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Are 2 Electrocardiographic Leads Enough for

Multilead Wave Boundary Location and QT Measuring?

R Almeida1,2, JP Mart´ ınez2,1, AP Rocha3,4, P Laguna2,1

1CIBER - Bioingenier´ ıa, Biomateriales y Nanomedicina, Spain

2Communications Technology Group, Arag´ on Institute of Eng. Research , Univ. de Zaragoza, Spain

3Departamento de Matem´ atica Aplicada, Faculdade de Ciˆ encias da Universidade do Porto, Portugal

4CMUP - Centro de Matem´ atica de Universidade do Porto, Portugal

Abstract

Different latencies on the cardiac electric phenomena

can be found across leads. Thus combining adequately the

information provided by multiple leads is essential for the

correct location of global wave boundaries. A multilead-

VCG strategy for boundaries location, by constructing a

transformed spatial lead obtained from 3 orthogonal leads

and optimized for delineation improvement, has been pre-

viously proposed and validated [1]. The goal of this work

was to study and to quantify the performance loss when

just 2 orthogonal leads are used. Combination of 2 leads

were considered, both using recorded Frank leads, leads

synthesised using inverse Dower transformation, and prin-

cipal component analysis. The errors in QRS onset and T

wave end location and in QT interval measurement were

evaluated over the PTB database files. Results indicate

that 2 leads properly selected are enough to locate QRS

onset but possibly not for T wave end.

1.Introduction

According to the dipolar hypothesis, the electrical ac-

tivity of the heart can be approximated by a time-variant

electrical dipole, called the electrical heart vector (EHV).

The voltage measured at a given lead would be the EHV’s

projection into the unitary vector defined by the lead axis

[2]. Choosing a particular lead for ECG delineation de-

termines a point of view over the cardiac phenomena and

different latencies on the waves’ onsets and ends are found

in different leads. Nevertheless, the onset and end of the

cardiac electric phenomena are indeed unique, and there-

fore a global feature for all the leads. Thus combining the

information from different leads is crucial to locate unique

lead-independent waves’ boundaries, which can be imper-

ceptible in a particular lead.

The need for a multilead (ML) based strategy is fre-

quently supplied by the use of post-processing decision

rules that choose global marks from single-lead (SL) based

sets of locations [3]. However this approach does not pro-

vide truly ML locations and it requires applying the SL

methodology to a large number of leads.

A novel automatic ML strategy for ECG boundaries de-

lineation was proposed and validated in [1]. The system

obtains, from 3 orthogonal leads, a transformed spatial

lead more fitted for the specific boundary delineation. SL

delineation is applied to the new synthesized lead, using

a wavelet transform (WT) based system [3]. Thus the ML

systemallowstodealwithmultipleleads, takingadvantage

of their availability to further improve the delineation. The

ML algorithms developed are general and can be applied

to any orthogonal lead set, real or derived. In particular, it

was validated considering the vectocardiographic (VCG)

system given by the recorded Frank leads (F), leads syn-

thesised from the standard 12-lead system using inverse

Dower transformation (D) and a subset of the 12-lead stan-

dard system [1].Using 3D WT loops the ML system

provided more robust and more accurate boundaries loca-

tions than any ECG lead by itself, outperforming strategies

based in selection rules after SL delineation. Best perfor-

mance was obtained considering lead set F.

Considering WT loops in a 2D plane instead of in a 3D

space is also possible, allowing to apply this methodology

to any 2 orthogonal leads, if the only available (e.g. in a

2-lead Holter recording). The hypothesis is that the loss

in performance will be negligible since normal VCG loops

are very planar [4]. The goal of this work is to study and to

quantify the performance loss when just 2 leads are used.

2.Methods

The SL and ML based delineation systems are described

in detail elsewhere [1,3] and only general features are re-

ferred in the next subsections. The implementation used

in this work is a revised version with minor modifications,

with respect to the implementations used in those papers.

ISSN 0276−6574

593

Computers in Cardiology 2009;36:593−596.

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2.1.Single-lead delineation

The WT provides a description of the signal in the time-

scale domain, allowing the representation of its temporal

features at different resolutions (scales) according to their

frequency content. Thus, regarding the purpose of locating

different waves with typical frequency characteristics, the

WT is a suitable tool for ECG automatic delineation.

The detection of the fiducial points is carried out across

the adequate WT scales, attending to the dominant fre-

quency components of each ECG wave: QRS waves cor-

respond to a simultaneous effect in scales 21to 24, while

the T and P waves affect mainly scales 24or 25.

