A program based on a ‘selective’ least-squares method for respiratory mechanics monitoring in ventilated patients

Computer Methods and Programs in Biomedicine 71 (2003) 39–61

A program based on a ‘selective’ least-squares method forrespiratory mechanics monitoring in ventilated patients

Andre Eberhard a, Pierre-Yves Carry b, Jean-Pierre Perdrix b,Jean-Marc Fargnoli c, Loıc Biot b, Pierre F. Baconnier d,*

a Laboratoire de Modelisation et Calcul (Institut IMAG), 51 rue des Mathematiques, BP 53, 38041 Grenoble Cedex 9, Franceb Ser�ice d’Anesthesie-Reanimation, CHU Lyon-Sud, Pierre Benite, 69495 Lyon, France

c Departement d’Anesthesie-Reanimation II, CHU Grenoble, BP 217, 38043 Grenoble Cedex 09, Franced Laboratoire Techniques en Imagerie, Modelisation et Cognition (Institut IMAG) - Equipe PRETA, Faculte de Medecine,

Domaine de la Merci, Uni�ersite Joseph Fourier, 38706 La Tronche Cedex, France

Received 14 January 2000; received in revised form 11 March 2002; accepted 21 March 2002

Abstract

This paper proposes a program for continuous estimation of respiratory mechanics parameters in ventilatedpatients. This program can be used with any ventilator providing airway pressure and flow signals without additionalequipment. Overall breathing resistance, dynamic elastance (E) and positive end expiratory pressure (P0) areperiodically estimated by multiple linear regression on selected parts of breathing cycles. Experimental validationtogether with justification of the selection procedure are based on signals obtained while ventilating a lung mechanicalanalogue with various intensive care ventilators. Clinical validity has been tested on 12 ventilated patients. The qualityof estimation has been assessed by mean square difference between measured and reconstituted pressure (MSE),coefficient of determination (R2) and the condition number (a confidence index), and by comparison of E and P0 withcorresponding static values. The high R2 and the low MSE obtained on most clinical cycles indicate that selectedparts of cycles obey closely the model underlying parameter estimation. Agreement between static and dynamicparameters demonstrates the clinical validity of our program. © 2002 Elsevier Science Ireland Ltd. All rightsreserved.

Keywords: Multiple linear regression; Respiratory mechanics; Monitoring; Ventilated patients; Signal analysis

www.elsevier.com/locate/cmpb

1. Introduction

The assessment of respiratory function is ofgreat importance for patients requiring respira-tory assistance since lung complications are recog-nised as a major source of morbidity and

mortality in these patients [1]. However, the soft-ware provided with some ventilators for respira-tory mechanics monitoring do not appear tosatisfy clinicians, as the latter have not yet pub-lished clinical studies on the importance of contin-uous respiratory mechanics monitoring. One ofthe reasons invoked is that some ventilators ob-tain respiratory mechanics with the help of spe-cific manoeuvres that cannot be carried out

* Corresponding author. Tel.: +33-476-768844; fax: +33-476-765047.

0169-2607/02/$ - see front matter © 2002 Elsevier Science Ireland Ltd. All rights reserved.

PII: S 0169 -2607 (02 )00030 -5

A. Eberhard et al. / Computer Methods and Programs in Biomedicine 71 (2003) 39–6140

continuously. Another reason is that the valuesprovided by ventilators are not validated [1,2].

In a previous paper, we proposed a programfor automatic measurement of respiratory me-chanics based on the end inflation occlusionmethod [3]. This method has not been widespread,probably because it presents two main drawbacks:(i) it requires a specific ventilatory mode, and (ii)inspiratory and expiratory resistive properties arenot distinguished [4]. Nowadays, alternativemathematical approaches are proposed for ex-tracting E and R from pressure and flow signals,namely the Fourier analysis (FA) [5,6], the multi-ple linear regression (MLR) [7–12] and the recur-sive least-squares (RLS) [13–16], MLR and RLSbeing based on the same least-squares technique.Moreover, these three methods allow the estima-tion of dynamic positive end expiratory pressure(PEEP) [8]. While FA and RLS methods rely on afirst order model representation of the respiratorysystem, MLR may take into account, and charac-terise, by few parameters, various non linearities[10–12] of the real system and particularly thoserelated to endotracheal tubes (parabolic pressure–flow relationship and difference between inspira-tory and expiratory behaviour) in intubatedpatients [17]. We, therefore, decided to improveour previous program by replacing the restrictingend inflation occlusion method with the moreflexible MLR. In order to make the method ro-bust towards ventilation modes and respiratorymechanics, we had to modify the classical MLRmethod. This includes a selection of the mostreliable parts of the signals (hence the name ‘selec-tive’ least-squares (SLS) given to the proposedmethod). Such a procedure has been previouslydescribed in the literature but poorly justified[8,9]. We present experimental data obtained on alung mechanical analogue that justify both theselection principle and the chosen selectionparameters.

The method provides estimations for relevantparameters such as dynamic positive end expira-tory pressure PEEP (P0) and elastance (E) and amean respiratory resistance over the breathingcycle (RM), as well as for other parameters (in-spiratory and expiratory resistances, and the con-stant (R0) and slope (�) parameters of the

resistance–flow relationship, R=R0+� �F �), theclinical importance of which remainscontroversial.

In order to demonstrate the clinical applicabil-ity of our SLS method, a program, partly drawnfrom a previous one [3], has been achieved whichperiodically carries out this SLS analysis. Theprogram allows the user to choose between differ-ent displays and to modify some parameters ofthese displays. It provides also means for back upof results and signals as structured text files. As inthe previous version [3], the program calculates anexpiratory time constant (Tau).

This program has been tested in various condi-tions on ventilated patients. In a first group ofpatients monitored by our program we simulta-neously acquired flow and pressure signals with aseparate recording set. In these patients, we peri-odically imposed 5 s pauses at end expiration andend inflation to measure static PEEP (PEEPst)[18] and static elastance (Est) [19] and we furthercompared estimated PEEP (P0) and elastance (E)with corresponding static values.

Our aim was to propose a program that can beused with any ventilator providing airway pres-sure and flow signals without any additionalequipment. Therefore, we tested our programupon patients ventilated with different ventilators.For all patients, the quality of the estimationprocess is assessed, similarly to previous studies[11,20], by the mean square difference betweenmeasured and reconstituted airway pressure(MSE) and by the coefficient of determination(R2).

2. Computational methods and theory

We present here the method together with itsexperimental validation. The method applies onpressure and flow signals provided by ventilators.

2.1. Data selection

Cycles are first delimited using the method de-scribed in [21] based on flow signal. This methodis merely the same as a previously described one[7], based on the confirmation of the zero flow

A. Eberhard et al. / Computer Methods and Programs in Biomedicine 71 (2003) 39–61 41

delimitation by a validation threshold. Briefly, wedefine the beginning of a cycle as the last ascend-ing zero crossing before the flow reaches a posi-tive validation threshold. The cycle (Fig. 1) isdelimited when we find two such successive zerocrossings: the index of the first is called Left ZeroCrossing (LZC), and the one of second is calledRight Zero Crossing (RZC). The end of inflationis located at the instant where the flow decreasesbelow another positive threshold: associated indexis called Zero Flow Index (ZFI). In this case, sincewe did not impose a pause at the end of inflation,this index was very close or identical to the Ex-piratory Start Index (ESI), the index of the instantwhere the flow decreases below a negativethreshold. Nevertheless, our method works evenwhen such a pause is present (see below).

Once a cycle is delimited, some parts of thecycle are selected:– first, pauses periodically imposed by the venti-

lator for its calibration at the end of inflationor at the end of expiration are discarded, aswell as periods when flow naturally stays closeto zero,

– second, there are transition phases where thesignals vary quickly and/or have oscillations.These transitions occur at beginning of inspira-tion and expiration. They are eliminated withthe use of a first delay (let Del.1 be the numberof samples in this delay),

– third, abrupt closure of the inspiratory valvemay introduce in some ventilators a transientwhere the observed system do not behave asexpected. We then finally introduced anotherdelay (let Del.2 be the number of samples inthis delay) allowing discarding the end of in-spiratory phase.Optimal delays were obtained from a prelimi-

nary study on partial data (see below).With these delays end procedure, we thus ob-

tained four indices:Inflation Index c1 (II1)=LZC+Del.1Inflation Index c2 (II2)=ZFI−Del.2Expiratory Index c1 (EI1)=ESI+Del.1Expiratory Index c2 (EI2)= last point beforean expiratory pause (if present) or RZC.These indexes define the intervals selected for

analysis [II1, II2] and [EI1, EI2].

