J. Biomedical Science and Engineering, 2013, 6, 1062-1071 JBiSE
http://dx.doi.org/10.4236/jbise.2013.611133 Published Online November 2013 (http://www.scirp.org/journal/jbise/)
A resonance-mode piezoelectric device for measurement of
respiratory mechanics
Hamed Hanafi Alamdari, Lucas Posada, Swati A. Bhatawadekar, Jeremy A. Brown,
Geoffrey N. Maksym
School of Biomedical Engineering, Dalhousie University, Halifax, Canada
Email: hamed.hanafi@dal.ca, gmaksym@dal.ca
Received 10 September 2013; revised 15 October 2013; accepted 26 October 2013
Copyright © 2013 Hamed Hanafi Alamdari et al. This is an open access article distributed under the Creative Commons Attribution
License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
This paper presents the design o f a nove l oscillometry
device for the measurement of respiratory mechanics
based on piezoelectric bimorph actuator technology.
To predict performance for measurement of human
respiratory mechanics, a dynamic model was devel-
oped based on a bimorph piezoelectric actuator driv-
ing a linear resistance mesh screen including subject’s
respiratory impedance loads, and realistic breathing
noise. Model performance was also validated in a pro-
totype device. We found that while breathing noise
substantially lowered SNR, the model could produce
sufficient pressure and flow for acceptable SNRs ex-
ceeding 35 dB, and accuracies exceeding 99%. Sat-
isfactory accuracy could be achieved with load impe-
dance errors less than 3%. Maintaining the air-gap
around the oscillating mesh with a resistance against
the leak greater than 0.38 cmH2O/L/s maintained good
performance, with an acceptable 4 dB decrease to
SNR. Moreover, this work provides multiple solutions
to host higher amounts of noise and nonlinearities.
These results indicate that the development of an ac-
curate lightweight portable single frequency FOT de-
vice is feasible.
Keywords: Forced Oscillation Technique FOT;
Respiratory Mechanics; Tidal Volume
Oscillometry also known as the Forced Oscillation Tech-
nique (FOT) superimposes fluctuations in airway pres-
sure on normal breathing to measure the mechanical im-
pedance to airflow of the respiratory system for diagnos-
ing and monitoring lung diseases [1]. Using FOT is pos-
sible in very young children to elderly patients as it is
easy to perform unlike the current standard approach,
which involves a learned maximal forced expiration that
is difficult for many patients. Respiratory impedance is a
complex quantity with a real part: respiratory resistance
(Rrs) largely due to airflow resistance and an imaginary
part: reactance (Xrs) arising from elastic properties of the
lung and chest wall and the inertia of the air. The resis-
tance is elevated in diseases such as asthma and COPD
associated with airway narrowing and the reactance can
also be altered due to loss of airspaces as airways close
and limit flow [2].
FOT Devices must reliably produce oscillatory wave-
forms even when perturbed by breathing, and must ac-
curately measure pressure and flow due to the oscilla-
tions, over a wide range of patient respiratory imped-
ances, and compensate for any self-impedance of the de-
vice and disposable filter. Current FOT devices use ei-
ther a loudspeaker or oscillating electromagnetic actuator
which results in a device that is larger or heavier than ty-
pical spirometers.
Piezoelectric actuators have been used for several years
in applications such as loudspeakers, mechanical damp-
ers, ultrasonic motors, precision position controlling, noise
control, relays, phonograph pick-up, acoustics, and pres-
sure sensing [3-6]. We have designed a smaller and less
costly FOT device, based on a piezoelectric bimorph ac-
tuator using a computer model to help explore the feasi-
bility and design requirements for a suitable device. The
design was tested in a prototype device.
2.1. Simulations
The device is based on a moving mesh in a flow tube and
was modeled in MATLAB/SIMULINK as described in
following paragraphs. The resonance of the oscillating
cantilever was tuned to 6 Hz by varying the mass on the
tip [7]. Forced air oscillation at 6 Hz was sent into a res-
H. H. Alamdari et al. / J. Biomedical Science and Engineering 6 (2013) 1062-1071 1063
piratory system that modeled different subject popula-
tions including healthy, COPD, normal children and asth-
matic children with representative impedance values indi-
cated in Table 1 [8-11]. We used actual measured breath-
ing waveforms of 6 voluntary subjects (without any ap-
paratus) as realistic noise. Subjects were recruited as part
of a research ethics approved study approved by the Ca-
pital Health Authority (Halifax, NS). The average RMS
amplitude of the breathing flow was used as the noise
gain of unity. The noise was adjusted in amplitude as a
perturbing input to assess the effects of breathing noise
on predicted values as well as on the actuator. The tidal
volume (VT) of the measured volunteer patients was 660
± 150 mL (±SD) while 1/3 of that was used as realistic VT
for the child patient [12]. The predicted actuation char-
acteristics for piezoelectric bimorphs are well known [5]
and therefore to achieve sufficient accuracy, signal-to-
noise ratio (SNR), low power consumption, and low cost,
the model incorporated a novel resonance based piezo-
electric actuator design. To model the leak resistance of
the moving mesh screen, the mesh resistance comprising
the holes on the mesh and the air-gap with the housing
was modeled as a resistance in parallel to the respiratory
system impedance. The device needs to reach high air-
gap resistance to conduct the least amount of air loss.
