In recent studies on the dynamic characteristics of ventilation system, it was considered that human had only one lung, and the coupling effect of double lungs on the air flow can not be illustrated, which has been in regard to be vital to life support of patients. In this article, to illustrate coupling effect of double lungs on flow dynamics of mechanical ventilation system, a mathematical model of a mechanical ventilation system, which consists of double lungs and a bi-level positive airway pressure (BIPAP) controlled ventilator, was proposed. To verify the mathematical model, a prototype of BIPAP system with a double-lung simulators and a BIPAP ventilator was set up for experimental study. Lastly, the study on the influences of key parameters of BIPAP system on dynamic characteristics was carried out. The study can be referred to in the development of research on BIPAP ventilation treatment and real respiratory diagnostics.
Mechanical ventilation is an intervention used to help patients breathe in ICU. The aim of mechanical ventilation is to improve gas exchange rate of patients’ respiratory system and help critically ill patients or patients with various forms of respiratory disorders reduce breathing work [
At present, there are a variety of mechanical ventilations controlled models, such as Pressure Controlled Ventilation (PCV) and Volume Controlled Ventilation (VCV) [
In recent researches on mechanical ventilation systems, it was considered that human had only one lung for easy analysis [
As is known, the coupling effects of double lungs on dynamic characteristics of mechanical ventilation system are of significant for the security and effect of mechanical ventilation, which can not be illustrated when just only one lung is considered [
Furthermore, the models of the mechanical ventilation systems with just only one lung are not comprehensive or precise which reduces their applicability and versatility and makes great error on the respiratory parameter identification [
However, till now, there are few studies on the mechanical ventilation system with double lungs.
In this paper, to lay a theoretical foundation for safe, efficient mechanical ventilation and accurate respiratory parameter identification, firstly, a mathematical model of a mechanical ventilation system, which consists of double lungs and a bi-level positive airway pressure (BIPAP) controlled ventilator, was proposed. To verify the mathematical model, a mechanical ventilation system prototype was set up for experimental study. Lastly, the influence of parameters of ventilation system on dynamic characteristics was discussed.
A BIPAP ventilation system of double lungs, as shown in Figure
Structures of mechanical ventilation system with double lungs and equivalent pneumatic system.
Mechanical ventilation system
Equivalent pneumatic system
According to these functions, an air compressor is used to imitate ventilator, three throttles are used to imitate exhalation valve and two tubes, and two lungs can be regarded as two variable volume containers. The matching of settings of ventilator to actual parameters of the respiratory system has an effect on efficiency of ventilation which is mainly made up of respiratory resistance (
However, the respiratory resistance
In order to facilitate research, the study was conducted under the assumptions that no air leaks during working process, and the dynamic process is a quasi-balanced process [
The air mass flow can be obtained by flow equation of throttles after air flows through the LAVAL nozzle. For each lung, when
The research is under the assumption that the inspiration and respiration are isothermal processes. The differential expression of the Clapeyron equation (
We can transform (
According to the definition of the respiratory compliance (
Then the volume of right lung and left lung can be calculated by
To verify the mathematical model described above, an experiment for the ventilation has been conducted. As shown in Figure
Experiment apparatus.
The pressure-flow sensor called FlowAnalyser ventilator tester PF-300 is provided by the
There are several main settings of ventilator: inspiratory positive airway pressure (IPAP), expiratory positive airway pressure (EPAP), breaths per minute (BPM), inspiratory time (
According to the mathematical model and the experiment described above, the curve of pressure in one lung from experiment and the fitted curve of the air pressure in one lung simulator from simulation are shown in Figure
Curve and fitted curve of air pressure in one lung simulator.
Curve of air mass flow of one lung simulator.
In addition, the two lung simulators are the same. In other words, for each lung the respiratory compliance (
The software, MATLAB/Simulink, is used for simulation.
From Figures The simulation results are in accordance with the experimental results. It verifies the mathematical model can be used in this research. As IPAP and EPAP offered by the ventilator are 23.5 cmH2O and 4.5 cmH2O, there exists little error, but the error can be neglected, and therefore the experiment results are authentic and reliable. The reason of difference between experimental results and simulation results is that there is a little air leakage during the working process in the experiment.
As humans have two lungs, different parameters between two lungs affect dynamic characteristics of the system. So it is necessary to study the effects of several main parameters on the dynamics of the ventilation system of the two different lungs in different conditions.
Since there are so many articles and studies about dynamic characteristics of ventilation system of one lung at present, it does not make any sense to study these dynamic characteristics of each lung simulator in this ventilation system. Among all kinds of dynamic characteristics, the ratio of air mass flow in right lung simulator (
In this study, the respiratory compliance (
Influence of
The relation between respiratory compliance and the ratio of tidal volume of right lung simulator (
Influence of
From Figures
As the ventilation system has inspiration process and expiration process, the ratio of air mass flow has two fluctuations in one period. When respiratory compliance (
Furthermore, when the air mass flow of one lung simulator comes to be 0, the other lung simulator still has air mass flow. That is the reason why the ratio can be 0 and 100%.
