Lessons from computer simulations of ablation of atrial fibrillation

Abstract

This paper reviews the simulations of catheter ablation in computer models of the atria, from the first attempts to the most recent anatomical models. It describes how postulated substrates of atrial fibrillation can be incorporated into mathematical models, how modelling studies can be designed to test ablation strategies, what their current trade‐offs and limitations are, and what clinically relevant lessons can be learnt from these simulations. Drawing a parallel between clinical and modelling studies, six ablation targets are considered: pulmonary vein isolation, linear ablation, ectopic foci, complex fractionated atrial electrogram, rotors and ganglionated plexi. The examples presented for each ablation target illustrate a major advantage of computer models, the ability to identify why a therapy is successful or not in a given atrial fibrillation substrate. The integration of pathophysiological data to create detailed models of arrhythmogenic substrates is expected to solidify the understanding of ablation mechanisms and to provide theoretical arguments supporting substrate‐specific ablation strategies.

Abbreviations

ACh

acetylcholine

AF

atrial fibrillation

CFAE

complex fractionated atrial electrogram

CT

computed tomography

CV

conduction velocity

ECG

electrocardiogram

MRI

magnetic resonance imaging

PVI

pulmonary vein isolation

Introduction

Atrial fibrillation (AF) is a major cardiac arrhythmia in terms of prevalence and cost of health care. Clinical AF classification is based on patient history (Levy et al. 2003). AF is marked by an insidious progression from its paroxysmal form, which appears to be driven from the pulmonary veno‐atrial junctions and may occur in a structurally normal heart, to persistent and permanent AF characterised by electrical and structural remodelling, including atrial dilatation and fibrosis. The pathophysiological mechanisms of persistent and permanent AF are highly complex and involve pro‐arrhythmogenic processes on multiple temporal and spatial scales (notably caused by successive AF episodes) inducing alterations to the substrate and the triggers (Andrade et al. 2014).

Catheter ablation is a therapy of choice for patients with AF refractory to anti‐arrhythmic drug treatment (Calkins et al. 2012). This therapy consists in creating lesions with a catheter using radiofrequency energy or cryoablation, thus forming barriers for impulse propagation. Ablations may isolate triggers, target structurally remodelled regions or trap fibrillation waves in a maze. Current AF management reflects the clinical history of AF. Pulmonary vein isolation (PVI) is the cornerstone of most strategies. Effective in paroxysmal AF patients, this approach was found to be insufficient to treat persistent AF, thus requiring further ablation targets (e.g. linear ablation, ectopic sources, fractionated electrograms, rotors or ganglionated plexi). However, due to conflicting outcomes and promising strategies that were less successful in large multicentre studies, there is no consensus on what to ablate after PVI in persistent AF patients and when to stop (Verma et al. 2015). A rational, mechanistic approach is needed to better optimise ablation strategy.

Computer models of atrial electrophysiology have been developed to contribute to the understanding of AF mechanisms, the design of diagnosis techniques, and the optimisation of therapeutic approaches (Jacquemet et al. 2008; Dossel et al. 2012; Virag et al. 2012; Trayanova, 2014; Zhao et al. 2015). The strengths of these models are the following: (1) they provide a theoretical basis supporting the design of clinical protocols; (2) hypotheses can be tested in a fully controllable environment (access to all variables everywhere); (3) different effects can be isolated or discriminated (e.g. imperfect ablation vs. inadequate ablation site); (4) the efficacy of many therapies can be assessed in the same AF model. As a result, modelling is emerging as a complementary approach to animal experiments and clinical trials to help design more effective therapies (Winslow et al. 2012).

While recent work emphasises the construction of patient‐specific anatomical models, this paper concentrates on the design of modelling studies to explore the mechanisms of AF ablation. The different electrophysiological targets for ablation are presented and their implementation in computer models is discussed through examples of recently developed models. The differences between clinical and modelling studies are highlighted, as well as their strengths and limitations.

Targets for ablation

This section outlines the mechanistic basis and clinical evidences of the ablation approaches that aim to be simulated. Complete discussions about the procedures are found in clinical reviews (Calkins et al. 2012; Magnani et al. 2015).

