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Validation of a New Method for Stroke VolumeVariation Assessment: a Comparaison with the PiCCO

TechniqueTaous-Meriem Laleg-Kirati, Claire Médigue, Yves Papelier, François Cottin,

Andry van de Louw

To cite this version:Taous-Meriem Laleg-Kirati, Claire Médigue, Yves Papelier, François Cottin, Andry van de Louw.Validation of a New Method for Stroke Volume Variation Assessment: a Comparaison with the PiCCOTechnique. [Research Report] RR-7172, INRIA. 2010, pp.22. �inria-00429496v3�

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INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE

Validation of a New Method for Stroke VolumeVariation Assessment: a Comparison with the

PiCCO Technique

Taous-Meriem Laleg-Kirati — Claire Médigue — Yves Papelier— François Cottin —

Andry Van de Louw

N° 7172

Janvier 2010

Centre de recherche INRIA Paris – RocquencourtDomaine de Voluceau, Rocquencourt, BP 105, 78153 Le ChesnayCedex

Téléphone : +33 1 39 63 55 11 — Télécopie : +33 1 39 63 53 30

Validation of a New Method for Stroke VolumeVariation Assessment: a Comparison with thePiCCO Te hniqueTaous-Meriem Laleg-Kirati ∗, Claire Médigue† , Yves Papelier‡ ,François Cottin§ , Andry Van de Louw¶Thème : Observation, modélisation et ommande pour le vivantÉquipe-Projet SISYPHERapport de re her he n° 7172 � Janvier 2010 � 22 pagesAbstra t: This paper proposes a novel, simple and minimally invasive methodfor stroke volume variation assessment using arterial blood pressure measure-ments. The arterial blood pressure signal is re onstru ted using a semi- lassi alsignal analysis method allowing the omputation of a parameter, alled the �rstsystoli invariant INV S1. We show that INV S1 is linearly related to strokevolume. To validate this approa h, a statisti al omparaison between INV S1and stroke volume measured with the PiCCO te hnique was performed during a15-mn re ording in 21 me hani ally ventilated patients in intensive are. In 94%of the whole re ordings, a strong orrelation was estimated by ross- orrelationanalysis (mean oe� ient=0.9) and linear regression (mean oe� ient=0.89).On e the linear relation had been veri�ed, a Bland-Altman test showed thevery good agreement between the two approa hes and their inter hangeability.For the remaining 6%, INV S1 and the PiCCO stroke volume were not orre-lated at all, and this dis repan y, interpreted with the help of mean pressure,heart rate and peripheral vas ular resistan es, was in favor of INV S1.Key-words: Arterial blood pressure, �rst systoli invariant, PiCCO, semi- lassi al signal analysis, stroke volume variation∗ Taous-Meriem Laleg-Kirati is with INRIA Bordeaux Sud-Ouest, MAGIQUE-3D proje tteam, UFR S ien es, Bâtiment B1, Université de Pau et des Pays de l'Adour BP 1155, 64013Pau, Fran e, (e-mail: Taous-Meriem.Laleg�inria.fr).† Claire Médigue is with INRIA-Ro quen ourt, B.P. 105, 78153 Le Chesnay edex, Fran e,(e-mail: Claire.Medigue�inria.fr).‡ Yves Papelier is with EA 3544 EFM H�pital Antoine Bé lère 92141, Clamart,Fran e,(e-mail: yves.papelier�kb.u-psud.fr)§ François Cottin is with Unité de Biologie Intégrative des Adaptations à l'Exer i e (IN-SERM 902 EA 3872, Genopole), 91000 Evry, Fran e, (e-mail: fran ois. ottin�bp.univ-evry.fr)¶ Andry Van de Louw is with Intensive Care Unit, Centre Hospitalier Sud-Fran ilien, 91014Evry, Fran e, (e-mail: andry.vandelouw� h-sud-fran ilien.fr)

Validation d'une nouvelle méthode pourl'estimation du volume d'éje tion systolique: omparaison ave le PiCCORésumé : Cet arti le propose une nouvelle méthode pour l'estimation du vo-lume d'eje tion systolique par des mesures de pression artérielle. Le signal depression est re onstruit à l'aide d'une méthode d'analyse semi- lassique permet-tant le al ul d'un paramètre, appelé le premier invariant systolique INV S1.On montre que INV S1 est linéairement relié au volume d'eje tion systolique.A�n de valider ette appro he, une omparaison statistique entre INV S1 etle volume d'eje tion systolique mesuré par la te hnique PiCCO a été e�e tuéepour un enregistrement de 15 minutes pour 21 patients mé aniquement ventiléset en soins intensifs. Pour 94% de l'enregistrement omplet, une forte orréla-tion a été estimée par une analyse ross- orrélation ( oe� ient moyen=0.9) etune regression linéaire ( oe� ient moyen =0.89). Une fois la relation linéairevéri�ée, un test de Bland-Altman a montré une bonne orrespondan e entre lesdeux appro hes et leur inter hangeabilité. Pour les 6% restant, INV S1 et levolume d'éje tion al ulé par PiCCO n'ont pas été orrélés, et ette di�éren e,interprétée à l'aide de la pression moyenne, de la fréquen e ardiaque et desrésistan es vas ulaires périphériques a été en faveur de INV S1.Mots- lés : Pression artérielle, premier invariant systolique, PiCCO, analysesemi- lassique du signal, variations du volume d'éje tion

