoracic gas volume. In inspiration, the expanding chest wall volume creates a negative pressure. Both of these processes affect the volume of the intrathoracic gas, which you can see from the difference of the expiratory thoracic volume and the expired gas volume - i.e. upon escaping the confines of the chest, the gas expands to a larger volume than that which it previously occupied. Obviously that compression and decompression are not without a certain energy cost, and this cost factors into the respiratory system resistance, albeit to some imperceptible minor extent.

How much does this really affect the mechanics of respiration? Well. The amount of work done to compress gas during expiration is probably minimal during normal respiration, mainly because the pressure changes are in the range of  2-4 cm H2O. At least that's what all the textbooks tend to use as an excuse not to discuss the subject any further (it does not help that there is minimal published data regarding this). However, when measuring peak expiratory flow, the pressure generated by respiratory muscles to produce a forceful expulsion of intrathoracic gas may do enough compression work to actually be a significant confounding factor. 

effect of gas compression on respiratory system resistance

The graph above comes from  Ingram & Schilder (1966); it has been cleaned up and colourised but is otherwise unchanged from the original paper. What this demonstrates is that basically during expiration, when there is high transpulmonary driving pressure, the expiratory flow will appear to be greater if you use the thoracic volume as the volume variable. At lower pressures (i.e. during normal quiet breathing) there is pretty much no difference between thoracic volume and expired gas volume, and therefore no meaningful compression of the intrathoracic gas.

Inertance

The lungs, chest wall and intrathoracic gas all have a nonzero mass, which like all matter resists being accelerated. Ergo, in normal respiration and mechanical ventilation, some of the resistance of the respiratory system is due to the need to overcome this inertia. Because this tends to get lost in the overall resistance, the contribution of this inertia is extremely difficult to estimate, and most textbooks will generally remark that it is negligible (or, fail to mention it at all). 

In order to determine how much it really contributes, Jere Mead (1956) designed an elegant experiment in which the only changing variable was the mass of inspired gas. Because it would have been unethical to make his subjects breathe pure radon, this was accomplished by means of increasing the ambient atmospheric pressure, thereby packing more air into every lungfull.

respiratory inertance at different ambient atomospheric pressures from Mead (1956)

The graph above demonstrates the changes in respiratory inertance for three of the healthy young subjects, who "cheerfully put up with the various discomforts of the procedure" (he shoved them into the pressure chamber and instructed them to pant at 180-300 breaths per minute). Approximating the results to normal respiration, Mead came to the conclusion that the pressure change required for volume acceleration would be 0.02 cm H2O, or less than 0.5% of the total respiratory pressure change. Even when one accelerates a breath during a cough to generate a transient flow rate of 1000L/sec, the associated inertance-related pressure would only be around 10 cm H2O.

So, in summary, inertance plays virtually no role in respiratory resistance under all but the most abnormal circumstances. One can of course conceive of scenarios where inertance becomes relevant, but these are sufficiently exotic that detailed knowledge of them would never be expected by any fair postgraduate examination process. For instance, inertance increases with increased respiratory rates and narrow tubes, as the velocity of gas increases; Lanteri et al (1999) explored this of mechanically ventilated puppies, presumably because they could not find anything smaller and cuter to ventilate. With respiratory rates in excess of 30, excluding inertance from predictive equations produced an error in the calculation of resistance (i.e the measured resistance was greater). Presumably, this is even more of an issue in HFOV, though there is no direct evidence of it. Straying even further from routine practice,  in the case of liquid ventilation, the added mass of the liquid being used as the respiratory medium increases the inertance significantly. Schmalisch (2003) found the inertance increased by 104% in perfluorocarbon-ventilated piglets.