2.2. Equations

2.2.1. System motion equationThe analysis is based on a mathematical model

involving two main components in the pressurePT resulting from a flow F and a volume V : (i) theelastic pressure Pel=P0+EV depending both ona constant elastance E and on a residual pressureP0 at the end of expiration (depending on theimposed ventilation pattern), (ii) the resistive pres-sure Pres= (� �F �+R0)F which points out a flowdependent resistance (R0 and � are, respectively,the constant and slope parameters of the resis-tance–flow relationship). The motion equation ofthe system, is then:

PT=P0+EV+ (� �F �+R0)F (1)

This mathematical model corresponds to theknown behaviour of the mechanical analogue.Moreover, it is likely to correspond to a systemmade up of a patient and a tracheal canula as thispart exhibits a similar flow dependent resistance.

Fig. 1. Selection of the parts of signals used for analysis. Flowand pressure signals are separated into inspiratory and expira-tory phases; then, initial and final parts of each phase areeliminated (see text for details). F, PT, respectively, flow andairway pressure signals. LZC and RZC, respectively, left andright zero crossings. ZFI, zero flow index; ESI, expiratory startindex. II1, II2 (EI1, EI2), respectively, Inflation (Expiratory)Index c1 and Index c2. Del.1 and Del.2: fixed delaysintended to eliminate transitions.


2.2.2. Reference equations for experimental dataIn the experimental validation (see Section 3

below), the instantaneous alveolar pressure PA ismeasured inside the bellows of a test lung. It givesthe possibility to directly evaluate the differentrespiratory mechanics. As PA can be assimilatedto the elastic pressure, the first reference equationis:

PA=P0+EV (2)

As a matter of course, if �P is the pressuredifference between airways and inside of the lung(�P=PT−PA), this pressure difference repre-sents the resistive pressure of the system andobeys the second reference equation:

�P= (� �F �+R0)F (3)

2.3. Algorithm

In parallel to the introduction of a MLR al-gorithm for measurement of respiratory mechan-ics, we used the MLR method to assess thereference values of our mechanical analogue. Al-gorithms are based on the least-squares algorithmthat minimises the mean squared difference be-tween measured and modelled signals.

2.3.1. NotationsAt each instant of the cycle, associated with an

index i, we have at one’s disposal: the measuredairway pressure: PTMi

, the flow: Fi, the volumeapproximated by:

Vi=1�

�i

j=LZC

Fj (4)

where � is the sampling rate.At this instant, the reconstituted airway pres-

sure (PTR) is defined by:

PTRi=P0+EVi+ (� �Fi �+R0)Fi (5)

Finally, we also get the measured alveolar pres-sure: PAMi

.

2.3.2. Least-squares equationWe want the four parameters P0, E, � and R0 to

minimise the quantity Q which is the sum uponthe retained intervals of the squares of the differ-

ences between reconstituted and measured airwaypressures:

Q(P0, E, �, R0)

= �II2

i=II1

+ �EI2

i=EI1

[P0+EVi+ (� �Fi �+R0)Fi−PTMi]2

(6)

By taking the partial derivatives of Q withregard to P0, E, � and R0 we get a linear system,the solution of which gives global estimations forP0, E, � and R0 during the cycle.

In fact, � and R0 are not very meaningful foranaesthetists and intensive care medical doctorswho care mainly about changes in global resis-tance and the appearance of a difference betweeninspiratory and expiratory resistance. So, with Nthe total number of samples in the retained inter-vals, we also calculate the mean value of resis-tance RM for the cycle:

RM=1N

�II2

i=II1

+ �EI2

EI1

(� �Fi �+R0) (7)

A similar algorithm allows estimation of inspira-tory and expiratory resistances.

2.4. Reference �alues

2.4.1. NotationsIn order to distinguish the values obtained by

means of PA (reference) from those obtained with-out it, reference values will be underlined in thetext. For example, if we have evaluated P0 bysolving the linear system issued from Eq. (6),when solving a reference least-squares system, weshall get the reference value: P0.

2.4.2. Elastance and residual pressureThe reconstituted alveolar pressure will be

PARi=P0+E� Vi. Then, P0 and E� are the solution

of the linear system associated to:

�(P0, E)= �II2

i=II1

+ �EI2

j=EI1

[P0+EVi−PAMi]2 (8)

2.4.3. Resistance–flow relationship characteristicsThe measured pressure drop �Pi=PTMi

−PAMi

, will be approximated by the reconstitutedresistive pressure (� �Fi �+R0)Fi. Then, � and R0

will minimise the following squares sum:


�(�, R0)= �II2

i=II1

+ �EI2

i=EI1

[(� �Fi �+R0)Fi−�Pi ]2 (9)

2.5. Assessment of results quality

We have chosen to value the proposed methodby pointing out three aspects:1. the intrinsic quality of the estimation of the

measured airway pressure (PTM) by means ofthe reconstituted pressure (PTR) is assessedwith the mean square error (MSE) and withthe coefficient of determination R2 [11]:

MSE=1N

�(PTRi−PTMi

)2

R2=�(PTRi

−PTR)2

�(PTMi−PTM)2

where PTR and PTM are the means of, respec-tively, reconstituted and measured airwaypressure. MSE, by quantifying the distancebetween the measured and the reconstitutedpressure, assesses the ‘fit goodness’ of thePTRi

’s with respect to the PTMi’s, but has a

dimension (square of a pressure). So it is noteasy to compare results from different ventila-tion modes when the pressure curves have notsimilar amplitudes. On the contrary, R2

quantifies the fit of the model to the data witha dimensionless number that lies between 0(when the reconstituted pressure is constantand equal to the mean of the measured pres-sure) and 1 (when the fit is perfect, whateverthe pressure shape).

2. an indication of the confidence one can have inthe results from the linear system (issued fromEq. (6) in Section 2.3.2) solution is given bythe condition number of the associated matrix.A condition number measures the sensitivityof the solution of a system of linear equationsto errors in the data. Among the various con-dition numbers proposed in the literature, wehave chosen the 2-norm condition number,cond(A), the ratio of the largest singular valueof a matrix A to the smallest [22]. Largecondition numbers indicate a nearly singularmatrix (‘ill conditionned system’ the solutionof which is very sensitive to errors in the data).

3. when possible, the accuracy of a calculatedparameter compared with its reference value isestimated by linear regression or paired t-test.

3. Experimental validation

3.1. Introduction

A common method of validation for estimationof mechanical parameters consists in comparingthe estimated mechanical parameters to theknown characteristics of a mechanical lung model[23,24]. In the present study, we validated ourmethod by using a test lung presenting two im-portant features: (i) its equivalent mathematicalmodel is well defined and (ii) it provides an addi-tional signal: the pressure measured inside thelung which can be assimilated to an ‘alveolar’pressure. This pressure signal allows the preciseestimation of the various lung model parameterscorresponding to the explored situations, i.e. thereference values. The assessment of the proposedmethod is carried out in two steps: (i) the qualityof the estimation result is evaluated by the MSE,the coefficient of determination (R2) while theconfidence one can have in the estimation proce-dure is evaluated by the condition number, and(ii) the estimated parameter values are comparedwith their reference values. The selection proce-dure and its optimal delays are first justified by apreliminary study.

3.2. Materials

We used a Training Test Lung™ (Model 2600iDual Adult TTL, Michigan Instruments®, GrandRapids, MI) as our mechanical analogue of therespiratory system. Bellows pressure simulating‘alveolar’ pressure (PA) is easily measured. Thismodel allows independent settings of resistanceand compliance over the ranges typically observedfrom patients mechanically ventilated in ICU. Ad-justing a movable spring sets elastance and vari-ous ‘Resistors’™ (Michigan Instruments®)simulate different airway resistances. These resis-tors (respectively, labelled 5, 20 and 50) are nonlinear resistances, their pressure–flow characteris-


Table 1Protocol array of the various ventilation modes and mechanical settings, which were carried out in order to test our method, eitherin volume (V) or pressure (P) controlled modes with CESAR ventilator

E Rr

5 20 50

v.m.

