J. Biomedical Science and Engineering, 2011, 4, 320-340 JBiSE
doi:10.4236/jbise.2011.44042 Published Online April 2011 (http://www.SciRP.org/journal/jbise/).
Published Online April 2011 in SciRes. http://www.scirp.org/journal/JBiSE
Theoretical modeling of airways pressure waveform for
dual-controlled ventilation with physiological pattern
and linear respiratory mechanics
Francesco Montecchia
Laboratorio Sperimentale Policentrico di Ingegneria Medica, Dipartimento di Ingegneria Civile, Università degli Studi di Roma “Tor
Vergata”, Rome, Italy.
Email:francesco.montecchia@uniroma2.it
Received 13 January 2011; revised 28 March 2011; accepted 7 April 2011.
ABSTRACT
The present paper describes the theoretical treat-
ment performed for the geometrical opt imization of
advanced and improved-shape waveforms as air-
ways pressure excitation for controlled breathings
in dual-controlled ventilation applied to anaesthe-
tized or severe brain injured patients, the respira-
tory mechanics of which can be assumed linear.
Advanced means insensitive to patient breathing
activity as well as to ventilator settings while im-
proved-shape intends in comparison to conventional
square waveform for a progressive approaching to-
wards physiological transpulmonary pressure and
respiratory airflow waveforms. Such functional fea-
tures along with the best ventilation control for the
specific therapeutic requirements of each patient
can be achieved through the implementation of
both diagnostic and compensation procedures ef-
fectively carried out by the Advance Lung Ventila-
tion System (ALVS) already successfully tested for
square waveform as airways pressure excitation.
Triangular and trapezoidal waveforms have been
considered as airways pressure excitation. The re-
sults shows that the latter fits completely the re-
quirements for a physiological pattern of endoal-
veolar pressure and respiratory airflow waveforms,
while the former exhibits a lower physiological be-
haviour but it is anyhow periodically recommended
for performing adequately the powerful diagnostic
procedure.
Keywords: Mathematical Modeling; Mechanical
Ventilation; Controlled Breathing; Pressure and Airflow
Waveforms; Respiratory Mechanics; Tidal and Minute
Vo l um e s
1. INTRODUCTION
The clinical applications of assisted/controlled ventila-
tion are mainly devoted to patients treated with anaes-
thesia or in Intensive Care Units or affected by the res-
piratory insufficient syndrome [1-3].
When spontaneous breathing of such patients is absent
or forbidden for the entire time of treatment, controlled
ventilation is required. The respiratory pattern during
controlled ventilation shows only controlled breathings,
i.e. breathings for which the control of lung ventilation is
completely carried out by an external ventilator, in series
with time [4,5].
Otherwise, when spontaneous breathing is present,
even if partially in time or below the standard physio-
logical level, assisted/controlled ventilation is recom-
mended. Allowing the patient the possibility of sponta-
neous breathing at his will or capability, assisted/ con-
trolled ventilation is so called because, it includes all that
modalities or techniques in which the ventilator supplies
the patient with controlled breathing only after a long
lasting interval of apnea (assisted ventilation) or at de-
tection of a very weak effort of spontaneous breathing
(triggered ventilation). The respiratory pattern during
assisted/controlled ventilation shows both controlled and
spontaneous breathings in random series with time [6-7].
The controlled breathings supplied to patient during
controlled or assisted/controlled ventilation can be prop-
erly classified considering the primary physical parame-
ters controlled during the inspiration by the ventilator
irrespective of load (respiratory characteristics of patient)
variations or fluctuations as well as ventilator settings [8,
9].
Volume-controlled ventilation (VCV) or pressure-
controlled ventilation (PCV) refer to different modalities
in which during the inspiration the ventilator supplies the
load (lungs) with the pre-established volume (tidal or
F. Montecchia / J. Biomedical Science and Engineering 4 (2011) 320-340
Copyright © 2011 SciRes. JBiSE
321
minute volume) through the selected respiratory airflow
waveform or applies to the load the pre-established air-
ways pressure waveform, respectively [8,9].
The historical background of both VCV and PCV as
well as their advantages and disadvantages in different
clinical applications of assisted/controlled ventilation have
been extensively described elsewhere [9,10]. In summary,
considering the higher physiological character along with
lower level of intrinsic pathological risks and functional
failure involved, nowadays PCV is certainly the most
adopted in the clinical practice [9-12].
The functional disadvantages of PCV which does not
provide for the control of lung volume (tidal or minute)
has been overcome with the implementation of dual-
controlled ventilation (DCV), i.e. PCV with ensured
tidal or minute volume [13,14]. In detail, DCV is an ad-
vanced form of PCV in which the magnitude of selected
airways pressure waveform is automatically regulated by
feedback control for delivering during the inspiration
time either the tidal volume required or, considering the
current breathing frequency, the minute volume pre-
established [9,15]. This is the so called DCV “breath to
breath” mode, representing the most diffused form of
DCV in the clinical practice [15,16]. In a different way,
the so called DCV “within a breath” mode is a DCV
mode in which the ventilator switches from pressure to
volume control in the middle of the breath [15,16].
In most cases during assisted/controlled ventilation,
the respiratory system of healthy anaesthetized or severe
brain injured patients exhibits a steady and reproducible
response to controlled breathings, if evaluated as a whole.
Moreover, the breathing dynamics involved is consid-
erably reduced on account of small tidal volume required.
Therefore, the respiratory mechanics of such patients can
be properly assumed steady and linear [9]. According to
PCV excitation hypothesis along with to steady and lin-
ear respiratory mechanics assumption, only DCV
“breath to breath” mode will be considered in the present
work. Moreover, DCV “breath to breath” mode is per-
fectly compatible with the feedback control adopted for
the ventilation process [9] which regulates the operative
parameters only between different breathings evaluated
as a whole, i.e. in steady conditions and does not within
the transient time of each breath [9,15,16].
Until today, PCV or DCV have been mainly imple-
mented with square waveform as airways pressure exci-
tation, i.e. two different constant levels of airways pres-
sure applied to patient during both inspiration and expi-
ration [12,14,16]. Such strong limitation in waveform
modeling of airways pressure controlled by the ventilator,
resulting from simplified hardware and software design,
reduces drastically the functional versatility of the venti-
lator performances.
Among the different systems proposed for removing
this limitation [8,9,17-28] and thus for evaluating the
effect of varying inspiratory airflow waveforms on cli-
nical parameters of mechanically ventilated patients [29-
31], the Advanced Lung Ventilation System (ALVS) has
been conceived and designed for the waveform optimi-
zation of airways pressure excitation when controlled
breathings have to be apply during assisted/ controlled
ventilation to anaesthetized or severe brain injured pa-
tients, the respiratory mechanics of which can be as-
sumed steady and linear [9,32-36]. The functional flexi-
bility and versatility of ALVS are both extremely useful
for the research activity with an optimal and advanced
ventilator as well as for its laboratory and clinical de-
velopment and testing [9].
The present work deals with the description of both
theory and ALVS settings performed for modeling a
more realistic approximation of airways pressure excita-
tion to physiological transpulmonary pressure waveform.
The optimization of such excitation for patient, i.e. air-
ways pressure waveform, has been carried out in order to
reach a more physiological reaction of patient, i.e. respi-
ratory airflow and endoalveolar pressure waveforms.
2. METHODS
The optimization of controlled breathing during assisted/
controlled ventilation obtained by the functional features
of ALVS, has been extensively reported and discussed
elsewhere [9]. Concerning the controlled breathings ap-
plied to patient during assisted/controlled ventilation, in
order to improve over the conventional PCV with en-
sured tidal or minute volume, i.e. dual-controlled venti-
lation (DCV), ALVS has been designed for performing
two subsequent functional steps.
The first step consists in the optimization of the venti-
lation control with conventional square waveform as
airways pressure excitation applied to patient. This result
has been already reached by means of two effective
functional procedures: The diagnostic and the compen-
sation procedures.
The theoretic approach on which the optimization of
the ventilation control as well as both the diagnostic and
the compensation procedures found, have been exten-
sively reported in a previous paper [9] in which the res-
piratory mechanics of considered patients, i.e. anaesthe-
tized or severe brain injured patients, has been properly
assumed linear. Moreover, the ventilation control works
by feedback regulation acting after the acquisition of
each controlled breathing accounted as a whole, i.e. in
steady conditions.
The diagnostic procedure establishes the optimal time
of both inspiration and expiration taking into account the
F. Montecchia / J. Biomedical Science and Engineering 4 (2011) 320-340
Copyright © 2011 SciRes. JBiSE
322
current respiratory characteristics (airways resistance
and lung compliance) of patient and his diagnostic eva-
luations. Practically, the procedure sets the time of both
inspiration and expiration as about five times the current
inspiratory and expiratory time constants, the determina-
tion of which, along with other useful diagnostic pa-
rameter, is obtained real-time by ALVS monitoring sys-
tem [37-39]. The determination of both airways resis-
tance and lung compliance of patient is currently per-
formed by the diagnostic procedure with high accuracy
and without any unfavourable deformation of respiratory
pattern otherwise introduced with the required artificial
respiratory airflow interruption [40,41]. The high accu-
racy results from the application of the compensation
procedure, described as follows, since it allows the cor-
rect implementation of the results available from the
theory developed assuming a real square waveform as
airways pressure excitation [9,42-44].
The compensation procedure stabilizes the airflow
across the external resistance which controls the airways
pressure applied to patient during the whole respiratory
time. The procedure is performed through the variation
during both inspiration and expiration of ALVS genera-
tor’s internal resistance around its steady equilibrium
value assumed during apnea, according to the respiratory
airflow waveform resulting from patient's breathing ac-
tivity and characteristics. The determination of the res-
piratory airflow waveform is obtained real-time by AL-
VS monitoring system. In such a way, ALVS behaves
like an ideal airways pressure generator, making possible
a real square waveform as airways pressure excitation
through a proper square waveform as external resistance
of ALVS controlling the airways pressure applied to pa-
tient, eliminating the airways pressure distortion induced
by the dependence on current value of load (airways
resistance and lung compliance) and its variations.
The experimental results obtained by ALVS connected
with a well suited and versatile lung simulator perform-
ing the implementation of both diagnostic and compen-
sation procedure for advanced square waveform as air-
ways pressure excitation are completely in agreement
with the theoretical ones, showing clearly that the venti-
lation control optimization has been reached. In particu-
lar, concerning the lung volume control, the results point
out that the tidal or minute volume are independent on
airways resistance or lung compliance, respectively [9].
The last results are very interesting from both clinical
and engineering point of view since an increase of air-
ways resistance (obstructive process) or a reduction of
lung compliance (restrictive process) does not affect the
control of tidal or minute volume, respectively, avoiding
a critical regulation of the airways pressure levels ap-
plied to patient.
The second step consists in the optimization of the
ventilation control with waveforms of improved shapes
as airways pressure excitation applied to patients con-
sidering their current clinical conditions and specific the-
rapeutic requirements. Improved shapes means more
realistic approximation of airways pressure waveform to
physiological transpulmonary pressure waveform indu-
cing a more physiological reaction of patient, i.e. respi-
ratory airflow and endoalveolar pressure waveforms.
The implementation of the diagnostic procedure in
these cases also ensures that the optimal time of both
inspiration and expiration is retained taking anyhow into
account the current respiratory characteristic of patient
(airways resistance and lung compliance) and his diag-
nostic evaluations. Moreover, the implementation of the
compensation procedure in these cases also, making the
selected airways pressure waveform insensitive to pa-
tient’s respiratory characteristics, allows any airways
pressure waveform of clinical interest during both inspi-
ration and expiration through an identical shape of ex-
ternal resistance waveform which controls the airways
pressure applied to patient.
In the present work, from a theoretical point of view,
two waveforms of increasing geometrical shape with
respect to conventional square waveform have been con-
sidered as airways pressure excitation applied to patient:
triangular and trapezoidal. Accordingly to the physiopa-
thological and clinical condition of patients considered
as well as to the physical characteristics of controlled
breathings in assisted/controlled ventilation modalities,
the theoretical treatment in both cases has been carried
out evaluating each controlled breathing as a whole, i.e.
in steady conditions and assuming linear the respiratory
mechanics of patients [9,32-36].
3. RESULTS
3.1. Advanced Square Waveform as Airways
Pressure Excitation (AD_SQUARE)
Figure 1 shows the airways (pAW(t)) and endoalveolar
(pEA(t)) pressures (p(t)) as well as the respiratory airflow
(
RES(t)) as a function of time (t) resulting from the ap-
plication to patient of the advanced square waveform as
airways pressure excitation (AD_SQUARE). The time,
the variables and the parameters relative to inspiration
and expiration will be denoted with the addition of a
specific pedix character (i) and (e), respectively. As de-
picted in Figure 1(b), on account of their opposite direc-
tions, the inspiratory (
INS(ti)) and expiratory (
EXP(te))
airflows are conventionally considered positive and
negative quantities, respectively.
The most relevant results obtained in the previous
work [9] are summed up as follows. The real time
F. Montecchia / J. Biomedical Science and Engineering 4 (2011) 320-340
Copyright © 2011 SciRes. JBiSE
323
Figure 1. (a) Airways (pAW(t)) and endoalveolar (pEA(t)) pres-
sures (p(t)) along with (b) respiratory airflow (
RES(t)) as a
function of time (t) resulting from the application of AD_
SQUARE. In (b) inspiratory (
INS(ti)) and expiratory (
EXP(te))
airflows are depicted as positive and negative quantities, re-
spectively, on account of their opposite directions.
monitoring of both
INS(ti) and
EXP(te) provides for the
determination of the following parameters: tTI; tTE;
INS(0);
EXP(0).
INS(0) and
EXP(0) are the initial maxi-
mum values assumed by
INS and
EXP, respectively,
while tTI and tTE are the times required for reaching the
end of transient inspiration and expiration times, i.e. for
observing a ninety nine percent (99%) reduction of
INS
and
EXP with regard to
INS(0) and
EXP(0), respectively.
If the upper (PI) and lower or external positive end
expiratory pressure (PEEPEXT) constant levels of square
waveform as pAW excitation are kept for an inspiration
(TI) and expiration (TE) times equals to tTI and tTE, re-
spectively, the following expressions occur:
55
TIINSINS P
TItR C
  (1)
55
TEEXPEXP P
TE tRC
  (2)


