Organization of ventricular fibrillation in the human heart: experiments and models

Exp Physiol 94.5 pp 553 562 553 Experimental Physiology Research Paper Organization of ventricular fibrillation in the human heart: experiments and models K. H. W. J. ten Tusscher 1,A.Mourad 2,M.P.Nash 3,R.H.Clayton 4,C.P.Bradley 5,D.J.Paterson 5,R.Hren 6, M. Hayward 7,A.V.Panfilov 8 and P. Taggart 7 1 Department of Scientific Computing, Simula Research Laboratory, Oslo, Norway 2 Department of Mathematics, Faculty of Science I, Lebanese University, Hadeth, Lebanon 3 Auckland Bioengineering Institute and Department of Engineering Science, The University of Auckland, New Zealand 4 The Department of Computer Science, University of Sheffield, Sheffield, UK 5 Department of Physiology, Anatomy and Genetics, University of Oxford, Oxford, UK 6 Institute of Mathematics, Physics and Mechanics, University of Ljubljana, Ljubljana, Slovenia 7 Department of Cardiology and Cardiothoracic Surgery, University College Hospital London, London, UK 8 Department of Theoretical Biology, Utrecht University, Utrecht, The Netherlands Sudden cardiac death is a major health problem in the industrialized world. The lethal event is typically ventricular fibrillation (VF), during which the co-ordinated regular contraction of the heart is overthrown by a state of mechanical and electrical anarchy. Understanding the excitation patterns that sustain VF is important in order to identify potential therapeutic targets. In this paper, we studied the organization of human VF by combining clinical recordings of electrical excitation patterns on the epicardial surface during in vivo human VF with simulations of VF in an anatomically and electrophysiologically detailed computational model of the human ventricles. We find both in the computational studies and in the clinical recordings that epicardial surface excitation patterns during VF contain around six rotors. Based on results from the simulated three-dimensional excitation patterns during VF, which show that the total number of electrical sources is 1.4 ± 0.12 times greater than the number of epicardial rotors, we estimate that the total number of sources present during clinically recorded VF is 9.0 ± 2.6. This number is approximately fivefold fewer compared with that observed during VF in dog and pig hearts, which are of comparable size to human hearts. We explain this difference by considering differences in action potential duration dynamics across these species. The simpler spatial organization of human VF has important implications for treatment and prevention of this dangerous arrhythmia. Moreover, our findings underline the need for integrated research, in which humanbased clinical and computational studies complement animal research. (Received 28 September 2008; accepted after revision 12 December 2008; first published online 23 January 2009) Corresponding author K. H. W. J. ten Tusscher: Department of Scientific Computing, Simula Research Laboratory, PO Box 134, 1325 Lysaker, Norway. Email: khwjtuss@hotmail.com The heart is an electromechanical pump. During a normal heart beat, contraction of the cardiac muscle fibresistriggeredandco-ordinatedbyanorderlywave of electrical excitation that arises in the sinus node, the natural pacemaker of the heart. In contrast, during ventricular fibrillation (VF), contraction of the heart is rapid, unco-ordinated and totally ineffective, causing this condition to be lethal within minutes unless halted by K. H. W. J. ten Tusscher and A. Mourad contributed equally to this work. defibrillation. During the last half-century an extensive line of research has emerged aimed at understanding the causes and organization of excitation patterns during VF and identifying targets for medical intervention. Experimental studies in animal hearts and tissue (Davidenko et al. 1992; Gray et al. 1998; Witkowski et al. 1998; Valderrabano et al. 2003; Huang et al. 2004a; Moreno et al. 2005) have demonstrated that underlying the turbulent activity typical of VF are multiple rotating waves of electrical excitation. Owing to their high rotation frequency and self-perpetuating character, these electrical DOI: 10.1113/expphysiol.2008.044065

554 ten Tusscher and others Exp Physiol 94.5 pp 553 562 rotors take over the control of cardiac excitation from the sinus node. The number of rotors present during VF is a good indicator of the complexity of excitation patterns and has been observed to increase with heart size. In rabbit hearts, VF can be driven by just one or two rotors (Gray et al. 1998), whereas in sheep hearts VF is driven by around 20 rotors (Moreno et al. 2005). In pig and dog hearts, which have a size comparable to that of the human heart, the number of rotors present during VF can be estimated at around 50 (Valderrabano et al. 2001, 2003; Huang et al. 2004a). Detailed information about excitation patterns during human VF has remained scarce until recently, leaving the organization of human VF an important question. There have been some early indications that the organization of human VF may be markedly different from that of VF in animal hearts of comparable size (Panfilov, 2006). One clue came from the electrocardiogram (ECG). During VF, the frequency spectrum of the ECG typically possesses a dominant peak that corresponds to rotor period (Mandapati et al. 1998). Lower dominant frequencies in the ECG correspond to longer rotor periods, longer activation pathways and less complex excitation patterns (Mandapati et al. 1998; Zaitsev et al. 2003; Moreno et al. 2005). The dominant frequency of human VF of 5 ± 1Hz(Claytonet