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The volume-dependent Forced Oscillation Technique
10th 10th IFAC IFAC Symposium Symposium on on Biological Biological and and Medical Medical Systems Systems São Paulo, Brazil, September 3-5, 2018 10th IFAC Symposium on Biological and Medical Systems Available online at www.sciencedirect.com São Paulo, Brazil, September 3-5, 2018 10th Paulo, IFAC Symposium on Biological and Medical Systems São Brazil, September 3-5, 2018 São Paulo, Brazil, September 3-5, 2018
ScienceDirect
IFAC PapersOnLine 51-27 (2018) 373–377
The volume-dependent volume-dependent Forced Forced Oscillation Oscillation The The volume-dependent Forced Oscillation Technique The volume-dependent Forced Oscillation Technique Technique Technique ∗∗ Klaus Tenbrock ∗∗ ∗∗ Chuong Ngo ∗∗ Falk Dippel ∗∗ Sylvia Lehmann ∗∗
∗ Sylvia Lehmann ∗∗ Klaus Tenbrock ∗∗ Chuong Ngo ∗∗ Falk Dippel ∗ Sylvia Lehmann ∗∗ Klaus Tenbrock ∗∗ ∗∗∗ Berno ∗ Steffen ∗ Chuong Ngo ∗Vollmer Falk Dippel Thomas Misgeld Leonhardt ∗∗∗ ∗ Steffen ∗ ∗ Sylvia ∗∗ Klaus ∗∗ Thomas Vollmer Berno Misgeld Leonhardt ∗∗∗ ∗ ∗ Chuong Ngo Falk Dippel Lehmann Tenbrock Thomas Vollmer ∗∗∗ Berno Misgeld ∗ Steffen Leonhardt ∗ Thomas Vollmer Berno Misgeld Steffen Leonhardt ∗ Chair of Information ∗ Chair of Medical Information Technology, Technology, Helmholz Helmholz Institut Institut for for Biomedical Biomedical ∗ Chair of Medical Medical Information Technology, Helmholz Institut for Biomedical Engineering, RWTH Aachen University Engineering, RWTH Aachen University ∗ ∗∗Chair of Medical Information Technology, Helmholz Institut for Biomedical Engineering, RWTH Aachen University of Pulmonology, University Hospital ∗∗ Department of Pediatric Pediatric Pulmonology, University Hospital RWTH RWTH Aachen, Aachen, ∗∗ Department Engineering, RWTH Aachen University Department of Pediatric Pulmonology, University Hospital RWTH Aachen, Germany ∗∗∗∗∗ Germany Department of Pediatric Pulmonology, University Hospital RWTH Aachen, Germany Philips Technologie GmbH Innovative Technologies, Aachen, Germany ∗∗∗ Philips GmbH Innovative Aachen, Germany ∗∗∗ Philips Technologie Germany Technologies, Technologie GmbH Innovative Technologies, Aachen, Germany ∗∗∗ Philips Technologie GmbH Innovative Technologies, Aachen, Germany Abstract: This Abstract: This paper paper describes describes aa novel novel extension extension of of the the Forced Forced Oscillation Oscillation Technique Technique (FOT), (FOT), namely namely the the Abstract: This paper describes a novelTechnique extension of the Forced Oscillation Technique (FOT), namely the volume-dependent Forced Oscillation (v-FOT). This extension is based on the measurement volume-dependent Forced Oscillation Technique (v-FOT). This extension is based on the measurement Abstract: This paper describes a novel extension the Forced Oscillation Technique namely the volume-dependent Forced Oscillation Technique (v-FOT). extension is based on(FOT), the measurement of the the respiratory respiratory impedance over the whole whole lung of volume. AThis new measurement protocol was introduced: of impedance over the lung volume. A new measurement protocol was introduced: volume-dependent Forced Oscillation Technique (v-FOT). This extension is based on the measurement of the respiratory impedance the whole lung to volume. A new measurement was are introduced: subjects breathe slowly slowly fromover residual volume to total lung lung capacity, while protocol oscillations are applied subjects breathe from residual volume total capacity, while oscillations applied of the respiratory impedance the whole lung volume. Aby new measurement protocol was introduced: subjects breathe The slowly fromover residual volume to total lung capacity, while oscillations are applied simultaneously. respiratory impedance is computed means of the windowed cosine fitting simultaneously. The respiratory impedance is computed by means of the windowed cosine fitting subjects breathe slowly from residual volume to total lung oscillations are applied simultaneously. The respiratory impedance isfrequencycomputed by capacity, means ofwhile the windowed cosine fitting method. The respiratory impedance becomes and volume-dependent Z( jω,V ). The novel method. The respiratory impedance becomes frequencyand volume-dependent Z( jω,V ). The novel simultaneously. The(ZV) respiratory impedance isfrequencycomputed by volume-dependent means of the windowed fitting method. The respiratory impedance becomes and Z( jω,Vcosine ). The novel impedance-volume diagram was introduced for diagnostic purposes. Least-squares parameter impedance-volume (ZV) impedance diagram was introduced for diagnostic purposes. Least-squares parameter method. The becomes frequencyand volume-dependent Z( jω,V ).both The novel impedance-volume (ZV) diagram was introduced purposes. Least-squares parameter estimation wasrespiratory performed for the the extended-RIC extended-RIC andfor the diagnostic constant phase models. However, models estimation was performed for and the constant phase models. However, both models impedance-volume (ZV) diagram was introduced for diagnostic purposes. Least-squares parameter estimation was performed for the extended-RIC and the constant phase models. However, both models failed in presenting the volume-dependency of Z. We proposed two new models: the volume-dependent failed in presenting the volume-dependency of Z.and We proposed two new models. models: However, the volume-dependent estimation wasand performed for the extended-RIC phase both models failed in presenting thevolume-dependent volume-dependency of Z. Wethe proposed two models: the volume-dependent extended RIC the Mead model forconstant a better better fitnew of the the data. The The extended RIC and the volume-dependent Mead model for a fit of data. volume-dependent failed in presenting the volume-dependency of Z. We proposed two new models: the volume-dependent extended RICyields and the Mead Mead model model thevolume-dependent smallest estimation estimation error.model for a better fit of the data. The volume-dependent Mead the smallest error. extended RICyields and the Mead Mead model yields thevolume-dependent smallest estimation error.model for a better fit of the data. The volume-dependent © 2018, IFACyields (International Federation of Automatic Mead model the smallest estimation error. Control) Hosting by Elsevier Ltd. All rights reserved. Keywords: Forced Forced Oscillation Oscillation Technique, Technique, volume-dependency, volume-dependency, extended extended RIC RIC model, model, nonlinear, nonlinear, Keywords: Keywords: Forced Oscillation Technique, volume-dependency, extended RIC model, nonlinear, parameter estimation, constant-phase model parameter constant-phase model Keywords:estimation, Forced Oscillation Technique, volume-dependency, extended RIC model, nonlinear, parameter estimation, constant-phase model parameter estimation, constant-phase model the 1. INTRODUCTION INTRODUCTION the measured measured value, value, and and the the alteration alteration of of the the values values in in presence presence 1. the measured value, and the alteration of the values in the presence 1. INTRODUCTION of lung pathologies. One major controversial issue is physof lung pathologies. One major controversial issue is the physthe measured value, and the alteration offrequency-dependency the values in the presence 1. INTRODUCTION of lung pathologies. One major controversial issue is physiological interpretation of the negative iological interpretation of the negative frequency-dependency Obstructive lung diseases are the conditions when patients of lung pathologies. One major controversial issue is the physObstructive lung diseases are the conditions when patients iological interpretation of the negative frequency-dependency (ω) at frequencies between 4-20 Hz. of the resistance Z frequencies between 4-20 Hz. The The the resistance ZRR (ω)ofat the Obstructive lungto areair when patients face difficulties difficulties to diseases exhale the the airthe outconditions of the the lungs. lungs. Causing by of face exhale out of Causing by iological interpretation negativethe frequency-dependency (ω) at frequencies between 4-20 Hz. The of the resistance Z eRIC, aRIC, and Mead model interpret change in Z (ω) by R R Obstructive lung diseases are the conditions when patients face difficulties to exhale the airasthma out ofand the chronic lungs. Causing by eRIC, narrowing of the small airways, obstructive aRIC, and Mead model interpret the change in Z (ω) by R at frequencies between 4-20 Hz. The of the resistance ZR (ω) narrowing of theto small airways, asthma and chronic obstructive eRIC, aRIC, and Mead model interpret the change in Z (ω) by the parallel pathway between the peripheral (bronchial) airways R face difficulties exhale the air out of the lungs. Causing by narrowing of the small airways, asthma and chronic obstructive pulmonary diseases have common symptoms such as shortness the parallel pathway between the peripheral (bronchial) airways aRIC, andThe Mead modelmodel interpret the change in ZRairways (ω) by pulmonaryof diseases have common symptoms such asobstructive shortness eRIC, the parallel pathway between the peripheral (bronchial) and the alveoli. DuBois explains this change by the narrowing the small airways, asthma and chronic and the alveoli. The DuBois model explains this change by the pulmonary diseases common symptomsSpirometry such as shortness of breath breath and and airwayhave hyper-responsiveness. Spirometry is the the the parallel pathway between the peripheral (bronchial) airways of airway hyper-responsiveness. is and the alveoli. The DuBois model explains this change by the parallel structure between tissue damping and gas compression. pulmonary diseases common such as shortness of breath non-invasive and airwayhave hyper-responsiveness. Spirometry is the parallel standard non-invasive method to symptoms assess airway airway obstruction, structureThe between tissue damping andthis gaschange compression. standard method to assess obstruction, the alveoli. DuBois model explains by the parallel structure between tissue damping and assume gas compression. The visco-elastic and constant-phase models the of breath is and airway hyper-responsiveness. Spirometry iswell the and standard non-invasive method cooperation to assess airway obstruction, however, limited on patients’ and hence, not The visco-elastic and constant-phase models assume the cause cause parallel structure between tissue damping and gas compression. however, is limited on patients’ cooperation and hence, not