P C R D P C R D P C R D

– – – – – –10 –25% – P.1 V.1 V.2 V.3P.4 V.4 V.5 V.6 P.7 V.7 V.833% V.9 P.10 V.10 V.11 V.12– – – – – –25% –20 – P.13 V.13 V.14 V.15P.16 V.16 V.17 V.18 P.19 V.19 V.20 V.21 P.2233% V.22 V.23 V.24P.25 V.25 V.26 V.27 P.28 V.2866% V.29 V.30 – – – –P.31 V.31 V.32 V.33 P.34 V.34 V.35 V.36 P.37 V.3750 V.3833% V.39P.40 V.40 V.41 V.42 P.43 V.43 V.44 V.45 – –66% – –

We used three Resistors (R) labelled ‘5’, ‘20’ and ‘50’, the elastance spring (E) was set at three different positions on the scale: 10,20 and 50 cmH2O l−1. Four ventilatory modes (v.m.) were tested: pressure controlled mode (P) and volume controlled mode withthree different inflation flow shapes (constant C, round-shaped R or decreasing D). The TI/TTOT ratio (r) could be 25, 33 or 66%.

tics being given in the instruction booklet in theform of a figure with parabolic curves and a tablegiving three points for each. This parabolic pres-sure–flow relationship mimics that described forendotracheal tubes.

This mechanical analogue was ventilated withthree different ventilators (Cesar™ Taema®,France, Evita™ Drager®, Germany, and 7200Bennett®, USA) operating in the volume con-trolled mode (tidal volume VT=0.5 l and cycleduration TTOT=4 s) or in the pressure controlledmode. In the volume controlled mode, variousinspiratory patterns were carried out: constant,round shaped and decreasing flow during inspira-tion, in combination with several TI/TTOT (infla-tion over total cycle duration) ratios. In thepressure controlled mode, when possible, the TI/TTOT ratios were similar to those of volume con-trolled situations. In order to avoid zero valuesfor P0, the external PEEP was random between 0and 10 cmH2O.

Each ventilator supplied analogue signals forairway pressure (PT) and flow (F). Volume signal(V) was determined by numerical integration offlow signal.

Signals (PA, PT and F) were fed to a portablemicrocomputer (PowerBook 190™, Apple®,

USA) through a 16 bits A/D acquisition system(MP 100 System™, Biopac Systems®, CA). Thesampling rate (�) was set at 60 Hz. Digitisedsignals (text files) were transferred and processedon a PowerMac 7200™ computer (Apple®, USA)using programs written in MATLAB™ (TheMathWorks®) language.

3.3. Protocol

Whichever the ventilator, pressure and flow sig-nals from the ventilator were used and beforehandcarefully calibrated.

3.3.1. Ventilation with CESAR �entilatorIn this ventilator, airway pressure is measured

on the inspiratory line inside the ventilator. Flowsignal is obtained either as the inspiratory flowsignal send to the inspiratory valve (during inspi-ration) or as the actually measured expiratoryflow (during expiration).

To test our method, 60 various settings, werechosen to cover as many mechanical ventilationsituations as possible (see Table 1). We startedwith a ‘standard’ ventilatory pattern (TI/TTOT ra-tio (r)=33%) and we explored the entire range ofcombinations between three available resistances


and three clinically observed values of elastance(nine combinations) and combined this with fourventilatory control modes (constant inspiratorypressure (P), constant inspiratory flow (C), round(R) and decreasing (D) inspiratory flow) whichgives a total of 36 situations. For elastances 10and 20, at high resistance (R 50) we added situa-tions with a low TI/TTOT ratio in order to getlower intrinsic PEEP. On the contrary, for elas-tances 20 and 50, at ‘low’ resistances (R 5 and R20), we added situations with a high TI/TTOT ratioin order to get higher intrinsic PEEP. In allsituations, the respiratory frequency of the venti-lator was set at 15 min−1.

3.3.2. Other �entilatorsThe same mechanical lung has been ventilated

by two other ventilators (model 7200 Bennett, andEvita 4 Drager). Again, our method was testedboth in volume controlled (respectively, BV. andEV. for Bennett 7200 and Evita 4) and pressurecontrolled (respectively, BP. and EP.) modes in aless extensive range of conditions due to the factthat these ventilators do not cover the same rangeof controlled flow shapes. Five situations corre-sponding to constant flow controlled mode andfive for pressure controlled mode have been ran-domly selected. Due to the Bennett 7200 ventila-tor limitations, it was not possible to obtain ther=66% situations (BP.30 and BP.42). These havebeen replaced by BP.33 (same as BP.42 but r=33% instead of 66%).

As the mechanical analogue of the respiratorysystem is perfectly stable, cycles recorded in onesituation are merely identical and their analysisgives values very close to each other. Only onecycle has then been analysed for each situation.

3.4. Optimal delays

3.4.1. Set of delays and dataThe transition phases at start inspiration and

expiration (Fig. 1) are variable from one situationto another but transients usually vanish in 0.2–0.3s. The closing time of inspiration valve is alsodifferent from one ventilator to another but itremains less than 0.2 s in general. For symmetryreason, the set of values for each delay was cho-sen identical: 0, 0.1, 0.2 and 0.3 s.

We restricted this preliminary study to the vol-ume-controlled situations with Cesar ventilator(situations V.1–V.45).

3.4.2. Set of selection proceduresWe decided to eliminate systematically the peri-

ods where flow is negligible as soon as we intro-duce any selection procedure (elimination of oneor two type of transition).

In order to find the optimal selection proce-dure, we tried all possible combination of delays,which gives 16 possibilities (see Table 2).

3.4.3. Optimal setTwo criteria were used to choose the optimal

set, namely R2 criterion and relative error onsimple mechanical parameters E and P0. We cal-culated R2, relative error made on P0 ((P0−P0)/P0) and E ((E−E� )/E� ) in each situation for eachselection procedure (16×45 cases). Mean valuesfor situations V.1–V.45 are gathered in Table3(a–c) (as this table is only aimed at choosing thebest delays, standard deviations (S.D.) are notgiven in detail). On the whole, introducing mini-mal delays (0.1s for both) induces a definite im-provement in R2 value as well as on E and P0

estimation. Clearly, delay 1 (Del.1) must be set at0.3 s in order to optimise R2. On the other hand,choosing delay 2 (Del.2) value seems less simple.We considered that 0.1 is the optimum value forDel.2, as this is the minimum acceptable value forR2 criterion and gives the best compromise for P0

while keeping the relative error on E reasonable.All estimations below are then obtained using

the above-defined optimal delays, i.e. Del.1=0.3 sand Del.2=0.1 s.

Table 2Set of selection procedures tested for optimal selection search

Del.1 (s) Del.2 (s)

0.1 0.20 0.3

0 x x x0x x x0.1 x

x xx x0.20.3 x xxx

0, no pause elimination; x, pause elimination+delay(s) elimi-nation.


Table 3Effect of delays

S.D.Del.2 (s)Del.1 (s)

0.1 0.2 0.30

(a) On R2 (expressed in %) for situations V.1–V.4596.430 96.2896.71 96.15 �1.7099.160.1 99.1399.13 99.09 �0.6099.65 99.6599.60 99.640.2 �0.50

99.74 99.7599.68 99.740.3 �0.50

(b) On relati�e error made on P0 (expressed in %) forsituations V.1–V.450 16.8514.62 17.24 17.770.1 13.4015.33 13.38 13.61

11.36 11.4314.32 11.410.2

12.90 13.7015.75 14.140.3

(c) On relati�e error made on E (expressed in %) forsituations V.1–V.45

16.05 16.18 15.960 13.5610.54 10.6210.18 9.940.1

0.2 10.009.44 10.56 10.26

9.430.3 10.33 11.38 11.92

Best values are written in bold characters. Standard deviations(S.D.) are very small and mainly determined by Delay 1 forR2; they are rather large (around the error itself) and notmentioned for both relative errors on P0 and E. Framed boxcorresponds to the retained set.

98.5] for V.11; R2� [98.5, 99.0] for EV.15, V.2,V.14, V.23, V.38, P.13 and P.22; R2� [99.0, 99.5]for P.1 and P.37). The condition number is higherthan 105 in five situations (V.1, V.10, V.22, BP.12and BP.24).