al. 1995; Nanthakumar et al. 2004; Nash et al. 2006b) is approximately half that in dog (10 ± 2 Hz; Huang et al. 2004a; Newtonet al. 2004) and pig hearts (10 ± 1.5 Hz; Nanthakumar et al. 2002; Newton et al. 2004), consistent with a simpler organization of excitation patterns during human VF. A second clue came from early studies in which partial mappings of the endo- or epidardial surface of human ventricles during VF were performed (Walcott et al. 2002; Nanthakumar et al. 2004), showing limited numbers of large wave fronts that repeatedly followed similar paths. Recently, more detailed and complete epicardial and endocardial surface recordings of VF in human hearts have been performed (Nash et al. 2006b; Massé et al. 2007; Nanthakumar et al. 2007). In these studies, small numbers of large excitation waves and rotors were reported, consistent with the idea that in the human heart VF has a simpler organization than in animal hearts of comparable size. In this article, we perform a detailed comparison of our previous studies involving clinical recordings of in vivo human VF using complete epicardial activation mappings (Nash et al. 2006b) and computational simulations of human VF in an anatomically and electrophysiologically realistic model of the human ventricles (Ten Tusscher et al. 2007). Using this unique combination of clinical data (which is restricted to surface recordings and therefore cannot exclude hidden intramural complexity) and computational analysis [which allows full 3-dimensional (3-D) observation of the wave patterns but requires clinical validation], we make a strong case that human VF indeed has a simple organization. Furthermore, we show that the longer minimal action potential duration in human cardiac tissue is the most likely cause for the small number of rotors underlying human VF. This minimal APD may thus constitute a potential new target for drug interventions aimed at stopping or preventing VF. Methods Clinical methods The organization of VF was studied in a group of 10 patients undergoing routine cardiac surgery. The study was approved by the local hospital ethics committee and written informed consent was obtained from all patients prior to the procedure. The study was performed according to the Declaration of Helsinki. Six patients were undergoing graft procedures for coronary artery disease, and the other four patients were undergoing aortic valve replacement and had no haemodynamically significant coronary artery disease. Ventricular fibrillation was induced by 50 Hz burst pacing. During the subsequent 20 40 s, electrical activity was recorded from the epicardial surface of the ventricles using an elasticated sock containing 256 unipolar contact electrodes (interelectrode spacing approximately 10 mm) that spanned the entire ventricular epicardium. Epicardial electrograms were sampled at 1 khz using a UnEmap system (Auckland UniServices Ltd, Auckland, New Zealand) with the reference electrode attached to the chest retractors. Dominant frequencies were computed for each electrode signal using the fast Fourier transform with a rectangular window size of 4096 ms. Epicardial voltage distributions were obtained by interpolation from the 256 electrode sites to a regular 100 100 grid. For each grid point, signals were de-trended, and the Hilbert transform was used to determine epicardial phase. This enabled the spatio-temporal identification of wavefronts and phase singularities (PS; epicardial electrical rotors). A more extensive description of patient details, clinical methods and analysis techniques can be found in the paper by Nash et al. (2006b). Numerical methods V t = I ion C m + x j D ij V x j (1) The organization of VF was studied in a detailed model of the human ventricles, where V is the transmembrane potential, I ion the sum of transmembrane ionic currents, C m the cellular capacitance, and D ij a tensor describing tissue conductivity. Ventricular excitation was simulated by integrating eqn (1) over the domain of the human ventricles, with description of the excitable

Exp Physiol 94.5 pp 553 562 Human ventricular fibrillation experiments and models 555 behaviour of individual ventricular cells using a detailed human ventricular cell model (ten Tusscher et al. 2004; ten Tusscher & Panfilov, 2006) that is based on an extensive set of human-based experimental data, and with a 3-D tensor, D, describing anisotropic conduction with respect to the muscle fibres. Ventricular anatomy and fibre direction anisotropy were derived from a structurally normal human heart (Hren, 1996), resulting in a 3-D model of the ventricles consisting of 13.5 million grid points. We used an anisotropy ratio of 4:1 for longitudinal versus transverse conductivity, and used a diffusion coefficient of 162 cm in the longitudinal direction. This results in a longitudinal conduction velocity of approximately 70 cm s 1, consistent with experimental measurements (Taggart et al. 2000). The structural data were validated by simulating the normal excitation sequence of the ventricles and comparing this with the classical experimental data from Durrer (Durrer et al. 1970; Hren, 1996). Equation (1) was integrated using standard forward Euler integration with a space step of 0.25 mm and a time step of 0.02 ms. Fibrillation was induced by applying an S1 S2 protocol to generate a single spiral wave, and by choosing parameter settings such that spiral break-up occurred [steep action potential duration (APD) restitution slopes; Panfilov & Holden, 1990; Karma, 1993; ten Tusscher & Panfilov, 2006]. A total of four different simulations of VF were performed