Physics and Pathophysiology of the Airway by Dr. Robert Holzman.
Hello everybody.
My name is Bob Holzman.
I'm an anesthesiologist at Children's Hospital in Boston.
And what I'd like to do is share with you some of my observations, some basic science,
and some basic physics having to do with the airway.
First, we'll review laminar versus turbulent flow.
Then we'll look at expansion and collapse of spheres and tubes.
And then finally turn our attention to turbulence and pressure, the Bernoulli versus Venturi
principles and effects.
Introduction.
Noisy breathing is often an ominous sign in infants and small children.
Stridor is noisy breathing coupled with increased inspiratory effort such as nasal and ribcage
flaring and suprasternal and sternal retraction.
[SOUND OF CHILD LABORED BREATHING] Severe airway obstruction can result in cyanosis
and respiratory distress, fatigue, pneumothorax, pneumomediastinum, and death.
In addition to congenital anomalies of the larynx, foreign bodies of the aerodigestive
track can also cause stridor.
Purely inspiratory stridor usually indicates lesions in the upper part of the airway.
[SOUND OF INFANT LABORED BREATHING] Lesions, distal to the vocal cords usually
produce expository stridor.
[SOUND OF CHILD LABORED BREATHING] Biphasic stridor is most characteristic of
obstruction at the level of the subglottic space.
[SOUND OF CHILD LABORED BREATHING] Physical laws not only help explain the basis
of these signs, but also provide guidance about how to intervene clinically on their
behalf, as therapy for patients with respiratory distress.
Obstruction can occur in various locations.
And a foreign body for example, in the middle of a trachea may present with this kind of
noisy airway breathing.
Always an ominous sign for clinicians.
Other obstructions can occur within the chest itself, such as intrathoracic tumors, or mediastinal
masses.
And the quality of that noisy breathing may be slightly different.
Yet other noisy breathing can occur within the parenchyma of the lungs, but surprisingly
enough, there may be commonalities in sounds, especially when patients are initially evaluated
in emergency situations.
So what I'd like to do is review with you some basic principles of physics that govern
these airway sounds, and how you can leverage that physics understanding in order to create
therapeutic interventions that are beneficial for patients.
Laminar versus turbulent flow.
Fluids or gas molecules moving through a tube under constant pressure separate into gradients
of velocity profiles with the fastest component in the center and the slowest components near
the wall.
When that cross-sectional area is reduced, velocity has to increase and therefore the
pressure decrease, in order to maintain the same volume flow rate.
Resulting gas flow will be much more turbulent.
The flow of this fluid through the tube is proportional to the pressure gradient, the
total pressure drop over the length of the tube.
The fourth power of the radius of the tube and inversely proportional to the viscosity
of the fluid.
This relationship is the Hagen-Poiseuille Law.
The most important implication of this law, is that halving the radius, for example, will
decrease the flow rate to the fourth power, or 16-fold.
Likewise, doubling the radius will increase the flow rate by 16-fold.
This is critically important for infants and small children, especially, and explains the
transformation of the clinical picture with appropriate treatment, for example, for croupe.
The efficiency of flow distal to this obstruction, decreases because of a different physics equation,
the Fanning equation for turbulent flow.
This equation supersedes the Hagen-Poiseuille equation for laminar flow.
This is where velocity, in both equations, is equal to the flow of the gas.
P is equal to the pressure drop between proximal and distal portions of the obstruction.
The r is the radius of the tube, the eta viscosity and the l the length.
The significance of that change, in the expression from the flow rate to the square of the flow
rate, illustrates that a much greater driving pressure is required to maintain gas flow
in a non-laminar flow situation.
Note also that the power of the radius has to increase to accommodate a more turbulent
and less efficient flow.
With abrupt narrowing, complete separation of the stream profiles will occur and the
center stream constricts to a minimal value.
The resulting turbulence may not be able to resume normal laminar flow.
When difficulty occurs with positive pressure ventilation under this circumstance, the natural
response of the anesthesiologist is to apply more pressure to the rebreathing bag, or the
ambu bag.
