A wearable pancreas implant that can be inserted into a diabetic’s arm to control insulin levels without requiring a lifelong regimen of immunosuppressant therapy is one step closer to becoming reality. Surprisingly, the breakthrough didn’t come from bioengineers, but rather, from mathematicians.

A team of mathematicians led by Professor Sunčica Čanić at the University of California, Berkeley, has developed a novel multiscale math model that enables bioengineers to ‘see’ for the first time what’s happening inside an implantable bioartificial pancreas (iBAP). 

The breakthrough ­­— recently featured in SIAM News, a publication of Society for Industrial and Applied Mathematics (SIAM) – uses state-of-the-art mathematical and computational methods to accurately simulate blood flow and oxygen transport in a small-scale implant. 

The work was done in partnership with the Biodesign Laboratory at the University of California, San Francisco, under the leadership of Director Shuvo Roy and is supported by grants from the National Science Foundation.

The model is significant because it gives bioengineers the information they need to optimize the flow of oxygen and nutrients to healthy implanted cells to prevent hypoxia (cell death), a major challenge facing the advancement of bioartificial organ design.

“Our model helps bioengineers understand how the blood is flowing, where the oxygen is concentrated, and what the nutrient supply looks like so they can tweak their designs to provide optimal flow,” said Čanić, whose team includes Yifan Wang, Assistant Professor at Texas Tech University and Martina Bukač, Associate Professor at Notre Dame University. 

“Up until now, scientists lacked the mathematical tools and scientific computation needed to understand how these porous, flexible materials interact with a patient’s blood inside bioartificial implants,” said Čanić. She explained that the model reveals details that can’t be accessed through measurements or experiments alone, such as oxygen and insulin concentrations at every point – rather than in total – inside the pancreas.

The Biodesign Lab’s most recent bioartificial pancreas design — currently being tested in animals — is a small device measuring roughly two-and-a-half by four inches that can be inserted into a forearm or shoulder with tubing to connect to an artery for blood intake and a vein for insulin output. Transplanted healthy pancreatic cells are housed in a sponge-like substance encased by a thin membrane and vertically drilled channels are used to deliver necessary oxygen and nutrients to the transplanted cells via blood. Once insulin-rich blood is produced, it is collected and distributed back out through the patient’s vein.

Applying their mathematical model, Čanić’s team conducted computational simulations to compare three different channel designs to support blood flow through the device: vertically drilled, branching and hexagonal. Their results showed that in the conventional vertical design, only about 13% of the transplanted cells receive enough oxygen to avoid hypoxia. In contrast, the branching design increased that percentage to nearly 52%, while the hexagonal design performed best, with more than 97% of the transplanted cells receiving oxygen concentrations above the threshold needed to prevent cell death.

Based on the findings, the Biodesign Lab team was able to refine their device to increase oxygen supply and is expected to develop and test a prototype using the hexagonal channel design in pig models next year. 

The breakthrough model is an important step forward in bioartificial organ design, said Čanić, because it is the first mathematical theory to capture what is called fluid-poroelastic structure interaction — the ‘dance’ between a free-flowing fluid like blood and the deforming of a sponge-like solid as it contracts and regains its shape. Not only is it removing a limitation in the field, but it is also bringing Dr. Roy’s team one step closer to moving from animal to human studies.

“Right now, their design is functioning, but they needed to find a way to measure and improve the flow of oxygen and nutrients in their scaffold in order to extend transplanted cell life,” she said. “By helping them to better understand how bioartificial organs carry oxygen and nutrients to cells, we’re making it possible to vastly improve oxygen and nutrient delivery, thereby prolonging the longevity of the implant.”

This model provides a powerful new computer tool that can guide the future design of bioartificial organs, Čanić explained. By combining advanced simulations with artificial intelligence (AI), the tool can quickly predict oxygen levels at the scale of individual cells – a task that previously required time-consuming and computationally expensive methods.

"We can now combine classical mathematical approaches with AI to rapidly predict oxygen concentrations for any new scaffold at the push of a button,” said Čanić. “This hybrid, AI-enhanced approach enables us to obtain detailed oxygen distribution information in real-life scaffolds far more quickly and efficiently than with traditional computational methods alone.”