key: cord-1046498-3zdqny0o
authors: Solís-Lemus, José A.; Costar, Edward; Doorly, Denis; Kerrigan, Eric C.; Kennedy, Caroline H.; Tait, Frances; Niederer, Steven; Vincent, Peter E.; Williams, Steven E.
title: A simulated single ventilator/dual patient ventilation strategy for acute respiratory distress syndrome during the COVID-19 pandemic
date: 2020-08-24
journal: R Soc Open Sci
DOI: 10.1098/rsos.200585
sha: caf6b477adc11f1e7977d27fd602042efe2b29bd
doc_id: 1046498
cord_uid: 3zdqny0o

The potential for acute shortages of ventilators at the peak of the COVID-19 pandemic has raised the possibility of needing to support two patients from a single ventilator. To provide a system for understanding and prototyping designs, we have developed a mathematical model of two patients supported by a mechanical ventilator. We propose a standard set-up where we simulate the introduction of T-splitters to supply air to two patients and a modified set-up where we introduce a variable resistance in each inhalation pathway and one-way valves in each exhalation pathway. Using the standard set-up, we demonstrate that ventilating two patients with mismatched lung compliances from a single ventilator will lead to clinically significant reductions in tidal volume in the patient with the lowest respiratory compliance. Using the modified set-up, we demonstrate that it could be possible to achieve the same tidal volumes in two patients with mismatched lung compliances, and we show that the tidal volume of one patient can be manipulated independently of the other. The results indicate that, with appropriate modifications, two patients could be supported from a single ventilator with independent control of tidal volumes.

The potential for acute shortages of ventilators at the peak of the COVID-19 pandemic has raised the possibility of needing to support two patients from a single ventilator. To provide a system for understanding and prototyping designs, we have developed a mathematical model of two patients supported by a mechanical ventilator. We propose a standard set-up where we simulate the introduction of T-splitters to supply air to two patients and a modified set-up where we introduce a variable resistance in each inhalation pathway and one-way valves in each exhalation pathway. Using the standard set-up, we demonstrate that ventilating two patients with mismatched lung compliances from a single ventilator will lead to clinically significant reductions in tidal volume in the patient with the lowest respiratory compliance. Using the modified set-up, we demonstrate that it could be possible to achieve the same tidal volumes in two patients with mismatched lung compliances, and we show that the tidal volume of one patient can be manipulated independently of the other. The results indicate single machine is strongly advised against. However, given the current unprecedented situation, it appears likely that there will not be enough ventilators worldwide, therefore leading to indirect deaths due to lack of available resources.

In this simulation study, we therefore develop, validate and make freely available a model of a mechanical ventilator supporting two patients using a simple T-junction splitter to supply air to both patients, based on the design proposed by Neyman & Babcock [7] . We use the model to simulate ventilating two patients with different degrees of lung disease from a single ventilator and estimate the delivered volumes and pressures in each patient. This provides a quantitative estimate of the potential risks involved in this strategy. We then propose the addition of variable resistances and oneway valves to the ventilator tubing system and show that in our model these can be used to regulate tidal volumes in each patient independently in the presence of mismatched respiratory physiology.

We designed an electrical circuit as an analogue to the ventilator, the system connecting the ventilator to the two patients and the lungs of each patient [16] . In mapping from the air flow to an electrical circuit, we equate volume to charge, flow rate to current, pressure to voltage, resistance to resistance and compliance to capacitance. In the ventilator model, this means that tubes appear as resistors, the lung and chest wall as a capacitor, the pressure source as a voltage source, a one-way valve as a diode and an open/closed valve as a switch.

Specifically, we designed two models. The first was a simple Standard Splitter configuration that involved connecting two T-junctions to the ventilator, as proposed previously [7] . This configuration is shown in figure 1 . The second was a Modified Splitter configuration, which had two elements added to each branch of the splitter: specifically, on the inspiration arms we added variable resistors (R V1 and R V2 ) to control pressure/flow/volume to each patient, and on the expiration arms, we added diodes to prevent backflow through each of the channels and stop the expiration arms acting as a short circuit between inspiration arms during inspiration. This configuration is shown in figure 2. The model outputs the pressure set by the ventilator (V M ) and the pressure (V L1 and V L2 ), flow (I L1 and I L2 ) and volume (Q L1 and Q L2 ) delivered to each patient. The ventilator pressure set by V M is defined as a square wave. The maximum value is set to the peak inspiration pressure (PIP). The minimum value is set to PEEP. The cycle rate is defined by the respiratory rate (RR) measured in breaths per minute. The ratio of time spent at the maximum and minimum values is defined by the inspiration to expiration ratio (I : E ratio). Figure 2 . Circuit diagram for the modified splitter. Compared to figure 1, variable resistors R V1 and R V2 have been added to control the pressure/flow/volume to each patient, and diodes have been added to stop the expiration arms acting as a short circuit between inspiration arms during inspiration. Changes with respect to the standard circuit are highlighted in red. royalsocietypublishing.org/journal/rsos R. Soc. Open Sci. 7: 200585 compliance reduction, 0.0324 L/cmH 2 O). The reduction in compliance for Lung Models B, C and D were chosen to represent a range of compliances around the reported median compliance for patients with ARDS [17] .

