a fan-based, low-frequent, forced oscillation technique apparatus

9
IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 63, NO. 3, MARCH 2014 603 A Fan-Based, Low-Frequent, Forced Oscillation Technique Apparatus Hannes Maes, Member, IEEE, Gerd Vandersteen, Senior Member, IEEE, Michael Muehlebach, and Clara Ionescu, Member, IEEE Abstract—The forced oscillation technique (FOT) is a non- invasive method to characterize the respiratory impedance (Z). Z is defined as the frequency-dependent ratio between pressure and flow. The FOT determines Z by superimposing small amplitude (in the order of 0.1 kPa) pressure oscillations on the normal breathing. It has been shown that a lot of useful information is contained in the frequency range of spontaneous breathing (0.1–1 Hz). In the current state-of-the-art methods, patient cooperation by means of voluntary apnea or mechanical ventilation is required to obtain the respiratory impedance at low frequencies. This article proposes a fan-based setup driven by a microcontroller. The setup allows to excite the respiratory mechanics at frequencies around the spontaneous breathing rate without requiring any patient effort. However, the (nonlinear) dynamic behavior of the setup and the pressure perturbations introduced by the subjects breathing jeopardize the spectral analysis of the measurement. Therefore, a combination of feedforward compensation of the excitation signal and linear feedback control are applied and discussed using measurements on a prototype device. A high-quality pressure signal is obtained, which makes it possible to obtain the respiratory impedance at low frequencies in a clinically practical way. Index Terms— Closed loop systems, control design, feedback, feedforward systems, medical diagnosis, modeling, nonlinear distortion, signal design, system identification. I. I NTRODUCTION T HE forced oscillation technique (FOT) is a widely studied noninvasive technique for lung function testing. The main idea of FOT is to study the dynamic mechanical properties of the respiratory system by analyzing its response to an externally applied excitation. In contrast to spirometric tests, where maximal inspiratory and expiratory efforts are required from the subject, the method of forced oscillation requires minimal patient cooperation. This makes the technique more appropriate for young children and older adults. The most common application of FOT is the measurement of the input impedance of the respiratory system, i.e., the complex ratio Manuscript received May 14, 2013; revised August 29, 2013; accepted August 30, 2013. Date of publication October 9, 2013; date of current version February 5, 2014. This work was supported in part by the Scientific Research, in part by the Flemish Government, and in part by the Belgian Federal Government under Grant IUAP VI/4. The Associate Editor coordinating the review process was Dr. Domenico Grimaldi. H. Maes, G. Vandersteen, and M. Muehlebach are with the Vrije Univer- siteit Brussel, Department of Electronics, Brussels 1050, Belgium (e-mail: [email protected]). C. Ionescu is with the Department of Electrical engineering, Systems and Automation, Ghent University, Gent 9000, Belgium. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIM.2013.2282188 of transrespiratory pressure to airflow at the airway open- ing as a function of frequency. These measurements yield frequency-dependent impedance curves, one representing the impedance’s real part, known as the respiratory resistance, and the other representing the impedance’s imaginary part, known as the respiratory reactance. The magnitude and shape of both impedance curves over low frequencies (0.1–10 Hz) can be a sensitive indicator for the changes of the lungs mechanical properties and can therefore be used for the monitoring of lung diseases. In the last two decades, many applications of FOT under various conditions have been studied. They can be divided into two main groups based on the frequency range in which the respiratory impedance is determined. On the one hand, the respiratory impedance is deter- mined outside the frequency range of spontaneous breathing (0.1–1 Hz). The respiratory impedance can be obtained at frequencies above (2–32 Hz) [1]–[5] or below the breathing frequency (0.01–0.1 Hz) [6]. In the first case, the pressure oscillations are generated by use of a piston or loudspeaker while in the latter a body chamber is used. In both cases, the effect of the breathing on the pressure and flow signals is considered as residual out-of-band noise and can easily be filtered out. This has the main advantage that the patient can breathe normally and no special cooperation of the patient is required. On the other hand, a lot of research has been done on measuring the respiratory impedance at frequency bands that partly or completely overlap with the frequency band of spontaneous breathing. In several applications, low-frequency measurements of the respiratory impedance are performed on patients who are maintained on artificial mechanical venti- lation [7]–[11]. The respiratory impedance is then assessed during end-expiratory pauses to avoid breathing disturbances. For these purposes, servo-controllers are often used in com- bination with pistons or loudspeakers to generate the desired pressure oscillations [7]–[9]. Apart from mechanical ventilation, other specific circum- stances are created to perform a measurement of the respira- tory impedance at low frequencies without the introduction of breathing disturbances. In [12], the respiratory impedance was measured at frequencies between 0.25 and 5 Hz on subjects familiar with lung function measurements. The subjects were in sitting position during voluntary apnea while they had to remain relaxed with open glottis for 32 s. This method required considerable training from the subjects, which makes it impractical for routine use in patients. In [13], modeling of 0018-9456 © 2013 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