Validation of a New Method for Stroke Volume Variation Assessment 3Contents1 Introdu tion 32 Materials and Methods 52.1 Patients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.2 Data a quisition . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.3 Signal analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.4 Statisti al analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 103 Results 113.1 Patients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113.2 Cross- orrelation analysis . . . . . . . . . . . . . . . . . . . . . . 123.3 Linear regression . . . . . . . . . . . . . . . . . . . . . . . . . . . 133.4 Bland-Altman method . . . . . . . . . . . . . . . . . . . . . . . . 134 Dis ussion 151 Introdu tionHemodynami monitoring is ru ial for riti al are patient management. Are ent international onsensus onferen e re ommended against the routine useof stati preloaded measurements alone to predi t �uid responsiveness [2℄, anddynami assessment now seems more useful. Several studies have do umentedthe ability of respiratory stroke volume variation (SV V ) to predi t the �uidresponsiveness in hemodynami ally ompromised patients [8℄-[13℄. Measuringrespiratory SV V requires a ontinuous monitoring of stroke volume (SV ) whi h an be obtained using invasive or non-invasive methods. Current invasive meth-ods used have the disadvantage of requiring the insertion of a entral venous atheter and the alibration of the ardia output measure with a old iso-toni sodium hloride bolus (PiCCO te hnology) [3℄ or a lithium hloride bolus(LiDCO te hnology) [9℄. An alternative method, whi h does not require ve-nous atheter insertion or alibration has been proposed (Flotra Vigileo) [5℄,but several lini al studies have pointed out its poor agreement with referen ete hniques [12℄, [16℄. Esophageal e ho-doppler is the main non-invasive method, al ulating aorti blood �ow from the e ho-derived aorti diameter and thedoppler-derived aorti blood velo ity [11℄. Nevertheless, this te hnique has po-tential ontraindi ations, su h as esophageal vari es or esophageal surgery, andseveral limitations: for instan e, it measures the blood �ow in the des endingaorta and not the whole ardia output. Moreover, the pre ision of the mea-surement depends on a urate probe positioning, whi h is not always easy toobtain [4℄. Thus, ea h of the above methods has its own drawba ks, and there isstill a need for an easily appli able, minimally invasive, a urate and a�ordablemethod to estimate SV V .Due to the fa t that Arterial Blood Pressure (ABP) an be measured us-ing minimally invasive or noninvasive methods, the idea of estimating SV fromABP has aptured s ientists for a long time. Thus, many methods have beendeveloped and whose obje tive is to �nd a relation between one or several pa-rameters hara terizing the shape of the pressure and SV or ardia output(CO), see for instan e [7℄, [15℄, [22℄, [23℄ and the referen es quoted there. TheseRR n° 7172

4 Laleg & Médigue & Papelier & Cottin & Van de Louwmethods, whi h are based on some models of systemi ir ulation, are alledpulse ontour methods. A omparison between some of the pulse ontour meth-ods has been proposed in [1℄, [26℄, [27℄, [29℄. The simplest model supposes aproportionality between CO and the Mean Arterial Pressure (MAP ). Otherapproa hes, based on windkessel models, link SV to di�erent lumped param-eters su h as pulse pressure, the systoli and diastoli pressures [7℄. Howeverthese approa hes onsider the arterial system as a lumped system whi h appearsnot su� iently a urate. So, other methods resulting from distributed arterialmodels use the pressure area so that SV is often supposed to be proportional tothe area under the systoli part of the pressure urve. Corre ted versions of thisrelation have been also proposed [15℄. However, this approa h requires dete tingthe end of the systole whi h is ompletely nontrivial, parti ularly in peripheralABP waveforms. Moreover, approa hes taking into a ount the nonlinear as-pe ts of the arterial system have been proposed, for example model�ow [28℄,but some studies have revealed the poor e� ien y of this method in a numberof ases [24℄.In this paper we introdu e a novel te hnique for SV V assessment usingABP measurements. This method is based on the analysis of ABP with a newsignal analysis method that was re ently proposed in [21℄, and alled Semi-Classi al Signal Analysis (SCSA). The new spe tral parameters provided bySCSA, eigenvalues and invariants, have already given promising results in someother appli ations, as summarized in the following.On the one hand, we assessed their ability to dis riminate between di�er-ent situations. In the �rst situation, nine heart failure subje ts were omparedto nine healthy subje ts. In the se ond situation, eight highly �t triathleteswere ompared before and after training. SCSA parameters always providedmore signi� ant results than lassi al parameters, regarding temporal as wellas spe tral parameters ([20℄, [21℄). On the other hand, we tested the ability ofthe invariants to represent physiologi al parameters of great interest, parti u-larly SV V , in two well-known onditions: the head-up 60 degrees tilt-test andthe handgrip-test [21℄. Let us fo us on the �rst invariants. The �rst globalinvariant (INV1) is, by de�nition, the mean value of the ABP signal, whi h isa standard parameter in lini al pra ti e. The �rst systoli (INV S1) and dias-toli (INV D1) invariants are less obvious. They result from the de ompositionof the pressure into its systoli and diastoli parts. In parti ular, INV S1 orre-sponds to the integral of the estimated systoli pressure with SCSA. Referringto the pulse ontour method stating that the area under the systoli part ofthe pressure urve is proportional to SV as des ribed above, one an show thatINV S1 variations give information on SV V .We study in this paper the orrelation between INV S1 and measured SV Vusing a referen e method; the PiCCO te hnique. The PiCCO te hnique usesthe pulse ontour method with a alibration by a transpulmonary thermodi-lution and is onsidered a reliable te hnique. In what follows, we present theexperimental proto ol and re all some basi aspe ts of the SCSA method. Weintrodu e INV S1 and its relation to SV V . Then, we present statisti al resultson 21 patients' re ordings.