that differed in the location at which the first spiral wave was initialized. Spiral wave filaments were detected as the intersection points of voltage isopotential lines at two consecutive moments in time (Fenton & Karma, 1998). Filaments were identified at 10 ms intervals. To allow comparison with the clinical data, we computed the number of phase singularities visible on the epicardium by intersecting the 3-D filaments with the epicardial surface. All simulations were written in C++ and parallelized in MPI and were run on 20 processors of a Beowulf cluster consisting of 10 Dell 650 Precision Workstations (dual Intel xeon 2.66 GHz). A more extensive description of the numerical methods and validation of the model can be found in the paper by Ten Tusscher et al. (2007). distribution patterns (right). We see that the spiral wave rotates around a single point of phase singularity (black). Such points can hence be counted to determine the number of surface rotors at any time instant. In Fig. 1B,we show a 3-D simulated rotor, the 3-D voltage distribution, and the resulting phase distribution pattern on the lower surface. We can see that a 3-D rotor rotates around a filament, which is a 3-D line of phase singularity points. We can also see that the rotor results in phase singularity points on the top and bottom surfaces, but not on the other surfaces of the tissue slab. Counting the number of filaments will thus determine the exact number of 3-D rotors present, whereas counting the number of surface phase singularity points can only provide an estimate because it depends on the orientation of the filament relative to the observation surfaces. A single filament can produce one, two or zero phase singularities at a given surface, depending on its orientation. Finally, Fig. 1C and D shows examples of human VF excitation patterns observed clinically (Fig. 1C, only surface patterns) and for a simulation study (Fig. 1D, surfaceandfig.1e 3-D patterns). It should be noted that in other studies different definitions have been used, and that this should be taken into account when comparing the number of rotors reported. For example, in the paper by Ten Tusscher et al. (2007) not all singular points about which rotation occurs are defined to represent a rotor. Instead, activity is counted asare-entrantsourceifatleastonefullcycleofre-entry is completed. Given the short lifespan of the majority of phase singularity points, it is clear that this will result in a significantly lower number of rotors than when using the definition we deployed in the present study. In addition, in the study of Kay et al. (2006) the concept of compound rotors is introduced, in which the rotor s organizing PS can change. The idea is that if a wave break occurs close to the original PS, and the original PS is subsequently replaced by a nearby new PS that results in the same overall spiral pattern, these PS can together be called a single, compound rotor. Clearly, counting compound rotors will also lead to a lower number of rotors than when counting all phase singularities as separate rotors (Kay et al. 2006). Definition of rotors In our clinical study, the number of phase singularities on the epicardial surface was used as an estimate of the number of rotors present during VF. In our simulation study, in addition to determining epicardial phase singularities, we determine the number of scroll wave filaments to determine the real number of rotors present during VF. The relation between phase singularities and filaments is illustrated in Fig. 1. In Fig. 1A, we show a 2-dimensional simulated rotor and the resulting voltage (left) and phase Results Figure 2 shows an example of a human VF recording from one patient. The electrogram shown, which was recorded from a single electrode on the epicardial surface (Fig.2A, lower graph), shows VF activity with a dominant frequency of 5.2 Hz. Fig. 2B and C shows two different views of a typical epicardial excitation pattern observed during VF. In striking contrast to the fragmented wave patterns observed during VF in pig and dog hearts (see, for example, Fig. 2 of Valderrabano et al. 2003), these excitation patterns are more organized, with just

556 ten Tusscher and others Exp Physiol 94.5 pp 553 562 a few large rotating waves. These waves re-enter and repeat themselves a number of times, following which a different excitation pattern arises. In the examples shown here, there are four phase singularities on the posterior (Fig. 2B) and three phase singularities on the left lateral epicardial surface (Fig. 2C). The surface observations therefore indicate the presence of at least seven rotors within the tissue. The number (Fig. 2A) and positions of these epicardial phase singularities varied considerably over time (see supplementary movies anterior.mpg and posterior.mpg). Figure 3 shows another example of a human VF recording in another patient. The ECG pattern, number of phase singularities and epicardial excitation patterns are similar to those shown in Fig. 2. However, here we see that while the excitation pattern on one side of the ventricles is very organized (Fig. 3C), the excitation pattern on the othersideismorecomplex(fig.3b). In a total of ten patients (see Nash et al. 2006b for details), we observed a similar degree of organization of VF excitation patterns and found an overall mean of 6.4 ± 1.3 epicardial rotors. No significant differences in VF organization or dynamics Figure 1. Single rotor in the human ventricles and its surface manifestation A compact way to describe dynamics in excitable media is to use a variable called phase (ϕ, ranging