From the model we set a design goal for a minimum air-
gap threshold resistance to achieve errors less than 10%
[13] for different subject loads. Differences between
groups due to the influence of breathing noise on SNR
between groups were performed at breathing noise gain
of 3 using one way ANOVA. Significant findings were
post hoc tested using Bonferroni correction. Analysis
was performed with SigmaPlot 12 version 12.3 (Systat
Software, Inc. Chicago, IL).
2.2. Experiments
The simulation was used to verify the design and con-
struction of a prototype device.
Figure 1(a) shows a diagram of the bimorph actuator
and Figure 1(b) shows a diagram of the prototype FOT
device incorporating the bimorph actuator. An off-the-
shelf bimorph actuator (40-2010, American Piezo Cera-
mics, Mackeyville, PA) with length (L) of 60 mm, width
(w) of 20 mm and thickness (h) of 0.7 mm was used. The
piezoelectric bimorph was derived by an AC voltage
source using a function generator and a pre-amplifier and
a mesh screen was attached to actuator’s tip in order to
generate air oscillation at 6 Hz. The airflow was directed
into calibrated reference resistive loads of 5 and 15
cmH2O/L/s (Hans Rudolph Inc, KS, USA). Pressure of
airway opening was measured using a differential pres-
sure transducer (TD-05-AS, SCIREQ Inc., Montreal,
Canada) across the mesh screen that was attached to the
cantilever and flow was calculated by dividing the pres-
sure across pneumotachograph’s mesh by the screen’s re-
sistance (Rp = 0.4 cmH2O/L/s). Prior to the tests, trans-
Ta b le 1. Mechanical properties of subject populations, used in
Equations (4) and (5), and implemented in the model Figure
4(c) [8-11].
Property Healthy MaleCOPD Child
(8-year-old boy)
(cmH2O/L/s) 2.35 10 6.86 9.5
(cmH2O/L) 33.3 60 82.84 100
(cmH2O/L/s2)0.0146 0.028 0.0092 0.0092
(a) (b)
Figure 1. (a) Structure of a bimorph actuator with parallel configuration. L, h and δ represent the length, thickness and displacement
respectively; (b) Schematic representation of the prototype device attached to the respiratory system model of different subjects for
Copyright © 2013 SciRes. OPEN ACCESS
H. H. Alamdari et al. / J. Biomedical Science and Engineering 6 (2013) 1062-1071
ducers were calibrated by applying steps of 0.5 cmH2O
using a manometer. Calibration coefficients were calcu-
lated based on the results. The breathing noise was gen-
erated using a ventilator pump (Bodine Electric Com-
pany, Chicago, ILL, USA). Measurements were repeated
for 6 times for each test. Pressure and Flow data were
sampled at 1000 Hz and the impedance was computed as
previously described [14]. The SNR was determined by
Fast-Fourier-Transforming (FFT) the entire duration of
data into the frequency domain, and calculating the ratio
of the magnitude of the FFT at the frequency of oscilla-
tion to the root mean squared average of noise in 1 Hz
bandwidth side bands adjacent to the oscillatory fre-
Section III describes the methods used to model the air
oscillometry device shown in Figure 1, including the
approach used to calculate the oscillation amplitude, and
to model the respiratory system and piezoelectric canti-
Unimorph, bimorph, and multimurph piezoelectric ac-
tuators are used in many different applications as a low
cost efficient means of converting electrical energy to
mechanical energy. Although the total potential energy
density remains the same for different multimorph ac-
tuators of the same geometry, the more layers incorpo-
rated into the multimorph, the lower the amplitude of the
required voltage is. Certain bimorph designs however
rely on a metallic spacer or vane separating the two rela-
tively thin piezoelectric plates. This type of bimorph ac-
tuator reduces the required electric field while maintain-
ing a reasonable displacement and actuator force at a frac-
tion of the cost of multimurph actuators. This is primar-
ily due to the less complicated manufacturing process.
