I&CPS -05-18

Dalziel Revisited: A Study of the Electrical Parameters Affecting Ventricular Fibrillation

Robert E. Nabours, Life Senior Member IEEE

Abstract-More than 32 years have passed since Charles F. Dalziel published his last of four seminal papers on ventricular fibrillation. His empirical formula for the current necessary to produce ventricular fibrillation in man has been recognized by scientists and engineers as forming the basis for an analytical understanding of this major cause of death from electrical shock. In addition, the concept of let go current for man has resulted in the standard for personnel safety used to design ground-fault interrupting circuit protection. In this paper the additional electrical parameters of energy, voltage and resistance are related analytically to Dalziel's work and the relationship of these parameters to the likelihood of ventricular fibrillation is established for humans ranging in mass from 50 kg to 90 kg, i.e. 110 to 198 Ibs in weight. Equations and graphical plots of these important relationships are given.

Index Terms-Dalziel. CharlesF.. Electrical parameters for ventricular fibrillation

I. Introduction

Electric shock can be detined as the immediate effects produced by the passage of an electric current through any part of the body, e.g. painful stimulation of nerves or tetanic contractions of muscles. Such shocks are the result of an electric current that enters the body, ranging from a minor static-electric discharge to a lightning strike accident, but most often resulting from contact with residential or commercial electrical systems.

The causes of death from electricity "electrocution" have been studied since the period 1880-1900 when physicians were presented with the victims of accidental electrocutions for postmortem examination.[l] Deaths from technical (commercial) electricity were first reported in 1879 and 1881 by Jex -

Blake in 1913[2] Some of the earliest scientific papers on this subject were published in 1899 by Prevost. [3] Later papers were published by Ferris (1936)[4] and Kouwenhoven (1955)[5] (1959)[6] (1964)[7].

Ventricular fibrillation (v-f) is probably the most common cause of death in electric shock cases and can be produced by moderately small currents that cause a chaotic, uncontrolled, rapid contraction of the heart muscle. The muscle writhes, something like a bag of wonns, though faster. During v-f the heart pumps no blood to the brain since the diminished blood pressure immediately following the v-fproducing shock, and lasting about eleven seconds, is insufficient to exceed the normal intra cranial pressure.[8] Following this brief (II sec) interval, there is no blood flow to the brain.

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II. Analysis

The seminal series of papers by Dalziel (1956)[9] (1968)[10] (1969)[11], concluding in (1972)[12] Conn the basis for the analysis of parameters affecting ventricular fibrillation presented in this paper. The fundamental equations, (I) and (2), for the onset of ventricular fibrillation (v-£) are:

The Dalziel equation,

I

(I) where I is in amperes, t is in seconds, and k is an empirical constant determined by the mass (weight) of the subject and the statistical distribution of individuals for the subject weight.

The energy equation for the delivered shock is expressed by Eqn. (2).

E == V (I)t (2)

where E is in Joules, V in volts, I in amperes, and t in seconds.

Substituting (1) for I into (2) and simplifying gives,

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E = V(k)10-3(�) (3)

This represents the shock source energy necessary to induce v-f according to weight and statistical distribution of subject.

An alternate form of the energy equation can be expressed in terms of the resistance that the subject presents to the source current.

E (4)

Now squaring (1) and substituting e into (4) gives,

(5)

Thus, the critical path resistance necessary for v-f is a function of the source energy and weight only and is given by,

R E (6)

The current necessary for v-f can also be expressed in terms of energy and voltage by substitUting for

Ji from (1) into (3),

1 = (7)

It has thus been shown that the critical path resistance, Eqn. (6), for an electrical shock to produce.v-fis a direct function of the shock energy and an inverse function of the k-factor squared, i.e. subject weight.

