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Modelling respiratory impedance in patients with kyphoscoliosis
Biomedical Signal Processing and Control 11 (2014) 36–41
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Biomedical Signal Processing and Control journal homepage: www.elsevier.com/locate/bspc
Modelling respiratory impedance in patients with kyphoscoliosis Clara M. Ionescu a,∗ , Eric Derom b , Robin De Keyser a a b
Department of Electrical Energy, Systems and Automation, Ghent University, Sint Pietersnieuwstraat 41, Blok B2, 9000 Ghent, Belgium Department of Respiratory Medicine, Ghent University Hospital, De Pintelaan 185, 7k12, B9000 Ghent, Belgium
a r t i c l e
i n f o
Article history: Received 6 January 2014 Received in revised form 6 February 2014 Accepted 10 February 2014 Available online 16 March 2014 Keywords: Respiratory system Recurrent anatomy Frequency response Ladder network Impedance kyphoscoliosis Detection lines (Non)linear analysis
a b s t r a c t When a nonlinear biological system is under analysis, one may employ linear and nonlinear tools. Linear tools such as fractional order lumped impedance models have not been previously employed to characterize difference between healthy volunteers and patients diagnosed with kyphoscoliosis (KS). Nonlinear tools such as detection lines from nonlinear contributions in frequency domain have also not been employed previously on KS patient data. KS is an irreversible restrictive disease, of genetic origin, which manifests by deformation of the spine and thorax. The forced oscillation technique (FOT) is a noninvasive, simple lung function test suitable for this class of patients with breathing difficulties, since it does not require any special maneuvre. In this work we show that the FOT method combined with both linear and nonlinear tools reveals important information which may be used as complementary to the standardized lung function tests (i.e. spirometry). © 2014 Elsevier Ltd. All rights reserved.
1. Introduction When extracting information from complex nonlinear biological systems, it is important to decide whether a linear or a nonlinear analysis is envisaged. The respiratory system is a complex nonlinear system, which changes properties with disease, i.e. the nonlinear behaviour may become more pronounced. A combination of both linear and nonlinear tools may be beneficial for the extraction of most information. In this work, we employ linear impedance extraction and detection of nonlinear distortions in the impedance data from patients diagnosed with kyphoscoliosis. Additionally, we employ a parametric model of fractional order which is directly linked to mechanical properties in the lungs, to identify quantitative differences between healthy volunteers and KS patients. Biological systems modelled by fractional order impedance models have received significant interest in the research community [35,7,6,22]. Initial characterizations of the lung’s mechanical properties have been reported in several invasive animal studies, showing the necessity of a fractional order (FO) integral [9,10]. Recent studies led to the conclusion that a FO model outperforms most of the integer-order models for characterizing the frequency-dependence in human respiratory input impedance
∗ Corresponding author. Tel.: +32 486331128. E-mail addresses: [email protected] (C.M. Ionescu), [email protected] (E. Derom), [email protected] (R. De Keyser). http://dx.doi.org/10.1016/j.bspc.2014.02.004 1746-8094/© 2014 Elsevier Ltd. All rights reserved.
[11]. The major advantage of the FO models over the integer order counterpart is not only their low number of parameters, but also their intrinsic capability to characterize the viscoelastic properties and the recurrent structures of biologic materials [1,15,16,33,4]. Fractional order models have been employed previously in both healthy subjects group [14] and various pathologies, such as asthma [18], Chronic Obstructive Pulmonary Disease (COPD) [17]. The respiratory impedance poses several resonant frequencies [21] and the validity of one fractional order model is restricted to the frequency range where its parameters have been identified [27]. As soon as the frequency range, in which the lung function is evaluated, changes, important variations in the frequency-dependence of the respiratory impedance may occur and the structure of the model must be revisited. Hitherto, to our knowledge, there is a lack of information on KS patients from the linear and nonlinear tools employed in this work. As such, the restrictive properties arise not from a lung parenchyma itself, but from the sub-optimal shape and anatomy of the thorax. The forced oscillation technique is a non-invasive, simple lung function test suitable for this class of patients with breathing difficulties, since it does not require any special maneuvre. In this work we show that the forced oscillation technique (FOT) combined with both linear and nonlinear tools revels important information which may be used as complementary to the standardized (spirometry) lung function tests. The only work which uses FOT in KS patients is that of Van Noord et al. [34]. There, the authors showed the ability of FOT to distinguish between various forms of restrictive and obstructive patterns.
C.M. Ionescu et al. / Biomedical Signal Processing and Control 11 (2014) 36–41 Table 1 Biometric parameters of the healthy subjects and KS patients. Values are presented as mean ± standard deviation.