INRIA

Validation of a New Method for Stroke Volume Variation Assessment 52 Materials and MethodsThis prospe tive study was ondu ted in the 16-bed medi al-surgi al intensive are unit (ICU) of the Sud-Fran ilien General Hospital (Evry, Fran e).2.1 Patients� In lusion riterion: all me hani ally ventilated patients whose ardia output was ontinuously monitored with a transpulmonary thermodilu-tion atheter (PiCCO, Pulsion Medi al Systems, Muni h, Germany) werein luded, ex ept those satisfying the following ex luding riteria. PiCCOis routinely used in this unit to monitor hemodynami ally ompromisedpatients.� Ex lusion riteria: patients presenting ardia arrhythmias or breath-ing spontaneously were ex luded be ause the SVV is not appli able forsu h patients.� Proto ol: all patients were sedated with midazolam and fentanyl indosages that were titrated to a hieve full adaptation to the ventilator.Ventilator settings were as follows: volume assist- ontrol mode; tidal vol-ume (Vt), 6ml/kg ideal body weight; breathing rate, 20 y les/minute;inspiratory/expiratory ratio, 1

2; and FiO2 adjusted to maintain trans u-taneous oxygen saturation in blood 94%. Positive end-expiratory pressure(PEEP) was set at 5cm H2O but some hypoxemi patients required anin rease in PEEP to 10 m H2O during the data a quisition, to improvearterial oxygenation. The in rease in PEEP was left to the dis retionof the attending physi ian, as well as the adaptation of vasoa tive drugsdosages, adjusted to maintain an adequate ir ulatory status during theproto ol.2.2 Data a quisitionOne-lead ele tro ardiogram, arterial pressure, and respiratory �ow signals werere orded during a 15-min period using a Biopa 100 system (Biopa systems,Goleta, CA, USA). All data were sampled at 1000Hz and stored on a harddisk. Cardia output was alibrated just before the data a quisition with a oldisotoni sodium hloride bolus of 20 ml. Then, CO and peripheral vas ularresistan es (PV R) were delivered every 30 se onds during the 15-min period.2.3 Signal analysisSignal pro essing was performed using the S ilab and Matlab environments atthe Fren h National institute for Resear h in Computer S ien e and Control(INRIA-Sisyphe team).A Semi-Classi al Signal Analysis methodIn this se tion, we introdu e the SCSA te hnique and some results of its appli- ation to ABP analysis. We also show the relation between INV S1 and SV V .RR n° 7172

6 Laleg & Médigue & Papelier & Cottin & Van de LouwThe SCSA prin iple Let y : t 7−→ y(t) be a real valued fun tion representingthe signal to be analyzed su h that:y ∈ L1

1(R), y(t) ≥ 0, ∀t ∈ R,

∂my

∂xm∈ L1(R), m = 1, 2, (1)with,

L11(R) = {V |

∫ +∞

−∞

|V (t)|(1 + |t|)dt <∞}. (2)The main idea in the SCSA onsists in interpreting the signal y as a mul-tipli ation operator, φ → y.φ, on some fun tion spa e. Then, instead of thestandard Fourier Transform, we use the spe trum of a regularized version ofthis operator, known as the S hrödinger operator in L2(R), for the analysis ofy:

H(h; y) = −h2 d2

dt2− y, (3)for a small h > 0. The SCSA method is better suited to the analysis of somepulse shaped signals than the Fourier Transform [21℄.In this approa h, the signal is a potential of the S hrödinger operatorH(h; y).We are interested in the spe tral problem of this operator whi h is given by:

− h2 d2ψ

dt2− yψ = λψ, t ∈ R, (4)where λ, λ ∈ R and ψ, ψ ∈ H2(R) 1 are respe tively the eigenvalues of H(h; y)and the asso iated eigenfun tions. Under equation (1), the spe trum of H(h; y) onsists of:� a ontinuous spe trum λ ≥ 0,� a dis rete spe trum omposed of negative eigenvalues. There is a non-zero,�nite number Nh of negative eigenvalues of the operator H(h; y). We put

λ = −κ2nh with κnh > 0 and κ1h > κ2h > · · · > κnh, n = 1, · · · , Nh. Let

ψnh, n = 1, · · · , Nh be the asso iated L2-normalized eigenfun tions [21℄.The SCSA te hnique onsists in re onstru ting the signal y with the dis retespe trum of H(h; y) using the following formula:yh(t) = 4h

Nh∑n=1

κnhψ2nh(t), t ∈ R. (5)Here, the parameter h plays an important role. As h de reases, the approxi-mation of the signal improves. However, as h de reases, the number of negativeeigenvalues Nh in reases and hen e the time required to perform the ompu-tation in reases. So, in pra ti e, what we are looking for is a value of h thatprovides a su� iently small estimation error with a redu ed number of negativeeigenvalues. We summarize the main steps for re onstru ting a signal with theSCSA as follows [21℄:1

H2(R) denotes the Sobolev spa e of order 2 INRIA

Validation of a New Method for Stroke Volume Variation Assessment 71. Interpret the signal to be analyzed y as a potential of the S hrödingeroperator H(h; y) (3) ;2. ompute the negative eigenvalues and the asso iated L2-normalized eigen-fun tions of H(h; y) ;3. ompute yh a ording to equation (5) ;4. look for a value of h to obtain a good approximation with a small numberof negative eigenvalues.ABP analysis with the SCSA Now, we introdu e some results on the ap-pli ation of the SCSA to ABP analysis. We denote by P the ABP signal and P̂its estimation with the SCSA su h that:P̂ (t) = 4h