from π to π) that indicates the progression of an excitable element through its cycle from rest to excited to refractory and back to rest. The excitation pattern produced by a rotor circulates around a point in space, which becomes a phase singularity: a point at which all possible different phases meet and hence the phase variable ϕ is not defined. A convenient way to determine the number of rotors present in an excitation pattern is to count the number of phase singularities. In 3-D excitable media, such as the thick-walled ventricles of the heart, rotors are called scroll waves. Scroll waves rotate around a line of connected phase singularity points called a filament. A shows a simulated rotor in an idealized 2-dimensional tissue sheet. The left panel shows the spatial distribution of membrane voltage (V m ), and the right panel shows the spatial distribution of phase (ϕ; Grayet al. 1998). The black dot indicates the phase singularity, and the arrow indicates the direction of rotation. B shows a simulated rotor in an idealized 3-D tissue slab, in which the 3-D wavefront (red) and scroll wave filament (blue) are shown. The phase distribution generated by this rotor is shown on the bottom surface of the tissue slab ( epicardium ). In our clinical studies, we have measured epicardial voltage distributions, whereas in simulation studies we can obtain complete 3-D wave patterns. As a consequence, in clinical studies we can only determine the number of epicardial phase singularities, whereas in simulations we can also determine the number of 3-D filaments. Note that the number of filaments represents the total number of 3-D electrical sources that are present, whereas the number of epicardial phase singularities represents only those rotors for which the filament intersects with the epicardium. C shows a snapshot of the epicardial phase distribution during VF in one patient. This panel shows a single rotor on the ventricular epicardial surface in a patient during the early stages of VF. The direction of rotation around the phase singularity point (black dot) is indicated by the arrow. D shows the epicardial phase distribution generated by a simulated single spiral wave in our virtual human ventricles model. E shows a 3-D wavefront (red) and phase singularity filament (blue) of the spiral wave shown in D.

Exp Physiol 94.5 pp 553 562 Human ventricular fibrillation experiments and models 557 Figure 2. In vivo episode of human VF A, upper panel shows an electrogram recorded from a single electrode of the epicardial electrode sock (see Methods). A, lower panel shows the number of phase singularities (PS) as a function of time. The arrows indicate the time corresponding to the snapshots in B and C. B, posterior view of the phase distribution on the ventricular epicardial surface at the time indicated by the arrows in A. C, concurrent left lateral view of the phase distribution. See supplementary material for movies and for observations from another case study. where found between patients with different pathology (Nash et al. 2006b); however, due to low patient numbers such differences cannot be entirely ruled out. Note that the number of epicardial phase singularities is not sufficient to establish the total number of rotors driving VF. Ventricular fibrillation is driven by 3-D rotors and, depending on their orientation, these rotors need not always be visible on the epicardial surface (Fig. 1). Further indications that VF in the human heart is driven by a small total number of rotors come from simulations in our computational model of the human ventricles (Ten Tusscher et al. 2007). This model has been constructed using a realistic representation of human ventricular anatomy (Hren, 1996), combined with a detailed model of electrical activity based on extensive studies in human ventricular cells (tentusscher et al. 2004; ten Tusscher & Panfilov, 2006; see Methods and Ten Tusscher et al. 2007 for details). An example of simulated VF in the computational model is shown in Fig. 4. The time series of electrical activity (Fig.4A) shows similar features to the data shown in Figs 2A and 3A, and has a dominant frequency of 4.8 Hz. Figure 4B and C shows snapshots of a typical excitation pattern observed during simulated VF on the anterior and left ventricular epicardial surfaces, respectively. These excitation patterns are consistent with the clinically observed excitation patterns (Figs 2 and 3), with similar numbers of excitation wavefronts and epicardial phase singularities. In Fig. 4D and E, we show the 3-D scroll wave filaments (blue) underlying the surface excitation patterns shown in Fig. 4B and C, respectively. The correspondence between the number of epicardial phase singularities and filaments depends on filament orientation. In Fig. 4D, a U-shaped filament oriented with both ends on the endocardium ( ) leads to zero epicardial phase singularities, whereas the Figure 3. In vivo episode of human VF A, upper panel shows an electrogram recorded from a single electrode of the epicardial electrode sock. A, lower panel shows the number of phase singularities (PS) as a function of time. B, posterior view of the wave phase distribution on the ventricular epicardial surface during VF. C, anterior view of the same wave phase distribution

