2020 IEEE International Conference on Automatic Control and Intelligent Systems (I2CACIS 2020), 20 June 2020, Shah Alam, Malaysia.
A Mathematical Model of Lung Functionality using
Pressure Signal for Volume-Controlled Ventilation
Husam Y. Al-Hetari
Faculty of Computing
University Malaysia Pahang, Malaysia
26300 Gambang, Kuantan, Malaysia
and
Dept. of Biomedical Engineering
Faculty of Engineering
University of Science and Technology
Yemen
husamalhetari@gmail.com
Noman Q. Al-Naggar
Dept. of Biomedical Engineering
Faculty of Engineering
University of Science and Technology
Yemen
nnagar845@gmail.com
Muhammad Nomani Kabir*
Faculty of Computing
University Malaysia Pahang, Malaysia
26300 Gambang, Kuantan, Malaysia
(*Corresponding author)
nomanikabir@ump.edu.my
Mahmoud A. Al-Rumaima
Dept. of Biomedical Engineering
Faculty of Engineering
University of Science and Technology
Yemen
m.alromaima@gmail.com
Yasser M. Alginahi
Dept. of Electrical and Computer
Engineering
University of Windsor
401 Sunset Ave, Windsor, Ontario
N9B 3P4, Canada
alginah@uwindsor.ca
Md Munirul Hasan
Faculty of Computing
University Malaysia Pahang, Malaysia
26300 Gambang, Kuantan, Malaysia
monirul.iiuc@gmail.com
Abstract— Mechanical Ventilation is used to support the
respiratory system malfunction by assisting recovery breathing
process which could result from diseases and viruses such as
pneumonia and COVID-19. Mathematical models are used to
study and simulate the respiratory system supported by
mechanical ventilation using different modes such as volumecontrolled ventilation (VCV). In this research, a single
compartment lung model ventilated by VCV is developed
during real time mechanical ventilation using pressure signal.
This mathematical model describes the lung volume and
compliance correctly considering positive end expiration
pressure (PEEP) value. The model is implemented using
LabVIEW tools and can be used to monitor the volume, flow
and compliance as outputs of the model. Two experiments are
carried out on the proposed lung model at three input scenarios
of volume (400, 500 and 600 ml) for each experiment considering
a PEEP value. To validate the model, an artificial lung
connected to a VCV with the same scenarios is used. Validation
check is conducted by comparing the outputs of the lung model
to that of the artificial lung. The experimental results showed
that the measured lung model outputs with negative feedback
are the same for pressure and flow as the outputs without
negative feedback, whereas the measured volume is
comparatively lower for negative feedback. Average percent
error in the experiment with negative feedback (5.14%) is
smaller compared to the experiment without negative feedback
(9.28%). Furthermore, the average error of the calculated
compliance decreases from 16% (without negative feedback) to
2% (with negative feedback). The obtained results of the
proposed method showed good performance and acceptable
accuracy. Thus, the model facilitates the clinicians and
practitioners as a training tool to learn real-time mechanical
ventilation functionalities.
Keywords—Mechanical Ventilation; Volume-Controlled
Ventilators; Lung Compliance; Positive End Expiration Pressure
(PEEP); Negative Feedback; Lung Model; COVID-19
I. INTRODUCTION
Mechanical Ventilation plays a crucial role in intensive
care unit (ICU) for life support of patients having lung
This research is supported by Universiti Malaysia Pahang (UMP)
through University Research Grant (RDU1901150).
malfunction as a result of diseases such as pneumonia,
COVID-19, etc. Mechanical ventilation process delivers and
controls flow, pressure and volume of air and gases to a
patient’s lung [1]. Mechanical ventilation tries to find optimal
positive end expiration pressure (PEEP) level [2, 3] and it uses
real time numeric data and waveforms interpretation that helps
to assess the patient response to ventilation and to maximize
patient comfort and therapeutic benefits [4-6]. Commonly,
there are two types of mechanical ventilation: volumecontrolled ventilation (VCV) and pressure-controlled
ventilation (PCV) [4, 7]. Both types deliver and control flow,
pressure and volume of air and medical gases to the patient’s
lung. VCV is commonly used to treat disordered lungs,
delivering constant volume to patient’s lung [8].