p
PEA
t
Cpt
(3)


e
i
I
NS
t
EAi iEXT
ptPIPI PEEP
  (4)


e
e
E
XP
t
EAe eEXTEXT
ptPEEPPI PEEP
 (5)
 
EAi AWi
pTIPAPpTIPI 
(6)

E
AeTOT AWeEXT
pTE PEEPpTE PEEP  (7)
0
E
Ai EAeEXT
ppTE PEEP (8)
I
NS
and
E
XP
are the inspiratory and expiratory
time constants, respectively, while
Pt
is the lung
volume as a function of time.
According to the assumption of linear respiratory
mechanics for controlled breathings accounted as a
whole, i.e. in steady conditions [9], the static lung
compliance (CP), defined by (3), can be considered as
constant during the whole respiration time, while the
different values assumed by the respiratory airways
resistance (RRES) during inspiration (RINS) and expira-
tion (REXP) can be both considered constant.
According to (6) and (7), the maximum or peak
(PAP) and minimum or total positive end expiratory
pressure (PEEPTOT) values of pEA assumed at the end
of inspiration (ti = TI) and expiration (te = TE), respec-
tively, can be easily detected since they equal the con-
stant PI and PEEPEXT values assumed by pAW during
the inspiration (0 ti TI) and the expiration (0 te
TE), respectively. (8) establishes that the value as-
sumed by pEA at the beginning of inspiration (pEAi(0))
should be equal to that assumed at the end of last ex-
piration (pEAe(TE)).
Concerning with vP, considering (3), (6) and (8) at
the beginning (ti = 0) and end (ti = TI) of inspiration,
the following expressions result:
00
pip EAipEXT
vCpC PEEPFRC  (9)
pip EAip
vTI Cp TI CPI (10)
 
0
TID pipipEXT
VvTIvC PIPEEP (11)
FRC and VTID denote the functional residual capacity and
the tidal volume delivered to patient for every inspira-
tion.
If TI and TE are expressed in seconds, considering
that the breathing period (TR) equals to the sum TI + TE,
from both (1) and (2), the breathing frequency (FR),
expressed in act for minutes, is defined as follows:

60 6060
5
P
INS EXP
FR TRTI TEC RR
 

(12)
Considering both (11) and (12), the so-called minute
volume (VMIN), i.e. the volume delivered to patient for
every minute, is given by the following expression:

12
E
XT
MINTID INS EXP
PI PEEP
VFRV RR
  (13)
As pointed out in § 2, (11) and (13) establish that VTID
or VMIN are independent on RRES (both RINS and REXP) or
CP, respectively. That is extremely relevant from both
clinical and engineering point of view since an increase
F. Montecchia / J. Biomedical Science and Engineering 4 (2011) 320-340
Copyright © 2011 SciRes. JBiSE
324
of RRES (obstructive process) or a reduction of CP (re-
strictive process) does not affect the control of VTID or
VMIN, respectively, avoiding a critical regulation of pAW
constant levels applied to patient.
As it is well known, the mean value (M) of a periodic
function of time (t) with period T (fT(t)) is defined as
follows:

0
1d
T
T
M
ftt
T
(14)
If pAW(t) and pEA(t) are considered as periodic functions
of time with period TR, the mean pAW(t) (MAP) and pEA(t)
(MEP) assume the following expressions:

0
1d
TR
AW
M
APptt
TR
(15)

0
1d
TR
EA
M
EPpt t
TR
(16)
From Figure 1(a), (1), (2), (4), (5), (12), (15) and (16), it
is easy to demonstrate that MAP and MEP values of
AD_SQUARE (MAPsqu and MEPsqu) result as follows:


E
XT INS
squ EXTINS EXP
PI PEEP
MAP PEEP

 (17)

