Spectral characterisation of ventricular intracardiac potentials in human post-ischaemic bipolar electrograms

Abnormal ventricular potentials (AVPs) are frequently referred to as high-frequency deflections in intracardiac electrograms (EGMs). However, no scientific study performed a deep spectral characterisation of AVPs and physiological potentials in real bipolar intracardiac recordings across the entire frequency range imposed by their sampling frequency. In this work, the power contributions of post-ischaemic physiological potentials and AVPs, along with some spectral features, were evaluated in the frequency domain and then statistically compared to highlight specific spectral signatures for these signals. To this end, 450 bipolar EGMs from seven patients affected by post-ischaemic ventricular tachycardia were retrospectively annotated by an experienced cardiologist. Given the high variability of the morphologies observed, three different sub-classes of AVPs and two sub-categories of post-ischaemic physiological potentials were considered. All signals were acquired by the CARTO® 3 system during substrate-guided catheter ablation procedures. Our findings indicated that the main frequency contributions of physiological and pathological post-ischaemic EGMs are found below 320 Hz. Statistical analyses showed that, when biases due to the signal amplitude influence are eliminated, not only physiological potentials show greater contributions below 20 Hz whereas AVPs demonstrate higher spectral contributions above ~ 40 Hz, but several finer differences may be observed between the different AVP types.


Materials and methods
This retrospective study was based on a dataset consisting of 450 bipolar EGM segments acquired from seven patients (86% male; mean age, 64 ± 9 years), affected by post-ischaemic VT, at the San Francesco Hospital (Nuoro, Italy) between 2017 and 2018. This study on anonymised patient data was approved by the Independent ATS Ethical Committee (Azienda Tutela Salute, Sardegna) and performed following the principles outlined in the 1975 Helsinki Declaration, as revised in 2000. All patients provided their informed consent. Recordings were performed in sinus rhythm during left ventricular electroanatomic mapping by using the CARTO ® 3 system (Biosense Webster, Inc., Diamond Bar, CA, USA) at a sampling frequency of 1 kHz. After the procedure, radiofrequency catheter ablation followed the usual clinical protocols.
Bipolar intracardiac EGMs were recorded using PENTARAY™ (Biosense Webster, Inc.) 2-6-2 mm, by exploiting only the 2-mm spaced electrode pairs, THERMOCOOL SMARTTOUCH ® and THERMOCOOL SMARTTOUCH ® SF (Biosense Webster, Inc.) catheters. All signals were band-pass filtered between 16 and 500 Hz by the CARTO ® 3 acquisition system. Whilst the duration of each exported CARTO ® recording was 2.5 s, only the biopotential around the reference annotation was guaranteed to be acquired by the multielectrode catheter in effective contact with the endocardium. Therefore, a window of 200 ms before and 300 ms after the reference point was identified as the portion of interest for all subsequent analyses. According to the sampling frequency adopted in the CARTO ® 3 system (i.e. 1000 Hz) and the chosen duration of the analysis window for each EGM (500 ms), the available frequency resolution for the discrete-time frequency analyses was 2 Hz.
All intracardiac EGMs were manually labelled by an experienced cardiologist using an ad hoc MATLAB graphical user interface implemented for this purpose. Specifically, by exploiting the corresponding simultaneous surface ECG leads, we considered all abnormal potentials occurring after or during the corresponding QRS complexes, as in other works 31,49,50 , and all physiological potentials from post-ischaemic damaged substrates, as detailed hereafter.
Abnormal potentials, i.e. AVPs, were divided into three types 31 , to take into account the high variability of the morphologies of all the bipolar intracardiac EGMs: • LP1: endocardial bipolar abnormal deflections spreading after the end of the corresponding surface QRS depolarisation, • LP2: endocardial bipolar depolarisations starting during the corresponding surface QRS depolarisation but vanishing after its end, and • EP: endocardial early EGM deflections completely falling within the corresponding surface QRS depolarisation boundaries.