Female/male Age (years) Height (m) Weight (kg) VC % pred FEV1 % pred FVC % pred Cobb angle (◦ ) Raw (kPa/l/s) Ccw pred* (l/kPa) VC % pred*
Healthy (80)
KS (11)
31/49 27 ± 5 1.73 ± 0.17 69 ± 9.6
4/7 62.25 ± 10.12 1.55 ± 0.08 63.25 ± 15.62 33.25 ± 14.15 31.62 ± 11.30 34.62 ± 12.12 75 ± 19.63 0.51± 0.12 0.98 ± 0.29 65.06 ± 10.48
The work presented in this paper aims to provide the reader with a proof of concept on the added value of using FOT as a complementary lung function test to the standardized spirometry test. The added value is shown by means of linear non-parametric identification of the respiratory impedance, further parameterization with a FO model. The FOT data is also processed for the detection of nonlinear contributions from the lungs in the measured air-pressure. The paper is organized as follows: the methods, patients and measurement protocol are described in the next section. Third section presents the results and a fourth section discusses these results. A conclusion section summarizes the main ideas of this paper. 2. Methods 2.1. Patients This study was approved by the local Ethics Committee of Ghent University Hospital and informed consent was obtained from all volunteers before inclusion in the study. The study involved subjects, of which were healthy and were adults diagnosed with kyphoscoliosis. Exclusion criteria were the inability to perform technically adequate spirometry or FOT measurements, evidence of current airway infection, acute exacerbation and any respiratory disease other than KS. All patients were in stable clinical condition at the moment of measurement. The healthy adult group evaluated in this study consists of 80 Caucasian volunteers (students) without a history of respiratory disease, whose lung function tests were performed in our laboratory, and Table 1 presents their biometric parameters. The measurements were performed over the 2005–2009 time interval. The healthy group of adults has been verified using the reference values from [29]. Although the age groups are significantly different, the lung volumes are similar, therefore providing similar conditions. The second group of adult patients was diagnosed with kyphoscoliosis. Kyphoscoliosis is a disease of the spine and its articulations, mostly beginning in childhood [8,3,30]. The deformation of the spine characteristically consists of a lateral displacement or curvature (scoliosis) or an antero-posterior angulation (kyphosis) or both (kyphoscoliosis). The angle of the spinal curvature called the angle of Cobb determines the degree of the deformity and consequently the severity of the restriction. Severe kyphoscoliosis may lead to respiratory failure, which often needs to be treated with non-invasive nocturnal ventilation. The study involved 11 adults diagnosed with kyphoscoliosis and their corresponding biometric and spirometric values are given in Table 1. In this table, the following notations apply: % pred: predicted values; VC: vital capacity; FEV1: forced expiratory volume in 1 s; FVC: forced vital capacity; Cobb angle: the angle of spinal deformity (one patient was excluded for it has outlier value for Cobb angle, i.e. 178◦ ; Ccw : chest wall
37
compliance; pred*: denotes values predicted from the Cobb angle, according to [23,34]; Raw : airway resistance from bodybox lung function test. All KS patients were on nocturnal ventilation. The measurements were performed during the June–August 2009 time interval. Using a closed circuit spirometer (JAEGER MasterLab, Germany) measurements for forced vital capacity (FVC), FEV1, the ratio FEV1/FVC and the ratio of forced expiratory flow (FEF) between 25% and 75% of FVC to FVC (FEF/FVC) were obtained for the KS patients in a sitting position. These parameters were presented as raw data and percentile of the predicted values (% pred) in a healthy subject with the same biometric details. Quality control of spirometry is given by the ATS criteria (American Thoracic Society), with the software allowing detection of non-acceptable maneuvres. The details from the KS patients are given in Table 1. 2.2. Input impedance measurement The impedance was measured using the Forced Oscillation Technique (FOT) setup, commercially available, assessing respiratory mechanics in two range of frequencies: 0.1–10 Hz and 4–48 Hz. Due to the fact that two distinct frequency ranges are used, two separate FOT devices were used, each optimized for the respective frequency interval. Both devices are based on standard FOT guidelines [28]. The subject is connected to the setup via a mouthpiece. The oscillation pressure is generated by an air fan (for the lower frequencies), respectively by a loudspeaker (for the higher frequencies). Both elements are moving according the fed voltage from a computer, which generates a multisine signal, creating air pressure oscillations. Opening of the main tubing allows the patient to have fresh air circulation, designed carefully not to lose significant air pressure power. During the measurements, the patient wears a nose clip and keeps the cheeks firmly supported. The FOT lung function tests were performed according to the recommendations described in [28]. The multisine signal was kept within a range of a peak-to-peak size of 0.1–0.3 kPa. All patients were tested in the sitting position, with cheeks firmly supported and elbows resting on the table. Each and every group of patients and volunteers has been tested in its unique location, using the same FOT devices, and under the supervision of the same FOT team. 2.3. Respiratory impedance The spectral representation of the respiratory impedance Zr is a fast, simple and fairly reliable evaluation [28,24]. Since the multisine signal is optimized such that it does not contain components of the breathing frequency of the patient, one can calculate the respiratory impedance as in: Zr (jω) =
SPU g (jω) SQU g (jω)
(1)
whereas Ug is the input signal send to the patient (i.e. sinusoidal variations in the air-pressure), the P corresponds to pressure (its electrical equivalent is voltage) and Q corresponds to air-flow (its electrical equivalent is current), the respiratory impedance Zr can be defined as their spectral (frequency domain) ratio relationship, with Sij (jω) the cross-correlation spectra between the various input–output signals, ω is the angular frequency and j = (− 1)1/2 [19,20]. 2.4. Parametric model and relation to lung properties In our previous work, we had shown that anatomical and morphological models of the respiratory tract [13] lead to ladder
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C.M. Ionescu et al. / Biomedical Signal Processing and Control 11 (2014) 36–41
network models [15], which in their lumped representation contain fractional order Laplace terms. In short, we found that the FO terms in the impedance models arise either from intrinsic viscoelastic (at low frequencies), either intrinsic fractal structure of the airway tree. From a manifold of possible FO models [11], the FO model proposed for evaluation in this paper is: ZFO4 (s) = Lr s˛r +
1 Cr sˇr
(2)
where Lr is the inductance, Cr is the compliance, and ˛, ˇ are the FO terms. This model is then fitted to the frequency domain response calculated with (1) using nonlinear least squares algorithm [31]. From the identified model parameters one can derive the tissue damping Gr and elastance Hr , defined as [9,10]: Gr =
1 Cr
ωˇr 1
Hr =
Cr
ωˇr
cos ˇr
2
sin ˇr
(3)
Gr Hr
(4)
This parameter characterizes the heterogeneity of the lung tissue and has been shown to vary significantly with pathology. Since all these parameters from (3) and (4) are frequency-dependent, the lumped identified values will in fact represent an averaged value over the 4–48 Hz frequency range. Apart from the identified model parameters, some additional parameters are introduced in this analysis. The real part of the complex impedance at 6 Hz (R6) can be used to characterize the total resistance at this frequency, a parameter often encountered in clinical studies. The resonant frequency (Frez) could also be used as a classifying parameter, since it has been shown that the balance between elastic and inertial properties change with pathology. We also introduce two dimensionless indexes, namely the quality factor at 6 Hz (QF6), denoted by the ratio of the reactive power to the real power: QF6 =
Im6 Re6
(5)
where Re6 and Im6 denote the real and imaginary parts of the complex impedance evaluated at 6 Hz. From (5), one can calculate the corresponding power factor PF6:
PF6 =
T=
2
both in l/kPa. The hysteresivity coefficient r (dimensionless) is defined as [5]: r =
described elsewhere [31]. In short, the principle is based on the fact that when sending a known frequency into a system, the output will be a combination of the linear and nonlinear dynamics of the system. The linear dynamics will be characterized by information measured at the same input frequency, while the nonlinear dynamics by the information measured at other frequencies. The nonlinear contributions can then be further splitted in odd and even frequency points, since it has been shown that these can bear different effects on the estimated models from such controlled data [31]. Using such concepts, an algorithm for the application of FOT to extract linear and nonlinear contributions from the respiratory mechanics has been presented and evaluated in [32,12]. To obtain a quantitative assessment of the amount of nonlinear contributions measured from the system, but normalized with respect to the input–output ratio, we introduce the following index:
1 QF62 + 1
Peven + Podd Uexc · Pexc Ueven + Uodd
where each variable is the sum of the absolute values of all the contributions in pressure signal and input flow signal respectively, at the even non-excited frequencies, the odd non-excited frequencies and the excited odd frequencies. Only the corrected output pressure has been taken into account when calculating (7). This index expresses a relative ratio of the contributions at the non-excited frequency points, with respect to the contributions at the excited frequency points. Furthermore, it gives a relative measure of the gain between contributions in the input and in the output of the system. Since this is a nonlinear system whose output depends on the input, the choice for this relative measure is technically sound. 3. Results The complex impedance values for the healthy and COPD patients have been obtained using (1), with resonant frequency (zero crossing in the imaginary part) around 8 Hz in the healthy group, respectively around 17 Hz for the KS group. The real part denotes mainly the mechanical resistance of the lung tissue, which is generally increased in the KS group, resulting in higher work of breathing. Also, the resistance at low frequencies is much
Table 2 Estimated and derived model parameters and modelling errors for the healthy and kyphoscoliosis groups. Values are given as mean ± standard deviation; values in brackets indicate the 95% confidence intervals.
