Spectral Analysis of Airflow Rate During Forced Expiratory Process
Purpose: To study the dynamic characteristics of spirometers, and development of method for analysis of airflow rate spectral density. Results: An explicit mathematical expression of airflow rate spectral density is obtained and studied, and the frequency range in which the dynamic characteristics o...
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Lopata, V.A. Popov, A.A. Myasnyi, I.S. 2015-07-09T21:23:29Z 2015-07-09T21:23:29Z 2014 Spectral Analysis of Airflow Rate During Forced Expiratory Process / V.A. Lopata, A.A. Popov, I.S. Myasnyi // Кибернетика и вычислительная техника. — 2014. — Вип. 178. — С. 82-90. — Бібліогр.: 18 назв. — англ. 0452-9910 https://nasplib.isofts.kiev.ua/handle/123456789/84537 621.3 Purpose: To study the dynamic characteristics of spirometers, and development of method for analysis of airflow rate spectral density. Results: An explicit mathematical expression of airflow rate spectral density is obtained and studied, and the frequency range in which the dynamic characteristics of spirometers should be standardized is defined as 0 – 80 Hz. С использованием модели процесса форсированного выдоха и преобразования Фурье определен частотный спектр его объемной скорости воздуха. Показано, что погрешность измерений показателей процесса спирометром, динамические характеристики которого нормированы в диапазоне 0–15 Гц, может достигать 7,5%. Диапазон нормирования должен быть расширен до 80 Гц. В этом случае погрешность измерений ограничивается в пределах 2%. В роботі з використанням моделі процесу форсованого видиху і перетворення Фур'є визначений частотний спектр швидкостей повітря в процесі. З отриманих даних випливає, що похибка вимірювань спірометра з амплітудно-частотною характеристикою, нормованою стандартом в частотному діапазоні 0–15 Гц, може сягати 7,5%, що неприпустимо. Діапазон частот, у якому мають бути стандартизовані динамічні характеристики спірометрів, сягає 80 Гц. У цьому випадку похибка вимірювання швидкостей повітря форсованого видиху лімітується в межах 2 %. en Міжнародний науково-навчальний центр інформаційних технологій і систем НАН України та МОН України Кибернетика и вычислительная техника Медицинская и биологическая кибернетика Spectral Analysis of Airflow Rate During Forced Expiratory Process Спектральный анализ скорости воздушного потока в процессе форсированного выдоха Спектральний аналіз швидкості потоку повітря в процесі форсованого видиху Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| title |
Spectral Analysis of Airflow Rate During Forced Expiratory Process |
| spellingShingle |
Spectral Analysis of Airflow Rate During Forced Expiratory Process Lopata, V.A. Popov, A.A. Myasnyi, I.S. Медицинская и биологическая кибернетика |
| title_short |
Spectral Analysis of Airflow Rate During Forced Expiratory Process |
| title_full |
Spectral Analysis of Airflow Rate During Forced Expiratory Process |
| title_fullStr |
Spectral Analysis of Airflow Rate During Forced Expiratory Process |
| title_full_unstemmed |
Spectral Analysis of Airflow Rate During Forced Expiratory Process |
| title_sort |
spectral analysis of airflow rate during forced expiratory process |
| author |
Lopata, V.A. Popov, A.A. Myasnyi, I.S. |
| author_facet |
Lopata, V.A. Popov, A.A. Myasnyi, I.S. |
| topic |
Медицинская и биологическая кибернетика |
| topic_facet |
Медицинская и биологическая кибернетика |
| publishDate |
2014 |
| language |
English |
| container_title |
Кибернетика и вычислительная техника |
| publisher |
Міжнародний науково-навчальний центр інформаційних технологій і систем НАН України та МОН України |
| format |
Article |
| title_alt |
Спектральный анализ скорости воздушного потока в процессе форсированного выдоха Спектральний аналіз швидкості потоку повітря в процесі форсованого видиху |
| description |
Purpose: To study the dynamic characteristics of spirometers, and development of method for analysis of airflow rate spectral density. Results: An explicit mathematical expression of airflow rate spectral density is obtained and studied, and the frequency range in which the dynamic characteristics of spirometers should be standardized is defined as 0 – 80 Hz.
