Collaborative Research: Mathematical Modeling of Respiratory Muscles

呼吸的过程是由呼吸肌驱动的，呼吸肌包括膈肌、胸腔肌和腹肌。更好地了解呼吸肌在健康和病理条件下的作用有望改善患者的预后。这项合作研究将开发呼吸肌肉的综合数学模型，特别关注呼吸的主要肌肉横膈膜。将开发计算方法来描述呼吸时隔膜的运动和机械载荷条件。该项目旨在提高对隔膜力学的理解，并将产生分析工具来量化隔膜的性能。特别是，该项目将提供在正常呼吸或激烈的体育活动中肌肉激活水平与横膈膜排出的空气量之间的定量关系。通过对呼吸肌功能的基本了解，该研究项目可以改善医院重症监护病房患者的管理，从而对公共卫生产生长期的积极影响。该项目将为休斯顿大学和贝勒医学院的学生提供培训、教育和学习机会，重点是培训代表性不足的学生。该项目将采用一种创新的方法来探索隔膜功能的基本力学，并开发能够模拟和预测呼吸过程中隔膜复杂形状、运动学和机械应力场的计算方法。主要目的是：(1)建立呼吸肌，特别是膈肌纤维的本构理论，膈肌纤维具有复杂的微观结构，以肌节为基本运动单位。本构函数将应力与膜片肌激活时的变形联系起来。(2)为活性物质表面建立连续介质力学理论来模拟膜片功能。该模型将准确地解释膈肌纤维的大变形。(3)推导出横膈膜的运动方程，与本构理论相结合，得到在肌肉激活和横膈膜压力作用下横膈膜运动的微分方程。将开发新的计算机程序以方便微分方程的解。(4)进行体外实验，提供隔膜本构功能所需的实验数据。(5)通过将预测膜片性能与实验测量值进行比较，验证理论和计算模型。精细的计算模型将允许研究人员根据用户输入的本构函数、几何形状和加载条件预测隔膜的运动。项目结果有望增加对健康和疾病中呼吸肌功能的生理学理解。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.