The energy delivered by th e source to the shock subject can also be expressed as follows:

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E (8)

Upon SUbstituting Eqn. (6) for R in Eqn. (8) and solving for V, one obtains

v (9)

III. The empirical k-factor

Dalziel (1968) evaluated the k-factor for Eqn. (1) at 50 kg (110 lbs) body weight for the 0.5% and 95.5% population statistics as 116 minimum and 185 maximum. Using the data relied upon by Dalziel, the minimum, median and maximum values afk were found for two additional body weights, i.e. 70 kg and 90 kg, these results are shown in Table 1.

Jlltib:. J,-r.dQt

M ... W.lpl M""iAl"1IJI Med •• D

Ma:J.imulB kg Lbo .q).s�. >95-5%

50 110 116 ISO 1115

70 15-4 154 205 256

!JO 198 In 261 330

Table I Dalziel k-factar vs Body Weight for Man

The v-f current for humans vs. subject weight and time is shown in Figure 1.

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I U.I' r---------;----------.,

I IO� t--..::--------f----------1 ."

.... "

'"n_L'---------'----------, _

Fig. I. Average ventricular fibrillation current III humans vs. subject weight and time. I for 50 kg (l1O lbs), J for 70 kg (154Ibs), K for 90 kg

(l 98Ibs). I, J, & K are averages for the subject weight, ill is the minimum for < 0.5%, M is the maximum for > 99.5% ofthe population. Current is in milli-amperes.

Utilizing the mlOlmum k-factor from Table 1, the minimum current necessary for v-f can be calculated for <0.5% of the population for a 3 sec shock interval.

where I is in rnA.

The minimum energy necessary for ventricular fibrillation in most of the population can then be calculated for a 120 V nns source and a 3 sec shock interval from Eqn. (2),

E > 24.11 E is in Volt-Ampere-Sec (Joules).

Since the critical path resistance necessary for ventricular fibrillation is a function of source energy and k only, we have from Eqn. (8) that

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R < V2 t = (120)2 3 = 1792 E 24.11

R is in ohms.

For values of R greater than 1,7 92 ohms, it is unlikely « 0.5%) that v-f will be produced for 120 V exposure times of 3 sec or less.

The energy required for v-f vs critical path resistance is shown in Figure 2 for three values of the k-factor.

". ,------,---

, .�.

Fig. 2. Energy required for v-f vs subject weight and critical path resistance R. e(R) is the minimum energy for < 0.5% of the population, a(R) is the average energy and E(R) is the maximum energy required for >99.5% of the popUlation.

Returning now to Eqn. (9) for voltage necessary to produce v-f vs weight, time and critical path resistance, Figure 3 is a plot of the v-f voltage for three values of k-factor and a critical path resistance of 1000 Ohms.

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"'ll.EI

I Wi .----------,-----------,

I-ID' 1---.:---------+----------:

I I I

i ... I------�;::---:;:;..., --,J

leo·�,--------':----------' ,

II�I

Fig. 3. v-f voltage vs time for minimum, average and maximum weight subjects with a critical path resistance of 1000 Ohms

Consider Eqn. (9) for V vs R, k, and t. This relationship

is shown in Figure 4.

, ,,' 1-------+------:;:�--1

''''

Figure 4. Voltage vs critical path resistance R for an exposure time of 3 seconds.

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IV. Conclusion

The fundamental equations for v-f have been utilized in this paper to derive two additional relationships for the electrical parameters of interest in the shock process that can produce ventricular fibrillation in humans.

The work of Dalziel has been relied upon to expand the v-f data to include humans of weights: 50 kg (110 Ibs), 70 kg (154 labs), and 90 kg (198 Ibs). Table 1 and Figure 1 provide these results. Additionally, the median v-f currents for these weights have been calculated and shown in this table and figure. It has been shown that the source energy necessary to produce v-f is a function only of the subject weight and the critical path resistance of the current path from made contact through the human body. At 1000 ohms, a typical value of resistance often used in v-f calculations, a minimum of approximately 13 joules of energy is required to produce v-f. When the source energy delivered in the shock is at least 109 joules, nearly all subjects will experience v-f.