Pulmonary vein isolation (PVI)

Triggers that initiate AF have been identified in the pulmonary veins (Haissaguerre et al. 1998). Electric isolation of the pulmonary veins by creating ablation lines encircling the veins was shown to be effective at preventing AF recurrence in paroxysmal AF patients (Ganesan et al. 2013). Success rates were lower in persistent or permanent AF patients (Lin et al. 2013). Incomplete or non‐transmural isolation may lead to AF recurrence and require another intervention. PVI is the basis of most strategies and may be supplemented by one of the techniques described below used as adjuvants, particularly in patients with persistent AF.

Linear ablation

Usually combined with PVI, this approach creates a predefined set of additional linear lesions (Calkins et al. 2012), typically a roof line and a mitral isthmus line, to block the pathways for anatomical reentries and form a maze in which wavelets are trapped, which may cause AF termination (Ernst et al. 2003). The extreme example of such an approach is the Cox Maze III (Cox et al. 1991). Not recommended for paroxysmal AF (Calkins et al. 2012), adjuvant linear ablation has been included in stepwise approaches (O'Neill et al. 2009), but remains controversial for persistent AF (Verma et al. 2015).

Ectopic foci

Non‐pulmonary vein triggers have been identified, for instance in the left posterior wall and near the venae cavae (Lee et al. 2005; Miyazaki et al. 2014). A stepwise ablation strategy may include successively eliminating these focal sources (Calkins et al. 2012). This approach has been successful in a sub‐group of paroxysmal AF patients (Lin et al. 2003).

Complex fractionated atrial electrograms (CFAEs)

Electrical mapping during AF has revealed regions where atrial electrograms have multiple high‐frequency low voltage deflections with very short cycle lengths (Konings et al. 1997). It has been hypothesised that these CFAEs identify sites of AF reentry and provide targets for catheter ablation (Nademanee et al. 2004). Others have argued that CFAEs are a signature of structural substrates that contribute to the progression from paroxysmal to permanent AF (Stiles et al. 2009). Despite promising outcomes reported for CFAE‐guided ablation of high risk AF patients (Nademanee et al. 2008), multicentre clinical trials have not demonstrated any improvement in sustained reversal of persistent AF when this approach is used in addition to PVI (Li et al. 2011; Verma et al. 2015).

Rotors

Instantaneous electroanatomic maps acquired with intracardiac basket catheters (Narayan et al. 2012) and from body surface potential recordings (Haissaguerre et al. 2014) have been used to identify the presence of rotors (defined as stable reentry) in the atria during AF. The location of these rotors tended to be consistent over time, although a wide range of rotor lifespan has been reported, from a few cycles (Cuculich et al. 2010; Haissaguerre et al. 2014) to thousands (Swarup et al. 2014). The location of rotors is believed to coincide with fibrotic regions that provide stable pathways for reentry. Late gadolinium‐enhanced magnetic resonance imaging (MRI) provides the technology to assess fibrotic structural remodelling non‐invasively (McGann et al. 2014). Narayan et al. (2014) showed that ablation of rotor cores markedly reduced long‐term recurrence of AF in a group of patients, most with persistent AF. However, a recent multicentre study failed to reproduce these positive results and advocated randomised studies (Buch et al. 2015). While panoramic, low‐resolution electrical mapping and phase analysis identifies rotors during persistent AF, high‐resolution mapping provides evidence of a highly complex disorganised multiple‐wavelet activity under these circumstances (Lee et al. 2014). How these two conflicting views might be resolved remains a subject of controversy (Zaman & Peters, 2014).

Ganglionated plexi

AF is expected to also have a neurogenic origin (Coumel, 1994; Efimov & Fedorov, 2005). Evidence of the involvement of atrial ganglionated plexi in pulmonary vein ectopy supports the idea of ablating ganglionated plexi to treat AF (Lu et al. 2009; Lim et al. 2011). A retrospective meta‐analysis demonstrated the efficacy of this approach at preventing AF recurrence when combined with PVI (Zhou et al. 2011).

Modelling framework

This section presents the elements composing an atrial model as well as the challenges encountered during its construction.