Bimorphs are available in series and parallel configu-
rations. We chose a parallel configuration (Figure 1(a))
since they deflect the same amount as the series for half
of the series configuration’s applied voltage [5].
3.1. Calculations and Piezoelectric Model
Equation (1) presents the governing equation for oscil-
lating flow through a mesh screen affixed to the top of
the actuator that calculates the oscillation amplitude, δ, at
frequency, f:
 (1)
where 2π
is the angular frequency, P is the mini-
mum pressure amplitude expected. Ra = 0.6 cmH2O/L/s
is the resistance of the actuating mesh screen and Ar =
πr2 is the area of the circular oscillating mesh of radius of
r = 2.45 cm.
Taking dielectric losses, structural damping and inertia
effects into account, a fixed-free cantilever bimorph ac-
tuator’s tip deflection (δ), as described in [5], can be pre-
dicted by Equation (2) as:
  (2)
where Vin is the applied voltage across the thickness of
the bimorph, α is the electro-mechanical coupling, F is
the external load perpendicular to the cantilever’s tip, m
is the mass, Cd is the damping coefficient, and K is the
Figure 2 shows the electro-mechanical representa-
tion of the Butterworth-Van-Dyke (BVD) [15] model
of the piezoelectric actuator. The parallel capacitor, Cp
represents the electrical side of the model. The me-
chanical side represents a mass-spring-damperresonant
Transforming Equation (2) into the frequency domain
with no load applied for the moment gives the electro-
mechanical transfer function (TFpiezo) of the piezo-elec-
tric actuator:
TFs msCs K
  (3)
m, K, Cd, and α where obtained by standard mechanical
experiments and using analytical formulas as follows
[16]. Briefly: To find m, we calculated and experimen-
tally measured the effective mass of the cantilever and
the mass on the tip needed to shift the bimorph resonance
down to 6 Hz. At resonance, K was determined from
where r
is the resonant angular frequency.
The displacement versus frequency data was produced
from applying a chirp signal and recording the displace-
ment using a non-contact type laser displacement sensor
(AR 200, Acuity, Ortonville, MI). From the curve we
obtained the damping ratio
the angular half-power bandwidth. The damping coeffi-
cient was computed as 2CKm
 
d. To find α,
this data was least mean squared fit to the transfer func-
tion (Equation (3)) with R2 = 0.97 (Ta ble 2). The move-
Figure 2. Electro-mechanical representation of Butterworth-
Van-Dyke (BVD) piezoelectric model.
Copyright © 2013 SciRes. OPEN ACCESS
H. H. Alamdari et al. / J. Biomedical Science and Engineering 6 (2013) 1062-1071 1065
Table 2. Properties of the piezoelectric cantileve; see text for
equations for fitting and experiment descriptions to determine
the properties.
Property Fitted Value Approach
α 2.6 N/V Fitting R2 = 0.97
Cp 190 nF Manufacturer
m 78 gr Experiment
Cd 0.53 Ns/m Experiment
K 110.8 N/m Experiment
ment amplification due to the distance between the tip of
the actuator and the center of the mesh screen is added to
the model by Lr
where (L + r is the location of
the center of mesh.
3.2. Respiratory System Model and Impedance
To model the respiratory system impedance, we used the
standard single compartment model which is the equa-
tion of motion (Equation (4)). The resistance (RRs) was
modeled as a single Newtonian resistive tube. The elas-
tance (ERs) represents the stored elastic energy largely
from surface tension, but also from tissue stretching and
some gas compression while the intertance (IRs) repre-
sents the inertia of the moving gas (Figure 3) [17].
PRVEVI V
where P is the airway pressure, V is volume, is flow
and is volume acceleration.
The respiratory system impedance, Zrs, is obtained by
transforming Equation (4) into the frequency-domain:
rs RsRS
ZjR jI
 (5)
This is well established model particularly well suited
for the healthy lung, and through altering Rrs, Ers and Irs,
the model can approximate the major changes in me-
chanics observed in common lung disease, although a
more accurate representation would include some in-
creasing frequency dependence of the parameters, par-
ticularly Rrs and Ers. For the purposes of design, we have
explored a range of mechanical parameters that describe
the gross changes commonly encountered using FOT
including COPD as well as a child [8-11] (Table 1). The
changes observed in asthma in an adult would be similar
to the increase in Rrs and Ers observed in a child.