Physiological biopotentials (i.e., those without any abnormal deflection) originating from damaged myocardial substrates were also considered, dividing them into border-zone and scar-related types. Only these physiological potentials were categorised according to their peak-to-peak amplitudes (A pp ) recorded in the bipolar EGMs. Conventionally 48 , endocardial border-zone potentials satisfied the constraint 0.5 mV < A pp < 1.5 mV, www.nature.com/scientificreports/ whereas scar-related ones were characterised by A pp < 0.5 mV. Amplitude categorisation was not applied to AVPs signals. All noisy or doubtful traces were discarded. Over all the procedures, equal numbers of examples were randomly selected for each type of potential, (90 per type) to provide an effective and balanced comparative assessment. Figure 1 reports some typical examples of each EGM type.
The power contents for all bipolar EGMs were evaluated in the frequency domain. This analysis was carried out by adopting PSD and multiple spectral features to characterise the signals and their spectra better, as detailed in the following section.
Spectral analysis methods. The spectral analysis included several steps. Firstly, the main frequency range of interest for these signals was identified, as described in "Definition of the main frequency range of interest", to reduce the dimensionality of the problem by focusing on the spectral range that contains the largest part of the signal power. We then assessed and compared the power contributions in different sub-bands to perform a finegrained analysis of the EGM spectral content. Sub-band partitioning with a bandwidth of 20 Hz was performed, as also described in a previous study 44 , on the basis of the frequency resolution imposed by the chosen window length. This choice allowed reducing the impact of both noise and intrinsic limitations of the signal analysis methods adopted, by trading off robustness and accuracy of the characterisation.
The PSD method was exploited for spectral power estimation; here, the results were studied over sub-band partitions of the main frequency range of interest. Furthermore, we computed the absolute and relative power contents of the potentials in the different sub-bands because relative power analysis allows the suppression of the signal amplitude influence, mainly due to the far field component, which clearly affects the power estimated from the spectral analysis. Finally, different spectral features were evaluated to characterise the different PSD morphologies and contents of the EGM types.
Definition of the main frequency range of interest. We performed a preliminary identification of the main frequency range of interest in order to focus the signal frequency analysis on the components that provide the largest part of information, leading to a more effective and understandable sub-band analysis of ventricular endocardial potentials. This approach allowed us to restrict the number of sub-bands whilst still guaranteeing fine granularity during spectrum partitioning. To this end, for each EGM, we computed the PSD and estimated its total power as the area under the PSD curve over the entire frequency band limited by the Nyquist frequency. Then, we identified the frequency f H corresponding to the value for which the 95% of the total PSD power was retrieved. Finally, considering the f H values for each of the five EGM types, we computed the 95th percentiles (ξ 95 ) separately for each EGM type and identified the lowest sub-band including the maximum ξ 95 . The frequency range of interest was defined as the band between zero and the upper boundary of that sub-band.  www.nature.com/scientificreports/ Spectral analysis by PSD. The power spectrum of the discrete-time signal represents its power as a function of the frequency bin ω k , which is the normalized frequency, defined as πf / f s /2 , where f s represents the adopted sampling frequency. When the discrete Fourier transform (DFT) is used, ω k assumes the discrete values 2πk/N . In fact, in its simplest non-parametric estimate, the power spectrum can be computed from the DFT of the windowed signal of interest ( x[n] ), consisting of N samples, by normalising its squared magnitude as follows 51 : where: and where S 1 is obtained by summing the values of the chosen window, while n and k span between 0 and N − 1 , being N the signal length. Specifically, in this work, fast Fourier transform was adopted along with a rectangular window function. The latter was chosen to avoid attenuation of the signal at its borders, as border effects are still limited by the high-pass pre-processing stage of the recording system. In this application, the choice of the periodogram estimate was imposed by the short duration of the EGM, thus providing a single epoch for each intracardiac potential.
The spectral power was estimated as the area under the PSD curve. PSD can be computed by dividing the power spectrum by the effective noise equivalent bandwidth 51 . According to this assumption, PSD can be mathematically expressed as: where S 2 is defined as the sum of the squared window values. In this work, absolute power analysis was carried out by computing the area under the PSD curves in each sub-band.
The relative powers were also computed to avoid any influence in the analysis due to the amplitude of the signals, which is mainly ascribable to the far field component. These powers were estimated as the percentage ratio between the absolute power values of each sub-band and the area under the whole PSD curve in the main frequency range, similarly to a previous work 39 .
