# Spatial-Temporal Signals and Clinical Indices in Electrocardiographic Imaging (I): Preprocessing and Bipolar Potentials

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## Abstract

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## 1. Introduction

## 2. Methods and Materials

#### 2.1. Notation and ECGI Signal Preprocessing Stages

#### 2.2. DSPO for Bipolar Potentials

#### 2.3. Time Derivative and Time Delay Analysis

#### 2.4. Data Sets

## 3. Experiments and Results

#### 3.1. Preprocessing and Spatial-Temporal Correlations

#### 3.2. Spatial Consistency of Bipolar Potentials

**Statistical consistency of the EGM:**The statistical distributions of the EGM amplitudes obtained with each DSPO are compared in terms of their individual histograms. For each EGM at each mesh point, the amplitude was calculated as the peak-to-peak value.

**Spatial consistency of the amplitude maps:**Figure 7 shows the map of peak-to-peak amplitudes of patient 7 for the unipolar EGM and each DSPO except that of the operator ${\theta}_{v}$, which was discarded after the previously performed analysis, where all the amplitudes were found below $1.5$ mV, the value set for the border region. For each DSPO, we can see that the different regions are consistent with the patient’s physiology- and pathology-known substrate, namely the right side, the zone of the valves, and the inferior part of the ventricle. The color scale of each map is adjusted to the maximum peak-to-peak amplitude of each DSPO. In the unipolar EGM map, the scar region is located in the inferior left wall of the ventricles and the region of the valves also corresponds to the red color assigned to smaller amplitudes. In the lateral-upper wall of the ventricles, we can see a zone of high amplitude that degrades toward the apex and towards the inferior wall of the ventricles, where the scar is located. Operator ${\theta}_{V}$ exhibits spatial consistency with respect to the unipolar EGM, which allows us to determine different regions in the cardiac tissue, and the scar region can be identified in the inferior left wall as well as the valve region. Similarity in the spatial consistency is lower with ${\theta}_{d}$ configuration, with more regions of low amplitudes which seem to be confused with the scar region. In the configuration with operators ${\theta}_{m}$, ${\theta}_{D}$, and ${\theta}_{r}$, there is a markedly reduced spatial consistency with respect to the unipolar EGM, since very small amplitudes in the former appear in regions of higher amplitudes in the latter, making the scar region very ambiguous. In general, correlation coefficients between maps were at most moderately high, as they measure different properties. For instance, the correlation coefficient of DSPO ${\theta}_{V}$ obtained of the peak-to-peak voltage in bipolar vs unipolar EGMs was 0.7140, whereas for ${\theta}_{d}$, it was 0.7804.

**Spatial consistency on neighbors:**Now, we analyze the spatial consistency with respect to the angle and distance at a point and its closest neighbors in two regions of cardiac tissue, namely scar and healthy myocardium tissue. For this purpose, we use the M-mode representations of the EGMs, which are defined as the time–space representation signal measurement in a set of points, i.e., $\mu ({d}_{j},t)$ or $\mu ({\varphi}_{j},t)$, where $j\in {\eta}_{i}$, d is the distance and $\varphi $ is the angle.

**Spatial consistency on lines:**An additional analysis of M-modes was performed in order to study the two DSPOs operators found to be optimal, ${\theta}_{V}$ and ${\theta}_{d}$. As referred before, M-modes are suitable representations to analyze the spatial consistency in a line of mesh points, passing through different regions of the cardiac tissue. Bipolar EGM of each selected consecutive point of the line are represented according to the DSPO selected. The purpose is to see the amplitude changes on the unipolar and bipolar EGMs between the cardiac tissue region so that we can choose the more faithful DSPO for the representation of the bipolar EGM signal in electrophysiology.

#### 3.3. Time Delay from Empirical Considerations

**Morphology analysis for FTD:**Figure 10 shows the bipolar EGM of mesh point 312, which corresponds to a healthy cardiac tissue. It can be seen that the magnitude of the time shift applied to the unipolar EGM affects the waveform of the resulting bipolar EGM. With a 10-sample shift, the morphology of the resulting bipolar EGM presents fragmentation in the depolarization wave and is accompanied by noise. In the case of a shift of 40 samples, the bipolar EGM does not exhibit fragmentation in the depolarization wave and the noise is smaller than in the previous case. For a time shift of 80 samples, the bipolar EGM shows non-fragmentation in the depolarization wave, though it introduces greater and nonphysiological width in its depolarization.

