Collaborative Research: Mathematical Modeling of Respiratory Muscles

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The process of breathing is driven by respiratory muscles that include the diaphragm, the rib cage muscles, and the abdominal muscles. Better understanding of the role of respiratory muscle in healthy and pathological conditions is expected to lead to improved patient outcomes. This collaborative research will develop comprehensive mathematical models for respiratory muscles, with a special focus on diaphragm, the major muscle of respiration. Computational methods will be developed to describe the motion and the mechanical loading conditions of the diaphragm during respiration. The project aims to improve understanding of diaphragm mechanics and will generate analytical tools to quantify the performance of the diaphragm. In particular, the project will provide quantitative relations between the level of muscle activation and the amount of air displaced by the diaphragm during normal breathing or intense physical activities. By providing a foundation for basic understanding of functionality of respiratory muscles, the research project could improve the management of patients in hospital intensive care units leading to a long-term positive impact on public health. The project will provide training, education and learning opportunities for students at the University of Houston and Baylor College of Medicine with a focus on training underrepresented students. The project will take an innovative approach to explore fundamental mechanics of diaphragm function and to develop computational methods that are capable of simulating and predicting the complex shape, kinematics, and the mechanical stress field in the diaphragm during respiratory efforts. The main objectives are to: (1) Develop a constitutive theory for respiratory muscles, especially diaphragm muscle fibers which have complex microstructures with sarcomeres as the basic motor unit. The constitutive function relates the stress to the deformation in response to activation of the diaphragm muscles. (2) Develop a continuum mechanics theory for active material surfaces to model the diaphragm function. The model will accurately account for large deformations of the diaphragm muscle fibers. (3) Derive the equations of motion for the diaphragm, which, in corporation with the constitutive theory, will lead to the differential equations governing the motion of the diaphragm under the actions of the muscle activation and the transdiaphragmatic pressures. Novel computer programs will be developed to facilitate the solutions of the differential equations. (4) Perform in vitro experiments to supply the experimental data needed for the constitutive functions of the diaphragm. (5) Validate the theory and the computational models by comparing the predicted behavior of diaphragm with experimental measurements. Refined computational models will allow researchers to predict the motion of diaphragm with user-input constitutive functions, geometry, and loading conditions. Project results are expected to increase physiologic understanding of respiratory muscle function in health and disease.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.