Efficient algorithm for pulmonary nonlinear model online estimation of
patients under assisted ventilation
DIEGO A. RIVA and CAROLINA A. EVANGELISTA and PAUL F. PULESTON
Instituto LEICI, Facultad de Ingeniería (UNLP)
Universidad Nacional de La Plata and CONICET
48 and 116 st., C.C. 91 (1900) La Plata
ARGENTINA
Abstract: An efficient algorithm to estimate a respiratory system nonlinear model of sedated patients under as-
sisted ventilation is presented. The considered model comprises an airways resistance and a volume-dependant
compliance and, for each respiratory cycle, the proposed algorithm provides online the model parameters guar-
anteeing a minimum accuracy, above a user-defined threshold. Relying on standard nonlinear identification tech-
niques, it exhibits computational burden reduction features, which contribute to its suitability for its online appli-
cation.
Key-Words: Nonlinear Identification, Mechanical Ventilation, Nonlinear Respiratory Modelling.
Received: July 22, 2022. Revised: September 29, 2023. Accepted: October 12, 2023. Published: October 18, 2023.
1 Introduction
Continuous respiratory monitoring is an important
tool for clinical supervision in the case of patients
under assisted ventilation, specially in the case when
there is a pathology involving the lungs, airways or
some other part of the respiratory system. It is based
on a model of the respiratory system and it relies on
measuring some biological signals of the patient.
Respiratory system models are an important tool to
simulate and assess effects which are hard to evaluate
in vivo, to contribute to functional diagnosis and, par-
ticularly, to determine the best treatment for patients
in intensive care, attaining weaning more quickly and
safely [1] [2] [3] [4] [5]. The most widespread model
of the respiratory system among clinicians is a sin-
gle compartment lung model which comprises two
lumped parameters: resistance and compliance [6].
The first one considers the effect of resistance to pass
of the air flow, and the second one takes into ac-
count the elastic properties of the tissues and chest
wall. Usually, their values are computed consider-
ing specific points of the pressure and airflow signals,
measured by the respiratory machine at the patient’s
mouth, PBand F, respectively [7].
Model-based methods may help clinicians with
decisions regarding the most appropriate ventilation
strategy to improve the patient’s situation and/or to
avoid or reduce potential posterior negative effects
of mechanical ventilation (MV) [8] [9]. They in-
clude finding a lung protective compromise either
while a respiratory pathology or while under general
anaesthesia [10] [11] [12], detection of asynchronies
between the patient and the mechanical ventilation
(MV) [13] [14], or ensuring patient safety regarding
high plateau pressure values [15]. These models have
the potential to enable predictive, personalised, and
potentially automated approaches to MV. However,
most of the models used in these works are linear,
since low computational cost is an important factor to
obtain useful information of the patient in real time.
In this work, an algorithm and its user interface are
developed, with the objective of providing online the
quadratic nonlinear model of the patient’s respiratory
system with a preset accuracy. The algorithm routines
resort to standard nonlinear identification techniques
to estimate the model parameters of the patient, using
the pressure and flow signals measured at their mouth.
To better deal with online time requirements, a fit
check process is run to avoid a new full model es-
timation at every respiratory cycle. Using the input
pressure signal of the current respiratory cycle and the
last estimated model, the process computes its out-
put’s fit to the real data and compares it to a speci-
fied threshold. If the fit is greater than the threshold,
a new estimation of the model is omitted, consider-
ing that the last one truly represents the patient, i.e.
the previous model is kept as valid. The fit check is
the mechanism that aims at decreasing the amount of
models estimates of the patient, consequently reduc-
ing the computational time and burden with respect to
the case of continuous estimation. The threshold that
defines the minimum acceptable fit can be adjusted
online by the clinician, depending on the accuracy re-
quired for each particular patient, condition or case
under study.
Some results are presented, obtained when using
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the algorithm with data measured on twelve sedated
patients with COVID-19, two of them measured while
undergoing a PEEP titration manoeuvre. Such ma-
noeuvre modifies the breathing and respiratory sys-
tem condition of the patient, thus making those data
appropriate to show the main characteristics of the al-
gorithm.
