Seediscussions,stats,andauthorprofilesforthispublicationat:https://www.researchgate.net/publication/23933067

FuzzyStructuralAlgorithmstoIdentifyandCharacterizeApneaandHypopneaEpisodes

ARTICLEinCONFERENCEPROCEEDINGS:...ANNUALINTERNATIONALCONFERENCEOFTHEIEEEENGINEERINGINMEDICINEANDBIOLOGYSOCIETY.IEEEENGINEERINGINMEDICINEANDBIOLOGYSOCIETY.CONFERENCE·FEBRUARY2008

DOI:10.1109/IEMBS.2008.4650396·Source:PubMed

CITATIONS

9

READS

28

4AUTHORS,INCLUDING:

AbrahamOtero

UniversityFoundationSanPabloCEU

53PUBLICATIONS213CITATIONS

SEEPROFILE

PauloFélix

UniversityofSantiagodeCompostela

58PUBLICATIONS291CITATIONS

SEEPROFILE

Availablefrom:AbrahamOtero

Retrievedon:04February2016

A Structural Knowledge-Based Proposal for

the Identification and Characterization of

Apnoea Episodes

Abraham Otero

Department of Information and Communications Systems Engineering. UniversitySan Pablo CEU. 28668 Madrid, SPAIN. Phone: +34 91 372 4048; Fax: +34 91

372 4049.

Paulo Felix

Dept. of Electronics and Computer Science, Universidade de Santiago deCompostela, 15782 Santiago de Compostela, SPAIN.

Senen Barro

Dept. of Electronics and Computer Science, Universidade de Santiago deCompostela, 15782 Santiago de Compostela, SPAIN.

Carlos Zamarron

Division of Respiratory Medicine. University Hospital Complex of Santiago deCompostela, 15782 Santiago de Compostela, SPAIN.

Abstract

This paper presents a new pattern recognition approach to the identification andcharacterization of multiple signal patterns in the domain of Sleep Apnoea Syn-drome. This approach has been employed to identify apnoeas (cessations in thesleeping patient’s respiratory airflow) and to relate them with the drops in bloodoxyhaemoglobin saturation they give rise to. As a starting point, our algorithmstake a projection over a computational representation of the morphological criteriawhich characterize apnoeas and desaturations. These criteria are obtained directlyfrom a physician. The Fuzzy Set Theory allows us to represent and handle thevagueness of the medical knowledge on which this proposal is based, and the Con-straint Satisfaction Problem Formalism supplies a computable representation forthis knowledge.

Thanks to the structural nature of the proposal, a detailed characterization ofany event identified can be carried out; this may serve as a starting point for ob-taining a deeper understanding of the physio-pathological phenomena underlying

Preprint submitted to Elsevier 15 September 2010

Sleep Apnoea Syndrome. It has also made it possible to construct a graphical toolwith which medical staff can easily edit the criteria that define apnoeas and de-saturations, meaning that apnoeas can be identified with those criteria that eachphysician considers most suitable.

Key words: Sleep Apnea Syndrome (SAS), Structural Pattern Recognition, FuzzySet Theory, Knowledge Representation, Constraint Satisfaction Problems,Biosignal Processing.

1 Introduction

Sleep Apnoea Syndrome (SAS) is a very frequent sleep-breathing disordercharacterized by interruptions of the respiratory airflow whilst the patientis sleeping (apnoeas); these are usually caused by obstructions of the upperairway. It is estimated to affect 4% of male adults and 2% of female adults[31], being especially prevalent in adult males with obesity problems, and isrecognized as an important public health issue [25].

Apnoeas give rise to drops in blood oxyhaemoglobin saturation (see Fig 1) andmay cause arousals. These arousals need not rouse the patient to a state ofconsciousness, but they do force him/her out of the stages of deeper sleep (inwhich sleep is most reparatory) and result in the patient spending a greaterpercentage of the nocturnal rest in sleep stages closer to vigil. The globalresult is a disruption of the normal sleep architecture, which reduces its re-freshing effects. Consequently, patients usually suffer from daytime drowsinessand cognitive deficits which increases the risks of accidents in the workplaceand when driving vehicles [5]. They may also suffer from depression, anxiety,excessive irritability and various sexual dysfunctions.

Polysomnography is the current gold standard for the diagnosis of SAS. Itis performed in a hospital Sleep Unit and consists in recording a wide rangeof physiological parameters whilst the patient is asleep; e.g. respiratory air-flow, blood oxyhaemoglobin saturation (SpO2), respiratory effort, electro-encephalography (EEG), electro-oculography (EOG), electromyography (EMG),electrocardiography (ECG), etc. The recording is then visually inspected by aphysician. In accordance with the criteria of the American Academy of SleepMedicine, a patient is diagnosed with obstructive sleep apnoea if he/she hasfive or more apnoeas during each hour of sleep throughout the entire night

Email addresses: abraham.otero@usc.es (Abraham Otero),paulo.felix@usc.es (Paulo Felix), senen.barro@usc.es (Senen Barro),carlos.zamarron.sanz@sergas.es (Carlos Zamarron).

2

Fig. 1. Fragment of a polysomnogram showing several apnoeas and the correspond-ing desaturations.

[19], where apnoea is understood as being a respiratory pause lasting at least10 seconds. A patient suffering from severe apnoea may have up to 500 ap-noeas during the night, each one of which has an average duration of a littleover half a minute.

Treatment of SAS depends on the severity of the illness: in lighter cases,changes in the patient’s behaviour (e.g. losing weight, avoiding alcoholic bev-erages and avoiding sleeping positions likely to trigger apnoeas, among others)may be sufficient; in the most serious cases, it may be necessary to resort tosurgery and, more frequently, to therapy with Continuous Positive AirwayPressure (CPAP). In this therapy, a CPAP device applies constant pressureon the airway by means of a nasal mask while the patient is asleep. This pres-sure prevents the collapse of the upper airway, thus avoiding apnoeas. Once apatient has started to use CPAP therapy, he/she may often have to continueusing it for the rest of his/her life.

The diagnosis of SAS is a tedious task which requires the visual inspection oflong signal recordings, habitually with the assistance of a computer. This hasgiven rise to research in biomedical engineering with the aim of developingtechniques to assist physicians in the diagnosis of SAS, or indeed automateit completely. One of the foremost initiatives in this field was the competi-tion held in 2000 jointly by PhysioNet and Computers in Cardiology, whichconsisted in developing an algorithm capable of diagnosing SAS on the ba-sis of an ECG derivation recorded during a patient’s nocturnal rest period

3

[23]. For this competition a database of ECG recordings was made availableto all participants [24]. Half of the records contained annotations indicatingthe presence of apnoeas (these made up the training set), and the other half(the test set) had to be diagnosed by the participants. Of the 13 algorithmscompeting, four obtained a perfect score for the test registers. In general, thebest performing algorithms were based on the spectral analysis of heart ratevariability.

As part of the competition, the participants also had to indicate whether ineach minute of the test recordings the patient had suffered any apnoeas. In thiscase, the best algorithm only managed to correctly classify a little over 90% ofthe minutes. None of the algorithms that took part in the competition allowsapnoea episodes to be identified; they were designed to indicate the presence orabsence of apnoeas over a temporal interval, offering no possibility of verifyinghow many have taken place, or when they start and finish.