Finally, with a rise of respiratory compliance (
Influence of
The relation between respiratory compliance and the ratio of tidal volume of right lung simulator (
Influence of
As shown in Figures
Firstly, there are two processes in the ventilation system, so the ratio of air mass flow has two fluctuations in one period. When the diameter (
Furthermore, the same as the influence of respiratory compliance (
Lastly, as a rise of the diameter (
So far, the dynamic characteristics which have been studied are under the fixed condition of ventilator. However, the key parameters of ventilator can make a difference on dynamic characteristics of mechanical ventilation system of two different lung simulators. Therefore, it is of great necessity to study the influence of the key parameters of ventilator on two different lung simulators.
The IPAP is set to 18 cmH2O, 22 cmH2O, and 24 cmH2O. The respiratory compliance (
Influence of IPAP on air mass flow when
Influence of IPAP on air mass flow when
With an increase in the respiratory compliance (
Influence of IPAP on tidal volume of different
As presented in Figures
Influence of IPAP on air mass flow when
Influence of IPAP on air mass flow when
With an increase in the diameter (
Influence of IPAP on tidal volume of different
From Figures
The EPAP is set to 4 cmH2O, 6 cmH2O, and 8 cmH2O. And the simulations are illustrated below.
Influence of EPAP on air mass flow when
Influence of EPAP on air mass flow when
With an increase in the respiratory compliance (
Influence of EPAP on tidal volume of different
As shown in Figures
Influence of EPAP on air mass flow when
Influence of EPAP on air mass flow when
With an increase in the diameter (
Influence of EPAP on tidal volume of different
As well as IPAP, the rising EPAP can make a higher percent of air mass flow in the inspiration process. However, to the ratio of tidal volume of right lung simulator (
The BPM is set to 20, 25, and 30, while the other parameters of ventilator do not change. The simulation results are shown below.
Influence of BPM on air mass flow when
Influence of EPAP on air mass flow when
With the increase of the respiratory compliance (
Influence of BPM on tidal volume of different
As shown in Figures
Influence of BPM on air mass flow when
Influence of BPM on air mass flow when
With different diameters (
Influence of BPM on tidal volume of different
As presented in Figures
The inspiration time (
Influence of
Influence of
As shown in Figures
Influence of
Influence of
Influence of
Influence of
When the diameter changes, the inspiration time (
The pressure rise time (
Influence of
Influence of
Influence of
From Figures
Influence of
Influence of
Influence of
From Figures
According to the description above, the conclusion can be gotten that the mathematic model of the system is correct. And each of the five key parameters has a regular effect on dynamic characteristics of the mechanical ventilation system with double lungs. As the system is based on two lungs, which increases its applicability and versatility, the dynamic characteristics must be more comprehensive and precise than the other studies based on single lung. The coupling effects of double lungs on dynamic characteristics of the system are more significative to the security and effect on respiratory medicine researches as well.
In this study, BIPAP ventilation system of double lungs was regarded as a pneumatic system, and then a new mathematical model of the BIPAP ventilation system was derived. To verify the mathematical model of the system, an experimental prototype of BIPAP mechanical ventilation system with double lungs was proposed. Then the influence of different parameters of two lung simulators and ventilator on dynamic characteristics of BIPAP mechanical ventilation system was studied. The conclusions are summed up as follows. The simulation results are consistent with experimental results. So it verifies the mathematical model of the system which can be used in BIPAP ventilation system of double lungs. With an increase in the respiratory compliance ( When the respiratory compliance ( Increasing IPAP and EPAP may lead to a distinct rise in the presence of air mass flow in inspiration. But to the ratio of tidal volume, the increasing IPAP and EPAP may lead to a slow growth. Influences of BPM, the inspiration time (
The study reveals the dynamic characteristics of mechanical ventilation with double lungs, and it can be referred to in the development of research on BIPAP ventilation treatment and real respiratory diagnostics. The research may promote research on the development of new respiratory clinic treatment.
Effective area of throttle (
Critical pressure ratio = 0.528
Respiratory compliance (L/cmH2O)
Diameter of effective area (m)
Length (m)
Mass of air (kg)
Pressure (pa)
Air mass flow (kg/s)
Gas constant = 287 (J/(kg·K))
Respiratory resistance (cmH2O/L/s)
Temperature (K)
Time (s)
Volume (
Friction coefficient
Density (kg/
Specific heat ratio = 1.4.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This project is supported by National Natural Science Foundation of China (Grant no. 51575020).