The paper is structured as follows: Section 2 intro-
duces the models used by the algorithm to describe
the respiratory system of sedated patients and, next,
Section 3 gives a detailed explanation of the devel-
oped algorithm flowchart and the operation of each
block; Section 4 then presents some results obtained
by using the algorithm with data of real patients and,
finally, conclusions and some still ongoing work are
pointed out in Section 5.
2 Respiratory system models
This work considers sedated patients under assisted
ventilation, which imply on one hand, that they cannot
exert any muscular pressure, and on the other, that the
pressure and airflow at their mouths, involved in their
breathing process, can be measured.
In this section, the linear and nonlinear respiratory
system models of a sedated patient under assisted ven-
tilation are presented.
The respiratory system dynamics of a sedated pa-
tient can be described via the equation of motion [16]:
PB(t) = ˙
VT(t)Raw +Pc(VT(t)) + P EEP, (1)
where VTis the tidal volume, defined as the amount
of air that moves in and out in each respiratory cy-
cle, PBis the pressure at the patient’s mouth, the air-
flow is F(t) = ˙
VT(t), i.e. it corresponds to the time
derivative of the volume, and Raw is the airways re-
sistance. Pc, a function of the volume, is the pressure
of the chest wall & lung, and P EEP corresponds to
the base level pressure value known as Positive End
Expiratory Pressure. Note that, as the patient is se-
dated, there is no pressure term corresponding to mus-
cular activity, and also that PB(t)and P EEP will be
both, in this case, imposed by the ventilator. To sim-
plify notation, the time dependency will not be written
in the rest of the paper.
An electric equivalent model of the respiratory
system of a sedated patient can be posed according to
(1), where pressures and airflow correspond to elec-
tric voltages and current, respectively (see Fig. 1).
Ground level is the atmospheric pressure, which is
normally considered as the zero or reference value.
The most spread and commonly used model both
in the literature and by physicians is linear, where
Raw is constant and where Pcand the tidal volume are
proportional one to the other. In many situations, like
Raw
F+
−
Pc(VT)
PB
Figure 1: Electrical equivalent model of the patient’s
respiratory system.
when doing sports, when considering a baby breath-
ing or in case of certain pathologies, a linear descrip-
tion represents poorly the behaviour of the respiratory
system. According to the particular condition to be
studied, different modifications can be considered to
get a better representation of the respiratory dynam-
ics [17] [18] [19]. Two different models have been
considered in this work, depending on the description
of the Pc(VT)relation, with Raw constant:
•Linear Model (LM). This is the most popular
model used among clinicians. It is adequate in
case the relation between the chest wall & lung
pressure and the tidal volume remains somewhat
constant during the respiratory cycle (i.e., the
variations of one of them is proportional to the
variations of the other). It can be written as:
Pc(VT) = VT/C, (2)
where Cis a constant value known as compli-
ance of the subsystem and accounts for the elastic
properties of the system.
•Nonlinear Model (NM). A more accurate char-
acterisation of the relation between Pcand VT
can be obtained by considering a volume depen-
dant compliance [20]. A quadratic description,
which is nonlinear but still rather simple, is anal-
ysed in this work:
Pc(VT) = (a1+a2VT)
| {z }
C−1(VT)
VT=a1VT+a2V2
T.
(3)
Equation (3) gives a better fit than the LM most of
the times, particularly when the patient is being
ventilated out of the range of normal breathing or
presents a respiratory pathology which modifies
the lung elasticity [21].
The algorithm developed in this work makes es-
timations and validation checks aiming to provide an
accurate NM for each respiratory cycle of a connected
sedated patient, with reduced computational burden.
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3 Proposed algorithm
A description of the proposed algorithm is detailed in
this section. Fed with data of PB(t)and F(t)as input
signals, both measured at the mouth of the patient, the
algorithm computes and provides the set of parame-
ters values of the NM that best describe the patient
data for every breathing cycle.