The automatic identification of individual episodes of apnoea is of great in-terest. In spite of the success of the Computers in Cardiology competition, itis still too early to consider doing without the intervention of physicians inthe diagnosis of SAS. With the automatic identification of apnoeas, improvedpolysomnographic recording analysis tools can be constructed which are capa-ble of highlighting those signal fragments in which relevant events have takenplace, thus simplifying the task of the physician.

On the other hand, CPAP therapy may be improved through the use of Auto-matic Positive Airway Pressure (APAP) [6]; this type of device increases theair pressure applied on the patient’s airway in the event of an apnoea. Whenthe patient is breathing normally, the pressure is reduced to a pre-set level. Onaverage, these devices apply less pressure, which increases the patient’s com-fort levels and solves a number of cases of intolerance to CPAP treatment. Theidentification of individual apnoea episodes is essential for the construction ofAPAP devices.

Finally, the identification of individual apnoea episodes may make it possibleto generate a set of descriptors characterizing each episode, and to study thevariability of the descriptors between patients, and within the same patientduring the evolution of the illness. This information may serve as a start-ing point for carrying out more detailed studies on the underlying physio-pathological complaints in SAS and for gaining a deeper insight into the dis-order. Thus, for example, there is evidence relating SAS with cardiovascularproblems [27], with arterial hypertension [18], with myocardial infarct [12],with sudden death during sleep [11], with coronary illness [32], and with cere-brovascular illnesses [4]. Nevertheless, the relationship between the respiratorydisorder and these complaints has yet to be elucidated.

4

The bibliography on medical informatics includes a number of works whichdeal with the identification of individual apnoea episodes. W. Bystricky andA. Safer combine neural networks with dynamic Markov models to assigneach instant in the recording to one of the following four states: “no apnoea”,“onset of apnoea”, “apnoea” and “end of apnoea” [7]. In this proposal, aneural network is employed to extract a set of morphological characteristicsfrom the beats on the basis of the ECG signal. These characteristics constitutethe input to a dynamic Markov model which only contemplates a sequence oftransitions permitted between the four aforementioned states (no apnoea ->onset of apnoea -> apnoea -> recovery from apnoea -> no apnoea). In thevalidation presented, the automatically generated annotations agreed withthose created by a physician in 84.1% of cases.

T. Al-Ani et al. also use Markov models in the detection of apnoea episodes [1],in this case using respiratory flow, oesophageal pressure and gastric pressuresignals. The last two measurements require invasive procedures and are nothabitually recorded in the polysomnographic study of sleep. In this work thereis no exhaustive validation of the proposal.

J.Y. Tian and J.Q. Liu have used a time delay network to identify apnoeason the basis of respiratory airflow and SpO2 signals [29]. The neural networkinputs are the area and the standard deviation, calculated within a mobiletemporal window, of the respiratory airflow signal; the basal level and de-saturation level of the SpO2 signal; and a correlation coefficient between theSpO2 and respiratory airflow signals. In a validation over 15 polysomnographicrecordings, the neural network obtained a sensitivity of 90.7% and a specificityof 81.4%.

O. Fontenla-Romero et al. propose an ad hoc technique for identifying apnoeasbased on the respiratory airflow signal [10]. In an initial stage using a mobilewindow, the absolute value of the difference between the instantaneous valueof the respiratory airflow signal and its average value in a mobile window iscalculated. An adaptive threshold is then applied to the samples of the signalgenerated in the previous stage to determine whether they correspond withnormal breathing or apnoea. The adaptive threshold is calculated using themean signal value within two other temporal windows of differing lengths: thelargest encompassing samples immediately before the current one, and thesmaller one those immediately after. This technique has a sensitivity of 91.0%and a positive predictive value of 76.6%.

H. Nazeran et al. have developed a fuzzy inference system which is capableof identifying apnoeas over a patient’s respiratory airflow signal [17]. Initially,the signal is filtered using a low pass filter, the baseline is eliminated and it isrectified. On the basis of the resulting signal, a set of descriptors is generated,and these constitute the input for a set of fuzzy rules which carry out the

5

classification. When validated, this technique succeeded in correctly classifying83% of the apnoea episodes, with 12% false positives.

A. Morsy et al. present a system of fuzzy rules for labelling each respiratoryairflow signal sample with the labels “normal event”, “abnormal event” and“unsure”[16]. These rules were obtained by means of interviews with clinicalstaff. The samples are then grouped into intervals in such a way that withinone single interval at least 70% of the samples have the same label. Almostall the respiratory airflow signal recording is labelled as “unsure” accordingto the rules. Then, using the events that have been classified as normal andabnormal, a clustering engine is trained and subsequently used to classifythe events labelled as “unsure”. The authors declare that their system has asensitivity of 0.999 and the specificity of 0.966, although information on howthe validation was carried out is somewhat scant.

In this work, we present a solution for identifying individual apnoea episodesand relating them with the desaturations that they produce, using two ofthe parameters that are recorded during a polysomnography: the respiratoryairflow and the SpO2. This solution is based on the Multivariable Fuzzy Tem-poral Profile model (MFTP) [22], a structural model that permits the projec-tion onto a computable representation of a signal pattern made up of a setof morphologies defined over the temporal evolution of a patient’s physiologi-cal parameters, and a series of relationships between these morphologies. TheFuzzy Set theory allows the MFTP model to represent and handle the vague-ness characteristic of human knowledge. The Constraint Satisfaction ProblemFormalism provides the computable support for the representation of thisknowledge.

In the following section, the MFTP model is presented, showing how it canbe used to represent an apnoea and the corresponding desaturation. Section3 covers the algorithm that permits the identification and characterization ofboth events and the tool TRACE. Section 4 includes a validation of our pro-posal over the data obtained in the polysomnographic study of ten patients. InSection 5 the results obtained are discussed and, finally, a series of conclusionson the paper are given and possible lines of extension are commented.

2 Apnea pattern representation: the MFTP model

An apnoea is defined as a decrease in the respiratory airflow of a patient to atleast 10% of its basal value, sustained for at least 10 seconds. This hypoventi-lation usually results in a drop in the SpO2. The standard polysomnographiccriteria consider such a drop in the SpO2 to be relevant only when it is of 4%or higher. The drop in the SpO2 begins approximately from 10 to 30 seconds

6

More thanapprox.10 sec.

Reduction to at least10% of the basal value.

Drop of at leastapprox. 4%.

Approx. from 10to 30 sec.

Shortly after

Fig. 2. Morphological criteria that define an apnoea and the desaturation it provokesdrawn over a real occurrence of an apnoea.

after the start of apnoea. Shortly after the hypoventilation ceases, the SpO2should begin to recover (see Fig. 2).

In this section we present the MFTP model, and show how it can be used torepresent the apnoea pattern. Before that we introduce some basic conceptsof fuzzy set theory upon which the model is based.

2.1 Basic concepts of fuzzy sets

Medical knowledge is characterized as being heuristic in nature, as it is basedon experience and contains high levels of vagueness; hence, fuzzy set theoryis a tool that is exceptionally well suited to representing and handling theknowledge available in this domain [3,28], and the MFTP makes use of it tothis end. We shall introduce some basic concepts from fuzzy set theory onwhich the MFTP model is based.

