A brief introduction to lungs
What do dinosaurs, ninjas, and The Fonz all have in common? If you said “they are all cool” then you are correct. Another acceptable (and more obvious) answer is that they all have lungs. Why is this more obvious? If they didn’t have lungs, they would be unable breathe, which would be most uncool. Imagine, for example, that The Fonz couldn’t breath. What would happen? For one thing, he wouldn’t be able to say “Ayyyyy”, the very line that earned him an honorary PhD in coolness. I'm sure you now realize why the lungs are so important. But what do they do?
The lungs are just one part of the respiratory system. The primary goal of the respiratory system is to deliver oxygen to the blood and to remove carbon dioxide from the blood to the environment. The respiratory system consists of the controller (signal generator in the brain), the pump (muscles such as the diaphragm and intercostals), and the site of gas flow and exchange (the lungs). Respiration occurs by pumping fresh, oxygenated air in through the trachea and delivering it to the alveoli, which are air sacs that form a blood/gas interface with capillaries to perform the gas exchange. By maintaining concentration gradients, oxygen diffuses through the alveoli to the blood while the carbon dioxide diffuses from the blood to the alveoli.
The trachea splits (bifurcates) in two directions to form airways in the left and right lungs. These airways continue to bifurcate for 15 more generations and become smaller each time. The branches of generation 16 are known as the terminal bronchioles. Up until this point the gas is transported by convection and no gas exchange occurs. Consequently, the first 16 generations are termed “anatomic dead space,” which sounds like something out of a science fiction movie. The next 7 generations are known as the “respiratory zone,” which consists of airways lined with alveoli that end in alveolar sacs (acini). The average person has 300 million alveoli, and each is of about 100 micrometers in diameter. They contribute collectively to a surface area of up to 100 square meters. This huge surface area is ideal for fast gas diffusion, since diffusion is proportional to the surface area.
High frequency oscillatory ventilation (HFOV)
Sometimes, for a variety of causes, the lungs will fail. At this point, the person will have two options: die, or be temporarily transformed into a cyborg. Those who choose the latter are placed on a mechanical ventilator, which allows control over the pressure, volume, and rate of air delivered to the alveoli. The volume of air in a single breath is known as the "tidal volume." Conventional ventilators can have a harmful effect on infants because normal tidal volumes may overstretch the lungs. HFOV is a highly effective alternative, which uses high frequency (10 - 15 breaths per second) and smaller tidal volumes, which reduces the risk of lung damage.
It is important to note that nobody (including The Fonz) really understands why HFOV works so well. Specifically, why do small tidal volumes at high frequencies ventilate so well? How strongly does the frequency depend on the geometry of the lung? We would like to know the answers, so we are in the process of constructing a mathematical model. I am currently continuing the work of the last two generations of immersion participants.
The simplest approach is to consider three parameters of airflow in the lungs: resistance, inertance, and compliance. Resistance arises from the geometry of the airway and the viscosity of air, and is essentially the proportionality constant between pressure and flowrate. Inertance is related to the force needed to accelerate air. In both a static model and low frequency spontaneous breathing, this term is absent. However, when you have high frequency oscillations in pressure (as in the case of HFOV), the air constantly has to be accelerated and decelerated. Consequently, inertance will play a much larger role. Finally, compliance is related to the “stretchiness” of the airway. It is defined as the change in volume per change in pressure. High compliance means stretchy, while low compliance means rigid. These three properties are analogous to resistance, inductance, and capacitance in electronic circuits. As a result, much insight regarding frequency response has been gained from studying RLC circuits.
In the past, Dr. Frayer and his students have attempted to model most of the major airways (down to generation 12) by constructing branched RLC circuits and solving for the voltage and current in each generation. So far, I have been able to solve for up to 17 generations including a capacitor model of the respiratory zone. In determining the transfer function (ratio of output pressure to input pressure), I have discovered multiple resonance peaks, the positions of which are highly dependent on the lung compliance. However, most of these peaks are out of the range of frequencies used in HFOV.
Dr. Frayer and I have recently decided to temporarily shelve this model, as it is far too oversimplified and tells us nothing about what occurs in the acinar units. Furthermore, we cannot assume that airflow is entirely convective throughout the lungs, as we have been doing. In both the respiratory zone and in the final generations of the dead space, diffusion plays a larger role than convection in gas transport. We have begun looking into modeling software (Fluent, in particular) to model these complex regions. I will write more about this in the next couple weeks, and hopefully I will have some totally radical and/or awesome pictures.