558 ten Tusscher and others Exp Physiol 94.5 pp 553 562 U-shaped filament (#) in Fig. 4D leads to two epicardial phase singularities (see supplementary movies for dynamics of surface excitation patterns, 3-D excitation patterns and filaments). The number of filaments (total number of rotors) and epicardial phase singularities (epicardially manifested rotors) during VF is shown in Fig. 4A, lower graph. As with the clinical data, the number of rotors initially grows and then fluctuates around an average of eight epicardial phase singularities and 12 filaments. In Fig. 5, we show details of another simulation of VF in our model of the human ventricles. Here we see that initially the ECG is more regular and filament numbers are lower. The excitation pattern snapshots are from this initial period. After 6 s, the filament numbers increase and a similar complexity of VF compared to that in Fig. 4 is reached. We obtained results for a total of four simulations, which differed in the position of spiral wave initiation. For the four simulations, we found an overall mean of 9.5 ± 1.1 filaments and 7.0 ± 0.7epicardial phase singularities. Dominant ECG frequencies varied between 4.5 and 5.0 Hz, with a mean of 4.7 ± 0.2 Hz. During simulated VF, the number of filaments was 1.4± 0.12 times larger than the number of epicardial phase singularities. Combining these simulation results with our clinical observations (6.4 ± 1.3 PS), we estimate that the total number of filaments sustaining in vivo human VF is 9.0 ± 2.6. Together, our clinical observations and simulation results indicate that human VF is indeed organized by a much smaller number of rotors than VF in animal hearts of comparable size. This finding implies that the spatial complexity of VF does not simply increase with heart size, as has been previously assumed, but that other factors need to be considered. An important and clinically relevant question is why VF in the human heart has a much simpler organization than VF in dog and pig hearts that are of comparable size. In an extensive modelling study (Ten Tusscher et al. 2007), we investigated the dependence of VF wave pattern complexity on axial resistivity properties, tissue excitability and conduction velocity (CV), steepness of APD restitution slope and minimal APD (shortest APD value reached with high stimulation frequencies). Table 1 summarizes the effects of varying these properties on VF Figure 4. Episode of simulated VF A, upper panel shows ECG during simulated VF. A, lower panel shows number of filaments (F, red line) and phase singularities (PS, black line) as a function of time. The arrows indicate the time corresponding to the snapshots in B E. B, anterior view of the phase distribution on the ventricular epicardial surface during simulated VF at the time indicated by the arrows in A. C, concurrent left lateral view of the phase distribution. D, anterior view of the 3-D scroll wave filaments underlying the phase distribution shown in B. E, concurrent left lateral view of the filaments underlying the phase distribution shown in C. See supplementary material for movies and for observations from another simulation.

Exp Physiol 94.5 pp 553 562 Human ventricular fibrillation experiments and models 559 complexity. We can see that differences in minimal APD provided the most likely explanation for differences in VF wave pattern complexity. The anisotropy ratio had a much smaller effect on VF, influencing wave pattern complexity primarily by altering the effective tissue size (Ten Tusscher et al. 2007). Increasing the excitability and conduction velocity by increasing sodium current conductance had no measurable effect on VF wave pattern complexity. This is an important finding given that increasing the wavelength by increasing CV is often suggested as a therapeutic intervention. A likely reason for the lack of effect is that although sodium current conductance has a significant effect on CV at normal heart rates, it does not have so much effect on CV at the very high rates occurring during fibrillation, when sodium current recovery properties dominate CV. This indicates that, similar to the minimal APD effect we show here, minimal CV rather than maximal CV should be the target of pharmacological intervention. Restitution slope did have a significant effect on VF complexity. However, explaining the difference between human VF and dog and pig VF by differences in restitution slope would require exceedingly steep slopes relative to slopes reported. It should be noted that although coronary artery disease and coronary valve disease patients in our studies displayed Table 1. Comparison of the average number of scroll waves occurring during simulated VF in our human ventricles model for different conditions Average number Condition of scroll waves Anisotropy Standard, 1:4 12 Decreased, 1:2 5 Increased, 1:7 16 Excitability/conduction velocity Standard, CV = 71 cm s 1 12 Increased, CV = 94 cm s 1 12 APD restitution slope Standard, 1.8 12 Increased, 2.8 28 Minimal APD Standard, 110 ms 12 Decreased, 70 ms 45 similar VF complexity, particular disease conditions may significantly affect VF wave pattern complexity. For example, cardiac hypertrophy, which leads to substantial increases in heart size, may substantially increase the complexity of VF dynamics. Indeed,VFinthehumanheartisknowntohavea lower frequency and longer excitation wavelength than in Figure 5. Episode of simulated VF A, upper panel shows ECG during simulated VF. A, lower panel shows number of filaments (F, red line) and phase singularities (PS, black line) as a function of time. B, anterior view of the phase distribution on the ventricular epicardial surface during simulated VF. C, right lateral view of the same phase distribution. D, anterior view of the 3-D scroll wave filaments underlying the phase distribution shown in B. E, right lateral view of the filaments underlying the phase distribution shown in C.

