Data based Modelling of Expired Airflow Clarifies Chronic

Obstructive Pulmonary Disease

Topalovic Marko

, Vasileios Exadaktylos

, Jean-Marie Aerts

, Thierry Troosters

1,3

, Marc Decramer

Daniel Berckmans

and Wim Janssens

Respiratory Division, University Hospital Leuven, Department of Clinical and Experimental Medicine,

KU Leuven, Leuven, Belgium

Measure, Model & Manage Bioresponses (M3 BIORES), Department of Biosystems, KU Leuven, Leuven, Belgium

Department of Rehabilitation Sciences, Faculty of Kinesiology and Rehabilitation Sciences, KU Leuven, Leuven, Belgium

Keywords: Data Based Modelling, Transfer Function, Chronic Obstructive Pulmonary Disease, Spirometry, Forced

Expiration.

Abstract: One of the major health challenges of the future is Chronic Obstructive Pulmonary Disease (COPD). It is

characterized by airflow limitations, although current diagnosis does not give attention to the flow

measurements. We aimed to develop a data-based model of the decline of the forced expiratory flow.

Moreover, we analysed the relationship of model parameters with COPD presence and its severity. The

data-based model was developed in 474 smoking individuals, who are at risk of having COPD, and have

performed complete pulmonary function tests in order to identify whether the disease is present and at

which stage. The time series of the decline of the flow was parameterised using the poles and steady state

gain (SSG) of a second order transfer function model. These parameters were then linked with the presence

of COPD. Observing SSG, median (IQR) in subjects with COPD was lower 3.9(2.7-5.6) compared to

8.2(7.1-9.3) in subjects without, (p<0.0001). Significant difference was also found when observing median

(IQR) of two poles in subjects without disease were 0.9868(0.9810-0.9892) and 0.9333(0.9010-0.9529),

respectively, compared to 0.9929(0.9901-0.9952) and 0.9082(0.8669-0.9398) in subjects with COPD

(p<0.001 for both poles). Forced exhaled air can be used to expand understanding of the COPD. Moreover,

the suggested parameterisation of the flow decline could be used to access COPD using spirometry.

1 INTRODUCTION

Chronic Obstructive Pulmonary Disease (COPD) is

one of the major health challenges of the next

decades. Currently it is 4th leading cause of death,

while the World Health Organization anticipates that

it will become the 3rd leading cause of death in less

than 20 years from now (Mathers and Loncar 2006;

Murray and Lopez 1997; WHO 2012). COPD is

characterised by airflow limitation that is not fully

reversible. It is usually progressive and associated

with an abnormal inflammatory response of the lung

to noxious particles or gases, most often from

cigarette smoke (Decramer et al. 2012). Up to

almost one quarter of the adults aged 40 years and

older may have mild airflow obstruction, according

to the latest prevalence surveys (Mannino and Buist

2007). One of the challenges in such a disease is to

identify patients at risk for brisk deterioration and to

develop diagnostic tools which are directly clinically

important (Agusti et al. 2010; Miravitlles et al.

2013).

Indications of COPD are production of sputum,

signs of dyspnea, chronic cough or/and a history of

exposure to the tobacco smoke (Rabe et al. 2007).

However, the diagnosis itself is based on measuring

differences in lung volume using a spirometer, as

most common signs of COPD and patient history

cannot accurately reflect COPD presence. Current

diagnosis is simple and inexpensive to perform, but

also lately debatable due to ability to overdiagnose

or underdiagnose (Garcia-Rio et al. 2011). Various

approaches have been developed to diagnose and

characterize COPD, either by measuring volatile

organic compounds in the exhaled air (Fens et al.

2009; Phillips et al. 2012), or by looking into

Marko T., Exadaktylos V., Aerts J., Troosters T., Decramer M., Berckmans D. and Janssens W..

Data based Modelling of Expired Airﬂow Clariﬁes Chronic Obstructive Pulmonary Disease.