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IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 63, NO. 3, MARCH 2014 603

A Fan-Based, Low-Frequent, Forced OscillationTechnique Apparatus

Hannes Maes, Member, IEEE, Gerd Vandersteen, Senior Member, IEEE, Michael Muehlebach,and Clara Ionescu, Member, IEEE

Abstract— The forced oscillation technique (FOT) is a non-invasive method to characterize the respiratory impedance (Z).Z is defined as the frequency-dependent ratio between pressureand flow. The FOT determines Z by superimposing smallamplitude (in the order of 0.1 kPa) pressure oscillations onthe normal breathing. It has been shown that a lot of usefulinformation is contained in the frequency range of spontaneousbreathing (0.1–1 Hz). In the current state-of-the-art methods,patient cooperation by means of voluntary apnea or mechanicalventilation is required to obtain the respiratory impedanceat low frequencies. This article proposes a fan-based setupdriven by a microcontroller. The setup allows to excite therespiratory mechanics at frequencies around the spontaneousbreathing rate without requiring any patient effort. However,the (nonlinear) dynamic behavior of the setup and the pressureperturbations introduced by the subjects breathing jeopardize thespectral analysis of the measurement. Therefore, a combinationof feedforward compensation of the excitation signal and linearfeedback control are applied and discussed using measurementson a prototype device. A high-quality pressure signal is obtained,which makes it possible to obtain the respiratory impedance atlow frequencies in a clinically practical way.

Index Terms— Closed loop systems, control design, feedback,feedforward systems, medical diagnosis, modeling, nonlineardistortion, signal design, system identification.

I. INTRODUCTION

THE forced oscillation technique (FOT) is a widely studiednoninvasive technique for lung function testing. The main

idea of FOT is to study the dynamic mechanical propertiesof the respiratory system by analyzing its response to anexternally applied excitation. In contrast to spirometric tests,where maximal inspiratory and expiratory efforts are requiredfrom the subject, the method of forced oscillation requiresminimal patient cooperation. This makes the technique moreappropriate for young children and older adults. The mostcommon application of FOT is the measurement of the inputimpedance of the respiratory system, i.e., the complex ratio

Manuscript received May 14, 2013; revised August 29, 2013; acceptedAugust 30, 2013. Date of publication October 9, 2013; date of current versionFebruary 5, 2014. This work was supported in part by the Scientific Research,in part by the Flemish Government, and in part by the Belgian FederalGovernment under Grant IUAP VI/4. The Associate Editor coordinating thereview process was Dr. Domenico Grimaldi.

H. Maes, G. Vandersteen, and M. Muehlebach are with the Vrije Univer-siteit Brussel, Department of Electronics, Brussels 1050, Belgium (e-mail:[email protected]).

C. Ionescu is with the Department of Electrical engineering, Systems andAutomation, Ghent University, Gent 9000, Belgium.

Color versions of one or more of the figures in this paper are availableonline at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TIM.2013.2282188

of transrespiratory pressure to airflow at the airway open-ing as a function of frequency. These measurements yieldfrequency-dependent impedance curves, one representing theimpedance’s real part, known as the respiratory resistance, andthe other representing the impedance’s imaginary part, knownas the respiratory reactance. The magnitude and shape of bothimpedance curves over low frequencies (0.1–10 Hz) can bea sensitive indicator for the changes of the lungs mechanicalproperties and can therefore be used for the monitoring of lungdiseases.

In the last two decades, many applications of FOT undervarious conditions have been studied. They can be dividedinto two main groups based on the frequency range in whichthe respiratory impedance is determined.

On the one hand, the respiratory impedance is deter-mined outside the frequency range of spontaneous breathing(0.1–1 Hz). The respiratory impedance can be obtained atfrequencies above (2–32 Hz) [1]–[5] or below the breathingfrequency (0.01–0.1 Hz) [6]. In the first case, the pressureoscillations are generated by use of a piston or loudspeakerwhile in the latter a body chamber is used. In both cases,the effect of the breathing on the pressure and flow signalsis considered as residual out-of-band noise and can easily befiltered out. This has the main advantage that the patient canbreathe normally and no special cooperation of the patient isrequired.

