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.
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 . 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 .
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.
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
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 . 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
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
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 XM at each of N
samples was compared with the value of XpM
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 .
All subsystems and the complete model of the
ventilator circuit were implemented and tested in the
software Multisim 11.0 (National Instruments, USA).
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 R1 (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 C1 = 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 R2 , R3 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 .
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 L1, L2, L4, and L5 were
calculated from the equation
where ρ0 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 L1 = L4 = 0,0036 kPA.s2.l-1 and L2 = L3 = 0.0027 kPa.s2.l-1.
The expiratory valve exhibits nonlinear resistance
which depends on the level of MAP. For MAP of
20 cmH2O, the relevant resistor is
where R7 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 L6 = 0.0046kPA.s2.l-1 . The
inertance was acquired from a step response
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
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 L3, a
resistor R4 , an elastor C2 , and a pressure source
connected in series. The resistor combines both the
A value of inertance was calculated from (4) as L3 = 0.0081 kPA.s2.l-1 . A value of the resistor was
estimated according to – as
R4 = 3.166 kPA.s.l-1. The elastor was set to C2 = 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.
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.
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
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.
Department of Biomedical Technology
Faculty of Biomedical Engineering
Czech Technical University in Prague
nám. Sítná 3105, CZ-272 01 Kladno
Phone: +420 728 229 991
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