well visco-elastic and constant-phase modelsofassume the itself. cause of this change to be the mechanical property the tissue standard non-invasive method to assess airway obstruction, however, is limited preschool on patients’ cooperation and hence, not well The suited for infants, children, or patients with severe of this change to be the mechanical property of the tissue itself. Thethis visco-elastic and constant-phase models assume the itself. cause suited forisinfants, preschool children, or patients withnot severe of change to be the mechanical property of the tissue Moreover, the official statement of the American Thoracic Sohowever, limited on patients’ cooperation and hence, well Moreover, the official statement of the American Thoracic Sosuited for infants, preschool children, or patients with severe diseases Miller Miller et et al. al. (2005). (2005). diseases of this change to be the mechanical property of the tissue itself. Moreover, the official statement of the American Thoracic Society (ATS) and European Respiratory Society (ERS) (Beydon suited forMiller infants, preschool diseases et al. (2005). children, or patients with severe ciety (ATS) and European Respiratory Society (ERS) (Beydon Moreover, the official statement ofZ(the American Thoracic SoFirst introduced by DuBois et al. (1956), the oscillation techciety (ATS) and European Respiratory Society (ERS) (Beydon et al. (2007)) supports the use of jω) in assessing lung mediseases Miller et al. (2005). First introduced by DuBois et al. (1956), the oscillation tech- et al. (ATS) (2007))and supports the Respiratory use of Z( jω)Society in assessing lung meciety European (ERS) (Beydon First introduced by DuBois et al. (1956), the oscillation techniques is is based based on on the the application application of of alternating alternating pressure/volpressure/vol- et al. (2007)) supports theany usefurther of Z( jω) in assessing lung mechanics, but not information on choice niques chanics, but does does not give give any information on the the choice First introduced by the DuBois the oscillation tech- et al. (2007)) supports theexact usefurther ofphysiological Z( jω) in assessing lung meniques is based on application ofsuperimposed alternating pressure/volume at at high frequencies (4 -- et 30al. Hz)(1956), superimposed on subjects’ subjects’ chanics, but does not give any further information on the choice of model as well as any interpretation of ume high frequencies (4 30 Hz) on of model as well as any exact physiological interpretation of niques based on the application ofsuperimposed alternating pressure/volchanics, but does not give anyfor further information on the choice ume at is high frequencies (4 - the 30 Hz) on subjects’ spontaneous breathing and measurement of pressure and of model as well as any exact physiological interpretation of Z( jω). Hence, there is a need further investigation on Z( jω) spontaneous breathing and the measurement of pressure and Z( jω). Hence, there is a need for further investigation on Z( jω) ume at the highairway frequencies (4 The - the 30 resulted Hz) superimposed on subjects’ model as well as isany exact physiological interpretation of spontaneous breathing and measurement of pressure and of flow at opening. respiratory mechanical Z( jω). Hence, there a need for further investigation on Z( jω) to understand the nature of this variable. flow at the airway opening. The resulted respiratory mechanical to understand the nature of this variable. spontaneous breathing andof the measurement of pressure and Z( jω). Hence, there is a need for further investigation on Z( jω) flow at the airway opening. The resulted respiratory mechanical (ω)) and impedance Z( jω) consists a real part (resistance Z understand the nature of this variable. impedance Z( jω) opening. consists of a real part (resistance ZRR (ω)) and to According to the Poiseuille law for flow at the airway The resulted respiratory to understand of this variable. impedance Z(part jω) (reactance consists of aXreal part (resistance Zmechanical an imaginary Z (ω)). The change of Z (ω) and According to the the nature Poiseuille law for laminar laminar fluid fluid dynamics, dynamics, RR(ω)) an imaginary part (reactance Z (ω)). The change of Z (ω) and X R According to the Poiseuille law for laminar fluid dynamics, lung volume level can have a strong impact on the real part (ω)) and impedance Z( jω) consists of a real part (resistance Z anX (ω) imaginary partfrequencies (reactance provides ZX (ω)). The change of ZRRstatus (ω) and Z over the clinical relevant of lung volume level can have a strong impact on the real part of of tolevel the Poiseuille law for laminar fluid dynamics, Z over the frequencies provides clinical relevant status of According X (ω) lung volume can have a strong impact on the real part of Z( jω). In this work, we introduce a new measurement modality an imaginary part (reactance Z (ω)). The change of Z (ω) and X R Z overConventional the frequencies provides clinical relevant/ status of Z( the lungs. forced oscillation technique impulse jω). In this work, we introduce a new measurement modality X (ω) lung volume level can have a strong impact on the real part of the lungs. forced oscillation technique / status impulse jω). this work, weof introduce a new measurement which is an extension the FOT. The focuses Z overConventional the frequencies provides clinical relevant of Z( X (ω) which isIn extension the classic classic FOT. The method methodmodality focuses the lungs. Conventional oscillation technique / impulse oscillometry systems available from companies, e.g. oscillometry systems are are forced available from several several companies, e.g. Z( jω). Inan this work, weof introduce a new measurement modality which is an extension of the classic FOT. The method focuses on the volume-dependency of Z( jω) over the whole lung level the lungs. Conventional forced oscillation technique / impulse oscillometry systemsCosmed, are available from several companies, e.g. on Jaerger CareFusion, Resmond or Respironics. the volume-dependency ofclassic Z( jω)FOT. over The the whole lung level which is an extension of the method focuses Jaerger CareFusion, Cosmed, Resmond or Philips Philips Respironics. on the volume-dependency of Z( jω) over the whole lung level from residual volume (RV) to total lung capacity (TLC). Hence, oscillometry systems are available from several companies, e.g. Jaerger CareFusion, Cosmed, Resmond or Philips Respironics. from residual volume (RV) to total lung capacity (TLC). Hence, on theresidual volume-dependency of Z( jω) over the lung level To interpret the impedance models volume (RV)). lung capacity (TLC). Hence, Z( jω) jω) becomes Z( jω,V jω,V ).to Intotal this work, we whole demonstrate the Jaerger CareFusion, Cosmed, Resmondphysiologically, or Philips Respironics. To interpret the measured measured impedance physiologically, models from Z( becomes Z( In this work, we demonstrate the from residual volume (RV)).toIn total lung capacity (TLC). models Hence, To interpret the measured impedance physiologically, models potential of lung mechanics are applied Ngo et al. (2018). An overview Z( jω) becomes Z( jω,V this work, we demonstrate the use of this method to re-evaluate the existing potential use of this method to re-evaluate the existing models of lung mechanics are applied Ngo et al. (2018). An overview To interpret the measured impedance physiologically, models Z( jω) becomes Z( jω,V ). In this work, we demonstrate the of lung mechanics are applied NgobyetDiong al. (2018). An overview various lung models is given et al. (2007) and potential use of this method to re-evaluate the existing models in lung mechanics. Measurement data are obtained from two of various lung models is given byetDiong et al.An (2007) and in lung mechanics. Measurement data are the obtained from two of lung mechanics are applied Ngo al. (2018). overview potential use of this method to re-evaluate existing models of various lungCommon models is given are by Diong et al. (2007) and in Bates (2009). models the lung mechanics. Measurement data are obtained from two lung healthy subjects (male, old, BMI = and 32 Bates (2009). Common models are the resistance-inertanceresistance-inertancehealthy subjectsMeasurement (male, 29 29 year year old,are BMI = 26.23, 26.23, andtwo 32 of various lung models is given(eRIC), by Diong et al. (2007)(aRIC), and lung in lung mechanics. data obtained from Bates (2009). Common models are the augmented-RIC resistance-inertancecompliance (RIC), extended-RIC lung healthy old, BMI = 26.23, and 32 year old, BMIsubjects = 21.8). 21.8).(male, 29 year compliance (RIC), extended-RIC (eRIC), augmented-RIC (aRIC), year old, BMI = Bates (2009). Common models are the resistance-inertancelung old, healthy compliance (RIC), extended-RIC (eRIC), augmented-RIC (aRIC), DuBois, Mead, visco-elastic, and constant-phase models. Each BMIsubjects = 21.8).(male, 29 year old, BMI = 26.23, and 32 DuBois, Mead, visco-elastic, and (eRIC), constant-phase models. (aRIC), Each year compliance (RIC), extended-RIC augmented-RIC DuBois, Mead, visco-elastic, and constant-phase models. Each year old, BMI = 21.8). model has advantages and disadvantages regarding the identimodel has advantages and disadvantages regarding the identiDuBois, Mead, visco-elastic, andphysiological constant-phase models. Each model advantages and disadvantages regarding the identifiabilityhas of the parameters, parameters, the interpretation of fiability of the the physiological interpretation of model has and disadvantages regarding the identifiability of advantages the parameters, the physiological interpretation of fiability the physiological of Hosting by Elsevier Ltd. All rights reserved. 2405-8963of © the 2018,parameters, IFAC (International Federation ofinterpretation Automatic Control)
Copyright © 2018 IFAC 373 Copyright 2018 responsibility IFAC 373Control. Peer review©under of International Federation of Automatic Copyright © 2018 IFAC 373 10.1016/j.ifacol.2018.11.611 Copyright © 2018 IFAC 373
IFAC BMS 2018 374 São Paulo, Brazil, September 3-5, 2018
Chuong Ngo et al. / IFAC PapersOnLine 51-27 (2018) 373–377
2. PRINCIPLES OF THE VOLUME-DEPENDENT FOT
+
2.1 The measurement system
-
Figure 1 illustrates the schematic setup of the measurement system. It comprises an FOT device (Cough Assist E70, Philips Respironics, Murrysville, USA), a bacteria filter (MicroGardTM II Filter), a heated pneumotachograph (PT 36, Jaeger Carefusion, San Diego, USA), and a data acquisition system (Oostveen et al. (2003); MacLeod and Birch (2001); Ngo et al. (2017a,b)).