0,80, 2
E
XT INSEXP
squ EXTINS EXP
PI PEEP
MEP PEEP




(18)
3.2. Advanced Improved-Shape Waveforms as
Airways Pressure Excitation
The favourable results obtained with the implementation
of AD_SQUARE in term of ventilation control optimi-
zation (§ 3.1), suggest theoretical effort for considering
advanced and improved-shape waveforms as pAW excita-
tion applied to patient. Advanced means insensitive to
patient breathing activity as well as to ventilator settings.
Improved-shape intends in comparison to conventional
square waveform for a progressive approaching to phy-
siological transpulmonary pressure waveform producing
a more suitable reaction of patient, i.e. a more realistic
approximation of
RES and pEA waveforms to physio-
logical ones.
For this reason, moving from AD_SQUARE, two
waveforms of different geometrical shape which pro-
gressively approach the best solution are going to be
considered: Triangular and trapezoidal. The problem to
be solved consists in the proper smoothing of
RES verti-
cal discontinuities occurring at the beginning of both
inspiration and expiration when
RES is reversed, as re-
sponse to upward and downward pAW vertical transitions
characteristic of square waveform. So that, the elimina-
tion of such pAW vertical transitions is the most relevant
change to be applied on AD_SQUARE.
3.3. Advanced Triangula r Waveform as Ai rways
Pressure Excitation (AD_TRIANG)
Figure 2 shows the advanced triangular waveform as
pAW excitation (AD_TRIANG). Unlike AD_SQUARE,
where pAW is kept constant during the whole time of in-
spiration (0 ti TI), in AD_TRIANG pAW increases
linearly from minimum or PEEPEXT to maximum or peak
(PIP) values assumed at the beginning (ti = 0) and at the
end (ti = TI) of the time during inspiration (ti), respec-
tively. The linear increase of pAW has been selected for
smoothing
RES discontinuity occurring at the beginning
of every inspiration as response to upward pAW vertical
transition of AD_SQUARE. As in AD_SQUARE, during
the whole time of expiration (0 te TE) pAW is kept
constant on PEEPEXT value.
AD_TRIANG can be carried out by connecting the
patient’s airways with an ideal generator creating a tri-
angular waveform of pAW. The electrical-equivalent cir-
cuit of AD_TRIANG generator connected to the patient's
airways is shown in Figure 3. The respiratory mechanics
of patient (lung simulator) has been treated with a steady
and linear physical model consisting of the respiratory
airways resistance (RRES) connected in series to the lung
compliance (CP) [9,45,46]. Such physical model does
not include any inductance on account of negligible in-
ertia of airflow as well as airways, lungs and chest tis-
sues at very low breathing frequencies involved (10 - 12
act/min).
3.3.1. Inspiration Time
The application of the second Kirchhoff’s law to the
circuit of Figure 3 provides for the following equation:

0
AWi iINSINSiEAi i
ptR tpt
 (19)
AD_TRIANG (Figure 2) requires the following expres-
sion of pAWi(ti):
Figure 2. The advanced triangular waveform as airways pres-
sure (pAW(t)) excitation (AD_TRIANG).
F. Montecchia / J. Biomedical Science and Engineering 4 (2011) 320-340
Copyright © 2011 SciRes. JBiSE
325
Figure 3. Electrical-equivalent circuit of AD_TRIANG gen-
erator connected to the patient’s airways.

1AWiiEXTi i
ptPEEPkt (20)
where k1i is the slope of pAWi(ti) linear increase with time
(ti).
As it is well known,
INS(ti) is defined as the time
derivation of vPi(ti), as follows:
 
d
d
P
ii
INS ii
vt
tt
(21)
Considering (3) as well as by inserting both (20) and (21)
into (19), the following equation results:

1
d0
d
Pi iPi i
EXTi iINSiP
vt vt
PEEPk tRtC

(22)
In order to solve Eq.22, i.e. to find out the transient
and steady expressions of vPi(ti), it is useful to transform
it from time (ti) to Laplace (s) variable domains, as fol-
lows:
 
1
200
Pi
i
EXT INS PiPiP
vs
k
PEEP Rsvsv
sC
s
 


(23)
On account of both (1) and (9), the solution of (23) con-
sists in the following expression:

21
21
i
I
NS INS
Pi
INS
k
FRC
FRCss R
vs
ss




(24)
Eq.24 can be properly decomposed as follows:

21
Pi
I
NS
A
BC
vs s
ss

(25)
The unknown constants A, B and C can be determined
by setting Eq.24 equal to Eq.25, resulting as follows:
1iP
A
kC
(26)
11
P
EXTi INSiP INS
BCPEEPkFRCk C
 (27)
1iPINS
CkC
(28)
Finally, by inserting (26), (27) and (28) into (25), the
following expression results:

111
21
iPiPINS iPINS
Pi
I
NS
kCFRCkCkC
vs s
ss
 
(29)
According to the Inverse Laplace Transform of (29), the
function vPi(ti) assumes the following expression:

11e
i
INS
t
Piii PiINS
vt FRCkCt


 


(30)
The functions
INS(ti) and pEAi(ti) can be determined
considering (21) and (3), respectively, as follows:

11e
i
INS
t
INSii P
tkC





(31)

11e
i
INS
t
EAi iEXTiiINS
ptPEEPk t





(32)
The functions vPi(ti),
INS(ti) and pEAi(ti) are reported in
Figure 4, Figure 5 and Figure 6, respectively.
The difference between pAWi(ti) and pEAi(ti) (pi(ti))
can be determined from both (20) and (32), as follows
(Figure 6):

11e
i
INS
t
ii iINS
pt k


 


(33)
The same result of (33) could also be obtained by in-
serting (31) into (19).
Considering (30), (31) and (32) at the beginning of
inspiration time (ti = 0), the following expressions result:
0
pi
vFRC (34)
00
INS
(35)

00
EAiEXT AWi
pPEEP p
(36)
(34) and (36) fit well (9) and (8), respectively (Figure 4
and Figure 6), according to the same steady conditions
occurring in AD_SQUARE at the beginning of inspira-
tion time (ti = 0) and thus at the end of last expiration
time (te = TE).
If TI is set equal to the time required for reaching the
F. Montecchia / J. Biomedical Science and Engineering 4 (2011) 320-340
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326
Figure 4. Lung volume (vP(t)) as a function of time (t) resulting
from the application of AD_TRIANG.
Figure 5. Respiratory airflow (
RES(t)) as a function of time (t)
resulting from the application of AD_TRIANG.
Figure 6 . Endoalveolar pressure (pEA(t)) as a function of time (t)
resulting from the application of AD_TRIANG.
steady condition, i. e. the end of transient inspiration time
(tTI = 5
INS), (20), (30), (31), (32) and (33) provide for
the following expressions:

1
55
AWiINSEXTiINS
pTIPIP PEEPk
 (37)


5
1
1
551e
4
piINSi PINSINS
iPINS
vTI FRCkC
FRCkC


 (38)

5
11
51e
I
NSINSi Pi P
TI kCkC

 
(39)
1
54
E
AiINSEXTi INS
pTIPAP PEEPk
 (40)
 
1
5
iINS iINS
pTIPIP PAPk
 (41)
(39) establishes that at the end of transient time (ti = TI =
5
INS), the increase of
INS reaches a saturation value
given by the product of CP with the linear slope (k1i)
selected for pAW (Figure 5). This result is remarkable
since
INS(5
INS) being independent on RINS, provides for
a more physiological
INS waveform adapting itself to
lung elastic characteristic (CP). Moreover,
INS(5
INS)
can be adequately adjusted by k1i regulation for a proper
compensation of the actual CP value.
According to our purpose, (35) establishes the real
smoothing of
RES discontinuity occurring at the begin-
ning of every inspiration time (Figure 5). Unfortunately,
unlike AD_SQUARE, according to (39), the final value
of
INS (
INS(5
INS)) is different from zero (Figure 5).
Such problem will be soon after removed with AD_
TRAPEZ (§ 3.4).
Both (33) and (41) establish that pi increases from
zero to a saturation value (Figure 6) given by the prod-
uct k1i
INS reached at the end of transient time (ti = TI =
5
INS). Moreover, (32) establishes that during the tran-
sient time (0 ti TI) the second time derivation of
pEAi(ti) is positive, the time rate of pEAi(ti) increasing
from 0 to k1i, that is the slope selected for pAWi(ti). The
last results are equally remarkable if compared to those
obtained with AD_SQUARE. Unlike AD_SQUARE,
indeed, where pEAi(ti) waveform can be controlled only
by selecting the maximum (PI) constant level of pAW
(control of first order), in AD_TRIANG pEAi(ti) wave-
form can be much safely controlled by selecting k1i value
under of which the pEAi(ti) increasing rate with time is
certainly kept (control of second order).
Considering both (34) and (38), VTID for an inspiration
time equal to TI (VTID(TI)), results as follows:

1
504
TIDpiINSpiiP INS
VTIvTIvkC
 (42)
From both (12) and (42), VMIN for an inspiration time
equal to TI (VMIN(TI)), results as follows:

1
48 iINS
MIN
I
NS EXP
k
VTIRR
(43)
(43) takes into account that TE is set equal to 5
EXP
3.3.2).
Expressions (37)-(43) provide the rationale for the op-
timization of ventilation control in AD_TRIANG during
the time of inspiration.
k1i value required for delivering in the same time (TI =
5
INS) the same VTID as in AD_SQUARE (ksqu1i) can be
determined by setting (42) equal to (11), obtaining the
F. Montecchia / J. Biomedical Science and Engineering 4 (2011) 320-340
Copyright © 2011 SciRes. JBiSE
327
following expression:
14
E
XT
squ iINS
PI PEEP
k
(44)
Under the last condition (k1i = ksqu1i), the following ex-
pressions result:
4
E
XT
PI PEEP
PIP PI
 (45)
PAP PI (46)
4
E
XT
PI PEEP
PIPPAP
 (47)

