Dielectric Properties of Biological Materials

CONTENTS 3.1 Introduction ......................................................................................................................... 52 3.2 Dielectric Properties-Molecular Origin ........................................................................ 53

3.2.1 Quasi-Static Response............................................................................................ 53 3.2.2 Permittivity of Low-Pressure Gases .................................................................... 54 3.2.3 Permittivity of Liquids and Dense Gases........................................................... 55

3.3 Time and Frequency Dependence of the Dielectric Response.................................... 56 3.3.1 Time-Dependent Polarization-Impulse

Response-Kramers-Kro¨nig Relations ............................................................... 56 3.3.2 Permittivity of a Polar Substance-The Debye Equation ................................ 57 3.3.3 Nonpolar Molecules............................................................................................... 60

3.4 Observed Responses of Real Systems-Conduction-Multiple Relaxations-The Universal Law..................................................................................... 60 3.4.1 Conduction .............................................................................................................. 60 3.4.2 Multiple Relaxation Models-Distribution of Relaxation

Times-Fractional Power Law Behavior ............................................................ 61 3.4.3 Universal Law of Dielectric Relaxation .............................................................. 66 3.4.4 Combined Response Model.................................................................................. 67

3.5 Dielectric Properties of Biological Materials-Main Components............................. 67 3.5.1 Water ........................................................................................................................ 68 3.5.2 Carbohydrates ......................................................................................................... 70 3.5.3 Proteins and Other Macromolecules................................................................... 70 3.5.4 Electrolytes............................................................................................................... 71 3.5.5 Dielectric Dispersions in Tissue........................................................................... 72

3.5.5.1 a Dispersion ............................................................................................. 73 3.5.5.2 b Dispersion ............................................................................................. 73 3.5.5.3 g Dispersion ............................................................................................. 73 3.5.5.4 d Dispersion ............................................................................................. 74

3.5.6 Effective Complex Permittivity of a Heterogenous System............................ 75 3.6 Dielectric Relaxation Mechanisms in Heterogenous Media........................................ 77

3.6.1 Interfacial Polarization........................................................................................... 77 3.6.1.1 Interface between Two Media............................................................... 78 3.6.1.2 Suspension of Spheroids ........................................................................ 79

3.6.2 Counterion Polarization Effects ........................................................................... 81

3.7 Dielectric Properties of Tissue-State-of-Knowledge................................................... 82 3.7.1 1996 Database.......................................................................................................... 82 3.7.2 Literature After 1996-A Brief Review............................................................... 85

3.7.2.1 Brain Tissue: Gray and White Matter.................................................. 85 3.7.2.2 Liver........................................................................................................... 87 3.7.2.3 Muscle ....................................................................................................... 88 3.7.2.4 Skin ............................................................................................................ 89 3.7.2.5 Bone ........................................................................................................... 92 3.7.2.6 Dielectric Properties of Cancerous Tissue .......................................... 92 3.7.2.7 Conductivity of Tissue at Low-Frequency.......................................... 93 3.7.2.8 Nonlinear Dielectric Properties............................................................. 94

References ..................................................................................................................................... 94

At some level of organization, all matter consists of charged entities held together by various atomic, molecular, and intermolecular forces. The effect of an externally applied electric field on the charge distribution is specific to the material; the dielectric properties are a measure of that effect; they are intrinsic properties of matter used to characterize nonmetallic materials. Biological matter has free and bound charges; an applied electric field will cause them to drift and displace, thus inducing conduction and polarization currents. Dielectric spectroscopy is the science that relates the dielectric properties to the underlying microscopic mechanisms of polarization and conduction. These dielectric phenomena are determined by and are informative about the structure and composition of the material. Consequently, knowledge of the dielectric properties is of practical importance in all fields of science where electromagnetic fields impinge or are used to probe or process matter. It is equally important in biomedical fields such as electrophysiology, where endogenous bioelectric sources provide signals that are sensed through various body tissues and are affected by their dielectric properties. The past decade has seen a dramatic increase in the exposure of people to electromag-

netic fields from wireless telecommunication devices and infrastructure. This situation sparked large research programs on the assessment and quantification of exposure of people and on the biological effects resulting from the exposure. Information on the dielectric properties of tissues is vital to these studies, for the computation of exposure metrics and the provision of a mechanistic explanation for biological effects. To satisfy the need of current research activity, this chapter will review the dielectric data for body tissue and the underlying mechanisms of interaction at the cellular, subcellular, and molecular levels. In doing so, we will draw on the authoritative article by Foster and Schwan (1996), published in the second edition of this book, which goes a long way toward establishing dielectric spectroscopy as a powerful tool for mechanistic studies. Another area of scientific activity in the last decade revolved around the formulation of

standard procedures for the experimental assessment of human exposure from electromagnetic sources, mostly telecommunication radio transceivers and their accessories. This created the need to formulate and measure the dielectric properties of tissue equivalent material and made dielectric measurement and the assessment of the associated uncertainty part of the compliance testing procedure. This chapter will deal with the fundamental issues that need to be established if dielectric measurement is to become a routine but accurate laboratory procedure.