Published online before print May 31, 2007, doi: 10.1161/CIRCRESAHA.107.150730
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© 2007 American Heart Association, Inc.
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Organization of Ventricular Fibrillation in the Human Heart
From the Department of Theoretical Biology (K.H.W.J.T.T., A.V.P.), Utrecht University, The Netherlands; and Institute of Mathematics (R.H.), Physics Mechanics, University of Ljubljana, Slovenia.
Correspondence to K.H.W.J. Ten Tusscher, Utrecht University, Department of Theoretical Biology, Padualaan 8, 3584 CH Utrecht, The Netherlands. E-mail khwjtuss{at}hotmail.com
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Abstract |
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Sudden cardiac death is a major cause of death in the industrialized world, claiming approximately 300 000 victims annually in the United States alone. In most cases, sudden cardiac death is caused by ventricular fibrillation (VF). Experimental studies in large animal hearts have shown that the uncoordinated contractions during VF are caused by large numbers of chaotically wandering reentrant waves of electrical activity. However, recent clinical data on VF in the human heart seem to suggest that human VF may have a markedly different organization. Here, we use a detailed model of the human ventricles, including a detailed description of cell electrophysiology, ventricular anatomy, and fiber direction anisotropy, to study the organization of human VF. We show that characteristics of our simulated VF are qualitatively similar to the clinical data. Furthermore, we find that human VF is driven by only approximately 10 reentrant sources and thus is much more organized than VF in animal hearts of comparable size, where VF is driven by approximately 50 sources. We investigate the influence of anisotropy ratio, tissue excitability, and restitution properties on the number of reentrant sources driving VF. We find that the number of rotors depends strongest on minimum action potential duration, a property that differs significantly between human and large animal hearts. Based on these findings, we suggest that the simpler spatial organization of human VF relative to VF in large animal hearts may be caused by differences in minimum action potential duration. Both the simpler spatial organization of human VF and its suggested cause may have important implications for treating and preventing this dangerous arrhythmia in humans.
Key Words: ventricular fibrillation • computer simulation • spatial organization
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Introduction |
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Ventricular fibrillation (VF) is the single most common cause of sudden cardiac death, the largest cause of death in the Western world. During VF, the contraction of the ventricles becomes rapid, uncoordinated, and highly ineffective, causing this condition to be lethal within minutes, unless halted by defibrillation. The highly disorganized contractions during VF are caused by a severely disturbed, turbulent conduction of the electrical excitation wave.
Experimental studies in animal hearts and tissue1–6 have shown that the turbulent electrical activity typical of VF is caused by the presence of multiple reentrant waves of electrical excitation. Because of their reentrant behavior and high frequency, these rotors act as self-perpetuating, independent sources of excitation that take over control from the slower sinus node. The number of rotors present during VF is a good quantifier of the complexity and amount of disorganization of the excitation pattern. Results in animal hearts suggest that the number of reentrant sources present during VF increases as a function of heart size. For example, in rabbit hearts, VF can be driven by just 1 or 2 sources,2,7 whereas in sheep hearts, VF is driven by 20 sources,4 and in the larger pig and dog hearts the number of reentrant sources can be estimated at approximately 50.5,6
Studies of VF in the human heart are very limited, because of obvious practical and ethical constraints on clinical research. As a consequence, detailed data on the organization of human VF have for a long time been unavailable. The spatiotemporal complexity of VF may have important consequences for its treatment. For example, in modeling studies, it has been shown that minimum defibrillation energy decreases with decreasing wave pattern complexity.8,9 It therefore remains an important question of whether human VF has a similar organization as VF in animal hearts of comparable size, such as the pig and dog hearts.
There were already some indications that human VF may be markedly different from VF in large animal hearts.10 Clinically reported dominant frequencies of human VF lie at approximately 5±1 Hz,11–13 which is approximately half that of the dominant frequency reported for VF in dog (10±2 Hz5,14) and pig (10±1.5 Hz14,15) hearts. Given that lower dominant frequencies correspond to longer rotor periods, longer activation pathways, and less complex excitation patterns,4,16,17 this suggests a considerably simpler organization of human VF.10
Recently, several mappings of in vivo human VF were performed. Walcott et al18 performed a small partial mapping of the left septal endocardium using a 36-pole catheter with 4-mm interelectrode spacing, and Nanthakumar12 performed a partial mapping of the left ventricular epicardium using a 20 cm2 plaque containing 504 electrodes with 2-mm interelectrode spacing. Nash et al13 performed mappings of the complete epicardial surface during in vivo human VF using an elasticated sock containing 256 unipolar electrodes with 10-mm interelectrode distance to fit over the entire ventricles. Very recently, Masse et al19 performed complete mappings of both endocardial and epicardial surfaces during human VF. For endocardial mappings an inflatable balloon catheter with an array of 112 bipolar electrodes was used for both ventricles, for epicardial mappings an elasticated sock with 112 bipolar electrodes was used. In all these studies, small numbers of large excitation waves repeatedly following the same pathways were reported, consistent with a simple organization of human VF. In addition, Nash et al13 reported a small number of epicardial phase singularity points (PSs), suggesting the presence of only a small number of rotors underlying human VF.
A limitation of clinical and experimental measurements is that recordings can only be made on the surface of the heart, whereas the ventricles are 3D. Such a limitation does not apply to modeling studies, in which the complete 3D wave patterns can be studied. In this article, we use a detailed model of the human ventricles to study the 3D organization of human VF. Our model incorporates an electrophysiologically detailed model for human ventricular cells,20,21 an anatomically detailed human ventricular geometry22 and fiber direction anisotropy.