Mathematical formulation

To simulate AF episodes and catheter ablation in a computer model, knowledge about atrial electrophysiology and anatomy is translated into mathematical equations. The bidomain model comprises two partial differential equations that describe the propagation of the electrical impulse within the cardiac muscle (Plonsey & Barr, 2000). The monodomain approximation decouples these two equations, resulting in faster computation that may be traded for finer spatial resolution; accuracy remains appropriate in the absence of external stimulation (Potse et al. 2006). The formulation relies on a model of cellular electrophysiology that integrates the contributions of different types of ion channels, ion exchangers and pumps and computes the resulting variations in ion concentrations, including the intracellular calcium dynamics. Coupling with neighbouring cells through gap junctions is incorporated as a diffusive process representing current flow in a continuous, homogenised intracellular medium. This coarse‐scale continuous representation of current flow enables the simulation of whole‐organ models but does not capture the effects of discontinuities at the microstructure level (Jacquemet & Henriquez, 2009; Hubbard & Henriquez, 2014).

Geometry

During AF, depolarisation wavelets exploit the complex atrial structure to propagate and create reentrant circuits. Although the basic properties of reentry in the presence of ablation lines can be studied in two‐dimensional geometries (Spector et al. 2012; Spector, 2013), realistic atrial size and topology are generally required. The duration of non‐sustained AF depends on the relation between tissue area and the number and lengths of the obstacles (veins, valves), which is very relevant to the investigation of ablation efficacy (Qu, 2006). Tremendous effort has been spent in streamlining the construction of patient‐specific geometries based on imaging modalities (Aslanidi et al. 2011; Gonzales et al. 2013; Krueger et al. 2013; Hwang et al. 2014; Trayanova, 2014). Some challenges persist. Spatial resolution (typically at most 0.5 mm for clinical MRI) is limited relative to atrial wall thickness. Some anatomical structures are barely visible on the images (rim of the valves, fibre bundles, discrete left–right connections). A solution is to register the geometry with a validated atlas atrial model (Neher et al. 2011).

Conduction properties

The conductivity tensor is determined by the local fibre orientation and the longitudinal and transverse conductivities. Fibre identification in the atria through high resolution imaging has been limited so far to animal models: Zhao et al. (2012) used structure tensor analysis of volume images acquired using serial block face imaging in the sheep; Aslanidi et al. (2013) used contrast‐enhanced micro‐CT in the dog. The problem is challenging due to the thinness of the atrial wall and possible transmural fibre rotation resulting from the superposition of multiple fibre bundles and dissociation of endo‐ and epicardial layers (Verheule et al. 2014; Hansen et al. 2015). For human atria, fibre orientation is currently either rule‐based, that is, interpolated from a set of lines generated from landmark points (Krueger et al. 2011), or atlas‐based, which consists in mapping a validated dataset of fibre orientation onto a newly acquired geometry (McDowell et al. 2012). These operations may be difficult or ill‐posed due to interpatient variability in anatomy, e.g. five pulmonary veins, absence of Bachmann's bundle (Platonov et al. 2002). Then, the longitudinal and transverse conductivities are adjusted to reproduce measured activation maps; different values are assigned in the fast conducting system such as Bachmann's bundle, terminal crest and pectinate muscles (Harrild & Henriquez, 2000). Clinical maps may be obtained using electrical mapping catheters. Spatial resolution is, however, limited; this enables the optimisation of conduction properties at the macroscale only. Additional validation may come from the comparison of body surface potential signals (Jacquemet et al. 2006). Some insights into local structural heterogeneity and fibrosis density may be inferred using late gadolinium‐enhanced MRI and hypotheses about the nature and the electrophysiological impact of fibrosis (McDowell et al. 2012).

Cellular properties

Detailed ionic models describing the membrane kinetics of human atrial cells have been developed and validated using cellular measurements and patch clamp data (Wilhelms et al. 2012). Variants of these models have been created to reproduce pathological conditions, notably electrical remodelling. Target ionic current responsible for regional changes in action potential morphology have been identified (Ramirez et al. 2000). The major challenge remains determining the spatial distribution of repolarisation properties in a patient and modifying the target ion channels accordingly. Repolarisation gradients play an important role in the occurrence of conduction blocks (Fareh et al. 1998). Clinically, effective refractory periods and possibly monophasic action potentials may be measured at selected locations. But hypotheses and extrapolations about local repolarisation properties remain unavoidable.

