Inflation of a pressure-limited cuff inside a model trachea

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Abstract

A theory of the elastic behaviour of thin rubber films is developed to describe inflation of pressure-limited tracheal tube cuffs (a) outside and (b) inside rigid cylindrical model tracheas. At each stage, assumptions and results were successfully checked against experiment. The theory predicts cylinder wall versus intracuff pressure. This allows, for any suitable cuff (of which there are many), the determination of a single intracuff pressure that ensures a satisfactory seal, for any diameter within the human adult range, the wall pressure staying below some chosen safety limit.

Introduction

The purpose of an inflatable cuff, mounted on a tracheal tube, is to provide a seal, preventing fluid leakage from mouth to lungs, without exerting a damaging pressure on the tracheal wall. The “red rubber” cuffs of the 1960s achieved such sealing but at uncontrolled pressures that later proved to be excessive [1]. The superseding “high-volume low-pressure” cuffs [2] favoured today provide pressure control but always allow mouth to lung leakage [3], [4]. Recently, however, Young, Ridley and Downward [5] have introduced a new cuff that promises to be satisfactory in both respects and this paper provides a theoretical background to their work.

Fig. 1 shows an example of the instrument under study. Initially, as in (a), a thin rubber cuff surrounds a tracheal tube and lies flat against it, the cuff ends adhering to the tube. A hand-operated pump and manometer, registering intracuff pressure, are attached and (b) and (c) illustrate inflation progress. In clinical use, the tube is inserted into the trachea in form (a) and inflated to achieve a seal between cuff and tracheal wall. The seal needs to prevent fluid leakage at a wall pressure that is physiologically acceptable (below about 3 kPa [3], [6]). This wall pressure is not the observed intracuff value and so is not immediately accessible.

The new cuffs, called pressure-limited for a reason that emerges shortly, improve on earlier versions by sealing effectively at controllable pressures. By the latter, we mean that the wall pressure is well monitored by the manometer reading, as we now explain.

Fig. 2(a) shows schematically how, outside the trachea, the intracuff pressure varies as inflation proceeds. After an initial steep rise, there is an extended plateau of almost constant values, this feature being seen in Fig. 1(b) and (c) where the manometer reading is visually unchanged. However, inside the trachea, while inflation is initially free, contact with the tracheal wall occurs in the plateau region, seal is achieved, and there is a sharp rise in intracuff pressure (Fig. 2(b)).

Because of the plateau, the operator is alerted to cuff contact with the (sight unseen) tracheal wall. Young et al. [5] argue that the pressure on the wall is then well indicated by the observed above-plateau rise and so, under clinical conditions, is directly monitored by the manometer. The investigation of this matter initially motivated the present work.

Given the various shapes, dimensions and rigidities of human tracheas, a simple general quantitative relationship between wall and manometer pressure seems unattainable. However, for a widely used model of proven practical value [5], [7], this problem is solved below for pressure-limited cuffs. Within this specific framework, we confirm Young et al.’s hypothesis and, building on their work, suggest a new, simple, quantitative and widely applicable method for clinical deployment.

The model tracheas are lubricated, rigid, hollow cylinders of circular section; they are also transparent so that the length of wall-cuff contact can be measured and used to check theoretical predictions. (To avoid confusion, model tracheas will be called cylinders for brevity, the word tube always implying a tracheal tube on which, as in Fig. 1, a cuff is mounted).

Fig. 3 describes longitudinal sections through the central axis of the cuff, symmetry requiring the display of only a quarter of each. Fig. 3(a) corresponds to Fig. 1(a), r being the radius and d the half-length of the uninflated cuff. Fig. 3(b) illustrates free inflation, as shown in Fig. 1(b) and (c), Rt (t = transverse) being the equatorial cuff radius. Fig. 3(c) describes the inflated cuff inside the model trachea and with a half-length h of contact. If R is the (inner) radius of the cylinder, then the transverse cuff displacement is limited to Rr after contact.

The cuff rubber is expected, and assumed, to be homogeneous and isotropic. Furthermore, shear is absent at the lubricated interface with the cylinder; consequently, throughout the region of contact, the cuff’s thickness, the longitudinal and transverse tensions within it, and its pressure on the wall are all constants. The basic problem is to find this pressure in terms of accessible parameters.

Section snippets

Rubber elasticity

Some basic properties of rubbers, to be used later, are now discussed.

Stretching of a rubber sheet

In this section, sufficient general theory is developed to address the particular problem of cuff inflation. The validity of Hooke’s law for large strains, demonstrated in §2.4, encouraged us to adopt its standard two-dimensional generalisation below. The merit of this approach is that only one free parameter (Ez0) appears in the theory and this proves sufficient for success over the clinical range. Other theoretical ‘off the peg’ prescriptions [9] are either non-linear or use more than one

Free cuff surfaces and their generation

We now describe the shape of the cuff section shown in Fig. 3(b) (see also Fig. 6) and its generation from that of Fig. 3(a). To do so, we invoke two hypotheses.

Hypothesis 1

(Profile shape). We suppose that free cuff lines of longitude are circular. Then, recalling that Rt (t = transverse) is the equatorial radius (i.e. the maximum sideways displacement from the central axis), simple geometry shows that the radius Rl (l = longitudinal) of the arc shown isRl=(1/2)[d2+(Rt−r)2]/(Rt−r).

Hypothesis 2

(Profile generation).

Wall and intracuff pressures; general features

Fig. 3(c) shows a fixed configuration after wall contact, the cuff consisting of a central cylinder and tapered ends that leave the wall tangentially. Infinitesimally right of the critical contact indicated, the excess (intracuff) pressure is normal to the wall and, by (3.7), is written in the form pcuff(h) = pl(h) + pt(h). To the left, however, the excess pressure is pcuff(h) – pwall(h) and is given by pt(h) only because, in this cylindrical region, the longitudinal curvature and corresponding

Wall pressure and above-plateau rise

Fig. 2 is next illustrated quantitatively. Elementary calculus and the circular arc hypothesis of §4.1 lead to simple (but long and, therefore, not quoted) formulae for the volume in terms of Rt, before wall contact, and R and h afterwards, the results in Fig. 8, Fig. 9 then transcribing into Fig. 10. This exercise is, however, a divertissement because explicit consideration of volume proves to be unnecessary for our purposes. The results are shown because the problem of relating wall to

Acknowledgements

We thank Prof. N E Cusack and Dr. M Silbert for valuable discussions and for their critical readings of the manuscript, Prof. N Riley for his continued interest, general help and encouragement and Dr. S J Meldrum for his initial advice.

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