Mathematical modelling for the study of respiratory mechanics

The target of this study was the development of mathematical models that best describe the behaviour of respiratory parameters. First of all, we studied lung volume in relation to time both for normal and maximal inspiration/expiration by developing mathematical models. For the construction of these equations the exponential model was used. Then we tried to study the flow-volume of a typical spirometer curve by dividing it into two parts: the first part reaches the Peak Expiratory Flow (PEF) point and the second follows until the volume reaches Vital Capacity (VC). For the first part we built an exponential equation; for the second part a number of existing prediction equations for the flow in various points of VC were used. For the volume-pressure diagram, we built exponential equations that describe the volume-pressure relation below Vo (Vo: lung volume where pressure is zero). The equations were coupled for expiration and inspiration. The modeling of respiratory mechanics led us to the conclusion that the developed models could offer new potentials in the description of other respiratory parameters as well.