# VENTILATOR CIRCUIT MODEL FOR OPTIMIZATION OF HIGH-FREQUENCY OSCILLATORY VENTILATION

Authors:
Jan Matějka; Jakub Ráfl; Michal Čech; Martin Rožánek

Authors‘ workplace:
Czech Technical University in Prague, Faculty of Biomedical Engineering, Kladno, Czech Republic
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Published in:
Lékař a technika - Clinician and Technology No. 2, 2012, 42, 61-64

Category:
Conference YBERC 2012

## Overview

Ventilators for high-frequency oscillatory ventilation (HFOV), Sensormedics 3100, were not designed to tolerate spontaneous breathing of a patient. An experimental Demand Flow System (DFS) is being developed to support spontaneous breathing during HFOV. A control system of the DFS requires a model of the ventilator circuit of Sensormedics 3100. A new model of the circuit was designed, including the oscillating membrane, the inspiratory and expiratory branches of the circuit, the expiratory valve, and a spontaneously breathing patient. The model was implemented in the Multisim software environment. A bench test suggests that the model predicts the basic changes in pressure within the ventilator circuit and that its modified version can be used in the DFS control algorithm.

**Keywords:**

high-frequency oscillatory ventilation (HFOV), ventilator circuit, lumped-parameter model, electro-acoustic analogy

## Introduction

High-frequency oscillatory ventilation (HFOV) is an unconventional method of mechanical ventilation. HFOV uses breathing frequencies of 3–15 Hz combined with tidal volumes about four times smaller than in conventional modes of ventilation. Low tidal volumes imply low changes in pressure in the lower airways which reduces mechanical damage to the lungs. That is especially important for patients suffering from Acute Respiratory Distress Syndrome (ARDS) and having reduced lung compliance.

The currently used ventilator for HFOV, Sensormedics 3100 (SensorMedics, USA), has not been designed to support or even tolerate spontaneous breathing of a patient. This is not an issue at severe state of ARDS patients, but it complicates gradual weaning of a patient from mechanical ventilator support: if a patient starts to breathe, his/her work of breathing raises, and high pressure changes in the ventilator circuit caused by spontaneous breathing can even impede the normal functioning of the ventilator.

An experimental device, called the Demand Flow System (DFS), is being developed to facilitate spontaneous breathing during HFOV [1]. The DFS runs concurrently with the Sensormedics 3100, measuring the proximal airway pressure at a patient’s airway opening. A control system of the DFS evaluates the proximal airway pressure swings caused by a patient’s spontaneous breathing. The spontaneous breathing is compensated by variable gas inflow into the ventilator circuit so that the mean airway pressure (MAP) in the circuit remains unaltered. Therefore, the functioning of the ventilator is not affected. Also, a patient’s respiratory effort does not increase.

The control system of the DFS employs the linear quadratic Gaussian (LQG) state feedback controller and requires a model of the ventilator circuit with a connected patient. The model should primarily describe how the proximal airway pressure is affected by a change in the gas inflow into the ventilator circuit. However, the linear model originally employed by the DFS neglects some physical properties of the ventilator circuit. Moreover, approximation of some parameters in the model seems to be oversimplified [1].

The aim of this study is to design a new model of the ventilator circuit of Sensormedics 3100 with revised structure and parameter values. The model should improve the performance of the DFS control algorithm.

## Ventilator Circuit

The ventilator circuit of Sensormedics 3100, presented in Fig. 1, connects the ventilator with a patient, assuring the delivery of fresh gas into a patient airways and removal of the expired gas. The DFS controls the gas inflow into the ventilator circuit. The gas passes through the inspiratory branch and the expiratory branch of the circuit and escapes via an expiratory valve. The expiratory valve flow resistance and gas volume flow rate determine the MAP.

An oscillating membrane is placed at the connection of the circuit and the ventilator. The membrane, similar to a loudspeaker membrane, generates pressure swings that travel through the inspiratory branch to a patient’s airway opening (a Y-piece of the circuit) and, while being attenuated, further down to the lungs. Due to the pressure oscillations, a portion of fresh gas flow from the ventilator circuit is diverted into the patient’s airways.

## Model Structure and Parameters

The new model of the ventilator circuit was divided
into subsystems according to functional parts of the
ventilator circuit with a connected patient: the
*membrane*, the* inspiratory branch*, the *expiratory
branch*, the* expiratory valve*, and *the patient*. The
ventilator circuit was disassembled into the functional
parts; structure and parameters of each subsystem were
identified independently of the rest of the circuit.