We then propose three criteria for discardingcycles: MSE�1 (cmH2O)2 and/or R2�99.5%and/or condition number�105. On the whole,17/79 situations present at least one unsatisfiedcriterion.

3.5.2. Comparison between �entilatorsValues obtained on the same model using dif-

ferent ventilators are presented in Table 4. Amongthese situations, seven can be rejected on one orthe other criterion defined above. When this is thecase, the comparison between ventilators has nomeaning. Situations BV.13, EV.15 and EV.24 ex-hibit large MSE and erroneous E values due tothe fact that, in these situations, ventilators arenot able to provide correct measurements of flowand pressure over all inflation. This has beenevidenced by specific separate measurements offlow and pressure done at the ‘airway opening’(close to the lung analogue). When no situation isrejected, the comparison holds only for E becauseexternal PEEP was random and RM may be dif-ferent due to the differences observed in the flowshapes actually realised by the ventilators.

3.5.3. Parameters accuracy

3.5.3.1. Bad circumstances. When running ourprogram, it came to light that for some situationsin our protocol array, we did not obtain fullysatisfactory results. We could distinguish twomain different reasons: (1) the main linear systemis ill conditioned (the condition number is high),(2) there exists a hysteresis of the resistive pressurefunction of flow (this circumstance is encounteredin extreme conditions, where Eq. (1) is no longersufficient to describe the physical system).

Type 1, ill conditioned system. When the higherresistance (R=50) is associated with the lowerelastances (E=10 or 20), the expiratory timeconstant (�R/E) is large and the absolute valueof the flow decreases very slowly during expira-tion. If, in addition, the flow is constant (C)

3.5. Results

3.5.1. Global qualityMSE is less than 1 (cmH2O)2 in 69/79 situations

that have then a good correspondence betweenmeasured and reconstituted airway pressure. Twosituations give an MSE�4.0 (cmH2O)2: situationV.38 and EV.24. These situations correspond to ahigh resistance (R=50). The remaining situationsare distributed as follows: MSE� [1.0, 2.0] for V.2,P.13, P.37 and BV.13; MSE� [2.0, 3.0] for V.14;MSE� [3.0, 4.0] for V.11, V.23 and EV.15. For70/79 situations we obtained a good coefficient ofdetermination (over 99%). R2 distribution isclearly separated into two populations: 68 situa-tions present an R2 over 99.5% and nine areunder 99.0% (R2�98% for EV.24; R2� [98.0,


Table 4Calculated values for residual pressure, elastance and mean resistance (P0, E and RM, respectively, in cmH2O, cmH2O l−1 andcmH2O l−1 s) for the situations where the three ventilators were used on similar lung model settings

Flow controlled mode Pressure controlled mode

E RM Rejected for Situation P0P0 ESituation RM Rejected for

2.4BV.16 19.8 5.3 BP.12 4.2 6.4 22.8 Cond21.7 2.9 P.105.2 9.2V.16 8.2 40.8

3.3EV.16 19.9 4.6 EP.12 8.2 9.6 35.83.9BV.13 28.8 42.3 MSE BP.21 2.4 22.4 7.2

21.2 22.6 P.195.5 0.4V.13 23.0 5.68.5EV.15 36.5 70.1 MSE, R2 EP.21 3.3 18.5 10.9

19.7 24.6 BP.24BV.22 2.82.8 24.4 16.3 Cond21.2 29.9 Cond P.226.6 0.6V.22 23.0 16.7 R2

10.0EV.24 21.9 52.8 MSE, R2 EP.24 6.4 21.3 37.446.9BV.40 5.91.7 BP.33 0.6 57.2 2.853.1 5.0 P.408.6 0.0V.40 49.8 4.1

3.7EV.40 49.3 5.6 EP.42 3.4 50.6 4.62.8BV.37 47.1 26.7 P.28 5.4 16.4 10.5

49.6 30.8 EP.309.8 12.0V.37 19.7 12.155.0 43.3EV.37 5.3

‘Rejected for’ indicates the criterion not satisfied in the corresponding situation: MSE=MSE�1 (cmH2O)2, R2=R2�99.5%,Cond=condition number�105.

during inflation, the sampled values of the flow inthe intervals that are used for analysis are notvery diversified. Three situations (V.1, V.1�0,V.22) correspond to this condition. SituationsBP.12 and BP.24 present similar conditions lead-ing to a high condition number. These situationsthat exhibit ‘normal’ R2 or MSE values, can bediscarded only from their condition number.

Type 2, hysteresis of the resisti�e pressure. Withhigh resistance (R=50), particularly when theflow was round shaped during inflation (withCesar ventilator, v.m.=R), we could verify thatthe resistive pressure presents a considerable hys-teresis during inflation: for a fixed flow, the levelof the resistive pressure during increasing flow islower than the level of the resistive pressure dur-ing decreasing flow. Of course, with these condi-tions, Eq. (1) does not apply and neither doesreference Eq. (3).

Eight ventilations correspond to this situation:V.2, V.11, V.14, V.23, V.38, BV.13, EV.15 andEV.24. These eight ‘bad circumstances’ of type 2exhibit R2�99.0% and/or MSE�4.0 (cmH2O)2.

3.5.3.2. Clinically rele�ant parameters. P0, E, andRM are considered here as clinically relevant asthey are commonly used in clinical practice. Allestimations are highly correlated with their re-spective reference values, P0, E� and RM (Table5). Moreover, the slope of the relationship isvery close to 1 and the constant term either notstatistically different from zero or rather small.

Table 5Regression coefficients for the estimated clinical parameters Xvs. the corresponding measured ones X� (n=79)

a bClinical parameters r2

0.852 (P�0.0001)1.03*0.44cP0 (cmH2O)1.2E (cmH2O l−1) 1.00* 0.972 (P�0.0001)

RM (cmH2O l−1 s) 1.07* 0.829 (P�0.0001)1.6c

a, b coefficients of the regression equation X=a+X� b. r :correlation coefficient. c : not significantly (P�0.05) differentfrom 0; *: not significantly (P�0.05) different from 1.


Fig. 2. Clinically relevant estimated parameters (P0, E, RM) plotted against their reference values (P0, E� , RM). Solid line, line ofidentity. Points distant from identity line and corresponding to at least one criterion not satisfied are identified.

In Fig. 2 are presented the calculated values forresidual pressure, elastance and mean resistance(P0, E and RM) versus their reference values (P0, E�and RM).

Fig. 2 suggests that P0 overestimates P0. How-ever, Table 5 shows that this is not statisticallysignificant. On the other hand, one can see fromTable 5 that E statistically overestimates E� . RM

seems correctly estimated, even though sometimesoverestimated for low values. Many ‘bad circum-stances’ give points far from identity line on oneor more graphs of Fig. 2.

Algorithms described above (data selection,MLR on selected parts and clinically relevantparameter computation) have been integrated in aprogram (see below) intended for continuousmonitoring of respiratory mechanics in ventilatedpatients.

4. Program description

4.1. Introduction

Our program deals with analogue airway pres-sure and flow signals supplied by respirators andacquired via an A/D conversion set. It containstwo main parts: the initialisation procedures and amain loop managing the automatic measurementsand the processing of user’s actions (see Fig. 3and Fig. 7).

4.2. Initialisations

First, the program offers to choose a specifica-tion file corresponding to the used hardware andsoftware configuration (see Section 4.5.2) andasks the user for a ‘Root Letter’ to identify thesession. A result file is created and initialised (see


Fig. 3. Program flow chart. User’s action process is described in Fig. 7.

Section 4.5.1). Then the program needs a zero-val-ues calibration: the respirator tube must be dis-connected (0 pressure=atmospheric pressure)and the flow has to be set to 0 for a short time (5s)1. Following which, the program runs automati-cally and no longer requires intervention on thepart of the user.

4.3. Main loop

This part is in charge of alternately driving theA/D card or computing and displaying results ofcomputations. When driving A/D card, the com-puter is unable to control display and recipro-cally. The program proposes three displayoptions: oscilloscope-like display allowing the userto check for signal quality, trend display givingsummarised information on previous computationresults and fit display for assessing parametersquality.

At any time, user may interfere with the pro-gram by keystrokes. Such interventions can– change displays (mode or scales),– increase transiently measurement frequency,– save part of signals,

1 Because of drift of zero lines, zero-values calibration isvery important and has to be performed at the beginning ofeach session. On the contrary, the scaling factors dependessentially on the ventilator and on the AD converter. So thefull scale calibration is performed previously by a specialprogram for each ventilator-AD converter couple, and thescaling factors for pressure and flow so obtained are put in thespecification file (see Section 4.5.3).