Moreover, a deeper characterization of the different PSD morphologies was obtained by exploiting some frequency-domain features 52 . Specifically, for each EGM, we considered: • the mean frequency (MF), which is computed as the weighted sum of the power spectrum contents PS j and the corresponding frequencies f j with respect to the total power estimated in the main frequency range of interest ( P): where P = j PS j ; on this basis, MF explains if the power spectrum contents are mostly localized at the higher or lower frequencies; • the mean spectral power (MP), which is defined as the mean power in the main frequency range of interest and, as such, expresses how much power, on average, is contained under each PSD in that range; • the maximum or peak frequency (PKF), which corresponds to the frequency at which the maximum of the power spectrum occurs; • the power spectrum ratio (PSR), which is estimated as the ratio between the spectral power included near the PKF and the total power estimated in the main frequency range of interest (P): where P 0 = PKF+δ j=PKF−δ P j . Specifically, δ was set to be equal to 4 Hz. As such, the estimation was performed on a spectral interval equal to 8 Hz centred around the PKF to give an overview of how much relative power is concentrated around the PKF, highlighting how sharp the PSD morphology is around its maximum.
Statistical analysis. The normality of all data distributions was preliminary assessed by Shapiro-Wilk's test, and the homogeneity of variances was evaluated with Levene's test. Data deviating from normality were presented as median values, and differences between groups were compared by the Kruskal-Wallis test. When the p value from Kruskal-Wallis test was statistically significant, a post hoc Conover's non-parametric multiple comparison test 53,54 was used to determine which group differed from the others. Several statistical inferences were simultaneously applied for all multiple comparisons, and the Bonferroni procedure for family-wise error rates was applied to control type-I errors by multiplying the uncorrected p-value with the total number of pair-wise tests; the adjusted p-value for all computations was reported. Following Bonferroni adjustment, p value < 0.025 was accepted as significant. All statistical analyses were performed using STATA 16 (StataCorp LP, College Station, TX, USA). (1)

Spectral investigations.
In this section, all spectral power estimations are reported as pair-wise comparisons amongst the different EGMs types. The results are organised into three groups according to the nature of the EGMs included in the comparison. In the first group, all the considered post-ischaemic physiological potentials (border and scar) were studied. In the second group, all AVPs (LP1, LP2 and EP) were examined; in the third group, physiological potentials were compared with AVPs. Table 1 summarises the spectral power results of pairwise comparisons for different spectral ranges. In the table, the different groups are identified by vertical dashed lines. The absolute and relative power contents obtained for each EGM type in the different spectral ranges are reported in Supplementary Tables S1 and S2 online. Figure 3 presents the results of relative power analysis in terms of median values graphically, and Fig. 4 describes the results in terms of spectral features.
Post-ischaemic physiological potentials. Conversely from absolute power and MP results, which were driven by the signal amplitude and confirmed that border power contents were significantly higher than scar ones in all examined ranges (p < 0.0001), relative power analyses revealed how scar power values were significantly higher than border ones at the lowest frequencies, i.e. 0-20 Hz (p < 0.0001). However, border relative powers were again higher than scar ones only up to 160 Hz, specifically in 20-60 Hz (p < 0.0001) and 80-160 Hz (p < 0.0074), although statistical significance was nearly achieved in the 60-80 Hz range (p = 0.0391). Scar MF and PKF values were significantly lower (p < 0.0001 for both cases) whereas scar PSR estimations were significantly higher (p < 0.0001) than border ones, thus confirming that this EGM type demonstrates its main contribution at lower frequencies than border cases.
Post-ischaemic abnormal potentials. LP1 and LP2 potentials. In terms of MP, our experiments revealed significantly higher values of LP1 than LP2 (p < 0.0001). Although absolute power analyses showed statistically significant differences only in the 0-40 Hz range, in which LP1 values were significantly higher than LP2 ones (p < 0.0001), relative power analysis revealed a different scenario. In this case, LP1 contents exceeded LP2 ones at low frequencies, in particular in the 20-40 Hz range (p = 0.0007), whereas LP2 showed significantly higher contributions at all the higher frequencies (p < 0.0120), except in the 200-220 Hz sub-band, in which no statistical significance was achieved. This finding was confirmed by the MF analysis, in which LP1 showed lower mean frequencies than LP2 (p = 0.0001). No statistical evidence was found between PKF and PSR.
