A small bubble bursting in a liquid seems more whimsical than traumatic. But millions of bursting vapor bubbles can cause significant damage to rigid structures like boat propellers or deck supports. Can you imagine the damage such bubbles could cause to soft human tissue like the brain? In head impacts and concussions, vapor bubbles form and collapse violently, damaging human tissue. Fluid mechanics researchers at Purdue University have taken a step closer to understanding these phenomena.
“When a bubble collapses inside a liquid, it generates pressure shock waves,” said Hector Gomez, professor of mechanical engineering and principal investigator. “The process of a vapor cavity forming and collapsing is what we call cavitation.”
“Cavitation has been studied since the 1800s,” said Pavlos Vlachos, professor of healthcare engineering at St. Vincent and director of the Regenstrief Center for Healthcare Engineering. “It is a very complex area of study as it involves non-equilibrium thermodynamics, continuum mechanics and many other micrometer and microsecond scale factors. After hundreds of years of research, we are starting hardly understand these phenomena.”
Even less is known about bubbles collapsing in soft porous materials, such as the brain or other bodily tissues. This is important, because understanding how these bubbles behave could lead to a better understanding of concussions – or even be used to deliver targeted drugs inside the body.
In new research published in the Proceedings of the Nexus of National Academies (PNAS)Gomez, Vlachos and collaborators presented the development of a mathematical model to describe the dynamics of these cavitation bubbles in a deformable porous medium.
Cavitation happens throughout the human body – for example, the cracking sound of your joints is the sound of bubbles bursting in the synovial fluid of your joints. When fluids inside the body are subjected to pressure waves – such as when football players are hit in the head – bubbles can form in the fluid surrounding the brain. And just like bubbles that damage boat propellers, bubbles that burst near the brain could damage its soft tissue.
“The human brain is like a spongy sponge filled with water; it has the consistency of gelatin,” Vlachos said. “Its material is porous, heterogeneous and anisotropic, creating a much more complex scenario. Our current knowledge of cavitation does not directly apply when such phenomena occur in the body.”
Gomez and his collaborators developed a theoretical and computational model showing that the deformability of a porous material slows the collapse and expansion of cavitation bubbles. This breaks down the classic scaling relationship between bubble size and time.
“Our model embeds bubbles in deformable porous materials,” said Yu Leng, the paper’s first author and postdoctoral research associate working with Gomez. “Then we can extend the study of cavitation bubbles in pure liquid to soft tissues such as the human brain.”
Although complex, this model can also be reduced to an ordinary differential equation. “A hundred years ago, Lord Rayleigh developed the equation that describes the dynamics of a bubble in a fluid,” Gomez said. “We were able to augment this equation to describe when the medium is poroelastic. It is quite amazing that this complex physics still leads to a simple and elegant equation.”
Gomez and Vlachos are currently planning experiments to physically validate their results, but they are also considering the big picture. “One potential application is targeted drug delivery,” Gomez said. “Let’s say you want to deliver a drug directly into a tumor. You don’t want that drug to disperse elsewhere. We’ve seen encapsulations that keep the drug isolated until it reaches its target. The encapsulation can be broken using bubbles.Our research provides a better understanding of how these bubbles collapse in the body and can lead to more efficient drug delivery.
“Another example of future possibilities is traumatic brain injury,” Leng said. “We can extend this research to study the impact of uncontrolled cavitation collapse on brain tissue when military personnel and civilians are exposed to shock waves.”
Gomez and Vlachos say they are excited to establish a new basic science to understand the dynamics of bubbles in soft porous materials. “It opens up all kinds of possibilities for future research,” Gomez said, “and we’re excited to see how we and others will use this knowledge in the future.”
This research was supported in part by the US Department of Defense under the DEPSCoR program (Award FA9550-20-1-0165), the National Science Foundation (Award 1805817), and the US Department of Energy (Grant DE-SC0018357 ).