– record a mark in the next record of the resultfile.

4.3.1. Oscillo modeThis is the default mode. Both flow and pres-

sure signals are sampled with a slow rate (about20 Hz) and they are drawn on the screen (Fig. 4).Periodically, a vertical line is displayed and the‘oscilloscope’ is stopped as long as the programsamples points for a measure and calculates. Onceresults are obtained, moving display of signalsresumes.

4.3.2. ‘Measure’Periodically (every minute, or every m minutes,

depending on the corresponding specificationparameter) a measure occurs: it consists in acquir-ing pressure and flow signals and extracting fromthem (when possible) respiratory mechanicparameters. This action includes the followingsteps:– curves are no longer displayed and a vertical

straight line is drawn (Fig. 4),– both pressure and flow signals are sampled

with a higher rate (50 Hz for adults) until 600points are obtained for each of them,

– the digital values are zero-corrected andbrought to scale using two other specificationparameters and then stored in buffers,

Fig. 5. Trends screen. PEEP (P0) and elastance (E) are dy-namic values, RM is the mean resistance (empty squares aredrawn instead of full circles when R2�0.99) and Tau is theexpiratory time constant computed from the slope of theflow–volume curve during expiration. m is a mark (keystrokefor an event). � means that, for the 6th measure, the attemptto delimit a cycle failed. f means that the previous sampling(600 pts for each signal) was saved in a file.

– the program attempts to delimit a whole cycle.If this attempt is successful, the program runsthe algorithm of selective least-squares de-scribed in Section 2.3 and the respiratory me-chanical parameters2 associated to this measureare stored in the result file. If this attempt fails,a bell rings and an error code is stored.The program then returns to its previous state

(oscillo mode or trend mode).

4.3.3. Trend modeWhen desired, the user can strike the space bar

on the keyboard of the computer. Immediately (orat the end of the measure, if one is occurring) thescreen displays the evolution of four ventilatorymechanics parameters: PEEP (P0), Elastance (E),mean Resistance (Rm) and expiratory time con-stant (Tau) (Fig. 5).

Fig. 4. Oscillo mode screen. Pressure and flow are displayedwith a slow rate (about 20 Hz). The vertical straight linemeans that a measure has been performed just before.

2 The computation of P0, E, R0 and � uses a classic Gausselimination method applied to the matrix of the least-squarelinear system described in part I. Time constant � is obtainedwith the regression method described in [3].


The X axes represent the time elapsed from thebeginning of the recording (time scale is adjustedautomatically). For each measure a circle point isdrawn for each parameter except in two situa-tions: (i) the fit quality is not sufficient (coefficientof determination R2�99%) and the point is re-placed by a square suggesting that the cliniciancannot be confident in these values; (ii) the at-tempt to delimit a cycle failed, in which case atriangle (�) is drawn at level 0. After a delay (10s), the program automatically re-enters the Oscillomode. If a measure occurs during the Trendmode, a square drawn in the middle of the screenadvises the user.

4.3.4. Fit modeThis display (Fig. 6) is obtained when hitting

the F5 key. It allows the user to visually evaluatethe quality of parameter assessment. If the analy-sis of the last measure was successful, the programdisplays the original curves (pressure and flow) ofthe cycle analysed in this measure, and, super-posed, their corresponding reconstitutedequivalents:

PTR=P0+EV+ (R0+� �F �)F for pressure,

FRec=K exp�− t

Tau�

for flow during deflation,

and the numerical values of these various parame-ters are given.

4.4. Manual inter�entions

They are summarised in Fig. 7.F1: This key (after a confirmation message)terminates execution.F2: This key induces creation of a disk file witha suffix WKS (see Section 4.5.1), containing thesampled values (both of flow and pressure) ofthe last measure, and the character f appears forthe corresponding values on the trend screen(see measure 7 in Fig. 5).F3: Alternately, this key multiplies and dividesthe vertical scales of the current drawing (eitherin Oscillo mode or in Trend mode) by 2. Origi-nal scales are initialised with specificationparameters.F4: This key operates only if the last measure issuccessful. It induces the program to work in aparticular way called the ‘Burst’ mode: fromthis moment, the measures follow one anotherwithout any delay between them. The screendisplays only the number of the current mea-sure. This feature is very useful when the userexpects rapid variations of any ventilatory me-chanics parameter consecutive to an action per-formed. The same key induces leaving ‘Burst’mode.F5: This key also operates only if the lastmeasure is successful. It must be used to reachthe Fit mode (see Section 4.3.4). After a mo-ment, the program re-enters the oscillo mode.

Any other key (except the space bar which is usedto switch from Oscillo mode to Trend mode) theuser strikes during the program run is consideredas a mark that will be associated with the nextmeasure (see measure c2 in Fig. 5).

4.5. Technical aspects

4.5.1. Files created by the programThe ‘Root Letter’ entered at the beginning of

the execution (see Section 4.2) and the date of theday are used to construct the Prefix : for example,if the ‘Root Letter’ is Z and if the date of the dayis the 28th of May, the Prefix will be Z0528. This

Fig. 6. Fit screen. Doted lines represent reconstituted signals:exponentially decreasing flow (absolute value) is obtained fromestimation of expiratory time constant, and the reconstitutedpressure as described in the text. Horizontal bars indicate theselected parts of the cycle.


Fig. 7. User’s action processing.

prefix is used to produce the names of all the filescreated by the program during execution.� RES.XL file: This is the text file so-called

Prefix RES.XL (the present example isZ0528RES.XL) that was created at the begin-ning of the execution of the program (see Sec-tion 4.2) for to receive the results. The headlinedescribes the contents of each column. Aftereach measure, the program opens this file, ap-pends a new line (c , time, detailed resultsincluding inspiratory and expiratory resis-tances, and possible mark for this measure)and saves it. So, if the program crashes, all thevalues for each measure are saved. Any spread-sheet software will be able to further read andprocess it.

� WKS files: We have seen (Section 4.4) that theF2 key induced the creation of a text file thatcontains the sample values of flow and pressure

signals of the last measure. The names of thesefiles are successively Prefix–01.WKS, Prefix–02.WKS, … (for our example: Z0528–01.WKS, Z0528–02.WKS, …).

4.5.2. Hardware and software specificationsOur program runs on any PC compatible

computer– linked to different respirators: Siemens (900C),

Taema (Cesar), Bennett (7200), Drager(Evita4),

– equipped with different Analogue to DigitalCards,

– in different clinical situations (Intensive Care,Anaesthesiology, Neonatology …),

– with different purposes (Monitoring, Experi-mentation, Equipment’s test …).The program works on real time mode; the

computer time needed for signal analysis is less


than 1 s (worst performance obtained with a80386 processor).

The programming language used is Borland™TurboPascal. Its Pascal and Matlab versions areavailable for researchers at author forcorrespondence.

4.5.3. Specification fileThis is the text file the user chooses to read

when the program starts. It contains informationthat permits the program to adapt to each hard-ware and software situation:1. Hardware (A/D card and ventilator

characteristics):� A/D indicator: 0, 1 or 2 (as three different

A/D cards are currently used),� physical channel’s numbers for Flow and

Pressure,� scaling factors for Flow and Pressure.

2. Software:� Sampling rate during measures (50 Hz for

adults and 200 Hz for neonates),� maximum scale values for Flow and Pres-

sure in Oscillo mode (respectively, 1 l s−1

and 40 cmH2O for adult anaesthesia;modified at demand for intensive care andneonates),

� maximum scale values for each ventilatoryparameter in Trend mode,

� delay between 2 measures (m minutes), de-fault is 1,

� thresholds for cycle delimitation (obtainedfrom successive trials and errors for eachventilator-AD converter couple).