(6)
In engineering, the quality factor QF compares the time constant for decay of an oscillating physical system’s amplitude with respect to its oscillation period. In other words, it compares the frequency at which a system oscillates to the rate at which it dissipates its energy, also known as the damping factor. For a second order linear time invariant system, a system is said to be over-damped if QF < 0.5, under-damped for QF > 0.5 and critically damped for QF = 0.5. In other words, a low QF denotes a high energy loss, while a high QF denotes a low energy loss. For the power factor PF, we have that for PF = 0 the energy flow is entirely reactive (hence the stored energy in the load returns to the source with each cycle), and if PF = 1, all the energy supplied by the source is consumed by the load.
(7)
Lr 1/Cr ˛r ˇr Gr Hr r R6 Frez
2.5. Nonlinear distortion analysis
QF6
The principle of detecting nonlinear contributions in the frequency domain when exciting nonlinear systems has been
PF6
Healthy
Kyphoscoliosis
0.032 ± 0.029 (0.019,0.045) 1.59 ± 1.10 (1.09,2.08) 0.42 ± 0.08 (0.38,0.47) 0.75 ± 0.11 (0.70,0.80) 0.44 ± 0.15 (0.37,0.50) 1.49 ± 1.14 (0.98,2.00) 0.41 ± 0.21 (0.32,0.51) 0.13 ± 0.05 (0.11,0.16) 10.48 ± 3.56 (8.75,13.87) 0.09 ± 0.09 (0.02,0.17) 0.99 ± 0.01 (0.98,0.99)
0.0173 ± 0.012 (0.007,0.02) 2.47 ± 0.76 (1.85,3.10) 0.54 ± 0.05 (0.49,0.58) 0.55 ± 0.05 (0.50,0.59) 1.55 ± 0.39 (1.25,1.86) 1.91 ± 0.73 (1.34,2.48) 0.85 ± 0.16 (0.72,0.98) 0.28 ± 0.06 (0.23,0.33) 15.01 ± 2.08 (12.80,18.02) 0.58 ± 0.15 (0.46,0.71) 0.85 ± 0.05 (0.81,0.90)
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(p < 0.75), as observed from Fig. 2. The boxplots for the quality factor QF6 and the power factor PF6 are given in Fig. 3, which were significantly different between the groups (p 0.01). Finally, the boxplot for the real part of impedance at 6 Hz, R6 (p 0.01), and for tissue hysteresivity r (p 0.01) are given in Fig. 4. The concept of nonlinear distortions cannot be evaluated between the healthy and the KS groups, since it is obvious that the differences in shape of thorax will bias the result. However, one may evaluate the amount of nonlinear distortions within KS group. For this purpose, we analyse the results of the detection algorithm on a patient with KS and one with combined KS with chronic obstructive pulmonary disease, given in Figs. 5 and 6, respectively. 4. Discussion
Fig. 1. Impedance plots for the KS patient and its estimated parametric model.
increased in the KS group, suggesting increased damping of the lung parenchyma [23,3,34,30,26]. Table 2 presents the results obtained from the identification of model parameters (2). A typical identified impedance data is shown in Fig. 1. From the identified model parameters, some quantitative measures were derived, as explained previously. There were significant variances between the groups for tissue damping Gr (p 0.01), but not for tissue elastance Hr
In kyphoscoliosis, lung volumes are reduced, respiratory elastance and resistance are increased, and breathing pattern is rapid and shallow. The total lung capacity can be markedly reduced in kyphoscoliosis, with a relative preservation of residual volume. The latter is due to the fact that residual volume remains trapped in the lungs since the patients cannot expire optimally due to mechanical restrictions of the rib cage. Another consequence of the mechanical restrictions is a reduction in volume capacity (VC). The fact that the predicted values in VC from the Cobb angle values were higher than measured, can be attributed to the fact that these patients may have secondary kyphoscoliosis, whereas the predicted values correlate better with idiopatic scoliosis [23,3,34,30,26]. Similarly, a stiff chest wall (low Ccw values from Cobb angle) will diminish the
Fig. 2. Tissue damping Gr (left) and tissue elastance Hr (right) in (1) healthy and (2) kyphoscoliosis. See corresponding p-values discussed in text.
Fig. 3. Quality factors QF6 (left) and power factors PF6 (right) evaluated at 6 Hz in (1) healthy and (2) kyphoscoliosis. See corresponding p-values discussed in text.