It begins by performing a full complete estima-
tion stage, which consists of quickly estimating the
LM parameters’ values for a first breathing cycle, and
then, using them to establish the NM initial condi-
tions, obtaining the NM parameters values for that
first cycle. For the following breathing cycles, instead
of repeating the whole process, it checks if the previ-
ous obtained NM parameters adjust properly. In case
it does, they are kept as the valid NM model for the
new cycle, without any other computation.
Only when the patient’s condition changes too
much, the fit to the new data is poor and it is nec-
essary to obtain a new model. To do this, firstly the
NM estimation routine is run, but initialised using the
last valid NM parameters. Only in case this new NM
estimation is not good enough, the complete Full Es-
timation stage is performed. The minimum accepted
level is established by means of the threshold value Γ
set by the user in terms of percentage of adjustment.
The flow chart of the algorithm is presented in Fig.
2 and its detailed operation is explained in the follow-
ing subsections, together with each of its blocks.
3.1 Respiratory cycle acquisition
The proposed algorithm uses digital data of the pa-
tient’s pressure PBand tidal volume (VT) signals to
estimate the models and, for that, the latter is obtained
indirectly, computed by conditioning and integrating
the Fsignal each respiratory cycle.
The pacient’s PBand Fdigital signals can be ob-
tained either directly from the ventilator that is assist-
ing their breathing or by means of an interconnected
external respiratory monitor. In particular, a respira-
tory monitor FluxMed®GrE [22] has been utilised in
this work. This device obtains the pressure signal PB
by using a differential pressure sensor, which mea-
sures the pressure at the patient’s mouth related to the
atmospheric pressure. In the case of the airflow signal
F, it uses a fixed orifice pneumotachograph, which
measures its value and direction.
3.2 Full estimation
In this block, a full estimation stage is performed, to
obtain the nonlinear model of the respiratory system
of a patient from their pressure and flow signals in
one respiratory cycle. The full stage, explained in de-
tail below, involves a first rapid estimation of the two
Linear Model parameters, which allow a rough ini-
Respiratory
cycle acquisition
NM Initialisation
based on LM
NM estimation
fit ≥Γ?
Show Results
warning
N
Y
Full Estimation
Show Results
Respiratory
cycle acquisition
Fit check with
last valid model
fit ≥Γ?Y
N
NM Initialisation
based on NM
NM estimation
fit ≥Γ?Y
N
Loop Block
Figure 2: Flow chart of the proposed algorithm.
tialisation of the proper Nonlinear Model estimation
routine, performed next.
NM Initialisation based on LM.
Firstly, the LM is computed. To do so, standard
routines of the Matlab® identification toolbox are
used, initialised by calculating Raw and Cas indi-
cated in [23]. The identification routine, based on
minimisation methods, finds the parameters values
that minimise the next quadratic error within the res-
piratory cycle:
M(θ) = X
kˆ
VT[k]−VT[k]2.(4)
ˆ
VTis the tidal volume computed using the estimated
model (1)-(2), with the patient’s current cycle PB
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pressure as input signal and parameters θ=θL, where
θL= (C, Raw ), i.e. the parameters of the model at
each step of the iterative routine.
Once obtained the LM of current respiratory cycle,
its value of resistance is used to generate the initial
vector θN= (Raw , a1, a2)for the NM estimation of
the cycle, together with the values of a1,a2, which
are computed via a polynomial fit of (1), rewritten as
PB−F Raw =a1VT+a2V2
T.(5)
NM Estimation.
Secondly, the nonlinear identification algorithm is
run to obtain the NM of the current respiratory cycle,
by minimising (4), with θ=θN. Note that the algo-
rithm utilises the Levenberg-Marquardt method [24],
although others can be used instead [25].
The goodness of fit obtained by the NM is quan-
tified for the cycle by a normalised root-mean-square
error
NRM SE%= 100 1−||VT−ˆ
VT||
||VT−¯
VT||!,(6)
where ¯
VTis the mean value of VT. This index equals
100% for a perfect fit between the model prediction
and the real data (||VT−ˆ
VT|| = 0) and diminishes
with poorer adjustment. In case the model prediction
is no better than using the average of the data, the er-
ror index gives 0%, as ||VT−ˆ
VT|| =||VT−¯
VT||.