We implemented the simulations using MathWork's Simscape (Simulink v4.8) Foundational Blocks and the tests were run via Matlab R2020a scripts and functions. All code is freely available on GitHub (https://github.com/splitvent/splitvent) under an MIT licence. Simulations were initialized with all state variables set to 0. Simulations visually reached quasi-steady equilibrium after the first pulse and all reported results are taken from the second pulse onwards. The default Simulink and Simscape settings were used to generate the data, namely automatic selection of solver and step sizes with a relative error tolerance of 10 −3 . Simulink/Simscape was able to reduce the model to an ordinary differential equation (ODE) and we chose to solve the ODE with the Dormand-Prince explicit, variable-step RungeKutta (4,5) formula (the Matlab ode45 solver), with a maximum step size of 0.3. The plots were generated using the resulting variable-step size data, but joined up with lines.

We designed four experiments to answer the research questions for this work:

(i) Model validation. Using the standard splitter, we connect patients that have lungs with identical parameters, i.e. Lung Models A-A, B-B, C-C and D-D, and ventilate using pressure control ventilation. (ii) Evaluating the standard splitter when ventilating two patients with mismatched lung compliance. Using the standard set-up, we connected patients with different levels of respiratory compliance, i.e. Lung Models A-B, A-C and A-D, to quantify the effect of delivering the same ventilator settings to two patient with mismatched lung compliance. (iii) Achieving equivalent tidal volumes in patients with mismatched lung compliance. Using the modified splitter, we connected patients with different levels of respiratory compliance, i.e. Lung Models A-B, A-C and A-D, to demonstrate whether, by adjusting the values of R V1 , R V2 and PIP, we are able to deliver equal tidal volumes to two patients with mismatched respiratory compliance. (iv) Independently adjusting tidal volumes in both patients. In two patients, both with Lung Model C (moderate ARDS), we aimed to achieve a 30% increase in tidal volume or a 30% decrease in tidal volume in one patient while maintaining the tidal volume in the other patient by adjusting R V1 , R V2 and PIP. For case A-A (healthy lungs), a tidal volume of 490 ml was achieved, which equates to 6.2 ml kg −1 ideal body weight for a 185 cm male [18] . The respiratory pressure curves (an estimate of alveolar pressure measured at the patient end of the simulated endotracheal tube, i.e. at the patient side of R ETT ) are shown in (figure 3b). As expected, we demonstrate a progressive reduction in tidal volume as respiratory compliance decreases (figure 3b, black arrow). Achieved PEEP was 5 cmH 2 O in each case. We then showed that tidal volume could be returned to normal for each Lung Model by increasing PIP. For the ARDS cases (B-B, C-C and D-D) PIP was increased to achieve a tidal volume within 10 ml of 490 ml (the tidal volume seen in Lung Model A patients and one-way valves (modelled as diodes) in the exhalation arm to stop pressure equilibration. We demonstrate the function of this on the cases of a patient with healthy lungs (Lung Model A) paired with a patient with increasing severity of ARDS (Lung Models B, C and D). We first show in the case of an A-A pairing that inclusion of the resistors and diodes/valves, with the resistance set to 0 recovers the standard set-up results of §3.1. We then show that by adjusting the PIP from the ventilator and altering the resistance of the resistor for the healthy patient (Patient 1 in this set-up), we can achieve tidal volume within 10 ml of 490 ml for each patient ( figure 5 and table 4) . This result can also be achieved when pairing patients with varying ARDS (B-C, B-D and C-D; one ventilator using our proposed modified splitter (figure 2), we simulated two moderately severe ARDS patients (Lung Model C). We then adjusted the inhalation pathway resistors for each patient and the PIP to achieve (i) equivalent tidal volume between Patient 1 and Patient 2 (C-C); (ii) a 30% decreased tidal volume in Patient 2 (C-C(−)); or (iii) a 30% increase in tidal volume in Patient 2 (C-C(+)). We show that, by elevating the resistance in the inhalation pathway in Patient 2, we can reduce tidal volume for Patient 2, while maintaining tidal volume for Patient 1. Similarly, we show that, by increasing the resistance for Patient 1 and elevating PIP, we can maintain the tidal volume for Patient 1 and increase the tidal volume for Patient 2 ( figure 6 and table 5 ). This shows that it is possible to independently adjust the tidal volume in Patient 2 from the tidal volume in Patient 1.