С использованием модели процесса форсированного выдоха и преобразования Фурье определен частотный спектр его объемной скорости воздуха. Показано, что погрешность измерений показателей процесса спирометром, динамические характеристики которого нормированы в диапазоне 0–15 Гц, может достигать 7,5%. Диапазон нормирования должен быть расширен до 80 Гц. В этом случае погрешность измерений ограничивается в пределах 2%.
В роботі з використанням моделі процесу форсованого видиху і перетворення Фур'є визначений частотний спектр швидкостей повітря в процесі. З отриманих даних випливає, що похибка вимірювань спірометра з амплітудно-частотною характеристикою, нормованою стандартом в частотному діапазоні 0–15 Гц, може сягати 7,5%, що неприпустимо. Діапазон частот, у якому мають бути стандартизовані динамічні характеристики спірометрів, сягає 80 Гц. У цьому випадку похибка вимірювання швидкостей повітря форсованого видиху лімітується в межах 2 %.
|
| issn |
0452-9910 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/84537 |
| citation_txt |
Spectral Analysis of Airflow Rate During Forced Expiratory Process / V.A. Lopata, A.A. Popov, I.S. Myasnyi // Кибернетика и вычислительная техника. — 2014. — Вип. 178. — С. 82-90. — Бібліогр.: 18 назв. — англ. |
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2025-11-26T07:56:07Z |
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| fulltext |
82
Медицинская и биологическая
кибернетика
UDK 621.3
SPECTRAL ANALYSIS OF AIRFLOW RATE
DURING FORCED EXPIRATORY PROCESS
V.A. Lopata1, A.A. Popov2, I.S. Myasnyi3
1Bogomolets Institute of Physiology, National Academy of Science of Ukraine
2National technical University of Ukraine “Kyiv Polytechnic Institute”
3Center of pulmonology, allergology and clinical immunology, Clinical Hospital
“Feofaniya”
С использованием модели процесса форсированного
выдоха и преобразования Фурье определен частотный спектр его
объемной скорости воздуха. Показано, что погрешность измерений
показателей процесса спирометром, динамические характеристики
которого нормированы в диапазоне 0–15 Гц, может достигать 7,5%.
Диапазон нормирования должен быть расширен до 80 Гц. В этом случае
погрешность измерений ограничивается в пределах 2%.
Ключевые слова: спирометр, динамические
характеристики, скорость потока воздуха, моделирование процесса
форсированного дыхания.
В роботі з використанням моделі процесу форсованого
видиху і перетворення Фур'є визначений частотний спектр швидкостей
повітря в процесі. З отриманих даних випливає, що похибка вимірювань
спірометра з амплітудно-частотною характеристикою, нормованою
стандартом в частотному діапазоні 0–15 Гц, може сягати 7,5%, що
неприпустимо. Діапазон частот, у якому мають бути стандартизовані
динамічні характеристики спірометрів, сягає 80 Гц. У цьому випадку
похибка вимірювання швидкостей повітря форсованого видиху
лімітується в межах 2 %.
Ключові слова: спірометр, динамічні характеристики,
швидкість потоку повітря, моделювання процесу форсованого дихання.
INTRODUCTION
Dynamic response is an important characteristic of spirometers for testing of
lung ventilation function (LVF) by measuring airflow rate during breathing. Since
first standard issued by American Thoracic Society (ATS) in 1979 [1], this
characteristic is standardized in all subsequent standards of ATS, European
Respiratory Society (ERS) and spirometry methodological recommendations of
Russian Federation (RF) [2–7] (Table I).
V.A. Lopata, A.A. Popov, I.S. Myasnyi, 2014
ISSN 0452-9910. Кибернетика и вычисл. техника. 2014. Вып. 178
83
Table 1.
Requirements for the frequency response nonlinearity in various standards
ATS [1,2,3] ERS [4,5] RF [6] ATS / ERS [7]
1979 1987 1994 1983 1993 2001 2005
± 10 %
in range 0 – 4 Hz
± 5 %
in range
0 – 20 Hz
± 5 %
in range
0 – 20 Hz
± 5 %
in range
0 – 15 Hz
Dynamic response is standardized in terms of the requirements for the
frequency response nonlinearity of the device in predefined frequency range. In
Table I the requirements are summarized, and it can be seen that by now there are
differences in frequency ranges and values of acceptable nonlinearity.