Fit evaluation: fit ≥Γ?
Finally, the fit of the NM to the data is compared
with a threshold value Γ, which corresponds to the ac-
cepted ‘percentage of adjustment’, selected and preset
by the user.
In case the fit equals or exceeds Γ, the NM is taken
as valid for the current respiratory cycle, and the al-
gorithm enters the Loop Block.
If, on the contrary, the fit is smaller than Γ, the ob-
tained parameters of the NM are not considered valid
and they are shown in a distinctive colour as a warn-
ing. A new respiratory cycle is then acquired and a
complete estimation stage has to be run on it (the al-
gorithm reenters the Full Estimation block).
3.3 Loop Block
Once there is a respiratory cycle with a valid NM, its
parameters are added to the plots in the user interface
window (description below in Show Results), and the
algorithm starts a loop in which it is decided, at each
respiratory cycle, whether or not to refresh the last
valid model.
To make the decision, the data of the next respira-
tory cycle is acquired and, instead of performing a full
estimation stage, a simpler computation is realised to
check how the last valid NM adjusts the real data. In
case it is accurate enough, i.e. the calculated fit is
higher than Γ, the last NM is considered valid for the
new cycle.
In case the NM is not good enough, an NM Esti-
mation is performed but, this time, initialised using
the last valid NM. It is likely that the patient’s con-
dition has not changed too much, and that those ini-
tial conditions allow for a low cost and rapid conver-
gence. A new fit check is realised and, only if this
check gives is below Γ, a complete estimation stage
is performed with the data, by returning to the Full
Estimation block.
The idea behind doing these checks in the first
place, is to reduce the computational burden and the
use of the microprocessor’s resources, while main-
taining an accurate tracking of the patient’s respira-
tory system evolution.
A detailed explanation of the blocks that have not
been presented yet, is given below.
Fit check with last valid model
To check how the last valid NM adjusts the real
data, the computation of a ˆ
VT, obtained by feeding
the last valid NM with the PBof the current respira-
tory cycle as input. Then, (6) is evaluated with that
ˆ
VTand the actual VTsignal (fit check), and this fit is
compared with Γ, resulting in two possible actions:
In case the fit is acceptable (fit ≥Γ), it means the
NM is still valid, so there is no need for a re estimation
and its parameters are kept as the valid NM for the
current cycle. The loop block is thus ready to show
the results, acquire the next respiratory cycle data and
repeat the fit check process with them.
Otherwise, fit < Γindicates that the last valid NM
no longer represents the patient with the required fi-
delity. Therefore, a new model must be obtained.
NM Initialisation based on NM.
When the last valid NM does not represent the pa-
tient anymore, a new estimation has to be performed.
However, instead of directly running the full estima-
tion stage, a simplified process is executed.
The parameter vector θNof the last valid NM is
taken as initial condition and only the NM Estimation
is performed. Note that the closeness of the initial-
isation values to the real ones increase the chance of
obtaining good results [26] therefore, although the pa-
tient’s condition changed, its last valid model seems
the best guess.
Show results
When the algorithm finishes processing the cur-
rent respiratory cycle signals, the results are (option-
ally) saved and added to the parameters display boxes
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in the user interface window. An illustrative presenta-
tion of its current version, still a preliminary one, can
be seen in Fig. 3.
Configuration
Start
Threshold [%]
85
Stop
Save models
Save data
Name
85_Pac_1_M
Name
85_Pac_1_D
Show
100
cycles
Signals
Time [s]
Nonlinear model
# Respiratory Cycle
# Respiratory Cycle
Figure 3: Preliminary user interface.
The window presents three distinguishable areas.
One of them is the Configuration area, where the user
can set the minimum accepted fit threshold, and select
some saving (optional) and viewing options. Regard-
ing the latter, the number of cycles to be shown can
be chosen, with a default of 100. In case 1 is estab-
lished, solely the current values of the signals, param-
eters and associated fit will be shown. The buttons to
start and to manually stop the estimation process are
also there.
A second area is identified as Signals, and both
input signals, airflow Fand pressure PB, are shown
there, in the time ranges corresponding to the set num-
ber of cycles.