4
E
XT
INS INS INS
PI PEEP
PIP PAP
TI RR
 (48)
So, the peak of
INS and PIP required in AD_TRIANG
for delivering in the same time (TI = 5
INS) the same
VTID and thus for reaching the same PAP as in
AD_SQUARE shows a 75% reduction and increases a
quarter of the difference between upper (PI) and lower
(PEEPEXT) pAW constant levels, respectively.
The diagnostic procedure has to be implemented as
follows. According to both (1) and (31), the measure-
ment of the time required for reaching the end of tran-
sient inspiration time (tTI = 5
INS), i.e. for observing a
differential increase of
INS with time lower than one
percent (1%) or saturated
INS (
INS(tTI=5
INS)), is useful
for the determination of
INS, as follows:
5
TI
INS
t
(49)
According to (39), for a given k1i value, the monitoring
of
INS(tTI=5
INS) leads to the determination of CP, as
follows:
1
(5)
I
NS TIINS
Pi
t
Ck
(50)
From (1), (49) and (50), RINS can be determined as fol-
lows:
1
5(5)
INSTI i
INS
P
INS TIINS
tk
RCt

 (51)
Once
INS, CP and RINS have been determined, TI should
be set equal to the measured tTI (TI = tTI) and k1i regula-
tion should be performed in order to fit the clinical re-
quirements on PIP, PAP, VTID or VMIN through (37), (40),
(42) or (43), respectively. In particular, concerning with
dual-control mode, k1i values ensuring the pre-set VTID
(k1iTID) or VMIN (k1iMIN) can be determined from (42) or
(43), as follows:
14
TID
iTID
P
INS
V
kC
(52)

148
M
IN INSEXP
iMIN INS
VR R
k
(53)
PIP values resulting from VTID (PIPTID) or VMIN (PIPMIN)
dual-control mode, can be obtained by inserting (52) or
(53) into (37), as follows:
5
4
TID
TID EXT
P
V
PIP PEEPC

(54)

5
48
MIN INSEXP
MIN EXT
VR R
PIP PEEP
 (55)
(54) and (55) show that PIPTID or PIPMIN are independ-
ent on RRES or CP, respectively. That is extremely rele-
vant from both physiopathological and clinical point of
view since an increase of RRES (obstructive process) or a
reduction of CP (restrictive process) does not affect the
maximum pAW value reached for dual-control mode with
pre-set VTID or VMIN, respectively.
The compensation procedure is required in order to
assimilate ALVS with an ideal pAW generator providing
for a real AD_TRIANG, i.e. triangular waveform as pAW
excitation insensitive to patient’s respiratory characteris-
tics and ventilator settings, through a proper triangular
waveform of external resistance (REXT) of ALVS which
controls pAW [9]. The electrical-equivalent network of
ALVS is shown in Figure 7. According to ALVS con-
figuration and performances [9], the compensation pro-
cedure requires that during both inspiration and expira-
tion the airflow crossing REXT, i.e. the external airflow
(
EXT), must be kept constant and equal to the equilib-
rium value assumed in initial steady conditions during
apnea (
EXT0), for which the following expressions re-
sult:
Figure 7. Electrical-equivalent network of ALVS. The compo-
nents crossed with folded arrows are devices whose character-
istic parameter output can be varied according to input setting
control.
F. Montecchia / J. Biomedical Science and Engineering 4 (2011) 320-340
Copyright © 2011 SciRes. JBiSE
328
0
RES
(56)
00
0
G
EXT VENG
P
R

 (57)
0
00
0
G EXT
EXTEXTEXTG
PR
PEEPR R
 (58)
VEN0 is the steady equilibrium value assumed by the
ventilation airflow (
VEN), i.e. the airflow delivered by
the generator. REXT0 is the lowest REXT value set for
PEEPEXT regulation by means of (58). PG and RG0 are the
output pressure and equilibrium value assumed by the
internal resistance (RG) of ALVS generator, respectively,
both set for
VEN0 regulation by means of (57), according
to the following initial steady condition:
00G EXT
RR (59)
Considering (58), (59) implies the following condition:
G EXT
PPEEP (60)
If
EXT is stabilized on constant steady
EXT0 value,
AD_TRIANG can be obtained by modeling REXT wave-
form (REXT(t)) as linear increasing of REXT from REXT0 to
its maximum value (*
E
XT
R) during inspiration (0 ti TI)
and as instantaneous fall of REXT from *
E
XT
R to REXT0
followed by constant keeping of REXT on REXT0 during
expiration (0 te TE). From (57) and (58), *
E
XT
R is
determined as follows:
*00
0
G EXT
EXT
E
XT GEXT
R PIPRPIP
PIP
RP PEEP
  (61)
In particular, concerning with dual-control mode,
*
E
XT
R values ensuring the pre-set VTID (*TID
E
XT
R) or VMIN
(*
M
IN
E
XT
R) can be obtained by inserting (54) or (55) into
(61), respectively, and considering (9), as follows:
*
0
5
14
TID TID
EXT EXT
V
RR
F
RC




(62)

*
0
5
148
MIN INSEXP
MIN
EXT EXTEXT
VR R
RR PEEP





(63)
So, R
EXT(ti) to be implemented for dual-control mode
during inspiration (0 ti TI) with pre-set VTID
(REXT(ti)TID) or VMIN (REXT(ti)MIN), assumes the following
expressions:

014
TID TID i
EXT iEXTINS
Vt
Rt RFRC




(64)
 
0148
M
ININSEXP i
MIN
EXT iEXTINS
VR Rt
Rt RR FRC





(65)
The stabilization of
EXT during inspiration (
EXTi(ti)) on
EXT0 can be carried out by proper modeling
VEN wave-
form during inspiration (
VENi(ti)) according to the first
Kirchhoff’s low applied at airways node of ALVS’s net-
work (Figur e 7):

0VENi iEXTi iINS iEXTINS i
ttt t

 (66)
By inserting both (57) and (31) into (66), the following
expression results:

1
0
1e
i
INS
t
G
VENiii P
G
P
tkC
R


 


(67)
The second Kirchhoff’s low applied to the circuit of
ALVS generator (Figure 7), assumes the following ex-
pression:
 
0
GGii VENiiAWii
PRtt p t
 (68)
RGi(ti) is the RG waveform to be implemented for per-
forming an effective compensation procedure during
inspiration. By inserting both (67) and (20) into (68),
RGi(ti) can be determined as follows:

1
1
0
1e
i
INS
GEXTi i
Gi it
GiP
G
PPEEP kt
Rt PkC
R





(69)
From (69), on account of (60), the maximum (RGi*)
and minimum (Gi
R
) values assumed by RGi(ti) at the
beginning (ti = 0) and at end (ti = TI) of the time during
inspiration (ti), respectively, result as follows:
*
0
0
Gi GiG
RR R (70)

1
0
Gi
G
Gi GiP
G
PPIP
RRTIPkC
R

(71)
So, considering that in coincidence with the end of in-
spiration (ti = TI ), i.e. the end of transient inspiration time,
RGi and REXTi assume their minimum (Gi
R) and maximum
(*
E
XT
R) values, respectively, RGi modeling must take into
account the following final steady condition:
*
Gi
E
XT
RR
(72)
According to both (70) and (71), i.e. to condition Gi
R
< RG0 and considering (61), (72) implies the following
condition:
G
PPIP (73)
Obviously, (72) and (73) replace (59) and (60), re-
spectively. On account of both (73) and (58), (69) and (71)
reduce to the following expressions, respectively:

1
0
0
10
1e
1e
i
INS
i
INS
G
Gi it
GiP
G
G EXT
t
EXTi EXTP
P
Rt PkC
R
R PEEP
PEEPk RC










(74)
F. Montecchia / J. Biomedical Science and Engineering 4 (2011) 320-340
Copyright © 2011 SciRes. JBiSE
329

0
10
1
0
Gi
GG EXT
Gi G
E
XTi EXTP
iP
G
PR PEEP
RRTIPPEEPk RC
kC
R

(75)
Moreover, in order to avoid that Gi
R reaches unpractical
reduced values, the following condition should be prop-
erly taken into account:
0
2
Gi
G
R
R (76)
Considering (75), (76) leads to the following functional
limitation on k1i value:
1
00
G
E
XT
iP GP EXT
PPEEP
kCRCR
 (77)
The function RGi(ti) is reported in Figur e 8.
3.3.2. Expiration time
The application of the second Kirchhoff’ law to the
circuit of Figure 3 provides for the following equa-
tion:
 
0
AWe eEXPEXP eEAe e
ptR tpt
 (78)
As AD_SQUARE, AD_TRIANG requires the fol-
lowing expression of pAWe(te):

AWe eEXT
p tPEEP (79)
As it is well known,

E
XP e
t
is defined as the time
derivation of vPe(te), as follows:
 
d
d
P
ee
EXP ee
vt
tt
 (80)
Considering (3) as well as by inserting both (79) and
(80) into (78), the following equation results:
Figure 8. Internal resistance (RG(t)) of ALVS generator as a
function of time (t) to be implemented for performing the
compensation procedure in AD_TRIANG.

d0
d
Pe ePe e
EXT EXPeP
vt vt
PEEP RtC
 (81)
In order to solve Eq.81, i.e. to find out the transient
and steady expressions of vPe(te), it is useful to trans-
form it from time (te) to Laplace (s) variable domains,
as follows:
 
00
Pe
EXT EXP PePeP
vs
PEEP Rsvsv
sC


(82)
From both (2) and (38), on account of continuity con-
dition on vP when the switching between inspiration
and expiration takes place (vPe(0) vPi (TI)), the solu-
tion of (82) consists in the following expression:


1
4
1
iPINS
XP
Pe
EXP
F
RC
FRCk Cs
vs
ss




(83)
Eq.83 can be properly decomposed as follows:

1
Pe
E
XP
AB
vs ss

(84)
The unknown constants A and B can be determined by
setting Eq.83 equal to Eq.84, resulting as follows:
A = FRC (85)
B = 4k1iCP
INS (86)
Finally, by inserting (85) and (86) into (84), the fol-
lowing expression results:

