A Stochastic Optimal Control Theory to Model Spontaneous Breathing

作     者：Kyongyob Min 

作者机构：Respiratory Division Department of Internal Medicine Itami City Hospital Itami Japan 

出 版 物：《Applied Mathematics》 (应用数学（英文）)

年 卷 期：2013年第4卷第11期

页      面：1537-1546页

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：Biological Variability Stochastic Processes Optimal Stochastic Control Theory Probability Density Function Shr?dinger’s Wave Equation 

摘      要：Respiratory variables, including tidal volume and respiratory rate, display significant variability. The probability density function (PDF) of respiratory variables has been shown to contain clinical information and can predict the risk for exacerbation in asthma. However, it is uncertain why this PDF plays a major role in predicting the dynamic conditions of the respiratory system. This paper introduces a stochastic optimal control model for noisy spontaneous breathing, and obtains a Shrödinger’s wave equation as the motion equation that can produce a PDF as a solution. Based on the lobules-bronchial tree model of the lung system, the tidal volume variable was expressed by a polar coordinate, by use of which the Shrödinger’s wave equation of inter-breath intervals (IBIs) was obtained. Through the wave equation of IBIs, the respiratory rhythm generator was characterized by the potential function including the PDF and the parameter concerning the topographical distribution of regional pulmonary ventilations. The stochastic model in this study was assumed to have a common variance parameter in the state variables, which would originate from the variability in metabolic energy at the cell level. As a conclusion, the PDF of IBIs would become a marker of neuroplasticity in the respiratory rhythm generator through Shr?dinger’s wave equation for IBIs.