Abstract:

BACKGROUND: Electrical impedance measurements have become an accepted tool for monitoring intracardiac radio frequency ablation. Recently, the long-established generator impedance was joined by novel local impedance measurement capabilities with all electrical circuit terminals being accommodated within the catheter. OBJECTIVE: This work aims at in silico quantification of distinct influencing factors that have remained challenges due to the lack of ground truth knowledge and the superposition of effects in clinical settings. METHODS: We introduced a highly detailed in silico model of two local impedance enabled catheters, namely IntellaNav MiFi™ OI and IntellaNav Stablepoint™, embedded in a series of clinically relevant environments. Assigning material and frequency specific conductivities and subsequently calculating the spread of the electrical field with the finite element method yielded in silico local impedances. The in silico model was validated by comparison to in vitro measurements of standardized sodium chloride solutions. We then investigated the effect of the withdrawal of the catheter into the transseptal sheath, catheter-tissue interaction, insertion of the catheter into pulmonary veins, and catheter irrigation. RESULTS: All simulated setups were in line with in vitro experiments and in human measurements and gave detailed insight into determinants of local impedance changes as well as the relation between values measured with two different devices. CONCLUSION: The in silico environment proved to be capable of resembling clinical scenarios and quantifying local impedance changes. SIGNIFICANCE: The tool can assists the interpretation of measurements in humans and has the potential to support future catheter development.

Abstract:

AIMS: The treatment of atrial fibrillation beyond pulmonary vein isolation has remained an unsolved challenge. Targeting regions identified by different substrate mapping approaches for ablation resulted in ambiguous outcomes. With the effective refractory period being a fundamental prerequisite for the maintenance of fibrillatory conduction, this study aims at estimating the effective refractory period with clinically available measurements. METHODS AND RESULTS: A set of 240 simulations in a spherical model of the left atrium with varying model initialization, combination of cellular refractory properties, and size of a region of lowered effective refractory period was implemented to analyse the capabilities and limitations of cycle length mapping. The minimum observed cycle length and the 25% quantile were compared to the underlying effective refractory period. The density of phase singularities was used as a measure for the complexity of the excitation pattern. Finally, we employed the method in a clinical test of concept including five patients. Areas of lowered effective refractory period could be distinguished from their surroundings in simulated scenarios with successfully induced multi-wavelet re-entry. Larger areas and higher gradients in effective refractory period as well as complex activation patterns favour the method. The 25% quantile of cycle lengths in patients with persistent atrial fibrillation was found to range from 85 to 190 ms. CONCLUSION: Cycle length mapping is capable of highlighting regions of pathologic refractory properties. In combination with complementary substrate mapping approaches, the method fosters confidence to enhance the treatment of atrial fibrillation beyond pulmonary vein isolation particularly in patients with complex activation patterns.

Abstract:

AIMS: The long-term success rate of ablation therapy is still sub-optimal in patients with persistent atrial fibrillation (AF), mostly due to arrhythmia recurrence originating from arrhythmogenic sites outside the pulmonary veins. Computational modelling provides a framework to integrate and augment clinical data, potentially enabling the patient-specific identification of AF mechanisms and of the optimal ablation sites. We developed a technology to tailor ablations in anatomical and functional digital atrial twins of patients with persistent AF aiming to identify the most successful ablation strategy. METHODS AND RESULTS: Twenty-nine patient-specific computational models integrating clinical information from tomographic imaging and electro-anatomical activation time and voltage maps were generated. Areas sustaining AF were identified by a personalized induction protocol at multiple locations. State-of-the-art anatomical and substrate ablation strategies were compared with our proposed Personalized Ablation Lines (PersonAL) plan, which consists of iteratively targeting emergent high dominant frequency (HDF) regions, to identify the optimal ablation strategy. Localized ablations were connected to the closest non-conductive barrier to prevent recurrence of AF or atrial tachycardia. The first application of the HDF strategy had a success of >98% and isolated only 5-6% of the left atrial myocardium. In contrast, conventional ablation strategies targeting anatomical or structural substrate resulted in isolation of up to 20% of left atrial myocardium. After a second iteration of the HDF strategy, no further arrhythmia episode could be induced in any of the patient-specific models. CONCLUSION: The novel PersonAL in silico technology allows to unveil all AF-perpetuating areas and personalize ablation by leveraging atrial digital twins.