On the other hand, a lot of research has been done onmeasuring the respiratory impedance at frequency bands thatpartly or completely overlap with the frequency band ofspontaneous breathing. In several applications, low-frequencymeasurements of the respiratory impedance are performed onpatients who are maintained on artificial mechanical venti-lation [7]–[11]. The respiratory impedance is then assessedduring end-expiratory pauses to avoid breathing disturbances.For these purposes, servo-controllers are often used in com-bination with pistons or loudspeakers to generate the desiredpressure oscillations [7]–[9].

Apart from mechanical ventilation, other specific circum-stances are created to perform a measurement of the respira-tory impedance at low frequencies without the introduction ofbreathing disturbances. In [12], the respiratory impedance wasmeasured at frequencies between 0.25 and 5 Hz on subjectsfamiliar with lung function measurements. The subjects werein sitting position during voluntary apnea while they hadto remain relaxed with open glottis for 32 s. This methodrequired considerable training from the subjects, which makesit impractical for routine use in patients. In [13], modeling of

0018-9456 © 2013 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

604 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 63, NO. 3, MARCH 2014

the low-frequent respiratory impedance in dogs was performedusing oscillations between 0.125 and 5 Hz generated by aloudspeaker. However, to obtain the required pressure and flowsignals, the dogs needed to be anesthetized and a metal tubewas inserted into the trachea. In [14], low-frequent respiratorymechanics were obtained from sedated infants by exploitingan apneic phase produced by triggering an inflation reflex.

In this paper, we present a FOT device based on the useof fans and a microcontroller that is capable of measuring therespiratory impedance in the low-frequency range (0.1–5 Hz)in a clinically practical way. Thus, we mean that no voluntaryapnea or mechanical ventilation is required to perform themeasurement. The patient can continue tidal breathing anda pressure oscillation is superimposed on the breathing. Toour knowledge, no FOT device has been developed thatapplies a high-quality pressure signal between 0.1 and 5 Hzduring spontaneous breathing without artificially ventilatingthe patient.

The determination of the respiratory impedance itself isbeyond the scope of this paper. To determine the respiratoryimpedance, the ratio of the flow and pressure signal needs tobe obtained as a function of frequency. However, since the flowsignal is cyclically varying over time because of the patientsbreathing, advanced processing techniques are required toobtain a good estimate of the respiratory impedance.

This paper focuses mainly on the operation of the deviceand on the closed-loop design developed to generate a desiredpressure oscillation during spontaneous breathing. The pres-sure oscillations are generated by means of two fans which aresteered to compensate for: 1) the dynamics and the nonlineardistortions induced by the setup itself and 2) the disturbancesintroduced by the subjects breathing.

First, the dynamics and the nonlinear distortions causedby the setup are compensated using a feedforward scheme.Second, a linear feedback controller is used to control thepressure to suppress the disturbances introduced by the sub-jects breathing and the residual errors that are not compensatedby the feedforward scheme.

The article is structured as follows. Section II describesthe hardware of the measurement device. In Section III, thetype of excitation signal used for the pressure oscillation isdiscussed. In Section IV, the performance of the measurementdevice in open loop is discussed by means of the static anddynamic behavior. Section V presents the combined feed-forward/feedback strategy to compensate for the distortionsintroduced by both the measurement setup and the breathingof the patient. Finally, Section VI presents the performanceof the final setup, followed by conclusions and remarks inSection VII.

II. EXPERIMENTAL SETUP

The setup consists of two fans, forcing air through apolyvinyl chloride (PVC) tube (Fig. 1). The fans are drivenby a pulse width-modulated (PWM) signal generated by a PIC18F4550 microcontroller. In that way, a pressure signal p(t)is imposed at the mouth of the patient. The pressure p(t) andflow at the mouthpiece q(t) can be obtained using two pressure

Fig. 1. Schematic representation of the experimental setup. The PVC tubehas an inner diameter of 46 mm and a length of 380 mm.

sensors and a pneumotachograph (Hans Rudolph, Inc.), whichis an apparatus to record airflow rates to and from the lungs.Both the inner and outer pressure sensor are used to measurethe differential pressure Y across the pneumotachograph. Theformer is used to measure the absolute pressure U on the innerside of the pneumotachograph. It is assumed that the pressureon the inner side of the pneumotachograph is the same as in thePVC tube. The excitation pressure signal p(t) is kept belowa peak-to-peak variation of 0.2 kPa at the airway opening asrecommended in [15].

The fans create turbulences [16], which result in increasedmeasurement noise. To reduce these turbulences, the PVC tubeis filled with thin tubes of 3 mm diameter whereas the middlepart of the tube is left empty to preserve a good air supply forthe subject. The measured pressure values are quantized withinthe pressure sensors and transmitted to the microcontrollerover an I2C bus. This is a commonly used synchronous serialbus, developed for data communication between all typesof ICs [17].

III. EXCITATION SIGNAL

The respiratory impedance Z is determined by the pressure(P)-flow (Q) relationship in the frequency domain ω.