Table 6Patient data and ventilation settings

nVentilatorWeight (kg) Imp PEEPVT (ml)Patient number FR (min−1)DiagnosisAge (year)(cmH2O)

Group I53 Cesar1 1172618ARF-COPD77 36

5 Cesar 352 Right lung6069 22 467resection-COPD

063516Obese-MOF 3577943 Cesar52 Cesar 3563 ARF-COPD 16 6164 6

Septic5 35Cesar46961695 53shock-Fournierdisease

74719 Cesar 30Multiple 1050766trauma-COPD

707 92 69 ARDS-COPD 14 613 0 Cesar

Group II52 64 Stroke attack 13 480 0 Evita4 67869 52 Recovery 239 16 600 0 Evita4

period14720005401670 Anoxic coma10 48

75 32 Recovery 1611 16 7200700 0period

16COPD74 208012 72004.7640

Diagnoses abbreviations: ARF, acute respiratory failure; COPD, chronic obstructive pulmonary disease; MOF, multiple organfailure; ARDS, acute respiratory distress syndrome. FR, respiratory frequency; VT, tidal (inflated or expired) volume; Imp PEEP,PEEP imposed by the ventilator; set by the clinician. n is the number of ‘measures’ for each patient (total=416).


Fig. 8. Experimental setting for group I. Flow and pressuresignals are fed both into a PC running the program and to acontinuous recording set.

pressure sensors with a water manometer and flowsensors with a RT200 Calibration Analyser™(Timeter Instrument Corp.®, St Louis, MO). Theclinician defined the ventilation mode and set-tings; in some patients (c 3, 6, 7 and 8), variousinspiratory patterns were carried out: constant,round shaped and decreasing flow during inspira-tion. Patient c10 was ventilated in pressure con-trolled mode. Seven patients (group I Table 6)were ventilated with Cesar® ventilator and under-went a specific protocol intended to compare theprogram results with the reference values obtainedin static condition. Pressure and flow signals givenby the ventilator (Fig. 8) were fed both into thePC running the program (as in group II Table 6)and to a recording set (analogue to digital inter-face, model MP100-Biopac systems-Inc®, con-nected to a portable PC, Powerbook 190-Apple®)for subsequent processing.

Static PEEP and elastance were obtained inthese patients thanks to imposed pauses at endinflation or end expirations. Pauses were carriedout separately at 1 min intervals (see Fig. 9) inorder to disrupt patient ventilation as slightly aspossible. We checked that cycles digitised by ourprogram for measures were always cycles withoutpause. Five patients (group II) were selected inorder to validate the program on differentventilators.

5. Test in clinical conditions

5.1. Protocol

We investigated 12 ICU patients (see Table 6for individual data).

In all patients, the program ran for at least 14min. Patients were ventilated with various ventila-tors (CESAR, Taema®, France, Evita 4, Drager®,Germany, 7200 Bennett®, USA) operating in thevolume controlled mode or in pressure controlledmode. These ventilators were able to provide ana-logue pressure and flow signals measured withinternal sensors. The supplied analogue signals for‘airway’ pressure (PT) and flow (F) were fed intoa 80386 PC compatible equipped with a 12 bitsA/D card (DC&C/TM/03) and running our pro-gram. The sampling rate was set at 50 Hz. For allventilators used, we have beforehand calibrated

Fig. 9. Experimental tracings (patient c7). Pressure and flow signals recorded from a CESAR ventilator in a 4 min period showthe imposed end inspiratory (I) and expiratory (E) pauses.


Fig. 10. Direct measurement of PEEPst and Pplat on pressure and flow tracings (patient c7). Mean values over one second aredirectly obtained. Tidal volume is the integral of flow during inflation (shaded area).

5.2. Data processing

Direct estimations of static PEEP (PEEPst) andelastance (Est) have been obtained by the classicalmethod (see Fig. 10): PEEPst is the mean value ofpressure during 1 s when a plateau has beenreached during an end-expiratory pause [18] In asimilar way, the static elastic recoil pressure atend inflation (Pplat) is the mean value of pressureduring 1 s when a plateau has been reachedduring an end-inflation pause and Est is obtainedas the ratio (Pplat−PEEPst)/VT [19] where tidalvolume (VT) is the integral of flow duringinflation.

In a similar way to Section 2.5, we have chosento value the proposed program by pointing outtwo aspects:1. the intrinsic quality of global estimation is

assessed with the mean square difference be-tween measured and reconstituted airway pres-sure (MSE) and with the coefficient ofdetermination (R2).

2. the accuracy of PEEP and elastance (dynamic)estimations as compared with their (static) ref-erence values is estimated by linear regression.

5.3. Results

Since last version installation (more than 500 hrunning), no break occurred due to dysfunction-ning of the program. When faced to signal inter-ruption (patient disconnection for aspiration orelectrical breakdown…), ‘fail’ messages arestored, but the program goes on.

5.3.1. Global qualityHistograms of MSE and R2 presented in Fig.

11 are very similar to those obtained on mechani-cal model (Section 3.5). On the whole, 12.5% ofanalysed cycles give R2�99% and only 3% aresuch that MSE�1 (cmH2O)2, individual patientdata are similar. Only 28/416 cycles do not satisfyat least one of the previously defined criteria(MSE�1 (cmH2O)2; R2�99.5%; conditionnumber�105).

5.3.2. Parameters accuracyA paired t-test between overall corresponding

dynamic PEEP estimations and reference staticvalues shows that P0 is systematically lower (P�0.001; mean difference�S.D.: 1.0�0.2 cmH2O)


Fig. 11. Histogram of mean square error (MSE) and determination coefficient (R2) for analysed cycles of all patients.

than PEEPst. A similar analysis on elastancesexhibits no statistical difference (P=0.26) be-tween corresponding static and dynamic values,even though such a difference exists for individualpatients (c1, 3, 4, 6 and 7)

Figs. 12 and 13 show that the agreement of P0

and E estimations with their respective static ref-erence values is generally good.

6. Discussion

6.1. Methods

The proposed program, based on SLS method,is supposed to provide a precise estimation of asimple mechanical system ventilated with a mod-ern ventilator. Obviously, this implies that themechanical system involved is passive, which is alimitation of the method in clinical practice, limi-tation shared with all methods dealing with me-chanical characteristics of respiratory system.

In the present paper, the assessment of theproposed method on experimental data is maderigorous thanks to the ‘alveolar’ pressure mea-sured in a lung mechanical model: we obtainreference values for all estimated parameters invarious ventilatory modes. A similar approachhas been followed by previous authors [23–25]but with a restricted parameter set and only oneinspiratory flow pattern. Other authors validatetheir methods on simulated [13] or animal [14]data. The various situations simulated here intendto cover most of the situations encountered inintensive care patients. Indeed the chosen parame-

ter set roughly corresponds to the one taken inanother study [25] that covers a ‘wide range ofclinician-set variables and impedance conditions’.

As we voluntarily used only the pressure andflow signals given by the ventilator, we exposedourselves to the risk that the measurement set ofthe ventilator is not perfect. Indeed, Table 3(c)results obtained with one ventilator exhibit quiteimportant relative errors between our evaluationand direct measurement of E (upto 11%). Thisdiscrepancy has to be attributed to (i) the tubingbetween the ventilator pressure transducer and the‘alveolar’ pressure transducer introducing phaselag and/or filtering and (ii) some ‘bad circum-stances’ giving wide departures from referencevalue. In a specific set of experiments, aimed at

Fig. 12. Representation of P0 vs. PEEPst. Solid line, line ofidentity. Patients are represented with different figures (num-bers indicated in the graph). Patient c4 exhibits a hugedifference between static and dynamic PEEP.


Fig. 13. Representation of E vs. Est. Solid line, line of identity.Patient c4 has a very low elastance. This is in agreement withhis diagnosis (acute respiratory failure) and confirms the prob-ability of an important time constants inequality leading to adiscrepancy between static and dynamic PEEP. See Fig. 12 forother comments.

resistances have never been observed in our clinicalstudy and we further demonstrate that, with allventilators the quality obtained in clinical condi-tions is satisfactory.

While some authors [10,11] compared severalpossible models of the ventilatory system, themathematical model used here is imposed by thephysical model and is the simplest including theclassical dependence of resistance on flow evokedby numerous authors for endotracheal tube. Thegood fits observed between experimentally mea-sured (PA) and estimated (Pel=P0+EV) elasticpressure values in various elastance conditions, aswell as between experimentally measured (�P=PT−PA) and estimated (�P= (� �F �+R0)F) resis-tive pressure values in various resistanceconditions, confirm that Eq. (1) well describes thephysical system. A more complex model may beused with slight modifications of the algorithm inorder to take into account other non linear be-haviours of the respiratory system evidenced bypast and recent studies [10–12,26–28]. However,we think that in the context of respiratory mechan-ics monitoring, our simple model should be satis-factory in most situations. Moreover, no one is ableto ascertain, yet the clinical importance of theparameters is estimated from more complex mod-els. Lastly, some situations like expiratory flowlimitation remain out of reach for modelling[10,29].