Abstract:

Research software has become a central asset in academic research. It optimizes existing and enables new research methods, implements and embeds research knowledge, and constitutes an essential research product in itself. Research software must be sustainable in order to understand, replicate, reproduce, and build upon existing research or conduct new research effectively. In other words, software must be available, discoverable, usable, and adaptable to new needs, both now and in the future. Research software therefore requires an environment that supports sustainability. Hence, a change is needed in the way research software development and maintenance are currently motivated, incentivized, funded, structurally and infrastructurally supported, and legally treated. Failing to do so will threaten the quality and validity of research. In this paper, we identify challenges for research software sustainability in Germany and beyond, in terms of motivation, selection, research software engineering personnel, funding, infrastructure, and legal aspects. Besides researchers, we specifically address political and academic decision-makers to increase awareness of the importance and needs of sustainable research software practices. In particular, we recommend strategies and measures to create an environment for sustainable research software, with the ultimate goal to ensure that software-driven research is valid, reproducible and sustainable, and that software is recognized as a first class citizen in research. This paper is the outcome of two workshops run in Germany in 2019, at deRSE19 - the first International Conference of Research Software Engineers in Germany - and a dedicated DFG-supported follow-up workshop in Berlin.

Abstract:

Background: Rate-varying S1S2 stimulation protocols can be used for restitution studies to characterize atrial substrate, ionic remodeling, and atrial fibrillation risk. Clinical restitution studies with numerous patients create large amounts of these data. Thus, an automated pipeline to evaluate clinically acquired S1S2 stimulation protocol data necessitates consistent, robust, reproducible, and precise evaluation of local activation times, electrogram amplitude, and conduction velocity. Here, we present the CVAR-Seg pipeline, developed focusing on three challenges: (i) No previous knowledge of the stimulation parameters is available, thus, arbitrary protocols are supported. (ii) The pipeline remains robust under different noise conditions. (iii) The pipeline supports segmentation of atrial activities in close temporal proximity to the stimulation artifact, which is challenging due to larger amplitude and slope of the stimulus compared to the atrial activity. Methods and Results: The S1 basic cycle length was estimated by time interval detection. Stimulation time windows were segmented by detecting synchronous peaks in different channels surpassing an amplitude threshold and identifying time intervals between detected stimuli. Elimination of the stimulation artifact by a matched filter allowed detection of local activation times in temporal proximity. A non-linear signal energy operator was used to segment periods of atrial activity. Geodesic and Euclidean inter electrode distances allowed approximation of conduction velocity. The automatic segmentation performance of the CVAR-Seg pipeline was evaluated on 37 synthetic datasets with decreasing signal-to-noise ratios. Noise was modeled by reconstructing the frequency spectrum of clinical noise. The pipeline retained a median local activation time error below a single sample (1 ms) for signal-to-noise ratios as low as 0 dB representing a high clinical noise level. As a proof of concept, the pipeline was tested on a CARTO case of a paroxysmal atrial fibrillation patient and yielded plausible restitution curves for conduction speed and amplitude. Conclusion: The proposed openly available CVAR-Seg pipeline promises fast, fully automated, robust, and accurate evaluations of atrial signals even with low signal-to-noise ratios. This is achieved by solving the proximity problem of stimulation and atrial activity to enable standardized evaluation without introducing human bias for large data sets.

Abstract:

In patients with atrial fibrillation, intracardiac electrogram signal amplitude is known to decrease with increased structural tissue remodeling, referred to as fibrosis. In addition to the isolation of the pulmonary veins, fibrotic sites are considered a suitable target for catheter ablation. However, it remains an open challenge to find fibrotic areas and to differentiate their density and transmurality. This study aims to identify the volume fraction and transmurality of fibrosis in the atrial substrate. Simulated cardiac electrograms, combined with a generalized model of clinical noise, reproduce clinically measured signals. Our hybrid dataset approach combines and clinical electrograms to train a decision tree classifier to characterize the fibrotic atrial substrate. This approach captures different dynamics of the electrical propagation reflected on healthy electrogram morphology and synergistically combines it with synthetic fibrotic electrograms from experiments. The machine learning algorithm was tested on five patients and compared against clinical voltage maps as a proof of concept, distinguishing non-fibrotic from fibrotic tissue and characterizing the patient's fibrotic tissue in terms of density and transmurality. The proposed approach can be used to overcome a single voltage cut-off value to identify fibrotic tissue and guide ablation targeting fibrotic areas.