Z(ω) = P(ω)

Q(ω)(1)

where P(ω) and Q(ω) are the frequency domain representa-tions of, respectively, p(t) and q(t) obtained using the discreteFourier transform (DFT) [18]. The pressure signal p(t) ischosen as the excitation signal and the flow q(t) is consideredas the response to this excitation.

A first step in measuring Z(ω) consists of choosing anappropriate form for the excitation signal p(t). In this setup,the frequency band of interest starts at 0.1 Hz and can goup to more than 20 Hz. To reduce the measurement time,a broadband signal is preferred over multiple experiments ofa single tone excitation. By using a periodic input signal, theinfluence of measurement noise can be attenuated by averagingover consecutive periods [19], [20]. In the literature, it isshown that random phase multisines are a powerful tool in theidentification of a linear system in the presence of nonlineardistortions [18]–[24]. Therefore, in this setup, the patientslungs are excited with a random phase multisine pressuresignal.

MAES et al.: FAN-BASED, LOW-FREQUENT, FOT APPARATUS 605

A random phase multisine is described by

x(t) = 1√N

N∑

k=1

Uk sin(2πk f0t + ϕk) (2)

where f0 is the frequency resolution of the signal, N ∈ N

is the number of frequency components, and Uk is theamplitude spectrum of the kth frequency line. The phases ϕk

are drawn from an independent uniformly distributed randomprocess on [0, 2π).

Random phase multisine excitations have the followinguseful properties [18].

1) The power spectrum can be defined by the user.2) The nonlinear distortions and the additive noise levels

can be separated and estimated by measuring consecu-tive periods of the periodic multisine signal.

3) The periodicity of the signals results in the absence ofspectral leakage.

4) The even and odd nonlinear contributions can be sep-arated by carefully selecting the excited frequencylines [18].

All these points are explained more thoroughly inSection IV-B.

IV. PERFORMANCE OF THE MEASUREMENT SYSTEM

The goal of the measurement setup is to excite the patientwith a random phase multisine with a well-defined powerspectrum. This can only be achieved if the performance ofthe measurement system in open loop operation is known.The measurement system is defined as the combination of themicrocontroller and the fans that generate the pressure oscil-lations. The input of this measurement system is the discretesignal generated by the microcontroller that corresponds to thePWM values that drive the fans. The output is the continuoustime signal measured by the pressure sensors and sampledusing an analog-to-digital converter (ADC).

In this section, the system is characterized to enable thedesign of a combined feedforward and feedback compensation.First, the nonlinear behavior of the system is evaluated usingstatic pressure measurements (Section IV-A). Then, a nonpara-metric (Section IV-B) and a parametric model (Section IV-C)are extracted using dynamic pressure measurements.

All the measurements in this section are done withoutfeedforward or feedback compensation and with a closedmouthpiece to obtain an airflow q(t) equal to zero.

A. Static Behavior

The static behavior is obtained by using static pressuremeasurements. A PWM signal generated by a microcontrollerand operating anti symmetrically around a duty cycle of 1/2 isused to drive the fans. Thus, if the pushing fan is running at aduty cycle of 1/2 + x , the pulling fan operates at 1/2 − x . Tomeasure the static behavior of the fans, several static pressuremeasurements are performed for changing values of x .

The static pressure measurements show that the measure-ment system has a very linear behavior (Fig. 2). The standarddeviation of the difference between the least-squares fit and

Fig. 2. Static pressure measurements and the least-squares fit ( ).

the measured points has a value of 11.4 Pa (about 1.3 % oftotal range). The small nonlinear deviation will be suppressedusing nonlinear feedforward compensation (Section V-A) andfeedback compensation (Section V-B).

B. Linear Dynamic Behavior

A good feedforward/feedback compensation can only berealized if the linear dynamics of the measurement systemare well known. To measure a nonparametric model of thefrequency response of the system, an odd random phasemultisine with a random harmonic grid [Uk = 0 for k evenand for a set of randomly chosen but known k odd in (2)][18], [20], [25] is applied to the fans. The even nonlinearitieswill then cause a response on even frequency lines only,whereas odd nonlinearities can be detected at the nonexcitedodd frequency lines.