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C.M. Ionescu et al. / Biomedical Signal Processing and Control 11 (2014) 36–41
Fig. 4. Real part of impedance R6 evaluated at 6 Hz (left) and the tissue hysteresivity r in (1) healthy and (2) kyphoscoliosis. See corresponding p-values discussed in text.
Fig. 5. Example of linear and nonlinear frequency response contribution in a patient suffering of KS only. The value calculated for the T index from (7) is 0.9804.
Fig. 6. Example of linear and nonlinear frequency response contribution in a patient suffering of combined KS with chronic obstructive pulmonary disease. The value calculated for the T index from (7) is 1.0081.
resting position of the chest wall, which in turn, reduces the functional residual capacity. Stiffening of the chest wall leads as well to an overall reduction in the lung compliance (increased damping). One must keep in mind that these changes are not resulted from a diseased parenchyma, but a consequence of the relatively immobile chest wall.
Compliance of both the chest wall and lungs is decreased in KS [25]. The restrictive nature of the disease (from reduced lung volume) was confirmed by a significantly increased tissue damping Gr , airway resistance R6 and quality factor QF6. The latter suggested an over-damped dynamical system. The reduced lung and chest wall compliances increase the elastic load on the respiratory muscles and therefore increase the inspiratory pressure needed to inhale a given air volume. Consequently, the work of breathing is increased, reflected in the lower values for the power factor PF6. Tissue elastance was not significantly different between the groups, but the tissue hysteresivity r provided a significantly increased heterogeneity in the lungs of the kyphoscoliosis group. Indeed, this result reflects the modified structure of the lungs as originated by the spinal deformity. For example, airway obstruction can occur in some cases as a consequence of changes in the geometry of the airways, or as a result of the aorta impinging on the tracheal wall. It is worth noticing that the ˇ value identified in healthy patients has very close values to that identified in [2]. This implies that the model structure is consistent within different studies. The relative preservation of the lung’s ability to function as a gas-exchange organ, if adequately ventilated, is also evidenced by the normal or low values for dead space in patients with KS. This is in contrast to patients with COPD, where increased dead space provides false increased elasticity of the lung parenchyma [17]. In this study, however, only restrictive patients were included (i.e. FEV1/FVC ratio higher than 80%). The structure may significantly vary when KS is combined with COPD, hence the concept of analysing linear and nonlinear contributions in the frequency response of the respiratory impedance has a great potential in follow-up studies. The index may not be directly useful for classification, but it may reveal that increased degree of nonlinear contributions, such as for the patient from Fig. 6, are correlated to added asymmetry and inhomogeneity in lung structure.
5. Conclusions This paper applied, for the first time in literature, the fractional order impedance modelling to respiratory impedance data in patients diagnosed with kyphoscoliosis. A novel concept, that of detecting and evaluating nonlinear contributions originating from the lung parenchyma and lung structure, has also been applied to this group of patients. The results indicate that the methods have great potential to offer complementary information to the clinical practice, next to standardized lung function tests such as spirometry.
C.M. Ionescu et al. / Biomedical Signal Processing and Control 11 (2014) 36–41
Acknowledgements For the measurements on healthy adult subjects, we thank Mr. Sven Verschraegen for the technical assistance for pulmonary function testing at the Department of Respiratory Medicine of Ghent University Hospital, Belgium. C.M. Ionescu is a post-doctoral fellow of Flanders Research Centre (FWO). References [1] J. Bates, Lung, Mechanics – An Inverse Modeling Approach, Cambridge Press, 2009. [2] A. Beaulieu, D. Bosse, P. Micheau, Measurement of fractional order model parameters of respiratory mechanical impedance in total liquid ventilation, IEEE Trans. Biomed. Eng. 59 (2) (2012) 323–331. [3] L.R. Bridges, G. Coulton, G. Howard, J. Moss, R. Mason, The neuromuscular basis of hereditary kyphoscoliosis in the mouse, Muscle Nerve 15 (2) (1992) 172–179. [4] A.S. Elwakil, Fractional-order circuits and systems: an emerging interdisciplinary research area, IEEE Circuits Syst. Mag. 10 (4) (2010) 40–50. [5] J. Fredberg, D. Stamenovic, On the imperfect elasticity of lung tissue, J. Appl. Physiol. 67 (1989) 2408–2419. [6] G. Losa, D. Merlini, T. Nonnenmacher, E.R. Weibel (Eds.), Fractals in Biology and Medicine, vol. IV, Birkhauser, Berlin, 2005, pp. 31–42. [7] J. Gao, Y. Cao, W. Tung, J. Hu, Multiscale Analysis of Complex Time Series: Integration of Chaos and Random Fractal Theory, and Beyond, Wiley Interscience, 2007, ISBN 0471654701. [8] A. Guyton, J. Hall, Textbook of Medical Physiology, 11th edition, W.B. Saunders, 2000. [9] Z. Hantos, B. Daroczy, B. Suki, S. Nagy, J. Fredberg, Input impedance and peripheral inhomogeneity of dog lungs, J. Appl. Phys. 72 (1) (1992) 168–178. [10] Z. Hantos, A. Adamicz, E. Govaerts, B. Daroczy, Mechanical impedances of lungs and chest wall in the cat, J. Appl. Phys. 73 (2) (1992) 427–433. [11] C.M. Ionescu, R. De Keyser, K. Desager, E. Derom, Fractional order models for the input impedance of the respiratory system, in: A Lazinica (Ed.), Advances in Biomedical Engineering, In-Tech, 2009 (open-access). [12] C.M. Ionescu, J. Schoukens, R. De Keyser, Detecting and analyzing nonlinear effects in respiratory impedance measurements, in: Proceedings of the American Control Conference, 29 June–1 July, San Francisco, USA, 2011, pp. 5412–5417, ISBN: 978-1-4577-0079-8. [13] C.M. Ionescu, P. Segers, R. De Keyser, Mechanical properties of the respiratory system derived from morphologic insight, IEEE Trans. Biomed. Eng. 56 (4) (2009) 949–959. [14] C.M. Ionescu, R. De Keyser, J. Sabatier, A. Oustaloup, F. Levron, Low frequency constant-phase behaviour in the respiratory impedance, Biomed. Signal Process. Control 6 (2011) 197–208. [15] C.M. Ionescu, I. Muntean, J.T. Machado, R. De Keyser, M. Abrudean, A theoretical study on modelling the respiratory tract with ladder networks by means of intrinsic fractal geometry, IEEE Trans. Biomed. Eng. 57 (2) (2010) 246–253.