+
+
+
-
-
+
+
pedal pushed -
-
+
+
-
TLC
RV FOT active
FOT active
FOT active
slow inspiration
slow inspiration
slow inspiration
time (s)
Fig. 2. The measurement protocol. 2.2 Bandpass filtering A band pass-filtered Butterworth IIR filter of second order is applied to separate the oscillations from spontaneous breathing. The upper and lower frequencies correspond to the oscillatory frequency fos with a tolerant of ±5%. The frequency response of the filter is illustrated in Fig 3. Alternatively, a FIR bandpass filter of higher order can also be applied (for example order 284 for a sampling time of 1 kHz and the oscillation frequency at 7 Hz).
FOT device
sensors Computer
Magnitude (dB)
Bacteria filter Pneumotachograph Mouth . V
volume (L)
+ -
-
pedal in neutral positition
-
Fig. 1. The measurement system of the forced oscillation technique.
0
-20
• The maneuver of v-FOT is a ”slow-flow-vital-capacity (VC) maneuver”. First, subjects perform spontaneous breathing at the beginning of the measurement. After several breathes, subjects exhale to residual volume (RV) and inhale slowly from RV to total lung capacity (TLC). During this time period, the FOT device superimposes high frequency oscillation on the subjects’ breathing. • The subjects wear a nose-clip during the measurement. To compensate disturbances caused by the upper airway vibration, subjects support their cheek during the test. • Subjects are asked to repeat the maneuver three times. The FOT should be activated and deactivated by the subjects themselves via a foot pedal (Fig. 2). 374
flow (L/s)
The major extension of the volume-dependent FOT, compared to the classic FOT, is in the measurement protocol and the data analysis. They are given as follow:
pressure (cmH2O) volume (L)
• Originally designed for loosening, mobilizing, and clearing secretions in the bronchi, the Cough Assist E70 gener-40 ates high frequency oscillatory vibrations while applying 5 6 7 8 9 10 a positive pressure to the airways, then suddenly switches Frequency (Hz) to a negative pressure (Res (2012)). The device can be adjusted to produce oscillations from 1 to 20 Hz with Fig. 3. The frequency response of the Butterworth filter for an amplitude between 4 cmH2 O and 10 cmH2 O. In this fos = 7 Hz. experiment, the baseline and the oscillation amplitude are set to 4 cmH2 O. measured after FIR filter after Butterworth filter • Flow resistance of the bacteria filter MicroGard is smaller than 0.4 cmH2 O/L/s at an airway flow of 1 L/s. 5 4 • The pneumotachograph is integrated in a body plethys3 TM 2 mography (Masterscreen , Jaeger/Carefusion, San Diego, 1 0 USA ). It has a measurement range from 0 to ±20 L/s with 8 an accuracy of ±2% between 0.2 and 12 L/s. 4 0 • Data are sampled at 1 kHz and stored in the Master-4 -8 screen system. Offline data analysis is performed in Mat-12 lab 2016b. 4 3 2 1 0 -1 -2 0
1
2
3 time (s)
4
5
6
Fig. 4. Volume, flow, and pressure before and after bandpass filtering. During slow inspiration, subjects inhale a respiratory volume of about 4-6 liters in a time interval of about 6 seconds. The inspiration started at about t = 0.2 seconds, the FOT device is activated by the foot pedal after a short delay. Figure 4 displays exemplary volume, flow, and pressure for one v-FOT inhalation at fos = 7 Hz. While the FIR bandpass filter requires a settling
Chuong Ngo et al. / IFAC PapersOnLine 51-27 (2018) 373–377
time, the Butterworth filters the measured original signal right at that time point. The latter enables a better calculation of the reactance and resistance at the beginning of inspiration and minimizes errors caused by a delay of the FOT device. The filters were applied forward and backward over the data to achieve a zero phase shift. 2.3 Window cosine fitting As reported in our previous work Ngo et al. (2015), the window cosine fitting (WCF) provides the dynamic changes of the impedance over time. After bandpass-filtering, the passfiltered flow and pressure signals consist of one main frequency component at fos and can be written as:
The WCF computes the change of Z( jω,V ) over the whole lung volume regarding data obtained during the slow-flow vital capacity maneuver. Plotting Z( jω,V ) over the whole lung volume gives the novel impedance-volume (ZV) diagram, where lung volume forms the ordinate and ZR (ω,V ) and ZX (ω,V ) the abscissa. In contrast to classic FOT, ZV diagram combines frequency- and volume-dependency in one plot (Fig. 5).
X
Z (cmH2O/L/s)
1
2 3 4 V − Voff (L)
5
6
3 Hz 5 Hz 7 Hz 10 Hz 15 Hz 20 Hz
6 4 2 0 -2 0
2.4 Impedance-volume diagram
R
2
-4
Z(ω = ωos ) = mean(Z(t))|ω=ωos .
Z (cmH2O/L/s)
3
8
Z X (cmH2 O/L/s)
ZX (N/2)|ω=ωos = AP /AV˙ · sin(φP − φV˙ )|ω=ωos , where ωos = 2π fos is the oscillation frequency. By sliding the window along P(t) and V˙ (t), the complex impedance Z(t) could be derived as:
Volume (L)
4
0 0
ZR (N/2)|ω=ωos = AP /AV˙ · cos(φP − φV˙ )|ω=ωos
f1 f4 f2 f 5 f3
3 Hz 5 Hz 7 Hz 10 Hz 15 Hz 20 Hz
1
P(t) = AP · cos(ωt + φP ) V˙ (t) = AV˙ · cos(ωt + φV˙ ).