1
4
1
iPINS
Pe
EXP
kC
FRC
vs ss

(87)
According to the Inverse Laplace Transform of (87),
the function vPe(te) assumes the following expression:

1
4e
e
E
XP
t
PeeiPINS
vtFRC kC
 (88)
The functions
EXP(te) and pEAe(te) can be determined
considering (80) and (3), respectively, as follows:

1
4e
e
E
XP
t
iINS
EXP e
EXP
k
tR
(89)

1
4e
e
E
XP
t
EAeeEXTi INS
p tPEEPk
 (90)
The functions vPe(te),
EXP(te) and pEAe(te) are re-
ported in Figure 4, Figure 5 and Figure 6, respec-
tively.
The difference between pAWe(te) and pEAe(te) (pe(te))
can be determined from both (79) and (90), as follows
F. Montecchia / J. Biomedical Science and Engineering 4 (2011) 320-340
Copyright © 2011 SciRes. JBiSE
330
(Figure 6):

1
4
e
E
XP
t
ee iINS
ptk v
 (91)
The same result of (91) could also be obtained by in-
serting (89) into (78).
Considering (88), (89) and (90) at the beginning of
expiration time (te = 0), the following expressions
result:
 
1
04
PeiP INSPi
vFRCkCvTI
 (92)

1
4
0iINS
EXP
EXP
k
R
(93)
 
1
04
EAeEXTi INSEAi
pPEEPkp TI
 (94)
(92) and (94) fit well (38) and (40), respectively, ac-
cording to continuity condition required between the end
of inspiration and the beginning of expiration (Figure 4
and Figure 6). Unlike our purpose, (39) together with (93)
establish a considerable discontinuity occurring on
RES at
the end of every inspiration when the switching between
inspiration and expiration takes place (Figure 5). Such
problem will be soon after removed with AD_ TRAPEZ
(§ 3.4).
If TE is set equal to the time required for reaching the
steady condition, i.e. the end of transient expiration time
(tTE = 5
EXP), (88), (89), (90) and (91) provide for the
following expressions:

5
1
54e 0
PeINSiP INSPi
vTEFRC kCFRCv


(95)


15
4
5e0
iINS
EXPINS EXP
k
TE R

  (96)


5
1
54e
0
EAeINSEXTi INS
EXTEAi
pTEPEEP k
PEEP p

 
 (97)

5
1
54e0
eINSi INS
pTEk

  (98)
(95) and (97) fit well (34) and (36), respectively, ac-
cording to continuity condition required at the transition
between the end of every expiration and the beginning of
the following inspiration (Figure 4 and Figure 6). More-
over, according to our purpose, (96) together with (35)
establish the real elimination of
RES discontinuity occur-
ring in coincidence with such a transition (Figure 5).
The diagnostic procedure has been implemented as
follows. According to both (2) and (89), the measure-
ment of the time required for reaching the end of tran-
sient expiration time (tTE = 5
EXP), i.e. for observing a
ninety nine per cent (99%) reduction of
EXP with regard
to its initial value (
EXP(0)), is useful for the determina-
tion of
EXP, as follows:
5
TE
EXP
t
(99)
According to (93), for a given k1i and
INS values, the
monitoring of
EXP(0) leads to the determination of REXP,
as follows:

1
4
0
iINS
EXP EXP
k
R
(100)
From (2), (99) and (100), CP can be determined as fol-
lows:

1
0
20
TE EXP
EXP
P
E
XPi INS
t
CRk
 (101)
(101) can be employed for confirming the result ob-
tained with (50). Once
EXP, REXP and CP have been de-
termined, TE should be set equal to the measured tTE (TE
= tTE).
So, considering (58) and (79), REXT(te) to be imple-
mented for dual-control mode during expiration (0 te
TE) with pre-set VTID (REXT(te)TID) or VMIN (REXT(te)MIN),
assume the following expression:

0
TID MIN
E
XT eEXT eEXT
Rt RtR (102)
The compensation procedure, i.e. the stabilization of
EXT during expiration (
EXTe(te)) on
EXT0 can be carried
out by proper modeling
VEN waveform during expiration
(
VENe(te)) according to the first Kirchhoff’s low applied
at airways node of ALVS’s network (Figure 7):

0VENe eEXTeeEXP eEXTEXP e
tttt

 (103)
By inserting both (57) and (89) into (103), the following
expression results:

1
0
4e
e
E
XP
t
GiINS
VENe eGEXP
Pk
tRR
 (104)
The second Kirchhoff's low applied to the circuit of
ALVS generator (Figure 7), assumes the following ex-
pression:
 
0
GGee VENeeAWee
PRttp t
 (105)
RGe(te) is the RG waveform to be implemented for per-
forming an effective compensation procedure during
expiration. By inserting both (104) and (79) into (105),
RGe(te) can be determined as follows:

1
0
4e
e
E
XP
G EXT
Ge et
GiINS
G EXP
P PEEP
Rt Pk
RR
(106)
From (106), on account of (60), the maximum (*
Ge
R) and
minimum (Ge
R
) values assumed by RGe(te) at the be-
ginning (te = 0) and at end (te = TE) of the time during
F. Montecchia / J. Biomedical Science and Engineering 4 (2011) 320-340
Copyright © 2011 SciRes. JBiSE
331
expiration (te), respectively, result as follows:

*
1
0
04
Ge
G
Ge GiINS
G EXP
P
RR Pk
RR

(107)

0
Ge Ge G
RRTER
 (108)
On account of both (58) and (60), (106) and (107) re-
duce to the following expressions, respectively:

1
0
0
10
4e
4e
e
EXP
e
E
XP
G
Ge et
GiINS
G EXP
GEXTt
iEXT INS
EXT EXP
P
Rt Pk
RR
RPEEP
kR
PEEP R
(109)

*0
10
04
Ge
G EXT
Ge iEXT INS
EXT EXP
R PEEP
RR kR
PEEP R

(110)
The function RGe(te) is reported in Figure 8.
So that, in conclusion, the implementation of (74) and
(109) during the inspiration (0 ti TI) and expiration
(0 te TE) times, respectively, ensures the compensa-
tion procedure to be carried out, providing for an effec-
tive AD_TRIANG.
From Figure 2, Figure 6, (12), (15), (16), (20), (32),
(44), (79) and (90), it is easy to demonstrate that MAP
and MEP values of AD_TRIANG (MAPtri and MEPtri)
result as follows:


0 625
E
XT INS
tri EXTINS EXP
PI PEEP.
MAP PEEP

 (111)



0425 02
tri EXT
E
XTINS EXP
INS EXP
MEP PEEP
PI PEEP..



(112)
In comparison with (17), (111) shows a 37.5% reduction
of the component of MAPtri above PEEPEXT with regard
to the same component of MAPsqu. Moreover, in com-
parison with (18), (112) shows a 31.3% reduction of the
component of MEPtri above PEEPEXT with regard to the
same component of MEPsqu, if the ratio between
EXP and
INS is estimated twice.
3.4. Advanced Trapez oida l Waveform as Airways
Pressure Excitation (AD_TRAPEZ)
Figure 9 shows the advanced trapezoidal waveform as
pAW excitation (AD_TRAPEZ). In AD_TRAPEZ the
time of inspiration (0 ti TI) is divided into two sub
Figure 9. The advanced trapezoidal waveform as airways pre-
ssure (pAW(t)) excitation (AD_TRAPEZ).
sequent intervals of time lasting t1 and t2. During first (0
ti t1) and second (t1 ti t1 + t2 = TI) intervals, pAW
increases linearly with an higher slope (k2i) from mini-
mum or PEEPEXT to maximum or peak (PIP) values and
keeps constant on PIP value, respectively. Therefore, t1,
t2 and k2i fit the following conditions:
12tt TI
(113)
21ii
kk (114)
As in AD_TRIANG, the linear increase of pAW has been
selected for smoothing
RES discontinuity occurring at
the beginning of every inspiration, but its duration has
been reduced (t1 < TI) for having a following interval (t2
= TI t1) with constant pAW available for reducing to
zero the final value of
INS. Unlike AD_SQUARE and
AD_TRIANG, during the time of expiration (0 te TE)
pAW is no more kept constant on PEEPEXT. During the
first interval of expiration (0 te t3), pAW linearly falls
with a slope k2e from PIP to PEEPEXT values for reduc-
ing to zero the initial value of
EXP, while during the
second interval of expiration (t3 te t3 + t4 = TE) pAW
keeps constant on PEEPEXT value for reducing to zero
the final value of
EXP. Obviously, t3 and t4 fit the fol-
lowing condition:
t3 + t4 = TE (115)
In such a way, according to our purpose, the discontinu-
ity on
RES occurring in AD_TRIANG at the end of
every inspiration when the switching between inspiration
and expiration takes place can be completely removed.
AD_TRAPEZ can be carried out by connecting the
patient’s airways with an ideal generator creating a
trapezoidal waveform of pAW. The electrical-equivalent
circuit of AD_TRIANG generator connected to the pa-
tient’s airways is shown in Figure 10.
3.4.1 Inspiration Time
Concerning the first interval of inspiration (0 ti t1),
F. Montecchia / J. Biomedical Science and Engineering 4 (2011) 320-340
Copyright © 2011 SciRes. JBiSE
332
Figure 10. Electrical-equivalent circuit of AD_TRAPEZ gen-
erator connected to the patient’s airways.
according to the results of § 3.3.1, if t1 is set equal to
2
INS (t1 = 2
INS), the following expressions result:

2
12 2
AWiINSEXTi INS
ptPIPPEEP k
 (116)