**Morphology analysis for ${\theta}_{V}$ and possible configuration:**Figure 11 shows the resulting bipolar EGM using the new DSPO ${\theta}_{{V}_{\alpha}}$ for several delay values of $\alpha $ seconds. As in the previous case, the bipolar EGM is determined at mesh point 312. Graphs on the left column depict the unipolar EGM, in blue, of the mesh point under analysis and the shifted unipolar EGMs ${\theta}_{{V}_{\alpha}}$, in red. The resulting bipolar EGMs for each time shift are represented on the left column. From top to bottom, the delays are considered to be 10, 40, and 80 samples. For a discrete time shift of 10 samples ($\alpha =10/{f}_{s}$ seconds, where ${f}_{s}=2048$ Hz is the sampling frequency), the bipolar EGM presents fragmentation in the depolarization wave (top right) as well as noise. Additionally, the amplitude with respect to the location of the reference point in the cardiac tissue is low. The remaining bipolar EGMs (middle and bottom left graphs) do not exhibit fragmentation anymore in the depolarization wave and they report a reasonable amplitude by considering that the cardiac tissue under consideration is corresponding to a healthy region. Finally, notice that the depolarization duration of the 80-sample shift bipolar EGM (bottom left graph) is greater.

**Analysis of ${\theta}_{{V}_{\alpha}}$ in border region and fragmentation:**This section tackles a comparative study of operators ${\theta}_{V}$, ${\theta}_{{V}_{\alpha}}$, and delayed reference at point 124 of the mesh, which corresponds to a border region of the cardiac tissue; the analysis aims to scrutinize morphology and amplitude. Wherever needed, the delay is set to be 40 samples $\left(\alpha =\frac{40}{{f}_{s}}\right)$. Just for reminder purposes, the peak amplitudes which define each region of the cardiac tissue in bipolar EGMs are $<0.5$ mV scar region, between $0.5$ mV and $1.5$ mV border region, and $>1.5$ mV healthy region. After the comparison study, a fragmentation analysis of the bipolar EGMs is addressed for the DSPO ${\theta}_{{V}_{\alpha}}$.

## 4. Discussion and Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**This figure depicts two Electrogram (EGM) signals taken from Electrophysiological Studies (EPS) at Hospital Virgen de la Arrixaca de Murcia in Spain. They are shown as examples of actual EGMs, though they correspond to a patient not related with the current study. The upper graph was recorded with the bipolar EGM configuration, and the lower one was recorded with the unipolar EGM configuration.

**Figure 2.**Unipolar EGM maximum potential map (color bar in mV) representing the ambiguity for the calculation of bipolar EGMs associated to the central point in terms of its nearest neighbors.

**Figure 3.**M-mode trajectories for the torso in (

**a**) and epicardium in (

**b**) and the corresponding measured or estimated signals in (

**c**,

**d**). The residuals of atomic baseline wander removal with a spline time-node spacing of 1 s are shown for both in (

**e**,

**f**).

**Figure 4.**Spatial–temporal autocorrelation of the M-mode potentials (

**a**,

**b**) and of the M-mode baseline wander residual potentials for ${T}_{w}=$ 1 s (

**c**,

**d**) and algorithm missadaptation when using ${T}_{w}=$ 0.5 and 2 s (e and f, respectively) on the torso (

**e**) and on the epicardium (

**f**).

**Figure 5.**Example of high-frequency filtering of the M-mode signals: We can see the M-mode residuals in (

**a**,

**b**), and their spatial-temporal autocorrelations both for the torso in (

**c**) and for the epicardium in (

**d**).

**Figure 6.**Analysis of the EGM statistical distribution in terms of the histogram of the EGM amplitudes for all the configurations.

**Figure 7.**Potential maps: the top left graph is the unipolar EGM, while the remaining ones are the bipolar EGM configuration.

**Figure 8.**Closest neighbor consistency in a healthy region (

**a**) and on a scar region (

**b**) of the infarcted patient: On each panel is (up, left) potential map, (up, right) M-mode of unipolar EGMs, and (down) spatial consistency of bipolar EGM with respect to the angle (left) and distance (right). Distance between nodes is in mm, time is in s, angle is in radians, and ${V}_{pp}$ is in mV. The selected locations are highlighted in the maps with white points and their reference number.

**Figure 9.**Line of points starting from epicardial scar up to a healthy region of cardiac tissue in the infarction patient with bipolar EGMs using the ${\theta}_{V}$ (

**a**) and the ${\theta}_{d}$ (

**b**) criteria: (up, left) map of potentials, (up, right) bipolar EGMs of the line of points, (down, left) M-mode of the bipolar EGMs of the dotted line, and (down, right) M-mode of bipolar EGMs adjusted by using the correlation coefficient.

**Figure 10.**Bipolar EGMs obtained with the delayed reference operator: Graphs on the left column depict the unipolar EGM (point 312), in red, and the same unipolar EGM delayed, in blue. Graphs on the right column show the bipolar EGM obtained as the subtraction of the unipolar ones taken from the left. From top to bottom, the results correspond to delays of 10, 40, and 80 samples.