560 ten Tusscher and others Exp Physiol 94.5 pp 553 562 pig and dog hearts, suggesting that minimal APD may be a valid explanation for the VF complexity differences. Only limited clinical and experimental data are available for minimal APD. From our survey of the literature, we found that minimal APD in pigs lies between 90 and 110 ms (Huang et al. 2004b), while for dogs this lies between 70 and 110 ms (Koller et al. 1998), whereas for humans it lies between 140 and 200 ms (Misier et al. 1995; Taggart et al. 2003). Note that the inverse of these APDs indeed matches the VF frequencies observed for the various species ( 10 Hz for dog and pig, and 5 Hz for human VF). Thus, we suggest that minimal APD is an important parameter for understanding VF organization and that differences in minimal APD can explain differences in VF frequency and wave pattern complexity. Figure 6 shows snapshots of filaments present during simulated VF in the rabbit heart (Arevalo et al. 2001), dog heart (Panfilov, 1999) and human heart. We clearly see that human VF is organized by far fewer filaments than dog VF. In addition, we see that rabbit VF is much more similar in complexity to human VF (Panfilov, 2006). Currently, pig and dog hearts are the model systems of choice when investigating mechanisms of human VF and testing potential drugs. The main reason for this is that their heart size is closest to that of humans. Figure 6 shows that heart size is not the major determinant of VF wave pattern complexity. This suggests that it may be more reasonable to extrapolate animal findings to human hearts from animal hearts that have a similar VF organization but perhaps smaller size than from animal hearts with considerably different VF organization but similar size. Discussion By using a unique combination of in vivo recordings of human VF and detailed simulation studies of VF in a computer model of the human ventricles, we have demonstrated that the excitation pattern underlying human VF involves only a small number of rotors. This simpler organization compared with VF in animal hearts of similar size is most likely to be due to the longer minimal APD in human hearts. A limitation of our present study is that we did not investigate the possibility of mechanisms other than steep APD restitution spiral break-up for causing VF in our simulation model, such as mother rotor fibrillation or instabilities in intracellular calcium handling. Mother rotor VF has thus far only been observed in small animal hearts (Gray et al. 1998; Chen et al. 2000; Zaitsev et al. 2000), despite an extensive search for mother rotors in large animal hearts (Rogers et al. 2003; Ideker & Huang, 2005; Huang et al. 2005; Kay et al. 2006). However, the simpler organization of human VF and the smaller effective size of the human heart (Panfilov, 2006) suggest that mother rotor fibrillation may be a possible mechanism for VF in humans. Large electrophysiological heterogeneities in the human ventricles, which were reported in another clinical study by our group (Nash et al. 2006a), may provide a substrate for mother rotor VF in the human heart. We are presently investigating this possibility in more detail (Keldermann et al. 2007). However, we expect that, irrespective of the mechanism causing the VF dynamics, VF in the human heart will be organized by a small number of rotors. Our findings may have important consequences for the treatment and prevention of human VF. In simulation studies, it has been shown that VF that is driven by a smaller number of rotors requires less energy for successful defibrillation (Hillebrenner et al. 2004; Plank et al. 2005). Likewise, drugs aimed at increasing wavelength or meander of re-entrant sources, to decrease the number of sources, may be more promising to treat human Figure 6. Simulated VF in the rabbit (A), dog (B) and human ventricles (C) To indicate size differences between the different hearts, a scale bar indicating 1 cm length is added to the left of each figure. A, filaments (purple) in the rabbit heart during VF (colours indicate phase of excitation). Reproduced from Aravelo et al.; Chaos;17: 015103; 2007, with permission. B, filaments (red) in the dog heart during VF. Reproduced from A.V. Panfilov; Phys. Rev. E; 59: R6251 R6254; 1999, with permission. C, filaments in the human heart during VF.

