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Bioelectromagnetics 22:97^105 (2001)

Energy Deposition P rocesses in B io logical

Tissue: Nonthermal B i ohazards Seem U nlik ely

intheUltra-HighFrequencyRange

William F. Pickard

* and Edua rdo G . Moros

Department of E lectr i cal Engi neer ing, W as hi ngton Univ e rs ity,

Saint Louis, Missouri

Radiation Oncology Section, Mallinckrodt Institute of Radiology,Washington University,

Saint Louis, Missouri

The prospects of ultra high frequency (UHF, 300±3000 MHz) irradiation producing a nonthermal

bioeffect are considered theoretically and found to be small. First, a general formula is derived

within the framework of macroscopic electrodynamics for the speci®c absorption rate of micro-

waves in a biological tissue; this involves the complex Poynting vector, the mass density of the

medium, the angular frequency of the electromagnetic ®eld, and the three complex electromagnetic

constitutive parameters of the medium. In the frequency ranges used for cellular telephony and

personal communication systems, this model predicts that the chief physical loss mechanism will be

ionic conduction, with increasingly important contributions from dielectric relaxation as the

frequency rises. However, even in a magnetite unit cell within a magnetosome the deposition rate

should not exceed 1/10 k

T per second. This supports previous arguments for the improbability of

biological effects at UHF frequencies unless a mechanism can be found for accumulating energy

over time and space and focussing it. Second, three possible nonthermal accumulation mechanisms

are then considered and shown to be unlikely: (i) multiphoton absorption processes; (ii) direct

electric ®eld effects on ions; (iii) cooperative effects and/or coherent excitations. Finally, it is

concluded that the rate of energy deposition from a typical ®eld and within a typical tissue is so

small as to make unlikely any signi®cant nonthermal biological effect. Bioelectromagnetics 22:97±

105, 2001.

# 2001 Wiley-Liss, Inc.

Key words: speci®c absorption rate; constitutive parameters; SAR; magnetosomes; dielectric

relaxation; multiphoton absorption

INTRODUCTION

Within the past decade, the worldwide public

acceptance of wireless technology has been remark-

ably swift. In the United States, for example, data

collected by the Cellular Telecommunications Industry

Association (http://www.wow-com.com/statsurv/sur-

vey/199906a.cfm) and available in Fall 1999, extra-

polate to a Summer 2000 subscribership between

80 and 90 million and a doubling time of approxi-

mately 3 years. This situation has resulted in studies

related to possible bioeffects which might be as-

sociated with the many different signals available

and entering the market [Repacholi, 1998; Burkhardt

et al., 1996; 1997; Moros et al., 1998, 1999;

Repacholi et al., 1997; Moulder et al., 1999].

However, despite the considerable concern docu-

mented at a variety of websites (e.g., http://www.

microwavenews.com/ or http://www.wow-com.

com/) and a long history of investigation

[Osepchuk, 1983; Steneck, 1984], a compelling

case

for the ``clear and present danger'' of ultra-

high-frequency irradiation (UHF, 300±3000 MHz) has

yet to be made for SARs below overtly thermalizing

levels [e.g., Moulder et al., 1999].

In this article we shall consider ®rst the

macroscopic electromagnetic theory of energy deposi-

tion in tissue, with special reference to prospects of

ß 2001Wiley-Liss,Inc.