For the patient whose airway is compromised, this results in more turbulence in the upper
airways, rather than less turbulence, and therefore a less effective airflow downstream.
Passive exhalation may also be impaired and air trapping can result.
If the change in pressure across the obstruction is reduced, for example, changing to spontaneous
breathing from controlled ventilation, in order to reduce the high pressure proximal
to the partial obstruction, then air flow is actually enhanced distally, because this
improves flow according to the Hagen-Poiseuille law.
This applies to airway narrowing regardless of intrinsic or extrinsic causes.
For example, with a mediastinal mass.
These mediastinal masses can occur anywhere, but classically the anterior mediastinum is
where the airways are compressed.
Mediastinal masses can occur in the anterior, middle, or posterior mediastinum, as well
as in the superior or inferior mediastinum.
Expansion and collapse of spheres and tubes.
So look at the dynamics within the chest.
We can examine the effect of gradually increasing intrathoracic mass on your available real
estate within that closed space.
And it's best to think of this as a linked cardiopulmonary system rather than a pulmonary
system or a separate cardiovascular system, because in fact, this is a restricted area.
And with an increase in intrathoracic mass, that restricted area is even more encroached
upon.
This therefore decreases the available diameter for airways and other intrathoracic structures.
In addition to that, in the anesthetized state or in the supine sedated and neuromuscularly
blocked state, the diaphragm rises, further decreasing functional residual capacity and
further restricting available intrathoracic volume.
This is a common situation in the operating room and in the critical care unit.
The approach to dealing with this problem, and this gradually increasing intrathoracic
mass in terms of the dynamics of spontaneous breathing versus controlled ventilation and
paralysis versus not is to allow patients to actually breathe on their own, maintaining
muscular integrity.
What happens, of course, is that there's a smaller encroachment within the intrathoracic
volume, and a greater stenting effect with spontaneous breathing on defense of the functional
residual capacity.
In addition to that, the diaphragm tends to rise, cephalad, in a less dramatic fashion,
therefore, additionally preserving intrathoracic volume.
What this might look like in a tubular illustration is something like this.
Less extrinsic or even intrinsic encroachment on the airway because of the stenting effect
of spontaneous breathing on airway dynamics, therefore hopefully promoting enhanced laminar
flow distal gas mixing and gas exchange.
This holds true as well for parenchymal disorders that result in bronchospasm.
An illustration of how this can be accomplished in the operating room is shown in this video,
where a patient with a subglottic hemangioma, an airway obstruction, is undergoing bronchoscopy.
In order to establish ideal conditions for the bronchoscopy, the ideal anesthetic technique,
at least in our institution, would be to have infants and small children breathing spontaneously
in order to preserve laminar flow and gas exchange and the distal alveoli.
We'll go on to look at Pascal's law, which is defined as the pressure inside an inflated
vessel or tube always being higher than the surrounding gas pressure because the surface
of the vessel is in a state of tension.
In this respect, alveoli resemble bubbles or spherical vessels.
LaPlace's law describes the relationship between the radius of a vessel and the wall tension
required to withstand the given internal fluid pressure.
This is different for cylinders and for spheres.
For a given vessel radius and internal pressure, a spherical vessel will have half the wall
tension of a cylindrical vessel.
And this is easily illustrated by a simple balloon.
One wonders why if the internal pressure of a balloon has to be equal by definition, why
the colors are always different.
And that's because the wall tension increases with the radius.
You can easily see that the color is more attenuated in the central cylindrical portion
of the balloon rather than at the tip, or even in the area just adjacent to the tip.
As the radius of curvature increases, the total tension needs to be greater in order
to obtain the same downward component of tension.
That's best illustrated by a rough analogy with a clothesline.
Hanging heavy clothing on a clothesline will produce tension on the clothesline, of course.
And in order for the clothesline to sag less, you have to increase its tension.
What it really is is a conservation of energy principle.
And this is demonstrated readily with the application of CPAP compared to zero end expiratory
pressure with regards to lowering the work of breathing.