We compare characteristics of our simulated VF to the data from Nanthakumar et al12 and Nash et al13 and demonstrate a good agreement between simulated and clinical data in terms of ECG pattern, ECG frequency, surface wave patterns, and occurrence of epicardial reentry. We study the 3D organization of human VF and show that VF in the human heart is organized by as little as 10 reentrant sources present in the entire ventricular mass. Our results suggest that human VF indeed has a much simpler spatial organization than VF in pig and dog hearts.
We investigate the dependence of VF organization (number of rotors) on tissue anisotropy ratio, excitability, maximum action potential duration (APD) restitution slope and minimum APD. We find that the number of rotors depends strongest on minimum APD, with a difference in minimum APD of 77 versus 110 ms, leading to a 5-fold increase in rotor numbers. The other factors investigated, anisotropy, excitability, and restitution slope, lead to maximally 2-fold increases in rotor numbers when varied within the physiological range. Interestingly, minimum APD differs substantially between humans and pigs and dogs.23–25 Therefore, we hypothesize that it is the difference in minimum APD that causes the much simpler spatial organization of human VF.
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Human Ventricular Electrophysiology
By neglecting the discrete character of microscopic cardiac cell structure, the excitable behavior of cardiac tissue can be modeled as a continuous system using the following partial differential equation26:
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where Cm denotes the cellular capacitance, Iion is the sum of the ionic transmembrane currents that together generate the action potential, and 
/xiDij/xjVm represents the axial diffusive current flow between cardiac cells that leads to action potential propagation. Dij is a 3D conductivity tensor describing the anisotropy of action potential propagation (see below, under Fiber Direction Field).
To represent the electrophysiological properties specific for human ventricular tissue, we use a detailed ionic model for human ventricular myocytes that describes the dynamics of the individual ionic currents and that is based on a large range of human electrophysiological data.20,21 In the Table, we summarize the different parameter settings we used for our model. All parameters not mentioned in the Table are left unchanged from the default parameter setting of our model described previously.21 Unless explicitly stated differently, we used the standard parameter setting of the Table.
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Human Ventricular Anatomy
A 3D voxel description of human ventricular anatomy was obtained from an excised, structurally normal heart as described in detail by Hren.22 In short, the heart was positioned as in the thorax and sliced in 1-mm-thick sections. The individual slices were digitized into 0.5-mm voxels. The data for the individual slices were stacked on top of one another to form a 3D voxel representation of the heart. Using interpolation techniques, a 0.25-mm voxel representation was derived from this 0.5-mm voxel model. The resulting model of the human ventricles consisted of approximately 13.5 million voxels.
Fiber Direction Field
Action potential propagation occurs faster in the direction parallel to the muscle fibers than in the direction perpendicular to the muscle fibers. To take this anisotropy into account, we needed a detailed description of the human ventricular myocardial fiber direction field. To obtain fiber orientation data for our human ventricular anatomy, we used the following approach. We constructed a fiber orientation field from general knowledge on fiber architecture in the human heart,27 combined with detailed data on the fiber architecture in the canine heart.28 The rationale behind this is that it is known from classic studies on cardiac muscle fiber architecture that fiber architecture in the human and canine heart are very similar27,29 and that the fiber orientation field in the dog heart has been studied in much more detail.
To construct our human ventricular fiber direction field, we first constructed principal surfaces that enclose the human ventricular myocardium and identified anatomical landmark points on these surfaces. Using surface data with these same anatomical landmarks for the canine geometry,28 we then obtained a matching between the surfaces of the human and canine ventricles. This surface mapping then allowed us to assign canine fiber directions to the human ventricular surfaces. Intramural fiber direction was then derived from the surface fiber directions and general knowledge of intramural fiber rotation.27 A full description of the construction method for the fiber direction field in our human ventricular anatomy is provided elsewhere.22
Recently, detailed data have become available for the fiber architecture of the human ventricles. We used these data to validate our fiber direction field. Winslow and coworkers used diffusion-tensor (DT)MRI30,31 to derive fiber architecture in a single adult human heart and Jouk and coworkers used quantitative polarized light microscopy32,33 to derive ventricular fiber architecture in young infants.
Figure 1 shows example cross-sections of the fiber direction field derived for our human ventricular geometry (Figure 1A and 1B) with the DTMRI data from Winslow and coworkers (Figure 1C and 1D)30,31 and the light microscopy data from Jouk and coworkers (Figure 1E and 1F).32,33 In our model, the elevation angle (Figure 1A) vary transmurally from approximately 5
/8 on the endocardium to 0 in the midwall, back to 5/8 on the epicardium in both the left and right ventricle, reflecting transmural fiber rotation. A similar transmural change in elevation angle can be observed quite clearly in the left ventricle of the DTMRI data set of Winslow (Figure 1C) and somewhat less clearly in the right ventricle. In the light microscopy data from Jouk (Figure 1E), this transmural change in elevation angle is much less clearly present; the small angles found in the midwall in the other 2 data sets seem to be largely missing here. However, as stated by Jouk et al,33 the polarized light microscopy method is not capable of resolving elevation angles close to 0. The absence of small midwall angles thus represents a limitation of their method rather than a difference among the 3 data sets.