LP1 and EP potentials. This comparison is similar to the previous one. MP values were significantly higher for LP1 than EP (p < 0.0001). Although absolute power analysis showed statistically significant significances mainly in the 0-40 Hz range, in which LP1 contributions were considerably higher than EP ones (p < 0.0001), relative power analysis demonstrated several statistically significant differences between 20 and 320 Hz. Specifically, although LP1 showed higher median contents at low frequencies, i.e. 20-40 Hz (p = 0.0002), EP values consistently exceeded those of LP1 between 60 and 320 Hz (p < 0.0249). Significant lower-frequency contributions for LP1 with respect to EP were also found when MF values were assessed (p < 0.0001).
LP2 and EP potentials. In general, no significant difference was found between the LP2 and EP classes below 200 Hz. For higher frequencies, EP demonstrated significantly higher values in the 200-320 Hz range (p < 0.0233) during absolute power analysis but only in the 200-220 Hz range in the corresponding relative power analysis (p = 0.0187).
Physiological versus abnormal potentials. Border and LP1 potentials. The MPs of border EGMs were significantly higher than those of LP1 EGMs (p = 0.0002). Statistical differences were rarely observed between these www.nature.com/scientificreports/ EGM types when absolute powers were analysed, i.e. essentially in the 0-40 Hz (p < 0.0217) range, in which border powers exceeded LP1 ones. However, when relative powers were analysed, LP1 spectral contents exceeded border ones in the range of 60-100 Hz (p < 0.0091) and above 180 Hz (p < 0.0156). Furthermore, border PSR values were significantly higher than LP1 ones (p = 0.0017), thus suggesting a lower dispersion of power contributions around the maximum frequency in border EGMs.
Border and LP2 potentials. Border EGMs showed statistically higher MP values than LP2 (p < 0.0001). During absolute spectral analysis, statistically significant differences were noted only at frequencies below 60 Hz, where border power contents exceeded LP2 ones (p < 0.0070). However, LP2 and border EGMs significantly differed in terms of relative power in all the sub-bands except in the 20-40 Hz one. Table 1 reveals that LP2 showed higher power contents in higher frequency ranges, i.e. between 40 and 320 Hz (p < 0.0001); the opposite behaviour was observed at the lowest frequencies, i.e. 0-20 Hz (p = 0.0048), where border EGMs exhibited higher power contributions. The main low-frequency contributions of border EGMs are also reflected by the MF results, in which border contributions were significantly lower than LP2 ones (p < 0.0001). PSR values suggested a major power gathering around the PKF for border EGMs (p < 0.0001).
Border and EP potentials. The MP values of border EGMs were significantly higher than those of EP EGMs (p < 0.0001). Conversely, EP MF values significantly exceeded border ones (p < 0.0001) with lower PSR contents (p < 0.0001). Absolute power analysis revealed statistically significant differences below 60 Hz, in which border power contents exceeded EP ones (p < 0.0156), and above 240 Hz, where the opposite trend was noted (p < 0.0063). In terms of relative power, border and EP EGMs significantly differed in all the sub-bands, with border potentials showing higher contributions at lower frequencies (i.e. 0-40 Hz, p < 0.0197) and EP above 40 Hz (p < 0.0001).
Scar and LP1 potentials. Scar EGMs consistently showed lower contributions than LP1 when absolute powers, MP, MF and PKF were examined (p < 0.0001). However, scar relative power values exceeded LP1 one in the lowest sub-band, i.e. 0-20 Hz (p < 0.0001, see Table 1). LP1 power contents were significantly higher than scar ones at higher frequencies, i.e. 20-240 Hz (p < 0.0119). Furthermore, scar PSRs exceeded LP1 ones (p < 0.0001). These results clearly indicate that scar EGMs exhibited lower powers in absolute terms, but higher relative lowfrequency contents (see Fig. 3) with a considerable amount of spectral power around their PKFs, which are typically observed below 25 Hz, as can be seen in Fig. 4.