DOI: 10.5220/0004735000050012

In Proceedings of the International Conference on Bio-inspired Systems and Signal Processing (BIOSIGNALS-2014), pages 5-12

ISBN: 978-989-758-011-6

 2014 SCITEPRESS (Science and Technology Publications, Lda.)

computed tomography images (Bodduluri et al.

2013; Sorensen et al. 2012), or even by applying

forced oscillation technique to stimulate respiratory

system (Amaral et al. 2012). However, none of the

techniques entered clinical practice, due to their

complexity, costly undertaking or unsatisfactory

results.

Surprisingly, mathematical data-based modelling

was never performed when it comes to revealing

background of COPD. Starting from that point and

knowing that COPD, by its definition, is flow

limited (Decramer, Janssens, & Miravitlles 2012;

Dellaca et al. 2004) we hypothesized that modelling

of the flow dynamics during exhalation may offer a

more precise indication of COPD presence. This

should lead to better understanding of the COPD and

additional tool for diagnosis.

In the present study our objective was firstly to

develop a mathematical data-based model for the

decline of the forced expiratory flow. Secondly, to

investigate how the parameters from the model are

linked with COPD presence and its severity.

2 METHODS

2.1 Study Population

This study included data of 474 individuals who had

performed complete pulmonary function testing

(PFT) at cohort entry, including post-bronchodilator

spirometry, body plethysmography and diffusing

capacity. All included subjects were tested between

October 2007 and January 2009 at the University

Hospital of Leuven (Belgium), as described earlier

(Lambrechts et al. 2010; Wauters et al. 2011).

Briefly, participants were all current or former heavy

smokers with at least 15 pack-years and with

minimal age of 50 years. As COPD is smoking

disease per se, restricting our study to only smoking

individuals increased chances to observe more

abnormal pulmonary functions and patients with

higher risk for COPD. Individuals with suspicion or

diagnosis of asthma were excluded, as well as

patients with exacerbations due to COPD within last

6 weeks and patients with other respiratory diseases.

The study was approved by the local ethical

committee of the University Hospital Leuven, (KU

Leuven, Belgium). All patients included in the study

provided informed consent. The study design of the

LEUVEN COPD cohort can be found on

www.clinicaltrials.gov (NCT00858520).

According to the international COPD GOLD

guidelines (Rabe et al. 2007), patients with COPD

were identified when the post-bronchodilator

FEV1/FVC ratio was <0.7, furthermore they were

lined over different severity stages. The population

consisted of 336 patients with diagnosed COPD

comparing to 138 healthy controls. Stratified for

disease severity from mild (GOLD I) to moderate

(GOLD II), severe (GOLD III) and very severe

(GOLD IV), the COPD population was comprised of

77, 101, 97 and 61 patients respectively. Table 1

describes the population characteristics within two

separate groups, revealing typical characteristics for

smoking and demographics of COPD patients

admitted in hospitals.

2.2 Pulmonary Function Tests

All pulmonary function tests were performed with

standardized equipment (Masterlab, Erich Jeager,

Würzburg, Germany) by experienced respiratory

technicians, according to the ATS/ERS guidelines

(Miller et al. 2005). Spirometry data are post-

bronchodilator measures and expressed as percent

predicted of normal reference values (Quanjer et al.

1994).

Table 1: Study population characteristics; Values are

median and IQR; BMI = body mass index; M = male; F =

female; FEV1= forced expiratory volume in one second;

FVC = forced vital capacity; M = male; %pred. = percent

predicted of normal reference values.

Healthy COPD

Patients, N 138 336

Sex, M/F 110/28 260/76

Age, years 60.7(57.3– 64.6) 65.1(59.5– 72.1)

Smoking,

pack yr.