Modelling ablations

The lesions created by catheter ablation are intended to be non‐conductive. Ablation is therefore simulated by setting tissue conductivity to zero in the ablated zone, usually defined by a fixed diameter of 3 mm (ablation lines; Reumann et al. 2008) to 7 mm (single points; McDowell et al. 2015) around the ablation catheter. To simulate reconnection of ablation lines or imperfect ablation, a gap is introduced along the line (Dang et al. 2005) or the line is made non‐transmural (Reumann et al. 2008). The location of ablation lines may be obtained using a catheter localisation system or designed based on clinician's conceptual drawings.

Design of virtual ablation experiments

This section highlights the differences in the design of clinical and modelling studies of AF ablation. A summary is provided in Table 1 and an illustration in the Abstract figure.

Table 1.

Summary of the differences between clinical and modelling studies (examples of study design)

	Clinical study	Modelling study
Patient selection	Group of patients satisfying inclusion/exclusion criteria	Multiple variants of one or several models (modification of the substrate)
Indications for ablation	Drug‐resistant paroxysmal or persistent AF	AF episode of duration >10–30 s
Study design	Same therapy in many patients	Several therapies in the same model (or a few different models)
	Statistics over patients	Statistics over simulations in the same substrate
	The substrate is sometimes characterised	The substrate is specified
	AF mechanism is studied	AF mechanism is postulated and is an input to the model
Ablation procedure	Step‐wise ablation	Instantaneous application of all ablation lines
Procedure time	Up to a few hours	2–30 s of simulation
Side effects	Inflammation, risk of complications	None simulated
Criteria for AF termination	No AF after the procedure and until patient release	AF termination within 2–30 s
Criteria for AF prevention	No symptomatic AF episodes (48 h or several months of follow‐up)	All induction attempts failed (ectopic in the pulmonary vein)
Access to physiological data	ECG, electrical mapping	All variables everywhere all the time
Reproducibility	Limited by inter‐patient variability; AF episodes may vary in the same patient	Yes; variability can be controlled
Unique features	Real patient, real heart	Validation is critical
	Ablation is irreversible	Possibility to ‘undo’ an ablation line and try another one
	Risks for the patients, including mortality and morbidity	No human life at risk

AF, atrial fibrillation.

Patient selection

To test an ablation strategy clinically, the same ablation pattern is performed in a group of selected patients. Inclusion criteria typically include having drug‐resistant paroxysmal or persistent AF episodes for months. In a modelling study, one or a limited number of atrial models are used. Parameters can be changed within the physiological range and sensitivity analysis can be performed. Multiple therapies can be tested in the same model, even for identical AF episodes, thus enabling the determination of the optimal therapy for a given AF mechanism, instead of searching for the therapy that is effective in most patients. However, the statistics of simulated interventions may not be the same as the patient population.

Arrhythmogenic substrate

In a clinical study, the atrial substrate can be controlled through inclusion–exclusion criteria, mostly based on patient history, symptoms, concomitant heart disease, electrical signal interpretation and failure of other therapies. Advances in electrocardiogram (ECG) signal processing may eventually help non‐invasively identify AF aetiology and refine the selection of AF substrates (Bonizzi et al. 2015). In modelling studies, the AF substrate is an input to the model and has to be postulated a priori. These substrates, some of which are presented in the next section, reproduce atrial dilatation, electrical or structural remodelling and originate from hypotheses about AF mechanisms. Clean, well‐defined AF mechanisms can be specified, controlled, modified and combined. The results of modelling studies are therefore substrate specific.

AF episodes

In paroxysmal AF patients, AF episodes may occur spontaneously. In computer models, a set of episodes have to be generated to enable statistical analysis of ablation success rate. The first approach is to apply several initiation protocols, for example by varying the sites of programmed stimulation or ectopic foci (Virag et al. 2002; Vigmond et al. 2004; Gong et al. 2007; McDowell et al. 2015). The second approach consists in running a very long AF simulation (up to 10 min), extracting the state of the atrial tissue at regularly distributed time instants and running simulations of AF ablation from each these states (Dang et al. 2005). Finally, fibrillatory initial conditions may be created de novo from the locations of reentrant circuits (Herlin & Jacquemet, 2011; Matene & Jacquemet, 2012).