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Figure 1B shows the variation of the azimuth angle through the ventricular walls in our model. We see a clear circular to spiral shaped succession of different azimuth angles in the ring formed by the left ventricular free and septal wall, with the whole range of angles (colors) being visited twice. This variation in azimuth angles reflects the spiral shaped muscle structure of the heart. A less clear succession of azimuth angles with the whole range of angles being visited only once is present in the right ventricular wall. We can see a very similar variation in ventricular azimuth angles in the data sets by Winslow and coworkers (Figure 1D)30,31 and Jouk and coworkers (Figure 1E).32,33
We carefully analyzed the complete datasets and found a similar correspondence between our model fiber field and the experimentally measured fiber fields of Winslow and coworkers30,31 and Jouk and coworkers32,33 for cross-sections taken at other positions or in different directions as for the cross-sections described above. We thus conclude that there is a good agreement between the fiber field we use in our model and the experimentally measured human ventricular fiber fields.
The derived and validated fiber direction field is used to derive the local conductivity tensor Dij from the local fiber direction vector. Assuming that transverse conductivity is the same in all directions orthogonal to the direction of the muscle fiber axis, we described the ventricular conductivity tensor using the following equation:
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where 
is the vector describing muscle fiber direction, and DL and DT are the conductivities in the longitudinal and transverse fiber directions, respectively. We use a ratio of 2:1 for the anisotropy of action potential conduction velocities, which is within the range of experimentally recorded ratios.34 This results in a ratio of 4:1 for DL to DT. For DL, we used 162 cm, which results in a longitudinal conduction velocity of approximately 70 cm/sec, consistent with experimental measurements.34
Numerical Integration
We used a forward Euler scheme to integrate Eq. 1, using a time step of 
t=0.02 ms and a space step of x=0.25 mm. To integrate Eq. 1, we needed to evaluate at each point of the ventricular geometry the following Laplacian: equation
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This Laplacian can be discretized to the following equation:
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where l is an index running over the 18 neighbors of the point (i, j, k) and the point itself, and wl is the weight with which the voltage of a particular neighbor grid point contributes to the Laplacian of the point (i, j, k). The weights wl were computed based on the local conductivity tensor Dij and the local boundary situation in the point (i, j, k): a neighbor l that lies outside the heart geometry receives a weight wl=0. These weights were precomputed and stored as an efficient means to evaluate the Laplacian and automatically handle boundary conditions during the simulations.
Normal Activation Sequence
Before using our model to study ventricular fibrillation, we first checked the validity of our model by simulating the normal activation sequence of the ventricles and comparing this with the classical data of Durrer et al.35
To simulate the normal ventricular activation sequence, we mimic activation by the Purkinje system by directly stimulating the endocardial sites of earliest activation as measured by Durrer.35 Figure 2 shows activation time isochrones in different cross-sections of the ventricles. Positions of the cross-sections are chosen at similar locations as the cross-sections shown in figures 1 and 2
in the report by Durrer. Our simulated activation sequence shows a good agreement with the data from Durrer. Earliest activation occurs high on the left anterior paraseptal wall (Figure 2C), central on the left surface of the septum (Figure 2B and 2D), low on the left posterior paraseptal wall (Figure 2A), and on the low and central part of the right surface of the septum (Figure 2A and 2D). Latest activation occurs in the posterobasal part of the left ventricle (Figure 2C).
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We find a total activation time of the ventricles of 95 ms, consistent with normal healthy QRS durations.
Induction of Ventricular Fibrillation
Scroll waves were initiated using a S1-S2 stimulus protocol, with the S2 stimulus applied in the refractory tail of the S1 wave, leading to partial propagation block and spiral wave formation. Stimulus currents were applied at twice the diastolic threshold. We used different parameter settings of the electrophysiological model such that always an APD restitution slope considerably steeper than 1 was obtained (see the Table for the different parameter settings). Thus it was ensured that action potential alternans instability leading to spiral breakup and fibrillation like excitation dynamics would occur.
Electrograms
Electrograms were obtained by assuming an infinite volume conductor and calculating the dipole source density of the membrane potential Vm in all voxel points of the ventricular myocardium, using the following equation36:
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where V is the domain of integration (ventricular volume), and r is the vector from each point in the tissue to the recording electrode. The recording electrode was placed 10 cm from the center of the ventricles in the transverse plane.
Quantification of the Complexity of Wave Patterns: Number of Filaments and Phase Singularities
Quantifying the complexity of wave patterns arising during VF can be done by determining the number of rotors driving the excitation dynamics.2,6,37–41 In the thick-walled ventricles, rotors are 3D scroll waves that rotate around a line of PSs called filaments. When such a filament intersects with the surface of the heart, a single PS occurs on the surface. In clinical and experimental studies, only detailed mappings of the surface of the heart can be performed. Therefore, only the number of epicardial (or endocardial) PSs can be determined. In simulation studies, both the number of filaments and the number of epicardial PSs can be determined.
Single voxels of scroll wave filaments were detected using an algorithm proposed by Fenton and Karma.42 The algorithm finds the singular point of a 2D spiral wave by intersecting an isopotential line (in our case –60 mV) with the dV/dt=0 line. The algorithm was applied in all 3 directions. Intersection points thus found were stored as voxel data.
Individual filaments were detected by iteratively joining neighboring filament voxels and giving all voxels belonging to a single filament a unique identifier. To determine the number of epicardial PSs, scroll wave filaments were intersected with the epicardial surface. Filaments and PSs were determined at 10-ms intervals.