Nh∑n=1

κnhψ2nh(t), (6)where −κ2

nh, n = 1, · · · , Nh are the Nh negative eigenvalues of the S hrödingeroperator H(h;P ) and ψnh the asso iated L2−normalized eigenfun tions.The ABP signal was estimated for several values of the parameter h andhen e Nh. Fig.1 illustrates measured and estimated pressures for one beat of anABP signal and the estimated error with Nh = 9. Signals measured at the aorta(invasively) and at the �nger (non invasively) respe tively were onsidered. Wepoint out that 5 to 9 negative eigenvalues are su� ient for a good estimation ofan ABP beat [17℄, [19℄.One appli ation of the SCSA to ABP signals onsists in de omposing thesignal into its systoli and diastoli parts. This appli ation was inspired bya redu ed model of ABP based on solitons solutions of a Korteweg-de Vries(KdV) equation 2 proposed in [10℄, [18℄. As des ribed in [17℄, [21℄, the idea onsists in de omposing (6) into two partial sums: the �rst one, omposed ofthe Ns (Ns = 1, 2, 3 in general) largest κnh and the se ond omposed of theremaining omponents. Then, the �rst partial sum represents rapid phenomenathat predominate during the systoli phase and the se ond one des ribes slowphenomena of the diastoli phase. We denote by P̂s and P̂d the systoli pressureand the diastoli pressure respe tively estimated with the SCSA. Then we have:P̂s(t) = 4h

Ns∑n=1

κnhψ2nh(t), (7)

P̂d(t) = 4h

Nh∑n=Ns+1

κnhψ2nh(t). (8)Fig.2 shows measured pressure and estimated systoli and diastoli pressuresrespe tively. We noti e that P̂s and P̂d are respe tively lo alized during the sys-tole and the diastole.2Solitons are solutions of some non-linear partial derivative equations like the KdV equationRR n° 7172

8 Laleg & Médigue & Papelier & Cottin & Van de Louw

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(b)Figure 2: (a) Estimated systoli pressure, (b) Estimated diastoli pressureINRIA

Validation of a New Method for Stroke Volume Variation Assessment 9SCSA parameters As seen previously, the SCSA te hnique provides a newdes ription of the ABP signal with some spe tral parameters whi h are thenegative eigenvalues and the so alled invariants 3. The latter onsist in somemomentums of the κnh, n = 1, · · · , Nh. So we de�ne the �rst two global invari-ants by:INV1 = 4h

Nh∑n=1

κnh, INV2 =16

3h

Nh∑n=1

κ3nh. (9)Systoli (INV S1,2) and diastoli (INV D1,2) invariants are dedu ed fromthe de omposition of the pressure into its systoli and diastoli parts and arethen given by:

INV S1 = 4h

Ns∑n=1

κnh, (10)INV S2 =

16

3h

Ns∑n=1

κ3nh, (11)

INVD1 = 4h

Nh∑n=Ns+1

κnh, (12)INV D2 =

16

3h

Nh∑n=Ns+1

κ3nh. (13)

INV S1 for SV V estimation We will see here how INV S1 is related toSV . For this purpose, we re all one approa h of the pulse ontour methodsthat supposes proportionality between SV and the area under the systoli partof the pressure urve as des ribed in the introdu tion. We denote this area byPsa (see �g.3). So we have:

SVPC = kPsa, (14)where k is a positive real and SVPC is the stroke volume estimated with thepulse ontour method.Referring to (7) and (10), and remembering that ψnh are L2-normalized, wehave:INV S1 =

∫ +∞

−∞

P̂s(t)dt. (15)So, INV S1 refers to the area under the systoli urve P̂s. Thus, one an remarkthat both Psa and INV S1 des ribe the area under the systoli pressure but theymay not be equal be ause the dete tion of the end systole in the two ases isnot the same (see �g.2.a and �g.3). Indeed, while Psa is omputed by dete tingthe di roti not h whi h is ompletely non trivial in peripheral ABP waves,INV S1 results from a nonlinear model of ABP based on solitons that onsidersthe propagation of the pulse wave [10℄, [18℄ as was des ribed in se tion II.C.1.b.We an write the following relation between the two areas:

INV S1 = Psa + b, (16)3We all these parameters invariants be ause they are related to the Korteweg-de Vriesinvariants in timeRR n° 7172

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Figure 3: Area under the systoli part of the pressure urve used to estimateSVwhere b ∈ R represents the di�eren e between the two areas. Then, we get:

INV S1 = aSVPC + b. (17)with a =1

k. Hen e, INV S1 and SVPC are linearly related.Resulting time series used to ompare INV S1 to PiCCO stroke vol-umeOn top of INV S1, two vas ular time series were analyzed: the heart rate (HR)was omputed from the pulse interval (PI), whi h is the distan e between twosystoli o urren es; MAP was al ulated from the systoli and diastoli val-ues. All data were resampled at 4 Hz, by the interpolation of a third orderspline fun tion to obtain equidistant data and to guarantee their syn hroniza-tion. They were then averaged over 15 se onds and delivered every 30 se onds,like the PiCCO proto ol. PiCCO ardia output was divided by HR to give astroke volume (SVPiCCO). A ording to the relation between INV S1 and SV ,

INV S1 was subsequently alled SVSCSA when it was estimated with the linearequation (17): SVSCSA = aSVPiCCO + b. Thus, in addition to the SVPiCCOand SVSCSA, temporal relations with HR,MAP and PV R time series were an-alyzed to help interpret SV behavior in ase of a divergen e between SVPiCCOand SVSCSA.2.4 Statisti al analysis1. Cross- orrelation analysis.The ross- orrelation analyzes the temporal similarity between two timeseries by estimating the orrelation between one time series at time t andthe other at time t ± x lags (in samples) [25℄. A ross- orrelation wasperformed between SVPiCCO and INV S1 time series averaged every 30se onds. Cross- orrelation oe� ients were omputed using the Matlabx orr fun tion (The MathWorks, In ) after subtra ting the means fromINRIA