Given as discourse universe the set of real numbers R, a fuzzy number C is anormal (∃ v ∈ R, μC(v) = 1) and convex (∀v, v′, v′′ ∈ R, v′ ∈ [v, v′′], μC(v′) ≥min {μC(v), μC(v′′)}) fuzzy subset of R [13]. We obtain a fuzzy number Cfrom a flexible constraint given by a possibility distribution πC , which definesa mapping from R to the real interval [0, 1]. A fuzzy constraint can be inducedfrom a piece of information such as “x has a high value”, and given a precisenumber v ∈ R, πC=high(v) ∈ [0, 1] represents the possibility of x being preciselyv.

7

Normality and convexity properties are satisfied by representing πC , for ex-ample, by means of a trapezoidal representation. In this way, C = (α, β, γ, δ),α ≤ β ≤ γ ≤ δ, where [β, γ] represents the core, core(C) = {v ∈ R| πC(v) =1}, and ]α, δ[ represents the support, supp(C) = {v ∈ R|πC(v) > 0}. We haveopted for this representation for possibility distributions owing to its compu-tational efficiency and the intuitiveness of its semantics for medical users.

2.2 The MFTP model

The MFTP model [22] makes it possible to represent signal patterns, compris-ing a set of morphologies defined over the evolution of a set of physiologicalvariables and temporal and magnitude relations between these morphologies.An MFTP is made up by a set of significant points defined over the temporalevolution of the physiological variables and a set of flexible constraints. Thesignificant points are samples in the evolution of the system which are espe-cially relevant for the physician. For example, in an apnoea the samples thatdelimit its beginning and ending are significant points. The flexible constraintslimit the evolution of the physiological variables between the significant points.They represent the possible temporal durations, changes in the parameter’smagnitude, and the allowed range of slopes for the parameters between eachpair of significant points. Constraints are represented by means of possibilitydistributions, allowing a pattern to be modelled as a flexible set of possibleevolutions between the significant points.

Let us define the model formally. We shall denote as P the set of physiologicalvariables obtained from the monitoring of a patient. In the case of the apnoeapattern, P = {PRa, P SpO2} where PRa is the respiratory airflow and P SpO2

the SpO2. Each of the physiological variables P p ∈ P is obtained by a signal-sampling process, in the form of a temporal series P p = {(vp[s], tp[s]); s ∈ N},where vp[s] is the value of P p at the instant tp[s].

We define a significant point Xpi over the temporal evolution of some parameter

P p ∈ P , as the pair formed by a variable of the domain V pi and a temporal

variable T pi , X

pi =< V p

i , Tpi >. In the absence of any constraints, the variables

V pi and T p

i may take any precise value vpi and tpi , respectively, where (vpi , t

pi ) =

(vp[i], tp[i]) ∈ P p. In this work we shall use the notation (vp[x], t

p[x]) to refer to any

sample of the parameter P p, and the notation (vpx, tpx) to refer to a sample of

the parameter P p which has been assigned to a significant point Xpx.

In order to obtain a computable representation of the pattern, we shall makeuse of the Constraint Satisfaction Problem (CSP) formalism. A CSPs is madeup by a finite set of constraints that limit the values that can be taken by afinite set of variables. Formally, a constraint satisfaction problem is defined as

8

a triple 〈X,D,C〉, where X is a set of variables, D is a domain of values forthe variables of X, and C is a set of constraints [9]. In the MFTP model, Xis made up by a set of significant points. D is the temporal evolution of thesystem –P– from which the significant points can take values. To completethe definition of our CSP, we must define the constraints that are allowed inthe MFTP model –C.

The description of a pattern will be obtained directly from physicians. Theyusually describe the evolution of a set of parameters limiting the possible val-ues of the temporal extension, changes in magnitude and slope between pairsof significant points. The constraints that physicians use in their descriptionsseldom are crisp, but they usually are soft. Therefore, we shall define threetypes of fuzzy constraints to capture physicians’ descriptions: constraints lim-iting temporal extensions, changes in magnitude and slopes between pairs ofsignificant points.

We define a constraint Lpqij over the temporal variables T p

i and T qj of the signifi-

cant points Xpi and Xq

j by means of the normal, convex possibility distribution

πLpqij (l) over Z, such that ∀ l ∈ Z : πLpq

ij (l) ∈ [0, 1]. Given a precise temporal

duration lpqij , πLpqij (lpqij ) represents the possibility of the temporal duration be-

tween T pi and T q

j being precisely lpqij ; thus Lpqij represents the fuzzy temporal

duration between T pi and T q

j . In the absence of any other constraints, the

assignments T pi = tpi and T q

j = tqj will be possible if πLpqij (tqj − tpi ) > 0.

With the constraints Lpqij it is possible to model linguistic descriptions that

limit the fuzzy temporal duration between a pair of significant points. If bothsignificant points are defined over the temporal evolution of the same param-eter, Lpp

ij ≡ Lpij normally represents a temporal extension during which the

value or rate of change of the parameter is constant; e.g. in Fig. 3, LRa12 models

the linguistic description“an apnoea must last for more than approximately 10seconds”. When the significant points are defined over different parameters,Lpqij describes the temporal layout of the two findings that form part of the

global pattern. For example, the desaturation which is produced by an apnoeamust start “approximately from 10 to 30 seconds after the start of apnoea”.This piece of linguistic information can be projected onto a constraint LRa SpO2

11

between the two significant points which mark the beginning of both findings.

We define a constraint Dpqij over the domain variables V p

i and V qj of the signif-

icant points Xpi and Xq

j by means of a normal, convex possibility distribution

πDpqij (d) over R, such that ∀ d ∈ R : πDpq

ij (d) ∈ [0, 1]. Given an increment

dpqij , πDpq

ij (dpqij ) represents the possibility of the increment between V pi and V q

j

being precisely dpqij ; thus Dpqij represents the fuzzy increment between V p

i andV qj . In the absence of any other constraints, the assignations of precise values

V pi = vpi and V q

j = vqj will be possible if πDpqij (vqj − vpi ) > 0.

9

D01Ra

Respiratory airflow

D02Ra

{Ra Ra Ra

}D12 , 12 , 12L M

"approximately zero"

"approximately zero"

"more than approx.10 seconds"

"less than approx. 10% of basal value"

X1Ra X2

Ra

-6 3 6-3

108

-0.3 0.2 0.3-0.2

-6 3 6-3

X0Ra

Fig. 3. Representation of a respiratory airway cessation with the MFTP model.

When both Xpi and Xq

j belong to the same parameter, i.e p = q, Dppij ≡

Dpij models linguistic descriptions that limit variations in the magnitude of a

parameter; e.g. in Fig. 3, DRa12 models the description“the respiratory airflow

must have approximately the same value at the beginning and at the endingof the apnoea”. When these are defined between significant points that belongto different parameters, relations between the magnitudes of both parameterscan be described; e.g.“the patient’s systolic blood pressure should be about 40units higher than the diastolic blood pressure”.