PROBLEM STATEMENT
Since spirometry technique implies the forced expiratory maneuver when
maximal airflow rate is achieved [8], standardization of frequency response
nonlinearity should take into consideration dynamics of forced expiratory
parameters, which is significant for the sake of diagnostics. This requirement is
emphasized in papers [9, 10] when discussing the characteristics of the spirometric
equipment, especially designed for LVF studies in children [11]. The literature
provides information about the frequency spectrum of the forced expiratory airflow
rate, which is considered as an objective criterion of the process dynamics.
In paper [12] it is determined that this frequency spectrum with amplitudes of
harmonics up to 5 % of the maximum were located in range 6,49 ± 1,8 Hz. Authors
of [8] have found that the amplitude of harmonics is reduced exponentially with
increasing frequency, and in the range up to 10 Hz the values are 3–5 % of
maximum amplitude. In [13] the bandwidth is defined in range from 0 up to
10.3 Hz. Thus all data about the frequency spectrum are rather contradictory and
must be clarified.
The purpose of this paper is to define by studying the model of forced
expiratory process the frequency range in which frequency response must be
standardized. The airflow process during breathing is simulated using the electrical
circuit analogy, and an explicit mathematical expression of airflow rate spectral
density is obtained. From this expression we define the frequency range in which
the dynamic characteristics of spirometers should be standardized.
THE CIRCUIT MODEL OF FORCED EXPIRATORY PROCESS
The analogy between the electric current flow and airflow can be used in the
respiration process modeling. Table 2 shows the correspondence between
parameters of airflow and electric circuit [14].
The considered model was used in [15, 16] for calculation of the measurement
errors, optimization and control of spirometer’s dynamic characteristics, generation
of test signals and spirometer metrology. It formalizes breathing in terms of electric
current flow, and gives clear analogy of volumetric and velocity parameters of
V.A. Lopata, A.A. Popov, I.S. Myasnyi, 2014
ISSN 0452-9910. Кибернетика и вычисл. техника. 2014. Вып. 178
84
forced expiratory, giving the possibility to model various states of LVF by varying
values of AWR , С, L and I.
Table 2.
Correspondence between airflow and electric current flow
Airflow system Electric circuit
AWR – airways resistance, Pa·sec / Liter R – resistance of the resistor, Ohm
LC – lung compliance, Liter/Pa С – capacitance of the capacitor, F
I – intertance, Pa·sec2 / Liter L – inductance of the inductor, H
V – air volume, Liter q – charge of capacitor, C
p – pressure, Pa U – voltage, V
Q – airflow rate, Liter / sec i – current, А
Forced expiratory can be modeled by transition process of aperiodic capacitor
discharge on the serial connection of resistor and inductance [15]. From the circuit
theory considerations, this process can be described using the equation:
2
2
1 0d i R di i
L dt L Cdt
+ ⋅ + ⋅ =
⋅
. (1)
The circuit model of forced expiratory process is given in Fig. 1.