Abstract:

Atrial flutter (AFL) is a common atrial arrhythmia typically characterized by electrical activity propagating around specific anatomical regions. It is usually treated with catheter ablation. However, the identification of rotational activities is not straightforward, and requires an intense effort during the first phase of the electrophysiological (EP) study, i.e., the mapping phase, in which an anatomical 3D model is built and electrograms (EGMs) are recorded. In this study, we modeled the electrical propagation pattern of AFL (measured during mapping) using network theory (NT), a well-known field of research from the computer science domain. The main advantage of NT is the large number of available algorithms that can efficiently analyze the network. Using directed network mapping, we employed a cycle-finding algorithm to detect all cycles in the network, resembling the main propagation pattern of AFL. The method was tested on two subjects in sinus rhythm, six in an experimental model of in-silico simulations, and 10 subjects diagnosed with AFL who underwent a catheter ablation. The algorithm correctly detected the electrical propagation of both sinus rhythm cases and in-silico simulations. Regarding the AFL cases, arrhythmia mechanisms were either totally or partially identified in most of the cases (8 out of 10), i.e., cycles around the mitral valve, tricuspid valve and figure-of-eight reentries. The other two cases presented a poor mapping quality or a major complexity related to previous ablations, large areas of fibrotic tissue, etc. Directed network mapping represents an innovative tool that showed promising results in identifying AFL mechanisms in an automatic fashion. Further investigations are needed to assess the reliability of the method in different clinical scenarios.

Abstract:

OBJECTIVE: Unipolar intracardiac electrograms (uEGMs) measured inside the atria during electro-anatomic mapping contain diagnostic information about cardiac excitation and tissue properties. The ventricular far field (VFF) caused by ventricular depolarization compromises these signals. Current signal processing techniques require several seconds of local uEGMs to remove the VFF component and thus prolong the clinical mapping procedure. We developed an approach to remove the VFF component using data obtained during initial anatomy acquisition. METHODS: We developed two models which can approximate the spatio-temporal distribution of the VFF component based on acquired EGM data: Polynomial fit, and dipole fit. Both were benchmarked based on simulated cardiac excitation in two models of the human heart and applied to clinical data. RESULTS: VFF data acquired in one atrium were used to estimate model parameters. Under realistic noise conditions, a dipole model approximated the VFF with a median deviation of 0.029mV, yielding a median VFF attenuation of 142. In a different setup, only VFF data acquired at distances of more than 5mm to the atrial endocardium were used to estimate the model parameters. The VFF component was then extrapolated for a layer of 5mm thickness lining the endocardial tissue. A median deviation of 0.082mV (median VFF attenuation of 49x) was achieved under realistic noise conditions. CONCLUSION: It is feasible to model the VFF component in a personalized way and effectively remove it from uEGMs. SIGNIFICANCE: Application of our novel, simple and computationally inexpensive methods allows immediate diagnostic assessment of uEGM data without prolonging data acquisition.

Abstract:

Under persistent atrial fibrillation (peAF), cardiac tissue experiences electrophysiological and structural remodeling. Fibrosis in the atrial tissue has an important impact on the myocyte action potential and its propagation. The objective of this work is to explore the effect of heterogeneities present in the fibrotic tissue and their impact on the intracardiac electrogram (EGM). Human atrial myocyte and fibroblast electrophysiology was simulated using mathematical models proposed by Koivumäki et al. to represent electrical remodeling under peAF and the paracrine effect of the transforming grow factor 1 (TGF-1). 2D tissue simulations were computed varying the density of fibrosis (10%, 20% and 40%), myofibroblasts and collagen were randomly distributed with different ratios (0%-100%, 50%-50% and 100%- 0%). Results show that increasing the fibrosis density changes the re-entry dynamics from functional to anatomical due to a block in conduction in regions with high fibrosis density (40%). EGM morphology was affected by different ratios of myofibroblasts-collagen. For low myofibroblast densities (below 50%) the duration of active segments was shorter compared to higher myofibroblasts densities (above 50%). Our results show that fibrosis heterogeneities can alter the dynamics of the re-entry and the morphology of the EGM.