Validation of a New Method for Stroke Volume Variation Assessment 11the time series. Cross- orrelation oe� ients were omputed for all lags(−30; +30), ea h lag orresponding to a 30-se ond interval. The orrela-tion oe� ients of the unlagged data stand at the midpoint (lag 0). A5% level of probability for the orrelation oe� ients was onsidered sig-ni� ant (Bravais-Pearson table). An average estimate of the orrelationover all the subje ts was allowed after homogeneity tests (non signi� antz-test and Jarque-Bera test) [14℄. The individual orrelation oe� ientswere averaged for ea h lag.2. Linear regression.A ording to the proportional relation between SVPiCCO and INV S1(equation (17)), a linear regression analysis was applied, using SigmaS-tat. This analysis provides the Pearson R oe� ient, whi h measures thedegree of linear orrelation between the two estimates, and the parametersof the linear equation (17), a and b. So, they allow an estimation of thestroke volume SVSCSA using (17). This transformation is required beforeusing the Bland-Altman test.3. Bland-Altman method.Unlike the �rst two approa hes whi h are not a�e ted by di�eren es inunits or the nature of results, the Bland-Altman method analyzes theagreement between two estimates of the same variable [6℄. Thus, weused SVSCSA instead of INV S1, and moreover, SVSCSA variations to ompare them to SVPiCCO variations (∆ := SV VPiCCO − SV VSCSAwith SV VPiCCO = SVPiCCO(n) − SVPiCCO(n − 1) and SV VSCSA =SVSCSA(n) − SVSCSA(n− 1)). The mean di�eren e between SV VPiCCOand SV VSCSA (mean ∆) is plotted against the average of the two volumevariations. Mean ∆ whi h represents the bias between the two methods,and the 95% on�den e interval ([CIinf∆ CIsup∆]) gives the variationof the values of one method ompared to the other.3 Results3.1 PatientsThe 21 patients re ordings were analyzed over 900 se onds, representing about30 averaged values, ex ept one re ording, analyzable only for the �rst 16 aver-aged values. In order to illustrate the main results, we hoose the �rst threesubje ts in Table 1, representing various onditions: subje t one was submit-ted to PEEP hanges (�g.8), subje t two was submitted to noradrenaline dose hanges (�g.9), subje t three had no hange in ventilatory parameters nor indrugs (�g.10).

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12 Laleg & Médigue & Papelier & Cottin & Van de LouwTable 1: Cross- orrelation and linear regression oe� ients between SVPiCCOand INV S1 Subje t Number of Cross Linearvalues orrelation regression1 30 0.99 0.982 30 0.97 0.973 30 0.97 0.974 30 0.96 0.965 30 0.96 0.966 30 0.95 0.957 30 0.95 0.958 30 0.93 0.949 30 0.91 0.9110 30 0.91 0.8911 30 0.90 0.8912 30 0.90 0.9013 30 0.86 0.8514 30 0.85 0.7715 30 0.85 0.8616 30 0.85 0.8517 21 0.84 0.8718 30 0.82 0.8319 16 0.82 0.8220 30 0.77 0.77The subje ts ( ol. 1) are listed in the de reasing order of ross- orrelation oe� ients.Col. 2 indi ates the number of measurements delivered every 30-se ond per subje t,a ording to the PiCCO proto ol and representing a 900 se onds analysis. Col. 3and 4 stand for oe� ients of ross- orrelation (mean: 0.90± 0.01 at lag 0) and linearregression (mean: 0.89 ± 0.01). Subje t 21 and the last third of Subje t 17, whoseINV S1 and SVPiCCO were not orrelated at all ( oe� ient < 0.1), were dis ardedfrom the table. The last part of Subje t 19 was dis arded before analysis be ause ofa PiCCO dysfun tion.3.2 Cross- orrelation analysisTable 1, olumn three, shows the oe� ients of ross- orrelation in de reas-ing order. The amount of well orrelated measures represents 94% of the allre ordings. Be ause of an obvious divergen e between SVPiCCO and INV S1( oe� ients < 0.1), Subje t 21 and the third part of Subje t 17 were dis ardedfrom the table. Thus, they represent only 6% of dis repan y among all there ordings. Fig.4 and �g.5 respe tively represent the time series of HR, MAP ,PV R, INV S1 and SVPiCCO for subje ts 21 and 17.Fig.6 represents the ross- orrelation oe� ients of the 20 remaining subje ts(dashed lines). As homogeneity was veri�ed, averaged values were also plotted(− • −). The verti al axis depi ts the orrelation oe� ients. The horizontalaxis depi ts the lag, in number of 30-se ond averaged values of one time serieson another. The orrelation oe� ients of the unlagged data are plotted at hori-zontal midpoint (lag 0). The two symmetri al ontinuous lines represent riti alINRIA

Validation of a New Method for Stroke Volume Variation Assessment 13Table 2: Bland-Altman test resultsSubje t Min∆ CIinf∆ Max∆ CIsup∆1 -.0056 -.0074 .0048 .00772 -.0026 -.0037 .0034 .00393 -.0030 -.0036 .0022 .00374 -.0043 -.0057 .0043 .00565 -.0034 -.0039 .0044 .00406 -.0048 -.0052 .0045 .00537 -.0059 -.0072 .0043 .00728 .0005 -.0009 .0009 .00099 -.0037 -.0051 .0046 .005010 -.0047 -.0055 .0042 .005711 -.0073 -.0114 .0095 .011512 -.0070 -.0096 .0068 .009613 -.0044 -.0072 .0078 .007914 -.0018 -.0031 .0023 .003215 -.0029 -.0053 .0060 ∗ .005416 -.0022 -.0026 .0026 ∗ .003017 -.0033 -.0041 .0024 .004618 -.0081 -.0100 .0079 .009419 -.0016 -.0045 .0035 .004620 -.0054 -.0080 .0079 .0080∆ = SV VPiCCO − SV VSCSA with SV VPiCCO = SVPiCCO(n) − SVPiCCO(n − 1) andSV VSCSA = SVSCSA(n)−SVSCSA(n−1). Min(∆) and max(∆) stand for the minimaland maximal values of ∆ respe tively. CI is 95% on�den e interval of the agreementlimits of ∆; [CIinf∆ CIsup∆]. ⋆ means that all the values are inside [CIinf δ CIsup∆]ex ept 1 value greater than CIsup∆ for two subje ts.r values for a level 5 of probability (Bravais-Pearson table). The greatest or-relation stands at lag 0 for all the remaining subje ts (mean orrelation= 0.90;sem = 0.01; p = 0.00001). This result shows an ex ellent temporal similaritybetween the su essive measures, indi ating that they hange in the same wayover time.3.3 Linear regressionTable 1, olumn four, shows the R oe� ients of linear regression. Cross- orrelation and R oe� ients are strongly orrelated (0.95 at Spearman rankorder orrelation test). The mean oe� ient, equal to 0.89 shows a great degreeof linearity between the two methods. Fig.7 shows the plots of linear regressionfor the �rst three subje ts.3.4 Bland-Altman methodFig.7 shows the Bland-Altman plots for the �rst three subje ts. Di�eren es inthe two mean SV V (SV VPiCCO − SV VSCSA) are plotted against the mean ofthe two SV V (SV VPiCCO + SV VSCSA