Summarizing the Dynamics of Wave Patterns: Tracking Filaments in Time
A good way to concisely describe the dynamics of the complex VF wave patterns is by tracking filaments (or wavefronts) in time.37,39,40
The temporal dynamics of filaments can be summarized by a number of events: birth, the breakup of a scroll wave into multiple scroll waves; death, the disappearance of a scroll wave because it runs into a boundary or into unrecovered tissue; bifurcation, the splitting of a filament into 2 filaments; and amalgamation, the merging of 2 filaments into 1 filament as they bump into each other and merge.
We traced filaments in time by determining the overlap between filaments found at 2 consecutive time steps, similar to the approach followed in the report by Clayton and Holden.40 If a filament present at time t+1 does not overlap with any filament at time t, then a birth event has occurred. If a filament present at time t does not overlap with any filament at time t+1, then the filament has died. If a filament at time t overlaps with 2 filaments at time t+1, then a bifurcation has occurred. If 2 filaments at time t overlap with 1 filament at time t+1, then an amalgamation has occurred. Filaments at time t that overlap with 1 filament at time t+1 simply continued.
If a new filament is born, it gets a unique new identity number. If a filament dies, this identity number is not reused. If a filament bifurcates into 2 filaments, the largest of the 2 new filaments keeps the identity number of the old filament; the smaller one gets a new number. If 2 filaments amalgamate into a single filament, the new single filament keeps the number of the longest existing of the 2 previous filaments.
We determined time of birth, death, bifurcation, and amalgamation, lifespan, and ultimate filament to which a filament can be traced back through bifurcation events, for all filaments. Because of the large total number of filaments (
500) and bifurcation and amalgamation events (500) during an entire episode of simulated VF, a directed graph displaying all filaments and all events becomes very tangled and hard to interpret. Therefore, we decided to plot for all filaments only their appearance (through either birth or bifurcation) and disappearance (through death or amalgamation) in time, without linking this to other filaments (in case they bifurcated from or amalgamated with another filament). Instead, we use different colors to display clusters of filaments that all descended from the same initial filament through bifurcation events. Ancestry trees showing the sequence of bifurcation events through which filaments have arisen are constructed for the largest filament clusters.
Implementation
All simulations were coded in C++ and MPI and were run on 20 processors of a Beowulf cluster consisting of 10 Dell 650 Precision Workstations (Dual Intel Xeon, 2.66 GHz). With this approach, simulating 1 second of wave propagation in the ventricles took approximately 12 hours of computational time. Ventricular geometry, wave patterns and scroll wave filaments were visualized using the marching cubes algorithm for isosurface detection in voxel data and OpenGL for isosurface rendering.
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Ventricular Fibrillation
We performed several simulations of VF by using a S1S2 protocol to initiate spiral waves in either the free wall of the left ventricle, the free wall of the right ventricle or the anterior wall of the ventricles. We used the standard parameter settings of our model (see the Table).
Figure 3 shows snapshots of consecutive wave patterns for the VF simulation in which a spiral wave was initiated in the left ventricle. Figure 3A shows the initial spiral wave pattern resulting from the S1S2 protocol. In Figure 3B, we show the occurrence of the first wave break shortly after the spiral wave was initialized. Figure 3C shows the wave pattern that has developed after 4 seconds. The ECG corresponding to these VF dynamics (Figure 3D) resembles clinically recorded ECGs of VF and has a dominant frequency of 4.8 Hz, similar to clinically reported frequencies.11–13
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Before performing a full, 3D analysis of simulated human VF wave patterns, we first compared simulated VF surface wave patterns with clinically recorded surface wave patterns.
Comparison With Clinical Data
Clinical Data of Nanthakumar et al
Nanthakumar et al12 were among the first to perform detailed mappings of wave patterns during in vivo human VF. They mapped epicardial activation patterns during 2-second intervals of VF in a 20 cm2 area on the anterior and lateral free wall of the left ventricle, with a spatial resolution of 2 mm. Nanthakumar et al performed a detailed analysis of wavefront organization and dynamics. Their main conclusions were that human VF is characterized by the presence of large wavefronts that repeatedly follow the same pathways. In addition, they observed breakthrough, fractionation, and collision events and transient occurrences of reentry. To allow comparison between their clinical findings and our VF simulations, we analyzed our simulated wavefront patterns in an epicardial surface area of similar size and position.
In Figure 4, we show an example of a recurrent breakthrough pattern. A single breakthrough entered the recording area at the right producing a wavefront that sweeps the entire recording area. This propagation pattern repeated itself 5 times before changing into another wave pattern. The repeating breakthrough pattern indicates the temporary presence of an intramural scroll wave. This wave pattern is very similar to the breakthrough wave pattern shown in figure 3 of the report by Nanthakumar et al.12
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Figure 5 shows an example of a wavefront fractionating into 2 separate wavefronts, leading to the formation of 2 spiral waves that subsequently collide and annihilate each other, similar to the sequence of breakup and collision events shown in figure 5, top 2 rows, in the report by Nanthakumar et al.12 This figure shows that our simulated VF wave patterns are qualitatively similar to the wave pattern characteristics reported by Nanthakumar et al.
