The MV consists of an input branch which mixes air and oxygen from the hospital reservoirs and feeds it into the patient mask, and an expiratory output branch which is opened or closed by the control system. Figure 1a shows a schematic illustration of the MV. The input compressed air and oxygen are supplied by the hospital central reservoirs. The flow from each of the reservoirs is controlled with a flow control valve. After the flow control valves, the gases flow through two similar pipes, mix and flow through the main pipe and mask pipe towards the breathing mask. A pressure relief valve marked Popoff is located between the Main pipe and the Mask pipe. This pressure relief is set to mechanically control the maximal pressure in the system and avoid over-pressuring the lungs. The expiratory air flows through a directional check valve which does not permit breathing the exhaled gasses. After the check valve, the outlet pipe leads to the expiratory flow control system which opens and closes the expiratory pipe flow path using an ON/OFF solenoid valve. The outlet of the control system is connected to a pressure relief valve that is set according to the required PEEP valve. Figure 1b shows a CAD drawing of the complete MV system, and Figure 1c shows a CAD drawing of the main components of the MV. Figure 1d is a photograph of the main components of the MV prototype.

In order to reduce the system costs to minimum, the MV operates with a single pressure sensor and a solenoid valve which controls the gas flow out of the system. The minimum and maximum pressure in the system are controlled with a hysteresis control scheme. This control strategy is realized with a pressure sensor located near the inlet to the solenoid valve and a relay which sets the state of the solenoid valve according to the measured pressure. In its initial state, the solenoid valve is closed directing the input air to the patient allowing the pressure to build up. When the patient exhales, the pressure at the expiratory pipe increases rapidly and after it reaches the expiratory positive airway pressure (EPAP), the relay opens the solenoid valve, the exhaled air is removed, and the pressure starts to drop. Once the patient starts to inhale, air is removed from the pipes and the pressure drops. When the pressure reaches the inspiratory positive airway pressure (IPAP) the solenoid valve closes, and the breathing cycle continues.

The MV model was built with MathWorks® Simulink® Simscape™ Gas system toolbox. The outline for the model followed the MathWorks® “Medical Ventilator with Lung Model” example and was modified to describe the MV design, control system as well as an autonomously breathing patient. The model source files, along with an elaborated description of model parameters, variables, Simulink® block parameters and their values can be found under the data availability section as well as in the model OSF webpage ² .

Figure 2 shows the block diagram of the model and Figure 3 shows a block diagram of the control system. The lungs are modeled as a translational mechanical converter that is coupled to a spring, a damper, and a force source. The spring and damper model the mechanical compliance and resistance of the lungs ³ and force source models the muscle induced pressure ⁴ which is a result of the patient autonomous breathing (patients that cannot breath autonomously can be modeled by replacing the variable muscle pressure term with a constant pressure). The pressure induced by the muscles contraction and relaxation, P _mus , is realized with exponential functions as described by Fresnel et al. ⁴ :

Where T ₁ is the time period for muscles contraction in every breathing cycle and T _tot is the breathing cycle length. τ _c and τ _r are the contraction and relaxation time constants, respectively, and P _max is the maximum pressure that can be induced by the muscles. All the parameters in Equation (1) can be easily derived from the mouth occlusion pressure, P _0.1 and the breathing frequency, f _v as described in 4. A block diagram of the lungs branch is shown in Figure 4.

Model calibration. The model was calibrated against the MV prototype in two steps. First, the parameters of the PEEP and Popoff pressure relief valves were calibrated by comparing the model output to the measured output when the lungs port was blocked. In this set of experiments, the pressure at the inlet to the solenoid control valve was measured as a function of the total input gas flow rate when the solenoid valve was open and when it was closed. The experiment was repeated for PEEP values of 2, 5 and 10 cmH ₂O. For each of the pressure relief valves in the model the set pressure differential and the maximum valve open area were tuned to provide the best fit to the measured data. Figure 5 shows the modeled and measured pressure as a function of the input gas flow rate and PEEP values of 2, 5 and 10 cmH ₂O.

Next, the model calibration was tested by comparing model results to the output of the MV prototype when it was connected to an IMTMedical Easylung test lung. In order to minimize the effects of the popoff and PEEP valves, the total input gas flow rate was set to 10 L/min and the PEEP was set to 2 cmH ₂O. To probe the transient response of the MV, the solenoid valve was opened and closed in intervals of 3.5 seconds. Under these conditions, pressure drops across the different parts of the system are low, the Popoff valve remains closed throughout the experiment and the pressure in the system is determined mostly by the mechanical lung parameters. This provides optimal conditions for calibrating the mechanical lungs’ compliance and resistance in the model. Figure 6 shows the measured and modeled pressure (a) and gas flow (b). The gray regions in the figure are time periods in which the solenoid valve is closed. The fitted spring and damper constants for the lungs model are 148.5 N/m and 40 N/(m/s), respectively. When the solenoid valve is closed, air is directed into the test lung, increasing the pressure in it. Then, when the solenoid valve is reopened, the air in the test lung along with air from the reservoirs flow out of the system through the PEEP pressure relief valve. The MV model was able to capture the measured transient response of the system well. Particularly, the modeled gas flow follows the measured values closely.