Mathematical models provide realistic solutions for
complex engineering problems [9-12]. A mathematical model
can be used to describe patient’s lung mechanics.
Furthermore, models are developed to optimize mechanicalventilation therapy. Many studies use a single compartment
lung model that can describe lung elastance (1/compliance)
and air way resistance [13-15]. The model incorporates lung
volume and air flow, as well as PEEP that exerts additional
pressure at the end of expiration to reduce alveoli collapse, and
reduces the risk of lung damage [3, 16]. In addition, in some
cases, PEEP is important to reduce work of breathing.
Moreover, titrating PEEP is important during mechanical
ventilation to optimize lung characteristics [16, 17]. However,
excessive increase in PEEP which adds extra volume can
cause ventilator induce lung injury syndrome [18].
Most of the previous works recorded (pressure and flow)
signals as input data to validate single compartment model
[14, 19, 20]. This study aims to optimize and validate a single
compartment lung model supported by VCV through applying
one input signal (i.e., pressure) during real-time mechanical
ventilation to describe lung volume and compliance correctly
[21, 22]. In real practice of VCV, the lung volume should
remain constant even in change of pressure [8]. Adding PEEP
in the lung model results in increase of lung model output
volume, and affects the compliance [23-26].
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2020 IEEE International Conference on Automatic Control and Intelligent Systems (I2CACIS 2020), 20 June 2020, Shah Alam, Malaysia.
To overcome this problem and keep the volume constant,
we add a negative feedback to the lung model to remove the
amount of volume which increases due to PEEP [5, 16]. The
pressure signal is collected at real time using interface device
(ID) which is made for collecting real-time pressure signal of
lung during mechanical ventilation. The model is
implemented in LabVIEW tool, which integrates pressure
with the volume, airflow and compliance. The proposed
model will help to investigate the efficiency of VCV and also
improve accuracy in measurement of lung compliance.
Moreover, it can help clinicians to minimize risk of lung injury
through studying the lung model in real-time mechanical
ventilation instead of working on real patient lungs.
III. METHODOLOGY
Fig. 2 shows the block diagram of the proposed method.
The pressure signal is collected at real time from breathing
circuit using an ID as shown in Fig. 3; and is sent to the lung
model which is implemented by LabVIEW platform as
demonstrated in Fig. 4.
The rest of the paper is organized as follows. Section II
provides the preliminaries of the research work. Section III
presents the methodology of building the proposed algorithm.
The results and discussion are provided in section IV and
finally, the conclusion is presented in section V.
II. PRELIMINARIES
Fig. 2. Main parts involved in the proposed method
Basic functionality of lung mechanics can be described by
a single compartment model [15, 19, 27] which is illustrated
by Fig. 1. Following this illustration, the lung model can be
presented by
(1)
where pt is the airway pressure, E is an overall lung elastance
(1/compliance), Vt represents lung volume, R represents
airway resistance, Qt is air flow which equals dVt/dt and p0
represents PEEP. Note that the subscript t represents the time.
Fig. 3. Interface device for recording the pressure signal
Fig. 1. Illustration of the lung model
Thus, the lung model can be formulated as
)
Fig. 4. The proposed model in LabVIEW platform
(2)
0,
which is a first-order ordinary differential equation.
The following equation can be used to describe
lung compliance (C) [28]:
/
)
(3)
The main components of ID are pressure sensor
(MPX2050), instrumentation amplifier (AD620) and
analogue to digital converter (ADC0808). LabVIEW is a
powerful software that can be used for biomedical control and
simulation; therefore, it is used to implement the lung model
as shown in Fig. 4.
The proposed model is based on a negative feedback from
the output volume to the model input as shown in Fig. 5. Thus,
the input pressure
in the lung model can be presented by
where ppl is the plateau pressure which represents pause
pressure before expiration and it is approximately equal to
the maximum of pressure signal; PEEP is approximately
theminimum pressure signal; and VT is the volume change.
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(4)
2020 IEEE International Conference on Automatic Control and Intelligent Systems (I2CACIS 2020), 20 June 2020, Shah Alam, Malaysia.