In derived Eqn. (9) and Figures 3 & 4, it is shown that the source voltage necessary to produce v-f is a function of the subject weight, the critical path resistance, and the shock duration time. Again, at 1000 ohms, a minimum of 116 volts is required to produce v­f in one second for the smallest of SUbjects. When the voltage of the source is at least 330 yolts, nearly all subjects will experience v-f in one second.

Since the voltage required for v-f is inversely proportional to --Jt , at 1000 ohms a minimum of 67 volts is required for three seconds to produce v-ffor the smallest person. At 190 volts or more, nearly all subjects will experience v-f in three seconds.

It was shown that the maximum critical path resistance with a 120 volt source and a three second exposure is 1,792 ohms. For R values greater than 1,792 ohms it is unlikely «0.5%) that v-fwill result unless exposure time exceeds 3 seconds,

References [I] Theodore Bernstein, "Theories of the causes of death from electricity in the late nineteenth century", Univ. of Wisconsin, Engineering Experiment Station, Reprint No. 1863, Medical Instrumentation, Vol. 9, No. 6, Nov.-Dec. 1975, Assoc. for the Advancement of Medical Instrumentation.

[2] lex-Blake, A. 1. The Goulstonian lectures on death by electric currents and by lightning. Brit. Med. J. I: 425-430,492-498,548-552,601-603,1913.

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[3] Prevost, 1. L. and F. BatteJIi, "Death by electric currents (alternating current)". C. R. Acad. Sci. Paris 128: 668-670, 1899.

[4] Ferris, L. P. "Effect of electric shock on the heart", AJEE Trans., 55: 498-515, May Section, 1936.

[5] Kouwenhoven, W. B. "Electric defibrillation", AlEE Trans. Paper No. 55-95, 1955.

.

[6] Kouwenhoven, W. B. "Ac shocks of varying parameters affecting the heart" , AlEE Trans.{Communications and Electronics) Vol. 78, 163-169, May 1959.

[7] Kouwenhoven, W. B. "The effects of electricity on the human body", Bull. Johns Hopkins Hasp. lIS; 425-446,1964.

[8] Nabours, Fish and Hill, Electrical Injuries Engineering, Medical and Legal Aspects, 2nd Ed., Lawyers & Judges Publishing Co., 418, 2004.

[9] Dalziel, Charles F. "Effects of Electric Shock on

Man", IRE Trans. on Medical Electronics, 44-62, 1956.

[10] Dalziel and Lee, "Reevaluation of lethal Electric Currents", IEEE Trans. on Industry and General Applications, Vol. IGA-4, No.5, 467-476, Sept.lOct. 1968.

[IIJ Dalziel and Lee, "Lethal Electric Currents", IEEE Spectrum Feb. 1969,44-50.

(12] Dalziel, "Electric shock hazard", IEEE Spectrum Feb. 1972,41-50.

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Robert E. Nabours received a BSEE degree from the Univ. of Arizona in 1957, a MS degree in electrical engineering from Stanford Univ. in 1959 and the PhD in electrical engineering from the Univ. of Arizona in 1965. He was an instructor in EE at the Univ. of Arizona, a project leader in adaptive communications research for Bell Aerosystems Co .•

and the Chief Engineer for Burr-Brown Research Corp. He has practiced consulting engineering since 1958, serving as a forensic electrical engineer in more than 450 cases and testifying as an electrical engineering expert in Court over 50 times. He has authored sixteen papers and three books on forensic electrical engineering. He has published frequently with the IEEE.

Dr. Nabours is a Registered Professional Engineer in the states of Arizona, California, and New Mexico.

Robert E. Nabours, Ph.D. , P.E., 5201 N. Salida Del Sol, Tucson, AZ 85718. e-m: rencee@comcast.net. TeL (520) 299-7273.

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