Scar and LP2 potentials. Scar EGMs showed significantly lower power contributions than LP2 in terms of MP (p < 0.0001) and in the absolute power analysis at frequencies above 20 Hz (p < 0.0001). However, similarly to the previous case, the relative power contributions of these potentials demonstrated some interesting characteristics. Specifically, scar EGMs showed higher relative power contents at the lowest frequencies, i.e. below 20 Hz (p < 0.0001), but lower contents at higher frequencies, i.e. above 40 Hz (p < 0.0001). As in the previous case, this www.nature.com/scientificreports/ finding was confirmed by the trends of MF and PKF, in which scar contents were significantly lower than LP2 ones (p < 0.0001), and PSR values, in which scar EGMs exceeded LP2 ones (p < 0.0001).
Scar and EP potentials. Scar EGMs showed significantly lower powers than EP EGMs in terms of MP (p < 0.0001). The comparison in terms of absolute and relative power analysis led to the same results obtained in the previous case. The MF and PKF distributions confirmed the previous findings, thus suggesting higher scar contributions than EP ones (p < 0.0001 and p = 0.0002, respectively) at low frequencies, with major gathering around PKF in terms of PSR rather than EP (p < 0.0001).

Discussion
In this work, different spectral power analyses were performed to characterise abnormal and physiological postischaemic bipolar potentials and provide an accurate and quantitative comparative assessment amongst the different EGM types analysed. The results were grouped in terms of comparisons between physiological potentials, abnormal potentials and physiological versus abnormal potentials, i.e. AVPs. Although the absolute power analysis is influenced by the amplitude of the signals, which is mainly driven by the far field component, its results are quite interesting when compared to the relative power analysis and the insights synthetically provided by the identified spectral features. According to the absolute power analysis results (see Table 1), scar EGMs consistently demonstrated lower power values than all other types of potentials, regardless of the frequency range analysed. However, the spectral feature analysis results (see Fig. 4) clearly show www.nature.com/scientificreports/ that scar MF and PKF are typically below 30 Hz, around which substantial power contributions are concentrated, as indicated by their higher PSRs. These findings suggest that scar power spectra are quite condensed around their maximum and may confirm the association between the lowest-frequency contributions and the scar areas, as further demonstrated by the relative power analysis results. While PKF allowed to statistically emphasize scar potentials, PSR contents allowed to discriminate physiological potentials from AVPs, since both border and scar EGMs showed major power contributions around PKF (i.e., higher PSR in Fig. 4). MF analysis seemed to delineate three clusters, namely, border and LP1, LP2 and EP, and scar. However, the absolute power results in Table 1 suggest that, below 40 Hz, border EGMs show higher contribution than all AVPs and that, amongst AVPs, LP1 EGMs involve greater slow components. The same finding could be confirmed by looking at the lower MF values in Fig. 4 for LP1 and border EGMs. Conversely, EPs showed higher contributions than border EGMs above 240 Hz, revealing significant high-frequency components, which also emerged in the comparison with LP2 above 200 Hz. This finding was supported by the MF evaluation, in which the values of EP were found to be generally higher than those of all other EGM types.
Although absolute power analysis results are interesting for the spectral characterization of physiological potentials and AVPs, the relative power analysis (see Table 1) provides several novel insights into the characterisation of these signals. Overall, our results indicate that physiological EGMs have greater contributions at lower frequencies (i.e. mainly below 20 Hz) than pathological ones, as conceivable according to the fragmented nature of AVPs. In particular, scar-related EGMs consistently indicated higher contributions at lower frequencies (i.e. 0-20 Hz) than all the other physiological and pathological types, which, however, gradually decreased when moving towards higher sub-bands. These findings are at least partially in accordance with previous scientific studies on post-ischaemic epicardial EGMs 39,40 . In fact, Mor-Avi and Akselrod 39 demonstrated that myocardial ischaemia is responsible for a shift of the major frequency contents below 40 Hz whilst attenuating highfrequency spectral components. Sierra et al. 40 concluded that most of the signal energy is concentrated below 30 Hz in monomorphic and polymorphic VT recordings. Relative powers of LP2 and EP exhibited significantly greater values from 40 Hz than post-ischaemic physiological potentials, even though statistical significance was not achieved on some spectral ranges (see Table 1). Conversely, whilst LP1 EGMs showed significantly higher power contents than scar potentials in the 20-240 Hz range, they generally did not assume significantly higher values than border potentials until 180 Hz. As such, AVPs presented greater relative powers at higher frequencies with respect to physiological potentials, with some differences in spectral ranges depending on the AVP type. Moreover, as regards the significances amongst AVPs, while LP1 showed lower power contributions than LP2 and EP mainly above 60 Hz, LP2 and EP EGMs statistically differed in 200-220 Hz sub-band.