Ablation

Clinical ablation procedures may last up to a couple of hours depending on the complexity and possible complications (Calkins et al. 2012). In contrast, all ablation lines are generally applied simultaneously in computer models. Even when a stepwise approach is simulated, the time interval between each ablation step is in the order of a few seconds only. Since computational requirements impose restrictions on the duration of the simulations, often limited to 10–30 s, computer studies investigate in detail acute effects of ablation (or reconnection) in critical time windows where the mechanisms of AF maintenance or termination are in action.

Definition of success

The clinical objective of ablation is to terminate any ongoing AF episode and to prevent short‐term or long‐term AF recurrence. The therapy is considered successful when the patient is free of symptomatic AF episodes for a short period (e.g. a few months) or over the long term (years of follow‐up). The detection of AF recurrence may not be perfect as some asymptomatic episodes may remain unnoticed. In modelling studies, AF termination and prevention are studied separately. Ablation is considered successful if AF termination is observed within 2–30 s, depending on the studies. One may wonder whether the AF episode would have self‐terminated anyway, since it is difficult to establish that a computer model of AF is persistent, except in the case of a regular form of AF perpetuated by a stable rotor anchored around a functional or structural obstacle. In general, simulated AF is said to be persistent when it lasts over some predefined duration, 30 s for instance, due to computational time. To assess the prevention of AF recurrence by ablation, the mechanism of AF initiation has to be postulated. Modelling studies measure the vulnerability to a certain type of AF trigger, typically ectopic foci in the pulmonary veins. This is similar to clinical attempts to electrically induce AF to assess the vulnerability of the substrate after an intervention. A limitation is that failure to induce AF might result from too low a number of attempts. In the months following an ablation procedure, a patient may have many more atrial ectopic beats than one could possibly simulate in a model; unlikely but possible events may occur at some point.

Unique features

Simulated ablations take computational time, but never cost human life. Many ablation strategies (including emerging techniques not yet proven safe) can be compared in the same modelling study, while conducting a randomised clinical study with 10–20 groups would necessitate too many patients to reach statistical significance.

Lessons from simulations of ablation

This section presents, for each ablation target, modelling studies attempting to reproduce the ablation approach and the lessons that have been learnt from these simulations. The substrate properties of these models are recapitulated in Table 2 and the types of ablation patterns compared are listed in Fig. 1.

Table 2.

Atrial substrates in simulation studies of catheter ablation

Reference	Geometry	Cell model	Conduction	AF dynamics
Virag et al. (2001)	Monolayer, both atria, idealised geometry	Simplified ionic model	Uniform isotropic, reduced CV	Multiple wavelets
Dang et al. (2005); Ruchat et al. (2007 a,b,c); Rotter et al. (2007)	Monolayer, both atria, MRI‐derived geometry	Simplified ionic model	Uniform isotropic, reduced CV	Multiple wavelets
Haissaguerre et al. (2007)	3‐D, both atria, MRI‐derived geometry	Modified Courtemanche et al. (1998) model, repolarisation heterogeneity	Isotropic + fast conducting bundles	Focal AF
Reumann et al. (2008)	3‐D, both atria, visible female	Advanced cellular automaton	Anisotropic, reduced CV	Focal AF
Hwang et al. (2014)	Monolayer, 20 patient‐specific CT‐derived left atrial geometries	Modified Courtemanche et al. (1998) model	Uniform isotropic, reduced CV	Multiple wavelets
McDowell et al. (2015)	3‐D, 4 patient‐specific MRI‐derived left atrial geometries	Krummen et al. (2012) model + fibroblasts	Anisotropic, LGE‐MRI‐based structural remodelling	Rotors

AF, atrial fibrillation; CT, computed tomography; CV, conduction velocity; LGE, late gadolinium‐enhanced; MRI, magnetic resonance imaging.

Figure 1. Schematic recapitulation of the types of ablation patterns tested and compared in computer models .

The horizontal axis symbolises the evolution of the substrate from paroxysmal (left) to persistent/permanent AF (right) and the vertical axis corresponds to the type of ablation patterns with increasing complexity (from top to bottom). Each circle represents a family of tested patterns. The number of patterns in each family is written within the circle. The lines connecting the circles indicate that a statistical comparison between the patterns has been performed. The value of n is the number of AF episodes simulated per group. The number of patients is reported in the case of patient‐specific models. PVI: pulmonary vein isolation.