A and φ are signal amplitude and phase. A finite-length sliding window with N data samples of P(t) and V˙ (t) was regarded (Jiang and Zhang (2004)). Applying Least-Squares fitting, AP , AV˙ , φP and φV˙ can be computed for each N samples. The impedance value is set to the position in the middle of the window N/2:
375
5
Z R (cmH2 O/ L /s )
IFAC BMS 2018 São Paulo, Brazil, September 3-5, 2018
1
2 3 4 V − Voff (L)
5
6
Fig. 6. ZV diagram from a lung healthy subject. Voff is a offset volume related to the residual volume of the subject. than the frequency-dependency in ZR (ω,V ). ZR (ω,V ) is between 2.9 - 4.8 cmH2 O at residual volume and falls to approx 0.8 - 1 cmH2 O at total lung capacity. Frequencies dependencies of ZR (ω,V ) is observed to decrease by increasing lung volume. In contrast, the frequency-dependency is stronger than the volume-dependency in the imaginary part ZX (ω,V ), which remains constant over a larger range of lung volume. 3. MODELING AND PARAMETER FITTING IN VOLUME-DEPENDENT FOT
f1 f4 f2 f 5 f3 Volume (L)
Fig. 5. The principle of ZV-diagram in v-FOT. ZR ( f ,V ) and ZX ( f ,V ) are frequency- and volume-dependent. f1−5 are different oscillation frequencies. ω = 2π f . 2.5 Results Figure 6 presents two ZV diagrams measured from the first healthy subject. The volume-dependency is obviously stronger 375
To achieve detailed assessment on lung mechanics, mathematical lung models are applied. In this work, we focus on the extended RIC, the Mead and the constant phase models (Diong et al. (2007); Bates (2009); Ionescu et al. (2011)). The eRIC and the Mead models consider a parallel structure between the bronchial compliance and the alveoli to present the frequency dependency of ZR (ω,V ), while the constant-phase (cp) model assumes that this dependency is mainly caused by the tissue damping H and elastance G (Fig. 7). The impedance of the eRIC and constant phase model are given as follow:
IFAC BMS 2018 376 São Paulo, Brazil, September 3-5, 2018
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Rp Rc
(1)
Rc= 2.8269 Rp = 2.7923 I = -0.0016783 Cb= 0.018158 S = 503.7264
eRIC
I
6
R Rc
Z R (cmH2 O/ (L/s)
Cb Cl
I
(2) Cb
C cw
5 4 3
Ce
2 (3)
I
0
(G, H)
Fig. 7. The extended RIC model (1), the Mead model (2), and the constant-phase model. ωR2pC Rp + j ωI − ZeRIC ( jω) = R + 1 + (ωRpC)2 1 + (wRpC)2 G − jH , (1) Zcp ( jω) = Raw + jωIaw + ωα where α is the constant-phase parameter α = π2 arctan( H G ). Parameter estimation is performed with non-linear LeastSquares, which minimizes the sum the quadratic error S: n
n
i=1
i=1
S = ∑ ri2 = ∑ (yi − f (xi , θ ))2 = yy − f 22 ,
(2)
where r is the residual error between model f (xi , θ ) and data yi for the i-th system equation, y ∈ Rn , f ∈ Rn and θ ∈ Rm . θ is the parameter vector, n is the number of measurements, and m the number of independent parameters. Figure 8 shows the results by applying the Least-Squares estimation on the eRIC and the constant-phase two models for data obtained from the second healthy subject. While the constantphase model yields a smaller residual error than the eRIC, the estimated parameters of the constant-phase model is unphysiological (Raw < 0). In general, model behavior differed from measured data; they failed to describe the volume-dependency of the respiratory impedance. 3.1 Nonlinear model with volume-dependency According to the law of Hagen-Poisseuille, the peripheral resistance can be computed from the dynamic viscosity η, the bronchial length l, and radius r as follow: Kp 8ηl(t) , (3) ≈ Rp (t) = 4 πr (t) V (t) −Voff where V (t) is the lung volume, K p is a resistance constant, and Voff corresponds to a shift in volume. The real part of the eRIC model becomes: Rp (ωRpCb )2 + 1 Kp (V −VOff ) = Rc + (ωCb Kp )2 + (V −VOff )2
ZR (ω,V ) = Rc +
(4) (5) 376
1
2 3 Volume (L)
constant-phase
Z R (cmH2 O/ (L/s)
Rc
6
4
5
Raw = -6.8448 G = 14.4067 I = 0.0071766 H = 2.0414 S = 484.0497
5
4 3 2 0
1
2 3 Volume (L)
4
5
Fig. 8. Measured (solid lines) and fitted (dashed lines) impedance curves with the eRIC (top) and constant-phase (bottom) models. Data was measured on a healthy subject (25 years old, BMI = 22.09). The volume-dependency can not be estimated using these two models. Blue = 3 Hz, red = 5 Hz, green = 7 Hz, yellow = 10 Hz, violet = 15 Hz. Considering the volume-dependency of the peripheral resistance in the eRIC and the Mead model leads to two new nonlinear models, which are called the volume-dependent eRIC (veRIC) and volume-dependent Mead (v-Mead) models. Figure 9 displays the estimation results with the v-eRIC and v-Mead models. The volume-dependency in ZR (ω) can be approximated in these two models. The v-Mead model yields the best fit with smallest error (S=57.7). All parameters of the v-eRIC and v-Mead fitting are in physiological range. 4. DISCUSSION AND CONCLUSION In this paper, we propose a novel extension to the classic FOT by focusing on the volume-dependency of the respiratory impedance Z( jω). By introducing the slow-flow vital-capacity forced oscillation maneuvers, the impedance can be computed as a function of both frequencies and lung levels, from residual volume to total lung capacity. The windowed cosine fitting method allows a calculation of Z( jω) over a moving window of data, thus the relation between Z( jω) and lung volume can be obtained. The ZV diagram is introduced which may be useful for diagnostics of Z( jω,V ).
IFAC BMS 2018 São Paulo, Brazil, September 3-5, 2018
v-eRIC
7
Kp = 9.0122 Rc = 1.204 C = 0.0037333 Voff = -0.56673 I = 0.0061492 S = 164.6723
6 Z R (cmH2 O/ L/s)
Chuong Ngo et al. / IFAC PapersOnLine 51-27 (2018) 373–377
5 4 3 2 0
2 3 Volume (L)
4
5
v-Mead‘s
7
Z R [cmH2 O/ (l/ s)]
1
K p = 7.8222 R c = 1.2516 C b = 0.003304 Voff = -0.50978 I = 0.0087162 C alv = 0.093908 C cw = 0.098131 S = 57.6917
6 5 4 3 2 0
1
2 3 Volume (L)
4
5
Fig. 9. Measured (solid lines) and fitted (dashed lines) impedance curves with the v-eRIC (top) and v-Mead (bottom) models. Data was measured on the same subject (25 years old, BMI = 22.09). The volume-dependency can be estimated by these two models. The v-Mead model yield the best fit. All parameter are in physiological ranges. Blue = 3 Hz, red = 5 Hz, green = 7 Hz, yellow = 10 Hz, violet = 15 Hz. Least-Squares parameter fitting was performed for data measured from healthy subjects. Both extended-RIC and constantphase models failed to describe the volume-dependency of Z( jω). While the error is smaller in the constant-phase model, its estimated parameters are rather unphysiological. A nonlinear modeling approach regarding the volume-dependency of the peripheral resistance Rp was introduced. The v-eRIC and vMead models are suited to model the volume-dependency of the respiratory impedance. The v-Mead model has the smallest residual error, while all of its parameters are in physiologically meaningful range. Future works should contain the validation of the proposed model and measurement methods on larger data including pathological conditions. REFERENCES (2012). CouchAssist E70 user manual. Philips Respironics. 377
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Bates, J. (2009). Lung Mechanics: An Inverse Modeling Approach: An Inverse Modeling Approach. Cambridge University Press, Leiden. Beydon, N., Davis, S.D., Lombardi, E., Allen, J.L., Arets, H.G., Aurora, P., Bisgaard, H., Davis, G.M., Ducharme, F.M., Eigen, H., et al. (2007). An official american thoracic society/european respiratory society statement: pulmonary function testing in preschool children. American journal of respiratory and critical care medicine, 175(12), 1304–1345. Diong, B., Nazeran, H., Nava, P., and Goldman, M. (2007). Modeling human respiratory impedance. Engineering in Medicine and Biology Magazine, IEEE, 26(1), 48–55. DuBois, A., Brody, A., Lewis, D., and Burgess, B. (1956). Oscillation mechanics of lungs and chest in man. Journal of Applied Physiology, 8, 587–594. Ionescu, C.M., Machado, J.A.T., and Keyser, R.d. (2011). Modeling of the lung impedance using a fractional-order ladder network with constant phase elements. IEEE Transactions on Biomedical Circuits and Systems, 5(1), 83–89. doi:10. 1109/TBCAS.2010.2077636. Jiang, J. and Zhang, Y. (2004). A revisit to block and recursive least squares for parameter estimation. Computers & Electrical Engineering, 30(5), 403–416. doi:10.1016/j. compeleceng.2004.05.002. MacLeod, D. and Birch, M. (2001). Respiratory input impedance measurement: forced oscillation methods. Medical & Biological Engineering & Computing, 39, 505–515. Miller, M.R., Crapo, R., Hankinson, J., Brusasco, V., Burgos, F., Casaburi, R., Coates, A., Enright, P., van der Grinten, C.M., Gustafsson, P., et al. (2005). General considerations for lung function testing. European Respiratory Journal, 26(1), 153– 161. Ngo, C., Kube, A., Kr¨uger, K., Vollmer, T., Winter, S., Leonhardt, S., and Misgeld, B. (2015). Identication of respiratory parameters in frequency and time domain with forced oscillation technique. In The International Federation of Automatic Control (ed.), The 9th IFAC Symposium on Biological and Medical Systems, 177–182. Ngo, C., Dahlmanns, S., Vollmer, T., Misgeld, B., and Leonhardt, S. (2018). An object-oriented computational model to study cardiopulmonary hemodynamic interactions in humans. Computer methods and programs in biomedicine, 159, 167–183. Ngo, C., Kr¨uger, K., Vollmer, T., Winter, S., Penzlin, B., Lehmann, S., Leonhardt, S., and Misgeld, B. (2017a). Effects of the nasal passage on forced oscillation lung function measurements. Biomedical Engineering/Biomedizinische Technik. Ngo, C., Spagnesi, S., Munoz, C., Lehmann, S., Vollmer, T., Misgeld, B., and Leonhardt, S. (2017b). Assessing regional lung mechanics by combining electrical impedance tomography and forced oscillation technique. Biomedical Engineering/Biomedizinische Technik. Oostveen, E., MacLeod, D., Lorino, H., Farre, R., Hantos, Z., Desager, K., and Marchal, F. (2003). The forced oscillation technique in clinical practice: methodology, recommendations and future developments. European Respiratory Journal, 22(6), 1026–1041. doi:10.1183/09031936.03.00089403.