38.0(29.3– 52.0) 45.0(32.6– 60.0)

BMI, kg/m

26.4(24.0– 28.7) 25.0(22– 28)

FEV

, %pred. 104.0(94–112) 53.0(35– 78)

FVC, %pred. 108.0(100–118) 89.0(71– 106)

FEV

/FVC 0.75(0.73– 0.78) 0.47(0.37– 0.62)

2.3 Data based Modelling

To develop our data-based model we used

MATLAB (7.14, The MathWorks, Natick,

Massachusetts) and compatible toolbox for non-

stationary time series analysis, system identification,

signal processing and forecasting – CAPTAIN

toolbox (Taylor et al. 2007). In all individuals the

best expiratory curve (rule of highest sum of FEV1

and FVC (Miller et al. 2005)) within one spirometry

was exported from the Masterlab system at a

sampling rate of 125Hz. By extracting data points it

was possible to reconstruct the best expiratory

BIOSIGNALS2014-InternationalConferenceonBio-inspiredSystemsandSignalProcessing

manoeuvre in MATLAB. To observe the dynamics

of the expiration, only the declining phase of

expiration was analysed. Declining is the area that

starts at peak flow and ends at the end of the

expiration, far right tail (Figure 1).

When starting with data-based modelling, the

appropriate model structure is determined using

objective methods of time series analysis from a

generic model class. The goal is to describe the data

in a parametrically efficient way, but still having

simplicity in the sense of model parameters and

model order. Considering our study and our data,

most appropriate model was a discrete-time transfer

function (TF) model for a single input single output

(SISO) system. The general form of such system is:























ξ



(1)

where y



is the output; u



is the input; ξ



 is additive

noise, assumed to be zero mean; L is the backward

shift operator; A(L) and B(L) are polynomials

defined by the order of the model in the following

form:





1a



L⋯a



(2)





b



b



L⋯b



(3)

where n represents the order of the system: a



, …,



and b



, b



, …, b



are the TF denominator and

numerator parameters, respectively.

Figure 1: Two examples of expiratory manoeuvres; Solid

line represents expiratory flow of an individual with

diagnosed very severe COPD, while dashed line represents

expiratory flow of a healthy individual. Decline is

considered the section when the flow starts dropping from

its maximum back to its minimum, over time.

Once the input-output data are available, TF

parameters (Eq. (2) and (3)) can be identified using

statistical procedures. For the input data, we used

step-down for each model, while output signal was

original measurements obtained from spirometry.

The parameters of a TF model can be estimated

using various methods of identification and

estimation procedures (Ljung L. 1987; Young PC.

1984). In this study the Simplified Refined

Instrumental Variable (SRIV) algorithm was used as

a method for model identification. The advantage of

SRIV lays not only in yielding consistent estimates

of the parameters, but also in exhibiting close to

optimum performance in the model order reduction

context (Figure 2).

Figure 2: Step down (dashed line) used for each model as

input signal; Solid line represents an example of

declination, meaning output signal (different for each

individual). We assumed that the time-series of the output

had a constant value (first 10 data samples) then the drop

started, it was also point for the step-down of the input.

Based on these two signals SRIV estimates TF parameters.

An equally important problem to the parameter

estimation is the identification of the objective

model order which will result in low complexity.

The process of model order identification can be

performed by the use of well-chosen mathematical

measures which indicate the presence of over

parameterization. Often used successful

identification procedure to select the most

appropriate model structure is based on the

minimisation of the Young identification criterion,

(YIC) (Young 1981) (Eq. (4)).

YICln









ln



σ



p



a









 (4)

where σ



is the sample variance of the model

residuals; σ





is the sample variance of the measured

DatabasedModellingofExpiredAirflowClarifiesChronicObstructivePulmonaryDisease

system output about its mean value; np is the total

number of model parameters; a





is the square of the

i-th element in the parameter vector a; p



is the i-th

diagonal element of the inverse cross product matrix

P(N); σ



p



can be considered as an approximate

estimate of the variance of the estimated uncertainty

on the i-th parameter estimate.