Fig. 1. Circuit model of respiratory process
Solving (1) for the capacitor charge q and current i, the equations for the
respiration parameters of interest can be obtained:
0 1
t t
t
e eV V
β αα β
α β
⋅ − ⋅
= − −
, (2)
( )0
t t
tQ V e eα βα β
α β
⋅
= −
−
, (3)
where 0V is forced vital capacity (FVC);
2
2
1,
2 4
AW AW
L
R R
I I CI
α β = − ± −
⋅
. (4)
V.A. Lopata, A.A. Popov, I.S. Myasnyi, 2014
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V.A. Lopata, A.A. Popov, I.S. Myasnyi, 2014
ISSN 0452-9910. Кибернетика и вычисл. техника. 2014. Вып. 178
85
In normal LVF conditions parameters α and β take the following values:
AWR = 110 – 350 Pa⋅sec/Liter, СL = 0,0015 – 0,003 Liter/Pa, I = 1 – 17 Pa⋅sec2/Liter
[17]. It is shown in [15] that for any possible combination of AWR , СL, I in normal
and pathologic conditions, the values of α and β are strictly real and negative since
the following condition always holds true:
2 .AW
L
IR
C
≥ (5)
FREQUENCY CHARACTERISTICS OF AIRFLOW RATE
To study the frequency characteristics of airflow, the Fourier spectrum of
airflow rate should be defined. It is known from [15] that the time when airflow
rate reaches its maximum during forced expiratory process (peak flow rate, PFR)
can be defined by:
ln
.PFRТ
β
α
α β
=
−
(6)
Fourier transform ( ) ( ) j tF x t e dtωω
+∞
−
−∞
= ∫
can be applied to (3) to obtain spectra of
airflow rate. To facilitate this, rewrite (3) in the form
( )max max max
t t t t
tQ Q e e Q e Q eα β α β= − = − , (7)
which is the difference of two exponential functions, and denote
( ) 0, 0tx t e for tα α⋅= > ≥ , (8)
( ) 0, 0ty t e for tβ β⋅= > ≥ . (9)
Spectral density can be written as
( ) ( ) ( )Q x yG j G j G jω ω ω= − , (10)
where ( )xG jω and ( )yG jω are spectral densities of exponential functions
(8) and (9) respectively. It is known that Fourier transform of function
( ) , 0, 0ctz t e c t−= > ≥ given by ( )
0
ct j tG j e e dtωω
+∞
− −= ∫ equals:
222222
1)(
ω
ω
ωω
ω
ω
ω
+
−
+
=
+
−
=
+
=
c
j
c
c
c
jc
jc
jGx
V.A. Lopata, A.A. Popov, I.S. Myasnyi, 2014
ISSN 0452-9910. Кибернетика и вычисл. техника. 2014. Вып. 178
86
Thus making all needed transforms and substitutions using (2) and (5) we
obtain finally the complex Fourier spectrum:
( ) ( ) ( )
( ) ( ) ( ){ }
max
2 2 2 2
2 2 2 2 2 2
Q
QG j
j
ω
α ω β ω
α β ω β α ω ω α β
= ×
+ +
× + − + − −
(11)
and spectral density:
( ) ( )( )
( ) ( ) ( )
max
2 2 2 2
2 22 2 2 2 2 2 2 ,
Q
QP ω
α ω β ω
α β ω β α ω ω α β
= ×
+ +
× + − + + −
(12)
where maxQ is PFR at a time instant PFRТ .
Having the expression of spectral density, it is possible to calculate it explicitly
for any combination of respiration system parameters.
RESULTS
It is proposed to select the spectral range in which dynamic characteristics
should be standardized, for the case when the spectral range of airflow rate is
widest. For this case the range with harmonic components with high magnitudes
should be defined at certain level of magnitudes.
0 1 2 3 4 5 6 7 8 9 10
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Time, sec
Q
(t)
/Q
m
ax
Fig. 2. Time dependence of airflow rate, normalized
To define the frequency range in which the harmonics with significant
magnitudes are located, the values of α and β should be substituted in (12). To
obtain the widest frequency range of airflow rate, which corresponds to the situation
with minimal PFRТ , expression (4) should be considered. It can be seen that
minimal PFRТ is reached when LC and I are minimal and AWR is maximal.
V.A. Lopata, A.A. Popov, I.S. Myasnyi, 2014
ISSN 0452-9910. Кибернетика и вычисл. техника. 2014. Вып. 178
87
0 10 20 30 40 50 60 70 80
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Frequency , Hz
P
(f)
/P
m
ax
Fig. 3. Spectral density of airflow rate, normalized
This case corresponds to the condition of severe LVF dysfunction, when:
AWR = 900 Pa⋅sec / Liter,
LC = 0,0015 Liter / Pa,
I = 1 Pa⋅sec2 / Liter.
In this case α = - 0,74 sec-1 and β = - 899,26 sec-1.
Figure 2 shows time dependence of airflow rate as the result of simulation the
respiration process using the model from Fig. 1 with formula (3) and parameters for
severe LVF dysfunction. In Fig. 3 its spectral density is shown.
Using the graph from Fig. 3 it can be seen that harmonics with magnitudes
larger than 2% of PFR are located in the frequency range from 0 to 70 Hz.
DISCUSSION
The results of defining the spectral range in which harmonics with high
magnitudes are located shows, that this range obtained in our study is significantly
wider than the frequency ranges reported in [8, 12]. Our result is close to the range
of airflow rates frequency spectrum during cough shock (5–70 Hz [18]), which is
similar to the forced expiratory process.