Sometimes physicians describe the temporal evolution of a parameter indicat-ing a value that the parameter must take at a certain time (“at the beginning ofthe apnoea the respiratory airflow must be less than approximately 10% of thebasal value”). In this case, the description of the magnitude of the parameteris not done relative to the magnitude of the parameter in other instant (“therespiratory airflow must have approximately the same value at the beginningand at the ending of the apnoea”). To obtaining a more compact notation,and following the bibliography on CSP [9], we will transform such absoluteconstraints into relative constraints with a fictitious origin significant pointXp

0 = < V p0 , T

p0 >. Any arbitrary value can be assigned to Xp

0 . It is habituallyassigned the value V p

0 = 0, T p0 = 0, although it may occasionally be more

practical to assign it the value V p0 = basal(P p), where basal(P p) represents

the value of the parameter P p under normal conditions. The latter assignationis especially useful in the medical domain, where the different physiologicalvariables for a given patient, under normal conditions and at rest, usually haveapproximately constant values. Physio-pathological alterations are habituallyreflected in physiological variables as deviations from this basal value; e.g. inFig. 3, DRa

01 and DRa02 model the linguistic description “less than approximately

10% of the basal value” as a relative constraint with XRa0 .

10

X2p

X1p

X2p

X1p

(a)

(b)

Fig. 4. The use of evolution constraints allows us to differentiate between evolutionsof the parameters which otherwise would be indistinguishable for the MFTP model.

A constraint Mpij between a pair of significant points Xp

i and Xpj , defined over

the same parameter P p, is defined by means of a normal and convex possibilitydistribution πMp

ij(m),m ∈ R, which represents the possibility of the fuzzy slopebetween Xp

i and Xpj being m. The assignments V p

i = vpi , Vpj = vpj , T

pi = tpi

and T pj = tpj are possible if πMp

ij(mpij) > 0, where mp

ij = (vpj − vpi )/(tpj − tpi ).

With the constraints Mpij it is possible to model linguistic descriptions of

the rate of change of a parameter; e.g. in Fig. 3 MRa12 models the descrip-

tion“decrease in respiratory airflow to at least less than approximately 10%of its basal value sustained for at least 10 seconds”, where “sustained” ismodelled by means of an approximately zero slope value.

The MFTP model proposed up to this point simplifies the representation of apattern to a set of events –the significant points– defined over a set of parame-ters. In this representation, the evolution between each two consecutive pointsis characterized only by those events which define its beginning and its end,which seems to be sufficient when the events are defined over different param-

11

eters. Nevertheless, when both events are defined over the same parameter,reducing the representation of an episode to its endpoints is usually not suf-ficient: different temporal evolutions of a parameter which coincide in the setof events represented by an MFTP, but which differ between them, would beindistinguishable for the model. Figure 4a shows how two different evolutionspresent the same degree of compatibility with an MFTP when no evolutionconstraint is used. The values of both evolutions coincide in the assignationsmade to both significant points –the samples shown with the arrows– and theseassignations are the only samples whose values are limited by the duration,increment and slope constraints. Figure 4b shows how the evolution constraintallows us to distinguish between both evolutions: only the one marked withcircles falls within the course path defined by the evolution constraint.

We shall restrict the evolution of a parameter P p between each pair of signif-icant points Xp

i and Xpj by means of a evolution constraint Sp

ij , represented

by a membership function μSpij(Ap

i ,Apj) which defines a fuzzy course (see Fig.

4b) within which the temporal evolution of the parameter must remain inorder to satisfy the constraint. A detailed explanation of the different formsthe constraint Sp

ij may take, and the relation of each one of them with nat-ural language can be found in [2]. In the following section we shall presenttwo different evolution constraints which will be used to model the apnoeapattern.

We define a Multivariable Fuzzy Temporal Profile (MFTP) M =< WM,XM,RM > as a finite set of MFTPs WM = {MM

1 , ...,MMs }, a finite set of signif-

icant points XM = {Xp1i1 , X

p2i2 , ..., X

pgig } and a finite set of constraints RM =

{R1, ..., Rf} amongst the points of WM and XM. Each of the Ri ∈ RM canbe a temporal extension, magnitude, slope or evolution constraint.

The recursive structure of the MFTP model is based in the way that humansdefine patterns; a complex pattern is often made up of a set of findings anda set of relations between them. Each of the findings of the pattern mayalso be a pattern, and may comprise a set of findings and relations betweenthem, and so on, successively. For example, the pattern which is used in thiswork to identify apnoea and its corresponding desaturation is made up oftwo findings (airway cessation and desaturation) which must satisfy certainrelations between them in order to be able to assert that the desaturation hasbeen caused by the airway cessation and, thus, identify the pattern (see Fig.5).

An MFTP can be represented by a graph in which nodes correspond to sig-nificant points, and arcs correspond to constraints (see Fig. 5c). The shapeof this graph resembles the shape of the pattern it represents; this makes ita useful visual metaphor which will be exploited in the knowledge acquisitionprocess.

12

X1Ra X2

Ra

D01Ra

Airway cessation MFTP

D02Ra

S12Sp S23

Sp

S12Ra

X2Sp

X3Sp

X1Sp

{Ra Ra Ra Ra

}D12 , 12 , 12 ,S12L M

{Sp Sp Sp Sp

}D12 , 12 , 12 ,S12L M

X0Ra

Ra SpL11

L22Ra Sp

"Approximately from10 to 30 sec."

"Afterwards"Desaturation MFTP

{Sp Sp Sp Sp

}D23 , 23 , 23 ,S23L M

Apnea MFTP

X1Ra

X2Ra

X1Sp

X2Sp

(a)

(b) (c)

X3Sp

X0Ra

D02Ra

D01Ra

Fig. 5. MFTPs that represent the airway cessation (a), the desaturation (b) and theoverall pattern that comprises both findings (c).

2.3 Apnoea pattern modelling with the MFTP model

An airway cessation compatible with an apnoea is projected onto an MFTPthat represents a straight section with a practically constant value (see Fig.5a). The temporal relationship between the significant points that delimit theextremes, XRa

1 and XRa2 , should be LRa

12 =“at least approximately 10 seconds”,the variation in magnitude DRa

12 =“approximately zero” and, consequently, theslope between them should be MRa

12 =“approximately zero”. The magnitudeof both points should be less than approximately 10% of the basal value ofthe respiratory airflow. These absolute value constraints can be representedas constraints relative to the origin significant point XRa

0 : DRa01 = DRa

02 =“lessthan approximately 10% of the basal value”.