The prototype wavelet used (a derivative of a smooth-

ing function) allows to obtain a WT at scale 2m, wx,m[n],

proportional to the derivative of the filtered version of the

signal x[n] with a smoothing impulse response at scale 2m.

Thus, ECG wave peaks correspond to zero crossings in the

WT and ECG maximum slopes correspond to WT’s max-

ima and minima. Depending on the number and polarity

of the slopes found, a wave morphology is assigned and

boundaries are located using threshold based criteria.

2.2.Multilead delineation

According to the dipole hypothesis, the VCG is an

EHV’s canonical representation defined by 3 orthogonal

leads [2], usually acquired as the corrected Frank leads

s[n] = [x[n],y[n],z[n]]T. As a consequence of the WT

prototype used, the spatial WT loop in a time window W

wm[n] = [wx,m[n],wy,m[n],wz,m[n]]T

(1)

for a given scale 2m??m∈{1,2,3,...} is proportional to the

VCG derivative and describes the velocity of evolution

of the EHV in W. Assuming that the noise is spatially

homogeneous, the direction with maximum projection of

the WT in the region close to the wave boundary location

would define the ECG lead maximizing the local SNR, and

thus, the most appropriate for boundary delineation. The

main direction u = [uX,uY,uZ]Tof EHV variations in a

scale 2mon any time interval W is given by the director

vector of the best straight linear fit to all points in the WT

loop wm[n]. By choosing adequately the time interval W

it is possible to find the u corresponding to the lead most

suited for delineation purposes.

Considering the VCG loop s[n] in any time interval I,

a derived lead d[n] defined by the axis u and combining

the information provided by the 3 leads in s[n], can be

constructed by projecting the points of the VCG loop. In-

stead, theWTloop(wm[n])canbeprojectedandaderived

wavelet signal wd,m[n], corresponding to the ECG lead de-

fined by the axis u is constructed, as:

wd,m[n] =wT

m[n].u

||u||

, n ∈ I.

(2)

The strategy proposed for ML boundary delineation using

WT loops is based in a multi-step iterative search for a bet-

ter spatial lead for delineation improvement (with steeper

slopes), particularized for each boundary. At each step (i),

the vector u(i)is determined separately for each beat and

boundary by total least squares fitting. The interval W

is defined specifically for each boundary and updated in

a way to increase the SNR and ensure steeper slopes in

w(i)

d,m[n] obtained by eq. (2). The goal is to construct a

derived wavelet transformed signal well suited for bound-

aries location, using the same detection criteria as in the

SL delineation.

2.3.Data and lead sets

RecordsfromthePTBdatabase(549filesat1000Hz, 12

standard leads + 3 Frank leads ) were used for validation.

A set of reference annotations for this data (one beat per

file) was published in [5], consisting in manual annotations

based in lead II, for QRS onset and T wave end.

In this work were considered the VCG systems given by

the recorded Frank leads (lead set F) and the leads syn-

thesised from the standard 12-lead system using inverse

Dower transformation (lead set D). Combination of each

pair of orthogonal leads were considered, defining the 2D

lead sets: FXY, FXZ, FY Z, DXY,DXZ, DY Z.

Principal component analysis (PCA) was used as alter-

native method for deriving orthogonal leads, as theoret-

ically it is the optimum transform in least square sense.

PCA is mathematically defined as an orthogonal linear

transformation such that the greatest variance by any pro-

jection of the data comes to lie on the new first coordi-

nate, called the first principal component (PC), the second

greatest variance on the second PC, and so on [6]. For Σ

the covariance matrix of the random vector that generates

the signal s[n], the kthPC is given by pk[n] = bT

where bkis the eigenvector of Σ corresponding to the kth

largest eigenvalue. For real data, the unknown matrix Σ is

replaced by the sample covariance matrix S.