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We also compared several quantitative characteristics of human VF reported by Nanthakumar et al with our simulation results. We found in our simulations that, on average, similar pathways were followed 7 times before wave patterns changed, close to the repeatability number of 8.3 reported by Nanthakumar et al. We observed reentry to be present 20% of the time, which is a factor of 2 to 3 higher than the value reported by Nanthakumar et al. However, this difference can be explained easily by the fact that their algorithm detects only reentry circuits completing at least 1 full cycle of reentry,38 whereas we observed reentries completing as little as one-eighth part of a cycle. Furthermore, we observed reentries close to the edge of the recording area. Such reentries could not be detected by the algorithm used by Nanthakumar et al.12 After correction for these differences, we observed similar frequencies of reentry occurrence as Nanthakumar et al.
Clinical Data of Nash et al
Recently, Nash et al13 performed mappings of wave patterns during in vivo human VF on the entire ventricular epicardial surface, with a spatial resolution of 10 mm. They mapped VF activation patterns in a total of 10 patients in 20- to 40-second VF episodes and analyzed both wavefront and PS numbers and dynamics. Their main conclusions were that human VF is characterized by the presence of a few large coherent wavefronts and a small number of epicardial rotors. One or more epicardial rotors were present at all times during VF. To allow comparison between their findings and our simulation results, we analyzed our VF episodes in terms of epicardial wavefront patterns and PSs.
Figure 6 shows an example of the presence of both organized and less organized epicardial wave patterns during the same episode of simulated VF. Figure 6A shows a fairly organized wave pattern with only 3 epicardial PSs present occurring at 1680 ms after the onset of VF. Figure 6B shows a far less organized wave pattern with a total of 11 PSs occurring at 2720 ms after the onset of VF. A similar dynamical interchange of organized and less organized wave patterns can be seen in figure 7 of the report by Nash et al.13
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Figure 7 shows an example of a persistent epicardial rotor that was present from 3940 until 5040 ms after the onset of VF. In the snapshots, we can also see the occurrence of wave breaks, leading to the presence of multiple much shorter-lived PSs. This wave pattern is also very similar to wave patterns observed by Nash et al (see figure 8A of Nash et al13). From these Figures, it follows that human VF is relatively organized and is characterized by a few large epicardial wavefronts and few PSs, with some PSs being present a longer period, whereas most PSs are very short lived. These findings are qualitatively similar to the VF characteristics described by Nash et al.
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For a quantitative comparison with the data from Nash et al, we computed the number of epicardial PSs. Figure 8A shows PS numbers as a function of time for the 3 episodes of simulated VF. In all 3 episodes, PS numbers increased during an initial transient of 1.5 second, and than fluctuated around an average of 8, 8, and 5 for initial spiral waves started in the left ventricle, right ventricle, or anterior of the ventricles, respectively. These numbers agree with the clinically reported numbers of epicardial PSs by Nash et al.13 In Figure 8B, we show a histogram of the number of epicardial rotors present in each frame tallied over the 3 different VF simulations. Figure 8 shows that very low, but especially very high, numbers of PSs occur rarely and that PS numbers of approximately 5 to 7 occur most frequently, similar to what Nash et al reported (see figure 8C in the report by Nash et al13).
Three-Dimensional Wave Patterns
From the previous 2 sections, we conclude that our episodes of simulated VF closely resemble clinically recorded VF in terms of ECG pattern, ECG frequency, type and repeatability of surface wave patterns, and occurrence of epicardially observable reentries. In contrast to the clinical experiments, in our simulations we can also observe and analyze the full 3D ventricular wave patterns.
In Figure 9A, we show a snapshot of a full 3D wavefront pattern with 3D scroll wave filaments during simulated VF. The figure illustrates how a scroll wave with a transmural filament (o) gives rise to a single epicardial surface reentry, how a scroll wave with a U-shaped filament corresponds to either 2 (*) or 0 (#) epicardial PSs, and how a ring-shaped scroll wave filament (&) gives rise to 0 epicardial PSs. This demonstrates that not all 3D reentries (filaments) give rise to surface reentries (epicardial PSs) and hence how observing only (part of) the epicardial surface is likely to lead to an underestimation of the number of rotors driving VF.
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Figure 9B shows the number of filaments as a function of time for 3 episodes of simulated VF. We see that after an initial transient filament, numbers fluctuate around an average of 12, 11, and 8 for initial spiral waves started in the left ventricle, right ventricle, or anterior of the ventricles, respectively. From a comparison with Figure 8A, it follows that the total number of rotors (number of filaments) is approximately a factor of 1.3 to 1.4 higher than the number of epicardially manifested rotors (epicardial PSs).
In addition to determining the number of rotors present at any given time point, we also determined the lifespan of individual rotors. Figure 10 shows filament lifespan histograms for 3 different VF simulations. We can see that for all 3 episodes of VF, many filaments (25%) have a lifespan of less than 50 ms, most filaments have lifespans between 50 and 200 ms (70%), and some filaments have lifespans between 200 and 1000 ms. Our filament lifespan distributions are very similar to the PS lifespan distributions reported by Kay et al37 and distributions of the number of reentry cycles per reentry found by Valderrabano et al43 and Rogers et al38 (all in pig hearts), which also showed that most rotors are short lived and only a few rotors are present for a large part of the VF episode.