The respiratory airflow signal oscillates continuously crossing the x-axis ap-proximately every 3 seconds (see Fig. 2). By assigning to the significant pointsXRa

1 and XRa2 the values when passing through zero of two such oscillations

separated by at least 10 seconds, we would have two signal samples whichsatisfy the constraints mentioned in the previous paragraph, without the mag-nitude of the oscillations between both points being of any consequence. Theconstraints LRa

12 ,DRa12 andMRa

12 only limit the values that the respiratory airflowparameter takes on the significant points XRa

1 and XRa2 , but not the evolution

of the signal between them (see Fig. 4). Nevertheless, in order to identify anairway cessation compatible with an apnoea the magnitude of all the signal

13

samples between both points should also be lower than approximately 10%of the basal value. Thus, the need arises to use an evolution constraint tolimit the values permitted for these samples. More specifically, the samplesof the respiratory airflow which lie between the assignations performed to thesignificant points XRa

1 and XRa2 should satisfy the constraint SRa

12 defined as:

μSRa12(ARa

1 , ARa2 ) = min

(vRa[s]

,tRa[s]

); tRa1 ≤tRa

[s]≤tRa

2

πDRa01 (vRa

[s] ),

where ARa1 = (vRa

1 , tRa1 ) and ARa

2 = (vRa2 , tRa

2 ) are the assignments to XRa1 and

XRa2 . This constraint forces the section samples to satisfy the same value

constraint as the first significant point; i.e., all samples between ARa1 and ARa

2

must have a value of less than approximately 10% of the basal value of therespiratory airflow (see Fig. 5a). Therefore, the MFTP representing an airwaycessation compatible with an apnoea would be:MAp

Ra =< ∅, {XRa0 , XRa

1 , XRa2 },

{DRa01 , D

Ra02 , L

Ra12 , D

Ra12 ,M

Ra12 , S

Ra12 } >, where XRa

0 is the origin significant pointfor the respiratory airflow parameter, and the ∅ models the fact that theapnoea pattern does not contain any subpattern.

Similarly, the drop in the SpO2 could be represented byMApSp =< ∅, {XSp

1 , XSp2 , XSp

3 },{LSp

12 , DSp12 ,M

Sp12 , S

Sp12 , L

Sp23 , D

Sp23 ,M

Sp23 , S

Sp23 } > where the constraints between

XSp1 and XSp

2 force a drop of at least 4% between them, and the constraintsbetween XSp

2 and XSp3 model the recovery in the value of the parameter. In

this case, the samples of each section should verify a certain change rate withrespect to the assignment carried out on the first significant point of the sec-tion: those between ASp

1 and ASp2 should show compatibility with MSp

12 takingassignment ASp

1 as a reference (see Fig. 5b); and those between ASp2 and ASp

3

should show compatibility with MSp23 taking assignment ASp

2 as reference (seeFig. 5b). Therefore, in this case we shall use the evolution constraint SSp

12 givenby:

μSSp12(ASp

1 , ASp2 ) = min

(vSp[s]

,tSp[s]

); tSp1

≤tSp[s]

≤tSp2

max

u

{μ(vSp[s]

−vSp1 )∩MSp

12 ⊗(tSp[s]

−tSp1 )(u)}, (1)

where ⊗ represents the fuzzy product of the fuzzy slope MSp12 by the crisp

number tSp[s] − tSp1 , ARa1 = (vRa

1 , tRa1 ) and ARa

2 = (vRa2 , tRa

2 ). The expressionbetween curly brackets evaluates the degree of membership of the signal sample(vp[s], t

p[s]) to the fuzzy straight line that is given by the constraint MSp

12 and the

assignment ARa1 = (vRa

1 , tRa1 ). SSp

23 is given by an analogous expression whereMSp

12 is replaced by MSp23 , A

Ra1 by ARa

2 and ARa2 by ARa

3 .

Given that we wish to associate each airway cessation with its correspondingdesaturation, we consider that both events form part of the pattern to be iden-

14

tified. The temporal relationship between the onset of the airway cessation andthe beginning of the drop in SpO2 is LRa Sp

11 =“approximately between 10 and30 seconds afterwards”, and the recovery in the SpO2 should be subsequentto the end of the airway (i.e. LRa Sp

22 =“afterwards”). Therefore, the patternthat models an airway cessation and its corresponding desaturation, which wedenote by MAp, would be made up by the two temporal constraints and bythe patterns that represent the apnoea and the desaturation: MAp =< {MAp

Ra,MAp

Sp}, ∅, {LRa Sp11 , LRa Sp

22 } > (see Fig. 5c).

3 Apnoea recognition and characterization

A solution to a CSP 〈X,D,C〉 is a set of assignations taken from D to all thevariables of X that satisfy the set of constraints C. The search for solutionsis carried out through backtracking algorithms [9]. Therefore, identifying apattern M over the physiological parameters P –our domain of values– ofthe patient is equivalent to finding a solution to the CSP defined by M; i.e.,finding assignations taken from P to all the significant points of M such thatthe assignations satisfy all constraints of M.

We define solution of an MFTPM as a set of assignationsA = {Ap1i1 , A

p2i2 , ..., A

pgig }

to all the significant points belonging to the MFTP that satisfy the set of con-straints that make up M with a degree higher than zero. In the specific casethat concerns us, the identification of a pattern MAp over P = {PRa, P SpO2}requires finding a solution AAp = {ARa

1 , ARa2 , ASp

1 , ASp2 , ASp

3 } constructed withassignations taken over the temporal evolution of the patient’s respiratoryairflow and SpO2.

The MFTP definition allows the matching task to be structured hierarchically,where a pattern M constitutes a processing level that incorporates a set offindings detected in the previous processing level. Thus, in order to matchMAp we start by searching for occurrences of the two findings that make itup: MAp

Ra and MApRa . In order to calculate the degree of compatibility of MAp

Ra

with AApRa = {ARa

1 , ARa2 } the following expression is used:

πMApRa(AAp

Ra) = min{πDRa01 (vRa

1 ), πDRa02 (vRa

2 ), πLRa12 (tRa

2 − tRa1 ), (2)

πDRa12 (vRa

2 − vRa1 ), πMRa

12 (mRa12 ), μSRa

12(ARa

1 , ARa2 )},

where the assignments ARa1 = (vRa

1 , tRa1 ) and ARa

2 = (vRa2 , tRa

2 ) are taken fromthe values recorded for the respiratory airflow and mRa

12 = (vRa2 − vRa

1 )/(tRa2 −

15

tRa1 ). A similar expression applies for MAp

Sp :

πMApSp (AAp

Sp) = min{πLSp12 (tSp2 − tSp1 ), πDSp

12 (vSp2 − vSp1 ), πMSp12 (mSp

12 ), μSSp12(ASp

1 , ASp2 ),

(3)

πLSp23 (tSp3 − tSp2 ), πDSp

23 (vSp3 − vSp2 ), πMSp23 (mSp

23 ), μSSp23(ASp

2 , ASp3 )},

where the assignments ASp1 = (vSp1 , tSp1 ), ASp

2 = (vSp2 , tSp2 ) and ASp3 = (vSp3 , tSp3 )

are taken from the values recorded for the SpO2. Solutions are then searchedfor MAp over the previously found occurrences for MAp

Ra and MApSp . The degree

of compatibility of MAp with AAp = {AApRa, AAp

Sp} is given by:

πMAp

(AAp) = min{πMApRa(AAp

Ra), πMAp

Sp (AApSp), π

LRa Sp11 (tSp1 −tRa

1 ), πLRa Sp22 (tSp2 −tRa

2 )}

where πMApRa(AAp

Ra) and πMApSp (AAp

Sp) are given by Eq. 2 and 3, respectively. Theyrepresent the compatibility of the airway cessation and desaturation episodes

which are associated in this pattern. πLRa Sp11 (tSp1 − tRa

1 ) and πLRa Sp22 (tSp2 − tRa

2 )represent the degree of satisfaction of the temporal relations between bothepisodes; i.e., the possibility that the airway cessation has caused the desatu-ration with which it was been associated.