4.1. Simulations
To verify the performance of the single frequency piezo-
electric forced oscillation device, simulations of the model
presented in Section III were performed (Figure 4(c)).
Figure 3. Single compartment model of the respiratory system
based on linear RLC circuit analogy: RRs is the resistance of the
tubing, ERs is the elastance of the tissue, and IRs is the inertance
of the flowing gases. Pawo is the pressure of airway opening and
Pms is the pressure created by muscle effort. is the breath-
ing flow/noise and
is the oscillation flow generated by pi-
ezoelectric actuator.
The normal breathing of a representative subject with
frequency of 0.2 Hz containing the 6 Hz oscillations
shown in Figure 4(b) caused fluctuations of approxi-
mately 0.2 mm on actuator’s tip displacement (Figure
4(a)). This distortion increased with increasing noise
gain. As expected, when the breathing noise amplitude
was increased, the flow SNR dropped. The decrease was
more severe for the COPD and child simulation with
adulttidal volume (VT) than other subjects (p < 0.001)
and decreased to 28 dB at the simulated noise gain of 2.5,
while the SNR remained higher than 35 dB for noise
gains up to 3 for the male subject, the child with realistic
VT and the asthmatic child (Figure 5).
The variability in the results is due to the difference in
volunteer patients breathing patterns, however, the rank
ordering at every breathing noise gain stayed the same
amongst subjects.
Increasing the breathing noise up to three times the
normal values showed that the error in estimation of im-
pedance of the lung exceeded 10% in the COPD simula-
tion with breathing gain of 2 or more and in the child
simulation with adult tidal volume with breathing gain of
3.2 or more, however, the error in the child simulation
with realistic tidal volume, the asthmatic child and the
healthy male was less than 5% at any breathing noise le-
vel (Figure 6). For breathing noise gain of unity, the lar-
gest absolute error in estimating Rrs was 0.175 cmH2O/L/s
that represents 1.7% error, which belongs to the COPD
subject. The COPD subject also had the largest absolute
error in estimating Xrs of 0.045 cmH2O/L/s. It is not ap-
propriate to use % error representation for Xrs because its
values are close to zero at respiratory system resonant
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H. H. Alamdari et al. / J. Biomedical Science and Engineering 6 (2013) 1062-1071
Copyright © 2013 SciRes.
(a) (b)
Figure 4. (a) Tip displacement affected by breathing noise gain of unity from simulations (b) Regenerated measured breathing flow
of a volunteer via a pneumotachograph with superimposed oscillations from simulations according to the same time scale as in (a). (c)
Schematic representation of the modeled system.
frequency. Also, Elastance and Inertance cannot be pre-
cisely distinguished due to the single frequency measure-
ment described here; therefore, the error in estimation of
Reactance is used (Figure 6).
Verifying the effect of leak due to air-gap on SNR and
the impedance estimation error showed that with total
resistance against the leak greater than 0.38 cmH2O/L/s
would give SNRs higher than 30 dB and errors lower
than 10% for the different simulated respiratory imped-
ances (Figure 7).
H. H. Alamdari et al. / J. Biomedical Science and Engineering 6 (2013) 1062-1071 1067
Figure 5. The effect of increasing breathing noise on measured
flow SNR ratio in different subject populations. Increasing the
breathing noise decreased the SNR. Error bars indicate SD for
all figures.
Figure 6. Magnitude estimation error of Zrs in percent for dif-
ferent subject populations at different noise levels. The estima-
tion error increased with increasing breathing noise. The insert
indicates Rrs and Xrs absolute estimation errors for unit breath-
ing noise gain.
Figure 7. SNR (a) and impedance estimation error (b) for different amounts of leak (mesh screen and airgap). As resistance against
the leak increases (leak decreases) the SNR increases and the estimation error decreases.
4.2. Nonlinearity
The respiratory system model used in this paper was a
linear single compartment model. However, there are non-
linearities that can arise such as form the pressure volume
curve, and the well-established Rohrer flow non-linearity
[18]. Here we explored the effects of the dependence of
the resistance of the airway on flow according to Rohrer
equation as follows (Equation (6)) that introduces a non-
linearity to the equation of motion (Equation (4)):
where Ru is the nonlinear flow resistance in the upper
airway, K1 is the linear resistive term and K2 is the
additional resistive term depending on flow. To assess
the influence of this nonlinearity on the performance of
the device, the linear resistance of the respiratory system
was set equal to RRs so that with zero flow the respiratory
resistance would be the same as linear model parameter
presented in Tabl e 1. The nonlinear coefficient (K2) was
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H. H. Alamdari et al. / J. Biomedical Science and Engineering 6 (2013) 1062-1071
set to 0.2 cmH2O/L2/s2 as representative of an adult sub-
ject, 7.7 cmH2O/L2/s2 as representative of a normal child
subject and 11 cmH2O/L2/s2 as representative of an as-
thmatic child subject [12,19,20].