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IFAC PapersOnLine 51-27 (2018) 373–377
The volume-dependent volume-dependent Forced Forced Oscillation Oscillation The The volume-dependent Forced Oscillation Technique The volume-dependent Forced Oscillation Technique Technique Technique ∗∗ Klaus Tenbrock ∗∗ ∗∗ Chuong Ngo ∗∗ Falk Dippel ∗∗ Sylvia Lehmann ∗∗
∗ Sylvia Lehmann ∗∗ Klaus Tenbrock ∗∗ Chuong Ngo ∗∗ Falk Dippel ∗ Sylvia Lehmann ∗∗ Klaus Tenbrock ∗∗ ∗∗∗ Berno ∗ Steffen ∗ Chuong Ngo ∗Vollmer Falk Dippel Thomas Misgeld Leonhardt ∗∗∗ ∗ Steffen ∗ ∗ Sylvia ∗∗ Klaus ∗∗ Thomas Vollmer Berno Misgeld Leonhardt ∗∗∗ ∗ ∗ Chuong Ngo Falk Dippel Lehmann Tenbrock Thomas Vollmer ∗∗∗ Berno Misgeld ∗ Steffen Leonhardt ∗ Thomas Vollmer Berno Misgeld Steffen Leonhardt ∗ Chair of Information ∗ Chair of Medical Information Technology, Technology, Helmholz Helmholz Institut Institut for for Biomedical Biomedical ∗ Chair of Medical Medical Information Technology, Helmholz Institut for Biomedical Engineering, RWTH Aachen University Engineering, RWTH Aachen University ∗ ∗∗Chair of Medical Information Technology, Helmholz Institut for Biomedical Engineering, RWTH Aachen University of Pulmonology, University Hospital ∗∗ Department of Pediatric Pediatric Pulmonology, University Hospital RWTH RWTH Aachen, Aachen, ∗∗ Department Engineering, RWTH Aachen University Department of Pediatric Pulmonology, University Hospital RWTH Aachen, Germany ∗∗∗∗∗ Germany Department of Pediatric Pulmonology, University Hospital RWTH Aachen, Germany Philips Technologie GmbH Innovative Technologies, Aachen, Germany ∗∗∗ Philips GmbH Innovative Aachen, Germany ∗∗∗ Philips Technologie Germany Technologies, Technologie GmbH Innovative Technologies, Aachen, Germany ∗∗∗ Philips Technologie GmbH Innovative Technologies, Aachen, Germany Abstract: This Abstract: This paper paper describes describes aa novel novel extension extension of of the the Forced Forced Oscillation Oscillation Technique Technique (FOT), (FOT), namely namely the the Abstract: This paper describes a novelTechnique extension of the Forced Oscillation Technique (FOT), namely the volume-dependent Forced Oscillation (v-FOT). This extension is based on the measurement volume-dependent Forced Oscillation Technique (v-FOT). This extension is based on the measurement Abstract: This paper describes a novel extension the Forced Oscillation Technique namely the volume-dependent Forced Oscillation Technique (v-FOT). extension is based on(FOT), the measurement of the the respiratory respiratory impedance over the whole whole lung of volume. AThis new measurement protocol was introduced: of impedance over the lung volume. A new measurement protocol was introduced: volume-dependent Forced Oscillation Technique (v-FOT). This extension is based on the measurement of the respiratory impedance the whole lung to volume. A new measurement was are introduced: subjects breathe slowly slowly fromover residual volume to total lung lung capacity, while protocol oscillations are applied subjects breathe from residual volume total capacity, while oscillations applied of the respiratory impedance the whole lung volume. Aby new measurement protocol was introduced: subjects breathe The slowly fromover residual volume to total lung capacity, while oscillations are applied simultaneously. respiratory impedance is computed means of the windowed cosine fitting simultaneously. The respiratory impedance is computed by means of the windowed cosine fitting subjects breathe slowly from residual volume to total lung oscillations are applied simultaneously. The respiratory impedance isfrequencycomputed by capacity, means ofwhile the windowed cosine fitting method. The respiratory impedance becomes and volume-dependent Z( jω,V ). The novel method. The respiratory impedance becomes frequencyand volume-dependent Z( jω,V ). The novel simultaneously. The(ZV) respiratory impedance isfrequencycomputed by volume-dependent means of the windowed fitting method. The respiratory impedance becomes and Z( jω,Vcosine ). The novel impedance-volume diagram was introduced for diagnostic purposes. Least-squares parameter impedance-volume (ZV) impedance diagram was introduced for diagnostic purposes. Least-squares parameter method. The becomes frequencyand volume-dependent Z( jω,V ).both The novel impedance-volume (ZV) diagram was introduced purposes. Least-squares parameter estimation wasrespiratory performed for the the extended-RIC extended-RIC andfor the diagnostic constant phase models. However, models estimation was performed for and the constant phase models. However, both models impedance-volume (ZV) diagram was introduced for diagnostic purposes. Least-squares parameter estimation was performed for the extended-RIC and the constant phase models. However, both models failed in presenting the volume-dependency of Z. We proposed two new models: the volume-dependent failed in presenting the volume-dependency of Z.and We proposed two new models. models: However, the volume-dependent estimation wasand performed for the extended-RIC phase both models failed in presenting thevolume-dependent volume-dependency of Z. Wethe proposed two models: the volume-dependent extended RIC the Mead model forconstant a better better fitnew of the the data. The The extended RIC and the volume-dependent Mead model for a fit of data. volume-dependent failed in presenting the volume-dependency of Z. We proposed two new models: the volume-dependent extended RICyields and the Mead Mead model model thevolume-dependent smallest estimation estimation error.model for a better fit of the data. The volume-dependent Mead the smallest error. extended RICyields and the Mead Mead model yields thevolume-dependent smallest estimation error.model for a better fit of the data. The volume-dependent © 2018, IFACyields (International Federation of Automatic Mead model the smallest estimation error. Control) Hosting by Elsevier Ltd. All rights reserved. Keywords: Forced Forced Oscillation Oscillation Technique, Technique, volume-dependency, volume-dependency, extended extended RIC RIC model, model, nonlinear, nonlinear, Keywords: Keywords: Forced Oscillation Technique, volume-dependency, extended RIC model, nonlinear, parameter estimation, constant-phase model parameter constant-phase model Keywords:estimation, Forced Oscillation Technique, volume-dependency, extended RIC model, nonlinear, parameter estimation, constant-phase model parameter estimation, constant-phase model the 1. INTRODUCTION INTRODUCTION the measured measured value, value, and and the the alteration alteration of of the the values values in in presence presence 1. the measured value, and the alteration of the values in the presence 1. INTRODUCTION of lung pathologies. One major controversial issue is physof lung pathologies. One major controversial issue is the physthe measured value, and the alteration offrequency-dependency the values in the presence 1. INTRODUCTION of lung pathologies. One major controversial issue is physiological interpretation of the negative iological interpretation of the negative frequency-dependency Obstructive lung diseases are the conditions when patients of lung pathologies. One major controversial issue is the physObstructive lung diseases are the conditions when patients iological interpretation of the negative frequency-dependency (ω) at frequencies between 4-20 Hz. of the resistance Z frequencies between 4-20 Hz. The The the resistance ZRR (ω)ofat the Obstructive lungto areair when patients face difficulties difficulties to diseases exhale the the airthe outconditions of the the lungs. lungs. Causing by of face exhale out of Causing by iological interpretation negativethe frequency-dependency (ω) at frequencies between 4-20 Hz. The of the resistance Z eRIC, aRIC, and Mead model interpret change in Z (ω) by R R Obstructive lung diseases are the conditions when patients face difficulties to exhale the airasthma out ofand the chronic lungs. Causing by eRIC, narrowing of the small airways, obstructive aRIC, and Mead model interpret the change in Z (ω) by R at frequencies between 4-20 Hz. The of the resistance ZR (ω) narrowing of theto small airways, asthma and chronic obstructive eRIC, aRIC, and Mead model interpret the change in Z (ω) by the parallel pathway between the peripheral (bronchial) airways R face difficulties exhale the air out of the lungs. Causing by narrowing of the small airways, asthma and chronic obstructive