Before applying the recognition procedures described herein both the respi-ratory airflow and the SpO2 were filtered. In the case of the SpO2 signal amedian filter with a two-second mobile window was employed. For the respira-tory flow a third-order Butterworth bandpass filter was designed with cut-offfrequencies of 0.20 Hz (one breath every 5 seconds) and 0.45 Hz (one breathevery 2.2 seconds). On average, during the night the patient breathes everythree seconds. In order to obtain a null-phase filter, after filtering in the for-ward direction, the filtered sequence is then reversed and run back through thefilter; the filtered signal is the reverse of the output from the second filteringoperation.

3.1 Apnoea characterization

Once the pattern has been identified, a set of descriptors characterizing thepattern are generated. The fact that a structural technique has been used in itsrecognition considerably simplifies this task, since the information generatedin the recognition, AAp, has a clear meaning and is easy to interpret. Theassignations to the temporal variables of the significant points of the patternare instants of the onset or end of events that are relevant in the study ofan apnoea episode (e.g. the beginning and the end of an apnoea episode, orthe onset of a drop in SpO2). Assignations to the magnitude variables are the

16

Fig. 6. TRACE showing the detection for the pattern which associates an apnoeaand the desaturation it provokes.

value of the parameter at one of the previous temporal instants (e.g. the SpO2value at the onset of the desaturation).

Directly from the information contained in AAp it is possible to calculate theduration of the apnoea (tRa

2 − tRa1 ); the duration and slope of the drop episode

(tSp2 − tSp1 and (vSp2 −vSp1 )/(tSp2 − tSp1 ), respectively) and of the recovery episode(tSp3 − tSp2 and (vSp3 − vSp2 )/(tSp3 − tSp2 ), respectively) of the desaturation; thetime elapsed from the beginning of the apnoea to the beginning of the drop inSpO2 (tSp1 − tRa

1 ); and the time elapsed from the end of the apnoea until theSpO2 begins to recover (tSp2 − tRa

2 ) and until it has fully recovered (tSp3 − tRa2 ).

Also, the maximum, minimum and average values of the SpO2 during thedesaturation episode are calculated, and the energy of the respiratory airflowsignal for the interval of apnoea normalized by the number of samples of thisinterval, which we denote by EAp

[tRa1 ,tRa

2 ]:

EAp

[tRa1 ,tRa

2 ]=

tRa2∑

tRa[s]

=tRa1

(vRa[s] )

2

tRa2 − tRa

1

where (vRa[s] , t

Ra[s] ), t

Ra1 ≤ tRa

[s] ≤ tRa2 are the respiratory airflow signal samples

17

LRa Sp

11

{Ra Ra Ra

}D12 , 12 , 12L M

LRa Sp

22

{Sp Sp Sp

}D12 , 12 , 12L M {Sp Sp Sp

}D23 , 23 , 23L M

RaD01

RaD02

Fig. 7. TRACE’s knowledge editor, showing the graph for the MFTP representingan apnoea and its corresponding desaturation.

within the apnoea episode.

3.2 Visual tool for the apnoea pattern acquisition and recognition

Based on the MFTP model we have constructed the Tool foR anAlyzing anddisCovering pattErns, TRACE, a tool for creating, editing and validatingMFTPs [21]. TRACE (see Fig 6) is a graphical tool that provides health carestaff with a set of utilities and wizards for modelling patterns defined overthe temporal evolution of a patient’s physiological variables. These patternscomprise a set of findings, each one of which is a morphology defined overthe temporal evolution of a physiological variable of the patient, and a set ofrelations between these findings.

TRACE handles each finding and, generally, any pattern, as a graph in whichnodes represent significant points and each arc represents a set of constraintsbetween the significant points it connects (see Fig 7). The graph can be con-structed using a set of morphology templates (peaks, pulses, etc.) from amongwhich users can choose the one which best approximates the finding that theywishes to model, or with the help of a wizard which allows a prototype patternto be constructed on the basis of a signal fragment in which the morphologywe wish to project over the MFTP model appears (see Fig 8). Constraints aremodelled visually: each constraint is defined as a possibility distribution whichcan be edited by clicking over the arc that represents it. A simple graphic inter-

18

Fig. 8. Wizard for defining morphological findings modelling a desaturation. Thehorizontal and vertical lines in black represent possibility distributions showing thedeviation admissible for an evolution of the parameter that is compatible with thefinding.

face enables the user to edit the trapezoidal representation of each possibilitydistribution, and changes are automatically reflected over the graph in such away that its shape reflects the morphology of the finding it represents.

With TRACE, a patient’s monitoring recordings in MIT-BIH format [15] canbe loaded and the recognition of an MFTP can be executed over the recordings.As a result of this execution over each physiological variable, those fragmentsof signal which have shown compatibility with the finding defined over thevariable are highlighted (see Fig 6). A signal –which we call Apnoea– is alsoadded to the environment, which gives (in percentage form) the possibilitythat the global pattern has occurred at each moment in time.

A series of flash videos showing the support TRACE supplies for the definitionof patterns over a set of temporal series, for the execution of the recognitionprocedures and for viewing the recognition results can be found at [20].

4 Experimental results

The Sleep Unit of the University Hospital Complex of Santiago de Compostelais equipped with a commercial polysomnographic device, manufactured byNicolet Biomedical Inc., with which signal recordings from patients subjectedto sleep study can be stored in MIT-BIH format. Recordings from 10 patientswere selected randomly to validate the technique proposed in the current work.Of the 10 patients, eight were subjected to nocturnal study, with an approx-

19

Table 1Results of the Validation.

Patient Record’s length Apnoeas Correct detections (%) False positives (%)

1 8 hours 20 min. 468 426 (91%) 12 (2.7%)

2 6 hours 15 min. 95 88 (93%) 5 (5.3%)

3 6 hours 117 103 (88%) 4 (3.7%)

4 8 hours 40 min. 208 172 (83%) 7 (3.9%)

5 2 hours 10 min. 18 17 (94%) 0 (0%)

6 5 hours 45 min. 180 155 (86%) 4 (2.5%)

7 3 hours 78 72 (92%) 1 (1.4%)

8 5 hours 30 min. 214 197 (92%) 6 (2.9%)

9 5 hours 20 min. 315 296 (94%) 8 (2.6%)

10 8 hours 10 min. 13 10 (77%) 2 (16%)

Total 59 hours 10 min. 1706 1536 (90%) 49 (3.2%)

Validation results. The percentage of correct detections is calculated withregard to the total number of apnoeas. The percentage of false positives iscalculated with regard to the total number of apnoeas identified by the algorithm.

imate duration of seven hours, and 2 carried out their study during a mid-afternoon nap, with an approximate duration of 150 minutes. The recordingstotalled 59 hours 10 minutes of signal, and contained 1,706 apnoeas. After thepolysomnographic study, all patients, except for the 10th one, were diagnosedwith SAS with different degrees of seriousness.