Thus,
(5)
Therefore, (2) can be formulated as:
0
(6)
where pt is the airway pressure,
is the lung model input
(pressure), Vt is the model output (volume), Vmin is the
minimum volume and α >1 is constant value.
The proposed method is validated using the agreement of
the output values of the lung model with that of the artificial
lung. The agreement is measured in terms of absolute
percentage error ∈, which is calculated using the following
equation:
O
∈
O
O
x 100
(7)
where OM is the model output and OT is the
experimental (true) output.
IV. RESULTS AND DISCUSSION
Fig. 5. The proposed model with a negative feedback
In general, the lung model depends on using two types of
input data (pressure and flow signals), but the proposed lung
model is based on only one type of input data (pressure
signal). The use of one signal as input signal of lung model
needs control, mathematical processing and validation. In the
present study, two experiments are conducted on reference
device and the lung model. The reference device depends on
(pressure and flow signals), whereas the lung model depends
on one signal (pressure signal) during real-time mechanical
ventilation with and without the feedback.
The lung model is used to study the outputs: volume V (ml),
flow Q (ml/s) and compliance C (ml/cmH2O) using the input
pressure p (cmH2O) during real-time mechanical ventilation
with and without negative feedback. It is noted that if
negative feedback is not considered, the model will act as the
previous model described by (1). The artificial lung is
connected to VT plus HF Gas Flow analyser [29] that
measures the signals of p, V, Q and C during real-time
mechanical ventilation. This artificial lung and the analyser
are well-known calibrated products manufactured by Fluke
Biomedical Corporation. The experimental procedure can be
described as follows:
• The artificial lung is ventilated using VCV (ICU Electric
Ventilator- Model SC-5). The operating mode is as
follows:
•
•
•
•
- Intermittent positive pressure ventilation with
respiration rate is 16 breaths per minute (bpm);
- Ratio of inspiration time (s) to expiration time (s) is 1:2;
- PEEP is taken up to 5 cmH2O.
The artificial lung which represents the patient lung is
adjusted to compliance C = 20 ml/cmH2O, resistance R =
20 cmH2O/L/s.
Two experiments carried out on artificial lung and the
lung model include three scenarios with lung volume: 400
ml, 500 ml and 600 ml. The first experiment is carried out
without adding feedback; and the second experiment, with
a negative feedback.
The main parameters of mechanical ventilation: pressure,
volume and flow are measured on artificial lung. The lung
model uses the same input pressure and computes the
corresponding output of volume and flow for three
scenarios of different volumes.
The compliance obtained by the lung model is calculated
and compared to the compliance of artificial lung in each
scenario.
Fig. 6. Pressure signal at volume 400 ml (without feedback).
Fig. 7. Volume signal at volume 400 ml (without feedback).
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2020 IEEE International Conference on Automatic Control and Intelligent Systems (I2CACIS 2020), 20 June 2020, Shah Alam, Malaysia.
volumes produced the error as 17.7%, 14.6% and 12.1% in
these three scenarios (400 ml, 500 ml and 600 ml),
respectively. The average percent error is 9.28% for
measured parameters at three scenarios.
Fig. 8. Flow signal at volume 400 ml (without feedback).
Fig. 11. Flow signal at volume 400 ml (with feedback).
Fig. 9. Pressure signal at volume 400 ml (with feedback).
Fig. 12. Pressure signal at volume 600 ml (without feedback).
Fig. 10. Volume signal at volume 400 ml (with feedback).
TABLE I shows the results that are obtained from the two
experiments (experiment 1 without feedback and experiment
2 with feedback) and the values of p, V and Q are illustrated
in Figs. 6-11 and Figs. 12-17 for VCV at 400ml and 600ml.
These results presented for experiment 1 show a clear shifting
and drift particularly in volume curves. The outputs of the
Fig. 13. Volume signal at volume 600 ml (without feedback).