Models of the subsystems were based on the electroacoustic analogy and derived from the combination of theoretical modeling and experimental identification. The theoretical part of the concept was based on similarity of the ventilator circuit components to basic acoustic elements described in [3]. When compared to the circuit dimension, wavelength of oscillations propagating through the circuit was assumed to be long enough to allow construction of a lumped-parameter model.

For the experimental identification, pressure in the subsystems was measured under static conditions at different levels of gas volume flow rate. Alternatively, a step response of the pressure signal was acquired as a reaction to a sudden increase of the gas volume flow rate. Median filters of various window sizes were used to remove the acoustic noise which corrupted the pressure measurements.

The method of least squares was employed to identify a desired parameter from a pressure step response. The method can be described by the equation

A measured value of pressure *X _{M}* at each of

*N*samples was compared with the value of X

^{p}

_{M}predicted by a model for the same flow input. The parameter of the model was altered by an iterative algorithm so that

*SSR*is minimal [4].

All subsystems and the complete model of the ventilator circuit were implemented and tested in the software Multisim 11.0 (National Instruments, USA).

### Membrane

Structure of the subsystem *membrane* is composed
of an acoustic elastor (“compliance”), a controlled
acoustic resistor and two sources of pressure. The first
pressure source represents oscillations of the ventilator
membrane. The second pressure source together with a
controlled acoustic resistor *R _{1}* (see Fig. 3) represents a
proportional valve of the DFS which controls the gas
inflow into the circuit.

The membrane structure was identified from pressure
step responses measured with and without the
membrane oscillations. The step responses
corresponded to a response of the first-order RC circuit
as illustrated in Fig. 2. The value of the acoustic elastor
was calculated using the least squares method as C_{1 }= 0.0139 l kPa^{-1} .

### Inspiratory and expiratory branches

Each of models of the inspiratory and expiratory branches consists of two nonlinear acoustic resistors and two inertors (“inertances”) connected in series.

In each branch the nonlinear behavior of the first resistor in described as

and the nonlinear behavior of the second resistor as

where *R _{2} , R_{3}* are given in kPa.s.l

^{-1}and

*q*is volume flow rate in l.s

^{-1}. The equations (2) and (3) were derived from static pressure measurements [6].

A nonlinear resistor was implemented in the software Multisim 11.0 with help of a current source controlled by the current (representing the gas flow) in the model. The current source was connected to a currentcontrolled voltage source and the voltage source governed the value of the resistor in the model.

The values of inertors *L _{1}, L_{2}, L_{4}*, and

*L*were calculated from the equation

_{5}

where* ρ _{0}* refers to the gas density,

*l*to the length of a tube, and

*S*to the cross-section area of the tube. In the final model

*L*and

_{1}= L_{4 }= 0,0036 kPA.s^{2}.l^{-1}*L*.

_{2}= L_{3}= 0.0027 kPa.s^{2}.l^{-1}### Expiratory valve

The expiratory valve exhibits nonlinear resistance
which depends on the level of MAP. For MAP of
20 cmH_{2}O, the relevant resistor is

where *R _{7}* is given in kPA.s.l

^{-1}and

*q*in l.s

^{-1}.

Reaction of the valve to a sudden change in flow is
modeled by the inertor *L _{6 }= 0.0046*

*kPA.s*. The inertance was acquired from a step response measurement.

^{2}.l^{-1}### Model of a patient

The model of a patient was created in two versions. The first one is a patient convalescent from ARDS with spontaneous breathing and the second one is a patient suffering from ARDS without spontaneous breathing. For both the structures a classic single-compartment model was chosen with all elements connected in series.

For the further simulations, the recovering patient
version was selected. The subsystem includes the
inertance and resistance of an endotracheal tube, the
resistance and compliance of a patient’s respiratory
system, and the work of breathing muscles. Therefore,
the model consists of combination of an inertor* L _{3}*, a
resistor

*R*, an elastor

_{4}*C*, and a pressure source connected in series. The resistor combines both the resistances.

_{2}A value of inertance was calculated from (4) as *L _{3} = 0.0081 kPA.s^{2}.l^{-1}* . A value of the resistor was
estimated according to [7]–[10] as

*R*. The elastor was set to

_{4}= 3.166 kPA.s.l^{-1}*C*.

_{2}= 0,501 l.kPa^{-1}### Complete model of the ventilator circuit

All subsystems were connected into the complete model of a ventilator circuit and a patient. The final model implemented in Multisim is presented in Fig. 3.