Tissue resistance

The lung tissue and the chest wall are reluctant to change shape, and therefore resist the intrathoracic flow of gas. As gas flows into the chest, some of the increase in pressure is due to the stretching of these solid tissues. Immediately at the end of a rapid inspiration, when these structures have been stretched rapidly, their resistance is maximal. When flow stops, the relaxation of the chest wall and lungs leads to a gradual decrease in airway pressure, which can be observed during an inspiratory hold manoeuvre. Some of this decrease in pressure is also due to pendelluft, the exchange of gas between lung units with different time constants, but in a normal lung that exchange should be fairly trivial (Otis et al, 1956) - i.e. all the lung units will have similar short time constants.

Tissue resistance contribution to respiratory resistance

The ventilator graphic above is added to the original waveforms published by D'Angelo et al (1989), an article which appears in virtually all the textbooks which discuss this topic. In that classic study, the investigators performed inspiratory hold manoeuvres of 3 seconds duration on some healthy volunteers, measuring the difference between early (P1) and late (P2) inspiratory hold pressure. To add accuracy, they used muscle relaxant so that actual muscle activity would not interfere with the measurements. Pendelluft being negligible in these normal individuals, the observed drop in pressure is wholely due to the viscoelastic properties of the lung and chest wall, and D'Angelo et al were able to demonstrate that it remains relatively stable over a relatively broad range of flow rates, lung volumes and respiratory pressures. 

In short, tissue resistance appears to contribute about half of the total airflow resistance in people who are not in the grip of severe bronchospasm. According to D'Angelo et al (1994), of the total tissue resistance (~1.5 cmH2O/L/s), about  0.4 cmH2O/L/s (27%) is due to the chest wall, and the rest is due to the resistance of the lung tissue itself.

Airway resistance

When people say "respiratory resistance", they usually mean airway resistance, i.e. the pressure generated by the resistance to gas flow produced by the walls of the airways. This pressure, and how it is affected by different factors, depends on what type of flow is occurring, which in turn affected by Reynold's number.

The relative contribution of this component varies depending on which textbook you read. Nunn's splits the relative contributions 50:50 between tissue resistance and airway resistance, whereas Levitzky's Pulmonary Physiology (2007) puts the airway resistance at the top with 80%. The superiority of either claim is difficult to determine considering that neither editor offered any references to support these figures.  Urbankowski & Przybylowski (2016) even give a breakdown of which structures contribute to the resistance the most, again without allusion to any specific experimental source. The numbers they produced are sufficiently authoritative-looking that one would be tempted to reproduce them in a totally unofficial non-peer-reviewed internet resource, in case they were not totally made up.

Components of total airway resistance
Component Resistance (cmH2O/L/s) Percentage of total
Mouth and pharynx 0.5 19%
Trachea and main bronchi 0.5 19%
Peripheral bronchi 0.2 8%
Lung tissue 0.2 8%
Chest wall 1.2 46%

Laminar flow, turbulent flow and Reynold's number

In summary, regarding flow, it can be safely said that none of the air flow in human airways is exclusively laminar or exclusively turbulent, but some mixture of the two. Without going into excessive detail regarding fluid and gas dynamics, the following are the definition of Reynold's number and characteristics of different types of flow as relevant to the human respiratory tract:

Reynold's number

  • Reynold's number is defined as the "the ratio of inertial forces to viscous forces" in fluid dynamics, or the ratio of gas density to gas viscosity. It is described by the equation,
    Reynolds%20number%20equation%201.jpg
    where
    • V is the velocity of the gas flow,
    • D is the diameter of the tube, 
    • ρ is the gas density, and
    • μ is the gas viscosity.
  • This number describes whether the flow will be turbulent or laminar 
  • Numbers under 2000: flow is mainly laminar
  • Numbers 2000-4000: flow is "transitional", laminar turning to turbulent
  • Numbers >4000: flow is mainly turbulent.