Elimination of some parts of the cycle hasalready been proposed [8,9], however, the pro-posed procedures differed depending on whether‘intrinsic PEEP’ or compliance and resistance wasdetermined, and the choice of selected parts wasnot quantitatively validated. Our method, usingcommon parts of pressure and flow signals for allparameters estimation, is likely to give more co-herent and stable results. The proposed elimina-tion process responds to various needs. Indeed, (i)zero flow during end-inspiratory pause does notallow one to estimate any parameter involvedwith flow, (ii) during the early and late inflationand early expiration, switching of valves mayintroduce transient pressure–volume conditionsnot covered by the simple model used [8] and (iii)fast flow variations render inadequate a modelneglecting inertia as demonstrated by the hugeresistance and elastance estimation variations in

explaining the results obtained for situations EV.15and EV.24, we measured flow and pressure signalsat the ‘airway’ opening of the mechanical lung. Wediscovered that signals provided by the Evita 4ventilator in these situations are not well correlatedto signals at the ‘airway’ opening (see Fig. 14).

The same observation has been made for 7200ventilator in situation BV.13. However, such high

Fig. 14. Flow signals given, respectively, by the ventilator(Evita 4, top) and by a Fleisch No. 2 pneumotachograph atthe Y piece connected to a differential pressure transducerDP45 Validyne (bottom) for the same cycle (situation EV.15).


these phases exhibited by RLS analysis [15]. Theelimination method proposed here relies on delaysthat have been empirically optimised. Obviously,these delays (0.3+0.1=0.4 s is removed fromsignals during inflation time) are not applicablefor ventilated neonates whose inflation durationsare often less than 0.5 s. An adaptation of ourmethod (increasing sampling frequency and short-ening delays) for this special case should be easy.

Our elimination procedure, particularly thechoice of ‘delays’ defining the discarded parts ofthe respiratory cycle, has been quantitatively vali-dated in experimental conditions (see Section 3.4).In order to evaluate this choice in clinical condi-tions, we tested the effect of various delays on theprogram performances. In three patients (c3, 4and 5), the estimation algorithm has been applied(Matlab implementation of the method) to thewhole recorded signal. Four different selectionprocedures were applied to these cycles:– procedure 1: no selection, corresponds to the

classical application of multilinear regressionanalysis,

– procedure 2: zero flow parts discarded, 0.1 sdiscarded at beginning of both inflation andexpiration (Del.1=0.1s) and 0.1 s discarded atend inflation (Del.2=0.1s), uses minimal ‘de-lays’ with exclusion of any pause,

– procedure 3: same as procedure 2 but Del.1=0.2 s,

– procedure 4: same as procedure 2 but Del.1=0.3 s, last two procedures used in order todemonstrate the progressive gain in qualitywith increasing delay 1.Result of this test presented in Fig. 15 for one

patient (c5, 120 consecutive analysed cycles) evi-dences the improvement in global quality of the fitwhen selecting parts of the cycle as finally definedin Section 3.4.3 (procedure 4 above, white bars infigure). Identical results are obtained on patientsc3 and 4.

Mean resistances have been calculated in orderto propose to the clinician a parameter valuewhich can be compared with ‘normal’ values asgiven in the literature. However, these calculatedvalues are no longer independent of flowwaveform.

Fig. 15. Histograms of (a) determination coefficient (R2) and(b) mean square difference between measured and reconsti-tuted pressure (MSE) calculated on all recorded cycles of onepatient (c5) for different selection procedures. Procedure 1:no selection; procedure 2: Del.1=0.1 s, Del.2=0.1 s; proce-dure 3: Del.1=0.2 s, Del.2=0.1 s; procedure 4: Del.1=0.3 s,Del.2=0.1 s. In procedures 2, 3, and 4, zero flow parts arediscarded. Procedure 4 gives obviously the best results, forboth R2 and MSE.

6.2. Program

The present study was designed to evaluate ifour continuous monitoring program based onSLS method is applicable in clinical conditionsand gives satisfactory real time estimations ofrespiratory mechanics parameters. Previous at-tempts to provide automated measurement of res-piratory mechanics in ventilated patients [16,25]did not end up in a real time program validated inclinical conditions.

As others [16] we voluntarily used pressure andflow signals given by the ventilator. Our results,obtained without any filtering, confirm that com-mon ventilator allows the assessment of respira-tory mechanics parameters of ventilated patientsand that the agreement of P0 and E estimationswith their respective static reference values is gen-


erally good. However, the estimation of the res-piratory mechanics parameters depending on thesensors’ position (i.e. the ventilator), these valuescannot be used to compare the mechanicalparameters of different patients. Incidentally, oneshould strongly recommend the ventilators’ man-ufacturers to develop sensors situated at the Ypiece.

Several authors used various criterions to evalu-ate the reliability of estimations [10,11,20].Bhutani et al. [20] as well as Peslin et al. [10] usethe mean square difference between measured andreconstituted airway pressure (or its square root)to discard cycles where the model is not suitable,while Kano et al. [11] take advantage of thecoefficient of determination to demonstrate theimprovement obtained with a non linear mod-elling of elastic properties. We think coefficient ofdetermination is more suitable to distinguish be-tween cycles as it is a dimensionless number andhas, in our results, the same discrimination per-formance as an empirical threshold level on MSE,taken at 1 (cmH2O)2 for example. This is why weindicate non reliable results (R2�99%) to theclinician.

One can expect dynamic PEEP to be lower thanstatic PEEP, due to stress relaxation or pendelluftencountered in patient respiratory systems. Thisexplains the systematic difference between P0 esti-mated by our program and PEEPst measuredafter long occlusions.

The residual pressure in the lung at the end ofexpiration (P0) is not always taken into account inpapers dealing with estimation of respiratory me-chanics parameters. One must keep in mind thatthis pressure is the sum of two different pressures:the end expiratory pressure imposed by the venti-lator (‘imposed PEEP’) and a residual pressurewhich develops when the lungs do not haveenough time to deflate passively during expiratoryduration (‘intrinsic PEEP’). As long as the al-gorithm in charge of estimating P0 is not aware ofimposed PEEP, it will not distinguish betweenthese two pressures and the clinician will have tomake the difference by himself.

The automatic on-line program using thismethod now runs daily in our ICU and is appliedon any patient, including anaesthetised patients

Table 7List of variable names and definitions

DefinitionsNames

Del.1, Del.2 Time duration of discarded parts atbeginning (Del.1) of both inflation andexpiration, and end (Del.2) of inflation(respectively, equal to 0.3 and 0.1 s)Estimation of patient’s dynamic elastanceEwith SLS methodExpiration Index c1=ESI+Del.1EI1Expiration Index c2: last point before anEI2expiratory pause (if present) or RZC

ESI Expiratory Start IndexDirect estimation of patient’s staticEstelastance

F FlowFR Respiratory frequency

Inspiration Index c1=LZC+Del.1 andII1, II2c2=ZFI−Del.2Left zero crossing (starting index for aLZCcycle)Mean squared error upon selected parts ofMSEboth inflation and expiration when solvingmain least-squares equations

PA Alveolar pressurePAM,R Alveolar pressure measured, resp.

ReconstitutedPEEP Positive end expiratory pressure

Elastic pressure Pel=P0+EV, reflected byPel

alveolar pressure in training test lungPEEPst Direct estimation of patient’s static PEEPPplat Patient’s static elastic recoil pressure at

end inflationResistive pressure: Pres= (R0+� �F �)F,Pres

reflected by �P=PT−PA in training testlung

PT Airway pressurePTM,R Airway pressure measured, resp.