Pulmonary vein isolation (PVI)

Ectopic foci can be simulated by periodically injecting current in a group of cells (Gong et al. 2007). Reumann et al. (2008) investigated the prevention of AF recurrence by three variants of PVI in a model with ectopic foci. As expected, perfect isolation of the sources prevented AF initiation (up to 100% success rate), while non‐transmural lesion created exit points for wavelets. This illustrates the difficulty in achieving a modelling equivalent of a double‐blind study. The modeller necessarily knows the exact location of the foci and atrial wall thickness, and of course in the model no new source could emerge elsewhere later. The outcome depended a lot on how much anatomical information was used to design ablation lines (location and depth). The lesson is that clinical success might be improved if these data were available.

AF termination by PVI was assessed in multiple‐wavelet AF models simulated in a structurally uniform substrate with remodelled membrane properties (Virag et al. 2002; Gong et al. 2007; Kharche et al. 2007). Ionic channels targeted for remodelling were typically I _CaL, I _to, I _Kr and I _Kur (Courtemanche et al. 1999; Pandit et al. 2005). Regional or fibre bundle‐specific repolarisation heterogeneities may be introduced to provide additional pathways for functional reentry (Jacquemet et al. 2005; Seemann et al. 2006; Colman et al. 2013). In these models, PVI terminated AF in 25% of the cases in Hwang et al. (2014), 20–55% in Ruchat et al. (2007 c) and 28–50% in Rotter et al. (2007), with higher success when isolated regions were larger. AF prevention was not studied. These low success rates suggest that AF termination and prevention of recurrence should be investigated separately since independent mechanisms may be involved. This also questions the use of multiple‐wavelet AF as a paradigm for paroxysmal AF. Note that success rates might have been better if longer periods had been simulated (instead of 3.5–30 s).

Linear ablation

The first simulation studies of ablation used a multiple‐wavelet AF model to test over a dozen clinically used patterns resulting from successive addition of lines to PVI until it formed a complete maze (Virag et al. 2001; Dang et al. 2005; Ruchat et al. 2007 c). These studies consistently indicated the superiority of more extensive ablation patterns and the importance of combining right and left lines. The addition of a roof line and a posterior mitral line after PVI improved AF termination rates from 25% to 55% (Hwang et al. 2014) and decreased the conversion to left atrial flutter (Rotter et al. 2007). Right lines were needed where AF originated from the right atrium. This occurs in a minority of patients (Vincenti et al. 2006) and was explained in the model by an AF perpetuation mechanism relying on short‐lived reentries in the free wall of the right atrium. Incomplete ablation lines sometimes led to atypical flutter as in the clinic (Jais et al. 2000). The lessons are that if the substrate is uniform, (1) more aggressive strategies have higher success rates, and (2) ablation is more effective when ablation lines uniformly cover the whole atrial surface. In a two‐dimensional simulation study, Spector et al. (2012) attributed this effect to the increased border length to tissue area ratio. Note that simulation results are relevant only to patients with AF mechanisms and atrial anatomical structure similar to the model used, which may be a small subgroup of AF patients.

The results of initial model‐based analyses of linear ablation attracted the attention of clinicians who used the approach to test the idea of simplifying the Maze III procedure (Ruchat et al. 2007 b) and then validated the computer‐derived reduced maze clinically (Ruchat et al. 2007 a). This was the first translational example where modelling stimulated the brain‐storming phase of the design of a new ablation pattern.

A limitation in the design of these studies is that a wide range of patterns from PVI to complete maze were tested in the same substrate, while these patterns are clinically applied to different types of AF (paroxysmal or persistent).

Ectopic foci

Provided that ectopic sources not isolated by PVI can be localised, they can be successively ablated. In a computer model of AF with repolarisation heterogeneities driven by eight active focal sources, Haissaguerre et al. (2007) monitored the AF cycle length along the progression of stepwise ablation of these sources. Each source ablation tended to prolong the cycle length until sinus rhythm was restored. The simulation study demonstrated that after suppression of a high frequency source, a previously masked lower frequency source may take control. The same time course of cycle length was observed in clinical recordings, although clinicians cannot guarantee that a source has effectively been removed (Haissaguerre et al. 2007). The lesson is that computer models can be used to determine what the outcome would be if the ablation strategy was perfectly executed, reinforcing the need for improved signal processing tools for ectopic focus detection.