Laminar flow

  • Flow is proportional to driving pressure, assuming the airway is straight (it rarely is) and unbranched (they never are). The relationship of pressure gradient and flow rate is linear, and can be represented by the equation ( ∆P = flow rate × resistance):
    pressure-flow relationship for laminar flow 
  • Resistance is described by the classical Hagen-Poiseuille equation:
    ​​
    Hagen-Poiseuille equation
    which means that airway characteristics (eg. length and radius) are the most important determinants of resistance, followed by the viscosity of the gas. 
  • A maximum flow rate exists; beyond which various eddies and vortices develop, making the flow becomes turbulent. The smaller the calibre of the airway, the lower the flow rate required to produce this effect. 
  • The volume of gas moving through the tube is smaller than the volume of the tube. This is because gas which is in contact with the walls is essentially motionless, at least in theory.  This makes it hard to purge the tube with laminar flow ("wall gas" will remain in the tube).
  • Viscosity is the most important gas property which influences the resistance to laminar flow. It is usually measured in Pa.s (Pascal-seconds, or kilograms per meter per second.). This becomes meaningless in medicine because the viscosity of most inhaled gas mixtures is fairly similar, i.e. its mainly air (RTP viscosity of 1.82 Pa.s) mixed with oxygen (viscosity of ~ 2.04 Pa.s). If one wants to get wild with one's gas mixtures, throwing caution to the wind can broaden the range of available viscosities. One can go as low as benzene (0.75 Pa.s) or as high as neon (3.13 Pa.s).
  • A minimum length of unbranched tube is required for laminar flow to be established;  the term to describe this is "entrance length" and it depends on the diameter of the tube and the Reynolds number of the gas. For an 8mm tube (eg. a secondary bronchus), the entrance length is about 21cm (Olson et al, 1970), i.e. in the vast majority of circumstances there is not enough airway length to establish laminar flow.

Turbulent flow

  • Flow is proportional to the square root of driving pressure. In other words, as the pressure gradient increases, flow increases less (i.e. the relationship is not linear): 
    pressure-flow relationship for turbulent flow
  • Resistance increases in proportion to flow rate, and cannot be described using the traditional Hagen-Poiseuille equation. In fact, because of that, you should't even use traditional units to measure it. It is usually represented in terms of a pressure gradient:

    Pressure gradient = K(flow)n

    where
    • K  is an empirical constant which, for the human respiratory tract, appears to be 0.24 ( when the pressure gradient is expressed in kPa), and
    • n is an exponent which is 1.0 for a purely laminar flow and 2.0 for a purely turbulent flow. According to the ancient Handbook of Physiology, empirical measurements suggest that for the human respiratory tract,  n=1.3 
  • The volume of gas moving through the tube is proportional to the volume of the tube, i.e. the "front" of the flowing gas is square rather than conical as in laminar flow.
  • Density is the most important determinant of whether or not flow will be turbulent, all other things being equal. This is where helium becomes useful, i.e. by decreasing the density of the inspired gas mixture helium improves the likelihood of laminar flow occurring in narrowed airways, and this decreases the resistance to flow.

"Real" flow in human airways

With these easily memorised factoids above now easily available for exam answer purposes, one might ask - what actually happens in the human airway? Fortunately, Olson et al (1970) have made this information available. Or rather, they have created a theoretical analysis of the pressure changes in the human airway, including the Reynolds number and entrance length for every Weibelian branching of the bronchi.. Their predicted numbers for a relatively average inspiratory flow rate of 30L/min are presented in the table below (copied directly from their 1970 paper):

Airway ressitance along the human airways, from Olson et al (1970)

As can be plainly seen from this, Reynolds number is expected to be high for the high-velocity upper airways which are shorter than their entrance length, and so turbulent airflow is to be expected there. As one moves further and further into the bronchial tree, the total cross-section of the bronchi increases massively, and the flow slows down, which decreases the Reynolds number. From generation 11 onward, flow is largely laminar. With flow of 30L/min, the pressure difference between mouth and alveolus ends up being only 0.36 cm H2O. This model's numbers are probably off by some factor (for example, it fails to take into account the effects of pulsatile flow, which produces turbulence at far lower Reynolds numbers) but it is probably good enough for government work.