YIC is a heuristic statistical criterion which

consists of two terms, as shown in Eq. (4). The first

term provides a normalised measure of how well the

model fits the original data: the smaller the variance

of the model residuals, in relation to the variance of

the measured output, the smaller this term becomes.

The second term is a normalised measure of how

well the model parameter estimates are defined. This

term tends to become bigger when the model is

over-parameterised and the parameter estimates are

poorly defined. Consequently, the best model should

minimise the YIC and provide a good compromise

between goodness of fit and parametric efficiency.

Finally, upon passing all listed steps, derivation

of additional parameters which describe exhaled

airflow was feasible. Firstly, using an individual TF

for each subject, we were able to derive poles of the

model. These poles were direct representatives of

the dynamics of the observed model. Secondly, the

steady-state gain (SSG) of the model is also derived.

SSG is the ratio of the output and the input of the

model in steady state, and it is obtained by:

SSG

∆

∆u



∑









1

∑









(5)

3 RESULTS

Using the already explained YIC, we discovered that

the most appropriate model would be a second-order

model. Looking into complete dataset, second-order

model explains data with a YIC of -14.5 (-15.7 – -

13.1) and R

of 0.997 (0.994 – 0.998) (values are

median and IQR). Confirmation of the good model

order identification is presented in Figure 3, where

the original output signal with the simulated one is

compared using the estimated parameters from

second-order model.

In total, analysis was performed employing two

poles (coming from second-order model) and SSG

of the model from 423 individuals. From the

included 474 individuals, 51 (=10.8%) had to be

excluded, where 32 (=6.8%) due to missing data

from the PFT and 19 (=4%) due to model instability.

More detailed investigation of poles of

the model, meaning the dynamics of the airflow

Figure 3: No difference between the original (marked with

x) and the simulated (solid line) output signal is noticed

= 0.999, YIC = -17.6091) when using second-order

model.

exhalation, resulted in clear difference when

comparing subjects with and without COPD (see

figure 4). Certainly, first pole was higher when

COPD was present, indicating that the system starts

faster when disease occurs. Median (IQR) poles in

subjects without disease were 0.9868 (0.9810-

0.9892) and 0.9333 (0.9010-0.9529), respectively,

compared to 0.9929 (0.9901-0.9952) and 0.9082

(0.8669-0.9398) in subjects with COPD (p<0.0001

for first pole and p<0.001 for second pole).

Stratifying for disease severity, same shift in poles

with disease progression was noticed (Figure 5).

This pointed that the dynamics of the system

become faster with higher severity. Median poles

were 0.9895 and 0.9346 for GOLD 1, 0.9916 and

0.9160 for GOLD 2, 0.9946 and 0.9009 for GOLD 3

and finally for GOLD 4 0.9959 and 0.8615.

When focusing the analysis on the SSG of the

model, similar conclusions as the ones with poles

can be made. Median (IQR) SSG in subjects with

COPD was significantly lower 3.9 (2.7-5.6)

compared to 8.2 (7.1-9.3) in subjects without COPD,

(p<0.0001). When disintegrating over severity of

COPD, SSG decreased significantly (p<0.0001) with

each GOLD stage: 6.8 (5.7-7.8), 5.0 (3.9-5.7), 3.1

(2.6-3.7) and 2.3 (1.7-2.8), respectively (Figure 6).

This is manifested due to lower flow change that

occurs when lungs are obstructive compared to

healthy lungs.

BIOSIGNALS2014-InternationalConferenceonBio-inspiredSystemsandSignalProcessing

Figure 4: Pole distribution within two observed groups, with centroids pointing the median value of each group.

Figure 5: Distribution of poles when stratified for COPD severity (GOLD stages). Dynamics are faster with increase of

severity. Centroids indicate median values of each GOLD stage. We see movement of centroids from left to right, in the

order: from no COPD over each growing GOLD stage.

DatabasedModellingofExpiredAirflowClarifiesChronicObstructivePulmonaryDisease

Figure 6: Decrease of SSG with each GOLD stage.

