[James P. Butler (left) is a light-weight physiologist (here in zero gravity, photo courtesy of K. Prisk), interested in all aspects of breathing including comparative physiology spanning birds to whales, and of course humans, both awake and asleep. At the whole organ level, he is particularly interested in lung mechanics, gas exchange, and aerosol transport; at the cellular level he works in the rheological properties of single cells and migrating monolayers, and their interaction with the mechanical microenvironment. By contrast and more down-to-earth, Andrew Wellman (right) is a heavyweight physiologist and physician, interested in the interplay of anatomy and control mechanisms influencing breathing patterns, especially during sleep. His particular expertise covers obstructive and central sleep apneas, and the role of loop gain in determining periodic breathing and breathing stability.]
The behaviour of Starling resistors has a long history, including an early physiological application to micturition (Griffiths, 1971), vascular waterfalls (Permutt et al. 1961), and, importantly in our understanding of expiratory flow, limitation during a maximal expiratory effort (Dawson & Elliott, 1977; Shapiro, 1977). More recently, Starling resistor behaviour has been applied to inspiratory flow limitation in the pharyngeal airway (Schwartz et al. 1988; Smith et al. 1988). In its simplest form, a Starling resistor is a compliant tube; the inlet and outlet pressures are specified, as is the pressure exterior to the tube. Because the exterior pressure and the upstream pressure are coupled (e.g. through lung recoil) such a system typically displays the phenomenon of flow limitation. Increases in driving and exterior pressure lead to increases in flow, but only up to a point beyond which flow is constant: the system is flow limited.
This phenomenon has been explained and interpreted on a number of grounds: the equal pressure point concept of Mead (Mead et al. 1967) and on a more theoretical basis by (Dawson & Elliott, 1977) and independently by Shapiro (Shapiro, 1977). The latter two theories are more complete, and invoke the concepts of wave speed and choke points, which rest on the fundamental idea that the area–pressure relationship of the tube, the so-called tube law, is local. By this we mean that the airway area, at any point, is uniquely defined by the transmural pressure in the airway at that same point. Upstream or downstream variations in pressure have no effect on this relationship. To be sure, variations in caudal traction (Begle et al. 1990) and posture (Malhotra et al. 2004) can influence the tube law, but for any given configuration of elastic properties of the upper airway, the tube law is taken to be local. If the tube law were truly local, then the Starling resistor approximation holds: flow will increase with increased driving pressure and then become limited.
This idea, however, is experimentally contradicted in a subset of individuals in whom profound inspiratory negative effort dependence is observed. Figure 1 shows an example of this: the continuous trace is experimental data in a subject with sleep apnoea. It shows that past the point of maximum flow further decreases in epiglottic pressure are accompanied by significant decreases in inspiratory flow rates. In some subjects this decrease may lead to complete occlusion of the airway and cessation of flow. These observations cannot be accounted for by a Starling resistor.
We therefore take an alternative view, in which the tube law may be described as lumped as opposed to local. The assumption that a tube law is local may indeed hold for blood vessels and intrathoracic bronchi, where gross masses of peri-structural tissues are largely absent. But these conditions are clearly not true in the upper airway, where neck tissue, muscle, fat, peripalatal tissue, etc. are all in large quantity. Importantly, the tongue itself is a large mass. It is this that we shall focus on in the context of promoting an idea of the ‘tippy tongue’.
Suppose that the tongue, as it is subjected to increasingly negative intrapharyngeal pressures during inspiration, moves posteriorly effectively as a rigid body, subjected only to a restoring torque that would otherwise hold the tongue (and perhaps the soft palate as the tongue pushes against it) in a neutral position. This situation is equivalent to a ‘lumped’ system that controls the luminal area of an entire segment of the upper airway. The distinction between local and lumped is important. For example, in a simple floppy tube, the cross-sectional area at a point is defined by the transmural pressure only at that point; this is a local tube law. By contrast, if tissue displacement in one area (e.g. tongue moving posteriorly) affects the cross-sectional area of the tube in another segment (e.g. tongue dragging the palate posteriorly as well) through tethering forces, then the cross-sectional area is determined by the distribution of pressures throughout that segment; this is a lumped tube law. For the lumped tippy tongue model, it is clear that with the application of sufficient negative downstream epiglottic pressure the lumen can be made arbitrarily small, and the flows will decrease, in some cases even to the point of complete closure – this mechanism can account for profound negative effort dependence. It is important to recognize that this simple model is based on dissipation, but does not feature any Bernoulli effect nor wave speed. There is no choke point; this is not a Starling resistor.
In the simplest model, we envision the tongue as a lumped piston in a uniform two-dimensional channel. The downstream pressure–flow relationship is given by:
where Pepi is epiglottic pressure, is flow per unit channel width, μ is gas viscosity, L is channel length, and is channel height. (The familiar formula for flow in a circular pipe is .) The simplest lumped tube law is a linear relationship between channel height and mean pressure in the segment, say , where Pc is the critical closing pressure under static conditions, and h0 is the channel height at passive equilibrium (). From these two elementary relationships, the flow–pressure relationship is given by:
The shape of this curve shows flow increasing as epiglottic pressure decreases up to a point, below which there is a sharp drop in flow with further decreases in Pepi. The continuous trace in Fig. 1 shows this flow–pressure relationship for parameters chosen as L= 9.7 cm, h0= 17 cm, Pc=−8.3 cmH2O. The long dashed continuation of this curve departs from the data, and is due to the model's linear channel height–mean pressure relationship. The actual data suggest that that the lumped segment law shows stiffening as the area decreases, which is consistent with strain stiffening of tissue as well as with reflex activation of, for example, the genioglossus muscle (Malhotra et al. 2004). For completeness, we also show in Fig. 1 the behaviour expected from a Starling resistor (short dashed line): past the point of maximal flow, the flow remains constant in spite of increased driving pressure.
We explicitly do not make claims about the particular details of our model. For example, the general behaviour noted above differs in only small ways (exponent, prefactors, etc.) depending on the manner of airway collapse (two-dimensional channel, three-dimensional circular lumen). The pressure drop in this model is also taken to be laminar Poiseuille, but even if the losses are turbulent, the same features are obtained. These issues are secondary to our main argument that a lumped tissue picture in fact can capture the qualitative essence of marked negative effort dependence that, in principle, cannot be found in a Starling resistor concept.
In summary, we assert that there is no mechanism in Starling resistors or wave speed theories that can account for the profound negative effort dependence seen in some patients. For these individuals, we claim that the upper airways do not behave as Starling resistors; wave speed and choke points are irrelevant.
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