Infusion Pump: Bond Graph Mathematical Modeling for Blood Pressure Control

One of the challenges in science is to establish mathematical relations to phenomena of the universe. In the context of Bioengineering, infusion of drugs offers risks in the administration via Infusion Pumps. This work presents the mathematical modeling process of the Systolic and Diastolic Blood Pressures to obtain as output the stabilization of the Average Arterial Pressure in an infusion pump. This study used the Simultaneous Engineering approach to ensure that Infusion Pump specifications and the mathematical model would not diverge. The components of the Infusion Pump were described using hypotheses and parameters to adapt the physical model to an analogous model with active and passive elements using the Bond Graph technique. This system was split into passive and active elements of one port and two ports and two junction elements. As result, we obtained the system equations in space state form and the mathematical model of the Infusion Pump system coupled to patient. Curves of the system response were plotted against the data obtained in the tests. It was possible to evaluate the variables in the space state in integral causality connections and obtain the equations of each diagram. This study enables the development of Infusion Pump interfaces with other devices, such as biosensors or medical monitoring applications for mobile devices.