A reliability analysis of cardiac repolarization time markers S. Scacchi a,1 , P. Colli Franzone b, * ,2 , L.F. Pavarino a,1 , B. Taccardi c,3 a Dipartimento di Matematica, Università di Milano, Via Saldini 50, 20133 Milano, Italy b Dipartimento di Matematica, Università di Pavia, Via Ferrata 1, 27100 Pavia, Italy c Cardiovascular Research and Training Institute, University of Utah, Salt Lake City, UT 84112, USA article info Article history: Received 12 September 2008 Received in revised form 2 March 2009 Accepted 13 March 2009 Available online 27 March 2009 Keywords: Bidomain model Repolarization sequence Electrograms Action potential duration Activation-recovery interval Parallel numerical simulations abstract Only a limited number of studies have addressed the reliability of extracellular markers of cardiac repo- larization time, such as the classical marker RT eg defined as the time of maximum upslope of the electro- gram T wave. This work presents an extensive three-dimensional simulation study of cardiac repolarization time, extending the previous one-dimensional simulation study of a myocardial strand by Steinhaus [B.M. Steinhaus, Estimating cardiac transmembrane activation and recovery times from uni- polar and bipolar extracellular electrograms: a simulation study, Circ. Res. 64 (3) (1989) 449]. The sim- ulations are based on the bidomain – Luo-Rudy phase I system with rotational fiber anisotropy and homogeneous or heterogeneous transmural intrinsic membrane properties. The classical extracellular marker RT eg is compared with the gold standard of fastest repolarization time RT tap , defined as the time of minimum derivative during the downstroke of the transmembrane action potential (TAP). Addition- ally, a new extracellular marker RT90 eg is compared with the gold standard of late repolarization time RT90 tap , defined as the time when the TAP reaches 90% of its resting value. The results show a good global match between the extracellular and transmembrane repolarization markers, with small relative mean discrepancy ð6 1:6%Þ and high correlation coefficients ðP 0:92Þ, ensuring a reasonably good global match between the associated repolarization sequences. However, large local discrepancies of the extracellular versus transmembrane markers may ensue in regions where the curvature of the repolarization front changes abruptly (e.g. near front collisions) or is negligible (e.g. where repolarization proceeds almost uniformly across fiber). As a consequence, the spatial distribution of activation-recovery intervals (ARI) may provide an inaccurate estimate of (and weakly correlated with) the spatial distribution of action potential durations (APD). Ó 2009 Elsevier Inc. All rights reserved. 1. Introduction Determining cardiac activation and repolarization times on the epicardium, endocardium and in the thickness of the ventricular walls is one of the main purposes of experimental and clinical electrocardiology. While methods for determining activation times from unipolar electrograms recorded directly from the heart have been firmly established during the past century (see e.g. [47,41] and the references therein), there are still uncertain- ties and controversies about the best method for determining recovery times. The excitation phase of the transmembrane action potential (TAP) is characterized by a fast upstroke with a well-de- fined activation time. On the other hand, local repolarization time can be assessed by different markers associated with the slow downstroke phase of the TAP. Widely used repolarization markers are the time of fastest repolarization RT tap , defined as the time of minimum derivative during the TAP downstroke and the time of late repolarization RT90 tap , defined as the time when the TAP reaches 90% of its resting value during the downstroke phase. These two markers are generally considered to be the gold stan- dards for comparison with other markers assessing repolarization from extracellular unipolar recordings. However, transmembrane recordings can not be performed simultaneously from hundreds of sites in vivo and only extracellular recording techniques are applicable when exploring large regions of a beating heart, see e.g. [18,46,23,8,21,5,50,51]. Therefore, it is important to validate methods for assessing local repolarization times from extracellular potential recordings, i.e. electrograms. The most widely accepted method consists in deter- 0025-5564/$ - see front matter Ó 2009 Elsevier Inc. All rights reserved. doi:10.1016/j.mbs.2009.03.004 * Corresponding author. E-mail addresses: simone.scacchi@unimi.it (S. Scacchi), colli@imati.cnr.it (P.C. Franzone), luca.pavarino@unimi.it (L.F. Pavarino), taccardi@cvrti.utah.edu (B. Taccardi). 1 This work was partially supported by grants of M.I.U.R (PRIN 200774A7LH_002), and of Progetto Istituto Nazionale di Alta Matematica, Roma, Italy. 2 This work was partially supported by grants of M.I.U.R (PRIN 200774A7LH_003), of the Istituto di Matematica Applicata e Tecnologie Informatiche, Pavia, Italy and of Progetto Istituto Nazionale di Alta Matematica, Roma, Italy. 3 This work was supported by an award from the Nora Eccles Treadwell Foundation and the Richard A. and Nora Eccles Harrison Fund for Cardiovascular Research. Mathematical Biosciences 219 (2009) 113–128 Contents lists available at ScienceDirect Mathematical Biosciences journal homepage: www.elsevier.com/locate/mbs