Elastic properties of the respiratory system

This chapter is most relevant to Section F3(ii) from the 2017 CICM Primary Syllabus, which expects the exam candidates to "relate this to the elastic properties of the respiratory system", where "this"  is the static and dynamic compliance of the aforementioned system. Compliance has found its way into all sorts of SAQs, but these "elastic properties" have not been asked about at any stage. 

What exactly this topic should contain, is hard to reconstruct, particularly without a strongly-worded examiner comment. For the majority of resources which mention them, "elastic properties" usually mean "influences of lung and chest wall on compliance", which have already bee discussed elsewhere. Occasionally, a textbook might digress on elastance, a related term which seems relevant.  Usually, a diagram is trotted out, often one which describes the relative contribution of the lungs and chest wall to static compliance.

In summary:

The book chapter by Brandolese & Andreose (1999) is particularly well suited to this topic, but it is inaccessible without paying Springer for access. Carvalho et al (2011) is free, and has a short section dedicated to elastic properties, which (given that this is not a popular exam topic) is probably enough. Wests' The Essentials (10th ed. from 2015) has a section on the elastic properties of the lung (p.111), and everybody probably already has a copy of this book, but the section itself is not particularly detailed.  Lastly, for a historical take on the evolution of these concepts, one may enjoy the excellent retrospective by Edith Rosenberg (1988).

The classical paper by Rahn, Otis and Chadwick (1946) is worth listing here, as every textbook out there seems to reproduce their diagrams. Not to be outdone, Deranged Physiology offers an illegal copy of their classical work below, stolen with absolute respect and gratitude to these early pioneers.   Though it tends to be copied in every textbook chapter on compliance, this relationship was described as "approximate" by the authors ("the evidence for this figure is indirect", they confessed in the text).  The speculative generosity which is required to produce it will hopefully become apparent in the discussion below. 

Definition of elastance

Elastance is usually defined as the reciprocal of compliance:

Elastance (E) =  ∆P/∆V

Or, "Elastance is the change in pressure per unit change in volume", if one prefers. It is usually expressed in cmH₂O/L. 

Elastic properties of lungs

In most textbooks, wherever the compliance of the respiratory system is discussed, most often one will find some reference to the "elastic recoil" of the lungs, or something similar. That an inflatable thing should have both elasticity to stretch and some degree of rubbery rebound is a completely normal thing to expect, and most people, upon handling a fresh lung specimen, will agree that it possesses those properties. In days gone by, those sorts of opportunities were apparently commonplace for students of physiology. James Carson, in 1820, remarked that

“it is commonly demonstrated in the lecture room, that, if a piece of the substance of the lungs be cut out and stretched it will recover its former dimensions when released from the extending power;” 

Though descriptive, these sorts of statements are hardly scientific, and they certainly do not help the CICM trainee to precisely define a pressure-volume relationship for a viva answer. Surely, in those dark ages of animal research when one could simply go around pulling on random animal lungs, somebody must have taken some measurements? A brief search reveals several articles answering that basic description, for instance Hoppin et al (1975). The picture below is from their paper; it is a little 1cm cube of lung tissue from a healthy mongrel, stretched sadistically between a hundred little hooks like something out of a Clive Barker movie.

Data derived from these experiments could be plotted on a graph of volume and pressure to represent elastance, which starts from somewhat above the volume of 3 ml/g of lung tissue. The graph below is a slightly Photoshopped version of Hoppin's original image:

So, from these data, it would appear that at lower pressures and volumes the pressure-volume relationship of the lung is relatively linear, and at higher volumes the pressure becomes greater. That sounds like a completely intuitive truth and one might assume that it applies directly to all mammalian lungs. Though cubed dog lung data is somewhat removed from the discussion on the elastic properties of the human respiratory system, most people tend to agree that a lung is a lung, and the same characteristics which make them fit for purpose are going to be uniform across all air-breathing species because we all have the same sort of mechanical expectations for these organs.