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Biomedical Signal Processing and Control journal homepage: www.elsevier.com/locate/bspc
Modelling respiratory impedance in patients with kyphoscoliosis Clara M. Ionescu a,∗ , Eric Derom b , Robin De Keyser a a b
Department of Electrical Energy, Systems and Automation, Ghent University, Sint Pietersnieuwstraat 41, Blok B2, 9000 Ghent, Belgium Department of Respiratory Medicine, Ghent University Hospital, De Pintelaan 185, 7k12, B9000 Ghent, Belgium
a r t i c l e
i n f o
Article history: Received 6 January 2014 Received in revised form 6 February 2014 Accepted 10 February 2014 Available online 16 March 2014 Keywords: Respiratory system Recurrent anatomy Frequency response Ladder network Impedance kyphoscoliosis Detection lines (Non)linear analysis
a b s t r a c t When a nonlinear biological system is under analysis, one may employ linear and nonlinear tools. Linear tools such as fractional order lumped impedance models have not been previously employed to characterize difference between healthy volunteers and patients diagnosed with kyphoscoliosis (KS). Nonlinear tools such as detection lines from nonlinear contributions in frequency domain have also not been employed previously on KS patient data. KS is an irreversible restrictive disease, of genetic origin, which manifests by deformation of the spine and thorax. The forced oscillation technique (FOT) is a noninvasive, simple lung function test suitable for this class of patients with breathing difficulties, since it does not require any special maneuvre. In this work we show that the FOT method combined with both linear and nonlinear tools reveals important information which may be used as complementary to the standardized lung function tests (i.e. spirometry). © 2014 Elsevier Ltd. All rights reserved.
1. Introduction When extracting information from complex nonlinear biological systems, it is important to decide whether a linear or a nonlinear analysis is envisaged. The respiratory system is a complex nonlinear system, which changes properties with disease, i.e. the nonlinear behaviour may become more pronounced. A combination of both linear and nonlinear tools may be beneficial for the extraction of most information. In this work, we employ linear impedance extraction and detection of nonlinear distortions in the impedance data from patients diagnosed with kyphoscoliosis. Additionally, we employ a parametric model of fractional order which is directly linked to mechanical properties in the lungs, to identify quantitative differences between healthy volunteers and KS patients. Biological systems modelled by fractional order impedance models have received significant interest in the research community [35,7,6,22]. Initial characterizations of the lung’s mechanical properties have been reported in several invasive animal studies, showing the necessity of a fractional order (FO) integral [9,10]. Recent studies led to the conclusion that a FO model outperforms most of the integer-order models for characterizing the frequency-dependence in human respiratory input impedance
∗ Corresponding author. Tel.: +32 486331128. E-mail addresses: [email protected] (C.M. Ionescu), [email protected] (E. Derom), [email protected] (R. De Keyser). http://dx.doi.org/10.1016/j.bspc.2014.02.004 1746-8094/© 2014 Elsevier Ltd. All rights reserved.
[11]. The major advantage of the FO models over the integer order counterpart is not only their low number of parameters, but also their intrinsic capability to characterize the viscoelastic properties and the recurrent structures of biologic materials [1,15,16,33,4]. Fractional order models have been employed previously in both healthy subjects group [14] and various pathologies, such as asthma [18], Chronic Obstructive Pulmonary Disease (COPD) [17]. The respiratory impedance poses several resonant frequencies [21] and the validity of one fractional order model is restricted to the frequency range where its parameters have been identified [27]. As soon as the frequency range, in which the lung function is evaluated, changes, important variations in the frequency-dependence of the respiratory impedance may occur and the structure of the model must be revisited. Hitherto, to our knowledge, there is a lack of information on KS patients from the linear and nonlinear tools employed in this work. As such, the restrictive properties arise not from a lung parenchyma itself, but from the sub-optimal shape and anatomy of the thorax. The forced oscillation technique is a non-invasive, simple lung function test suitable for this class of patients with breathing difficulties, since it does not require any special maneuvre. In this work we show that the forced oscillation technique (FOT) combined with both linear and nonlinear tools revels important information which may be used as complementary to the standardized (spirometry) lung function tests. The only work which uses FOT in KS patients is that of Van Noord et al. [34]. There, the authors showed the ability of FOT to distinguish between various forms of restrictive and obstructive patterns.
C.M. Ionescu et al. / Biomedical Signal Processing and Control 11 (2014) 36–41 Table 1 Biometric parameters of the healthy subjects and KS patients. Values are presented as mean ± standard deviation.