In summary, AVPs demonstrated higher relative power contributions at higher frequencies (i.e. mainly above 40 Hz) when compared with physiological potentials, as can be also deduced from Fig. 5. These findings are quite consistent with the a priori assumptions described in one work 36 , in which spectral contents above 80 Hz were identified as a marker of highly fragmented EGMs, and another study 37 , which identified the range of 70-180 Hz to be the useful spectral range for the arrhythmogenic potentials identification. Moreover, our results partially agree with another study 38 , which indicated the 40-100 Hz range to be of interest for fractionated EGM recognition, and an earlier analysis 44 , in which arrhythmogenic scar potentials showed significantly higher root mean square powers than non-arrhythmogenic ones from approximately 40 Hz, at least in dense scar tissue. However, in all these previous studies, no justification behind the choice of the specific spectral range was provided. Indeed, differently to the previous works, our study characterises the spectral signatures of human endocardial post-ischaemic EGMs, both normal and abnormal, quantitatively by analysing their power contents in different sub-bands and looking at their spectral morphologies. Our analysis not only focuses on scar-related and arrhythmogenic substrates but also describes, in detail, the different AVP and physiological EGM types, thus providing additional important information for their characterisation. Whilst the rigorous assessment described above allows for studies on statistical differences, the generalisability of our results is affected by some limitations of this study. Specifically, our analysis was carried out on a limited set of bipolar EGMs acquired from seven post-ischaemic VT patients. Thus, larger datasets are necessary to reinforce the results or reduce the strength of our findings. Moreover, all recordings were annotated by a single cardiologist, whose experience may have biased the subsequent analyses. Furthermore, the labelling process and the subsequent analyses were carried out simply based on the signals as they were recorded by the CARTO ® 3 system and as exploited during the clinical procedures, without taking into account any dependence from wavefront directionality and electrode parameters, which however affect the substrate-guided mapping techniques inherently [55][56][57][58] .
Other studies are in progress to address the far-field effect on AVP power estimations to provide a deeper characterisation of these potentials after the influence of global ventricular depolarisation is removed.

Conclusions
Despite the widespread association of AVPs with high-frequency spectral contents in post-ischaemic intracardiac bipolar EGMs, a rigorous spectral analysis of these signals was missing in the scientific literature. In this work, we addressed this gap and reveal that the main frequency contributions of physiological and pathological postischaemic EGMs are found below 320 Hz. Moreover, when amplitude influences are eliminated, physiological potentials show greater contributions at lower frequencies whereas AVPs demonstrate higher spectral contributions at frequencies above ~ 40 Hz. Conversely, when looking at AVPs only, LP1 showed lower power contributions than LP2 and EP mainly above 60 Hz, whereas LP2 and EP EGMs statistically differed in 200-220 Hz sub-band. In the light of the above-mentioned spectral signatures of AVPs and physiological potentials, our findings may be valuable not only because they represent a spectral characterisation of these potentials, moving a step forward in the direction of a deeper understanding of arrhythmogenic substrate mechanisms, but also to www.nature.com/scientificreports/ support the development of automatic tools for the efficient and targeted distinction of different physiological and abnormal EGM types.

Figure 5.
Absolute and normalised PSDs for all EGM types. Representative PSDs for both physiological and pathological signals in terms of medians (black solid line) and 5th and 95th percentiles (grey zones). From top to bottom: PSDs for border, scar, LP1, LP2 and EP EGMs. The left column illustrates standard PSD curves, whilst the right column depicts the same PSD curves after normalisation so that the area under each curve is unitary, thus allowing for a comparative overview of both absolute and relative power contents for all EGM types in different sub-bands.