Breathing Life Into Calculus: Using Simulation to Enhance Students' Understanding of the Relevance of Calculus to Physiology

ABSTRACT

Relating mathematics learned in the classroom to real situations increases student motivation and enhances learning. In this paper, we provide an example of a classroom application of calculus to physiology in two courses: Differential Equations and Calculus I for Biology and Medicine. We designed and implemented a project that uses calculus to model the volume, flow, and pressure of air inside the lungs of a patient receiving positive pressure ventilation. After comparing mathematical models to a mechanically ventilated high-fidelity breathing simulator, students reported heightened interest in, and a greater appreciation for, the relevance of the calculus in both courses.

Keywords:

• Calculus
• differential equations
• applications
• biology
• physiology

Additional information

Notes on contributors

Melissa A. Stoner

Melissa A. Stoner is an associate professor of mathematics in the Henson School of Science and Technology at Salisbury University in Salisbury, MD. She earned a B.S.Ed. in Mathematics from West Chester University and a M.S. and Ph.D. in Mathematics from Lehigh University with a focus on modeling neuronal networks using differential equations. Upon completion of her degree in 2011, she began teaching at Salisbury University. Her research interests are in modeling physiology with differential equations, pedagogy, and teaching mathematics content to pre-service elementary teachers.

Robert L. Joyner

Robert L. Joyner is the director of the Richard A. Henson Research Institute at Peninsula Regional Medical Center. Prior to July 2019, he was a professor of respiratory therapy and the director of the College of Health and Human Services at Salisbury University in Salisbury, MD. He earned his B.S. in Respiratory Therapy from Salisbury University in 1991 and his Ph.D. from Dartmouth College in cardiovascular physiology in 1998. Dr. Joyner joined the Respiratory Program faculty in 1998 as an assistant professor and accepted the position of Program Director in the Fall of 2003. Dr. Joyner was promoted to professor in the Fall 2011 as well as being appointed as Associated Dean of the Henson School in the fall of the same year. His current research interests include patient-ventilator interaction during invasive and non-invasive ventilation as well as interdisciplinary education and practice to improve critically ill patient outcomes.