Abstract:

Catheter ablation is a curative therapeutic approach for atrial fibrillation (AF). Ablation of rotational sources based on basket catheter measurements has been proposed as a promising approach in patients with persistent AF to complement pulmonary vein isolation. However, clinically reported success rates are equivocal calling for a mechanistic investigation under controlled conditions. We present a computational framework to benchmark ablation strategies considering the whole cycle from excitation propagation to electrogram acquisition and processing to virtual therapy. Fibrillation was induced in a patient-specific 3D volumetric model of the left atrium, which was homogeneously remodelled to sustain reentry. The resulting extracellular potential field was sampled using models of grid catheters as well as realistically deformed basket catheters considering the specific atrial anatomy. Virtual electrograms were processed to compute phase singularity density maps to target rotor tips with up to three circular ablations. Stable rotors were successfully induced in different regions of the homogeneously remodelled atrium showing that rotors are not constrained to unique anatomical structures or locations. Phase singularity density maps correctly identified and located the rotors (deviation < 10 mm) based on catheter recordings only for sufficient resolution (inter-electrode distance = 3 mm) and proximity to the wall (< 10 mm). Targeting rotor sites with ablation did not stop reentries in the homogeneously remodelled atria independent from lesion size (1-7 mm radius), from linearly connecting lesions with anatomical obstacles, and from the number of rotors targeted sequentially (up to 3). Our results show that phase maps derived from intracardiac electrograms can be a powerful tool to map atrial activation patterns, yet they can also be misleading due to inaccurate localization of rotor tips depending on electrode resolution and distance to the wall. This should be considered to avoid ablating regions that are in fact free of rotor sources of AF. In our experience, ablation of rotor sites was not successful to stop fibrillation. Our comprehensive simulation framework provides the means to holistically benchmark ablation strategies in silico under consideration of all steps invol

Abstract:

Beat acceptance and rejection during atrial tachycardia are crucial for the compilation of meaningful electroanatomical maps during an electrophysiological study. State of the art methods compare the delays in activation time between two or more electrograms recorded with electrodes of a spatially stable reference catheter. This work introduces morphology-based measures for beat selection in the context of mapping atrial tachycardia. Active segments were extracted from bipolar reference electrograms with the help of the non-linear energy operator. After prealignment by means of maximum cross-correlation, the correlation coefficient as well as the normalized 1-norm distance yielded a similarity measure for each pair of prealigned active segments. The morphology-based measures were then compared to the delay-based measure. In an exemplary patient with 5163 recorded beats, the delay-based measures were strongly dependent on the accuracy of the local activation times as well as on the selection of reference leads. The morphology-based measures emphasized changes in the target tachycardia which were not detectable by the delay-based method. The correlation and the distance measure showed similar behavior but stressed different aspects of morphological changes. Ventricular components in active segments caused minor changes in morphology which were also reflected in the morphology-based measures. The morphology-based measures introduced in this work enhanced beat selection in the exemplary patient. A follow-up study with a representative patient cohort needs to quantify the improvement across patients and translate the measure to clinical practice. A combination of activation delays and morphological similarity is strongly expected to exploit the advantages of both methods for beat selection.

Abstract:

Intracardiac electrograms (EGMs) form the basis for the diagnosis of arrhythmia mechanisms. Bipolar EGMs dominate clinical practice despite major disadvantages over unipolar EGMs since noise strongly distorts the latter. In this study, we quantified and reduced the noise level of uni- and bipolar EGMs recorded with Rhythmia HDx and the Orion catheter. Distinct noise frequencies in the power spectral density (PSD) were detected with a sliding win- dow of variable width and subsequently removed by notch filtering. The absolute peak to peak voltage remaining in the inactive segments after baseline removal quantified the noise level of the system. An international, multi-center selection of 33 patients served as a broad sample cohort. The case-specific detection and removal of noise peaks reduced the noise level in unipolar EGMs by 30% to 0.076 mV compared to standard clinical filtering. With a bipolar noise level of 0.01 mV, we saw that Rhythmia HDx meets the low noise floor claimed in the system specifica- tions. Certain noise frequencies presented permanently in all cases whereas others showed up only intermittently or in individual cases. The suggested extension of filter settings lowers the noise level, enhances the detailed segmentation of low volt- age areas, and encourages to exploit the advantages of unipolar over bipolar EGMs in clinical practice.

