Coordinating the einthoven body impedance model for ECG signals with IEC 60479–1:2018 electrocution heart current factors

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Highlights

  • The heart current source feeds a resistance network, develops ECG potentials.

  • ECG resistance network models can be used to assess risk of electrocution.

  • Risk varies with ratio of ECG signal of threat path to ECG lead III (LL-LH).

  • In-vivo measurements suggest electrocution risk from leg-leg exposure is low.

  • Measurements suggest risks from LH-RH, LH-LL and RH-LL contacts are similar.

Abstract

The Einthoven electrical circuit for electrocardiogram (ECG) measurement has been modeled as a 2.5 mA impulse current source at the heart, feeding a 13-resistor network. This model can be inverted to establish heart threat currents from electrocution potentials applied at extremities. Using designation of R (right), L (left), H (hand) and L (leg), electrical safety standard IEC 60479–1:2018 defines risk factors for LH-RH and LL-RL paths compared to reference LH-LL path. Heart current reduction factors can be fitted by adjusting some resistor values and by adding a cross-hip resistance to make nodes at each hip. Reciprocity suggests an approach to validate IEC heart current factors by comparing ECG signal magnitudes for different contacts. Hypothetically, the LH-RH ECG signal should be 10x larger than the LL-RL signal if their IEC heart current split factors are correct. In-vivo tests verify some of the electrocution heart current factors using three-lead and two-lead ECG instruments.

Section snippets

Introduction: ECG with string galvanometer

The non-invasive, low-cost, and effective process to measure the electrocardiogram (ECG) is a medical invention that has been in continuous use for more than 100 years. An ECG is a voltage-time graph of the electrical activity of the heart, obtained from recordings of measurement systems such as electrometers, galvanometers, electronic amplifiers and chart or digital recorders. In the 1910s and 1920s, string galvanometers as shown in Fig. 1 were the instruments available for ECG studies [1, 2].

Effect of path on fibrillation current

The IEC 60479–1 (2018) Standard, clause 3.2.6 [6] defines F, the heart-current factor that relates the electric field strength (current density) in the heart for a given current path to the electric field strength (current density) in the heart for a touch current of equal magnitude flowing from left hand to both feet. It provides Table I that uses the same value of F = 1 for LH-LL, LH-RL, LH-2L and 2H-2L paths where 2H refers to contact with both hands and 2L to both legs through the feet on

Inversion of the Einthoven resistor network

The slight imbalance in resistor values, with unequal values of R1 and R2 in Fig. 2 is an important aspect of the model in electrocution calculations. Consider a potential of 100 V applied to LH with both LL and RL grounded. Ignoring skin breakdown resistance, the model in Fig. 2 suggests that a current of 233 mA will flow into LH and equal currents of 116.5 mA will flow out of each leg. The imbalanced resistors lead to ac current flow of 2.6 mA through the heart, about the same magnitude as

Adding cross-hip resistance to the Einthoven resistor network

The traditional ECG circuit model in Fig. 2 can be improved further to match the heart-current split factors in Table I. This is achieved by separating the single node at the hip (H) into two nodes, RH and LH in Fig. 4. A cross-hip resistance on the order of 10–100 Ω is supported by measurements of electrocution resistance of pigs as well as by the other values of peripheral torso resistance. Resistors R3, R4, R5 and R6 now connect each side of the heart, nodes (a) and (b), to each hip,

Process for validation of heart current split factors: comparison of lead I: lead III and lead II: lead III ECG signal amplitudes

The “Einthoven Triangle” research of Mann [18] suggested the Lead I (LH-RH) peak-to-peak signal would be about one-half of the RH-L and LH-L signals. The analysis is based on the projection of the heart axis (origin to upper right) of an equilateral triangle. The quality of a set of three-lead ECG signals is established by verifying that the area of this “triangle” is greater than zero. A comparison of peak magnitudes from the three independent galvanometers could verify the heart current

Process for validation of leg-leg heart current split factor using three-lead ECG

A literature survey did not turn up any measurements of the RL-LL ECG. A preliminary investigation [23] was carried out using three subjects and a GE Case Stress System V6.51 Exercise ECG monitoring system at an ECG clinic. Each subject was measured using a standard three-lead configuration using the right leg as the body voltage reference point. In common with the results in [21], there was a considerable variation in the peak ECG Lead III signal (0.5–1.5 mV) as well as subject-to-subject

Process for validation of heart current split factors using two-lead ECG

Considerable progress has been achieved in two-terminal ECG monitors, intended for personal fitness use, as shown in Fig. 12. This ECG instrument [24] combines internal batteries, contact electrodes, internal signal conditioning, display, and storage. Data are saved and exported for additional analysis, including monitoring of peak-to-peak voltage. The instrument in Fig. 12 is configured to measure either Lead I (LH-RH), Lead II (RH-LL) or chest lead (RH-chest, giving the highest signal

Conclusions and recommendations

A traditional model for the appearance of ECG signals at the extremities in response to the electrical activity of the human heart can be inverted to estimate the effects of electrocution potentials applied at those extremities.

The “Einthoven” model with 2.5-mA current source and a network of 13 resistors provides, to first order, a good match to the path impedance values in IEC 60479–1. Some imbalance in two of the resistors is physically plausible based on distance from hip to top and bottom

Author statement

Ms. Ref. No.: EPSR-D-22–01,932

Coordinating the Einthoven Body Impedance Model for ECG Signals with IEC 60479–1:2018 Electrocution Heart Current Factors

I confirm that I am the main author of this contribution.

There was no financial or non-financial assistance from third parties.

I do not have any financial interest related to the subject matter.

I am not aware of any relevant patents or copyrights that affect this work.

The acknowledgements mention the work of a translator, and two paragraphs from

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

acknowledgements

The authors acknowledge the cooperation of Rockland Clinic, Montréal, QC; Sylvie Laprise, Directrice administrative des cliniques médicales as well as Dr. Susan Hunt in carrying out non-standard ECG tests on volunteer subjects. Professor Chris Andrews provided the Sam reference [9] used by IEC and Lesley Chisholm translated it into English.

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