**Figure 11.**Left column depicts, in blue, the unipolar EGM of the node under study, and, in red, the delayed unipolar EGM of the neighborhood chosen according to DSPO ${\theta}_{{V}_{\alpha}}$. Right column exhibits the resulting bipolar EGMs obtained by subtraction. Panels, from top to bottom, represent the computation of bipolar EGMs for different time delays $\left(\alpha =\frac{\#\phantom{\rule{3.33333pt}{0ex}}\mathrm{samples}}{{f}_{s}}\right)$, namely 10, 40, and 80 time shift samples, respectively.

**Figure 12.**DSPO comparison: the left column depicts the obtained bipolar EGM of point 124 of cardiac tissue. From top to bottom are ${\theta}_{V}$, ${\theta}_{{V}_{\alpha}}$, and delayed reference. The right-hand plot represents the amplitude map of the DSPO ${\theta}_{{V}_{\alpha}}$ and the location of the analyzed point.

**Figure 13.**Fragmentation maps and bipolar EGMs with the DSPO ${\theta}_{{V}_{\alpha}}$: The left column shows the fragmentation maps and the selected points of the mesh. From top to bottom are 312, 395, and 136. The curves on the right column depict the bipolar EGM for each corresponding points of the left.

**Table 1.**Digital Signal Processing Operator (DSPO) definitions to choose the neighbor node ${\overline{s}}_{k}$ which characterizes the reference bipolar EGM associated to a given point ${\overline{s}}_{i}$ in the Electrocardiographic Imaging (ECGI) mesh.

DSPO | ${\overline{\mathit{s}}}_{\mathit{k}}$ | $\mathit{v}({\overline{\mathit{s}}}_{\mathit{k}},{\mathit{t}}_{\mathit{w}})$ |
---|---|---|

Amplitude | ${\theta}_{V}\left({C}_{i}\right)$ | $\underset{j\in {\eta}_{i}}{max}\left\{\left|v\right({\overline{s}}_{j},{t}_{w}\left)\right|\right\}$ |

${\theta}_{v}\left({C}_{i}\right)$ | $\underset{j\in {\eta}_{i}}{min}\left\{\left|v\right({\overline{s}}_{j},{t}_{w}\left)\right|\right\}$ | |

Random | ${\theta}_{r}\left({C}_{i}\right)$ | ${\mathrm{rand}}_{j\in {\eta}_{i}}\left\{v({\overline{s}}_{j},{t}_{w})\right\}$ |

Mean | ${\theta}_{m}\left({C}_{i}\right)$ | ${\mathrm{mean}}_{j\in {\eta}_{i}}\left\{\left|v\right({\overline{s}}_{j},{t}_{w}\left)\right|\right\}$ |

Distance | ${\theta}_{D}\left({C}_{i}\right)$ | $\underset{j\in {\eta}_{i}}{max}\left\{|{\overline{s}}_{i}-{\overline{s}}_{j}|\right\}$ |

${\theta}_{d}\left({C}_{i}\right)$ | $\underset{j\in {\eta}_{i}}{min}\left\{|{\overline{s}}_{i}-{\overline{s}}_{j}|\right\}$ |

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**MDPI and ACS Style**

Caulier-Cisterna, R.; Sanromán-Junquera, M.; Muñoz-Romero, S.; Blanco-Velasco, M.; Goya-Esteban, R.; García-Alberola, A.; Rojo-Álvarez, J.L. Spatial-Temporal Signals and Clinical Indices in Electrocardiographic Imaging (I): Preprocessing and Bipolar Potentials. *Sensors* **2020**, *20*, 3131.
https://doi.org/10.3390/s20113131

**AMA Style**

Caulier-Cisterna R, Sanromán-Junquera M, Muñoz-Romero S, Blanco-Velasco M, Goya-Esteban R, García-Alberola A, Rojo-Álvarez JL. Spatial-Temporal Signals and Clinical Indices in Electrocardiographic Imaging (I): Preprocessing and Bipolar Potentials. *Sensors*. 2020; 20(11):3131.
https://doi.org/10.3390/s20113131

**Chicago/Turabian Style**

Caulier-Cisterna, Raúl, Margarita Sanromán-Junquera, Sergio Muñoz-Romero, Manuel Blanco-Velasco, Rebeca Goya-Esteban, Arcadi García-Alberola, and José Luis Rojo-Álvarez. 2020. "Spatial-Temporal Signals and Clinical Indices in Electrocardiographic Imaging (I): Preprocessing and Bipolar Potentials" *Sensors* 20, no. 11: 3131.
https://doi.org/10.3390/s20113131