Abstract:

Acquiring adequate mapping data in patients with atrial fibrillation is still one of the main obstacles in the treatment of this atrial arrhythmia. Due to the lack of catheters with both a panoramic field of view and sufficient electrode density for simultaneous mapping, electrophysiologists are forced to fall back on sequential mapping techniques. But, because activation patterns change rapidly during atrial fibrillation, they cannot be mapped sequentially. We propose that mapping tissue properties which are time independent, in contrast, allows a sequential approach. Here, we use the shortest measured electrogram cycle length to estimate the effective refractory period of the underlying tissue in a simulation study. Atrial fibrillation was simulated in a spherical model of the left atrium comprised of regions with varied refractory period. We found that the minimal measured electrogram cycle length correlates with the effective refractory period of the underlying tissue if the regions with distinct refractory properties are large enough and if the absolute difference in effective refractory periods is sufficient. This approach is capable of identifying regions of lowered effective refractory period without the need for cardioversion. Those regions are likely to harbor drivers of atrial fibrillation, which emphasizes the necessity of their localization.

Abstract:

This work aimed at the detection of rotor centers within the atrial cavity during atrial fibrillation on the basis of phase singularities. A voxel based method was established which employs the Hilbert transform and the phase of unipolar electrograms. The method provides a 3D overview of phase singularities at the endocardial surface and within the blood volume. Mapping those phase singularities from the inside of the atria at the endocardium yielded rotor center trajectories.We discuss the results for an unstable and a more stable rotor. The side length of the areas covered by the trajectories varied from 1.5mm to 10 mm. These results are important for cardiologists who target rotors with RF ablation in order to cure atrial fibrillation.

Abstract:

Quantifying the atrial conduction velocity (CV) reveals important information for targeting critical arrhythmia sites that initiate and sustain abnormal electrical pathways, e.g. during atrial flutter. The knowledge about the local CV distribution on the atrial surface thus enhances clinical catheter ablation procedures by localizing pathological propagation paths to be eliminated during the intervention. Several algorithms have been proposed for estimating the CV. All of them are solely based on the local activation times calculated from electroanatomical mapping data. They deliver false values for the CV if applied to regions near scars or wave collisions. We propose an extension to all approaches by including a distinct preprocessing step. Thereby, we first identify scars and wave front collisions and provide this information for the CV estimation algorithm. In addition, we provide reliable CV values even in the presence of noise. We compared the performance of the Triangulation, the Polynomial Fit and the Radial Basis Functions approach with and without the inclusion of the aforementioned preprocessing step. The evaluation was based on different activation patterns simulated on a 2D synthetic triangular mesh with different levels of noise added. The results of this study demonstrate that the accuracy of the estimated CV does improve when knowledge about the depolarization pattern is included. Over all investigated test cases, the reduction of the mean velocity error quantified to at least 25 mm/s for the Radial Basis Functions, 14 mm/s for the Polynomial Fit and 14 mm/s for the Triangulation approach compared to their respective implementations without the preprocessing step. Given the present results, this novel approach can contribute to a more accurate and reliable CV estimation in a clinical setting and thus improve the success of radio-frequency ablation to treat cardiac arrhythmias.

Abstract:

The outcomes of ablation targeting either reentry activations or fractionated activity during persistent atrial fibrillation (AF) therapy remain suboptimal due to, among others, the intricate underlying AF dynamics. In the present work, we sought to investigate such AF dynamics in a heterogeneous simulation setup using recurrence quantification analysis (RQA). AF was simulated in a spherical model of the left atrium, from which 412 unipolar atrial electrograms (AEGs) were extracted (2 s duration; 5 mm spacing). The phase was calculated using the Hilbert transform, followed by the identification of points of singularity (PS). Three regions were defined according to the occurrence of PSs: 1) no rotors; 2) transient rotors and; 3) long-standing rotors. Bipolar AEGs (1114) were calculated from pairs of unipolar nodes and bandpass filtered (30-300 Hz). The CARTO criterion (Biosense Webster) was used for AEGs classification (normal vs. fractionated). RQA attributes were calculated from the filtered bipolar AEGs: determinism (DET); recurrence rate (RR); laminarity (LAM). Sample entropy (SampEn) and dominant frequency (DF) were also calculated from the AEGs. Regions with longstanding rotors have shown significantly lower RQA attributes and SampEn when compared to the other regions, suggesting a higher irregular behaviour (P≤0.01 for all cases). Normal and fractionated AEGs were found in all regions (respectively; Region 1: 387 vs. 15; Region 2: 221 vs. 13; Region 3: 415 vs. 63). Region 1 vs. Region 3 have shown significant differences in normal AEGs (P≤0.0001 for all RQA attributes and SampEn), and significant differences in fractionated AEGs for LAM, RR and SampEn (P=0.0071, P=0.0221 and P=0.0086, respectively). Our results suggest the co-existence of normal and fractionated AEGs within long-standing rotors. RQA has unveiled distinct dynamic patterns–irrespective of AEGs classification–related to regularity structures and their nonstationary behaviour in a rigorous deterministic context.