pulmonary diseases have common symptoms such as shortness the parallel pathway between the peripheral (bronchial) airways aRIC, andThe Mead modelmodel interpret the change in ZRairways (ω) by pulmonaryof diseases have common symptoms such asobstructive shortness eRIC, the parallel pathway between the peripheral (bronchial) and the alveoli. DuBois explains this change by the narrowing the small airways, asthma and chronic and the alveoli. The DuBois model explains this change by the pulmonary diseases common symptomsSpirometry such as shortness of breath breath and and airwayhave hyper-responsiveness. Spirometry is the the the parallel pathway between the peripheral (bronchial) airways of airway hyper-responsiveness. is and the alveoli. The DuBois model explains this change by the parallel structure between tissue damping and gas compression. pulmonary diseases common such as shortness of breath non-invasive and airwayhave hyper-responsiveness. Spirometry is the parallel standard non-invasive method to symptoms assess airway airway obstruction, structureThe between tissue damping andthis gaschange compression. standard method to assess obstruction, the alveoli. DuBois model explains by the parallel structure between tissue damping and assume gas compression. The visco-elastic and constant-phase models the of breath is and airway hyper-responsiveness. Spirometry iswell the and standard non-invasive method cooperation to assess airway obstruction, however, limited on patients’ and hence, not The visco-elastic and constant-phase models assume the cause cause parallel structure between tissue damping and gas compression. however, is limited on patients’ cooperation and hence, not well visco-elastic and constant-phase modelsofassume the itself. cause of this change to be the mechanical property the tissue standard non-invasive method to assess airway obstruction, however, is limited preschool on patients’ cooperation and hence, not well The suited for infants, children, or patients with severe of this change to be the mechanical property of the tissue itself. Thethis visco-elastic and constant-phase models assume the itself. cause suited forisinfants, preschool children, or patients withnot severe of change to be the mechanical property of the tissue Moreover, the official statement of the American Thoracic Sohowever, limited on patients’ cooperation and hence, well Moreover, the official statement of the American Thoracic Sosuited for infants, preschool children, or patients with severe diseases Miller Miller et et al. al. (2005). (2005). diseases of this change to be the mechanical property of the tissue itself. Moreover, the official statement of the American Thoracic Society (ATS) and European Respiratory Society (ERS) (Beydon suited forMiller infants, preschool diseases et al. (2005). children, or patients with severe ciety (ATS) and European Respiratory Society (ERS) (Beydon Moreover, the official statement ofZ(the American Thoracic SoFirst introduced by DuBois et al. (1956), the oscillation techciety (ATS) and European Respiratory Society (ERS) (Beydon et al. (2007)) supports the use of jω) in assessing lung mediseases Miller et al. (2005). First introduced by DuBois et al. (1956), the oscillation tech- et al. (ATS) (2007))and supports the Respiratory use of Z( jω)Society in assessing lung meciety European (ERS) (Beydon First introduced by DuBois et al. (1956), the oscillation techniques is is based based on on the the application application of of alternating alternating pressure/volpressure/vol- et al. (2007)) supports theany usefurther of Z( jω) in assessing lung mechanics, but not information on choice niques chanics, but does does not give give any information on the the choice First introduced by the DuBois the oscillation tech- et al. (2007)) supports theexact usefurther ofphysiological Z( jω) in assessing lung meniques is based on application ofsuperimposed alternating pressure/volume at at high frequencies (4 -- et 30al. Hz)(1956), superimposed on subjects’ subjects’ chanics, but does not give any further information on the choice of model as well as any interpretation of ume high frequencies (4 30 Hz) on of model as well as any exact physiological interpretation of niques based on the application ofsuperimposed alternating pressure/volchanics, but does not give anyfor further information on the choice ume at is high frequencies (4 - the 30 Hz) on subjects’ spontaneous breathing and measurement of pressure and of model as well as any exact physiological interpretation of Z( jω). Hence, there is a need further investigation on Z( jω) spontaneous breathing and the measurement of pressure and Z( jω). Hence, there is a need for further investigation on Z( jω) ume at the highairway frequencies (4 The - the 30 resulted Hz) superimposed on subjects’ model as well as isany exact physiological interpretation of spontaneous breathing and measurement of pressure and of flow at opening. respiratory mechanical Z( jω). Hence, there a need for further investigation on Z( jω) to understand the nature of this variable. flow at the airway opening. The resulted respiratory mechanical to understand the nature of this variable. spontaneous breathing andof the measurement of pressure and Z( jω). Hence, there is a need for further investigation on Z( jω) flow at the airway opening. The resulted respiratory mechanical (ω)) and impedance Z( jω) consists a real part (resistance Z understand the nature of this variable. impedance Z( jω) opening. consists of a real part (resistance ZRR (ω)) and to According to the Poiseuille law for flow at the airway The resulted respiratory to understand of this variable. impedance Z(part jω) (reactance consists of aXreal part (resistance Zmechanical an imaginary Z (ω)). The change of Z (ω) and According to the the nature Poiseuille law for laminar laminar fluid fluid dynamics, dynamics, RR(ω)) an imaginary part (reactance Z (ω)). The change of Z (ω) and X R According to the Poiseuille law for laminar fluid dynamics, lung volume level can have a strong impact on the real part (ω)) and impedance Z( jω) consists of a real part (resistance Z anX (ω) imaginary partfrequencies (reactance provides ZX (ω)). The change of ZRRstatus (ω) and Z over the clinical relevant of lung volume level can have a strong impact on the real part of of tolevel the Poiseuille law for laminar fluid dynamics, Z over the frequencies provides clinical relevant status of According X (ω) lung volume can have a strong impact on the real part of Z( jω). In this work, we introduce a new measurement modality an imaginary part (reactance Z (ω)). The change of Z (ω) and X R Z overConventional the frequencies provides clinical relevant/ status of Z( the lungs. forced oscillation technique impulse jω). In this work, we introduce a new measurement modality X (ω) lung volume level can have a strong impact on the real part of the lungs. forced oscillation technique / status impulse jω). this work, weof introduce a new measurement which is an extension the FOT. The focuses Z overConventional the frequencies provides clinical relevant of Z( X (ω) which isIn extension the classic classic FOT. The method methodmodality focuses the lungs. Conventional oscillation technique / impulse oscillometry systems available from companies, e.g. oscillometry systems are are forced available from several several companies, e.g. Z( jω). Inan this work, weof introduce a new measurement modality which is an extension of the classic FOT. The method focuses on the volume-dependency of Z( jω) over the whole lung level the lungs. Conventional forced oscillation technique / impulse oscillometry systemsCosmed, are available from several companies, e.g. on Jaerger CareFusion, Resmond or Respironics. the volume-dependency ofclassic Z( jω)FOT. over The the whole lung level which is an extension of the method focuses Jaerger CareFusion, Cosmed, Resmond or Philips Philips Respironics. on the volume-dependency of Z( jω) over the whole lung level from residual volume (RV) to total lung capacity (TLC). Hence, oscillometry systems are available from several companies, e.g. Jaerger CareFusion, Cosmed, Resmond or Philips Respironics. from residual volume (RV) to total lung capacity (TLC). Hence, on theresidual volume-dependency of Z( jω) over the lung level To interpret the impedance models volume (RV)). lung capacity (TLC). Hence, Z( jω) jω) becomes Z( jω,V jω,V ).to Intotal this work, we whole demonstrate