2). Continuous lines respe tively standRR n° 7172

14 Laleg & Médigue & Papelier & Cottin & Van de Louw

Figure 4: Cardiovas ular time series of subje t 21, submitted to ventilatoryand pharma ologi al hanges. The la k of orrelation between INV S1 andSVPiCCO ( ross- orrelation oe� ient=0.039) is in favor of INV S1. Beforein reasing PEEP, nothing happens, HR, MAP , PV R are stable, thus no SV hange an be expe ted. Nevertheless, SVPiCCO de reases then in reases whileINV S1 remains quite stable. During in reasing adrenaline, in reasing PV R isa ompanied, as expe ted, by in reasingMAP and de reasingHR. An in reasein SV is also expe ted, whi h is done by INV S1 while SVPiCCO remains quitestable.for the mean of di�eren es ∆ between the two results, and the 95% on�den einterval. Ea h dot stands for the di�eren e between SV V measured by the twomethods. In the three ases, mean ∆ is equal to 0 and all values are withinthe two 95% on�den e intervals. Table 2 gives results for all the subje ts.When omparing min(∆) to CIinf∆ ( olumns 1 and 2) and max(∆) to CIsup( olumns 3 and 4), one an see that all values are inside [CIinf CIsup] ex eptone value greater than CIsup∆ in two subje ts (∗). These global results allowus to on lude that a good proximity exists between the two methods with thesame order of dispersion and that they are inter hangeable.

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Validation of a New Method for Stroke Volume Variation Assessment 15

Figure 5: Cardiovas ular time series for subje t 17, submitted to ventilatoryand pharma ologi al hanges. INV S1 and SVPiCCO are strongly orrelated( ross- orrelation oe� ient = 0.84) during period A, and they are divergentduring period B. De reasing noradrenaline is naturally a ompanied by de reas-ing PV R and MAP and in reasing HR. A de rease in SV is also expe ted,whi h is done by INV S1 while SVPiCCO strongly in reases.4 Dis ussionA new method for a simple and minimally invasive SV V estimation from ABPmeasurements has been validated in this study. The ABP signal is re onstru tedwith a semi- lassi al signal analysis method SCSA whi h enables the de omposi-tion of the signal into its systoli and diastoli parts. Some spe tral parameters,that give relevant physiologi al information, are then omputed and espe iallythe �rst systoli invariant INV S1, given by the area under the estimated sys-toli pressure urve. Thus, we have shown that INV S1 yields reliable SV Vassessment.So, in order to validate this approa h, we ompared INV S1 estimated fromABP measurements with SV measured with a referen e method: the PiCCOte hnique. Three statisti al methods were applied for this validation: ross- orrelation analysis, linear regression and the Bland-Altman test. Among the315 minutes duration of all the 21 re ordings, 94 % presented a very high or-relation between INV S1 and SVPiCCO. The mean oe� ient was equal to 0.9RR n° 7172

16 Laleg & Médigue & Papelier & Cottin & Van de Louw

Figure 6: Cross- orrelation between the 30-se ond averaged SVPiCCO andINV S1 values in 20 subje ts Ea h line (dashed) stands for a subje t; the strongline (−•−) represents the average of the 20 subje ts; ontinuous lines represent riti al r values for a 5% level of probability (Bravais-Pearson table). The verti- al axis depi ts the orrelation oe� ients. The horizontal axis depi ts the lag,in number of 30-se ond measures, of one time series on another. The orrelation oe� ients of the unlagged data are shown at horizontal midpoint (lag 0). Alltime series are exa tly syn hronized, with a mean orrelation oe� ient equalto 0.9 at lag 0 (p=0.00001).for ross- orrelation, and equal to 0.89 for linear regression. The remaining 6%without orrelation, on erned two subje ts: all of subje t 21 and the last thirdof subje t 17. This dis repan y, interpreted with the help of the syn hronizedHR, MAP , PV R time series, an be explained by the following remarks:� For subje t 21 (�g.4), before in reasing PEEP, nothing happens, HR,

MAP , PV R are stable, thus no SV hange an be expe ted. Never-theless, SVPiCCO de reases then in reases while INV S1 remains quitestable. During in reasing adrenaline, in reasing PV R is a ompanied, asexpe ted, by in reasing MAP and de reasing HR. An in rease in SVis also expe ted, whi h is done by INV S1 while SVPiCCO remains quitestable.� For the last third of subje t 17 (�g.5, B), de reasing noradrenaline is nat-urally a ompanied by de reasing PV R andMAP and in reasing HR. Ade rease in SV is also expe ted, whi h is done by INV S1 while SVPiCCOstrongly in reases.The divergen e between INV S1 and SVPiCCO is in favor of INV S1 for thesetwo subje ts.On the 94% re ordings with well orrelated INV S1 and SVPiCCO, theBland-Altman test showed a very good agreement between the two approa hesINRIA

Validation of a New Method for Stroke Volume Variation Assessment 17

Figure 7: Linear regression plots (at the top) and Bland-Altman plots (at thebottom) for the three �rst subje ts. The oe� ient of orrelation is greaterthan .95 for ea h of them, meaning a strong linear relation. All the di�eren esin SV VPiCCO and SV VSCSA are in luded in the 95 % on�den e interval forea h of them, meaning a good agreement between the two methods.