The standard 12-lead system is a redundant under the

dipole model assumptions. Eight independent leads out of

the 12-lead system are assumed, as the precordial leads are

considered to describe also non dipole components. In this

work, the first 3 PC, based on the 8 independent leads out

of the 12-lead system, were considered to define a VCG

system (lead set P). The 2D subsystem given by the first

2 PC define the lead set P2D: p2D[n] = [p1[n],p2[n]]T.

In order to better describe the relevant information in the

ECG, the matrix S is calculated over the samples between

each QRS complex onset and T wave end, in all beats in

the analised segment of signal. The intervals for obtaining

S were based in the locations provided by SL delineation

over lead II.

ks[n],

594

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−60

−40

−20

0

20

40

60

80

ε (ms)

(542) (536)(536)(532) (534)(513) (520)(536)(535)(519)(515)(530) (514) (540)(540) (539) (540) (539)(539) (542) (540)(541) (542)(541)(541) (542)(537) (541)(541)(541)

(#)

(494)(494) (494) (494)(494)(494) (494)(494)(494)(494)(494)(494)(494)(494)(494)(494)(494)(494)(494)(494)(494)(494)(494)(494)(494)(494)(494)(494)(494)(494)

QRSonset

−60

−40

−20

0

20

40

60

80

ε (ms)

Tend

(484)(484)(520)(494)(521)(494)(505)(494)(516)(494)(491)(491)(502)(494)(520)(494)(521)(494)(508)(494)(500)(494)(510)(494)(495)(494)(517)(494)(520)(494)(516)(494)(524)(494)(516)(494)(517)(494)(511)(494)(503)(494)(499)(494)(504)(494)(514)(494)(516) (494)(514)(494)(515)(494)(522)(494)(501)(494)(500)(494)

(#)

−60

−40

−20

0

20

40

60

80

ε (ms)

QT

lead set

(484)(441)

SLR

(520)

(460)

F

(521)

(455)

D

(505)

(459)

P

(516)

(458)

V

(491)

(475)

FXY

(502)

(469)

DXY

(520)

(455)

FXZ

(521)

(456)

DXZ

(508)

(470)

FYZ

(500)

(475)

DYZ

(510)

(461)

P2D

(495)(477)

V2D

(517)

(453)

X

(520)

(465)

Y

(516)

(455)

Z

(524)

(455)

I

(516)

(455)

II

(517)

(461)

III

(511)(452)

aVR

(503)

(454)

aVL

(499)

(450)

aVF

(504)

(455)

V1

(514)

(454)

V2

(516)

(455)

V3

(514)

(455)

V4

(515)

(462)

V5

(522)

(454)

V6

(501)

(453)

P1

(500)

(452)

V1

(#)

Figure 1. Results in PTBDB: error ǫ on QT boundaries location and QT length. The symbol # denotes the number of TP

out of 542 reference marks provided (black) or after excluding extreme cases in each approach (grey).

Additionally, was also considered PCA based only in

the precordial leads, together with the aV l[n] lead, which

corresponds to a spatial axis orthogonal to the transver-

sal plane, defining the lead sets V and V2D: v[n] =

?pV

1[n],pV

2[n],aV l[n]?Tand v2D=?pV

1[n],aV l[n]?T.

3.Results and discussion

The errors in QRS onset, T wave end location and in

QT interval measurement were evaluated over the PTB

database files as overall mean (m) and standard deviation

(s). The detection performance was evaluated calculating

the Sensitivity: Se = 100

TP+FN, where TP is the num-

ber of true positive detections and FN stands for the num-

ber of false negative detections. The error (ε) was taken

as the automatic locations (measures) minus the respective

referee mark (measure). Se and m ± s of ε across files

were calculated considering all TP detections and also af-

ter the exclusion of the 10% most extreme cases for each

boundary, more likely to be outliers.

Results for lead sets with 3 orthogonal leads (F, D,

P, V ) and with 2 orthogonal leads (FXY, FXZ, FY Z,

DXY,DXZ, DY Z, P2D,V2D) can be found in Figure 1.

For comparison purposes are also presented the values

found for using a post processing decision rules over the

12-lead standard system (SLR) [3] and SL delineation over

each of the 15 leads available, p1[n] and pV

ues of Se and m ± s for all 3D approaches and some 2D

are also presented in Tables 1 and 2. Notice that for QT

length the Se value over all TP detections corresponds to

the values for T wave end. In Table 1 are also presented

TP

1[n]. The val-

the tolerance values (2sCSE) for the standard deviation of

the error, according to the recommendations of [7]. All s

values found for T wave end error using ML delineation

and none for QRS onset are within the tolerance provided.

The error in T wave delineation represents the main con-

tribution for QT measure error, as lower Se and higher

standard deviation of the error (s) are found for T wave

end than for QRS onset, across all methods, as result of

the lower SNR. The best combination of 2 leads out of F

or D are obtained for lead sets excluding the lead Y , as

expected as this particular lead is likely to be noisy. The

loss of performance is small for QRS onset but relevant for

T wave end. Using PC based lead sets allows to reduce

the s of the error for QRS onset, in accordance with previ-

ous results over different data [8], but not for T wave end

location. A substantial performance lost is found for lead

set V2D, with a much lower Se. Thus, directly recorded

Frank leads (or the use of inverse Dower transformation to

obtain those) should be preferred.

