Several processes occurring in the respiratory system involve complex solid and fluid mechanics. In the lungs, the multiscale nature of the airway network is coupled with the multiphysical processes that govern phenomena such as airway ventilation, gas exchange, airway closure/reopening, mucus rheology, surfactant transport and formation of respiratory aerosols. The deep lung - the tens of thousands of peripheral airways that lie below the resolution of many imaging modalities - provides abundant examples of mechanical processes that are fundamental to understanding the origins, and treatment, of disease. While engineers and mathematicians have modeled individual processes for decades, integrative first-principle modeling has recently gained more traction in the medical community as a useful tool to better understand and also predict biological processes. Substantial improvements, made in recent years, allow descriptions of fundamental physical processes to be integrated in models with increasing physiological realism.

We aim to provide a comprehensive overview of the modeling techniques used to study the respiratory system, comparing their strengths, limitations, and potential for future development. We will explore a range of methodologies: (i) first-principle models, used in detailed computational simulations; (ii) reduced-order models, which exploit asymptotic methods and perturbation techniques; (iii) integrative multiphysics models, focused on the interactions across multiple spatial and temporal scales, from molecular-level processes that regulate mucus rheology to organ-scale multiphase dynamics; (iv) neural networks and digital twin models, which became valuable tools for refining model predictions owing to the increasing availability of medical imaging and experimental data. Moreover, a significant part of the course is dedicated to in-vitro and on-a-chip models, providing a bench-top microfluidic framework for probing the mechanics of the deep lung. Throughout the course, the physiological relevance of models will be critically evaluated.

Beyond discussing these methodologies, we will provide a comparative assessment of their applicability in different scenarios, highlighting their respective advantages and trade-offs in terms of accuracy, computational efficiency, and feasibility for clinical integration. We will also discuss emerging trends in respiratory modeling, such as the role of artificial intelligence in automating model calibration, the development of patient-specific simulations, and the integration of real-time sensing data into predictive frameworks.

The course will cover a wide range of topics — from modeling and numerical simulations to experiments, from fundamental mechanics to lungs on-a-chip — and requires participants to engage across disciplinary boundaries. The course is designed for researchers in Engineering, Applied Mathematics, Physics, and Medical Science who have a solid background in mathematical modeling and mechanics. Ideal participants are familiar with the principles of continuum mechanics and have experience in translating complex physical systems into numerical simulations or analytical models.