Fundamentals of modelling and simulation in physiology: a step-by-step cardiopulmonary model tutorial

Abstract Over half a century ago, modelling and simulation of human cardiopulmonary physiology emerged as a research methodology, comparable to laboratory experiments and clinical studies. However, teaching fundamental physiological modelling to students and applying these methods in research and simulation training remain limited by the absence of a clear, accessible introduction that guides users from model conception to interpretation of results. This tutorial addresses this gap by providing a structured, five-step introduction to physiological modelling using an established cardiopulmonary model as a worked example. It is intended as an educational resource and does not introduce a new modelling framework. The workflow covers defining model requirements, developing the conceptual model, formulating the mathematical equations, implementing and verifying the code, and validating the model. The material assumes only secondary school–level knowledge of physiology, physics, and mathematics, plus basic programming skills. A complete Python implementation used to generate the presented simulations is openly available at https://github.com/CRPH-CPM/CPtutorial . Educators in medical sciences and biomedical engineering can integrate this tutorial into curricula, while researchers can adapt it for physiological modelling projects. The framework is open-source, modular and extensible, facilitating education and development of reproducible and transferable computational physiological models.