Markov Chain Modeling and Simulation of Breathing Patterns
  The lack of large video databases obtained from real patients with respiratory disorders makes the design and optimization of video-based monitoring systems quite critical. The purpose of this study is the development of suitable models and simulators of breathing behaviors and disorders, such as respiratory pauses and apneas, in order to allow efficient design and test of video-based monitoring systems. More precisely, a novel Continuous-Time Markov Chain (CTMC) statistical model of breathing patterns is presented. The Respiratory Rate (RR) pattern, estimated by measured vital signs of hospital-monitored patients, is approximated as a CTMC, whose states and parameters are selected through an appropriate statistical analysis. Then, two simulators, software- and hardware-based, are proposed. After validation of the CTMC model, the proposed simulators are tested with previously developed video-based algorithms for the estimation of the RR and the detection of apnea events. Examples of application to assess the performance of systems for video-based RR estimation and apnea detection are presented. The results, in terms of Kullback-Leibler divergence, show that realistic breathing patterns, including specific respiratory disorders, can be accurately described by the proposed model; moreover, the simulators are able to reproduce practical breathing patterns for video analysis. The presented CTMC statistical model can be strategic to describe realistic breathing patterns and devise simulators useful to develop and test novel and effective video processing-based monitoring systems. 
Davide Alinovi, Gianluigi Ferrari, Francesco Pisani, Riccardo Raheli
stat.AP cs.CV