The amplitude developed at the airway opening is recom-mended to have a maximal peak-to-peak pressure variation of0.2 kPa [15]. To obtain a high signal-to-noise ratio (SNR) atthe excited frequencies, we want the magnitude of the powerspectrum of the pressure oscillation to be as high as possibleat these frequencies. The power of the pressure signal canbe maximized while holding the maximal peak-to-peak valuewithin the allowed range by optimizing the phases at eachexcited frequency line [7]. In this paper, this is achieved usingthe crest factor of the signal which is defined as

CF(u) = |upeak|urms

(3)

where upeak and urms are, respectively, the peak and the rootmean square values of the signal u [18], [26]. The crest factoris an accurate indication of how extreme the peaks are in asignal. A crest factor of 1 means no peaks (dc signal) while ahigher crest factor indicates higher peaks. In this measurementsetup, the crest factor of the multisines is minimized asdescribed in [18] and [26] by the use of the FDIDENT Toolboxof MATLAB [27].

The nonparametric characterization of the measurement sys-tem is performed by applying two multisines. Both multisinescontain the same power but excite different frequency bands.First, a frequency band from 0.1–20 Hz is excited to obtain agood idea of the dynamics of the system [Fig. 3(a)]. However,in the real measurements we use a frequency band from

606 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 63, NO. 3, MARCH 2014

(a)

(b)

Fig. 3. Power spectrum of the measured pressure and the input signalfor: (a) an excitation band of 0.1–20 Hz and (b) an excitation band of0.1–5 Hz. : the input signal. The amplitude of the input signal is higherfor the excitation band of 0.1–5 Hz because the same amount of power as theexcitation band of 0.1–20 Hz is injected but needs to be spread over fewerfrequencies. The power spectrum of the measured pressure signal is shown.

: the excited frequency lines. : the even nonlinear distortions. : the oddnonlinear distortions. : the sample variance over the periods. A higher SNRis obtained for the band of 0.1−5 Hz but a higher level of nonlinear distortionappears.

0.1−5 Hz to obtain a higher SNR at the excited frequency linesfor the same power of the excitation signal [Fig. 3(b)]. As isshown, the nonlinear behavior of the measurement system andthe power that can be induced at low frequencies (0.1–1 Hz)depends on which frequency band is used.

Seven consecutive periods of the multisine were measured.It was verified experimentally that the transients only took afew seconds. Since the frequency resolution is 0.1 Hz, everyperiod takes 10 s so that the transients could be eliminated byremoving the first period. The measured power spectrum of thepressure (Fig. 3) clearly shows the dynamic behavior of thesystem on the excited lines. We can see that an uncompensatedsystem has a 3 dB bandwidth of approximately 0.4 Hz.Also a higher SNR is obtained in the low-frequency range(0.1–1 Hz) when a smaller frequency band is excited. Thisis the main motivation why a frequency band of 0.1–5 Hz ischosen for the excitation signal. Furthermore, we can see that ahigher level of nonlinear distortions appears when more poweris injected in the lower frequencies. This nonlinear behaviorwill be compensated using the feedforward compensation(Section V-A).

C. Parametric Model

Apart from the nonparametric model, a parametric modelof the frequency response function (FRF) of the measurement

TABLE I

LIST OF FIVE MODEL STRUCTURES WITH THEIR ASSOCIATED VALUES

FOR VML, MDL, AND AIC. THE 0/2 MODEL HAS A HIGHER VALUE FOR

VML THAN THE 1/3 MODEL BUT LOWER VALUES FOR MDL AND AIC.

THIS INDICATES THAT THE 0/2 MODEL IS THE OPTIMAL MODEL IN

TERMS OF MODEL COMPLEXITY AND VARIABILITY

system is required for the feedforward/feedback compensation.This FRF is defined as the ratio of the measured pressuresignal to the digital signal generated in the microcontroller.The parametric s-domain model is extracted by minimizingthe maximum likelihood cost function

VML(θ) =∑

k

|G(k) − G(k, θ)|2σ 2

G(k)(4)

with respect to the parameter set θ [18], [28]. In (4), G(k)represents the measured FRF with k the frequency line andG(k, θ) a parametric model that approximates G(k). σ 2

G(k)represents the sample variance and is approximated by theestimated variability introduced by the nonlinear distortionsand the additive noise [18]. Different model complexities areanalyzed. The number of poles and zeros in the model isobtained using a computer aided model scan performed bythe FDIDENT Toolbox of MATLAB [27]. In this model scan,two methods called the Akaike information criterion (AIC)and minimum description length (MDL) are used to find theoptimal model complexity [18] (Table I). These methods aimat finding the optimal balance between model complexity andmodel variability. A smaller maximum likelihood cost functioncould be obtained by using a model with higher complexity,however the extra parameters no longer reduce the systematicerrors but follow the actual noise realization on the data. Usingthese methods, a second-order model with no zeros, two stablepoles, and a time delay is chosen. The time delay is addedto the model to account for the time needed to push the airthrough the PVC tube from the generator (fans) to the placewhere the measurement data are acquired (pressure sensors).