Once the lungs parameters were found, the model predictions were compared to experimental measurements at input flow rates of 20L/min and 30 L/min and a PEEP of 5 cmH ₂O, which better represent the operating conditions of the MV. Figure 7 shows the modeled and measured pressure and flow rates with input gas flow rates of 20 L/min ( Figure 7 a and b) and 30 L/min ( Figure 7 c and d). The regions with the gray background in Figure 7 are the time periods in which the solenoid valve was closed. Unlike the lung calibration experiments in which the Popoff valve remains constantly closed, at a flow rate of 20 L/min the Popoff valve opens when the pressure rises above 13 cmH ₂O and closes back when it drops below 8 cmH ₂O. This transition, which is not instantaneous, is not captured well in the simulation, resulting in a deviation between the measured and modeled responses. Nevertheless, the simulation was able to predict fairly well the minimum and maximum pressure in the system, which are most important for its safe operation. In a similar manner, there is a deviation between the measured and modeled flow in the system when the input gas flow rate. The overestimation of the calculated air flow under higher input flow rates may be a result of leakages in the system that are not considered in the model.

Open source implementation. The model can be implemented using similar or equivalent components in the open source OpenModelica software utilizing Modelica.Fluid and Modelica.OpenHydraulics libraries. In Table 1, we detail equivalent or most similar components, together with component names that could be used in construction of an equivalent model.

After the model is calibrated and tested, we turn to simulate the ventilation of autonomously breathing patients. We start by simulating the ventilation of a healthy person which is embodied by a breathing rate of 15 breaths per minute ⁵ , and an occlusion pressure of 4 cmH ₂O ⁴ . The simulated lungs spring and damper constants are as in Figure 6. Figure 8 a, b and c show the simulated pressure, flow and tidal volume, respectively. Positive flow denotes gas flow out of the system, for example when air is inhaled into the lungs. The gas flow is negative when gas flows into the MV, for example when the patient is exhaling. The pink regions in the figure are the periods in which the patient is trying to inhale and the solenoid valve is closed, the light blue regions are the periods in which the solenoid valve is open and the patient is trying to exhale, the purple regions are periods where the patient is attempting to inhale while the solenoid valve is open and white areas are periods in which the patient is attempting to exhale while the solenoid valve is closed. The color coding for the patient breathing state and the state of the solenoid valve is summarized in Table 2. As the patient begins to inhale (purple region), the lungs expand, air flows into the lungs, and the pressure in the expiratory pipe drops. Once the pressure reaches the IPAP, the solenoid valve closes (pink region) and the input gas is inhaled by the patient, resulting in a nearly constant gas flow at a rate that is determined by the flow regulating valves at the inputs to the system. The pressure in the lungs decreases at the beginning of this stage as the lungs are still expanding and then it increases slowly as the lungs fill with air. When the patient attempts to exhale the pressure increases rapidly in the system. At first the solenoid valve is still closed and gas flows into the patient’s lungs (white region), but once the EPAP is reached, the solenoid valve opens and the air flows out of the MV through the expiratory pipe (light blue region).

Figure 9 shows the time evolution of the pressure, air flow and tidal volume simulating the ventilation of an acute respiratory distress syndrome (ARDS) patient. The patient breathing rate was taken to be 20 breaths per minute ⁵ , the occlusion pressure is 6.65 cmH ₂O ⁶ , IPAP was set to 5 cmH ₂O and the EPAP was set to 13 cmH ₂O ⁵ . The color coding is as described in Table 2. It can be easily seen that MV output ventilation of the ARDS patient is very similar to that shown in Figure 8. The slight decrease in tidal volume is a result of the higher breathing rate which is recommended for patients with ARDS ⁵ . The low variance in the MV output with respect to the patient condition is a result of the fairly constant gas flow upon inhalation. This may be an advantage since it allows simple tuning of the ventilation parameters according the guidelines for specific respiratory syndromes.

Perfect synchronization between the MV and the patient is obtained if the solenoid valve opens and closes exactly when the patient attempts to inhale and exhale. Thus, the synchronization level of the MV can be optimized by attempting to minimize the white and purple regions in the output plot.

Open Science Framework: A simulation of a controlled medical ventilator with a realistic lungs model. https://doi.org/10.17605/OSF.IO/XJKC8 ² .

This project contains the following underlying data:

Peep and Popoff calibration (data underlying Figure 5):

RC and C values calibration (underlying Figure 6)

Model - MV prototype Comparison (underlying Figure 7)

Healthy Patient model testing (underlying Figure 2, 3, 4 and 8)

ARDS patient model testing (underlying Figure 9)

Open Science Framework: A simulation of a controlled medical ventilator with a realistic lungs model. https://doi.org/10.17605/OSF.IO/XJKC8 ² .

This project contains the following extended data:

Data are available under the terms of the Creative Commons Zero "No rights reserved" data waiver (CC0 1.0 Public domain dedication).