Using the Wizard supplied by TRACE for importing data in MIT-BIH for-mat, the patient’s respiratory airflow and SpO2 signals were loaded into thetool. All the physiological parameters recorded with the Nicolet device weresampled at 68.25 Hz. When the recordings were imported into TRACE thesampling frequency was reduced to 4 Hz, which is sufficient to work over thetwo parameters that were the object of our study.

TRACE was used to identify the pattern of apnoea presented in the previoussection. The results were subsequently revised by a pneumologist. Table 1 givesa summary of the validation results (both for each patient and globally). Thepercentage of correct detections is calculated with regard to the real numberof apnoeas contained in the recording. The percentage of false positives iscalculated with regard to the number of events that the algorithm labelled asapnoea episodes. Of the 1,706 apnoeas, 1536 were identified correctly (90%),and there were a total of 49 false positives (3.2%).

20

5 Discussion

The results of the evaluation allow us to be optimistic regarding the potentialof our proposal serving as a support in the diagnosis of SAS. The number of ap-noea episodes identified correctly, 90%, is similar to that of other proposals inthe bibliography which allow the individual identification of apnoea episodes.The number of false positives, 3.2%, is significantly lower than for the ma-jority of proposals; the low rate of false positives was obtained thanks to theintegration of information coming from two different parameters (respiratoryairflow and SpO2) into the detection.

In certain cases, integrating information from both parameters into the de-tection may be counterproductive. Although it is not very frequent, certainpatients (habitually young ones with high lung capacity) may present apnoeasthat are not accompanied by desaturation episodes. Given the hierarchical na-ture of the MFTP model’s matching procedures, the detection of a patternwhich links an apnoea with its corresponding desaturation requires the prioridentification of both events. Thus, the MFTP model makes it possible toidentify apnoea episodes independently of the desaturations. In this case, asinformation coming from two parameters is not integrated, the false positiveswill increase; although an increase in correctly identified apnoeas is also to beexpected.

There is no absolute consensus in the bibliography regarding the criteria thatan apnoea episode or its associated desaturation must comply with. In Europe,the most widely used criterion for apnoeas may be the one used in this work: areduction in the volume of air inhaled of to least 10% which is sustained for atleast 10 seconds. Nevertheless, some studies defend the idea that the reductionin the volume of air inhaled must be 5% [14] or some similar criterion. Withregard to the drop that must appear in SpO2, the most widely used criterionis to consider that for a desaturation to be relevant it must have a fall of atleast 3% or 4%, although some authors believe that it must be of 5% [26].There are also a number of works which require a minimum duration for thedesaturation episode [30], although most commonly only the magnitude ofthe SpO2 drop is considered. Lastly, although there is general consensus thatthe duration of apnoea must be at least 10 seconds, there is no reason whya nine-second interruption of the respiratory airflow should not disrupt thearchitecture of sleep in a similar manner to an interruption of 10 seconds

The structural nature of the algorithm, combined with the availability ofTRACE (a graphical tool for editing the morphological criteria of the ap-noea pattern) supplies support for analyzing polysomnographic recordingswith those criteria with which the pneumologist feels most comfortable. Onthe other hand, being able to define these criteria in a fuzzy manner means

21

that it is possible to identify episodes which, even though they do not showtotal compatibility with the standard criteria, are close. For example, withour approach it is possible to identify airflow reductions that last eight or nineseconds, assigning them a level of compatibility with the criteria that definean apnoea inferior to the one that may have a similar reduction in magnitude,but with a duration equal to or greater than 10 seconds.

The set of descriptors that our algorithms employ to characterize apnoeas werechosen in collaboration with the medical team, in order to serve as a basis forcarrying out a detailed study of the physio-pathological processes that underlieSAS, and thus gain a deeper insight into this disorder. Thus, for example, thedistances between the end of the apnoea and the onset and the end of therecuperation in SpO2, along with the slope of this recuperation, reflect thepatient’s capacity for recovering from hypoxia. It is well known that patientswith chronic obstructive pulmonary disease who suffer from SAS recover moreslowly from hypoxia, owing to their ventilatory problems. Nevertheless, thereare no detailed studies on how this recovery capacity reflects the differentlevels of seriousness of the complaint, or whether it should have some effecton the therapy. We believe that the quantitative characterization informationthat our algorithms generate, with the help of data mining techniques, mayprovide insight into these questions.

The high specificity of the algorithm enhances the value of the characteriza-tion information it generates since, if it had a high rate of false positives, itcould contaminate this information. In this sense, and with a view to the char-acterization of episodes, it is preferable to sacrifice the sensitivity of matchingprocedures in favour of specificity. Another feature of the solution proposedin this paper which increases the value of the characterization informationgenerated is the capability of linking apnoeas with the desaturation that theycause. While there are algorithms proposed in the bibliography that allow theidentification of episodes of desaturation and of apnoeas, to the best of ourknowledge, none has been proposed which allows both events to be linked.

6 Conclusions and future work

In this work we have presented a proposal which permits the identification ofapnoeas over the respiratory airflow signal and relates them with the drops inSpO2 that they give rise to. As a starting point, the algorithm takes medicalknowledge on the morphology of these events, and uses fuzzy set theory tohandle and represent the vagueness that is characteristic of this knowledge.Fuzzy set theory also solves the problem of correctly classifying those eventswhich lie in the border between those which are considered pathological andthose which are not.

22

Using the graphical tool TRACE, clinical staff can edit the morphologicalcriteria defining the events to be identified. This supplies support for usingcustomized criteria in the analysis of a polysomnographic recording and, thus,solves the problem of the lack of a universal agreement on these criteria in thebibliography.

The algorithm was validated using 10 polysomnographic recordings from pa-tients subjected to a sleep study in the General Hospital of Galicia. The record-ings totalled 59 hours 10 minutes of signal, and contain 1,706 apnoeas. In thisvalidation 90% of detections were correct, with only 3.2% being false positives.From these results, special mention should be made of the low number of falsepositives obtained thanks to the integration of information coming from twoparameters: respiratory airflow and SpO2.

Thanks to the structural nature of the algorithm, a set of descriptors whichmake up a detailed characterization of each apnoea episode, each desatura-tion, and the temporal relation between both can be obtained. The value ofthis information is increased by the high specificity of the detection. Thischaracterization may serve as a basis for obtaining a deeper insight into thephysio-pathological processes underlying SAS. One of our future lines of workis orientated in this direction: we intend to process a database of polysomno-graphic recordings with the algorithm and apply data-mining techniques tothe information generated, with the aim of uncovering new medical knowl-edge. We also intend to develop new algorithms, based on the MFTP model,to identify other events recorded during polysomnographic studies that maybe relevant for the study of cardio-pulmonary sleep disorders.

Acknowledgements

This work was supported by the Spanish MICIN and the European FEDERunder the grant TIN2009-14372-C03-03.

References

[1] T. Al-Ani, Y. Hamam, R. Fodil, F. Lofaso, and D. Isabey. Using hidden Markovmodels for sleep disordered breathing identification. Simulation modelling,12:117–128, 2004.

[2] S. Barro, P. Felix, P. Carinena, and A. Otero. Systematic Organization ofInformation in Fuzzy Systems, volume 184, chapter Extending Fuzzy TemporalProfile model for dealing with episode quantification, pages 205–228. NATOScience Series, IOS Press, 2003.