From our data it follows that the spirometer with frequency response
normalized following the standard [7] in the frequency range of 0–15 Hz, in the
considered case can measure the data with an accuracy of less than 7.5 %, which
might be considered as rather high error. We can recommend from our results that if
the error of forced expiratory airflow rates measurement is bounded by ± 2 %, the
frequency range for standardization should be extended up to 80 Hz.
CONCLUSIONS
Our findings demand to normalize the dynamic characteristics of spirometers,
adequate to frequency spectrum of forced expiratory airflow rates. Using an explicit
mathematical expression of airflow rate spectral density, the frequency range in
V.A. Lopata, A.A. Popov, I.S. Myasnyi, 2014
ISSN 0452-9910. Кибернетика и вычисл. техника. 2014. Вып. 178
88
which the dynamic characteristics of spirometers should be standardized is defined
as 0–80 Hz. A further area of research should be focused on simulation of forced
expiratory process for various combinations of AWR , LC and I in the normal LVF
state and its possible violations.
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V.A. Lopata, A.A. Popov, I.S. Myasnyi, 2014
ISSN 0452-9910. Кибернетика и вычисл. техника. 2014. Вып. 178
89
UDK 621.3
SPECTRAL ANALYSIS OF AIRFLOW RATE
DURING FORCED EXPIRATORY PROCESS
V.A. Lopata1, A.A. Popov2, I.S. Myasnyi3
1Bogomolets Institute of Physiology, National Academy of Science of Ukraine
2National technical University of Ukraine “Kyiv Polytechnic Institute”
3Center of pulmonology, allergology and clinical immunology, Clinical Hospital
“Feofaniya”
Introduction: The dynamics of airflow rate using the circuit model of
respiration system is considered with respect to standardization of requirements for
the frequency response nonlinearity of spirometers. Dynamic response is an
important characteristic of spirometers for investigation of lung ventilation
function by measuring airflow rate of air during breathing. Since spirometry
technique implies the forced expiratory maneuver when maximal airflow rate is
achieved, standardization of frequency response nonlinearity should take into
consideration dynamics of forced expiratory parameters, which is meaningful for
the sake of diagnostics.
Purpose: To study the dynamic characteristics of spirometers, and
development of method for analysis of airflow rate spectral density.
Methods: The analogy between the electric current flow and airflow is used to
model the respiration process. It formalizes breathing in terms of electric current
flow, and gives clear analogy of volumetric and velocity parameters of forced
expiratory, giving the possibility to model various states of lung ventilation
function. Frequency charanteristics of the volumetric airflow rate are obtained
using Fourier analysis of respiration parameters.
Results: An explicit mathematical expression of airflow rate spectral density
is obtained and studied, and the frequency range in which the dynamic
characteristics of spirometers should be standardized is defined as 0 – 80 Hz.
Conclusions: Our findings demand to normalize the dynamic characteristics
of spirometers, adequate to frequency spectrum of forced expiratory airflow rates.
Using an explicit mathematical expression of airflow rate spectral density, the
frequency range in which the dynamic characteristics of spirometers should be
standardized is defined as 0 – 80 Hz. A further area of research should be focused
on simulation of forced expiratory process for various combinations of respiration
parameters.
Keywords: spirometer; dynamic response; airflow rates; forced expiratory
process modeling.
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90
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for improving informativeness of pneumotachometry. PhD thesis, Moscow, 1983, 22 p.
(in Russian).
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2004, vol. 14, № 82, Suppl. “Trends in clinical and experimental Physiology”, p. 80.
17. Tikhonov M.A. External respiration. Mechanics of Respiration. Fiziologia cheloveka I
zhivotnykh, Moscow, 1972, pp. 72–131 (in Russian).
18. Svatosh Y. Biosignals from the engineering point of view. Ukrainskii zhurnal meditsinskoi
tekhniki i tekhnologii, 1998, № 1–2, pp. 93–97 (in Russian).
Получено 11.06.2014
V.A. Lopata, A.A. Popov, I.S. Myasnyi, 2014
ISSN 0452-9910. Кибернетика и вычисл. техника. 2014. Вып. 178
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