Exp Physiol 94.5 pp 553 562 Human ventricular fibrillation experiments and models 561 VF than might be expected based on observations from dog and pig hearts. Finally, minimal APD may present a potential new target for pharmacological interventions aimed at stopping or preventing fibrillation. However, more research is needed to establish whether its positive effects of increasing wavelength and decreasing re-entry probabilities are not offset by a higher likelihood of early after-depolarizations. Although we found that increasing maximal CV had no effect on VF organization, a pharmacological intervention increasing the minimal CV occurring at high frequencies may be an alternative way to increase wavelength and decrease re-entry probabilities. Again, research will be needed to establish whether this is associated with proarrhythmic effects. Our studies demonstrate that computational models are a valuable tool for gaining insights into complex physiological processes that cannot be obtained experimentally due to limited observability of the processes (e.g. surface versus 3-D) or limited separability of variables and processes (e.g. APD and APD restitution slope). Finally, by demonstrating the significant differences between VF in human and large animal hearts, our results underline the critical importance of complementing insights obtained from animal studies with human-based clinical and computational research. References Arevalo HJ, Rodriguez B & Trayanova NA (2007). Arrhythmogenesis in the heart: Multiscale modeling of the effects of defibrillation shocks and the role of electrophysiological heterogeneity. Chaos 17, 015103. Chen J, Mandapati R, Berenfeld O, Skanes AC & Jalife J (2000). High-frequency periodic sources underlie ventricular fibrillation in the isolated rabbit heart. Circ Res 86, 86 89. Clayton RH, Murray A & Campbell RW (1995). Objective features of the surface electrocardiogram during ventricular tachyarrhythmias. Eur Heart J 16, 1115 1119. Davidenko JM, Pertsov AM, Salomonsz R, Baxter W & Jalife J (1992). Stationary and drifting spiral waves of excitation in isolated cardiac muscle. Nature 355, 349 351. Durrer D, Van Dam RT, Freud GE, Janse MJ, Meijler FL & Arzbaecher RC (1970). Total excitation of the isolated human heart. Circulation 41, 899 912. Fenton F & Karma A (1998). Vortex dynamics in threedimensional continuous myocardium with fiber rotation: filament instability and fibrillation. Chaos 8, 20 47. Gray RA, Pertsov AM & Jalife J (1998). Spatial and temporal organization during cardiac fibrillation. Nature 392,75 78. Hillebrenner MG, Eason JC & Trayanova NA (2004). Mechanistic inquiry into decrease in probability of defibrillation success with increase in complexity of preshock reentrant activity. Am J Physiol Heart Circ Physiol 286, H909 H917. Hren R (1996). A realistic model of the human ventricular myocardium: application to the study of ectopic activation. PhD thesis, Dalhouse University, Halifax. Huang J, Rogers JM, Killingsworth CR, Sing KP, Smith WM & Ideker RE (2004a). Evolutionofactivationpatternsduring long-duration ventricular fibrillation in dogs. Am J Physiol Heart Circ Physiol 101, H1139 H11200. Huang J, Walcott GP, Killingsworth CR, Melnick SB, Rogers JM & Ideker RE (2005). Quantification of activation patterns during ventricular fibrillation in open-chest porcine left ventricle and septum. Heart Rhythm 2, 720 728. Huang J, Zhou X, Smith WM & Ideker RE (2004b). Restitution properties during ventricular fibrillation in the in situ swine heart. Circulation 16, 3161 3167. Ideker RE & Huang J (2005). Our search for the porcine mother rotor. Ann Noninvasive Electrocardiol 10(4 Suppl), 7 15. Karma A (1993). Spiral breakup in model equations of action potential propagation in cardiac tissue. Phys Rev Lett 71, 1103 1106. Kay MW, Walcott GP, Gladden JD, Melnich SB & Rogers JM (2006). Lifetimes of epicardial rotors in panoramic optical maps of fibrillating swine ventricles. Am J Physiol Heart Circ Physiol 291, H1935 H1941. Keldermann RH, ten Tusscher KHWJ, Hren R & Panfilov AV (2007). Mother rotor fibrillation in a heterogeneous anatomically based model of the human ventricles. Heart Rhythm 4(5S), S160. Koller ML, Riccio ML & Gilmour RF Jr (1998). Dynamic restitution of action potential duration during electrical alternans and ventricular fibrillation. Am J Physiol Heart Circ Physiol 275, H1635 H1642. Mandapati R, Asano Y, Baxter WT, Gray R, Davidenko J & Jalife J (1998). Quantification of effects of global ischemia on dynamics of ventricular fibrillation in isolated rabbit heart. Circulation 98, 1688 1696. Massé S, Downar E, Chauhan VS, Sevaptsidis E & Nanthakumar K (2007). Ventricular fibrillation in myopathic human hearts: mechanistic insights from in vivo global endocardial and epicardial mapping. Am J Physiol Heart Circ Physiol 292, H2589 H2597. Misier AR, Opthof T, van Hemel NM, Vermeulen JT, de Bakker JM, Defauw JJ, van Capelle FJ & Janse MJ (1995). Dispersion of refractoriness in noninfarcted myocardium of patients with ventricular tachycardia or ventricular fibrillation after myocardial infarction. Circulation 91, 2566 2572. Moreno J, Zaitsev AV, Warren M, Berenfeld O, Kalifa J, Lucca E, Mironov S, Guha P & Jalife J (2005). Effect of remodelling, stretch and ischaemia on ventricular fibrillation frequency and dynamics in a heart failure model. Cardiovasc Res 65, 158 166. Nanthakumar K, Huang J, Rogers JM, Johnson P, Newton JC, Walcott GP, Justice RK, Rollings DL, Smith WM & Ideker RE (2002). Regional differences in ventricular fibrillation in the open-chest porcine left ventricle. Circ Res 91, 733 740. Nanthakumar K, Jalife J, Massé S, Downar E, Pop M, Asta J, RossH,RaoV,MironovS,SevapsidisE,RogersJ,WrightG & Dhopeshwarkar R (2007). Optical mapping of Langendorff-perfused human hearts: establishing a model for the study of ventricular fibrillation in humans. Am J Physiol Heart Circ Physiol 293, H875 H880.