23

[3] S. Barro, R. Marın, F. Palacios, and R. Ruız. Fuzzy logic in a patient supervisionsystem. Artificial Intelligence in Medicine, 21:193–199, 2001.

[4] C. Bassetti and M.S. Aldrich. Sleep apnea in acute cerebrovascular diseases:final report on 128 patients. Sleep, 15:217–223, 1999.

[5] D. W. Beebe and D. Gozal. Obstructive sleep apnea and the prefrontal cortex:towards a comprehensive model linking nocturnal upper airway obstruction todaytime cognitive and behavioral deficits. Journal of Sleep Research, 11(1):1–16, 2002.

[6] K. Behbehani, Y. Fu-Chung, J.R. Burk, E.A. Lucas, and J.R. Axe. Automaticcontrol of airway pressure for treatment of obstructive sleep apnea. IEEETransactions on Biomedical Engineering, 42:1007–1016, 1995.

[7] W. Bystricky and A. Safer. Identification of individual sleep apnea events fromthe ECG using neural networks and a dynamic markovian state model. InComputers in Cardiology, pages 297–308, 2004.

[8] R. Dechter. Constraint Processing. Morgan Kaufmann Publishers, 2003.

[9] R. Dechter, I. Meiri, and J. Pearl. Temporal constraint networks. ArtificialIntelligence, 49:61–95, 1991.

[10] O. Fontenla-Romero, B. Guijarro-Berdinas, A. Alonso-Betanzos, and V. Moret-Bonillo. A new method for sleep apnea classification using wavelets andfeedforward neural networks. J. Am. Med. Assoc., 34:65–76, 2005.

[11] A.S. Gami, D.E. Howard, E.J. Olson, and V.K. Somers. Day-night pattern ofsudden death in obstructive sleep apnea. N Engl J Med, 352:1206–1214, 2005.

[12] J. Hung, E.G. Whitford, E.W. Parsons, and D.R. Hillman. Association of sleepapnea with myocardial infarction in men. Lancet, 336:261–264, 1990.

[13] A. Kaufmann and M.M. Gupta. Introduction to Fuzzy Arithmetic. VanNostrand Reinhold Company Inc., 1984.

[14] P. Koves. Obstructive Sleep Apnea Syndrome. Springer Verlag, 1999.

[15] G.B. Moody and R.G. Mark. The MIT-BIH arrhythmia database on cd-romand software for use with it. In Computers in Cardiology, pages 185–188, 1990.

[16] A.A. Morsy and K.M. Al-Ashmouny. Sleep apnea detection using an adaptivefuzzy logic based screening system. In 27th IEEE EMB Conference, pages6124–6127, 2005.

[17] H. Nazeran, A. Almas, K. Behbehani, and E. Lucas. A fuzzy inference systemfor detection of obstructive sleep apnea. In 23th IEEE EMB Conference, pages1645–1648, 2001.

[18] F.J. Nieto, T.B. Young, B.K. Lind, E. Shahar, J.M. Samet, S. Redline, R.B.DAgostino, A.B. Newman, and M.D. Lebowitz e T.G. Pickering. Association ofsleep disordered breathing, sleep apnea, and hypertension in a large communitybased study. Sleep heart health study. J. Am. Med. Assoc., 14:1829–1836, 2000.

24

[19] American Academy of Sleep Medicine Task Force. Sleep-related breathingdisorders in adults: recommendations for syndrome definition and measurementtechniques in clinical research. Sleep, 22:667–689, 1999.

[20] A. Otero. TRACE’s website. https://www.gsi.dec.usc.es/trace, 2006.

[21] A. Otero, P. Felix, and S. Barro. TRACE, a graphical tool for the acquisitionand detection of signal patterns. Expert Systems With Applications, 2008. Toappear.

[22] A. Otero, P. Felix, S. Fraga, S. Barro, and F. Palacios. A hierarchical patternmatching procedure for signal abstraction. In Lecture Notes in ArtificialIntelligence, volume 4177, pages 31–41, 2006.

[23] T. Penzel, J. McNames, R. de Chazal, B. Raymond, A. Murray, and G. Moody.Systematic comparison of different algorithms for apnea detection based onelectrocardiogram recordings. Med. Biol. Eng. Comput, 40:402–407, 2002.

[24] T. Penzel, G. Moody, R.G. Mark, A.L. Goldberger, and J.H. Peter. The apnea-ecg database. Computers in Cardiology, 27:255–258, 2000.

[25] E.A. Phillipson. Sleep apnea. A major public health problem. N Engl J Med,328:1271–1273, 1993.

[26] J.I. Salisbury and Y. Sunb. Rapid screening test for sleep apnea using anonlinear and nonstationary signal processing technique. Medical Engineering& Physics, 29:336–343, 2007.

[27] A.S. Shamsuzzaman, M. Winnicki, P. Lanfranchi, R. Wolk, T. Kara, V. Accurso,and V.K. Somers. Elevated C-reactive protein in patients with obstructive sleepapnea. Circulation, 105:2462–2464, 2002.

[28] F. Steimann. Fuzzy set theory in medicine. Artificial Intelligence in Medicine,11:1–7, 1997.

[29] J.Y. Tian and J.Q. Liu. Apnea detection based on time delay neural network.In 27th IEEE EMB Conference, pages 2571–2574, 2005.

[30] P. Varaday, T. Micsik, S. Benedeck, and Z. Benyo. A nobel method forthe detection of apnea and hypoapnea events in respiration signals. IEEETransactions on Biomedical Engineering, 49:936–942, 2002.

[31] T. Young, M. Palta, J. Dempsey, J. Skatrud, S. Weber, , and S. Badr. Theoccurrence of sleep-disordered breathing among middle-aged adults. Med. Biol.Eng. Comput, 328(17):1230–1235, 1993.

[32] C. Zamarron, A. Amaro, F. Fernandez, F. Gude, and A. Mazaira andJ.R. Rodrıguez. Sleep apnea syndrome and ischemic heart disease. Anepidemiological study. J. Am. Med. Assoc. Marca, 159:520–529, 1999.

25

7 Figure captions

Figure 1: Fragment of a polysomnogram showing several apnoeas and thecorresponding desaturations.

Figure 2: Morphological criteria that define an apnoea and the desaturationit provokes drawn over a real occurrence of an apnoea.

Figure 3: Representation of a respiratory airway cessation with the MFTPmodel.

Figure 4: The use of evolution constraints allows us to differentiate betweenevolutions of the parameters which otherwise would be indistinguishable forthe MFTP model.

Figure 5: MFTPs that represent the airway cessation (a), the desaturation(b) and the overall pattern that comprises both findings (c).

Figure 6: TRACE showing the detection for the pattern which associates anapnoea and the desaturation it provokes.

Figure 7: TRACE’s knowledge editor, showing the graph for the MFTP rep-resenting an apnoea and its corresponding desaturation.

Figure 8: Wizard for defining morphological findings modelling a desatura-tion. The horizontal and vertical lines in black represent possibility distribu-tions showing the deviation admissible for an evolution of the parameter thatis compatible with the finding.

26