4 CONCLUSIONS

Our study demonstrates that chronic obstructive

pulmonary disease observed at forced expiration can

be described by a second order data based model,

whereas model parameters relate very well with the

presence and severity of COPD. Our method

confirms that COPD is indeed a flow limited

disease, and in certain way raise a question whether

future diagnostic for COPD should go back to its

basis, its definition, and take flow values at

examination.

To the best of our knowledge, our study is the

first to validate the concept of COPD-associated

airflow dynamics in larger group of individuals

comprising COPD patients of all severity stages, as

well as smoking controls. In our population, we

found that poles and steady state gain match well

with severity of COPD. Interestingly, the estimated

model resulted in significantly lower steady state

gain within each severity stage. Moreover steady

state gain was significantly different comparing to

the healthy cases. This undoubtedly confirms that

obstructive lungs are having much more difficulties

to exhale flow and therefore, exhale it in much lower

speed.

The concept we are introducing opens new

opportunities for research in the field of respiratory

mechanism and respiratory diseases. In general, by

using airflow dynamics, with this study we provided

additional explanation of COPD behaviour. We see

that they anticipate that the faster dynamics of the

system are probability to notice presence of COPD

will increase. Moreover, with increase of dynamics,

the severity stages of COPD are also increasing.

This probably means that bigger obstruction of lungs

cause decreased exhalation of air which results in

faster emptying of the lungs (faster dynamics of the

exhalation). Various reasons influence such

occurrence, firstly it is common to observe airway

narrowing or airway collapse to cause suddenly

diminished airflow (Healy et al. 1984). Furthermore,

in COPD, the greatest reduction in air flow occurs

during expiration, as the pressure in the chest tends

to compress rather than expand the airways

(Koulouris and Hardavella 2011). One would

assume that loss of lung tissue elasticity, typical for

emphysematous type of COPD, plays additional role

in accelerating exhalation dynamics, as it might be

the case that lungs get faster its limits while exhaling

(Papandrinopoulou et al. 2012).

When comparing with the other alternative

approaches, advantage is that parameters obtained

from model-based method can have physiological

validity. Further, when used with routine spirometry

during patient examination, this method is de facto

simplest, fastest and cheapest to perform.

Additional strength of this study is the fact that

observing dynamics of the flow decay represents

same approach that many researchers had performed

in the past, but based only on a visual basis of

typical patterns (Bass 1973; Jayamanne et al. 1980).

Today routinely, clinicians are capable to presume

presence of Chronic Obstructive Pulmonary Disease,

on the basis of visual assessment of flow decay,

whereas with this study we offer more precise and

automated way of inspection. Furthermore, we

believe that the concept which we are introducing, is

easy to understand and linked to physiological

behaviour of the lungs. Moreover, we believe that

extra value of this study comes from the study

cohort itself. All patients are heavy smokers older

than 50 years, meaning that they are all labelled as

having risk of COPD, consequently inducing bigger

challenge to distinguish between diseased and not

diseased.

Finally, our method failed to provide valid

measurements in 4% of the cases. This occurrence is

inevitable, as we tried to automatize process where

data selection and estimation algorithm are not

always the optimal ones. Certainly, this could be

avoided in most of the cases, if ensuring that

exhalation ends with plateau (having stable ending).

Taken together, our data provide strong evidence

that dynamics of the forced exhaled air can be used

to get elevated understanding of the chronic

obstructive pulmonary disease. Moreover, if

characterized like in our model, flow decline can be

used to access Chronic Obstructive Pulmonary

Disease by spirometry.

BIOSIGNALS2014-InternationalConferenceonBio-inspiredSystemsandSignalProcessing

ACKNOWLEDGEMENTS

The authors would like to thank Geert Celis and co-

workers (Respiratory Division, University Hospital

Leuven, Belgium) for helping in collection of patient

data and their technical support in extracting data

from the Masterlab.

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