So, how does this reflect in the pressure-flow relationship of the entire system? From the above it would follow that flow at lower flow rates should increase in proportion to the pressure gradient, until the flow rate exceeds a certain critical threshold beyond which flow becomes turbulent, at which stage further increases in pressure gradient would produce only a modest improvement in flow. In terms of representing this graphically, one could do worse than this:

flow-pressure curve from Mead et al (1967)

It comes from a famous paper by Mead et al (1967), and demonstrates the concept very well. Beyond a pressure gradient of 15 cm H2O or so, there is no further improvement in flow, i.e. Subject D.L. clearly reached some sort of performance plateau at that point.

Flow resistance at different points long the airways

At this stage, in various textbooks a couple of graphs are usually brought out which demonstrate the distribution of resistance across the generations of airways. This appears to have special importance to the examiners, as in their answer to Question 23 from the second paper of 2013 they commented that  "better answers discussed the transitional point in the airway and the paradox about size vs. total cross sectional area and its influence on total resistance". This usually means one needs to combine the crossectional airway area diagram from Weibel's Morphometry of the Human Lung (1963) and the airway resistance diagram from Pedley et al (1970). The latter was not derived from a set of measurements but rather calculated from a model. 

relationship of increasing airway crossectional area and airflow resistance (from Webel and Pedley)

Instead of illegally copying these graphs and reproducing them side by side like most normal people, the author has for some reason chosen to combine them in Illustrator, under the impression that this somehow enhances their educational properties. If one had to reproduce this in an exam setting, an important feature to label would be the "transition point", which is variably quoted as lying somewhere in the 5th-8th generation of bronchi. This is where the airway resistance is maximal. The "paradox" alluded to by the college is probably referring to the fact that the airways get narrower, and one might expect the resistance to increase because of this, but because their total crossectional area becomes exponentially greater the flow in them slows down to the point where all the airways distal to Generation 10 contribute less than 16% to the total airway resistance.

References

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Sharafkhaneh, Amir, et al. "The confounding effects of thoracic gas compression on measurement of acute bronchodilator response." American journal of respiratory and critical care medicine 175.4 (2007): 330-335.

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Brown, Nathan J., et al. "Reference equations for respiratory system resistance and reactance in adults." Respiratory physiology & neurobiology 172.3 (2010): 162-168.

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Otis, Arthur B., et al. "Mechanical factors in distribution of pulmonary ventilation." Journal of applied physiology 8.4 (1956): 427-443.

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D'Angelo, E., M. Tavola, and J. Milic-Emili. "Volume and time dependence of respiratory system mechanics in normal anaesthetized paralysed humans." European Respiratory Journal 16.4 (2000): 665-672.

D'Angelo, E., et al. "Chest wall interrupter resistance in anesthetized paralyzed humans." Journal of Applied Physiology 77.2 (1994): 883-887.

Lanteri, Celia J., et al. "Influence of inertance on respiratory mechanics measurements in mechanically ventilated puppies." Pediatric pulmonology 28.2 (1999): 130-138.

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Beaulieu, Alexandre, et al. "Measurement of fractional order model parameters of respiratory mechanical impedance in total liquid ventilation." IEEE transactions on biomedical engineering 59.2 (2011): 323-331..

Olson, Dan E., GLADYS A. Dart, and GILES F. Filley. "Pressure drop and fluid flow regime of air inspired into the human lung." Journal of applied physiology 28.4 (1970): 482-494.

Pedley, T. J., R. C. Schroter, and M. F. Sudlow. "The prediction of pressure drop and variation of resistance within the human bronchial airways." Respiration physiology 9.3 (1970): 387-405.

Weibel, Ewald R. "Geometric and dimensional airway models of conductive, transitory and respiratory zones of the human lung." Morphometry of the human lung. Springer, Berlin, Heidelberg, 1963. 136-142.

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Mead, J., et al. "Significance of the relationship between lung recoil and maximum expiratory flow." Journal of Applied Physiology 22.1 (1967): 95-108.