# Sensitivity of Electrocardiogram on Electrode-Pair Locations for Wearable Devices: Computational Analysis of Amplitude and Waveform Distortion

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

_{2}and V

_{3}in the standard 12-lead. These findings will facilitate the placement of ECG electrodes and interpretation of the measured ECG signals for wearable devices.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Anatomical Human Model

#### 2.2. Bipolar Electrode Pairs

#### 2.3. Scalar-Potential Finite-Difference Methods

**J**,

**n**

_{B}, Ω, and B

_{S}are the electrical conductivity, current density, unit vector outwardly normal to the body surface, volume conductor, and body surface, respectively. Equation (1) was discretized on the basis of a quasi-static approximation [25] to obtain the following equation:

_{n}, q, and S

_{n}denote the node index, electric scalar potential at the n-th node, angular frequency, electrical charge at the 0-th node, and edge conductance from the n-th node to the 0-th node derived from the tissue conductivity of the surrounding voxels, respectively.

^{−6}.

#### 2.4. Quasi-Static Finite-Difference Time-Domain Methods

#### 2.5. Modeling Cardiac Potentials and Construction of the ECG

#### 2.6. Dynamic Time Warping Methods

_{max}and V

_{min}represent the maximum and minimum values of the QRS wave, respectively.

_{i}and t

_{j}represent the coordinate data and each subscript represents the order of the observed time. δ(ω

_{k}) represent the distance between the points associated with the stretching transformation, and i

_{k}and j

_{k}represent the indices of S and T associated with the stretching transformation, respectively.

#### 2.7. Multivariate Analysis

#### 2.8. Evaluation Procedure

_{1}to V

_{6}of a 12-lead ECG and compared it with the measured data [37]. Then, we computationally constructed an ECG waveform for 35 different bipolar lead combinations to evaluate individual differences in body size (N = 4, Figure 1), heart size (N = 7, Figure 2a), and orientation (N = 7, Figure 2b).

_{N}C

_{2}pattern, which is a combination of N different human body models. The mean DTW for all combinations was calculated to represent the individual differences in the ECG amplitude for the corresponding bipolar lead combination. This procedure was repeated for different body and heart sizes and heart orientations. The same method was used to calculate the normalized DTW, an index of ECG waveform variability.

## 3. Results

#### 3.1. Verification in the Construction of the ECG Waveform Using the 12-Lead ECG

_{1}to V

_{6}, respectively. For further verification, our computational results were compared with measured ECG data [37] in terms of the R-wave amplitude (refer to Figure 5a) at each chest lead (V

_{1}to V

_{6}). Figure 6 shows the box plot diagram comparing the R-wave amplitude for the measured values. Furthermore, the computed value for the original XCAT model is also shown for comparison. Because the R-wave amplitude of each chest lead differs greatly depending on the transition zone, the measured data for 74 subjects were used with a transition zone at V

_{2}and the maximum R-wave amplitude at V

_{3}. Figure 6 shows the computed amplitude of the R wave at different electrode positions, together with the measured results for the 74 subjects. Computational values were generally within the quartile range. QRS width (Figure 4a) was 0.115 [s] in the computation, whereas it ranged from 0.058 to 0.126 [s] in the measured waveforms.

#### 3.2. Validation in the Signal Amplitude of the QRS Wave

_{2}and V

_{3}for different geometrical factors, as observed for columns 6, 7, and 8 in row 4 of the BSPM electrode positions (Figure 7).

#### 3.3. Variation in DTW and Normalized DTW

_{2}. These electrode positions have higher amplitude values, indicating a trade-off between amplitude and waveform variations in bipolar ECG measurements. However, within row 4, the signal amplitude variation in column 6 was lower than that in columns 7 and 8. The distributions of misalignment were more spread out. For normalized DTW, high and low values were observed at high SA in the lower part of V

_{2}and row 4, respectively.

#### 3.4. Statistical Analysis of the Geometrical Factors

#### 3.5. Optimal Position of the Electrodes

_{1}to V

_{4}in the standard 12-lead ECG are included in the region of electrode positions for the top 20% of the waveform quality.