We all know that CPAP will lower the work of breathing in a variety of ventilation systems,
whether they're masks or LMAs or endotracheal tubes.
The work of breathing decreases with CPAP in all of these groups except for a very small
amount in the endotracheal tube group.
This would suggest that some of the initial mechanisms that were suggested decades ago
that the work of breathing decreased because of alveolar distension may be far less important
than actual distention of the conducting airways, rather than the gas exchanging airways.
So it may be that CPAP has a more important role for improving the patency of the upper
airway rather than increasing the functional residual capacity and lung compliance, as
had initially been thought.
Turbulence and Pressure-- Bernoulli versus Venturi.
Another example of airway circumstances where physics plays a crucial role is in the role
of emergency or elected transtracheal jet ventilation.
And this is where the distinction between Bernoulli's principle and Venturi's effect
comes in.
Bernoulli actually preceded Venturi by several decades.
In 1738, Bernoulli demonstrated that the pressure of a fluid is at least where its speed is
greatest.
This is Bernoulli's law or principle.
The decrease in pressure, which follows a region of constriction, is the basis of Venturi's
effect.
And that was demonstrated about 60 years later, when Venturi showed that as a liquid passes
beyond a constriction to a wider part of the tube, its speed gradually decreases.
This is accompanied by a gradual increase in pressure.
In addition to that, Venturi showed that in order for a streaming fluid-- and in our case,
it's typically air, which is the fluid.
In order for a streaming fluid to regain a pressure much higher than that of the constriction,
the tube immediately distal to the constriction has to open out very gradually, usually not
more than a cone angle of about 15 degrees.
With Venturi jet ventilation, which is actually based on Bernoulli's principle and initially
described by Sanders in 1967, a jet replaces the constriction of the tube and the oropharynx
or the trachea acts as the diffuser.
An activating toggle switch, which is attached to the oxygen source, at 50 pounds gauge pressure
via a variable pressure reducing valve is usually used, for example, for laser surgery
of the vocal cords.
It can also be used as an emergency access for the airway and for ventilation if you
have a patent proximal airway.
Since the pressure is subatmospheric at the distal end of the jet, the air is entrained
to swell the stream of gas.
We use this principle for supplemental oxygen therapy, the Venturi mask with variable orifice
air entrainment port as well.
And it is also used as the basic principle of atomizers.
You have to be careful about jetting the patient, regardless of whether it's an emergency airway
with a cricothyroidotomy or the use of an injection technique for transglottic ventilation.
A sufficiently patent proximal airway is a constant requirement.
We take advantage of the salient features of these laws of gas flow in very logical
ways in circumstances of a foreign body, in circumstances of extrinsic compression, or
in circumstances of intrinsic airway narrowing, for example, due to inflammation.
First of all, the change in pressure can be minimized by allowing a patient to breathe
spontaneously, therefore lowering the delta P of the Hagen-Poiseuille equation.
Secondly, a small amount of CPAP applied to the breathing circuit will decrease the work
of breathing by optimizing alveolar stretch and stretching of the conducting airways.
The density of the gas mixture can be optimized by the use of helium, although this invariably
decreases the inspired oxygen concentration, which may not be the best overall strategy
for hypoxic patients who require supplemental oxygen therapy.
An example of one way where spontaneous breathing may be useful is illustrated by this foreign
body.
This is actually the metal cap of a pen after the spring was unloaded and was fired into
the airway of a toddler.
And these are notoriously difficult objects to extract from the airway, because they're
smooth and difficult to grab with forceps.
Mechanical energy applied to alveolar distention and distention of the conducting airways has
clearly been shown to decrease the work of breathing by augmentation of the functional
residual capacity and by augmentation of the conducting airways and even the oropharynx.
So this is an application of the mechanical effect of LaPlace's Law.
The same is accomplished with surfactant.
I'm glad to have had a chance to review some basic airway physics principles and how they
can potentially be applied to emergency airway situations.
Thank you.
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