This study does not encourage, endorse or support the use of a single ventilator to support two patients. The aim of this study was to quantify the potential risks and provide a quantitative test of a potential solution. In this study, we have therefore (i) predicted the effects of mismatched lung compliance on achieved tidal volumes when supporting two patients from a single ventilator, and (ii) demonstrated that independent control of tidal volume can theoretically be achieved by the inclusion of variable resistance and one-way valves into the inhalation and exhalation paths of the circuit. Our results show that when using an unmodified splitter, tidal volumes for two mismatched patients with differing lung physiology are different ( figure 4 and table 3 ) and that it is not possible to independently control tidal volumes in these patients. Consistent with these observations, very recent technical feasibility studies of adjusting ventilator settings to achieve an optimal compromised set-up for two mismatched patients 'were not able to identify reliable settings, adjustments or any simple measures to overcome the hazards of the technique' [20] . Together these observations confirm the recent consensus statement [15] that existing equipment cannot be used to adequately ventilate two mismatched patients without an addition to the standard ventilator control system.

Here, we have proposed a closed-loop system that requires the addition of a variable resistance (modelled by a variable resistor) on the inhalation pathway. In our simulations, a decrease in compliance by 40% required the addition of a 17.35 cmH 2 O/L/s resistance to achieve balanced tidal volumes (table 4). In this case, the total resistance to Patient 1 and Patient 2 are 25.4 cmH 2 O/L/s and 8.05 cmH 2 O/L/s, respectively, or approximately three times larger resistance for the healthy patient to achieve balanced tidal volumes. This compares with a 10-fold increase in resistance for a healthy lung to achieve balanced tidal volumes when a healthy lung and a diseased lung (31% decreased compliance) were paired together under a volume control ventilator set-up [20] . This discrepancy may be attributed to the way resistance was added. In a system proposed by Tronstad et al. [20] , resistance was added to both patients' inhalation pathways, whereas in our simulations resistance was only added to the healthy patient pathway.

An open-loop variant of the solutions proposed has been very recently demonstrated in benchtop and large animal testing [21] . This system relies on a valve that releases excess volume/pressure as opposed to a variable resistor on the inspiration pathway. This is a potentially less complex system to control, but will increase the contamination risk, as compared to the closed-loop system described here. An additional consideration in this approach may be the excess loss of medical gases which could become a limiting factor in some healthcare settings [22] .

The WHO guidelines for the management of severe respiratory disease in patients with suspected COVID-19 infection recommend that, in intubated patients with ARDS, mechanical ventilation settings should be targeted to specific tidal volumes (4-8 ml kg −1 predicted body weight) [13] . Therefore, manipulating tidal volume for individual patients, as we have demonstrated is possible with this technique, is key to these recommendations if a single ventilator/dual patient strategy is to be pursued.

Given the current interest globally on finding alternative ventilation strategies, the UK Medicines and Healthcare Products Regulatory Agency (MHRA) have released guidelines of the minimum requirement for rapidly manufactured ventilation system [23] . They state that, for the option of using pressurecontrolled ventilation, both the PIP and the PEEP must be controlled. It is known that this is particularly important in this cohort of patients who will have differing lung physiology and therefore differing ventilatory requirements. In this work, we have shown that through adaptation to the conventional ventilator splitter using variable resistances it is possible to control the tidal volume to each patient through controlling the specific PIP delivered to each patient. We hypothesize that the addition of resistors on the expiratory limbs, and diodes on the inspiratory limbs, would also allow individualized control of PEEP delivered to each patient.

The adoption of one ventilator to support two patients as a last resort would require several key developments, three of which are outlined below. Crucially, monitoring of both patients independently will be essential and strategies to implement monitoring and alarm systems at scale will be required. Second, technical translation of these proposed and preliminarily tested [21] solutions into clinically acceptable solutions that can be delivered at scale, delivered rapidly and once in place are easy to maintain (given the inherent staff shortages) is required. This will require simple, robust designs with limited/no connections, moving parts or electronics and designs that rely only on available equipment or components within an intensive care unit or parts that can be produced, royalsocietypublishing.org/journal/rsos R. Soc. Open Sci. 7: 200585 perhaps via three-dimensional printed, locally. Third, the development of standard protocols for controlling/calibrating the systems to deliver desired tidal volumes and pressures to each patient is required. To this end, it might be necessary to add check valves directly after the variable resistances in order to prevent flow from one patient to the other; it is possible that cases exist where there is flow from one patient to the other if check valves are not inserted. Though these check valves would involve adding components, it significantly simplifies the analysis and design of control protocols. Future work would need to establish if control protocols can be developed to allow selection of the appropriate variable resistances/PIP combinations to achieve target tidal volume for both patients, or whether additional patient monitoring is required to facilitate this proposed solution. Finally, the process for triaging, selecting and consenting pairs of patients to be supported by one ventilator needs to be established. This consideration raises ethical issues. In a ventilator-limited healthcare system the decision protocols for therapy selection need to be considered urgently, alongside the technical developments outlined above, such that appropriate clinical implementation strategies encompassing both engineering and clinical solutions could be proposed in a timely manner.