2
2
2
122 1e
114
piINSi PINSINS
iPINS
vtFRCk C
FRC.k C


 (117)


2
22
121e0.86
I
NSINSi Pi P
tkC kC

  (118)


2
12
12
1.14
pi INS
EAi INSP
E
XTi INS
vt
pt C
PEEPk


(119)

2
1212 12
0.86
i INSAWi INSEAi INS
iINS
ptptpt
k

 
(120)
According to AD_SQUARE analysis (§ 3.1), during
the second interval of inspiration (t1 ti t1 + t2 = TI),
on account of initial conditions (ti = t1) established by
(116)-(120), the following expressions can be deduced:


2
12
AWiiAWiEXTi INS
pt ptPIPPEEPk
 (121)

 
1
1
2
11e
20.86e
i
INS
i
INS
tt
EAi iAWii
tt
EXTiINS
pt ptpt
PEEP k






(122)
 
1
220.86e
i
INS
Pi iEAiiP
tt
iPINS
vtp tC
FRCk C


 


(123)
 
1
2
0.86 e
i
I
NS
tt
i iAWi iEAi iiINS
ptptptk
(124)

1
2
0.86 e
i
I
NS
tt
ii
INSii P
INS
pt
tkC
R
 (125)
The functions vPi(ti),
INS(ti) and pEAi(ti) are reported in
Figure 11, Figure 12 and Figure 13, respectively.
If t2 is set equal to 3
INS (t2 = 3
INS) and from (113), the
following conditions result:
5
I
NS
TI
(126)
21.51tt
(127)
Condition (126) allows the best functional comparison
between AD_SQUARE, AD_TRIANG and AD_TRA-
PEZ, while condition (127) represents the best trade-off
for minimizing the final value of
INS anyhow retaining a
sufficient degree of smoothing on
INS rising at the be-
ginning of inspiration (Figure 12).
At the end of inspiration time (ti = TI) with an
AD_TRAPEZ for which both (126) and (127) result, the
following expressions can be deduced:
 
2
512
2
AWiINS AWiINS
EXTi INS
pTIptPIP
PEEP k

 
 (128)
3
2
2
5
2 0.86e
2
EAiINS
EXTi INS
EXTi INS
pTI PAP
PEEP k
PEEP k





(129)
 
2
55
2
p
i INSEAiINSP
iPINS
vTIpTIC
FRCk C

 
 (130)
 
555
0
i INSAWi INSEAi INS
pTIpTIp TI

 
(131)


5
50
iINS
INS INSINS
pTI
TI R



(132)

2
5502
TIDINSpiINSpiiP INS
VTIvTIv kC

  
(133)
From both (12) and (133), VMIN for an inspiration time
equal to TI (VMIN(TI)), results as follows:

2
24 iINS
MIN
I
NS EXP
k
VTIRR
(134)
(134) takes into account that TE is set equal to 5
EXP
3.4.2).
According to our purpose, (131) and (132) establish the
reduction to zero of both pi(TI) and
INS(TI).
F. Montecchia / J. Biomedical Science and Engineering 4 (2011) 320-340
Copyright © 2011 SciRes. JBiSE
333
Figure 11. Lung volume (vP(t)) as a function of time (t) result-
ing from the application of AD_TRAPEZ.
Figure 12. Respiratory airflow (
RES(t)) as a function of time (t)
resulting from the application of AD_TRAPEZ.
Figure 13. Endoalveolar pressure (pEA(t)) as a function of time
(t) resulting from the application of AD_TRAPEZ.
Expressions (116)-(134) provide the rationale for the
optimization of ventilation control in AD_TRAPEZ
during the time of inspiration.
k2i value required for delivering in the same time (TI =
5
INS) the same VTID as in AD_TRIANG (k1i), can be de-
termined by setting (133) equal to (42), as follows:
21
2
ii
kk (135)
Therefore, by comparing Eqs.37-43 with Eqs.116-134 in
those the condition (135) has to be taken into account, the
following consideration can be deduced. With the same
TI, VTID and thus PAP values, pAW increasing slope of
AD_TRAPEZ is practically doubled while the compo-
nent of PIP above PEEPEXT and the peak of
INS (
INS
(ti=t1)), still independent on RINS, show a 20% reduction
and a 72% increase, respectively, compared to those of
AD_TRIANG. According to our purpose, pi(TI) and
thus
INS(TI) are both practically reduced to zero Figure
13 and Figure 12).
k2i value required for delivering in the same time (TI =
5
INS) the same VTID as in AD_SQUARE (ksqu2i), can be
determined by setting (133) equal to (11), obtaining the
following expression:
21
2
2
EXT
s
quisqu i
INS
PI PEEP
kk

(136)
Under the last condition (k2i = ksqu2i), the following
expressions result:
PIP PI
(137)
PAP PI
(138)
0PIPPAP
(139)
 
043
1
E
XT
INS INS
.PIPEEP
tR
(140)
So, the peak of
INS and PIP required in AD_TRAPEZ for
delivering in the same time (TI = 5
INS) the same VTID and
thus for reaching the same PAP as in AD_SQUARE
shows a 57% reduction and keeps equals to the upper (PI)
pAW constant level, respectively.
The diagnostic procedure has to be implemented as
follows. The time required for reaching the end of tran-
sient inspiration time (tTI = 5
INS) cannot be precisely
measured with AD_TRAPEZ, due to the influence of
unknown
INS on t1 and t2. The regular application of
AD_TRIANG (§ 3.3.1) every few minutes represents the
most suitable way to solve such problem. Once tTI has
been evaluated in such a way,
INS can be determined by
means of (49). According to (118), for a given k2i value,
the monitoring of
INS(t1=2
INS) leads to the determina-
tion of CP, as follows:
2
12
0.86
I
NS INS
Pi
t
Ck

(141)
From (1), (49) and (141), RINS can be determined as fol-
lows:

2
0.86
512
INSTI i
INS P
I
NS INS
tk
RCt

 (142)
Once
INS, CP and RINS have been determined, TI should
F. Montecchia / J. Biomedical Science and Engineering 4 (2011) 320-340
Copyright © 2011 SciRes. JBiSE
334
be set equal to the measured tTI (TI = tTI) and k2i regulation
should be performed in order to fit the clinical require-
ments on PIP, PAP, VTID or VMIN through (128), (129),
(133) or (134), respectively. In particular, concerning
with dual-control mode, k2i values ensuring the pre-set
VTID (k2iTID) or VMIN (k2iMIN) can be determined from (133)
or (134), as follows:
22
TID
iTID
P
INS
V
kC
(143)

224
MIN INSEXP
iMIN INS
VRR
k
(144)
PIP values resulting from VTID (PIPTID) or VMIN (PIPMIN)
dual-control mode, can be obtained by inserting (143) or
(144) into (128), as follows:
TID
TID EXT
P
V
PIPPEEPC

(145)

12
M
IN INSEXP
MIN EXT
VR R
PIP PEEP
 (146)
In the same way as (54) and (55), (145) and (146) show
that PIPTID or PIPMIN are independent on RRES or CP,
respectively. That is, again, extremely relevant from both
physiopathological and clinical point of view since an
increase of RRES (obstructive process) or a reduction of CP
(restrictive process) does not affect the maximum pAW
value reached for dual-control mode with pre-set VTID or
VMIN, respectively. Moreover, by comparing (145) and
(146) with (54) and (55), respectively, the component of
PIPTID and PIPMIN above PEEPEXT of AD_TRAPEZ both
show a 20% reduction with respect to those of AD_
TRIANG.
The compensation procedure is required in order to
assimilate ALVS with an ideal pAW generator providing
for a real AD_TRAPEZ, i.e. trapezoidal waveform as pAW
excitation insensitive to patient’s respiratory characteris-
tics and ventilator settings through a proper trapezoidal
waveform of external resistance (REXT) of ALVS which
controls pAW [9]. The electrical-equivalent network of
ALVS is shown in Figure 7. With the same approach
described in § 3.3.1, if
EXT is stabilized on constant
steady
EXT0 value, AD_TRAPEZ can be obtained by
modeling REXT waveform during inspiration (REXTi(ti)) as
linear increasing of REXT from REXT0 to *
E
XT
R in the first
interval (0 ti t1) and as constant keeping of REXT on
*
E
XT
R in the second interval (t1 ti t1 + t2), respectively,
while during expiration (REXTe(te)) as linear decreasing of
REXT from *
E
XT
R to REXT0 in the first interval (0 te t3)
and as constant keeping of REXT on REXT0 in the second
interval (t3 te t3 + t4), respectively. In particular,
concerning with dual-control mode, *
E
XT
R values en-
suring the pre-set VTID (*TID
E
XT
R) or VMIN (*
M
IN
E
XT
R) can be
obtained by inserting (145) or (146) into (61), respec-
tively, and considering (9), as follows:
*
01
TID TID
EXT EXT
V
RR
F
RC




(147)

*
0112
MIN INSEXP
MIN
EXT EXTEXT
VR R
RR PEEP

(148)
So, REXT(ti) to be implemented for dual-control mode
during the first (0 ti t1) and second (t1 ti TI) in-
terval of inspiration (0 ti TI) with pre-set VTID
(REXT(ti)TID) or for VMIN (REXT(ti)MIN), assume the following
expressions:
0
(01)12
TID TIDi
EXT iEXTINS
Vt
RttRFRC

 



(149)
 
0
01 124
M
ININSEXP i
MIN
EXT iEXTINS
VR Rt
RttR RFRC

 



