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...

Повний опис

Збережено в:
Бібліографічні деталі
Опубліковано в: :Кибернетика и вычислительная техника
Дата:2014
Автори: Lopata, V.A., Popov, A.A., Myasnyi, I.S.
Формат: Стаття
Мова:English
Опубліковано: Міжнародний науково-навчальний центр інформаційних технологій і систем НАН України та МОН України 2014
Теми:
Онлайн доступ:https://nasplib.isofts.kiev.ua/handle/123456789/84537
Теги: Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати: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.

Репозитарії

Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-84537
record_format dspace
spelling 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
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection 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.
work_keys_str_mv AT lopatava spectralanalysisofairflowrateduringforcedexpiratoryprocess
AT popovaa spectralanalysisofairflowrateduringforcedexpiratoryprocess
AT myasnyiis spectralanalysisofairflowrateduringforcedexpiratoryprocess
AT lopatava spektralʹnyianalizskorostivozdušnogopotokavprocesseforsirovannogovydoha
AT popovaa spektralʹnyianalizskorostivozdušnogopotokavprocesseforsirovannogovydoha
AT myasnyiis spektralʹnyianalizskorostivozdušnogopotokavprocesseforsirovannogovydoha
AT lopatava spektralʹniianalízšvidkostípotokupovítrâvprocesíforsovanogovidihu
AT popovaa spektralʹniianalízšvidkostípotokupovítrâvprocesíforsovanogovidihu
AT myasnyiis spektralʹniianalízšvidkostípotokupovítrâvprocesíforsovanogovidihu
first_indexed 2025-11-26T07:56:07Z
last_indexed 2025-11-26T07:56:07Z
_version_ 1850614868627947520
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 ISSN 0452-9910. Кибернетика и вычисл. техника. 2014. Вып. 178  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. 1. ATS Statement — Snowbird workshop on standardization of spirometry. Amer. Rev. Resp. Dis., 1979, vol. 119, pp. 831–838. 2. Standardization of spirometry — 1987 update. Amer. J. Resp. Dis., 1987, vol. 136, pp. 1285–1298. 3. Standardization of spirometry -1994 update. Amer. J. Respir. Crit. Care. Med., 1995, vol. 152, pp. 1107–1136. 4. Quanjer Ph.H. Standardized lung function testing. Report Working Party Standardization of Lung Function Tests, European Community for Coal and Steel. Bull. Eur. Physiopathol. Respir., 1983, vol. 19, pp. 1–95. 5. Quanjer Ph.H., Tammeling G.J., Cotes J.E. Lung volumes and forced ventilatory flows: report of working party, standardization of lung function tests. European Community for Coal and Steel — official statement of the European Respiratory Society. Eur. Respir. J., 1993, vol. 6, pp. 5–40. 6. Kuznetsova V.K., Aganezova E.S., Yakovleva N.G. Methods of conduction and unificated evaluation of results of functional investigation of mechanical parameters of ventillation system using spirometry. Saint Petersburg, 2001 (in Russian). 7. Miller M.R., Hankinson J., Brusasco V. Standardisation of spirometry. Eur. Respir. J, 2005, vol. 26, pp. 319–338. 8. Peslin R., Jardin P., Bohadana A., Hannhart B. Contenu harmonique de signal de debit pendant l’expiration forcee chez l’homme normal. Bull. Eur. Physiopath. Resp., June 1982, vol. 18, pp. 491–500. 9. Lopata V.A. Criteria and estimates of functional characteristics of spirometers. Medichne obladnanna ta vytratni materialy, December 2010 –January 2011. pp. 34–36 (in Ukrainian). 10. Salas T., Rubies C., Gallego C., Munoz P., Burgos F., Escarrabill J. Technical requirements of spirometers in the strategy for guaranteeing the access to quality spirometry. Arch. Bronconeumol. 2011, vol. 47, pp. 466–469. 11. Lesnick B. L., Davis S.D. Infant pulmonary function testing overview of technology and practical considerations — new current procedural terminology codes effective. Chest, 2011, vol. 139 № 5, pp. 1197–1202. 