ÐÐÐÐÐÐ

Contract grant sponsor: Florida Corporate Electromagnetic

Research Laboratory of Motorola

*Correspondence to: William F. Pickard, Department of Electrical

Engineering, Washington University, One Brookings Drive, Saint

Louis, Missouri 63130. E-mail: wfp@ee.wustl.edu

Received 22 November 1999; Final revision received 20 March

2000

To be precise we shall anticipate our Discussion and de®ne

``compelling case'' as one so robust that (a) it can be reproduced at

will and (b) has had its variation with both intensity and frequency

studied in detail.

nonthermal effects at the levels of irradiation expected

from wireless personal communication devices; and

we shall show that the density of absorbed photons is

well below that which would make nonthermal effects

credible from the viewpoint of known physics and

reported mechanisms. We shall then explicitly esti-

mate the probability of accumulating suf®cient energy

from a multiphoton absorption process to produce a

nonthermal effect; and we shall show that the

probability of so happening is vanishingly small. We

shall next ask whether the exogenous electric ®elds

propagated into the tissue are large enough to produce

signi®cant electrophysiological effects. Finally, we

shall examine the case for a typical coherent effect, the

conjectural biological Bose±Einstein-like condensa-

tion. And, upon failing to unearth a compelling

mechanism, we shall conclude that, since signi®cant

and consistent experimental data to the contrary are

absent, there is as yet no persuasive basis in science

that nonthermal effects can occur.

MACROSCOPIC ELECTRODYNAMICS OF

ENERGY DEPOSITION: THE SPECIFIC

ABSORPTION RATE

Overview

The transfer and deposition of electromagnetic

energy in macroscopic electrodynamics is normally

approached from the viewpoint of Maxwell's ®eld

equations and in particular from Poynting's theorem, a

deduction made using them [Stratton, 1941; Adler

et al., 1960; King, 1963; Haus and Melcher, 1989]:

``As a general integral of the ®eld equations, the

validity of Poynting's theorem is unimpeachable. Its

physical interpretation, however, is open to some

criticism'' [Stratton, 1941, p. 133]

. We shall not here

endeavor to resolve the subtleties of interpretation

inherent in the formal theory, but shall set forth views

commonly held to be valid in ordinary situations.

Moreover, the reader uninterested in technical electro-

magnetics may skip directly to the end of this section

and the practical example relating to brain tissue: this

reveals that, absent ``new physics'' and/or unrealisti-

cally high power levels, it is dif®cult to see how

absorption of UHF electromagnetic energy can do

much except raise tissue temperature.

Propagation of Electromagnetic Energy

For the time-harmonic steady state±situation, the

vector power ¯ow in three dimensions at a given

frequency f s

ÿ1

 Hz is

S  E H



; 1

where S [W/m

] is the Poynting vector, E [V/m] is the

electric ®eld strength, and H



[A/m] is the complex

conjugate of the magnetic ®eld strength. As this

representation is in the frequency-domain, S, E, and



are complex quantities. Physically, S may be

thought of as the ``illumination.'' If now we consider a

plane wave propagating in a x-direction through an

isotropic, linear, passive, simple homogeneous med-

ium, S will have only an x-component given by

 S

expÿk k



x; 2

where k m

ÿ1

is the complex propagation constant and

[W/m

] is the complex power density at x 0. In

particular, proceeding from the time-harmonic forms

of the ®eld equations [Adler et al., 1960, s. 8.1.2; King,

1963, s. III.14]

 ioms  ioe 3a

 E

s  ioe

 



; 3b

where i 



ÿ1

; E

is the root-mean-square electric

®eld at x  0 and is real, o  2p f [rad/s] is the angular

frequency, m [H/m] is the complex permeability

m  m

ÿ im

; 4a

e [F/m] is the complex permittivity

e  e

ÿ ie

; 4b

s [S/m] is the complex conductivity

s  s

ÿ is

; 4c

and the six parameters of Eqs. (4) are all non-negative.

Physically, m is an index of the medium magnetization

induced by H; e is an index of the medium polarization

induced by E; s is an index of the drift of unbound

charge (e.g., ions) in response to E; and the imaginary

parts describe the physical reality that the medium

cannot respond instantaneously to the applied ®elds.

ÐÐÐÐÐÐ

Where appropriate, pointers will be given to page (p.), section

(s.), chapter (ch.), equation (eq.), or ®gure (®g.) of the pertinent

reference.

98 Pickard and Moros

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