The model can be represented as

G(s) = a0

(s − 2π · f p1)(s − 2π · f p2)e−sτ (5)

where s is the Laplace variable. The two poles found arelocated at the frequencies f p1 = 0.39 Hz and f p2 = 16.8 Hz,the delay τ equals 6.4 ms, and the gain a0 equals 2.1. Theobtained cost function VML(θ) is significantly larger than thevalue of the sample variance, which means that model errorsare still present [18]. However, when we take a look at theobtained model (Fig. 4) and its residuals, we see that the modelis sufficiently accurate for our application.

MAES et al.: FAN-BASED, LOW-FREQUENT, FOT APPARATUS 607

Fig. 4. Quality of the parametric model with the obtained model G(k, θ) (bluesolid line), the measured FRF G(k) (red solid line), the estimated variabilityσ 2

G (k) (green dashed line), and the residuals of the model ( ). The level ofthe residuals is approximately equal to the sample variance.

Fig. 5. Measurement setup. G(s): the continuous time parametric model ofthe measurement system. This measurement system is defined as the ratio ofthe generated pressure signal, which is sampled by the ADC of the pressuresensors, to the input signal of the PWM that drives the fans. The pressuresignal Pmeas(z) is sampled and compared with the wanted pressure signalP0(z). A feedforward compensation F F(z) and feedback controller C(z) areused to compensate the dynamics, the nonlinear distortions and the breathingdisturbances. P0(z), F F(z), and C(z) are calculated in the microcontrollerand are therefore represented in the discrete domain.

V. COMPENSATION OF DYNAMIC BEHAVIOR AND

BREATHING DISTURBANCES

Two complementary methods are used to compensate thelinear dynamic behavior of the measurement system to obtaina predefined power spectrum and to suppress the nonlin-ear distortions generated by the measurement system andthe disturbances introduced by the breathing of the patient.First, a feedforward compensation of the excitation signal isproposed to suppress the nonlinear distortions and to compen-sate the linear dynamic behavior of the measurement system(Section V-A). Second, the residual dynamic nonlinear dis-tortions (after the feedforward compensation) and the distur-bances resulting from the subjects breathing are suppressedby a feedback control loop (Section V-B). The measurementsystem with feedforward/feedback compensation is visualizedin Fig. 5.

A. Feedforward Compensation

The feedforward compensation of the measurement systemhas two goals. First, a feedforward signal FF is used as inputsignal so that the generated pressure signal has a flat powerspectrum with high amplitude up to frequencies higher thanthe 3 dB bandwidth of the fans (0.4 Hz). Second, the nonlinear

distortions are suppressed using an iterative scheme in whichFF is changed recursively.

The goal is to excite the patient with a random phasemultisine with a flat power spectrum and a high SNR inthe frequency band 0.1–5 Hz. Using a flat power spectrum,a constant SNR can be obtained over the whole frequencyband, which is beneficial for later estimation of the respiratoryimpedance [18].

First, the linear dynamics of the measurement system arecompensated using a feedforward signal FF as input for themeasurement system. The spectrum of the wanted pressuresignal is represented by P0(k) with k the frequency line.The measurement system is represented by the parametricmodel G(k, θ) as obtained in Section IV-C. The feedforwardsignal FF to compensate for the linear dynamics of the systemG(k, θ) is then computed as

F F(kExc) = G−1(kExc, θ)P0(kExc) (6)

at the excited frequency lines kExc. If a random phase multisinewith a flat power spectrum and a high magnitude is chosen asthe wanted pressure signal P0(k), the input signal FF(k) putsthe fans into saturation. This is due to the fact that FF(k) needsto inject an increasing amount of power at frequencies above0.4 Hz to compensate for the dynamics of the fans. To avoidsaturation of the fans we have chosen to change P0(k) to aflat random phase multisine filtered by a 3rd order butterworthfilter with a cutoff frequency at 1.2 Hz (Fig. 6). This increasesthe bandwidth of the generated pressure signal from 0.4 Hz(Section IV-B) to 1.2 Hz while a high magnitude is obtainedin the frequency band of spontaneous breathing. As illustratedin Fig. 6, a SNR of about 50 dB is obtained. However, bylooking at the generated pressure at the nonexcited frequencylines, it is clear that the level of nonlinear distortions is morethan 10 dB above the noise level.

Therefore, the second step consists in compensating forthese nonlinear distortions by adapting the feedforward signalFF at the nonexcited lines. This is done using the followingiterative scheme [19], [29], [30].

1) A feedforward signal F F0(kExc) calculated as previouslymentioned and only containing power at the excitedfrequency lines kExc is used as an input for the fansof the measurement system.

2) An iteration n is then executed by measuring the gen-erated pressure signal Pn and updating the feedforwardsignal FF at the nonexcited frequency lines by subtract-ing the generated nonlinear distortions.

