Theoretical Assessment of a Repolarization Time Marker Based on theIntracardiac Bipolar Electrogram

Michele Orini1,2, Stefan Van Duijvenboden1, Neil Srinivasan2, Malcolm Finlay2,Peter Taggart1, Pier D Lambiase1,2

1 University College London, London, United Kingdom2 Barts Heart Centre, St Bartholomew’s Hospital, London, United Kingdom

Abstract

The spatio-temporal organization of cardiac repolariza-tion modulates the vulnerability to dangerous ventriculararrhythmias. Methodologies that provide accurate assess-ment of cardiac repolarization are of primary importancefor a better understanding of cardiac electrophysiologyand represent a potentially useful tool for clinical applica-tions. The most commonly used repolarization time (RT)marker from extracellular recordings is derived from theunipolar electrogram (UEG). However, far field potentialsand remote activity may in certain conditions bias thismarker. In this paper, a RT marker based on the bipo-lar electrogram (BEG) is proposed. An analytical expres-sion of the BEG based on a simple model of the cardiacextracellular potential is derived. According to the pro-posed analytical framework the BEG exhibits a repolariza-tion wave whose extremum (maximum or minimum) corre-sponds to the average of the local RTs at the two electrodesof the bipole. The amplitude of this extremum is a func-tion of the steepness of phase 3 of the action potentials,inter-electrode distance, conduction velocity and directionof wave-back propagation. A simulation study based onthis analytical framework showed that for noisy to goodsignal quality (SNR of the UEG ≥ 10 dB), and for a typ-ical inter-electrode distance of 2 mm, conduction velocitybetween 0.2 and 0.6 m/s, and an angle between conductiondirection and the inter-electrode axis ≤ π/4, the medianabsolute error was lower than 6.8 ms while the medianlinear correlation between estimated and theoretical RTwas higher than 0.91. Examples of RT derived from BEGrecorded in a structurally normal heart in both the rightand left ventricles demonstrate that the proposed proce-dure is feasible in human in-vivo studies.

1. Introduction

The spatio-temporal organization of cardiac repolariza-tion modulates the vulnerability to dangerous ventricular

arrhythmia and sudden cardiac death [1]. Methodologiesthat provide accurate assessment of cardiac repolarizationare of primary importance for a better understanding ofcardiac electrophysiology and represent a potentially use-ful tool for clinical applications. The most commonly usedrepolarization time (RT) marker from extracellular record-ings is the time of the maximum upslope of the T-wavein the unipolar electrogram (UEG). Previous theoretical[2–5] and experimental [6] work has demonstrated that theRT markers from the intracardiac UEG is accurate in idealconditions, but its accuracy critically depends on remotecomponents (far fields, distant activity etc.) that affect theT-wave of the UEG. Extracellular potentials recorded in abipolar configuration as the difference between UEG fromtwo adjacent cardiac sites, so called bipolar electrograms(BEG), are commonly used in electrophysiological stud-ies to measure local activation time, but not RT. The bipo-lar configuration has the advantage of offering informationthat only depends on local repolarization dynamics and is(almost) independent of remote electrical activity, whichbeing (almost) equal at both electrodes of the bipole is can-celed. The purpose of this paper is to conduct a theoreticalinvestigation of a cardiac RT marker based on the BEGalong with supportive human data.

2. Method

2.1. Conceptual Framework

Simulated transmebrane and extracellular potentialswith realistic shapes are generated using a simple analyti-cal model as in previous studies [7, 8]. The repolarizationphase of an action potential (AP) recorded at a given car-diac site xi is defined by a logistic function (Fig. 1):

Vi(t) = V (t, xi) = A

(1− 1

1 + exp(−β(t− τi))

)− V0

(1)where β is a constant that determines the steepness ofthe repolarization downslope during phase 3 of all APs,

Computing in Cardiology 2017; VOL 44 Page 1 ISSN: 2325-887X DOI:10.22489/CinC.2017.220-241

A and V0 are the amplitude and the resting potential ofVi(t). τi is the RT at cardiac site xi, defined as the themoment of the steepest downslope in the AP, i.e. τi =arg min(dVi(t)/dt). According to a simple model, theUEG recorded at the same cardiac site is [4]:

U(t, xi) = C (VR(t)− Vi(t)) (2)

where C is a scaling factor that takes into account the dif-ference between intra- and extracellular conductances [4],and VR(t) is a position-independent potential that repre-sents far field activities, defined as the arithmetic mean ofall V (t, xi). A bipolar electrogram, Bi,j(t), is defined asthe potential difference between two adjacent extracellularcardiac sites xi and xj (Fig. 1):

Bi,j(t) = U(t, xj)− U(t, xi) = C (Vi(t)− Vj(t)) (3)

Inserting (1) into (3), the analytical expression of the bipo-lar electrogram becomes:

Bi,j(t) = ACexp(ki)− exp(kj)

(exp(ki) + 1)(exp(kj) + 1)(4)

where

ki = −β(t− τi) = −β(t− τ0 + ∆τ/2) (5)

τ0 = (τi + τj)/2 and ∆τ = τi − τj . In 2D, the inter-electrode repolarization interval is a function of the inter-electrode distance, d, conduction (wave-back) velocity, v,and direction, θ, i.e. ∆τ = (d cos θ)/v. It is worth notingthat in this framework, UEG and RT are both affected bythe remote component VR(t), while the BEG only dependson local transmembrane potentials. Also, the BEG as de-fined in (3) has a local extremum (either a maximum or aminimum) in correspondence of τ0.In real signals contaminated by noise, the likelihood of cor-rectly localize the extremum of the BEG corresponding toτ0 is determined by its amplitude. The amplitude can benumerically obtained from (4). However, an analytical ap-proximation is obtained by considering exp(ki) ≈ ki + 1for t → τi and ∆τ → 0. Then, the amplitude of the ex-tremum associated with local RT is:

Bi,j(t = τ0) ≈ 4βAC∆τ

16− β2∆τ2≈ −ACβdcosθ

4v(6)

This expression shows that the repolarization wave of theBEG increases with larger and steeper AP (through A andβ) and larger inter-electrode distance, d, while it decreasesfor increasing conduction velocity, v, and for θ approach-ing 90◦. Figure 2 shows the amplitude of the repolarizationwave, Bi,j(t = τ0), as a function of {β, d, v, θ}.

Figure 1. From top to bottom: Action potentials and theremote component (bold grey line), UEGs exhibiting pos-itive (left) and negative (right) T-waves (associated withearly and late RT, respectively) and BEG. Vertical linesrepresent RT τi and τj . The extremum of the BEG corre-sponds to τ0 = (τi + τj)/2.

2.2. Simulation Study

As shown in Fig. 3, a squared grid of 5 × 5 cmwas considered. Four lines of 10 electrodes were dis-tributed to simulate 4 decapolar catheters. Parameterswere d = {1, 2, 4} mm, v = {0.2, 0.4, 0.6} m/s, θ ={0, π/8, π/4, 3/8π}, β = 35 s−1, and sampling frequencywas 4KHz. RT at each point xi = (a, b) was defined as:

τxi = τi =a cos θ + b sin θ

v+ τmin (7)

with τmin = 225 ms. Trasmembrane potentials were gen-erated using (1). White Guassian noise was created foreach point of the grid and spatially filtered with a disk ofradius equal to 5 mm in order to introduce a spatial correla-tion between noise contamination in adjacent electrodes asobserved experimentally. Noise with SNR={5,10,15,20}dB was added to Ui(t), and Bi,j(t) was computed as in(3). Bipolar electrograms were low pass filtered at 25 Hzand RT, τi,j , were estimated as the time of the extremum inthe BEG. For each configuration {v, d, θ,SNR}, the sim-ulation process was repeated 25 times providing 1000 RTestimates. The absolute error |τi,j − τi| and the correlationcoefficient between τi,j and τi were computed.

2.3. Experimental Data

During an electrophysiological study for supraventricu-lar tachycardia in a patient with structurally normal ventri-cles, two decapolar catheters were placed in the left and

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right ventricles. Unipolar electrograms were referencedagainst the WCT, sampled at 2 KHz and recorded with am-plifier with bandwidth 0.05–500 Hz as in previous studies[9]. Ventricular pacing was established from the RV apex.Bipolar electrograms were computed off-line as the differ-ence between UEG from 5 pairs of adjacent poles (d = 2mm). Bespoke algorithms were used for the analysis as inprevious studies [10, 11].