Generally, across literature, the most accepted and widely quote source for this curve is  Rahn et al (1946), who in turn borrowed animal data from a 1913 article by M Cloetta, titled "Untersuchungen über die Elastizität der Lunge und deren Bedeutung für die Zirkulation". Remarkably, the original article text is still available from Springer, Without going into allen Einzelheiten, it is possible to summarise Cloetta's findings by saying that the lung pressure-relaxation curve was also essentially a straight line within the normal range of pressures, and flattened out at high volumes and pressures when the lung was stretched to the limit and no further distension was possible. Borrowing the vague shape of the Cloetta data, the following curve can be plotted:

So. The transmural pressure is generally thought to be zero at some minimal lung volume, it increases trivially over the lower range of lung volumes, and then increases exponentially at high lung volumes which represents a state of bursting-point hyperinflation.  For this relationship, the transmural pressure is the pressure across the lung wall, i.e. alveolar pressure minus intrapleural pressure. This pressure, at the end of a normal expiration (at FRC), is about 4 cm H₂O; in other words the lung tissue puts 4 cm H₂O of pressure on the FRC volume.  The exact figure tends to vary across different textbooks; for instance in the Rahn paper 4 mmHg (about 5.4 cm H₂O) is given, a value borrowed from Bunta (1936). 

Speaking of which. The lower end of this relationship stretches towards something which the author decided to label as "minimum lung volume", but in actual fact this is a fairly imprecise and unscientific thing to do.  For the record, the minimum volume of a lung is probably not zero, as it does not vanish into a singularity. Nor is this the residual volume (RV), because that is the minimum volume to which a forced expiration can get you, which is limited by the structural properties of the thorax., i.e. the collapsed lung can get even smaller than that. According to some data from Frazer et al (2015), a lung which is allowed to collapse completely will still occupy some 13% of its total maximum volume, largely owing to the fact that some gas will be trapped inside alveolar units which have been disconnected from the atmosphere by the collapse of their small tributary airways. 

Elastic properties of the chest wall

The chest wall, for the purpose of this discussion, is basically a flexible bellows which has a certain resting volume. The pressure-volume relationship of the chest wall can be described by the diagram below. For exam purposes, the trainee would need to remember two important intersects: where the curve meets the FRC volume, and the point at which the chest wall pressure is zero.

As can be seen from this diagram, the pressure exerted by the chest wall is generally negative, i.e. the chest wall basically wants to expand to a resting volume which is quite a bit greater than the FRC. This is demonstrated by the fact that the chest wall, when opened, tends to expand. Bunta (1936) opened the chests of some experimental animals to explore this; Hurtado et al (1934) caused pneumothoraces in a series of COPD patients. Left to its own devices and free from the effects of negative pleural pressure, the chest walls of these experimental subjects tended to expand up to a higher volume, for which Rahn et al give a value of about 72% of the vital capacity. That 72% figure was appropriated from measurements of chest volume changes in COPD patients, and whenever one draws this curve for one's exams, one ought to ensure that the chest wall pressure curve intersects the zero pressure line at 72%, even though Rahn et al themselves confessed that "the position of this point is largely a matter of guesswork".

At the upper end of the curve, beyond the 72% volume, the chest wall is overstretched as well, and contributes to the decrease in respiratory compliance.  At the lower end of the curve, the author decided to stop plotting at the residual volume (RV), because that probably represents some sort of physiologically normal minimum for the volume of the chest wall (i.e. you can't get it any smaller without destroying it).

Relationship of compliance to elastic properies of the respiratory system

To describe the relationship between the elastic tissue components which make up lung compliance, Rahn et al (1946) created the diagram shown below, which has subsequently been reproduced throughout the world of physiology textbooks. This diagram represents the elastic components which contribute to the static compliance of the respiratory system. 

There is probably one other point on this diagram which would be essential if one is ever called upon to hastily scribble this diagram in an exam. Because of the additive effect of chest wall pressure and elastic lung pressure, the total respiratory relaxation curve for the system rapidly flattens above roughly 72% of the vital capacity (i.e. the static compliance decreases rapidly).