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18 Laleg & Médigue & Papelier & Cottin & Van de Louw

Figure 8: Cardiovas ular time series of subje t 1, submitted to Positive EndExpiratory Pressure hanges. A: de reasing PEEP; B: in reasing PEEP; C:de reasing PEEP; D: in reasing PEEP. INV S1 and SVPiCCO are strongly or-related ( ross- orrelation oe� ient = 0.99).and demonstrated their inter hangeability. It is worth noti ing that this agree-ment is obtained in unstable hemodynami and/or noisy onditions whi h provethe robustness of the SCSA method. Several great ventilatory or pharma olog-i al hanges are illustrated in �g.8, �g.9 and �g.10 but also by the non averagedtime series in �g.11. A noisy ondition is illustrated by subje t 3 on the right.Despite a raw PI (top right) disturbed by extra-systoles and artefa ts, INV S1(bottom right) is well estimated.Therefore, this study shows that SCSA is a reliable method for SV V assess-ment and more suitable in the two ases of divergen e. The good agreementbetween the two approa hes ould be explained by the fa t that the main ideain the SCSA te hnique is quite similar to the PiCCO and onsists in using thearea under the systoli part of the pressure urve. However, the dete tion of theend systole with the SCSA is di�erent from the pulse ontour approa h. Indeed,while the pulse ontour approa h uses an algorithm to dete t the di roti not h,the SCSA uses an ABP model based on solitons that takes into a ount nonlin-ear phenomena, as des ribed in se tion II.C.1.b. This di�eren e ould explainthe greater reliability of SCSA when dis repan ies between the two approa hesappear. Moreover, this explanation agrees with the observation of the raw ABPsignal for subje t 17: its shape is very di�erent between the �rst and last partof the re ording.Finally, unlike the PiCCO te hnique whi h needs periodi alibration bya thermodilution te hnique, SCSA is easier to use, requiring less equipments,only for ABP measurements. It is mu h less invasive and ould be totallyINRIA

Validation of a New Method for Stroke Volume Variation Assessment 19

Figure 9: Cardiovas ular time series of subje t 2, submitted to a vasoa tivedrug. A: in reasing noradrenaline; B: de reasing noradrenaline. INV S1 andSVPiCCO are strongly orrelated ( ross- orrelation oe� ient = 0.97).

Figure 10: Cardiovas ular time series of subje t 3, without any hange in ven-tilatory or pharma ologi al ondition. INV S1 and SVPiCCO are strongly or-related ( ross- orrelation oe� ient = 0.97).RR n° 7172

20 Laleg & Médigue & Papelier & Cottin & Van de Louw

Figure 11: Pulse interval (PI), Systoli Blood Pressure (SBP ) and INV S1 timeseries for the three �rst subje ts with a strong orrelation between SVPiCCOand INV S1. The INV S1 is pre isely estimated despite unstable hemodynami onditions (subje ts 2 and 3) and noisy onditions su h as extra-systoles andartefa ts (subje t 3).noninvasive if we used a FINOMETER devi e, for instan e. This latter point,already experimented in our previous studies [21℄, should be a new perspe tivefor a simple non-invasive SV V assessment.Referen es[1℄ E. L. Alderman, A. Branzi, W. Sanders, B. W. Brown, and D. C. Harrison.Evaluation of the pulse- ontour method of determining stroke volume inman. Cir ulation, XLVI:546�558, September 1972.[2℄ M. Antonelli, M. Levy, P.J. Andrews, J. Chastre, LD. Hudson, C. Mant-hous, GU. Meduri GU, RP. Moreno, C. Putensen, T. Stewart, and A. Tor-res. Hemodynami monitoring in sho k and impli ations for management.In International Consensus Conferen e, pages 27�28, April 2006.[3℄ B. Bein, F. Worthmann, PH. Tonner, A. Paris, M. Steinfath, J. Hedderi h,and J. S holz. Comparison of esophageal doppler, pulse ontour analysis,and real-time pulmonary artery thermodilution for the ontinuous measure-ment of ardia output. J. Cardiothora Vas Anesth, 18(2):185�9, April2004.[4℄ G. Bernardin, F. Tiger, R. Fou hé, and M. Mattéi. Continuous noninva-sive measurement of aorti blood �ow in riti ally ill patients with a newesophageal e ho-doppler system. Crit Care, 13(4):177�83, De ember 1998.INRIA

