Modelling Fluid Movement in the Body

Our health and wellbeing depends on the movement of fluid around the body. This is especially important during surgery, when fluids are introduced intravenously (IV) to maintain appropriate fluid levels as well as to administer vital therapeutics. Mathematical models that describe the movement of fluid around the body in response to IV treatment are relied on to understand the body’s response.  

The body is a highly complex system. Presently, the standard mathematical model used simplifies many important processes such as the differences in pressure between various fluid spaces in the body. Improving our understanding of how the body responds to stresses, such as IV fluids during surgery, is important for ensuring the safety of patients – both human and animal alike. 

A Biophysical Model

Researchers at the Ontario Veterinary College (OVC) worked with Dr. Allan Willms, a Professor in the Department of Mathematics and Statistics, to develop a better model. Spearheaded by undergraduate student Sarah Abel (currently pursuing a master’s degree at the University of Ottawa), the team thought about how improvements could be made. 

“The current model assumes the body is trying to maintain target volumes in various places around the body,” said Willms. “We wanted to develop a pressure-based model that better incorporates biophysical processes.”

The model by Abel and Willms was tested against the current model using data collected by researchers at the OVC for cats undergoing surgery. Hemoglobin and blood pressure measurements were taken at regular time intervals over 3 hours for cats both awake and under anesthesia after an IV fluid was administered. The data were then fit to both models and compared. The team found that the new pressure-based model better fit the experimental data in all but one case, demonstrating an improvement over the current model.

A Continuing Collaboration

These results help to improve our understanding of fluid dynamics in the body and could aid in the success of surgeries for both animals and humans.

“There are extra stresses on the body during surgery,” says Willms. “A better model could impact surgery outcomes.”

Willms plans to continue working with the OVC on projects where mathematics could be used to improve animal health.  

This story was written by Carley Miki as part of the Science Communicators: Research @ CEPS initiative. Miki is a PhD candidate in the Department of Physics under Dr. John Dutcher. Her research focus is on understanding the forces and interactions between soft, sugar-based nanoparticles and how they differ when charged.

This work is supported by the Ontario Veterinary College Pet Trust.

Abel, S., et. al.  A Pressure-Based Model of IV Fluid Therapy Kinetics. Bull. Math. Biol. 2024, 86, 133. doi: https://doi.org/10.1007/s11538-024-01362-5