Limitations of Dower’s Inverse Transform for the Study of Atrial Loops during Atrial Fibrillation MAR ´ IA S. GUILLEM, PH.D.,* ANDREU M. CLIMENT, M.S.,* ANDREAS BOLLMANN, M.D.,† DANIELA HUSSER, M.D.,† JOS ´ E MILLET, PH.D.,* and FRANCISCO CASTELLS, PH.D.* From the *ITACA, Universidad Polit´ ecnica de Valencia, Valencia, Spain; and †Department of Electrophysiology, Heart Center, University of Leipzig, Leipzig, Germany Introduction: Spatial characteristics of atrial fibrillatory waves have been extracted by using a vectorcar- diogram (VCG) during atrial fibrillation (AF). However, the VCG is usually not recorded in clinical practice and atrial loops are derived from the 12-lead electrocardiogram (ECG). We evaluated the suitability of the reconstruction of orthogonal leads from the 12-lead ECG for fibrillatory waves in AF. Methods: We used the Physikalisch-Technische Bundesanstalt diagnostic ECG database, which con- tains 15 simultaneously recorded signals (12-lead ECG and three Frank orthogonal leads) of 13 patients during AF. Frank leads were derived from the 12-lead ECG by using Dower’s inverse transform. Derived leads were then compared to true Frank leads in terms of the relative error achieved. We calculated the orientation of AF loops of both recorded orthogonal leads and derived leads and measured the difference in estimated orientation. Also, we investigated the relationship of errors in derivation with fibrillatory wave amplitude, frequency, wave residuum, and fit to a plane of the AF loops. Results: Errors in derivation of AF loops were 68 ± 31% and errors in the estimation of orientation were 35.85 ± 20.43 ◦ . We did not find any correlation among these errors and amplitude, frequency, or other parameters. Conclusions: In conclusion, Dower’s inverse transform should not be used for the derivation of orthog- onal leads from the 12-lead ECG for the analysis of fibrillatory wave loops in AF. Spatial parameters obtained after this derivation may differ from those obtained from recorded orthogonal leads. (PACE 2009; 32:972–980) atrial fibrillation, vectorcardiogram, ECG analysis, Dower’s inverse transform Introduction Atrial fibrillation (AF) is a supraventricular ar- rhythmia in which the electrical activation shows an uncoordinated pattern. The 12-lead electrocar- diogram (ECG) is the most extended noninvasive technique in the diagnosis of AF. However, the standard ECG does not provide spatial informa- tion that can be obtained with a vectorcardio- gram (VCG). The VCG allows the observation of the contribution of a specific tissue region on the morphology of P waves after isolation of the pul- monary veins, 1 and spatial parameters derived from the VCG constitute a risk factor in postmy- ocardial infarction patients. 2 Also, the study of the VCG during AF allows the extraction of spatial characteristics of AF waves that have been related This work was supported by Spanish Ministry of Education and Science under TEC2005-08401 and Universidad Polit ´ ecnica de Valencia through its research initiative program. D. Husser was supported by a German Ministry of Education and Research Grant (01ZZ0407). Address for reprints: Mar´ ıa S. Guillem, Ph.D., Instituto ITACA, Ciudad Polit´ ecnica de la Innovaci ´ on, Universidad Polit´ ecnica de Valencia, Camino de Vera s/n, 46022, Valencia, Spain. Fax: 34-963877279; e-mail: mguisan@eln.upv.es Received July 22, 2008; revised November 10, 2008; accepted February 2, 2009. to the organization of the atrial activity during AF. 3 The VCG is not usually recorded during clini- cal practice and it can be derived from the 12-lead ECG. The VCG is usually approximated by using the so-called Dower’s inverse transform 4,5 despite the existence of other proposed transforms that achieve better reconstruction indexes. 6 Dower’s inverse transform has been used for the deriva- tion of atrial waves in case of atrial flutter (AFl) and AF. 3,7 Ng et al. studied the orientation of atrial loops by computing the plane of best fit of AF loops and observed that some patients presented prefer- ential orientations that were attributed to higher organization degrees. More recent studies 8 have made use of a similar approach and also used Dower’s inverse transform for the derivation of AF loops and concluded that it is possible to relate AF frequency and spatial characteristics. The use of Dower’s inverse transform for the derivation of atrial waves was first questioned by Dower 4,5 who reported a poorer performance of his transformation matrix on P waves compared to its performance on QRS complexes or T waves. Recent studies have proved that this derivation method is not optimum for the study of atrial activ- ity during sinus rhythm. 9 The present study inves- tigates the suitability of Dower’s inverse transform C 2009, The Authors. Journal compilation C 2009 Wiley Periodicals, Inc. 972 August 2009 PACE, Vol. 32