## 4. Discussion

_{2}and V

_{3}electrode positions for different geometrical factors, corresponding to the heart. As in a previous study [16], the signal amplitude was larger in row 4. The most influential geometrical factor was the model’s physique. Because of the electrode–heart distance, the amplitude was high for the underweight and normal models, with average values of 2.05 mV and 1.2 mV, respectively. The highest amplitudes were observed for columns 6, 7, and 8 in row 4 of the BSPM electrode positions.

_{2}for the considered geometrical factors (Figure 8). In contrast, a higher normalized DTW appeared approximately 6 cm below V

_{2}for all geometrical factors, except heart size. These electrode positions exhibited higher amplitude values, indicating a trade-off between amplitude and waveform variations in the bipolar ECG. However, within row 4, the signal amplitude variation in column 6 was lower than that in columns 7 and 8 of the BSPM electrode positions. The distributions of misalignment were more spread out. For normalized DTW, high and low values were observed in the lower part of V

_{2}and row 4, respectively, for high signal amplitude.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Malmivuo, J.; Plonsey, R. Bioelectromagnetism Principles and Applications of Bioelectric; Oxford University Press: Oxford, UK, 1995; p. 512. [Google Scholar]
- Garcia, T.B. 12-Lead ECG: The Art of Interpretation; Jones & Bartlett Learning: Burlington, MA, USA, 2013. [Google Scholar]
- Montague, T.J.; Smith, E.R.; Cameron, D.A.; Rautaharju, P.M.; Klassen, G.A.; Felmington, C.S.; Horacek, B.M. Isointegral Analysis of Body Surface Maps: Surface Distribution and Temporal Variability in Normal Subjects. Circulation
**1981**, 63, 1166–1172. [Google Scholar] [CrossRef] - Bergquist, J.; Rupp, L.; Zenger, B.; Brundage, J.; Busatto, A.; MacLeod, R.S. Body Surface Potential Mapping: Contemporary Applications and Future Perspectives. Hearts
**2021**, 2, 514–542. [Google Scholar] [CrossRef] - Rahul, J.; Sora, M.; Sharma, L.D. A Novel and Lightweight P, QRS, and T Peaks Detector Using Adaptive Thresholding and Template Waveform. Comput. Biol. Med.
**2021**, 132, 104307. [Google Scholar] [CrossRef] [PubMed] - Boineau, J.P.; Spach, M.S. The Relationship between the Electrocardiogram and the Electrical Activity of the Heart. J. Electrocardiol.
**1968**, 1, 117–124. [Google Scholar] [CrossRef] [PubMed] - Van Oosterom, A.; Hoekema, R.; Uijen, G.J.H. Geometrical Factors Affecting the Interindividual Variability of the ECG and the VCG. J. Electrocardiol.
**2000**, 33, 219–227. [Google Scholar] [CrossRef] [PubMed] - Mincholé, A.; Zacur, E.; Ariga, R.; Grau, V.; Rodriguez, B. MRI-Based Computational Torso/Biventricular Multiscale Models to Investigate the Impact of Anatomical Variability on the ECG QRS Complex. Front. Physiol.
**2019**, 10, 1103. [Google Scholar] [CrossRef] [PubMed] - Huiskamp, G.J.M.; van Oosterom, A. Heart Position and Orientation in Forward and Inverse Electrocardiography. Med. Biol. Eng. Comput.
**1992**, 30, 613–620. [Google Scholar] [CrossRef] [PubMed] - Sameni, R.; Clifford, G.D. A Review of Fetal ECG Signal Processing Issues and Promising Directions. Open Pacing Electrophysiol. Ther. J.
