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Volume controlled mechanical ventilation system is a typical time-delay system, which is applied to ventilate patients who cannot breathe adequately on their own. To illustrate the influences of key parameters of the ventilator on the dynamics of the ventilated respiratory system, this paper firstly derived a new mathematical model of the ventilation system; secondly, simulation and experimental results are compared to verify the mathematical model; lastly, the influences of key parameters of ventilator on the dynamics of the ventilated respiratory system are carried out. This study can be helpful in the VCV ventilation treatment and respiratory diagnostics.

Mechanical ventilation is an important treatment which is usually utilized to ventilate patients who cannot breathe adequately on their own [

As well known, the VCV ventilation system is a typical time-delay system. Due to the respiratory resistance and compliance, the dynamics of the ventilated lung always lags behind the output dynamics of the VCV ventilator. Time delays are usually the main causes of instability and poor performance of system [

Because the dynamics of the ventilated lung is influenced by the parameters of the VCV ventilator, in order to lay a foundation for the VCV ventilation treatment, the influences of the VCV ventilator’s parameters on the dynamics of the ventilated lung should be illustrated. But the dynamics of the ventilated lung cannot be measured directly and precisely. Therefore, a simulation study of the ventilation system (including a VCV ventilator and a patient’s respiratory system) is needed.

In the present modelling and simulation studies of the mechanical ventilation system, the system is commonly considered as an electrical system [

In this paper, in order to improve the versatility and applicability of the mathematical models of the VCV ventilation systems, the VCV ventilation system is considered as an equivalent pneumatic system. Then a new mathematical model of the VCV ventilation system can be derived.

Furthermore, through the simulation study on the VCV ventilation system, its dynamic characteristics can be obtained. Simulation and experimental results [

Lastly, in order to provide guidance for the VCV ventilation treatment, influences of key parameters of the VCV ventilator on the dynamics of the ventilated respiratory system are studied.

A VCV ventilation system is composed of a human lung, a respiratory tract, a flexible tube, and a VCV ventilator. In the inspiration process, positive pressure ventilation (generated by the ventilator) is utilized to force airflow into the lung. In the expiration process, due to the elasticity of the lung, air is expelled to the atmosphere through an exhalation valve, which is embedded in the ventilator. Therefore, according to their functions, the ventilator can be regarded as an air compressor, the exhalation valve can be considered as a throttle, and the human lung can be regarded as a variable volume container. The minimum inner diameter of the respiratory tracts is influenced by the secretion deposition, so the respiratory tract can be considered as a throttle.

Therefore, the VCV ventilation system can be regarded as a pneumatic system, as shown in Figure

Structure of the equivalent pneumatic system.

When the variable volume container is ventilated, the flexible tube and the compressor are connected with the solenoid valve. Then the compressed air, output from the compressor, flows into the variable container through the solenoid valve, flexible tube, and throttle 2. During the expiration, the flexible tube and throttle 1 are connected with the solenoid valve. Then the compressed air, output from the variable volume container, flows into the atmosphere through the solenoid valve, flexible tube, and throttles 2 and 1.

Therefore, the versatility and applicability of the mathematical models of the VCV ventilation systems are better than the mathematical models when the VCV ventilation system is commonly considered as an electrical system.

To facilitate research, the following assumptions are made:

air of the system follows all ideal gas laws;

the dynamic process is a quasi-balanced process;

there is no air leakage during the working process.

_{2}O, the ratio of the downstream pressure to the upstream pressure is always bigger than 0.528; the air flow through the exhalation valve and the respiratory tract can be given by

The VCV ventilation system can be considered as an open thermodynamic system, and its work can be regarded as an isothermal process. The differential expression of the Clapeyron equation (

After transformation of (

The compliance

Then, the volume of the lung can be calculated by the following formula:

In [_{2}O and 25.7 mL/cmH_{2}O. The effective areas of the exhalation valve and respiratory tract are 16 mm^{2} and 9 mm^{2}. The experimental VCV ventilation system [

Experimental results in the reference.

Simulation results.

The curves of the pressure (

As can be seen in Figures

the simulation results are consistent with the experimental results, and this verifies the mathematical model; therefore, the mathematical model can be used in the study on the VCV system;

as can be seen, the air pressure in the lung always lags behind the pressure in the flexible tube and that is why the pressure in the lung cannot be maintained precisely; the main reason of the difference between the simulation and the experimental results is that the respiratory resistance and compliance block the fluctuation of the pressure in the lung simulator.

The key parameters of the VCV ventilator consist of its structure parameters (

According to the simulation above, each parameter can be changed for comparison while all other parameters are kept constant, and the simulation results for varying each parameter are illustrated in Figures

Influences of the effective area of the exhalation valve.

Influences of the

Influences of the

Relationship between the

Influences of the tidal volume (

Influences of the

Influences of the

Relationship between the

Relationship between the

Influences of the exhaust time (

Influences of the

Influences of the

Relationship between the

Relationship between the

The effective area (^{2}, 8 mm^{2}, 12 mm^{2}, 16 mm^{2}, 20 mm^{2}, and 24 mm^{2}, and the simulation results are illustrated in Figure

As shown in Figure

The tidal volume (

As shown in Figure

When the tidal volume (

The exhaust time (

As shown in Figure

Furthermore, with an increase in the exhaust time (

Moreover, with an increase in the exhaust time (

Finally, when the exhaust time (

In this paper, the VCV ventilation system was compared to a pneumatic system, and then a new mathematical model of the VCV ventilation system was derived. In order to verify the mathematical model, an experimental prototype VCV ventilation system was simulated mathematically. Simulation studies on the influences of the key parameters of the VCV ventilator on the dynamics of the ventilated respiratory system were done, and the conclusions of this study are summarized as follows.

The simulation results are consistent with the experimental results, which verify the mathematical model. Therefore, the mathematical model can be used in the study on the VCV system, and it has better versatility and applicability.

With an increase in the effective area of the exhalation valve, the maximum exhaust air flow of the lung increases more and more slowly.

With an increase in the tidal volume of the ventilator, the peak pressure in the lung increases proportionally, but when the tidal volume is larger than 600 mL, the peak pressure in the lung increases slowly.

When the tidal volume is smaller than 600 mL, the maximum exhaust air flow of the lung proportionally increases with an increase in the tidal volume. When the tidal volume is larger than 600 mL, the maximum exhaust flow of the lung increases more and more slowly.

When the exhaust time of the ventilator is shorter than 1.6 s, the maximum flow of the lung increases with an increase in the exhaust time. When the exhaust time of the ventilator is longer than 1.6 s, the maximum flow is constant.

This study can be of use in the VCV ventilation treatment and respiratory diagnostics. In the future, the clinical study will be done to verify the conclusions.

Equivalent effective area [m^{2}]

Respiratory compliance [L/cmH_{2}O]

Mass [kg]

Pressure [Pa]

Air mass flow [kg/s]

Air volume flow [m^{3}/s]

Gas constant = 287 [J/(kg·K)]

Time [s]

Volume [m^{3}]

Density [kg/m^{3}]

Specific heat ratio = 1.4

Temperature [K].

The standard reference atmosphere state

Exhalation valve

Functional residual capacity

Inspiration/input

Peak/maximum

Lung

Output

Platform

Respiratory tract

Tidal

Tube

Ventilator.

The authors declare that there is no conflict of interests regarding the publication of this paper.

_{2}gain performance of Markovian jump singular time-delay systems