## Model Bench Test

The performance of the complete model was compared with the real ventilator circuit. For the purpose of the bench test, the complete ventilator circuit was connected to the ASL 5000 breathing simulator (IngMar Medical, USA). A pressure sensor was placed at the Y-piece of ventilator circuit, close to a patient’s airway entrance.

A recorded pressure waveform compared to the respective output of the model is in Fig. 4.

## Discussion

A mathematical model of the ventilator circuit of Sensormedics 3100 high-frequency oscillatory ventilator was built. The model was implemented in the Multisim software environment, using an electroacoustic analogy. The model consists of several subsystems that were identified independently of the rest of the circuit. The modular approach enables more detailed identification of the ventilator circuit components, and also allows a gradual improvement of the model in future if more precise measurements are taken or if a part of the circuit is enhanced.

According to the results of the bench test (see Fig. 4), the model correctly predicts the basic pressure changes in the Y-piece of the ventilator circuit caused by the membrane oscillations during a constant gas flow in the circuit. The bench test showed swings in the measured pressure signal that were not observed during the simulation. This could be caused by acoustic compliance of the inspiratory and expiratory branches of the circuit which has been neglected so far.

The pressure signal generated by a model is smoother compared to the measured signal. A model with distributed parameters could achieve a more accurate simulation, involving, for example, reflections of pressure waves.

Finally, one of the problems of the final model is a question how to model the pressure signal generated by the oscillating membrane of the ventilator. In the presented model an ideal source of pressure pulses was used; however, experiments showed that shape and amplitude of the pressure signal is influenced by amount of gas flow from the DFS and by amplitude and frequency of oscillations.

## Conclusion

A new model of a ventilator circuit for HFOV ventilation was designed, including a spontaneously breathing patient. Simulations suggest that the model, after some modifications, can be used in a control system supporting spontaneous breathing of a patient on HFOV.

### Acknowledgement

*The authors thank Ondřej Čadek for construction of a
device for accurate real-time pressure measurement.
The work has been supported by grant
SGS11/171/OHK4/3T/17 of the Czech Technical
University in Prague. *

**Jakub Ráfl **

*Department of Biomedical Technology *

*Faculty of Biomedical Engineering *

*Czech Technical University in Prague *

*nám. Sítná 3105, CZ-272 01 Kladno*

*
E-mail: rafl@fbmi.cvut.cz *

*Phone: +420 728 229 991*

##### Sources

[1] Roubík, K., Ráfl, J., van Heerde, M., Markhorst, D. G. Design and control of a demand flow system assuring spontaneous breathing of a patient connected to an HFO ventilator. IEEE Trans Biomed Eng, 2011, vol. 58, no. 11, p. 3225–3233.

[2] van Heerde, M., et al. Unloading work of breathing during high-frequency oscillatory ventilation: A bench study. Critical Care, 2006, vol. 10, no. 4, p. R103.

[3] Škvor, Z. Vibrating systems and their equivalent circuits. 2nd ed. Prague: Academia, 1991.

[4] Bates, J. H. T. Lung mechanics: An inverse modeling approach. 1st ed. New York: Cambridge University Press, 2009.

[5] Matějka, J. Model pacientského okruhu pro optimalizaci vysokofrekvenční oscilační ventilace. [Bachelor thesis]. Prague: CTU FBMI, 2012.

[6] Čech, M. Modelování a měření základních komponent v respirační péči. [Bachelor thesis]. Prague: CTU FBMI, 2012.

[7] van Genderingen, H. R., et al. Reduction of oscillatory pressure along the endotracheal tube is indicative for maximal respiratory compliance during high-frequency oscillatory ventilation: A mathematical model study. Pediatric Pulmonology, 2001, vol. 31, no. 6, p. 458–463.

[8] Schranz, C., Moeller, K. Inverse modeling supports quantification of pressure and time depending effects in ARDS patients. In: 33rd Annual International Conference of the IEEE EMBS, Boston, Aug 30–Sep 3, 2011, p. 1013–1016.

[9] Schranz, C., Moeller, K. Model-based quantification of pressure and time depending effects in ARDS patients. In: 5th International Conference on Bioinformatics and Biomedical Engineering (iCBBE), Wuhan, May 10–12, 2011, p. 1–4.

[10] Pino, A. V., Giannella-Neto, A. A new method to obtain a positive end-expiratory pressure. In: Proceedings of the 18th Annual International Conference of the IEEE EMBS, Amsterdam, Oct 31–Nov 3, 1996, p. 1689–1690.

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