Finally, the area at the bottom, headed Nonlinear
Model displays the values of the valid NM parameters
for the chosen range of last cycles, as well as their
achieved fit.
In case the algorithm could not reach a fit ≥Γ,
then the resulting ‘invalid’ parameters and the cycle
signals are shown to the user, but using a distinctive
red colour.
Regarding the displayed graphs, only a first ver-
sion of the user interface is presented, while an inquiry
is currently going on, in order to establish which in-
formation to present and how to show it, so that it best
helps clinicians.
4 Results using real patient’s data
The main features of the algorithm are demonstrated
and analysed through some tests and comparisons
performed with data obtained from twelve sedated pa-
tients with COVID-19 under assisted ventilation. The
graphical results correspond to patients #1and #2.
Note that, to simplify the presentation and discussions
of some results, focusing on some particular aspects,
they are not shown within the user interface.
Firstly, the results obtained by the algorithm for
160 respiratory cycles of patient #1are presented and
discussed. Their original PB(t)and F(t)signals can
be seen in Fig. 4. A PEEP titration manoeuvre was
Figure 4: 160 respiratory cycles of patient #1signals
PB(t)and F(t)to be processed by the algorithm.
performed on the patient during the 50 to 215 sec-
ond interval. Such treatment consists in increasing the
PEEP value in stepped stages until a maximum admis-
sible pressure value is reached, and then decreasing
it, making it possible to detect the region of highest
compliance in the process [27]. During a manoeuvre
of this kind, significant changes in the respiratory me-
chanics of the patients are produced [28] and, thus, it
is expected that the algorithm needs to re estimate the
NM at least at each change of the PEEP value.
Additionally, in order to compare results and per-
formance, the same signals are processed using a
‘continuous estimation’ loop, where an estimation of
the nonlinear model is performed undoubtedly for ev-
ery respiratory cycle. Except for the first respiratory
cycle, where a Full Estimation is performed, the loop
consists in acquiring the next respiratory cycle and
performing an NM estimation, initialised based on the
last NM. The obtained estimation is taken as the valid
NM whichever the fit, unless the rare case where the
algorithm fails to converge. Although this did not
happen for the tested data, in such a case, the cycle
would be discarded and marked as ‘no model avail-
able’, and the new cycle would be initialised using
the previous NM.
Therefore, the three top boxes in Fig. 5 depict
the parameters of the NM of each respiratory cycle
obtained when using the developed algorithm with
Γ = 85%, compared to the ones obtained by estimat-
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ing a new model every cycle (continuous estimation).
Additionally, the fourth plot indicates whether a new
estimation was realised to obtain the NM for the cy-
cle (‘on’ indication), as opposed to considering valid
the previous one after the fit check (‘off’). Of course,
the indication corresponding to the continuous esti-
mation process is permanently ‘on’. Lastly, the fifth
row shows the fits obtained in the two cases, together
with the selected threshold Γ. As it can be observed
Figure 5: The upper three plots show the parame-
ters values of the NM computed by the algorithm,
compared to those obtained by continuous estimation.
The fourth plot indicates whether a new estimation
was realised to obtain the NM for the cycle. The last
plot shows the fit obtained at each respiratory cycle.
by the ‘on’ indications, there are several re estima-
tions during the PEEP titration manoeuvre but, after
it, when the ventilator’s configuration is set and left
fixed, the estimated NM remains valid for the rest of
the interval, with an accuracy higher than Γ. It is ex-
pected that the algorithm activates a new model es-
timation only when there is a significant change in
the respiratory system, due to some health condition,
or when an irregular event occurs, i.e. the ventila-
tor makes an inspiratory pause to measure the plateau
pressure, the clinician modifies the PEEP or other set-
ting, among others.
As it can be seen, once a new NM is estimated
for one respiratory cycle with the proposed algorithm,
that NM remains valid for some of the following cy-
cles, where the fit lies between the established thresh-
old and the maximum attainable fit, given by the con-
tinuous estimation.