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Finally, we analyzed how rotors were created and destroyed over time through birth, bifurcation, death, and amalgamation events for the entire episodes of simulated VF. Figure 11 shows the history of filaments present during 3 episodes of simulated VF. Horizontal lines indicate individual filaments. Lines start at the time a filament arises (through birth or bifurcation from another filament) and lines end at the time a filament disappears (through death or amalgamation with another filament). Short lines thus correspond to short-lived filaments and long lines correspond to long-lived filaments. New filaments get assigned a unique identity number (numbers are not reused once the old filament has disappeared). As a consequence, identity numbers of filaments being present at a certain time point increase over the course of time. With color, we indicate filaments belonging to the same cluster. We clustered filaments that descended through bifurcation from the same initial filament, ignoring clusters with less than 5 filaments. Filaments not belonging to a cluster (because they arose by birth rather than bifurcation) or belonging to a small cluster are drawn in black.
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In Figure 11, we can see that over time, new filaments are steadily formed, whereas old filaments are continuously disappearing. From the figure, it is also clear that most filaments are present for only a short amount of time (many short lines), whereas only a few filaments are present during a large part of the episode (few long lines). We can also see that during VF, only a few larger filament clusters are present. In the 3 VF episodes, we found 10, 10, and 5 clusters, for the initial spiral started in the left, right, or anterior ventricle. These clusters accounted for 29%, 31%, and 22% of the total number of filaments, respectively. The largest cluster contained 109, 63, and 58 filaments for these 3 VF episodes, representing 18%, 13%, and 15% of the total number of filaments. In the insets of Figure 11, we show the ancestry trees for the 1 or 2 largest filament clusters detected during the VF episode. The horizontal lines indicate all the filaments belonging to the same cluster, the vertical lines link a newly arising filament to an older filament it has just bifurcated from. We can clearly see that at the core of these large filament clusters is a single long lived scroll wave filament from which during its long lifespan numerous other filaments arise through bifurcation events.
For the episode of VF in which the initial spiral wave was started in the left ventricle, we detected a total of 609 filaments, 252 births, 331 deaths, 357 bifurcations, and 278 amalgamations. Adding birth and bifurcation events, a total of 609 events occurred in which new filaments were formed. Similarly, adding death and amalgamation events, a total of 609 events occurred in which filaments disappeared. For the other 2 episodes of VF, numbers of filaments and events were of similar magnitude. Total number of filament creation events was balanced by an equal number of filament destruction events for each of the three VF episodes. So, similar to the findings by Clayton and Holden,44 our simulated VF dynamics are characterized by a finely tuned balance of rotor formation and destruction.
Dependence of VF Organization on Conditions
Overall, we find that VF in the human heart is organized by a much smaller number of rotors than in animal hearts of comparable size. An important question thus is which factors determine the number of rotors driving VF. To answer this question, we investigated the influence of tissue anisotropy, excitability, maximum APD restitution slope, and minimum APD on the number of reentries present during VF.
Dependence on Anisotropy Ratio
Thus far, we assumed an anisotropy ratio of 1:4 between transversal and longitudinal conductivity.
However, reported ratios between longitudinal and transversal conduction velocities vary. Here we performed simulations with anisotropy ratios of 1:2, 1:4, and 1:7 to study the influence of anisotropy on the complexity of wave patterns during VF. Model parameter settings were the same as in the previous sections. Spiral waves were initiated in the left ventricle.
For all anisotropy ratios, spiral breakup and subsequent fibrillation-like dynamics occurred. Figure 12A through 12C shows snapshots of wave patterns during VF, and Figure 12D through 12F shows snapshots of the scroll wave filaments driving VF for the different anisotropy ratios. We can see that the complexity of the wave patterns and the number of filaments driving VF increase with increasing anisotropy ratio.
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In Figure 13A and 3C, we show the number of filaments and PSs as a function of time for the different anisotropy ratios. We see that after an initial transient, average filament numbers approach 5, 12, and 16, and average PS numbers approach 4, 8, and 12 for anisotropy ratios 1:2, 1:4, 1:7, respectively. In all 3 cases, ratios between total number of rotors (filaments) and epicardially manifested rotors (PSs) were around 1.3 to 1.4.
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An increase in anisotropy ratio effectively increases ventricular volume. In Figure 13B and 13D, we show the number of filaments and PSs for the different anisotropy ratios normalized relative to the effective ventricular volume resulting from the 1:4 anisotropy ratio. We see very similar normalized filament and PS numbers, indicating that the increase in number of reentrant sources driving VF as anisotropy ratio increases is entirely caused by an increase in effective tissue volume.
Dependence on Excitability
Another factor that may be subject to some variation is tissue excitability. We investigated the effect of excitability on wave pattern complexity during VF by increasing the maximum conductance of the fast sodium current.
Figure 14A and 14B shows the wave pattern and scroll wave filaments for an episode of fibrillation when conductance of the fast sodium current is increased by a factor of 3 (parameter setting increased excitability in the Table). We can see that wave pattern complexity and number of filaments are somewhat larger than for the standard parameter setting (compare with Figures 3 and 9
A). Figure 14C shows the time dynamics of the number of filaments and epicardially manifested rotors driving VF. After an initial transient, filament numbers approach an average of 12, and PS numbers an average of 8. Compared with Figures 8A and 9B, we can see that increasing GNa by a factor of 3 has no significant effect on the number of rotors driving VF. Figure 14D shows the ECG of this episode of VF, which has a dominant frequency of 5.2Hz.
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Dependence on APD Restitution, Maximum Slope
Maximum slope of the APD restitution curve has been found to differ between individuals and within individuals45 and can clearly differ between species. Therefore, we investigated the effect of increasing restitution slope on VF complexity.