Abstract:

Cardiac arrhythmias such as atrial fibrillation occur frequently in industrialized countries. Radiofrequency ablation (RFA) is a standard treatment if drug therapy fails. This minimally invasive surgery aims at stabilizing the heart rhythm on a permanent basis. However, the procedure commonly needs to be repeated because of the high recurrence rate of arrhythmias. Non-transmural lesions as well as gaps within linear lesions are among the main problems during the RFA. The assessment of lesion formation is not adequate in state of the art procedures. Therefore, the aim of this study is to investigate the short-term reversibility of lesions using human electrograms recorded by a high-density mapping system during an electrophysiological study (EPS). A predefined measurement protocol was executed during the EPS in order to create three ablation points in the left atrium. Subsequently, after preprocessing the recorded signals, electrogram (EGM) paths were formed along the endocardial surface of the atrium. By analyzing changes of peak to peak amplitudes of unipolar EGMs before and after ablation, it was possible to distinguish lesion area and healthy myocardium. The peak to peak amplitudes of the EGMs decreased by 40-61% after 30 seconds of ablation. Furthermore, we analyzed the morphological changes of EGMs surrounding the lesion. High-density mapping data showed that not only the tissue, which had direct contact with the catheter tip during the RFA, but also the surrounding tissue was affected. This was demonstrated by low peak to peak amplitudes in large areas with a width of 14 mm around the center of the ablation lesion. After right pulmonary vein isolation, high-density mapping was repeated on the previous lesions. The outer region of RFA-treated tissue appears to recover as opposed to the central core of the ablation point. This observation suggests that the meaningfulness of an immediate remap after ablation during an EPS may lead the physician to false conclusions.

Abstract:

Atrial tachycardia and atrial flutter are frequent arrhythmia that occur spontaneously and after ablation of atrial fibrillation. Depolarization waves that differ significantly from sinus rhythm propagate across the atria with high frequency (typically 140 to 220 beats per minute). A detailed and personalized analysis of the spread of depolarization is imperative for a successful ablation therapy. Thus, catheters with several electrodes are employed to measure multichannel electrograms inside the atria. Here we propose a new concept for spatio-temporal analysis of multichannel electrograms during atrial tachycardia and atrial flutter. It is based on the calculation of simultaneously active areas. The method allows to identify atrial tachycardia and to automatically distinguish between subtypes of focal activity, micro-reentry and macro-reentry.

Abstract:

Atrial fibrillation is a common irregular heart rhythm. Until today there is still a need for research to quantify typical signal characteristics of rotors, which can induce atrial fibrillation. In this work, signal characteristics of a stable and a more unstable rotor in a realistic heart model including fiber orientation were analyzed with the following methods: peak-to-peak amplitude, Hilbert phase, approximate entropy and RS-difference. In this simulation model the stable rotor rotated with a cycle length of 145 ms and stayed in an area of 1.5 mm x 3 mm. Another more unstable rotor with a cycle length of 190 ms moved in an area of 10 mm × 4 mm. In a distance of 2 mm to the rotor tip, the peak-to-peak amplitude decreased significantly, whereas the RS-difference and the approximate entropy were maximal. The rotor center trajectories were detected by phase singularity points determined by the Hilbert transform. We showed that more unstable rotors resulted in more amplitude changes over time and also the cycle length differed more. Furthermore, we presented typical activation time patterns of the Lasso catheter centered at the rotor tip and in different distances to the rotor tip. We suggest that cardiologists use a combination of the described methods to determine a rotor tip position in a more robust manner.