ReconstitutedEstimation of patient’s dynamic PEEPP0

with SLS methodReference values for parameters when theP0, E� , R0, �, …Alveolar pressure is accessible

�P PT−PA: difference between Airwaypressure and Alveolar pressure in trainingtest lungResistance: R=R0+� �F �RCoefficient of determinationR2

Mean value of resistance upon selectedRM

parts of both inflation and expirationRight zero crossing (ending index for aRZCcycle)

R0, � Constant and slope parameters of theresistance–flow relationship: R=R0+� �F �Expiratory time constant estimated fromTauthe Flow–Volume curve

TI Inflation durationTTOT Cycle duration (4 s)

Volume signalVTidal (inflated or expired) volumeVT

Zero flow index (end of inspiration)=ESIZFI


[30] and patients under assisted ventilation. Forthe latter, our program works satisfactorily withwell adapt patients. One may consider the oppor-tunity of a cycle-by-cycle implementation of ouralgorithm, leading to a true continuous monitor-ing of respiratory mechanics, e.g. to monitor theeffect of short-acting medication that can occurwithin seconds. Such a development of ourmethod is in progress. Table 7 gathers the vari-ables used and their definitions.

Acknowledgements

This work was carried out within and with thehelp of Groupe de Recherche et Modelisation enMecanique Ventilatoire (Grenoble, Lyon). P.Y.Carry is supported by Hospices Civils de Lyon.Financial support has been obtained from Delega-tion Regionale a la Recherche Clinique du CHUde Grenoble.

References

[1] R.A. Caplan, K.L. Posner, R.J. Ward, F.W. Cheney,Adverse respiratory events in anaesthesia: a closed claimanalysis, Anaesthesiology 72 (1990) 828–833.

[2] V. Neve, R. Cremer, F. Leclerc, R. Logier, A. Sadik, L.Storme, A. Martinot, Y. Riou, B. Grandbastien, Mea-surement of respiratory mechanics in paediatric intensivecare: in vitro assessment of a pulmonary function device,Intensive Care Med. 24 (1998) 1083–1088.

[3] P.F. Baconnier, A. Eberhard, P.-Y. Carry, J.-P. Perdrix,J.-M. Fargnoli, A computer program for automatic mea-surement of respiratory mechanics in artificially ventilatedpatients, Comput. Methods Programs Biomed. 47 (1995)205–220.

[4] M. Seear, D. Wensley, H. Werner, Comparison of threemethods for measuring respiratory mechanics in venti-lated children, Pediatr. Pulmonol. 10 (1991) 291–295.

[5] P.J. Chowienczyk, P.J. Rees, J. Payne, T.H.J. Clark, Anew method for computer-assisted determination of air-ways resistance, J. Appl. Physiol. 50 (1981) 672–678.

[6] R. Peslin, C. Gallina, C. Saunier, C. Duvivier, Fourieranalysis versus multiple regression to analyze pressure-flow data during artificial ventilation, Eur. Respir. J. 7(1994) 2241–2245.

[7] R.R. Uhl, F.J. Lewis, Digital computer calculation ofhuman pulmonary mechanics using a least square fittechnique, Comput. Biomed. Res. 7 (1974) 489–495.

[8] L. Eberhard, J. Guttman, G. Wolff, W. Bertschmann, A.

Minzer, H.-J. Kohl, J. Zeravik, M. Adolph, J. Eckart,Intrinsic PEEP monitored in the ventilated ARDS patientwith a mathematical method, J. Appl. Physiol. 73 (1992)479–485.

[9] J. Guttmann, L. Eberhard, G. Wolff, W. Bertschmann, J.Zeravik, M. Adolph, Manoeuvre-free determination ofcompliance and resistance in ventilated ARDS patients,Chest 102 (1992) 1235–1242.

[10] R. Peslin, J. Felicio da Silva, F. Chabot, C. Duvivier,Respiratory mechanics studied by multiple linear regres-sion in unsedated ventilated patients, Eur. Respir. J. 5(1992) 871–878.

[11] S. Kano, C.J. Lanteri, A.W. Duncan, P.D. Sly, Influenceof nonlinearities on estimates of respiratory mechanicsusing multilinear regression analysis, J. Appl. Physiol. 77(1994) 1185–1197.

[12] T.D. Officer, R. Pellegrino, V. Brusasco, J.R. Rodarte,Measurement of pulmonary resistance and dynamic com-pliance with airway obstruction, J. Appl. Physiol. 85(1998) 1982–1988.

[13] A.-M. Lauzon, J.H.T. Bates, Estimation of time-varyingmechanical parameters by recursive least squares, J. Appl.Physiol. 71 (1991) 1159–1165.

[14] J.H.T. Bates, A.-M. Lauzon, A nonstatistical approach toestimating confidence interval about model parameters:application to respiratory mechanics, IEEE Trans.Biomed. Eng. 39 (1992) 94–100.

[15] G. Avanzolini, P. Barbini, A. Cappello, G. Cevenini,Influence of flow pattern on the parameter estimates of asimple breathing mechanics model, IEEE Trans. Biomed.Eng. 42 (1995) 394–402.

[16] G. Avanzolini, P. Barbini, A. Cappello, G. Cevenini, L.Chiari, A new approach for tracking respiratory mechan-ical parameters in real-time, Ann. Biomed. Eng. 25 (1997)154–163.

[17] H.K. Chang, J.P. Mortola, Fluid dynamic factors intracheal pressure measurement, J. Appl. Physiol. 51(1981) 218–225.

[18] P.E. Pepe, J.J. Marini, Occult positive end-expiratorypressure in mechanically ventilated patients with airflowobstruction, Am. Rev. Respir. Dis. 126 (1982) 166–170.

[19] A. Rossi, S.B. Gottfried, L. Zocchi, B.D. Higgs, S.Lennox, P.M.A. Calverley, P. Begin, A. Grassino, J.Milic-Emili, Measurement of static compliance of totalrespiratory system in patients with acute respiratory fail-ure during mechanical ventilation, Am. Rev. Respir. Dis.131 (1985) 672–678.

[20] V.K. Bhutani, E. Sivieri, S. Abbasi, T.H. Shaffer, Evalua-tion of neonatal pulmonary mechanics and energetics: atwo factor least mean square analysis, Pediatr. Pulmonol.4 (1988) 150–158.

[21] J.P. Bachy, A. Eberhard, P. Baconnier, G. Benchetrit, Acycle by cycle shape analysis of biological rhythms: appli-cation to respiratory rhythm, Comput. Methods Pro-grams Biomed. 23 (1986) 297–307.

[22] P. Lascaux, R. Theodor, Analyse numerique matricielleappliquee a l’art de l’ingenieur, Masson, Paris, France,1993, p. 142.


[23] A.M. Lorino, D. Benhamou, H. Lorino, A. Harf, Acomputerized method for measuring respiratory mechan-ics during mechanical ventilation, Bull. Eur. Physio-pathol. Respir. 22 (1986) 81–84.

[24] R.J. Korst, R. Orlando III, N.S. Yeston, M. Molin, A.C.de Graff Jr, E. Gluck, Validation of respiratory mechan-ics software in microprocessor-controlled ventilators, Crit.Care Med. 20 (1992) 1152–1156.

[25] W.C. Burke, P.S. Crooke III, T.W. Marcy, A.B. Adams,J.J. Marini, Comparison of mathematical and mechanicalmodels of pressure-controlled ventilation, J. Appl. Phys-iol. 74 (1993) 922–933.

[26] D. Benhamou, A.M. Lorino, H. Lorino, F. Zerah, A.Harf, Automated measurement of respiratory mechanicsin anaesthetised ventilated patients, Bull. Eur. Physio-pathol. Respir. 23 (1987) 423–428.

[27] A.D. Bernsten, Measurement of overinflation by multipleregression analysis in patients with acute lung injury, Eur.Respir. J. 12 (1998) 526–532.

[28] G. Mols, I. Brandes, V. Kessler, M. Lichtwarck-Aschoff,T. Loop, K. Geiger, J. Guttmann, Volume-dependentcompliance in ARDS: proposal of a new diagnostic con-cept, Intensive Care Med. 25 (1999) 1084–1091.

[29] E. Bijaoui, S.A. Tuck, J.E. Remmers, J.H.T. Bates, Esti-mating respiratory mechanics in the presence of flowlimitation, J. Appl. Physiol. 86 (1999) 418–426.

[30] P.Y. Carry, D. Gallet, Y. Francois, J.P. Perdrix, A.Sayag, F. Gilly, A. Eberhard, V. Banssillon, P. Baconnier,Respiratory mechanics during laparoscopic cholecystec-tomy: the effects of abdominal wall lift, Anesth. Analg. 87(1998) 1393–1397.

Documents

A program based on a ‘selective’ least-squares method for respiratory mechanics monitoring in ventilated patients