**2010**, 3, 4–20. [Google Scholar] [CrossRef] - Sharma, M.; Dhiman, H.S.; Acharya, U.R. Automatic Identification of Insomnia Using Optimal Antisymmetric Biorthogonal Wavelet Filter Bank with ECG Signals. Comput. Biol. Med.
**2021**, 131, 104246. [Google Scholar] [CrossRef] [PubMed] - Zhang, P.; Ma, C.; Sun, Y.; Fan, G.; Song, F.; Feng, Y.; Zhang, G. Global Hybrid Multi-Scale Convolutional Network for Accurate and Robust Detection of Atrial Fibrillation Using Single-Lead ECG Recordings. Comput. Biol. Med.
**2021**, 139, 104880. [Google Scholar] [CrossRef] - Kania, M.; Rix, H.; Fereniec, M.; Zavala-Fernandez, H.; Janusek, D.; Mroczka, T.; Stix, G.; Maniewski, R. The Effect of Precordial Lead Displacement on ECG Morphology. Med. Biol. Eng. Comput.
**2014**, 52, 109–119. [Google Scholar] [CrossRef] - Georgiou, K.; Larentzakis, A.V.; Khamis, N.N.; Alsuhaibani, G.I.; Alaska, Y.A.; Giallafos, E.J. Can Wearable Devices Accurately Measure Heart Rate Variability? A Systematic Review. Folia Med.
**2018**, 60, 7–20. [Google Scholar] [CrossRef] - Hashimoto, Y.; Sato, R.; Takagahara, K.; Ishihara, T.; Watanabe, K.; Togo, H. Validation of Wearable Device Consisting of a Smart Shirt with Built-In Bioelectrodes and a Wireless Transmitter for Heart Rate Monitoring in Light to Moderate Physical Work. Sensors
**2022**, 22, 9241. [Google Scholar] [CrossRef] - Puurtinen, M.; Viik, J.; Hyttinen, J. Best Electrode Locations for a Small Bipolar ECG Device: Signal Strength Analysis of Clinical Data. Ann. Biomed. Eng.
**2009**, 37, 331–336. [Google Scholar] [CrossRef] - Noh, H.W.; Jang, Y.; Lee, I.B.; Song, Y.; Jeong, J.W.; Lee, S. A Preliminary Study of the Effect of Electrode Placement in Order to Define a Suitable Location for Two Electrodes and Obtain Sufficiently Reliable ECG Signals When Monitoring with Wireless System. In Proceedings of the 2012 Annual International Conference of the IEEE Engineering in Medicine and Biology Society, San Diego, CA, USA, 28 August–1 September 2012; pp. 2124–2127. [Google Scholar] [CrossRef]
- Geneser, S.E.; Kirby, R.M.; MacLeod, R.S. Application of Stochastic Finite Element Methods to Study the Sensitivity of ECG Forward Modeling to Organ Conductivity. IEEE Trans. Biomed. Eng.
**2008**, 55, 31–40. [Google Scholar] [CrossRef] [PubMed] - Farina, D.; Jiang, Y.; Dössel, O. Acceleration of FEM-Based Transfer Matrix Computation for Forward and Inverse Problems of Electrocardiography. Med. Biol. Eng. Comput.
**2009**, 47, 1229–1236. [Google Scholar] [CrossRef] [PubMed] - Fischer, G.; Tilg, B.; Modre, R.; Huiskamp, G.J.M.; Fetzer, J.; Rucker, W.; Wach, P. Bidomain Model Based BEM-FEM Coupling Formulation for Anisotropic Cardiac Tissue. Ann. Biomed. Eng.
**2000**, 28, 1229–1243. [Google Scholar] [CrossRef] [PubMed] - Nakane, T.; Ito, T.; Matsuura, N.; Togo, H.; Hirata, A. Forward Electrocardiogram Modeling by Small Dipoles Based on Whole-Body Electric Field Analysis. IEEE Access
**2019**, 7, 123463–123472. [Google Scholar] [CrossRef] - Nakano, Y.; Rashed, E.A.; Nakane, T.; Laakso, I.; Hirata, A. Ecg Localization Method Based on Volume Conductor Model and Kalman Filtering. Sensors
**2021**, 21, 4275. [Google Scholar] [CrossRef] [PubMed] - Segars, W.P.; Mahesh, M.; Beck, T.J.; Frey, E.C.; Tsui, B.M.W. Realistic CT Simulation Using the 4D XCAT Phantom. Med. Phys.