F Fn+1(knExc) = F Fn(knExc)−G−1(knExc, θ)Pn(knExc)

(7)

where knExc are the in-band nonexcited lines. The out-of-band nonexcited lines are not updated to preventovercompensation since G−1(knExc, θ) goes to infinityfor increasing values of knExc.

3) The level of the nonlinear distortions is compared to thenoise level. Step 2 is repeated until the level of nonlineardistortions is not significantly decreasing. The newestfeedforward signal F Fn+1 is then saved for furtheruse (Fig. 5).

608 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 63, NO. 3, MARCH 2014

Fig. 6. Amplitude spectrum of generated pressure signal after compensationof the linear dynamics of the measurement system by use of the feedforwardsignal FF. : the wanted signal P0(k). : the generated pressure on theexcited lines. : the generated pressure on the in-band nonexcited frequencylines. : the sample variance.

After seven iterations, this yields the results shown in Fig. 7.The nonlinear distortions are strongly suppressed and theirgenerated power is no longer significantly higher than thenoise level. This is a very satisfying result for the open loopoperation of the measurement system without any externalbreathing disturbances.

However, in the practical use of the measurement setup,the generated pressure signal will constantly be perturbed bythe breathing of the patient. A measurement on a patientintroducing breathing disturbances (Fig. 8) clearly shows thatfeedforward compensation is not sufficient to obtain a usablepressure signal. By only applying feedforward compensation,the breathing disturbances are not suppressed and stronglydeteriorate the quality of the pressure signal. This showsthat, without applying feedback compensation, the pressuresignal is useless as an input signal for the eventual impedanceestimation. To suppress unknown disturbances introduced bythe breathing of the patient, feedback compensation is addedto the measurement system.

B. Feedback Compensation

Feedback control is applied to suppress the disturbancesintroduced by the patients breathing and the residual dynamicnonlinear distortions. In the setup, a discrete-time digitalcontroller C(z) is implemented in the microcontroller buthere we will elaborate the design of the feedback con-troller by use of a continuous time representation to reducecomplexity.

Since the plant is approximated well by a second-ordersystem (Section IV-C), a PI-controller is proposed [31].

C(s) = k p(1 + 1

Ti s)

where kp is the proportional gain and Ti is the time constantof the integrator. To enhance the bandwidth of the open-looptransfer function

L(s) = C(s)G(s)

Fig. 7. Amplitude spectrum of generated pressure signal after seveniterations of the feedforward compensation. : the wanted signal P0(k). :the generated pressure on the excited lines. : the generated pressure onthe in-band nonexcited frequency lines. : the sample variance. The level ofthe generated nonlinear distortions has decreased strongly. The power of thenonlinear distortions is only a few db higher than the noise level.

a dominant pole compensation is applied by choosingTi = 1

2π ·| f p1| = 0.4 s, where f p1 is the frequencyof the dominant pole of the measurement system(Section IV-C).

To achieve a good disturbance rejection, the gain kp ismaximized. This maximization is based on the open-looptransfer function L(s) and the sensitivity function

S(s) = 1

1 + G(s)C(s)

which is a measure of how the controller suppresses externaldisturbances, in this case the breathing of the patient [32]. Thefollowing criteria are taken into account to find an optimalvalue for k p [33].

1) To assure a large gain (±20 dB) of L(s) at the frequencyof the breathing disturbances, the crossover frequency fc

of L(s) should be about one decade higher than thefrequency of the breathing disturbances fbr. Since forexample asthmatic patients can have a breathing rate offbr = 1 Hz, an ideal value of kp would enforce fc = 10·fbr = 10 Hz.

2) A sufficiently large phase margin (PM > 60◦) of L(s)is required to minimize overshoot of the closed looptransfer function T (s) = L(s)

1 + L(s) [32].3) A good disturbance rejection is guaranteed up to the

closed loop bandwidth fB , which is defined as thefrequency at which |S| = −3 dB [32].

4) The maximum peak of the sensitivity Ms = max|S|should stay below 6 dB [32].

Both L(s) and S(s) for the optimal kp are depicted inFig. 9. As shown, a fair compromise for the above-mentionedcriteria is met. The obtained value for kp is not given since itdepends on the scaling factors used in the PWM signal, whichdepends on the physical realization of the measurement setup.In Section VI, the measurement results for breathing patientsobtained through this feedback compensation are discussed.

MAES et al.: FAN-BASED, LOW-FREQUENT, FOT APPARATUS 609

Fig. 8. Amplitude spectrum of generated pressure signal for a breathingpatient without feedback compensation. In the frequency band of the breathingrate, the sample variance reaches values up to 10 dB. : the wantedsignal P0(k). : the generated pressure on the excited lines. : the samplevariance.