Figure 15A shows 2 APD restitution curves, 1 for the standard parameter setting used thus far and 1 for an alternative parameter setting that results in a higher maximum APD (386 versus 329 ms), a similar minimum APD (100 versus 110 ms), and a significantly higher maximum restitution slope (2.8 versus 1.8) (see the Table for parameter settings).
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Figure 15B and 15C shows snapshots of wave patterns and scroll wave filaments arising after spiral breakup for the alternative parameter setting. Wave patterns appear more complex and filament numbers are larger than for the standard parameter setting (compare with Figures 3 and 9A). Figure 15D shows the number of filaments and epicardially manifested PS as a function of time. We can see that a steeper restitution slope leads to a 2- to 2.5-fold higher number of total rotors (average 24) and epicardial rotors (average 16) (compare with Figures 8A and 9B). Figure 15E shows the ECG of this simulated episode of VF, which has a dominant frequency of 4.8 Hz, comparable to that of the standard parameter setting.
Dependence on APD Restitution, Minimum APD
Another electrophysiological characteristic that may be subject to variation is minimum APD. Minimum APD is the shortest APD that can be reached during restitution protocols and fibrillation and is found to vary significantly between human and animal hearts (compare, for example, with previous reports23–25).
Figure 16A shows APD restitution curves for the standard parameter setting used thus far and for an alternative setting that results in a lower maximum APD (280 versus 329 ms), lower minimum APD (77 versus 110 ms), and similar maximum restitution slope (1.8) (see the Table for parameter settings).
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Figure 16B and 16C shows snapshots of the wave pattern and scroll wave filaments arising after spiral breakup for the alternative parameter setting. We can see that the wave pattern consists of more and smaller waves (compare with Figure 3) and is organized by a larger number of filaments (compare with Figure 9A) than for the standard parameter settings. In Figure 16D, we show the time dynamics of the number of rotors (filaments) and number of epicardially manifested rotors (PSs). We can see that after an initial increase, rotor numbers approach an average of 45 and PS numbers approach an average of 35, which is a factor of 4 to 5 higher than for the standard parameter setting (compare with Figures 8A and 9B). Figure 16E shows the ECG of this simulated episode of VF. We can see that the ECG is more irregular than for the standard parameter setting (compare with Figure 3D). The ECG has a dominant frequency of 6.7 Hz, which is significantly higher than the frequencies found for the standard parameter setting.
We thus find that of the different factors studied, minimum APD has the largest influence on the number of rotors underlying VF.
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Discussion |
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TopAbstractIntroductionMaterials and MethodsResultsDiscussionReferences |
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Our understanding of VF in the human heart is still largely based on experimental studies using animal hearts. These studies have shown that the turbulent excitation pattern typical of VF is organized by multiple reentrant sources. Furthermore, these studies suggest that the number of rotors underlying VF increases with heart size. In the pig and dog heart, which have a size comparable to that of the human heart, VF is organized by approximately 50 reentrant sources.
Recent clinical measurements reporting a few large wavefronts and a small number of epicardial PSs12,13,18 suggest that VF in the human heart could be much more organized than VF in large animal hearts. However, clinical and experimental measurements of VF are only made on the surface of the heart, leaving the possibility of larger numbers of rotors present inside the ventricular mass.
In this study, we used our detailed human ventricular model to study the wave organization during VF. Our model incorporates a detailed description of human ventricular anatomy, fiber direction anisotropy, and the electrophysiological behavior of human ventricular cells. We validated our model by simulating a normal ventricular activation sequence and comparing this with the classic data by Durrer et al.35 We then simulated VF by using a S1S2 protocol to initiate a spiral wave in the ventricles. We used a parameter setting that corresponds to a steep APD restitution curve (maximum slope 1.8) and results in breakup of the initial spiral wave and VF-like dynamics.
First, we performed an extensive comparison of our VF simulations with the clinical data from Nanthakumar et al12 and Nash et al.13 We showed that our simulated episodes of VF agree qualitatively with clinical VF in terms of ECG morphology and frequency, type and repeatability of surface wave patterns, and number of epicardially observable rotors. Following this, we studied the full 3D organization of simulated human VF. We illustrated how observing only (part of) the epicardial surface rather than the entire ventricular mass leads to an underestimation of the occurrence of reentry during VF. We found that the total number of rotors present during fibrillation lies at approximately 10 and is a factor of 1.3 to 1.4 higher than the number of epicardially manifested rotors.
We analyzed the history of filaments during episodes of VF, how they arise through birth and bifurcation events and disappear through death and amalgamation events, and the length of their lifespans. Similar to experimental observations on epicardially manifested rotors in animal hearts,37,38,43,46 we found that most rotors are very short lived, whereas only one or a few long-lived rotors are present during a single episode of VF. We have shown that these longer-lived rotors are at the core of large clusters of filaments that all have arisen from the same initial filament through bifurcation events.
Our 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 as well.
Why does VF in the human heart have a much simpler organization than VF in the dog and pig heart? To answer this question, we investigated the influence of a number of electrophysiological properties of cardiac tissue that may vary between human and animal hearts. Characteristics that were considered were tissue anisotropy ratio, tissue excitability, maximum APD restitution slope, and minimum APD. We found that VF wave pattern complexity and number of rotors were dependent on all factors studied. An increase in anisotropy ratio, excitability, and restitution slope and a decrease in minimum APD all led to more complex wave patterns and higher rotor numbers. For tissue anisotropy, the increase in rotor numbers could be explained by the increase in effective tissue mass. For tissue excitability and restitution slope, the increased wave pattern complexity probably resulted from an increase in the dynamical instability, leading to wave break formation. For minimum APD, the higher number of rotors was most likely caused by a shorter wave length, allowing a larger number of rotors to fit in the same tissue size.