the Jaerger CareFusion, Cosmed, Resmondphysiologically, or Philips Respironics. To interpret the measured measured impedance physiologically, models from Z( becomes Z( In this work, we demonstrate the from residual volume (RV)).toIn total lung capacity (TLC). models Hence, To interpret the measured impedance physiologically, models potential of lung mechanics are applied Ngo et al. (2018). An overview Z( jω) becomes Z( jω,V this work, we demonstrate the use of this method to re-evaluate the existing potential use of this method to re-evaluate the existing models of lung mechanics are applied Ngo et al. (2018). An overview To interpret the measured impedance physiologically, models Z( jω) becomes Z( jω,V ). In this work, we demonstrate the of lung mechanics are applied NgobyetDiong al. (2018). An overview various lung models is given et al. (2007) and potential use of this method to re-evaluate the existing models in lung mechanics. Measurement data are obtained from two of various lung models is given byetDiong et al.An (2007) and in lung mechanics. Measurement data are the obtained from two of lung mechanics are applied Ngo al. (2018). overview potential use of this method to re-evaluate existing models of various lungCommon models is given are by Diong et al. (2007) and in Bates (2009). models the lung mechanics. Measurement data are obtained from two lung healthy subjects (male, old, BMI = and 32 Bates (2009). Common models are the resistance-inertanceresistance-inertancehealthy subjectsMeasurement (male, 29 29 year year old,are BMI = 26.23, 26.23, andtwo 32 of various lung models is given(eRIC), by Diong et al. (2007)(aRIC), and lung in lung mechanics. data obtained from Bates (2009). Common models are the augmented-RIC resistance-inertancecompliance (RIC), extended-RIC lung healthy old, BMI = 26.23, and 32 year old, BMIsubjects = 21.8). 21.8).(male, 29 year compliance (RIC), extended-RIC (eRIC), augmented-RIC (aRIC), year old, BMI = Bates (2009). Common models are the resistance-inertancelung old, healthy compliance (RIC), extended-RIC (eRIC), augmented-RIC (aRIC), DuBois, Mead, visco-elastic, and constant-phase models. Each BMIsubjects = 21.8).(male, 29 year old, BMI = 26.23, and 32 DuBois, Mead, visco-elastic, and (eRIC), constant-phase models. (aRIC), Each year compliance (RIC), extended-RIC augmented-RIC DuBois, Mead, visco-elastic, and constant-phase models. Each year old, BMI = 21.8). model has advantages and disadvantages regarding the identimodel has advantages and disadvantages regarding the identiDuBois, Mead, visco-elastic, andphysiological constant-phase models. Each model advantages and disadvantages regarding the identifiabilityhas of the parameters, parameters, the interpretation of fiability of the the physiological interpretation of model has and disadvantages regarding the identifiability of advantages the parameters, the physiological interpretation of fiability the physiological of Hosting by Elsevier Ltd. All rights reserved. 2405-8963of © the 2018,parameters, IFAC (International Federation ofinterpretation Automatic Control)
Copyright © 2018 IFAC 373 Copyright 2018 responsibility IFAC 373Control. Peer review©under of International Federation of Automatic Copyright © 2018 IFAC 373 10.1016/j.ifacol.2018.11.611 Copyright © 2018 IFAC 373
IFAC BMS 2018 374 São Paulo, Brazil, September 3-5, 2018
Chuong Ngo et al. / IFAC PapersOnLine 51-27 (2018) 373–377
2. PRINCIPLES OF THE VOLUME-DEPENDENT FOT
+
2.1 The measurement system
-
Figure 1 illustrates the schematic setup of the measurement system. It comprises an FOT device (Cough Assist E70, Philips Respironics, Murrysville, USA), a bacteria filter (MicroGardTM II Filter), a heated pneumotachograph (PT 36, Jaeger Carefusion, San Diego, USA), and a data acquisition system (Oostveen et al. (2003); MacLeod and Birch (2001); Ngo et al. (2017a,b)).
+
+
+
-
-
+
+
pedal pushed -
-
+
+
-
TLC
RV FOT active
FOT active
FOT active
slow inspiration
slow inspiration
slow inspiration
time (s)
Fig. 2. The measurement protocol. 2.2 Bandpass filtering A band pass-filtered Butterworth IIR filter of second order is applied to separate the oscillations from spontaneous breathing. The upper and lower frequencies correspond to the oscillatory frequency fos with a tolerant of ±5%. The frequency response of the filter is illustrated in Fig 3. Alternatively, a FIR bandpass filter of higher order can also be applied (for example order 284 for a sampling time of 1 kHz and the oscillation frequency at 7 Hz).
FOT device
sensors Computer
Magnitude (dB)
Bacteria filter Pneumotachograph Mouth . V
volume (L)
+ -
-
pedal in neutral positition
-
Fig. 1. The measurement system of the forced oscillation technique.
0
-20
• The maneuver of v-FOT is a ”slow-flow-vital-capacity (VC) maneuver”. First, subjects perform spontaneous breathing at the beginning of the measurement. After several breathes, subjects exhale to residual volume (RV) and inhale slowly from RV to total lung capacity (TLC). During this time period, the FOT device superimposes high frequency oscillation on the subjects’ breathing. • The subjects wear a nose-clip during the measurement. To compensate disturbances caused by the upper airway vibration, subjects support their cheek during the test. • Subjects are asked to repeat the maneuver three times. The FOT should be activated and deactivated by the subjects themselves via a foot pedal (Fig. 2). 374
flow (L/s)
The major extension of the volume-dependent FOT, compared to the classic FOT, is in the measurement protocol and the data analysis. They are given as follow:
pressure (cmH2O) volume (L)
• Originally designed for loosening, mobilizing, and clearing secretions in the bronchi, the Cough Assist E70 gener-40 ates high frequency oscillatory vibrations while applying 5 6 7 8 9 10 a positive pressure to the airways, then suddenly switches Frequency (Hz) to a negative pressure (Res (2012)). The device can be adjusted to produce oscillations from 1 to 20 Hz with Fig. 3. The frequency response of the Butterworth filter for an amplitude between 4 cmH2 O and 10 cmH2 O. In this fos = 7 Hz. experiment, the baseline and the oscillation amplitude are set to 4 cmH2 O. measured after FIR filter after Butterworth filter • Flow resistance of the bacteria filter MicroGard is smaller than 0.4 cmH2 O/L/s at an airway flow of 1 L/s. 5 4 • The pneumotachograph is integrated in a body plethys3 TM 2 mography (Masterscreen , Jaeger/Carefusion, San Diego, 1 0 USA ). It has a measurement range from 0 to ±20 L/s with 8 an accuracy of ±2% between 0.2 and 12 L/s. 4 0 • Data are sampled at 1 kHz and stored in the Master-4 -8 screen system. Offline data analysis is performed in Mat-12 lab 2016b. 4 3 2 1 0 -1 -2 0
1
2
3 time (s)
4
5
6
Fig. 4. Volume, flow, and pressure before and after bandpass filtering. During slow inspiration, subjects inhale a respiratory volume of about 4-6 liters in a time interval of about 6 seconds. The inspiration started at about t = 0.2 seconds, the FOT device is activated by the foot pedal after a short delay. Figure 4 displays exemplary volume, flow, and pressure for one v-FOT inhalation at fos = 7 Hz. While the FIR bandpass filter requires a settling
Chuong Ngo et al. / IFAC PapersOnLine 51-27 (2018) 373–377
time, the Butterworth filters the measured original signal right at that time point. The latter enables a better calculation of the reactance and resistance at the beginning of inspiration and minimizes errors caused by a delay of the FOT device. The filters were applied forward and backward over the data to achieve a zero phase shift. 2.3 Window cosine fitting As reported in our previous work Ngo et al. (2015), the window cosine fitting (WCF) provides the dynamic changes of the impedance over time. After bandpass-filtering, the passfiltered flow and pressure signals consist of one main frequency component at fos and can be written as:
The WCF computes the change of Z( jω,V ) over the whole lung volume regarding data obtained during the slow-flow vital capacity maneuver. Plotting Z( jω,V ) over the whole lung volume gives the novel impedance-volume (ZV) diagram, where lung volume forms the ordinate and ZR (ω,V ) and ZX (ω,V ) the abscissa. In contrast to classic FOT, ZV diagram combines frequency- and volume-dependency in one plot (Fig. 5).
X
Z (cmH2O/L/s)
1
2 3 4 V − Voff (L)
5
6
3 Hz 5 Hz 7 Hz 10 Hz 15 Hz 20 Hz
6 4 2 0 -2 0
2.4 Impedance-volume diagram
R
2
-4
Z(ω = ωos ) = mean(Z(t))|ω=ωos .