Globally, the results indicate that 2 leads properly se-

lected are enough to locate QRS onset but possibly not for

T wave end. This can indicate that the EHV changes at

the beginning of the QRS are mainly along a single plane,

while the T wave end comprehends spatial changes that

require a 3D description. Nevertheless, the 2D approach

allows to locate T wave end better than SL over any lead

by itself or over p1[n] or pV

Se is achieved, specially compared with SLR.

The s of the error on QT length using 2 leads only in-

creases around 4 ms for Frank leads, and around 2 ms un-

der Dower transformation, compared with 3D approach.

1[n]. Notice also that an higher

595

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all filesafter extreme exclusion

QRS onset

Se, %

m ± s, ms

91.1−4.6 ± 7.3

91.1−5.1 ± 6.3

91.1−4.4 ± 6.9

91.1−4.7 ± 6.2

91.1−3.3 ± 8.1

91.1−4.6 ± 7.1

91.1−3.3 ± 7.5

91.1−3.2 ± 7.8

±6.50

QRS onset

m ± s, ms

−4.7 ± 11.0

−4.5 ± 12.8

−4.4 ± 9.6

−4.1 ± 13.2

−2.8 ± 11.9

−3.8 ± 10.9

−3.3 ± 10.1

−2.8 ± 14.0

±6.50

T end

m ± s, ms

7.3 ± 20.0

7.1 ± 23.0

6.9 ± 24.2

7.4 ± 21.8

8.2 ± 24.1

7.9 ± 24.9

7.6 ± 23.8

6.2 ± 23.0

±30.6

T end

m ± s, ms

7.7 ± 13.8

7.4 ± 16.4

7.0 ± 20.6

7.4 ± 16.7

8.2 ± 18.4

7.6 ± 18.1

7.2 ± 19.9

6.5 ± 22.2

±30.6

Se, %

98.9

98.9

98.2

98.9

98.9

98.7

97.8

95.0

Se, %

95.9

96.1

93.2

96.1

95.9

96.1

94.1

91.3

Se, %

91.1

91.1

91.1

91.1

91.1

91.1

91.1

91.1

F

D

P

V

FXZ

DXZ

P2D

V2D

2sCSE

Table 1. QT delineation results: Se and m ± s of the error for 3D and 2D approaches.

QT length

all files

m ± s, ms

11.8 ± 22.1

12.1 ± 24.9

11.3 ± 26.2

12.0 ± 23.8

11.0 ± 25.9

11.7 ± 27.6

10.8 ± 26.3

9.5 ± 25.3

after extreme exclusion

Se, %

m ± s, ms

84.912.2 ± 15.9

83.912.7 ± 17.4

84.711.2 ± 21.8

84.711.8 ± 17.6

83.911.7 ± 19.9

84.112.6 ± 19.1

85.110.4 ± 20.9

87.69.7 ± 23.3

F

D

P

V

FXZ

DXZ

P2D

V2D

Table 2. QT length measuring results: Se and m ± s of

the error for 3D and 2D approaches.

Similar Se values are found with a bias reduction, still out-

performing the performance of SLR. These results indicate

than using ML method, even in the case of only 2 avail-

able orthogonal leads, is preferable to SL delineation for

QT measuring.

4.Concluding remarks

The VCG based ML delineation methods considered in

this work allows to take advantage of the spatial informa-

tion provided by multilple leads, in order to better estab-

lish the onset and end of the cardiac electrical phenom-

ena. Using 2 orthogonal leads instead of 3 reduces the

stability of the locations provided, specially with respect

to the T wave end. Nevertheless it still performs better

than SL delineation and allows to measure the QT length

over more beats, with more stable measuresand less biased

marks than post-processing rules over SL based marks.

Acknowledgements

This work was partially supported by project TEC2007-

68076-c02-02 from MCyT and FEDER, Grupo Consoli-

dado GTC from DGA T:30, and CMUP, financed by FCT,

Portugal, through the programmes POCTI and POCI 2010,

with national and European Community Structural Funds.

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New York:

Address for correspondence:

Rute Almeida

Dpto. de Ingenier´ ıa Electr´ onica y Comunicaciones

Edificio Ada Byron, Mar´ ıa de Luna 1, 50018 Zaragoza, Espa˜ na

rbalmeid@unizar.es

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