However, the results of p, V and Q obtained from the
second experiment which uses the lung model with negative
feedback provide that the values of p and Q of the lung model
and artificial lung are approximately the same as the measured
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2020 IEEE International Conference on Automatic Control and Intelligent Systems (I2CACIS 2020), 20 June 2020, Shah Alam, Malaysia.
values and significant improvement is obtained for V, which
is also clear from the curves as shown in Figs. 7 and 10, and
Figs. 13 and 16. The calculated percent errors in the second
experiment are almost the same for p compared to the first
experiment, whereas, the calculated percent errors of
measured volume V and Q decreased for three scenarios
compared to that obtained in first experiment as shown in
TABLE I. The average percent of error in the second
experiment (5.14%) is much smaller compared to the first
experiment (9.28%).
Error (∈)
(No Feedback)
Error (∈)
(With Feedback)
22.08
22.53
2.0
2.0
337.9
335.2
17.7
0.8
38.15
41.64
8.4
8.4
27.22
0.5
0.5
424.4
14.6
1.4
51.42
3.9
3.9
32.4
2.2
2.2
505
12.1
0.9
49.53
18.6
18.6
9.28
5.14
Lung model
Output (OM)
(No Feedback)
Lung model
output (OM)
(With feedback)
Artificial lung
measurement (OT)
COMPAISON OF P, V AND Q VALUES.
Measured
Parameters
Scenario
TABLE I.
Pressure
22.08
1
(cmH2O)
(Volume
at
Volume (ml) 394.59
400ml)
Flow (ml/s)
38.15
Pressure
2
27.09 27.09
(Volume (cmH2O)
at
500ml) Volume (ml) 486.24 430.44
Flow (ml/s)
49.42
49.42
Pressure
3
31.7
31.7
(Volume (cmH2O)
at
600ml) Volume (ml) 566.17 509.43
Flow (ml/s)
58.76
Average error
TABLE II.
one sensor (pressure sensor) instead of two sensors (flow and
pressure sensors) for measuring and calculating the outputs of
single compartment model of lung achieves good results with
small error (5.14%). Moreover, using one data (pressure
signal) instead of two types of data (flow and pressure signals)
can be used to minimize the related devices and consequently
reduce cost.
58.75
Fig. 14. Flow signal at volume 600 ml (without feedback).
COMPARISON OF LUNG COMPLIANCE VALUES
Artificial lung Absolute
Lung Model
C
Percentage
Experiment Scenario C (ml/cmH2O)
(ml/cmH2O)
OM
Error ∈ (%)
OT
1
22
18.3
20.2
1
2
21.2
18.6
14
(without
3
20.6
18.1
13.8
feedback)
Average error
16.00
1
18.9
18.3
3.3
2
2
18.7
18.6
0.5
(with
3
18.5
18.1
2.2
feedback)
Average error
2.00
Obviously, improvement of lung model based on the use
of negative feedback is checked by the reduced error in the
measured outputs as well as in calculated compliance as
shown in TABLE II. The average error in the calculated
compliance decreased from 16% (without negative feedback)
to 2% (with negative feedback). Thus, in this approach using
Fig. 15. Pressure signal at volume 600 ml (with feedback).
Fig. 16. Volume signal at volume 600 ml (with feedback).
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2020 IEEE International Conference on Automatic Control and Intelligent Systems (I2CACIS 2020), 20 June 2020, Shah Alam, Malaysia.
[9]
[10]
[11]
[12]
[13]
Fig. 17. Flow signal at volume 600 ml (with feedback).
V. CONCLUSION
The lung model normally depends on two types of input
data: pressure and flow signals, but in case of using pressure
signal, the lung model needs to be optimized by minimizing
the error between the model output and the actual lung output.
In addition, using just one signal will minimize the related
devices and reduce cost. In this study, a single compartment
lung model supported by VCV is developed using one input
pressure signal during real-time mechanical ventilation. The
model is implemented using LabVIEW platform, and
validated against a reference gas flow analyser – Fluke
Biomedical. The proposed model based on negative feedback
shows good performance and acceptable accuracy as
demonstrated by experimental results. Therefore, it can be
used to compute volume, flow and compliance using the
pressure signal of the mechanical ventilation in real time.
Hence, the model can be used to evaluate mechanical
ventilation performance. This can help the clinicians and
apprentices minimize the risk of lung injury through studying
on the lung model instead of actual patient lung.
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