A mathematical model for the first derivative wave analysis of the volumetric capnogram from the perspective of erythrocyte motion profiles

Current trends in monitoring system are leading to the adoption of volumetric capnogram (Vcap). The first derivative wave analysis (FDWA) of Vcap represented the cardiogenic oscillations (CarO) as a propagated wave and the slope of phase III (SIII) as a constant. Until today the genesis of CarO and SIII is however under debate. In this study, we defined motion profiles of erythrocytes in the pulmonary parenchyma as pulsated-run and random-walk, on the basis of which we obtained a new mathematical expression describing FDWA of Vcap. The mathematical model of Vcap provided theoretical explanation concerned with motion profiles of erythrocytes about the genesis of CarO and SIII. As the results, the mathematical model predicted the close relationship between SIII and the transfer factor of carbon monoxide, which will be used for estimating validity of this mathematical model. In addition, the velocity of propagated wave in the phase III was suggested as a new physiological variable to estimate elastic properties of pulmonary arterioles, and a new measuring method of VD was proposed based on the theoretical reason, as well. Clinical investigations of the new VD to test its efficacy of monitoring are needed.