There are several limitations of the current work. First, given that the I : E ratio and respiratory rate would need to be identical for both patients, it is likely to be necessary to cohort patients based on body weight, lung disease severity and required ventilatory parameters. Such cohorting is likely to reduce the factor by which split ventilation could increase ventilatory capacity and would need to be considered in the design of clinical protocols seeking to implement this strategy. Second, we have assumed in this model that small airways resistance remains constant under disease conditions. This is a simplifying assumption. While inspiratory resistance is only minimally increased in ARDS compared to normal subjects, increased expiration resistance has been observed [24] . Further model development using flow directional resistances in the patient model would be required to capture this complexity. Finally, the assumption of Poiseulle flow within the ventilator tubing is an approximation, and at higher flow rates, it is possible that flow becomes turbulent, especially given that the tubing is often ribbed. Future work should consider this, and/or the inclusion of nonlinear, e.g. quadratic, resistances.

Supporting two patients from a single ventilator is currently untested and the work presented here does not change the current clinical recommendations relating to this approach. If this approach is attempted, however, then we have shown that a simple standard set-up delivering the same PIP to both patients will result in the desired tidal volumes only if patients have the same predicted body weight and respiratory compliance. If patients are mismatched, then the difference between the achieved and target tidal volumes in our simulations was as great as 35%. The inclusion of a variable resistance and check valves into the inhalation and expiration arms of the splitter, respectively, is shown to allow the tidal volume to be set for each patient independently of their respiratory compliance.

Data accessibility. The Simulink models used in this research have been uploaded to a Git repository at the following

Understanding of COVID-19 based on current evidence

Coronavirus disease (COVID-19) pandemic

Clinical predictors of mortality due to COVID-19 based on an analysis of data of 150 patients from Wuhan, China

Rapid risk assessment: novel coronavirus disease 2019 (COVID-19) pandemic: increased transmission in the EU/EEA and the UK -sixth update

Ventilator stockpiling and availability in the US

Critical supply shortages-the need for ventilators and personal protective equipment during the COVID-19 pandemic

A single ventilator for multiple simulated patients to meet disaster surge

Increasing ventilator surge capacity in disasters: ventilation of four adulthuman-sized sheep on a single ventilator with a modified circuit

Coronavirus: could one ventilator be used to treat multiple patients

Department of Health & Human Services. 2020 Optimizing ventilator use during COVID-19

Nurses sent to London as capital faces 'tsunami' of virus patients. The Guardian

Trump administration tells hospitals ventilators can be shared among coronavirus patients

World Health Organization. 2020 Clinical management of severe acute respiratory infection (SARI) when COVID-19 disease is suspected: Interim guidance V 1

Acute respiratory distress syndrome: the Berlin definition

American Association of Critical-Care Nurses (AACN) and AC of CP (CHEST)

2020 splitvent/splitvent: splitvent: Version v0

Parameters for simulation of adult subjects during mechanical ventilation

Ventilation with lower tidal volumes as compared with traditional tidal volumes for acute lung injury and the acute respiratory distress syndrome

The electrical analogue of lung

Splitting one ventilator for multiple patients -a technical assessment

2020 Individualized system for augmenting ventilator efficacy (iSAVE): a rapidly deployable system to expand ventilator capacity. bioRxiv

A low oxygen consumption pneumatic ventilator for emergency construction during a respiratory failure pandemic

Medicines & Healthcare products Regulatory Agency. 2020 Rapidly Manufactured Ventilator System (RMVS

Fifty years of research in ARDS: respiratory mechanics in acute respiratory distress syndrome

Authors' contributions. J.A.S.-L. was involved in code implementation and performing simulations. E.C. and D.D. were involved in study motivation, experimental design and writing the paper. E.C.K. was involved in model development, code verification, study design and paper writing. C.H.K. and F.T. were involved in study motivation, experimental design and writing the paper. S.N., P.E.V. and S.E.W. were involved study motivation, model design, experimental design and writing the paper.Competing interests. We declare we have no competing interests. Funding. This work was supported by the Wellcome/EPSRC Centre for Medical Engineering [WT 203148/Z/16/Z].