Female/male Age (years) Height (m) Weight (kg) VC % pred FEV1 % pred FVC % pred Cobb angle (◦ ) Raw (kPa/l/s) Ccw pred* (l/kPa) VC % pred*
Healthy (80)
KS (11)
31/49 27 ± 5 1.73 ± 0.17 69 ± 9.6
4/7 62.25 ± 10.12 1.55 ± 0.08 63.25 ± 15.62 33.25 ± 14.15 31.62 ± 11.30 34.62 ± 12.12 75 ± 19.63 0.51± 0.12 0.98 ± 0.29 65.06 ± 10.48
The work presented in this paper aims to provide the reader with a proof of concept on the added value of using FOT as a complementary lung function test to the standardized spirometry test. The added value is shown by means of linear non-parametric identification of the respiratory impedance, further parameterization with a FO model. The FOT data is also processed for the detection of nonlinear contributions from the lungs in the measured air-pressure. The paper is organized as follows: the methods, patients and measurement protocol are described in the next section. Third section presents the results and a fourth section discusses these results. A conclusion section summarizes the main ideas of this paper. 2. Methods 2.1. Patients This study was approved by the local Ethics Committee of Ghent University Hospital and informed consent was obtained from all volunteers before inclusion in the study. The study involved subjects, of which were healthy and were adults diagnosed with kyphoscoliosis. Exclusion criteria were the inability to perform technically adequate spirometry or FOT measurements, evidence of current airway infection, acute exacerbation and any respiratory disease other than KS. All patients were in stable clinical condition at the moment of measurement. The healthy adult group evaluated in this study consists of 80 Caucasian volunteers (students) without a history of respiratory disease, whose lung function tests were performed in our laboratory, and Table 1 presents their biometric parameters. The measurements were performed over the 2005–2009 time interval. The healthy group of adults has been verified using the reference values from [29]. Although the age groups are significantly different, the lung volumes are similar, therefore providing similar conditions. The second group of adult patients was diagnosed with kyphoscoliosis. Kyphoscoliosis is a disease of the spine and its articulations, mostly beginning in childhood [8,3,30]. The deformation of the spine characteristically consists of a lateral displacement or curvature (scoliosis) or an antero-posterior angulation (kyphosis) or both (kyphoscoliosis). The angle of the spinal curvature called the angle of Cobb determines the degree of the deformity and consequently the severity of the restriction. Severe kyphoscoliosis may lead to respiratory failure, which often needs to be treated with non-invasive nocturnal ventilation. The study involved 11 adults diagnosed with kyphoscoliosis and their corresponding biometric and spirometric values are given in Table 1. In this table, the following notations apply: % pred: predicted values; VC: vital capacity; FEV1: forced expiratory volume in 1 s; FVC: forced vital capacity; Cobb angle: the angle of spinal deformity (one patient was excluded for it has outlier value for Cobb angle, i.e. 178◦ ; Ccw : chest wall
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compliance; pred*: denotes values predicted from the Cobb angle, according to [23,34]; Raw : airway resistance from bodybox lung function test. All KS patients were on nocturnal ventilation. The measurements were performed during the June–August 2009 time interval. Using a closed circuit spirometer (JAEGER MasterLab, Germany) measurements for forced vital capacity (FVC), FEV1, the ratio FEV1/FVC and the ratio of forced expiratory flow (FEF) between 25% and 75% of FVC to FVC (FEF/FVC) were obtained for the KS patients in a sitting position. These parameters were presented as raw data and percentile of the predicted values (% pred) in a healthy subject with the same biometric details. Quality control of spirometry is given by the ATS criteria (American Thoracic Society), with the software allowing detection of non-acceptable maneuvres. The details from the KS patients are given in Table 1. 2.2. Input impedance measurement The impedance was measured using the Forced Oscillation Technique (FOT) setup, commercially available, assessing respiratory mechanics in two range of frequencies: 0.1–10 Hz and 4–48 Hz. Due to the fact that two distinct frequency ranges are used, two separate FOT devices were used, each optimized for the respective frequency interval. Both devices are based on standard FOT guidelines [28]. The subject is connected to the setup via a mouthpiece. The oscillation pressure is generated by an air fan (for the lower frequencies), respectively by a loudspeaker (for the higher frequencies). Both elements are moving according the fed voltage from a computer, which generates a multisine signal, creating air pressure oscillations. Opening of the main tubing allows the patient to have fresh air circulation, designed carefully not to lose significant air pressure power. During the measurements, the patient wears a nose clip and keeps the cheeks firmly supported. The FOT lung function tests were performed according to the recommendations described in [28]. The multisine signal was kept within a range of a peak-to-peak size of 0.1–0.3 kPa. All patients were tested in the sitting position, with cheeks firmly supported and elbows resting on the table. Each and every group of patients and volunteers has been tested in its unique location, using the same FOT devices, and under the supervision of the same FOT team. 2.3. Respiratory impedance The spectral representation of the respiratory impedance Zr is a fast, simple and fairly reliable evaluation [28,24]. Since the multisine signal is optimized such that it does not contain components of the breathing frequency of the patient, one can calculate the respiratory impedance as in: Zr (jω) =
SPU g (jω) SQU g (jω)
(1)
whereas Ug is the input signal send to the patient (i.e. sinusoidal variations in the air-pressure), the P corresponds to pressure (its electrical equivalent is voltage) and Q corresponds to air-flow (its electrical equivalent is current), the respiratory impedance Zr can be defined as their spectral (frequency domain) ratio relationship, with Sij (jω) the cross-correlation spectra between the various input–output signals, ω is the angular frequency and j = (− 1)1/2 [19,20]. 2.4. Parametric model and relation to lung properties In our previous work, we had shown that anatomical and morphological models of the respiratory tract [13] lead to ladder
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network models [15], which in their lumped representation contain fractional order Laplace terms. In short, we found that the FO terms in the impedance models arise either from intrinsic viscoelastic (at low frequencies), either intrinsic fractal structure of the airway tree. From a manifold of possible FO models [11], the FO model proposed for evaluation in this paper is: ZFO4 (s) = Lr s˛r +
1 Cr sˇr
(2)
where Lr is the inductance, Cr is the compliance, and ˛, ˇ are the FO terms. This model is then fitted to the frequency domain response calculated with (1) using nonlinear least squares algorithm [31]. From the identified model parameters one can derive the tissue damping Gr and elastance Hr , defined as [9,10]: Gr =
1 Cr
ωˇr 1
Hr =
Cr
ωˇr
cos ˇr
2
sin ˇr
(3)
Gr Hr
(4)
This parameter characterizes the heterogeneity of the lung tissue and has been shown to vary significantly with pathology. Since all these parameters from (3) and (4) are frequency-dependent, the lumped identified values will in fact represent an averaged value over the 4–48 Hz frequency range. Apart from the identified model parameters, some additional parameters are introduced in this analysis. The real part of the complex impedance at 6 Hz (R6) can be used to characterize the total resistance at this frequency, a parameter often encountered in clinical studies. The resonant frequency (Frez) could also be used as a classifying parameter, since it has been shown that the balance between elastic and inertial properties change with pathology. We also introduce two dimensionless indexes, namely the quality factor at 6 Hz (QF6), denoted by the ratio of the reactive power to the real power: QF6 =
Im6 Re6
(5)
where Re6 and Im6 denote the real and imaginary parts of the complex impedance evaluated at 6 Hz. From (5), one can calculate the corresponding power factor PF6:
PF6 =
T=
2
both in l/kPa. The hysteresivity coefficient r (dimensionless) is defined as [5]: r =
described elsewhere [31]. In short, the principle is based on the fact that when sending a known frequency into a system, the output will be a combination of the linear and nonlinear dynamics of the system. The linear dynamics will be characterized by information measured at the same input frequency, while the nonlinear dynamics by the information measured at other frequencies. The nonlinear contributions can then be further splitted in odd and even frequency points, since it has been shown that these can bear different effects on the estimated models from such controlled data [31]. Using such concepts, an algorithm for the application of FOT to extract linear and nonlinear contributions from the respiratory mechanics has been presented and evaluated in [32,12]. To obtain a quantitative assessment of the amount of nonlinear contributions measured from the system, but normalized with respect to the input–output ratio, we introduce the following index:
1 QF62 + 1
Peven + Podd Uexc · Pexc Ueven + Uodd
where each variable is the sum of the absolute values of all the contributions in pressure signal and input flow signal respectively, at the even non-excited frequencies, the odd non-excited frequencies and the excited odd frequencies. Only the corrected output pressure has been taken into account when calculating (7). This index expresses a relative ratio of the contributions at the non-excited frequency points, with respect to the contributions at the excited frequency points. Furthermore, it gives a relative measure of the gain between contributions in the input and in the output of the system. Since this is a nonlinear system whose output depends on the input, the choice for this relative measure is technically sound. 3. Results The complex impedance values for the healthy and COPD patients have been obtained using (1), with resonant frequency (zero crossing in the imaginary part) around 8 Hz in the healthy group, respectively around 17 Hz for the KS group. The real part denotes mainly the mechanical resistance of the lung tissue, which is generally increased in the KS group, resulting in higher work of breathing. Also, the resistance at low frequencies is much
Table 2 Estimated and derived model parameters and modelling errors for the healthy and kyphoscoliosis groups. Values are given as mean ± standard deviation; values in brackets indicate the 95% confidence intervals.