(150)
*
1TID TID
E
XT iEXT
RttTI R (151)
*
1
M
IN MIN
E
XT iEXT
RttTI R (152)
According to (66), the stabilization of
EXT during inspi-
ration (
EXTi(ti)) on
EXT0 can be carried out by proper
modeling
VEN waveform during inspiration (
VENi(ti)).
Concerning the first interval of inspiration (0 ti t1),
on account of (20) and (31) with k2i instead of k1i as well
as (57), (66) and (68), the following expressions result:

2
0
1e
i
INS
t
G
VENiii P
G
P
tkC
R


 


(153)

2
2
0
1e
i
INS
GEXTii
Gi it
GiP
G
PPEEPkt
Rt PkC
R





(154)
With k2i instead of k1i, (70)-(77) can be retained and in
particular, (74) assumes the following expression:

2
0
0
20
1e
1e
i
INS
i
INS
G
Gi it
GiP
G
G EXT
t
EXTiEXTP
P
Rt PkC
R
RPEEP
PEEPk RC










(155)
Concerning the second interval of inspiration (t1 ti
t1 + t2 = TI), on account of (121) and (125) as well as (57),
(66) and (68), the following expressions result:
F. Montecchia / J. Biomedical Science and Engineering 4 (2011) 320-340
Copyright © 2011 SciRes. JBiSE
335

1
2
0
0.86 e
i
I
NS
tt
G
VENiiiP
G
P
tkC
R
 (156)

2
1
2
0
2
0.86 e
i
INS
GEXTi INS
Gi itt
GiP
G
PPEEP k
Rt PkC
R

(157)
On account of (73) and (58), (157) reduces to the fol-
lowing expressions:

1
2
0
0
1
20
0.86 e
0.86 e
i
INS
i
I
NS
G
Gi itt
GiP
G
G EXT tt
EXTi EXTP
P
Rt PkC
RRPEEP
PEEPk RC
(158)
The function RGi(ti) is reported in Figur e 14.
So that, the implementation of (155) and (158) during
the first (0 ti t1) and second (t1 ti t1 + t2 = TI)
intervals, respectively, ensures the compensation proce-
dure to be carried out during the whole inspiration time (0
ti TI).
3.4.2. Expiration Time
Concerning to the first interval of expiration (0 te t3),
according to (128) and to Figure 9, AD_TRAPEZ re-
quires the following expression of pAWe(te):

2
21
3
e
AWeeEXTi INS
t
p tPEEPkt

 


(159)
Considering both (3) and (9) as well as by inserting both
(159) and (80) into (78), the following equation results:
 
2
21
3
d0
d
e
EXTi INS
Pe ePe e
EXP eP
t
PEEP kt
vt vt
RtC





(160)
In order to solve Eq.160, i.e. to find out the transient and
steady expressions of vPe(te), it is useful to transform it
from time (te) to Laplace (s) variable domains, as follows:
 
2
2
2
2
23
00
iINS
EXTi INS
Pe
EXP PePeP
k
PEEP kt
ssvs
Rsvsv C



(161)
Figure 14. Internal resistance (RG(t)) of ALVS generator as a
function of time (t) to be implemented for performing the
compensation procedure in AD_TRAPEZ.
From (2) and (130), on account of continuity condition on
vP when the switching between inspiration and expiration
takes place (vPe(0) vPi(TI)), the solution of (161) con-
sists in the following expression (see * in the end):
Eq.162 can be properly decomposed as follows:

21
Pe
E
XP
AB C
vs s
ss

(163)
The unknown constants A, B and C can be deter-
mined by setting Eq.162 equal to Eq.163, resulting as
follows:
2
2
3
iPINS
kC
At
 (164)
2
2
21
3
21
3
EXP
PEXTiINS
EXP
iPINS
B CPEEPkt
FRCk Ct








(165)
2
2
3
iP INSEXP
kC
Ct
 (166)
Finally, by inserting (164), (165) and (166) into (163),
*


222
2
2
22
23
1
E
XT iINSiINS
iPINS EXP
EXP
Pe
E
XP
PEEP kk
FRCk CsstR
R
vs
ss

 





(162)
F. Montecchia / J. Biomedical Science and Engineering 4 (2011) 320-340
Copyright © 2011 SciRes. JBiSE
336
the following expression results:

2
2
2
2
2
3
21
3
2
3
1
iPINS
Pe
EXP
PEXTi INS
iPINSEXP
EXP
kC
t
vs s
CPEEPkt
s
kC
t
s









(167)
According to the Inverse Laplace Transform of (167), the
function vPe(te) assumes the following expression:

2
2
2
2
3
21
3
2e
3
e
E
XP
iPINS
Pe ee
EXP
iPINS
t
iP INSEXP
kC
v ttFRC
t
kC t
kC
t

 




(168)
The functions
EXP(te) and pEAe(te) can be determined
considering (80) and (3), respectively, as follows:

2
21e
3
e
EXP
t
iPINS
EXP e
kC
tt





(169)

2
2
2
2
3
21
3
2e
3
e
EXP
iINS
E
Ae eeEXT
EXP
iINS
t
i INSEXP
k
ptt PEEP
t
kt
k
t

 




(170)
The difference between pAWe(te) and pEAe(te) (pe(te))
can be determined from both (159) and (170), as follows
(Figure 13):

2
21e
3
e
EXP
t
iINSEXP
ee
k
pt t



 


(171)
The same result of (171) could also be obtained by in-
serting (169) into (78).
Considering (168), (169) and (170) at the beginning of
expiration time (te = 0), the following expressions result:
 
2
02
peiP INSpi
vFRCkCvTI
 (172)

00
EXP
(173)
 
2
02
EAeEXTi INSEAi
pPEEPkpTI
 (174)
(172) and (174) fit well (130) and (129), respectively,
according to continuity condition required at the transi-
tion between the end of inspiration and the beginning of
expiration (Figure 11 and Figure 13). Moreover, ac-
cording to our purpose, (173) together with (132) estab-
lish the real elimination of
RES discontinuity occurring in
coincidence with such transition and the reduction to zero
of
EXP(0) (Figure 12).
If t3 is set equal to
EXP (t3 =
EXP), the following ex-
pressions result:
3
AWe EXPEXT
p tPEEP
 (175)
2
3126
P
eEXP iPINS
vt FRC.kC
 (176)
2
126
3iINS
EXP EXPEXP
.k
(t) R

 (177)
2
3126
E
AeEXPEXTi INS
ptPEEP. k
  (178)
2
3126
eEXPiINS
pt .k
  (179)
According to AD_SQUARE analysis (§ 3.1), during
the second interval of expiration (t3 te t3 + t4 = TE),
on account of initial conditions (te = t3) established by
(175)-(179), the following expressions can be deduced:
3
AWe eAWeEXT
p tptPEEP (180)

 
3
3
2
33e
1.26 e
e
EXP
e
E
XP
tt
EAe eAWee
tt
EXTiINS
pt ptpt
PEEP k






(181)
 
3
2
1.26e
e
E
XP
tt
PeeEAeePiP INS
vtp tC FRCkC

(182)


33
2
3 e1.26e
ee
E
XP EXP
tt tt
ee eiINS
pt ptk


  (183)

3
2
1.26 e
e
E
XP
tt
ee iINS
EXP eEXP EXP
pt k
tRR
  (184)
The functions vPe(te),
EXP(te) and pEAe(te) are reported
in Figure 11, Figure 12 and Figure 13, respectively.
If t4 is set equal to 4
EXP (t4 = 4
EXP) and from (115),
the following conditions result:
5
I
NS
TE
(185)
443tt
(186)
Condition (185) allows the best functional comparison
between AD_SQUARE, AD_TRIANG and AD_TRA-
PEZ, while condition (186) represents the best trade-off
for minimizing the final value of
EXP along with the
increase of MAP (see (203)) and MEP (see (204)), any-
how retaining a sufficient degree of smoothing on
EXP
F. Montecchia / J. Biomedical Science and Engineering 4 (2011) 320-340
Copyright © 2011 SciRes. JBiSE
337
raising at the beginning of expiration (Figure 12).
At the end of expiration time (te = TE) with an
AD_TRAPEZ for which both conditions (185) and (186)
result, the following expressions can be deduced:


3
5
AWeEXP AWeEXT
pTE ptPEEP
 (187)
4
2
5126e
E
AeEXPEXTi INSEXT
p
TEPEEP.kPEEP


(188)


4
2
5
1.26e
PeEXP EAeP
iPINS
vTEp TEC
FRCk C
FRC


(189)

4
2
51.26e0
eEXPi INS
pTE k

  (190)

4
2
1.26 e
50
iINS
EXP EXPEXP
k
TE R

  (191)
(189) and (188) fit well (34) and (36), respectively, ac-
cording to continuity condition required at the transition
between the end of every expiration and the beginning of
the following inspiration (Figure 11 and Figure 13).
Moreover, according to our purpose, (191) together with
(35) and (190) establish the real elimination of
RES dis-
continuity occurring in coincidence with such transition
and the reduction to zero of both pe(TE) and
EXP(TE)
(Figure 12 and Figure 13). Finally, from (177) together
with (93), the peak of
EXP (
EXP(te=t3)) shows a 37%
reduction compared to those of AD_TRIANG and AD_
SQUARE (
EXP(te = 0)).
Therefore, the waveforms reported in Figure 11, Fig-
ure 12 and Figure 13 compared to those reported in
Figure 4, Figure 5 and Figure 6, respectively, show
clearly that AD_TRAPEZ induces a more physiological
reaction than AD_TRIANG. This is essensially due to the
elimination in AD_TRAPEZ of discontinuity on
RES
occurring in AD_TRIANG when the switching between
inspiration and expiration takes place.
The diagnostic procedure has to be implemented as
follows. The time required for reaching the end of tran-
sient expiration time (tTE = 5
EXP) cannot be precisely
measured with AD_TRAPEZ, due to the influence of
unknown
EXP on t3 and t4. The regular application of
AD_TRIANG (§ 3.3.2) every few minutes represents the
most suitable way to solve such problem. Once tTE has
been evaluated in such a way,
EXP can be determined by
means of (99). According to (177), for a given k2i and
INS
values, the monitoring of
EXP(t3=
EXP) leads to the de-
termination of REXP, as follows:

2
1.26
3
iINS
EXP
E
XP EXP
k
Rt

(192)
From (2), (99) and (192), CP can be determined as fol-
lows:

2
3
6.3
TE EXPEXP
EXP
PEXPi INS
tt
CRk

 (193)
(193) can be employed for confirming the result obtained
with (141). Once
EXP, REXP and CP have been determined,
TE should be set equal to the measured tTE (TE = tTE).
So, considering (58), (133), (134), (159) and (180),
REXT(te) to be implemented for dual-control mode during
the first (0 te t3) and second (t3 te TE) interval of
expiration (0 te TE) with pre-set VTID(REXT(te)TID) or
VMIN (REXT(te)MIN), assumes the following expressions:

0
031 1
3
TID e
TID
EXT eEXT
t
V
RttRFRC t


 




(194)

0
03 11
12 3
MIN INSEXP
MIN e
EXT eEXTEXT
VR Rt
RttRPEEP t
 

(195)
 
0
33
TID MIN
E
XT eEXT eEXT
RttTERttTER
(196)
According to (103), the compensation procedure, i.e.
the stabilization of
EXT during expiration (
EXTe(te)) on
EXT0 can be carried out by proper modeling
VEN wave-
form during expiration (
VENe(te)).
Concerning the first interval of expiration (0 te t3),
on account of (57), (159) and (169) as well as (103) and
(105), the following expressions result:

2
0
21e
3
e
EXP
t
GiPINS
VENe eG
PkC
tRt





(197)

2
2
0
21
3
21e
3
e
EXP
e
GEXTiINS
Ge et
GiPINS
G
t
PPEEP kt
Rt PkC
Rt

 







(198)
On account of both (73) and (58), (198) reduces to the
following expression:

2
0
0
20
21e
3
21e
3
e
EXP
e
EXP
G
Ge et
GiPINS
G
G EXT
t
iEXTP INS
EXT
P
Rt PkC
Rt
RPEEP
kR C
PEEP t










(199)
F. Montecchia / J. Biomedical Science and Engineering 4 (2011) 320-340
Copyright © 2011 SciRes. JBiSE
338
Concerning the second interval of expiration (t3 te
t3 + t4 = TE), on account of (57), (180) and (184) as well
as (103) and (105), the following expressions result:

3
2
0
1.26 1e
e
EXP
tt
GiINS
VENe eGEXP
Pk
tRR


 


(200)

3
2
0
1.26 1e
e
EXP
G EXT
Ge ett
GiINS
GEXP
PPEEP
Rt Pk
RR





(201)
On account of both (60) and (58), (201) reduces to the
following expressions:

3
2
0
0
3
20
1.26 1e
1.26 1e
e
EXP
e
EXP
G
Ge ett
GiINS
G EXP
G EXT
tt
i EXTINS
EXT EXP
P
Rt Pk
RR
RPEEP
kR
PEEP R










(202)
The function RGe(te) is reported in Figure 14.
So that, the implementation of (199) and (202) during
the first (0 te t3) and second (t3 te t3 + t4 = TE)
intervals, respectively, ensures the compensation proce-
dure to be carried out during the whole expiration time (0
te TE).
From Figure 9, F igure 1 3, (12), (15), (16), (116), (119),
(121), (122), (136), (159), (170), (180) and (181), it is
easy to demonstrate that MAP and MEP values of AD_
TRAPEZ (MAPtra and MEPtra) result as follows:



08 01
tra EXT
E
XTINS EXP
INS EXP
MAP PEEP
PI PEEP..



(203)



0.604 0.297
tra EXT
E
XTINS EXP
INSEXP
MEP PEEP
PI PEEP



(204)
If the ratio between
EXP and
INS is estimated twice, in
comparison with (17) and (18), (203) and (204) show that
MAPtra and MEPtra assume quite the same values of
MAPsqu and MEPsqu, respectively.
4. DISCUSSION AND CONCLUSIONS
The promising experimental results, according to theo-
retical ones, carried out in a previous work with the Ad-
vanced Lung Ventilation System (ALVS), set for apply-
ing a real square waveform as airways pressure excitation
to a proper lung simulator reproducing the steady and
linear respiratory mechanics of anaesthetized or severe
brain injured patients, have suggested and motivated the
present work.
It consists in the theoretical study in the field of as-
sisted/controlled ventilation with advanced and impro-
ved-shape waveforms as airways pressure excitation for
the optimization of controlled breathings applied to pa-
tients the respiratory mechanics of which can be assumed
steady and linear. Advanced means insensitive to patient
(load) breathing activity as well as to ventilator settings.
Improved-shape intends in comparison to conventional
square waveform for a progressive approaching to phy-
siological transpulmonary pressure waveform producing
a more suitable reaction of patient, i.e. a more realistic
approximation of respiratory airflow and endoalveolar
pressure waveforms to physiological ones.
The problem to be solved has been the proper smoothing
of respiratory airflow vertical discontinuities occurring at
the beginning of both inspiration and expiration when the
respiratory airflow is reversed, as response to upward and
downward airways pressure vertical transitions charac-
teristic of square waveform. So that, the elimination of
such airways pressure vertical transitions is the most
relevant change to be applied on square waveform as
airways pressure excitation. For the purpose, two wave-
forms of different geometrical shape (triangular and
trapezoidal) as airways pressure excitation which pro-
gressively approach the best solution have been consid-
ered.
The results show that the application of both the di-
agnostic and compensation procedures together with the
setting of the time of inspiration and expiration equal to
five times the inspiratory and expiratory time constants,
respectively, ensure the optimization of the ventilation
control in all cases with the following different functional
implications.
Advanced triangular (AD_TRIANG) and trapezoidal
(AD_TRAPEZ) waveforms have been considered in
comparison to conventional advanced square waveform
(AD_SQUARE) as airways pressure excitation. The
geometrical parameters of AD_TRAPEZ has been opti-
mized in such a way the resulting respiratory airflow
waveform does not show any vertical discontinuity ap-
proximating as much as possible the smoothed shape of
physiological waveform as well as keeping quite the same
values of mean airways (MAP) and endoalveolar pres-
sures (MEP) of AD_SQUARE.
AD_SQUARE shows a low physiological profile due
to the presence of two different considerable disconti-
F. Montecchia / J. Biomedical Science and Engineering 4 (2011) 320-340
Copyright © 2011 SciRes. JBiSE
339
nuities on respiratory airflow waveform occurring when
the switching between inspiration and expiration and vice
versa, take place. Concerning with dual-control mode,
tidal (VTID) and minute (VMIN) volumes are independent
on respiratory resistance and lung compliance, respec-
tively. That is extremely relevant from physiological,
clinical and engineering point of view because an in-
crease of respiratory resistance (obstructive process) or a
reduction of lung compliance (restrictive process) does
not affect the control of VTID or VMIN, respectively.
AD_TRIANG eliminates the discontinuity on respira-
tory airflow waveform between expiration and following
inspiration but increases the amount of the discontinuity
on respiratory airflow between inspiration and expiration.
Moreover, the diagnostic procedure is available for ac-
curate results. Keeping the same values of inspiration (TI)
and expiration (TE) times and thus of breathing frequency
(FR), as well as of external positive end expiratory
pressure (PEEPEXT) and VTID and thus of peak endoal-
veolar pressure (PAP) with regard to AD_SQUARE, the
peak inspiratory airways pressure (PIP) increases less
than 25% while the components of MAP and MEP above
PEEPEXT show a 37.5% and 31.3% reduction, respec-
tively.
AD_TRAPEZ eliminates both the discontinuities on
respiratory airflow waveform providing for the desired
physiological shape of both respiratory airflow and en-
doalveolar pressure waveforms. Unfortunately, the di-
agnostic procedure is not available for accurate results.
Keeping the same values of TI, TE and thus of FR,
PEEPEXT and VTID and thus PAP with regard to
AD_SQUARE, PIP as well as both MAP and MEP are
quite the same.
In both AD_TRIANG and AD_TRAPEZ, PIP result-
ing from dual-control mode with pre-set VTID or VMIN, are
independent on respiratory resistance and lung compli-
ance, respectively. That is extremely relevant from both
physiopathological and clinical point of view since an
increase of respiratory resistance (obstructive process) or
a reduction of lung compliance (restrictive process) does
not affect the maximum value of airways pressure
reached for dual-control mode with pre-set VTID or VMIN,
respectively.
So, in conclusion, AD_TRAPEZ fits well the re-
quirements for a physiological respiratory pattern con-
cerning endoalveolar pressure and airflow waveforms,
while AD_TRIANG exhibits a lower physiological be-
haviour but is anyhow periodically recommended for
performing adequately the powerful diagnostic proce-
dure.
The promising results of the present work establish the
rationale for laboratory and clinical test in the field of
dual-controlled ventilation with AD_TRAPEZ along with
AD_TRIANG.
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