Complex fractionated atrial electrograms

Complex electrogram waveforms can be reproduced by introducing structural heterogeneities (Ellis et al. 1995; Jacquemet & Henriquez, 2009; Campos et al. 2013). In contrast, Hwang et al. (2014) identified CFAE in a uniform model of the left atrium. In one of the very few attempts to simulate a CFAE ablation protocol, they ablated the CFAE regions in the model after PVI. Consistent with recent clinical findings (Verma et al. 2015), this additional intervention did not improve success rate. The nature of the substrate (uniform conduction) might have taken precedence over the apparent electrical disturbances caused by the complex AF dynamics. The lesson is that the signal processing techniques used to identify the targets (both clinical and simulated) add another level of complexity and further uncertainties that may interfere with the interpretation of AF mechanisms. This study should be repeated in a structurally remodelled substrate to improve clinical relevance.

Rotors

Atrial models have been used by a number of groups to investigate the effects of fibrosis and myofibre disarray on rotor formation (McDowell et al. 2012; Gonzales et al. 2014; Krueger et al. 2014). All incorporated patient‐specific atrial geometry and representative myofibre arrangement, but fibrosis was either introduced explicitly from late gadolinium‐enhanced MRI (McDowell et al. 2012; Krueger et al. 2014) or simulated as inexcitable regions (Gonzales et al. 2014). In these studies, rotors were sustained and stabilised by fibrosis. However, McDowell et al. (2013) needed to include electrical coupling between myofibroblasts and myocytes, in addition to the conduction barriers created by collagen deposition, to replicate arrhythmogenesis. They also demonstrated that when cores of stable rotors were ablated, AF was no longer inducible (McDowell et al. 2015). This suggests that the distribution of fibrosis determines the location of rotors as well as targets for ablation. It remains to be seen whether the optimal target might be identified from imaging data alone (without simulations). An advantage of such models of structurally remodelled tissue is that the key parameter (the distribution of fibrosis) can be extracted to some extent from patient data.

Ganglionated plexi

The incorporation of an acetylcholine (ACh)‐modulated K⁺ current (Kneller et al. 2002) enabled the simulation of ACh‐induced repolarisation heterogeneity and its influence on AF vulnerability (Vigmond et al. 2004). A new atrial membrane model has been proposed to simulate ACh and β‐adrenergic challenges (Grandi et al. 2011). Matene et al. (2014) investigated the changes in atrial dynamics resulting from progressive time‐dependent variations in local ACh concentration, including the occurrence of self‐termination of a reentry following the elimination of vagal stimulation. This study may be relevant to the ablation of neurogenic targets, but much remains to be done in this area in terms of modelling.

Discussion and perspectives

Current state of research

The years 2000–2007 may be viewed as a successful first iteration of AF ablation modelling research. With the development of more realistic atrial models, it became possible to address specific clinical questions about the efficacy of ablation patterns. During this period, however, AF models based on the multiple wavelets hypothesis in a uniform tissue were challenged by new data and concepts (Efimov & Fedorov, 2005). A second iteration has followed. This has been built on more realistic representations of pathophysiological atrial substrates, including arrhythmogenic ion‐channel remodelling (Colman et al. 2013), anisotropic conduction (Krueger et al. 2013), as well as structural remodelling and fibrosis (McDowell et al. 2012). Meanwhile, AF treatment has evolved (Calkins et al. 2012), with the establishment of PVI as a basic approach and the successive advent of sometimes controversial new targets such as CFAE and rotors. Modelling research is now slowly catching up with state‐of‐the‐art AF management and has the capacity to contribute to it.

Future directions

Although most ablation strategies have now been modelled, Fig. 1 reveals a large knowledge gap (bottom right). The majority of simulation studies have used models that relate best to paroxysmal AF, because they do not incorporate heterogeneous electrical properties and structural remodelling. However, both factors intensify during persistent AF and PVI alone is least successful in this patient group. This calls for a systematic comparison of all strategies (PVI and adjuvant targets) in terms of both AF termination and prevention in a sequence of substrates that correspond to the progression of AF. Despite the limited spatial resolution of clinical late‐gadolinium MRI, the Utah staging system for fibrosis provides a tool to move in that direction (McDowell et al. 2015). Computational ablation analysis has two major advantages in this setting: the capacity to compare many ablation patterns and the ability to specify the substrate and draw substrate‐specific or mechanism‐specific conclusions.