In order to illustrate the advantages of perform-
ing only a fit check instead of having to re estimate a
model, both the proposed algorithm and the ‘contin-
uous estimation’ loop were applied to the data corre-
sponding to twelve sedated patients of different char-
acteristics. The times taken to process those two
stages were counted, averaged and compared. Thus,
Table 1 shows the relation between the average time
taken to perform a fit check and the average time
taken to run a ’continuous estimation’. As it can be
Patient tF C /tCE .100%
#1 4.16%
#2 3.68%
#3 3.94%
#4 4.72%
#5 5.08%
#6 3.87%
#7 4.06%
#8 4.82%
#9 4.02%
#10 3.91%
#11 4.89%
#12 3.29%
Table 1: Average ratio of the time per cycle taken to
perform the fit check (tF C ) versus the time per cycle
taken to perform a ‘continuous estimation’ (tCE ).
appreciated, the fit check requires a very small por-
tion of the processing time required by a ‘continu-
ous estimation’. Therefore, it is immediate to infer
that the developed algorithm allows a more efficient
use of the processing resources, resulting in computa-
tional load and time reduction. The improvement of
the presented algorithm over the continuous estima-
tion method is notorious, having a favourable impact
regarding less energy consumption, i.e. less use of
battery and longer equipment service life of the mon-
itoring device.
A second set of tests aims to clarify the role of the
threshold Γ, illustrating how an appropriate selection
could drastically reduce the required estimation time
and resources, while demanding an accuracy too high
may result in long-time computations and end with
not being able to obtain valid models. To this end, the
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algorithm was run using the data set of patient #2us-
ing five different values for the minimum desired ac-
curacy, in particular Γ = 75,80,85,90 and 95 were
selected. A PEEP titration manoeuvre was also per-
formed on the patient, in this case during almost the
whole displayed interval (160 respiratory cycles, ap-
prox. 500 sec). The PB(t)signals from each of the
cases are shown in Fig. 6.
A respiratory cycle is shown in blue when a valid
NM was obtained for it through a complete estima-
tion stage; instead, a cycle is shown in black when
the valid NM of the previous cycle was adequate to
represent it, and therefore, kept as valid; finally, a red
cycle indicates that no valid model could be obtained
for that data with the required accuracy.
Figure 6: Signal pressure data for five different values
of the threshold. The colour code indicates whether
a valid NM could be obtained for each cycle, by per-
forming a new estimation (blue) or only by a fit check
(black), or not (red).
It can be immediately noted that, when a high ac-
curacy is requested, such as when selecting Γ = 95,
the algorithm tried to obtain a new model in almost
every respiratory cycle, thus increasing the computa-
tional burden. What is more, analysing the final fits,
it could be noted that when a high value was speci-
fied for Γ, there were a large number of cycles where
many of the NM, even the re estimated ones, failed to
achieve the minimum set fit. For example, in the test
with Γ = 95, only in 88% of the cycles it was possible
to obtain a valid NM, and in most of them, 79%, the
NM had to be re estimated. But, if Γis set to 85%, a
valid NM was obtained in 99,35% of the cycles, and
only 30% of them were re estimated.
To illustrate this situation, Fig. 7 shows a few cy-
cles of the estimated tidal volume signal ˆ
VT, com-
puted with the models obtained by the algorithm with
Γ = 95, together with the original VTdata of the pa-
tient. Although the signals are overlapping and look
practically coincident, three of the models could not
reach the minimum requested fit (95%), thus the al-
gorithm consider them invalid and they are shown in
red.
Figure 7: Interval from 187 −211.2s of the esti-
mated tidal volumes ˆ
VTof patient #2, together with
their original VTdata, corresponding to the test with
Γ = 95 (Fig. 6, fifth row).
On the contrary, when a low value is selected for
Γ, the algorithm performs less calculations at the ex-
pense of showing parameters values that less accu-
rately represent the patient. When Γis around 85
or 90%, a good compromise between getting a good
model and computational load is achieved. In some
cases there is no noticeable improvement, such as dur-
ing the PEEP titration manoeuvre in the examples, as
the patient’s description needed to be constantly re-
freshed and the estimation process was activated at
least at each change of PEEP value, no matter the Γ.
