Computer simulations are invaluable tools in research and design. Used to predict the behavior of physical systems, these mathematical models can forecast the path of a hurricane, reveal the inefficiencies of a transportation network, replicate the birth of a galaxy, and more. Tweaking variables—for example, wind speed or ocean temperature in the case of hurricanes—produces different outcomes, enabling researchers to see multiple potential scenarios.
But the strength of some simulations to forecast an outcome is also their weakness, says Dr. Sam Raymond, a postdoctoral scholar at Stanford University. Many types of simulations only work in one direction. The program starts at one point in time and uses the laws of physics and certain user-defined parameters to end up at another. Over and over again, the simulations run, with the outcome changing incrementally each time as parameters are refined. They produce thousands—even tens of thousands—of slightly different answers to the same question, as these variables are altered before each run. But, for many types of problems, it doesn’t work in the opposite direction.
“You can ask a question and get an answer,” Raymond says. “But knowing an answer doesn’t always tell you what the question was.”
One micrometer particle (green) inside the shaped channel (white) when an acoustic wave traverses the surface of the area. Image credit: Sam Raymond.
Until now, that is. When he was a Ph.D. candidate at the Massachusetts Institute of Technology (MIT), Raymond and his colleagues combined computer simulation data with a deep learning neural network to do what neither technology can do alone: use an answer to find a question—or, to think of it another way, use a final design to create a blueprint. His technique, published in Scientific Reports, was tested on biochips that arrange cells for a variety of applications, including drug screening and tissue engineering. Not only did the research push the design of these biochips, called acoustofluidic devices, to new levels, the team’s “physics-informed machine learning” approach could be used to design other biomedical devices and optimize areas of engineering where form and function are closely related, giving designers the ability to work backward from the solution. That would save researchers development time and even help them produce biochips that have never been imagined before.
Making Waves
The biochips that Raymond and his colleagues developed are miniaturized laboratories built into silicon or glass. Those designed for cultivating organs or tissue contain a large central cavity where cells are arranged in a particular formation to encourage proper growth. But living cells are delicate and moving them around is tricky. Manipulation techniques borrowed from research on non-living particles, such as using heat, magnetism, or electrostatic forces, often harm the cells.
“Acoustics is one of the few ways that you can do this without risking damage to biological materials,” says Raymond.
Researchers use an ultrasonic transducer to turn the cavity into a microscopic wave pool. Vibrations from a range of frequencies concentrate cells in high-pressure areas and sweep them away in low-pressure areas. The boundary shape of the etched cavity dictates the pattern of the high- and low-pressure sound wave fields and ultimately the arrangement of the cells.
“Forward simulations can’t go in reverse. There’s no equation that starts from the sound wave pressure field back to tell us what the shape of the cavity should be.” - Dr. Sam Raymond, postdoctoral scholar at Stanford University
Cell positioning devices designed by a neural network trained with simulation data. Image credit: Sam Raymond.
It’s not obvious, though, what kind of pressure field a cavity’s boundary shape will produce. To find out, scientists could run these traditional forward simulations—going from question to answer—and create different cavities to see what pressure field they create. But as the complexity of the configuration—of the desired cell and therefore of the pressure field—increases, the task becomes more difficult. And, forward simulations can’t go in reverse. There’s no equation that starts from the sound wave pressure field back to tell us what the shape of the cavity should be, says Raymond.
He likens it to baking a cake. If someone produced the world’s most delicious chocolate cake and then said, “Here’s the cake, now tell me how to make it,” he says, how would one do it? This is where Raymond and his physics-informed machine learning method comes in. “We learned how to go from the baked cake to the recipe,” he says.
Recycling Data
The method came together during the second year of Raymond’s Ph.D. studies at MIT. A long way from his home in Australia, Raymond sought out biomedical engineer David Collins, then a postdoctoral researcher, who like Raymond, had studied at Monash University in Clayton, Victoria. The two started hanging out, meeting for beer and discussing their research. Raymond, whose background is in numerical simulation, was studying the interaction of solids and liquids. Collins was doing his postdoctoral work on microfluidic devices, investigating how biochip cavity boundary shapes could produce complex sound wave pressure fields. He told Raymond that he was struggling with a way to optimize the research. Raymond showed Collins his idea for combining simulation with machine learning.
“I was blown away by some of the machine learning work that Sam had shown me, where, if applied appropriately, it can replicate real-world physics with a minimum of computational expense,” says Collins, who is now a lecturer in the Biomedical Engineering Department at the University of Melbourne, Australia.
“The nice thing, or the scary thing, about deep learning is that it doesn’t care about the laws of physics. It will find the relationships, even if it has to create them out of thin air.” - Dr. Sam Raymond, postdoctoral scholar at Stanford University
They agreed to partner. Raymond used MATLAB® to create simulations, based on previous research from Collins and collaborators from the Singapore University of Technology and Design, to generate tens of thousands of potential cavity boundary shapes and their resulting sound wave field. He also used MATLAB to create the deep learning neural network that would learn from the simulations’ synthetic data. Being able to write everything in the same language on the same platform, including the underlying workflow that tied the two together, without having to switch between different programs, enabled him to focus on the problem without getting distracted by compatibility issues, he says.
The deep learning neural network used the simulation results to determine the relationships between the cavity shapes and the resulting sound wave fields. Image credit: Sam Raymond.
Once the system was built, most of the simulations generated were “just random results,” says Raymond, and in normal circumstances would be tossed out. But the deep learning neural network used them to figure out, statistically, what the best possible relationships were between the cavity boundary shapes and sound wave fields—even if no equation could relate the two. “The nice thing, or the scary thing, about deep learning is that it doesn’t care about the laws of physics. It will find the relationships, even if it has to create them out of thin air,” he says.
Working Back to the Question
Raymond says he remembers the night he first ran the system. He was alone in his office at MIT. He fed the deep learning algorithm a sound wave field shape and then asked it what the cavity boundary should look like. The answer came and then as a sanity check, Raymond put the result back into the simulator, where it was run forward to see if the boundary shape predicted would in fact create the sound wave pressure field that was desired. To his surprise, the result from the simulator showed the correct answer.
“This unique approach at the intersection of physics and design has unique applications in tissue engineering, biomedical devices, and optimized design generally.”
- David Collins, lecturer in the Biomedical Engineering Department at the University of Melbourne, Australia
Raymond jokes, “I was pretty sure it was wrong.” He ran it again and got the same answer. To be sure that this wasn’t some strange fluke, Raymond and his team created many different designs that they had built and tested in the lab. He fed the AI these other sound wave fields and got more correct answers.
But their success was both a blessing and curse, says Raymond, because they ended up with many new questions. The researchers are now looking at the underlying workflow to assess why this proof of concept worked so well. Eventually, they’ll try to create more complex sound wave field shapes and push deeper into this new domain of physics-informed machine learning.
“I’m excited about what we were able to accomplish, this being the first demonstration that we can use machine learning to tune a device geometry to define an acoustic field,” says Collins. “We also think that this unique approach at the intersection of physics and design has unique applications in tissue engineering, biomedical devices, and optimized design generally.”
Left: Simulations of the shaped cavities show how the pressure minima locations will form when an acoustic wave propagates from left to right. Right: The green florescent 1μm particles align in the predicted locations within the channels when the wave is applied. Image credit: Sam Raymond.
Source: MATLAB
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