(6)
In engineering, the quality factor QF compares the time constant for decay of an oscillating physical system’s amplitude with respect to its oscillation period. In other words, it compares the frequency at which a system oscillates to the rate at which it dissipates its energy, also known as the damping factor. For a second order linear time invariant system, a system is said to be over-damped if QF < 0.5, under-damped for QF > 0.5 and critically damped for QF = 0.5. In other words, a low QF denotes a high energy loss, while a high QF denotes a low energy loss. For the power factor PF, we have that for PF = 0 the energy flow is entirely reactive (hence the stored energy in the load returns to the source with each cycle), and if PF = 1, all the energy supplied by the source is consumed by the load.
(7)
Lr 1/Cr ˛r ˇr Gr Hr r R6 Frez
2.5. Nonlinear distortion analysis
QF6
The principle of detecting nonlinear contributions in the frequency domain when exciting nonlinear systems has been
PF6
Healthy
Kyphoscoliosis
0.032 ± 0.029 (0.019,0.045) 1.59 ± 1.10 (1.09,2.08) 0.42 ± 0.08 (0.38,0.47) 0.75 ± 0.11 (0.70,0.80) 0.44 ± 0.15 (0.37,0.50) 1.49 ± 1.14 (0.98,2.00) 0.41 ± 0.21 (0.32,0.51) 0.13 ± 0.05 (0.11,0.16) 10.48 ± 3.56 (8.75,13.87) 0.09 ± 0.09 (0.02,0.17) 0.99 ± 0.01 (0.98,0.99)
0.0173 ± 0.012 (0.007,0.02) 2.47 ± 0.76 (1.85,3.10) 0.54 ± 0.05 (0.49,0.58) 0.55 ± 0.05 (0.50,0.59) 1.55 ± 0.39 (1.25,1.86) 1.91 ± 0.73 (1.34,2.48) 0.85 ± 0.16 (0.72,0.98) 0.28 ± 0.06 (0.23,0.33) 15.01 ± 2.08 (12.80,18.02) 0.58 ± 0.15 (0.46,0.71) 0.85 ± 0.05 (0.81,0.90)
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(p < 0.75), as observed from Fig. 2. The boxplots for the quality factor QF6 and the power factor PF6 are given in Fig. 3, which were significantly different between the groups (p 0.01). Finally, the boxplot for the real part of impedance at 6 Hz, R6 (p 0.01), and for tissue hysteresivity r (p 0.01) are given in Fig. 4. The concept of nonlinear distortions cannot be evaluated between the healthy and the KS groups, since it is obvious that the differences in shape of thorax will bias the result. However, one may evaluate the amount of nonlinear distortions within KS group. For this purpose, we analyse the results of the detection algorithm on a patient with KS and one with combined KS with chronic obstructive pulmonary disease, given in Figs. 5 and 6, respectively. 4. Discussion
Fig. 1. Impedance plots for the KS patient and its estimated parametric model.
increased in the KS group, suggesting increased damping of the lung parenchyma [23,3,34,30,26]. Table 2 presents the results obtained from the identification of model parameters (2). A typical identified impedance data is shown in Fig. 1. From the identified model parameters, some quantitative measures were derived, as explained previously. There were significant variances between the groups for tissue damping Gr (p 0.01), but not for tissue elastance Hr
In kyphoscoliosis, lung volumes are reduced, respiratory elastance and resistance are increased, and breathing pattern is rapid and shallow. The total lung capacity can be markedly reduced in kyphoscoliosis, with a relative preservation of residual volume. The latter is due to the fact that residual volume remains trapped in the lungs since the patients cannot expire optimally due to mechanical restrictions of the rib cage. Another consequence of the mechanical restrictions is a reduction in volume capacity (VC). The fact that the predicted values in VC from the Cobb angle values were higher than measured, can be attributed to the fact that these patients may have secondary kyphoscoliosis, whereas the predicted values correlate better with idiopatic scoliosis [23,3,34,30,26]. Similarly, a stiff chest wall (low Ccw values from Cobb angle) will diminish the
Fig. 2. Tissue damping Gr (left) and tissue elastance Hr (right) in (1) healthy and (2) kyphoscoliosis. See corresponding p-values discussed in text.
Fig. 3. Quality factors QF6 (left) and power factors PF6 (right) evaluated at 6 Hz in (1) healthy and (2) kyphoscoliosis. See corresponding p-values discussed in text.
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Fig. 4. Real part of impedance R6 evaluated at 6 Hz (left) and the tissue hysteresivity r in (1) healthy and (2) kyphoscoliosis. See corresponding p-values discussed in text.