However, once the manoeuvre was finished and the
patient was ventilated with stable PBand Fsignals, a
new estimation had to be activated only in a few res-
piratory cycles, except when an almost perfect fit is
solicited (see both Figs. 5 and 6).
Note that, during some situations or changes, it is
not possible to obtain a valid NM, even with a not so
exigent accuracy requirement. This is the case that
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can be observed for the time interval 452.5−469.5s,
where one cycle is shown in red for all the five pre-
sented tests (see Fig. 6). The estimated tidal volumes
ˆ
VTfor these cycles are shown together with their orig-
inal VTdata, corresponding to the algorithm test with
Γ = 85 are depicted in Fig. 8. The red cycle, where
Figure 8: Five-cycles window of the estimated tidal
volumes ˆ
VTof patient #2, together with their original
VTdata, corresponding to the time interval 452.5−
469.5s of the algorithm test with Γ = 85 (see Fig. 6,
third row).
no valid NM could be obtained with any of the tested
thresholds, possibly corresponds to the large step set
for the PEEP at the end of the PEEP titration manoeu-
vre.
5 Conclusions
A new method to obtain online the model of the res-
piratory system of patients under assisted ventilation
was presented. Typically, standard equipment rely
on linear models, allowing low computational bur-
den for real-time implementation, at the expense of
accuracy. Conversely, the proposed algorithm works
with a more accurate nonlinear characterisation, and
it proved to be able to provide the parameters’ val-
ues of the nonlinear model ensuring a fit greater than
a threshold Γ, without necessity to re-estimate the
model in every respiratory cycle.
Therefore, the main advantages of this algorithm
are twofold. In the first place, enhanced modelling
can be attained with the nonlinear characterisation,
and with an accuracy that can be selected by the clin-
icians in accordance with the required estimation fit.
In the second place, after an empirical analysis, it was
established that setting the threshold Γto get a fit be-
tween 85% - 90%, resulted in a satisfactory trade-off
between good accuracy and reduced computational
cost (such percentage can be adjusted, in case it is
needed for any particular patient). Effectively, for this
range of Γ, it was observed that the estimation was
triggered in those respiratory cycles with an irregular
event, but during regular cycles the process was rarely
activated. The consequent decrease in computation
time, compared to continuous estimation algorithms,
contributes to its implementation in actual equipment.
Ongoing work on this research aims to investigate
how to improve, not only the algorithm efficiency, but
also the user interface. Joint discussions with clini-
cians are being held, regarding which results to show
and the better format for them, to maximise its useful-
ness while treating a patient. Additionally, an offline
analysis of the nonlinear models obtained by using the
estimation algorithm with a large group of varied pa-
tients is also in progress, in order to draw conclusions
on the potential of the tool.
Acknowledgment:
The authors would like to thank MD W.L. Corsiglia
and Kin. N. Dargains, from the Hospital I.E.A y C.
San Juan de Dios de La Plata, La Plata, Argentina.
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Contribution of Individual Authors to the
Creation of a Scientific Article (Ghostwriting
Policy)
The authors equally contributed in the present re-
search, at all stages from the formulation of the prob-
lem to the final findings and solution.
Sources of Funding for Research Presented in a
Scientific Article or Scientific Article Itself
This work was carried out with the support of the fol-
lowing Argentinian institutions and projects: Univer-
sidad Nacional de La Plata (UNLP 11/I255), CON-
ICET (PIP 112-2020-010281CO and PUE 229-2018-
0100053CO), Agencia I+D+i (PICT 2018-3747),
Facultad de Ingeniería UNLP, Project COVID-19
#873 (Fundación Bunge y Born - Agencia I+D+i,
recognised by the Ministry of Ciencia, Tecnología e
Innovación, Argentina as PDTS-0549) and Hospital
I.E.A y C. San Juan de Dios de La Plata.
Conflicts of Interest
The authors have no conflicts of interest to
declare that are relevant to the content of this
article.
Creative Commons Attribution License 4.0
(Attribution 4.0 International , CC BY 4.0)
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Creative Commons Attribution License 4.0
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