3. Results

For levels of noise that corresponded to UEG withSNR≥ 15 dB, the median absolute error was lower than10 ms while the median correlation coefficient was higherthan 0.90, for all combinations of {d, v, θ} (Fig. 4). Theselevels of noise are considered normal in human recordingsfrom cathlabs and cardiac theaters [12]. In these condi-tions, τi,j ≈ τ0, and parameters associated with smaller∆τ , i.e. lower d and higher v, provided better RT esti-mates because |τi − τ0| = |τj − τ0| = ∆τ/2. However,for SNR≤ 10 dB, combinations of parameters associatedwith longer ∆τ may provide better estimates because along ∆τ is associated with a higher amplitude of the repo-larization wave in the BEG. In general, for noisy to goodquality signals (SNR of the UEG ≥ 10 dB) and for a typi-cal inter-electrode distance d = 2 mm, a conduction veloc-ity 0.2 ≤ v ≤ 0.6 m/s, and an angle between conductiondirection and the inter-electrode axis θ ≤ π/4, the medianabsolute error was lower than 6.8 ms and the median linearcorrelation with theoretical values was higher than 0.91.Figure 5 shows the repolarization wave of UEG and BEGfrom a human heart recorded in the RV and LV endo-cardium during ventricular pacing. The BEG exhibited arepolarization wave whose extremum τ0 (vertical line) cor-responded to the upslope of both the positive and negativeUEG T-wave. The amplitude of the BEG repolarizationwave was about 15% of the UEG T-wave.

4. Discussion

This paper provides the first theoretical investigation ofa RT marker based on the BEG, a signal that has the advan-tage of being the sole results of local repolarization dynam-ics and largely independent of far field potentials and re-mote activities. This marker has the potential to overcomethe limitations of the traditional markers based on the UEG[2, 3, 6, 13]. According to the simple analytical frameworkused in this study, the extremum of the BEG correspondsto the mean of the RT at the two electrodes of the bipole.The amplitude of this extremum is a function of the ampli-tude and shape of the local transmembrane potentials, therelation between intra- and extra-cellular conductance andthe inter-electrode repolarization interval, which in turndepends on the inter-electrode distance, the local conduc-

Figure 2. Amplitude of the repolarization wave in thebipolar electrogram as a function of inter-electrode repo-larization interval ∆τ , inter-electrode distance, d, conduc-tion velocity, v, and conduction direction, θ. These curvesare computed using (4), for t = τ0 and AC = 1.

Figure 3. Schematic of the simulation study, representingelectrodes from 4 decapolar catheters (black dots). Param-eters d, v and θ represent the inter-electrode distance, con-duction velocity and direction, respectively. Colors repre-sent a uniform repolarization wave as in (7).

Figure 4. Results of the 2D simulation study. Upper andlower panels represent absolute error and linear correla-tion coefficient (median ± median absolute deviation) asa function of SNR added to the UEG, inter-electrode dis-tance, d, conduction velocity, v, and direction, θ.

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Figure 5. Unipolar (top) and bipolar (bottom) recordingsfrom an intact human heart recorded in the right (left panel)and left (right panel) ventricle during ventricular pacing.The BEG were computed as the difference of the UEG. Inthe bottom panel, blue and black lines represent unfilteredand filtered signals, respectively. Vertical line representsRT marker from the BEG.

tion velocity and direction. An analytical expression thatdescribes these relations has been proposed. The simula-tion study shows that although the RT measured from theBEG can be accurate even in noisy signals, it critically de-pends on parameters such as conduction velocity and di-rection. The analysis of recordings from an intact humanheart suggests that this marker may be applied to the studyof the spatio-temporal organization of human cardiac repo-larization, with potentially interesting applications in car-diac mapping.The analytical expression implemented to simulatetransembrane potentials was based on [14], while the de-scription of the UEG in terms of local and remote com-ponents was based on [4]. The proposed model assumesisotropic conditions, uniform and planar wavefronts forelectrical recovery, and describes phase 3 of the cardiacaction potential as a logistic function. Its main purpose isto provide a simple conceptual framework for the study ofthe BEG, rather than to reproduce realistic conditions.

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Address for correspondence:

Name: Michele OriniUniversity College London, Gower Street, London, UK.E-mail address: m.orini@ucl.ac.uk

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