Simulating Single-Ventilator, Dual-Patient Ventilation Strategies

The initial shortage of ventilators caused by the COVID-19 pandemic led our team to revisit a solution first proposed and published about 15 years ago: using a single ventilator to treat several patients simultaneously. While most of the hardest hit areas now have sufficient ventilator capacity, the potential need for ventilator sharing still exists in underserved regions.

The principal challenge in ventilator sharing is that ventilation parameters must be adjusted for patients with differing lung physiology. When a simple T-splitter is used to supply air to two patients from a single ventilator, the tidal volume (the amount of air moved into a patient’s lungs in one breath or ventilator cycle) is significantly reduced for the patient with the lower respiratory compliance (the lung’s ability to expand).

Our cross-disciplinary team¹ has developed a model of a mechanical ventilator that can support two patients with mismatched lung compliances. This model, developed in Simulink^® with Simscape™ blocks, maps respiratory flow to an electrical circuit in which volume equates to charge, flow rate to current, pressure to voltage, air flow resistance to electrical resistance, and compliance to capacitance (Figure 1).

Using the model, we demonstrated the feasibility of a modified splitter design. We showed that it is theoretically possible to manipulate the tidal volume for one patient independently of the other by introducing a variable resistance in each inhalation pathway and one-way valves in each exhalation pathway.

While the modified splitter design with variable resistances and valves shows promise, there are other clinical issues, such as potential cross-contamination, yet to be addressed. To help researchers working on these issues develop improved designs, we have made our Simulink models available on File Exchange.

Developing Ventilator Models in MATLAB and Simulink

We began the project by developing a MATLAB^® model of a simple ventilator T-splitter design based on hand-derived differential equations. While this mathematical model yielded satisfactory results, it was cumbersome to modify. Adding elements to the model involved deriving additional equations and then implementing them in the MATLAB code. 

To make the model easier to understand and modify, we re-implemented it in Simulink using Simscape blocks. In the Simulink model, frictional and entry losses due to tubing are represented as electrical resistors, the lung air volumes as capacitors, the ventilator’s pressure source as a voltage source, a one-way valve as a diode, and an open/closed valve as a switch. Each patient is represented as a module with a resistor to model upper airway resistance and a capacitor to model the compliance of the lungs and chest wall. Resistance and capacitance parameter values are adjusted for different patient physiologies. To validate the model, we ran simulations and compared the results with those produced by our MATLAB model.

With the basic ventilator model in Simulink, it was much easier for the members of our group to experiment with design ideas. New elements could be added simply by dragging and dropping components from the Simscape library. 

Working and collaborating remotely due to pandemic-related shutdowns, we rapidly came up with a new design: a modified splitter that includes two variable resistors and two diodes for independently controlling the electrical current delivered to each patient module (Figure 2). 

The ability to work with and share physical models instead of code increased the pace of development because there was a one-to-one mapping between objects in the physical world and elements of the model. Another advantage of working in Simulink was the ability to insert scopes to view signals as they varied over time (Figure 3). For example, to view the pressure difference between the lung and the endotracheal tube, we could insert a scope at the node between the resistor and capacitor in the patient module and see the pressure vary throughout a simulation. These capabilities enabled us to progress from concept to a workable solution and a finished paper in a matter of weeks.

Control System Development

Once we saw that we could adjust the flow of air to each patient independently with our modified splitter design, we began developing control strategies for delivering ideal tidal flows to patients with differing lung compliances. We focused on strategies that could be implemented with relatively little additional cost. For example, we avoided approaches that would require expensive new sensors in favor of low-cost changes, such as adding sections of tubing to increase resistance or simply adjusting the pressure profile of the ventilator.

During this phase of the project, we developed a MATLAB algorithm for estimating the flows being delivered to each patient during the inhale-exhale cycle (Figure 4). This algorithm uses a series of flow measurements to fit the equivalent resistance-compliance values and determine the tidal volume for each patient.

We showed that it is possible to provide patients with tidal volumes tailored to their specific physiologies by adjusting only ventilator pressures and adding or removing sections of tube.

Ongoing Research

We are currently developing a real-world implementation of our design using 3D-printed one-way valves. This setup will enable us to validate the results of our simulations in the lab and will serve as a proof-of-principle for further research. In addition, we are exploring several areas of improvement in the model. For example, the current model assumes the same levels of resistance during inspiration and expiration. We are updating the model to capture varying levels of resistance.

There are other clinical issues that would need to be addressed before the designs we have simulated could be used to treat patients. We acknowledge that some of these issues will be very challenging and require detailed further research to develop innovative solutions. Nevertheless, we hope that the availability of a shared ventilator model that is easy to understand and modify will help accelerate research in this area.

Acknowledgements

We gratefully acknowledge the contributions of our colleagues on this project: Edward Costar, Denis Doorly, Caroline H. Kennedy, Frances Tait, and Steven Niederer.

¹ Our cross-disciplinary project team included experts in the fields of computational fluid dynamics, 3D printing, intensive care, anesthesiology, and medical physics from Imperial College London, King’s College London, and Guys’ and St Thomas’ NHS Foundation Trust.