Validation of a New Method for Stroke Volume Variation Assessment 21[5℄ M. Biais, K. Nouette-Gaulain, S. Roullet, A. Quinart, P. Revel, and F. Sz-tark. A omparison of stroke volume variation measured by vigileo/�otra system and aorti doppler e ho ardiography. Anesth Analg, 109(2):466�9,August 2009.[6℄ J. M Bland and D. G Altman. Statisti al methods for assessing agreementbetween two methods of lini al measurement. The Lan et, pages 307�310,February 1986.[7℄ M. J. Bourgeois, B. K. Gilbert, G. von Bernuth, and E. H. Wood. Con-tinuous determination of beat to beat stroke volume from aorti pressurepulses in the dog. Cir ulation Resear h, 39(1):15�24, 1976.[8℄ M. Cannesson, H. Musard, O. Desebbe, C. Bou au, R. Simon, R. Hé-naine, and JJ. Lehot. The ability of stroke volume variations obtainedwith vigileo/�otra system to monitor �uid responsiveness in me hani allyventilated patients. Anesth Analg, 108(2):513�7, February 2009.[9℄ M. Ce oni, D. Dawson, RM. Grounds, and A. Rhodes. Lithium dilution ardia output measurement in the riti ally ill patient: determination ofpre ision of the te hnique. Intensive Care Med, 35(3):498�504, Mar h 2009.[10℄ E. Crépeau and M. Sorine. A redu ed model of pulsatile �ow in an arterial ompartment. Chaos Solitons & Fra tals, 34:594�605, 2007.[11℄ PM. Dark and M. Singer. The validity of trans-esophageal doppler ultra-sonography as a measure of ardia output in riti ally ill adults. IntensiveCare Med., 30(11):2060�6, November 2004.[12℄ RB. de Wilde, BF. Geerts, PC. van den Berg, and JR. Jansen. A ompari-son of stroke volume variation measured by the lid oplus and �otra -vigileosystem. Anaesthesia, 64(9):1004�9, September 2009.[13℄ CC. Huang, JY. Fu, HC. Hu, KC. Kao, NH. Chen, MJ. Hsieh, and YH. Tsai.Predi tion of �uid responsiveness in a ute respiratory distress syndromepatients ventilated with low tidal volume and high positive end-expiratorypressure. Crit Care Med., 36(10):2810�6, O tober 2008.[14℄ C. M Jarque and A. K. Bera. A test for normality of observations andregression residuals. International Statisti al Review, 55(2):1�10, 1987.[15℄ N. T. Kou houkos, L. C. Sheppard, and D. A. M Donald. Estimation ofstroke volume in the dog by a pulse ontour method. Cir ulation Resear h,XXVI:611�623, May 1970.[16℄ D. Lahner, B. Kabon, C. Mars halek, A. Chiari, G. Pestel, A. Kaider,E. Fleis hmann, and H. Hetz. Evaluation of stroke volume variation ob-tained by arterial pulse ontour analysis to predi t �uid responsivenessintraoperatively. BrJ Anaesth, 103(3):346�51, September 2009.[17℄ T. M. Laleg, E. Crépeau, Y. Papelier, and M. Sorine. Arterial blood pres-sure analysis based on s attering transform I. In Pro . EMBC, S ien esand Te hnologies for Health, Lyon, Fran e, August 2007.RR n° 7172

22 Laleg & Médigue & Papelier & Cottin & Van de Louw[18℄ T. M. Laleg, E. Crépeau, and M. Sorine. Separation of arterial pressure intoa nonlinear superposition of solitary waves and a windkessel �ow. Biomed-i al Signal Pro essing and Control Journal, 2(3):163�170, 2007.[19℄ T. M. Laleg, E. Crépeau, and M. Sorine. Travelling-wave analysis andidenti� ation. A s attering theory framework. In Pro . European ControlConferen e ECC, Kos, Gree e, July 2007.[20℄ T. M. Laleg, C. Médigue, F. Cottin, and M. Sorine. Arterial blood pressureanalysis based on s attering transform II. In Pro . EMBC, S ien es andTe hnologies for Health, Lyon, Fran e, August 2007.[21℄ Taous Meriem Laleg. Analyse de signaux par quanti� ation semi- lassique.Appli ation à l'analyse des signaux de pression artérielle. Thèse en mathé-matiques appliquées, INRIA Paris-Ro quen ourt \ Université de VersaillesSaint Quentin en Yvelines, O tobre 2008.[22℄ N. W. F. Linton and R. A. F. Linton. Estimation of hanges in ardia output from the arterial blood pressure waveform in the upper limb. BritishJournal of Anaethesia, 86(4):486�496, 2001.[23℄ R. Mukkamala, A.T. Reisner, H.M. Hojman, R.G. Mark, and R.J. Cohen.Continuous ardia output monitoring by peripheral blood pressure wave-form analysis. IEEE Transa tions on Biomedi al Engineering, 53(3):459�467, Mar h 2006.[24℄ J. J. Remmen, W. R. Aengevaeren, and F. W. Verheugt et al. Finapresarterial pulse wave analysis with model�ow is not a reliable non-invasivemethod for assessment of ardia output. Clini al S ien e, (103):143�149,2002.[25℄ R. H. Shumway and D. S. Sto�er. Time Series Analysis and Its Appli a-tions, volume Chapter 1, Measures of Dependen e: Auto and Cross Corre-lation. Springer Editions, 2000.[26℄ C. F. Starmer, P. A. M hale, F. R. Cobb, and J. C. Green�eld. Evaluation ofseveral methods for omputing stroke volume from entral aorti pressure.Cir ulation Resear h, 33:139�148, August 1973.[27℄ J. X. Sun, A. T. Reisner, M. Saeed, and R.G. Mark. Estimating ardia output from arterial blood pressure waveforms: A riti al evaluation usingthe mimi ii database. Computers in Cardiology, pages 295�298, 2005.[28℄ K. H. Wesseling, J. R. C. Jansen, J. J. Settles, and J. J. S hreuder. Com-putation of aorti �ow from pressure in humans using a nonlinear, threeelement model. J. Appl. Physiol, 74:2566�2573, 1993.[29℄ Y. Yu, J. Ding, L. Liu, R. Salo, J. Spinelli, B. To kman, and T. Po het.Experimental validation of pulse ontour methods for estimating strokevolume at pa ing onset. In Pro eedings of the 20 th Annual InternationalConferen e of the IEEE Engineering in Medi ine and Biology So iety, vol-ume 20, pages 401�404, 1998. INRIA

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