**2008**, 35, 3800–3808. [Google Scholar] [CrossRef] [PubMed] - Gabriel, S.; Lau, R.W.; Gabriel, C. The Dielectric Properties of Biological Tissues: III. Parametric Models for the Dielectric Spectrum of Tissues. Phys. Med. Biol.
**1996**, 41, 2271–2293. [Google Scholar] [CrossRef] - Dimbylow, P.J. Induced Current Densities from Low-Frequency Magnetic Fields in a 2 Mm Resolution, Anatomically Realistic Model of the Body. Phys. Med. Biol.
**1998**, 43, 221–230. [Google Scholar] [CrossRef] - Carlsson, M.; Cain, P.; Holmqvist, C.; Stahlberg, F.; Lundback, S.; Arheden, H. Total Heart Volume Variation throughout the Cardiac Cycle in Humans. Am. J. Physiol. Circ. Physiol.
**2004**, 287, H243–H250. [Google Scholar] [CrossRef] - Kawai, N.; Sotobata, I.; Noda, S.; Okada, M.; Kondo, T.; Yokota, M.; Yamauchi, K.; Tsuzuki, J. Correlation between the Direction of the Interventricular Septum Estimated with Transmission Computed Tomography and the Initial QRS Vectors. J. Electrocardiol.
**1984**, 17, 401–407. [Google Scholar] [CrossRef] [PubMed] - Shahidi, A.V.; Savard, P. Forward Problem of Electrocardiography: Construction of Human Torso Models and Field Calculations Using Finite Element Method. Med. Biol. Eng. Comput.
**1994**, 32, 25–33. [Google Scholar] [CrossRef] [PubMed] - Dawson, T.W. Analytic Validation of A Three-Dimensional Solar-Potential Finite- Difference Code for Low-Frequency Magnetic Induction. Appl. Comput. Electromagn. Soc. J.
**2022**, 11, 72–81. [Google Scholar] - Hirata, A.; Takano, Y.; Nagai, T. Quasi-Static FDTD Method for Dosimetry in Human Due to Contact Current. IEICE Trans. Electron.
**2010**, E93-C, 60–65. [Google Scholar] [CrossRef] - Rajbhandary, P.L.; Nallathambi, G.; Selvaraj, N.; Tran, T.; Colliou, O. ECG Signal Quality Assessments of a Small Bipolar Single-Lead Wearable Patch Sensor. Cardiovasc. Eng. Technol.
**2022**, 13, 783–796. [Google Scholar] [CrossRef] [PubMed] - Raghavendra, B.S.; Bera, D.; Bopardikar, A.S.; Narayanan, R. Cardiac Arrhythmia Detection Using Dynamic Time Warping of ECG Beats in E-Healthcare Systems. In Proceedings of the 2011 IEEE International Symposium on a World of Wireless, Mobile and Multimedia Networks, Lucca, Italy, 20–24 June 2011; pp. 1–6. [Google Scholar] [CrossRef]
- Yang, H.; Wei, Z. Arrhythmia Recognition and Classification Using Combined Parametric and Visual Pattern Features of ECG Morphology. IEEE Access
**2020**, 8, 47103–47117. [Google Scholar] [CrossRef] - Müller, M. Information Retrieval for Music and Motion; Springer: Berlin/Heidelberg, Germany, 2007; pp. 1–313. [Google Scholar] [CrossRef]
- Senin, P. Dynamic Time Warping Algorithm Review. Science
**2008**, 2007, 1–23. [Google Scholar] - Rencher, A.C.; Christensen, W.F. Methods of Multivariate Analysis; Wiley Online Library: Hoboken, NJ, USA, 2012; ISBN 9781118391686. [Google Scholar]
- Wagner, P.; Strodthoff, N.; Bousseljot, R.D.; Kreiseler, D.; Lunze, F.I.; Samek, W.; Schaeffter, T. PTB-XL, a Large Publicly Available Electrocardiography Dataset. Sci. Data
**2020**, 7, 154. [Google Scholar] [CrossRef] [PubMed] - Shiroma, E.J.; Lee, I.-M. Physical Activity and Cardiovascular Health. Circulation
**2010**, 122, 743–752. [Google Scholar] [CrossRef] [PubMed]