12. Lemen R.J., Gerdess C.B., Wegmann M.J., Perrin K.J. Frequency spectra of flow and volume events of forced vital capacity. J. Appl. Physiol., 1982, vol. 53 № 4. pp. 977–984. 13. McCall C.B., Hyatt R.E., Noble F.W., Fry D.L. Harmonic content of certain respiratory flow phenomena of normal individuals. J. Appl. Physiol., 1957, vol. 10, iss. 2, pp. 215–218. 14. International system of units for measurement of lung functions. Ekspres-Informatsia: seria Promyshlennost meditsinskoi tekhniki, 1976, № 24. pp. 2–16 (in Russian). 15. Lopata V.A. Research and regulation of the dynamic characteristics of pneumotachometers for improving informativeness of pneumotachometry. PhD thesis, Moscow, 1983, 22 p. (in Russian). 16. Lopata V. Modeling of forced expiration process for the purposes of spirometry. Physiology, 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).  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. 1. ATS Statement — Snowbird workshop on standardization of spirometry. Amer. Rev. Resp. Dis., 1979, vol. 119, pp. 831–838. 2. Standardization of spirometry — 1987 update. Amer. J. Resp. Dis., 1987, vol. 136, pp. 1285–1298. 3. Standardization of spirometry -1994 update. Amer. J. Respir. Crit. Care. Med., 1995, vol. 152, pp. 1107–1136. 4. Quanjer Ph.H. Standardized lung function testing. Report Working Party Standardization of Lung Function Tests, European Community for Coal and Steel. Bull. Eur. Physiopathol. Respir., 1983, vol. 19, pp. 1–95.  V.A. Lopata, A.A. Popov, I.S. Myasnyi, 2014 ISSN 0452-9910. Кибернетика и вычисл. техника. 2014. Вып. 178 90 5. Quanjer Ph.H., Tammeling G.J., Cotes J.E. Lung volumes and forced ventilatory flows: report of working party, standardization of lung function tests. European Community for Coal and Steel — official statement of the European Respiratory Society. Eur. Respir. J., 1993, vol. 6, pp. 5–40. 6. Kuznetsova V.K., Aganezova E.S., Yakovleva N.G. Methods of conduction and unificated evaluation of results of functional investigation of mechanical parameters of ventillation system using spirometry. Saint Petersburg, 2001 (in Russian). 7. Miller M.R., Hankinson J., Brusasco V. Standardisation of spirometry. Eur. Respir. J, 2005, vol. 26, pp. 319–338. 8. Peslin R., Jardin P., Bohadana A., Hannhart B. Contenu harmonique de signal de debit pendant l’expiration forcee chez l’homme normal. Bull. Eur. Physiopath. Resp., June 1982, vol. 18, pp. 491–500. 9. Lopata V.A. Criteria and estimates of functional characteristics of spirometers. Medichne obladnanna ta vytratni materialy, December 2010 –January 2011. pp. 34–36 (in Ukrainian). 10. Salas T., Rubies C., Gallego C., Munoz P., Burgos F., Escarrabill J. Technical requirements of spirometers in the strategy for guaranteeing the access to quality spirometry. Arch. Bronconeumol. 2011, vol. 47, pp. 466–469. 11. Lesnick B. L., Davis S.D. Infant pulmonary function testing overview of technology and practical considerations — new current procedural terminology codes effective. Chest, 2011, vol. 139 № 5, pp. 1197–1202. 12. Lemen R.J., Gerdess C.B., Wegmann M.J., Perrin K.J. Frequency spectra of flow and volume events of forced vital capacity. J. Appl. Physiol., 1982, vol. 53 № 4. pp. 977–984. 13. McCall C.B., Hyatt R.E., Noble F.W., Fry D.L. Harmonic content of certain respiratory flow phenomena of normal individuals. J. Appl. Physiol., 1957, vol. 10, iss. 2, pp. 215–218. 14. International system of units for measurement of lung functions. Ekspres-Informatsia: seria Promyshlennost meditsinskoi tekhniki, 1976, № 24. pp. 2–16 (in Russian). 15. Lopata V.A. Research and regulation of the dynamic characteristics of pneumotachometers for improving informativeness of pneumotachometry. PhD thesis, Moscow, 1983, 22 p. (in Russian). 16. Lopata V. Modeling of forced expiration process for the purposes of spirometry. Physiology, 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