Mathematical Modeling For The Physical Process Of End-inspiratory Plateau Ventilation

Objective:To establish the mathematical model for the physical process of end-inspiratory plateau ventilation.Methods:The physical process of end-inspiratory plateau ventilation,which is devided into inspiratory phase,end-inspiratory pause phase,expiratory phase and end-expiratory phase,were analyzed according to fundamental hydromechanics theory.Then the mathematical functions of the flow velocity(v),flow rate(Q),pulmonary volume(V_t),alveolar pressure(P_A) and airway pressure(P_aw) along with the time(t) changing during the mechanical ventilation process,were deduced.Excel 2003 was choosed in order to found the computer simulation system for the mathematical expressions of mechanical ventilation.The theory simulated curves obtained from the Excel sheets which contain the mathematic functions,were compared with those obtained from clinical monitoring.Results:The simulation system of the mathematical model operated normally.The theory curves of the simulation system were highly similar to those captured from clinical monitors. The simulation system can reproduce the clinical working curves of some kinds of ventilators in different condition.Conclusion:Based on data and image analyses,the simulation curves were much the same as the workings curves from clinical monitoring.The facts proved that the deduction of the physical process of end-inspiratory plateau ventilation was reasonable and the computer simulation was exact without error.The mathematical model for the physical process of end-inspiratory plateau ventilation can be established undoubtedly.The mathematical model system indicated the existence of airflow in end-inspiratory pause phase and can represent the physical process of mechanical ventilation well.It can provide a reliable theory platform for research this ventilation mode further and it will make a base of computer simulation system of mechanical ventilation in future.