We found that anisotropy ratio, excitability and restitution slope, when varied within the physiological range, could only account for a maximum increase of a factor of around 2 in rotor numbers. Decreasing minimum APD resulted in a factor of 5 more rotors and a significantly higher VF frequency, similar to rotor numbers and VF frequencies found in pig and dog hearts.5,6,14,15 Interestingly, minimum APD in the pig and dog heart is significantly lower than in the human heart (140 to 200 ms for human,23 70 to 110 ms for dog,25 and 90 to 110 ms24 for pig). Therefore, we propose that it is the difference in minimum APD that causes the difference in spatial complexity, number of rotors, and frequency between human VF and dog and pig VF.
Our findings may have important consequences for the treatment and prevention of human VF. For example, in simulation studies, VF that is driven by a smaller number of rotors requires less energy for successful defibrillation.8,9 Likewise, drugs aimed at increasing wave length or meander of reentrant sources to decrease the number of sources could be more promising to treat human VF than would be expected based on dog and pig heart experiments. Furthermore, our results suggest that minimum APD is an important determinant of VF wave pattern complexity. Increasing minimum APD leads to less reentrant sources and more coherent wave patterns. Minimum APD may thus be a potential new target for pharmacological interventions.
Limitations
Although our simulation model incorporates a detailed description of human ventricular anatomy, fiber direction anisotropy, and cellular electrophysiology, it does not include all characteristics of human ventricular anatomy and function.
Laminar Sheets
Cardiac muscle fibers are organized into laminar tissue sheets separated by connective tissue. As a consequence, conductivity transversal to fibers but within sheets is faster than conductivity transversal to both the fibers and tissue sheets (orthotropic anisotropy).47–49 In our current model, these 2 transversal conductivities are assumed to be equal. The effect of orthotropic anisotropy on human VF organization thus remains an important topic for future research.
We feel that adequate incorporation of laminar sheets into cardiac models is not a trivial subject. Before one can do this, 2 important issues need to be addressed. (1) Is a continuous description of cardiac tissue suited for describing sheet structure, considering that sheets are separated by discrete nonconducting cleavage planes and, as was recently shown, that orientation of the cleavage planes is not uniquely defined by transmural location50? (2) How should we describe the laminar structure of the heart in a general (nonindividual specific) sense considering the reported variation among individual hearts of the same species50? Some important initial steps in solving these issues were taken in a report by Hooks et al,49 in which a continuous versus discrete approach for modeling laminar structure were compared. However, this study was restricted to small rectangular tissue blocks, and the model simulation results were not compared with experimental wave propagation data.
We therefore think that the appropriate implementation of laminar sheet structure in cardiac models and an analysis of their possible effects on wave propagation during VF should be the subject of a separate study, results of which should be compared with the results of our present simulations.
Heterogeneity
The current ventricular model consists of identical cells. However, in human and animal hearts, different types of electrophysiological heterogeneities have been reported, such as the base–apex gradient, the transmural epicardial–endocardial gradient, and the left–right ventricular gradient.51–54 Modeling studies have shown that transmural electrophysiological gradients may enhance spiral wave breakup,55 whereas planar gradients may enhance spiral wave drift.56 Thus, heterogeneities may play a role in the initiation of VF. It remains to be investigated whether the presence of heterogeneity affects the number of re-entrant sources driving VF.
Purkinje System
The ventricular model used in this study does not include a Purkinje system. However, clinical and simulation studies suggest that the Purkinje network may play an important role in arrhythmogenesis, both as a source of premature ectopic activations57 and by offering extra routes for the propagating excitation wave.58,59 Whether the presence of the Purkinje system also influences the number and dynamics of reentrant sources driving VF still needs to be investigated.
Disease State
VF occurs predominantly in hearts that are abnormal, anatomically, electrophysiologically, or both. However, our human ventricular model represents a normal healthy human heart. The particular disease or condition of a patient, for example, ischemic heart disease, cardiomyopathy, heart failure, Brugada syndrome, or long or short QT syndrome, may affect both the mechanism by which VF arises and the spatiotemporal complexity of VF.
Note that despite these limitations, we find very similar ECG morphology, ECG frequency, surface activation patterns, and number of epicardial PSs during simulated VF as compared with clinically recorded VF.
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Acknowledgments |
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We are grateful to Dr P. A. Helm and Dr R. L. Winslow at the Center for Cardiovascular Bioinformatics and Modeling of The Johns Hopkins University and Dr. E. R. McVeigh at the National Institutes of Health for providing the adult human heart DTMRI fiber direction data. We thank Dr P. S. Jouk and Dr Y. Usson from the Department of Genetics, Grenoble Teaching Hospital, Grenoble, France, and from the Equipe Reconnaissance des Formes et Microscopie Quantitative, Laboratoire TIMC, Grenoble, France, for providing the infant human heart microscopy fiber direction data. We thank Dr R. H. Clayton for helpful suggestions regarding this manuscript and to R. H. Keldermann for help with the construction of the filament ancestry figures.
Sources of Funding
K.H.W.J.T.T. was supported by the Research Council for Physical Sciences of the Netherlands Organization for Scientific Research.
Disclosures
None.
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Footnotes |
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Original received February 15, 2007; revision received May 2, 2007; accepted May 23, 2007.
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References |
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