# Opening Airways

## Modeling how to reopen collapsed airways

Scientists are breathing new life into airway modeling. Using a three-dimensional mathematical model of the delicate passages in the lungs, researchers have found that strongly collapsed airways are actually easier to reopen than partially collapsed ones.

“Everybody I have mentioned it to has said, ‘No, but surely, that’s the wrong way around,’” says Matthias Heil, PhD, a reader in applied mathematics at the University of Manchester, United Kingdom.

Heil and Andrew Hazel, PhD, a mathematics lecturer at the University of Manchester, created a model of the respiratory tracts to study how a stream of air can open a closed airway. The work was published in the August 2006 issue of the Journal of Biomechanical Engineering.

A surfactant layer of proteins and lipids normally lines airways, reducing surface tension along the fluid-covered walls. However, many premature babies lack surfactant, and adults who have gulped air filled with smoke or noxious fumes can destroy their surfactant layers. In these cases of respiratory distress syndrome, the surface tension increases, the airways collapse, and the fluid lining becomes a blockage. Doctors treat this collapse by forcing pressurized oxygen vigorously into the airways to redistribute the fluid. They often add surfactant to avoid damaging lungs with over pressure.

“You want to reopen the lung as soon as possible,” says Heil. “The easiest way to do this is to apply an enormous amount of pressure, but then you can actually damage the lung tissue. So there’s a fine balance to be found.”

Heil and Hazel’s three-dimensional model surpassed previous two-dimensional models by taking the fluid’s viscosity, inertia, and surface tension into account. With this more realistic model, they revealed that less pressure is required to reopen airways that have collapsed more completely. The smaller cross-section of fully collapsed airways means a smaller volume of fluid to redistribute. This takes less energy, and less air pressure, than moving around fluid that clogs a partially collapsed airway.

However, the researchers acknowledge shortcomings in their model. Airways are not infinitely long tubes, as Heil and Hazel assumed. “The airway branches are relatively short before they branch again,” says Heil. “You have this tree structure, and that is something we do not take into account.”

Oliver Jensen, PhD, professor of applied mathematics at the University of Nottingham, United Kingdom, says the new model is a step forward compared to older ones. “They’ve developed an absolutely wonderful tool,” says Jensen. He notes the model also should apply to other systems with fluid-lined tubes, such as blood vessels.

For doctors who treat collapsed airways, Heil and Hazel’s work eventually could lead to fine-tuned air pressure for different patients. For now, when doctors sit down to use a ventilator, says Jensen, “It’s nice if they can at least understand what is happening in the airways.”

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