562 ten Tusscher and others Exp Physiol 94.5 pp 553 562 Nanthakumar K, Walcott GP, Melnick S, Rogers JM, Kay MW, Smith WM, Ideker RE & Holman W (2004). Epicardial organization of human ventricular fibrillation. Heart Rhythm 1, 14 23. Nash MP, Bradley CP, Sutton PM, Clayton RH, Kallis P, Hayward M, Paterson DJ & Taggart P (2006a). Whole heart action potential duration restitution properties in cardiac patients: a combined clinical and modelling study. Exp Physiol 91, 339 354. Nash MP, Mourad A, Clayton RH, Sutton PM, Bradley CP, Hayward M, Paterson DJ & TaggartP(2006b). Evidence for multiple mechanisms in human ventricular fibrillation. Circulation 114, 536 542. Newton J, Smith W & Ideker R (2004). Estimated global transmural distribution of activation rate and conduction block during porcine and canine ventricular fibrillation. Circ Res 94, 836 842. Panfilov AV (1999). Three dimensional organization of electrical turbulence in the heart. Phys Rev E 59, R6251 R6254. Panfilov AV (2006). Is heart size a factor in ventricular fibrillation? Or how close are rabbit and human hearts? Heart Rhythm 3, 862 864. Panfilov A & Holden AV (1990). Self-generation of turbulent vortices in a two-dimensional model of cardiac tissue. Phys Lett A 151, 23 26. Plank G, Leon LJ, Kimber S & Vigmond EJ (2005). Defibrillation depends on conductivity fluctuations and the degree of disorganization in reentry patterns. J Cardiovasc Electrophysiol 16, 205 216. Rogers JM, Huang J, Melnick SB & Ideker RE (2003). Sustained reentry in the left ventricle of fibrillating pig hearts. Circ Res 92, 539 545. Taggart P, Sutton P, Chalabi Z, Boyett MR, Simon R, Elliott D & Gill JS (2003). Effect of adrenergic stimulation on action potential duration restitution in humans. Circulation 107, 285 289. Taggart P, Sutton PMI, Opthof T, Coronel R, Trimlett R, Pugsley W & Kallis P (2000). Inhomogeneous transmural conduction during early ischemia in patients with coronary artery disease. JMolCellCardiol32, 621 639. Ten Tusscher KHWJ, Hren R & Panfilov AV (2007). Organization of ventricular fibrillation in the human heart. Circ Res 100, e87 e101. ten Tusscher KHWJ, Noble D, Noble PJ & Panfilov AV (2004). A model for human ventricular tissue. Am J Physiol Heart Circ Physiol 286, H1573 H1589. ten Tusscher KHWJ & Panfilov AV (2006). Alternans and spiral breakup in a human ventricular tissue model. Am J Physiol Heart Circ Physiol 291, H1088 H1100. Valderrabano M, Chen P & Lin SF (2003). Spatial distribution of phase singularities in ventricular fibrillation. Circulation 108, 354 359. Valderrabano M, Lee MH, Ohara T, Lai AC, Fishbein MC, Lin SF, Karagueuzian HS & Chen PS (2001). Dynamics of intramural and transmural reentry during ventricular fibrillation in isolated swine ventricles. Circ Res 88, 839 848. Walcott GP, Kay GN, Plumb VJ, Smith WM, Rogers JM, Epstein AE & Ideker RE (2002). Endocardial wave front organization during ventricular fibrillation in humans. JAm Coll Cardiol 39, 109 115. Witkowski FX, Leon LJ, Penkoske PA, Giles WR, Spano ML, Ditto WL & Winfree AT (1998). Spatiotemporal evolution of ventricular fibrillation. Nature 392, 78 82. Zaitsev AV, Berenfeld O, Mironov SF, Jalife J & Pertsov AM (2000). Distribution of excitation frequencies on the epicardial and endocardial surfaces of fibrillating ventricular wall of the sheep heart. Circ Res 86, 408 417. Zaitsev AV, Guha PK, Sarmast F, Kolli A, Berenfeld O, Pertsov AM, de Groot JR, Coronel R & Jalife J (2003). Wavebreak formation during ventricular fibrillation in the isolated, regionally ischemic pig heart. Circ Res 86,546 553. Acknowledgements The clinical studies were supported by the Wellcome Trust. K. H. W. J. ten Tusscher was supported by the Netherlands Organization for Scientific Research (NWO) through grant number 635100004 of the Research Council for Physical Sciences (EW).A.MouradwassupportedbytheUniversityofAuckland Research Committee Postdoctoral Fund. M. P. Nash gratefully acknowledges the Royal Society of New Zealand Marsden Fund for supporting this collaboration. R. H. Clayton acknowledges previous support from the British Heart Foundation.