Fig. 5. Example of linear and nonlinear frequency response contribution in a patient suffering of KS only. The value calculated for the T index from (7) is 0.9804.
Fig. 6. Example of linear and nonlinear frequency response contribution in a patient suffering of combined KS with chronic obstructive pulmonary disease. The value calculated for the T index from (7) is 1.0081.
resting position of the chest wall, which in turn, reduces the functional residual capacity. Stiffening of the chest wall leads as well to an overall reduction in the lung compliance (increased damping). One must keep in mind that these changes are not resulted from a diseased parenchyma, but a consequence of the relatively immobile chest wall.
Compliance of both the chest wall and lungs is decreased in KS [25]. The restrictive nature of the disease (from reduced lung volume) was confirmed by a significantly increased tissue damping Gr , airway resistance R6 and quality factor QF6. The latter suggested an over-damped dynamical system. The reduced lung and chest wall compliances increase the elastic load on the respiratory muscles and therefore increase the inspiratory pressure needed to inhale a given air volume. Consequently, the work of breathing is increased, reflected in the lower values for the power factor PF6. Tissue elastance was not significantly different between the groups, but the tissue hysteresivity r provided a significantly increased heterogeneity in the lungs of the kyphoscoliosis group. Indeed, this result reflects the modified structure of the lungs as originated by the spinal deformity. For example, airway obstruction can occur in some cases as a consequence of changes in the geometry of the airways, or as a result of the aorta impinging on the tracheal wall. It is worth noticing that the ˇ value identified in healthy patients has very close values to that identified in [2]. This implies that the model structure is consistent within different studies. The relative preservation of the lung’s ability to function as a gas-exchange organ, if adequately ventilated, is also evidenced by the normal or low values for dead space in patients with KS. This is in contrast to patients with COPD, where increased dead space provides false increased elasticity of the lung parenchyma [17]. In this study, however, only restrictive patients were included (i.e. FEV1/FVC ratio higher than 80%). The structure may significantly vary when KS is combined with COPD, hence the concept of analysing linear and nonlinear contributions in the frequency response of the respiratory impedance has a great potential in follow-up studies. The index may not be directly useful for classification, but it may reveal that increased degree of nonlinear contributions, such as for the patient from Fig. 6, are correlated to added asymmetry and inhomogeneity in lung structure.
5. Conclusions This paper applied, for the first time in literature, the fractional order impedance modelling to respiratory impedance data in patients diagnosed with kyphoscoliosis. A novel concept, that of detecting and evaluating nonlinear contributions originating from the lung parenchyma and lung structure, has also been applied to this group of patients. The results indicate that the methods have great potential to offer complementary information to the clinical practice, next to standardized lung function tests such as spirometry.
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Acknowledgements For the measurements on healthy adult subjects, we thank Mr. Sven Verschraegen for the technical assistance for pulmonary function testing at the Department of Respiratory Medicine of Ghent University Hospital, Belgium. C.M. Ionescu is a post-doctoral fellow of Flanders Research Centre (FWO). References [1] J. Bates, Lung, Mechanics – An Inverse Modeling Approach, Cambridge Press, 2009. [2] A. Beaulieu, D. Bosse, P. Micheau, Measurement of fractional order model parameters of respiratory mechanical impedance in total liquid ventilation, IEEE Trans. Biomed. Eng. 59 (2) (2012) 323–331. [3] L.R. Bridges, G. Coulton, G. Howard, J. Moss, R. Mason, The neuromuscular basis of hereditary kyphoscoliosis in the mouse, Muscle Nerve 15 (2) (1992) 172–179. [4] A.S. Elwakil, Fractional-order circuits and systems: an emerging interdisciplinary research area, IEEE Circuits Syst. Mag. 10 (4) (2010) 40–50. [5] J. Fredberg, D. Stamenovic, On the imperfect elasticity of lung tissue, J. Appl. Physiol. 67 (1989) 2408–2419. [6] G. Losa, D. Merlini, T. Nonnenmacher, E.R. Weibel (Eds.), Fractals in Biology and Medicine, vol. IV, Birkhauser, Berlin, 2005, pp. 31–42. [7] J. Gao, Y. Cao, W. Tung, J. Hu, Multiscale Analysis of Complex Time Series: Integration of Chaos and Random Fractal Theory, and Beyond, Wiley Interscience, 2007, ISBN 0471654701. [8] A. Guyton, J. Hall, Textbook of Medical Physiology, 11th edition, W.B. Saunders, 2000. [9] Z. Hantos, B. Daroczy, B. Suki, S. Nagy, J. Fredberg, Input impedance and peripheral inhomogeneity of dog lungs, J. Appl. Phys. 72 (1) (1992) 168–178. [10] Z. Hantos, A. Adamicz, E. Govaerts, B. Daroczy, Mechanical impedances of lungs and chest wall in the cat, J. Appl. Phys. 73 (2) (1992) 427–433. [11] C.M. Ionescu, R. De Keyser, K. Desager, E. Derom, Fractional order models for the input impedance of the respiratory system, in: A Lazinica (Ed.), Advances in Biomedical Engineering, In-Tech, 2009 (open-access). [12] C.M. Ionescu, J. Schoukens, R. De Keyser, Detecting and analyzing nonlinear effects in respiratory impedance measurements, in: Proceedings of the American Control Conference, 29 June–1 July, San Francisco, USA, 2011, pp. 5412–5417, ISBN: 978-1-4577-0079-8. [13] C.M. Ionescu, P. Segers, R. De Keyser, Mechanical properties of the respiratory system derived from morphologic insight, IEEE Trans. Biomed. Eng. 56 (4) (2009) 949–959. [14] C.M. Ionescu, R. De Keyser, J. Sabatier, A. Oustaloup, F. Levron, Low frequency constant-phase behaviour in the respiratory impedance, Biomed. Signal Process. Control 6 (2011) 197–208. [15] C.M. Ionescu, I. Muntean, J.T. Machado, R. De Keyser, M. Abrudean, A theoretical study on modelling the respiratory tract with ladder networks by means of intrinsic fractal geometry, IEEE Trans. Biomed. Eng. 57 (2) (2010) 246–253.
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