Fig. 9. Magnitude and phase plots of the loop transfer function L(s) (full line)and the sensitivity function S(s) (dashed line) together with the obtainedvalues of the criteria for optimal kp .

VI. MEASUREMENT RESULTS

Both compensation methods are enabled and a measure-ment with a breathing patient is performed. The aim is tocompensate for the disturbances generated by the breathing ofthe patient to obtain a high quality of the generated pressuresignal. As the measurement results show (Fig. 10), the wantedpressure signal P0(k) can be generated with a SNR of about40 dB in the frequency band of spontaneous breathing. Thisis a very satisfying result that shows that the pressure signalcan be generated without large spectral impurities and withoutthe generation of significant nonlinear distortions.

VII. CONCLUSION

A new FOT lung impedance measurement setup is pro-posed that allows to excite the patient with a multisineexcitation in the frequency range of spontaneous breathing(0.1–1 Hz). A high-quality pressure signal P is generatedand can later be used in combination with the flow signalQ to obtain the respiratory impedance Z . Imposing a pressuresignal with a SNR of 40 dB on the patient’s breathing will

Fig. 10. Amplitude spectrum of generated pressure signal when a breathingpatient is measured. The controller can suppress the breathing disturbancesvery well. : the wanted signal P0(k). : the generated pressure on the excitedlines. : the generated pressure on the in-band nonexcited frequency lines.

: the sample variance.

make it possible to obtain a good estimate of Z in thefrequency range of spontaneous breathing. Several methodsto obtain Z at low frequencies have been studied (Section I).However, to our knowledge, no method that can apply ahigh-quality pressure signal to the patients lungs in the fre-quency range of spontaneous breathing without the need forapnea or mechanical ventilation has been proposed. In thispaper, a new measurement setup is developed that can obtainthis result. The measurement setup is characterized and twocomplementary methods are applied to compensate the lineardynamic behavior and to suppress the nonlinear distortionsand the patients breathing disturbances. The measurementsshow that a pressure oscillation can be imposed even when apatient’s breathing is constantly disturbing the pressure signal.These high-quality measurements enable the measuring of therespiratory impedance at low frequencies without the needfor apnea or mechanical ventilation. As a result, this methodis more comfortable for the patient and therefore useful forroutine use in lung function measurements.

In future research, we aim to use the high-quality FOTmeasurements to analyze the health conditions of the patients.We will do this by considering not only the (linear dynamic)respiratory impedance, but also its possible nonlinear behaviorand the dependency on the varying state of the lungs duringbreathing. The latter will lead us to the study of cyclicallychanging respiratory impedance to obtain an accurate analysisof the patients health condition.

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Hannes Maes (M’12) received the Degree in Elec-trical Engineering in electronics and informationprocessing from Vrije Universiteit Brussel, Brussels,Belgium, in 2012.

He joined the Department ELEC as a Ph.D. Stu-dent. His current research interests include systemmodeling for biomedical applications and nonlinearmodeling.

Gerd Vandersteen (SM’07) received the ElectricalEngineering degree from Vrije Universiteit Brussel(VUB), Brussels, Belgium, in 1991 and the Ph.D.degree in electrical engineering from VUB/ELEC in1997.

He was with the Wireless Group, Micro Elec-tronics Research Center, IMEC, Leuven, Belgium,as a Principal Scientist, on modeling, measurement,and simulation of electronic circuits in state-of-the-art silicon technologies. Since 2008, he has beena Professor with VUB/ELEC within the subject of

measuring, modeling, and analysis of complex linear and nonlinear systems.

MAES et al.: FAN-BASED, LOW-FREQUENT, FOT APPARATUS 611

Michael Muehlebach received the bachelor’sdegree in mechanical engineering from ETH Zurich,Zurich, Switzerland, in 2012. He is currently pursu-ing the master’s degree.

His current research interests include the model-ing, identification, and control of a wide range ofdynamical systems.

Clara Ionescu (S’06–M’09) was born in Cimpu-lung, Romania, in 1979. She received the M.Sc.degree in industrial informatics and automation fromDunarea de Jos University, Galati, Romania, in 2003and the Ph.D. degree from Ghent University, Ghent,Belgium, in 2009, on identification of human respi-ratory system by means of fractional order models.

She is a Post-Doctoral Researcher with GhentUniversity, financially supported by the FlandersResearch Foundation. She is involved in severalinternational projects with both industrial and bio-

medical applications for identification and control. She has published over100 peer-reviewed publications in journals, conferences, and books, beingactively involved in promoting the concept of fractality in biological systemsand their applications to medicine.