The effect of introducing this nonlinearity lowered the
SNR at all breathing gains with typically less than 3 dB
difference for all subjects except in the child with adult
VT where the SNR lowered for about 13 dB at normal
breathing level. The impedance estimation error increased
with breathing gain but remained less than 3% at normal
breathing amplitudes except for the child with adult VT.
The error in child with adult VT subject reached 10% at
breathing gain of 0.7 while COPD reached the maximum
recommended error at breathing gain of 1.7. The asth-
matic child, the normal child and the male subject reached
the maximum recommended error at breathing noise gain
of about 2 (Figure 8).
4.3. Experiments
To verify the feasibility of the single frequency piezo-
electric forced oscillation device in experiments, the pro-
totype device was tested on flow resistive test loads of 5
and 15 cmH2O/L/s as representatives of a normal and an
extremely high respiratory loads with and without gener-
ated breathing noise of unit gain using a ventilator pump.
Using the prototype device on test loads with no brea-
thing, the measurement error was less than 1% with SNR
of 39.9 dB for the 5 cmH2O/L/s test load and error less
than 5% with SNR of 30.1 dB for the 15 cmH2O/L/s test
load (Figure 9). Adding the simulated breathing of unit
gain through a ventilation pump had an apparent influ-
ence on the measurement error where it went up to 5%
with deteriorated SNR of 29 dB for the 5 cmH2O/L/s test
load while the measurement error on 15 cmH2O/L/s test
load went up to10% and its SNR dropped to 19.9 dB
(Figure 9).
5.1. Simulations
The aim of this paper was to design an efficient low po-
wer forced oscillation device that can meet the standards
proposed by Oostveen et al. [13] where they recommend
a maximum error of 10%. Simulation results presented in
the previous section showed that this criterion can be met
even with higher noise levels. The healthy male subject
and the asthmatic child were influenced similarly by the
increasing noise both in SNR drop and the increase in the
impedance estimation error. The impedance estimation
error in the simulated COPD and child (with high tidal
volume) subjects was higher than the healthy male sub-
ject (Figure 6). The same trend can be seen in Figure 5
where the SNR drop in simulated COPD and child im-
pedance was higher than the healthy male subject. To ve-
rify the mechanism for this, we calculated the transfer
function of the noise on the respiratory system of differ-
ent subjects (Appendix), taking into account the affect of
the breathing noise feedback on the oscillation dynamics
of the piezoelectric actuator.
Equation (7) presents the total noise transfer function
Rs d
RsRS leak
leak RsRs
smsCs K
 
Figure 8. The comparison of the nonlinear and linear model in terms of SNR and impedance estimation error for increasing breathing
noise in a representative subject. Nonlinearity reduced the SNR and increased the error.
Copyright © 2013 SciRes. OPEN ACCESS
H. H. Alamdari et al. / J. Biomedical Science and Engineering 6 (2013) 1062-1071 1069
(a) (b)
Figure 9. (a) Schematic representation of the experimental test set up on the prototype device. The tests on the air-flow resistive test
loads were performed with and without ventilator generated breathing noise of unit gain; (b) Experimentally determined test load
measurements. The generated breathing noise increased the estimation error.
Figure 10 shows the magnitude of bode plot of Equa-
tion (7) around the frequency of oscillation for different
subjects. It can be noticed that the noise magnitude in
simulated COPD was the highest, the simulated child has
a lower peak while the average male impedance has the
lowest noise peak at 6 Hz. This is in agreement with the
results in Figures 5 and 6. It should be noted that the
peaks of the bode plot (Figure 9(b)) would shift in mag-
nitude in reality depending on the tidal breathing gain of
the specific subject. For example, as shown in Figure 5,
the simulated child subject with adult tidal breathing
exhibits a severe drop in SNR that resembles the COPD
simulation. This is because the mechanical impedance of
the child and COPD respiratory systems are both high in
value (Ta ble 1). However when the realistic amounts of
tidal volume is applied to the child’s respiratory system,
the noise decreases, and the SNR is maintained even high-
er than that of the healthy male simulation.