**Figure 1.**Anatomical numerical human body models developed using the 4D extended cardiac-torso (XCAT) phantom representing (

**a**) underweight (BMI: 17.2), (

**b**) normal (BMI: 23.2), (

**c**) pre-obese (original) (BMI: 28.5), and (

**d**) obese (BMI: 34.2).

**Figure 2.**Variations in the XCAT cardiac model showing (

**a**) 90%, 95%, 98%, 100%, 102%, 105%, and 110% of the original model volume (front view of the body) and (

**b**) −8, −5, −3, 0, +3, +5, and +8 degree rotations (above view of the head) from left to right.

**Figure 3.**(

**a**) Definition of the upper bipolar electrode positions (shown in gray) for evaluating the effect of geometrical factors. (

**b**) Electrode misalignment in eight directions with 2 cm: white, black, and green dots indicate original BSPM electrodes, misaligned electrodes displaced by 2 cm, and the upper electrode used as a reference point, respectively.

**Figure 4.**(

**a**) ECG outline and the parameter names for waveform characteristics. (1) SA (signal amplitude), (2) R-wave amplitude, and (3) QRS width. (

**b**) Visualized image of d (heart–electrode distance) and θ (solid angle of the heart viewed from the electrode) formed by one electrode and one current path. The two blue lines extend from the electrode’s center and connect to the uppermost and lowermost points of the myocardial tissue in the model. The yellow line represents the distance between the electrode’s center and the current path. (

**c**) Positions of the electric dipoles in the heart of the anatomical model that sequentially propagate from (4) to (8). (4) A–V node to bundle of His, (5) bundle of His to bundle branches, (6) bundle branches, and (7) and (8) Purkinje fibers.

**Figure 7.**Contour plot of the ECG signal amplitude variability for different bipolar electrodes. The vertical and horizontal axes correspond to the rows and columns in Figure 3a. There are variations due to (

**a**) physique, (

**b**) heart size, (

**c**) heart orientation, and (

**d**,

**e**) misalignment by 1 cm and 2 cm, respectively. The red oval corresponds to the heart’s position when the human body is viewed from the front. The red square indicates the position of the chest electrode in the standard 12-lead ECG as a reference.

**Figure 8.**Contour plot of (

**a**–

**e**) DTW and (

**f**–

**j**) normalized DTW for different bipolar electrodes. Variations due to (

**a**,

**f**) physique, (

**b**,

**g**) heart size, (

**c**,

**h**) heart orientation, and (

**d**,

**i**) and (

**e**,

**j**) misalignment by 1 cm and 2 cm, respectively. The vertical and horizontal axes correspond to the rows and columns in Figure 3a. The red oval corresponds to the heart’s position when the human body is viewed from the front. The red square indicates the position of the chest electrode in the standard 12-lead ECG as a reference.

**Figure 9.**Electrode attachment area, which is insensitive to geometric and misalignment factors. The vertical and horizontal axes correspond to the rows and columns in Figure 3a. The thick black line indicates the region of electrode positions for the top 20% of the waveform quality factors. The red oval corresponds to the heart’s position when the human body is viewed from the front. The red square indicates the position of the chest electrode in the standard 12-lead ECG as a reference.

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Sanjo, K.; Hebiguchi, K.; Tang, C.; Rashed, E.A.; Kodera, S.; Togo, H.; Hirata, A.
Sensitivity of Electrocardiogram on Electrode-Pair Locations for Wearable Devices: Computational Analysis of Amplitude and Waveform Distortion. *Biosensors* **2024**, *14*, 153.
https://doi.org/10.3390/bios14030153

**AMA Style**

Sanjo K, Hebiguchi K, Tang C, Rashed EA, Kodera S, Togo H, Hirata A.
Sensitivity of Electrocardiogram on Electrode-Pair Locations for Wearable Devices: Computational Analysis of Amplitude and Waveform Distortion. *Biosensors*. 2024; 14(3):153.
https://doi.org/10.3390/bios14030153

**Chicago/Turabian Style**

Sanjo, Kiyoto, Kazuki Hebiguchi, Cheng Tang, Essam A. Rashed, Sachiko Kodera, Hiroyoshi Togo, and Akimasa Hirata.
2024. "Sensitivity of Electrocardiogram on Electrode-Pair Locations for Wearable Devices: Computational Analysis of Amplitude and Waveform Distortion" *Biosensors* 14, no. 3: 153.
https://doi.org/10.3390/bios14030153