In parallel, further advances in modelling the arrhythmogenic substrate of AF are needed, notably on the effect of the autonomic nervous system in paroxysmal AF and the effect of fibrosis, microstructure and layer dissociation in persistent AF. The triggering mechanisms are of particular importance to appropriately simulate the prevention of AF recurrence. These advances in substrate modelling will contribute to the debate on rotors vs. multiple wavelets by determining the tissue conditions under which each type of AF dynamics can occur and by identifying the critical pathways of reentry in relation to the substrate. An ensemble of models with random distribution of parameters around pathophysiological values may be used to reproduce inter‐patient variability and assess the robustness of the results (Sanchez et al. 2014).

The disappointing outcome of the Star AF II trial (Verma et al. 2015) and poor correlation between CFAE and AF sources (Narayan et al. 2013) suggest that the criteria for electrogram morphology analysis should be at least rethought. Modelling electrical mapping systems (Sabouri et al. 2014) during AF might contribute to better signal processing techniques for characterising regions in which reentry occurs. In combination with imaging‐based fibrosis detection, this could further improve the identification of ablation targets.

Obstacles to patient‐specific modelling

The ultimate goal would be to create patient‐specific models and determine in silico the optimal treatment for each patient (Winslow et al. 2012). Efficient construction of atrial models with patient‐specific geometry (Trayanova, 2014) is an important step toward this end in AF ablation. Nevertheless, one may humbly argue against overuse of the expression ‘patient‐specific modelling’. Limited accuracy in conduction properties determination corresponds to inaccurate geometry reconstruction. Indeed, a local reduction in conductivity by a factor k is equivalent to a local dilatation by a factor √k. What matters is the timing of depolarisation (Young & Panfilov, 2010) and repolarisation, which are known at only limited spatial resolution. Any uncertainty in action potential duration becomes an uncertainty in wavelength, the critical pathway length for reentry (Jacquemet et al. 2005; Krogh‐Madsen et al. 2012). Another problem is accounting for the role of microstructure in arrhythmogenesis (Hubbard & Henriquez, 2014). It is difficult to identify structural heterogeneities at scales <1 mm using existing clinical imaging modalities, but emerging technologies might alleviate this limitation (Lasher et al. 2009; Xu et al. 2014). An interim approach is to create retrospective patient‐specific models from explanted human hearts. Integrated 3‐D structural and functional mapping of ex vivo human atria at the sub‐millimetre scale (Hansen et al. 2015) may open the way to more accurate, high‐resolution modelling of diseased human tissue (including action potential waveforms derived from optical mapping, but lacking autonomic regulation) and potentially fill the gap between clinical and basic research.

Conclusion

Atrial models are not intended to predict the population‐based success rate of a therapy, but rather to discover whether (and why) the therapy succeeds or fails in a specific AF substrate. In the case of failure, it is possible to ‘click on the cancel button’ and try another strategy until a successful one is found. Another key advantage is the ability to differentiate between ‘incompletely burning the target’, ‘missing the target’ and ‘trying to burn the wrong target’, which all result in a similar clinical failure although the actual problem may implicate catheter technology, signal processing or cardiac pathophysiology. Modelling research is expected to reduce the ‘learning by burning’ approach by providing an objective basis for the design of ablation patterns. Most of the learning so far has been by the scientists and engineers developing models; hopefully, future lessons will inform clinical cardiac electrophysiologists.

Additional information

Competing interests

None declared.

Funding

This work was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC grant RGPIN‐2015‐05658).

Biography

Vincent Jacquemet obtained an MSc in physics and a PhD in biomedical engineering at École Polytechnique Fédérale de Lausanne in Switzerland. After postdoctoral studies at Duke University, he moved to Montreal where he is currently Associate Professor at Université de Montréal in the Department of Molecular and Integrative Physiology and in the research centre of the Sacré‐Coeur Hospital. His research interests include biophysical modelling, cardiac electrophysiology and signal processing.