Producing oscillations of air through a moving mesh
screen includes the intrinsic problem of some of the re-
sistance originating from the mesh screen with the re-
mainder arising from the gap between the mesh and the
housing tube. Considering the impedance using an elec-
trical analog model, the resistance of air-gap is in parallel
with mesh resistance and thus the total equivalent resis-
tance is smaller than the mesh resistance. In this work the
equivalent resistance of the mesh screen and air-gap was
defined to be 0.6 cmH2O/L/s (Figure 7). An interesting
conclusion from Figure 7 is that if the resistance against
the leak due to air-gaps in the device is maximum (open
circuit), the mesh screen can be replaced with one with
resistance as low as 0.38 cmH2O/L/s while maintaining
the impedance estimation error less than 10% and the
SNR higher than 30 dB.
Figure 10. Magnitude of the bode diagram of noise transfer
function and the noise magnitude vs impedance at 6 Hz. In-
creasing the impedance increased the noise.
Simulating the effects of nonlinearity on different simu-
lated subjects had the most substantial effect on the im-
pedance estimation error of the child with adult VT. The
effects on the male, the child with realistic VT and the
asthmatic child subject were also substantial while the
effect on the COPD was the smallest (Figure 8). The
small effects of the nonlinearity in the COPD subject
were because the nonlinear term was small relative to the
linear resistance, while in the healthy male the linear re-
sistance is small relative to the nonlinear term. However,
while nonlinearity led to increases in errors, the errors
were only unacceptable for the healthy male, the realistic
child and the asthmatic child subjects at larger flows than
normal. At normal flow levels and at the normal tidal
volume for the child subject, the error was acceptable in
all subjects.
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H. H. Alamdari et al. / J. Biomedical Science and Engineering 6 (2013) 1062-1071
5.2. Experiments
The tests on the prototype device without breathing noise
resulted in very low errors and high SNRs. As expected,
after adding the breathing noise the SNR dropped and
errors increased. However in the case of the 15 cmH2O/L/s
test load which is higher than would be anticipated for
adult subjects, but possible for children with airway ob-
struction [13] the error reached the maximum recom-
mended value (Figure 9(b)). Children fortunately have
lower breathing noise, and thus this design is likely suit-
able for a large range of subjects. These are for normal or
nearly normal tidal volumes. However if measurements
are to be made under larger ventilation conditions such
as with exercise, the reduction in SNR would begin to
cause larger errors in estimating impedance. If this is un-
acceptable then larger oscillatory flows would be recom-
mended using one or a combination of following techni-
Movement amplification techniques including me-
chanical lever and/or using longer customized piezo-
electric multimurphs and/or using multiple actuators
at the same time for increasing the applicable force.
Using an actuator with higher surface area to generate
higher pressure oscillations.
Reducing the amount of leak due to air-gaps.
In this paper, for the first time, an oscillometry device
was designed based on optimization in a simulation that
included the device characteristics together with changes
in subject impedance including perturbations from brea-
thing. Although breathing noise reduced the SNR, the per-
formance remained acceptable and demonstrated a useful
design approach that led to the development of a feasible
accurate lightweight portable single frequency FOT de-
vice. Reducing the leak and improving the measurement
accuracy of the transducers as well as modifications in
the oscillating mesh and the actuator can improve the
results from the prototype device.
Hamed Hanafi and Lucas Posada were supported by the NSERC
CREATE program at Dalhousie University, S. A. Bhatawadekar was
supported by the NSERC.
The authors thank Guy Drapeau at Thorasys Medical Systems for his
great feedback especially for experiments. They also thank Andre Be-
zanson for his help with piezoelectric actuators.
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APPENDIX influence on oscillations of piezo actuator. Transforming
Equation (4) into s-domain we have the transfer function
of the respiratory system as below:
The aim of this appendix is to calculate the total noise
transfer function that appears in output pressure includ-
ing the effect of breathing noise on the screen mesh. Rs
 (A.3)
From Figure 4(c) we can write:
inPP bdP
 
 x
(A.1) Therefore we can write (Figure 4(c)):
bb NORs aw
 
If we assume Vin = 0 and knowing that b
Rearranging and using Equations (A.2) and (A.3), giv-
es the total noise transfer function (TFNT) of:
 , with rearrangement we have:
TF VmsCs K
Rs leakNO
leak Rsb
Where TFNO is the transfer function of feedback noise