Z (cmH2O/L/s)
3
8
Z X (cmH2 O/L/s)
ZX (N/2)|ω=ωos = AP /AV˙ · sin(φP − φV˙ )|ω=ωos , where ωos = 2π fos is the oscillation frequency. By sliding the window along P(t) and V˙ (t), the complex impedance Z(t) could be derived as:
Volume (L)
4
0 0
ZR (N/2)|ω=ωos = AP /AV˙ · cos(φP − φV˙ )|ω=ωos
f1 f4 f2 f 5 f3
3 Hz 5 Hz 7 Hz 10 Hz 15 Hz 20 Hz
1
P(t) = AP · cos(ωt + φP ) V˙ (t) = AV˙ · cos(ωt + φV˙ ).
A and φ are signal amplitude and phase. A finite-length sliding window with N data samples of P(t) and V˙ (t) was regarded (Jiang and Zhang (2004)). Applying Least-Squares fitting, AP , AV˙ , φP and φV˙ can be computed for each N samples. The impedance value is set to the position in the middle of the window N/2:
375
5
Z R (cmH2 O/ L /s )
IFAC BMS 2018 São Paulo, Brazil, September 3-5, 2018
1
2 3 4 V − Voff (L)
5
6
Fig. 6. ZV diagram from a lung healthy subject. Voff is a offset volume related to the residual volume of the subject. than the frequency-dependency in ZR (ω,V ). ZR (ω,V ) is between 2.9 - 4.8 cmH2 O at residual volume and falls to approx 0.8 - 1 cmH2 O at total lung capacity. Frequencies dependencies of ZR (ω,V ) is observed to decrease by increasing lung volume. In contrast, the frequency-dependency is stronger than the volume-dependency in the imaginary part ZX (ω,V ), which remains constant over a larger range of lung volume. 3. MODELING AND PARAMETER FITTING IN VOLUME-DEPENDENT FOT
f1 f4 f2 f 5 f3 Volume (L)
Fig. 5. The principle of ZV-diagram in v-FOT. ZR ( f ,V ) and ZX ( f ,V ) are frequency- and volume-dependent. f1−5 are different oscillation frequencies. ω = 2π f . 2.5 Results Figure 6 presents two ZV diagrams measured from the first healthy subject. The volume-dependency is obviously stronger 375
To achieve detailed assessment on lung mechanics, mathematical lung models are applied. In this work, we focus on the extended RIC, the Mead and the constant phase models (Diong et al. (2007); Bates (2009); Ionescu et al. (2011)). The eRIC and the Mead models consider a parallel structure between the bronchial compliance and the alveoli to present the frequency dependency of ZR (ω,V ), while the constant-phase (cp) model assumes that this dependency is mainly caused by the tissue damping H and elastance G (Fig. 7). The impedance of the eRIC and constant phase model are given as follow:
IFAC BMS 2018 376 São Paulo, Brazil, September 3-5, 2018
Chuong Ngo et al. / IFAC PapersOnLine 51-27 (2018) 373–377
Rp Rc
(1)
Rc= 2.8269 Rp = 2.7923 I = -0.0016783 Cb= 0.018158 S = 503.7264
eRIC
I
6
R Rc
Z R (cmH2 O/ (L/s)
Cb Cl
I
(2) Cb
C cw
5 4 3
Ce
2 (3)
I
0
(G, H)
Fig. 7. The extended RIC model (1), the Mead model (2), and the constant-phase model. ωR2pC Rp + j ωI − ZeRIC ( jω) = R + 1 + (ωRpC)2 1 + (wRpC)2 G − jH , (1) Zcp ( jω) = Raw + jωIaw + ωα where α is the constant-phase parameter α = π2 arctan( H G ). Parameter estimation is performed with non-linear LeastSquares, which minimizes the sum the quadratic error S: n
n
i=1
i=1
S = ∑ ri2 = ∑ (yi − f (xi , θ ))2 = yy − f 22 ,
(2)
where r is the residual error between model f (xi , θ ) and data yi for the i-th system equation, y ∈ Rn , f ∈ Rn and θ ∈ Rm . θ is the parameter vector, n is the number of measurements, and m the number of independent parameters. Figure 8 shows the results by applying the Least-Squares estimation on the eRIC and the constant-phase two models for data obtained from the second healthy subject. While the constantphase model yields a smaller residual error than the eRIC, the estimated parameters of the constant-phase model is unphysiological (Raw < 0). In general, model behavior differed from measured data; they failed to describe the volume-dependency of the respiratory impedance. 3.1 Nonlinear model with volume-dependency According to the law of Hagen-Poisseuille, the peripheral resistance can be computed from the dynamic viscosity η, the bronchial length l, and radius r as follow: Kp 8ηl(t) , (3) ≈ Rp (t) = 4 πr (t) V (t) −Voff where V (t) is the lung volume, K p is a resistance constant, and Voff corresponds to a shift in volume. The real part of the eRIC model becomes: Rp (ωRpCb )2 + 1 Kp (V −VOff ) = Rc + (ωCb Kp )2 + (V −VOff )2
ZR (ω,V ) = Rc +
(4) (5) 376
1
2 3 Volume (L)
constant-phase
Z R (cmH2 O/ (L/s)
Rc
6
4
5
Raw = -6.8448 G = 14.4067 I = 0.0071766 H = 2.0414 S = 484.0497
5
4 3 2 0
1
2 3 Volume (L)
4
5
Fig. 8. Measured (solid lines) and fitted (dashed lines) impedance curves with the eRIC (top) and constant-phase (bottom) models. Data was measured on a healthy subject (25 years old, BMI = 22.09). The volume-dependency can not be estimated using these two models. Blue = 3 Hz, red = 5 Hz, green = 7 Hz, yellow = 10 Hz, violet = 15 Hz. Considering the volume-dependency of the peripheral resistance in the eRIC and the Mead model leads to two new nonlinear models, which are called the volume-dependent eRIC (veRIC) and volume-dependent Mead (v-Mead) models. Figure 9 displays the estimation results with the v-eRIC and v-Mead models. The volume-dependency in ZR (ω) can be approximated in these two models. The v-Mead model yields the best fit with smallest error (S=57.7). All parameters of the v-eRIC and v-Mead fitting are in physiological range. 4. DISCUSSION AND CONCLUSION In this paper, we propose a novel extension to the classic FOT by focusing on the volume-dependency of the respiratory impedance Z( jω). By introducing the slow-flow vital-capacity forced oscillation maneuvers, the impedance can be computed as a function of both frequencies and lung levels, from residual volume to total lung capacity. The windowed cosine fitting method allows a calculation of Z( jω) over a moving window of data, thus the relation between Z( jω) and lung volume can be obtained. The ZV diagram is introduced which may be useful for diagnostics of Z( jω,V ).
IFAC BMS 2018 São Paulo, Brazil, September 3-5, 2018
v-eRIC
7
Kp = 9.0122 Rc = 1.204 C = 0.0037333 Voff = -0.56673 I = 0.0061492 S = 164.6723
6 Z R (cmH2 O/ L/s)
Chuong Ngo et al. / IFAC PapersOnLine 51-27 (2018) 373–377
5 4 3 2 0
2 3 Volume (L)
4
5
v-Mead‘s
7
Z R [cmH2 O/ (l/ s)]
1
K p = 7.8222 R c = 1.2516 C b = 0.003304 Voff = -0.50978 I = 0.0087162 C alv = 0.093908 C cw = 0.098131 S = 57.6917
6 5 4 3 2 0
1
2 3 Volume (L)
4
5
Fig. 9. Measured (solid lines) and fitted (dashed lines) impedance curves with the v-eRIC (top) and v-Mead (bottom) models. Data was measured on the same subject (25 years old, BMI = 22.09). The volume-dependency can be estimated by these two models. The v-Mead model yield the best fit. All parameter are in physiological ranges. Blue = 3 Hz, red = 5 Hz, green = 7 Hz, yellow = 10 Hz, violet = 15 Hz. Least-Squares parameter fitting was performed for data measured from healthy subjects. Both extended-RIC and constantphase models failed to describe the volume-dependency of Z( jω). While the error is smaller in the constant-phase model, its estimated parameters are rather unphysiological. A nonlinear modeling approach regarding the volume-dependency of the peripheral resistance Rp was introduced. The v-eRIC and vMead models are suited to model the volume-dependency of the respiratory impedance. The v-Mead model has the smallest residual error, while all of its parameters are in physiologically meaningful range. Future works should contain the validation of the proposed model and measurement methods on larger data including pathological conditions. REFERENCES (2012). CouchAssist E70 user manual. Philips Respironics. 377
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