# Derivation of extracellular fluid volume fraction and equivalent dielectric constant of the cell membrane from dielectric properties of the human body. Part 1: Incorporation of fat tissue into cell suspension model in the arm

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## Abstract

The non-invasive characterisation of cell pathophysiology is clinically important. A cell suspension model is applied to derive the extracellular fluid (ECF) volume fraction and the equivalent dielectric constant of the cell membrane ɛ_{m} from the dielectric properties of human arms. Frequency-dependent dielectric constants and electrical conductivities of arms are obtained from 35 surgical patients over a frequency range of 5–1000 kHz. The cell suspension model is applied to fit the data using a complex non-linear least-squares method. The arms show typical dielectric dispersions, although the cell suspension model yields a poor fitting in dielectric constants at lower frequencies and electrical conductivities at higher frequencies. In contrast, a new cell suspension model, taking into account the fat tissue component, remarkably improves the overall fitting performance, allowing estimation of the volume fractions of ECF (0.34±0.05) and fat tissue (0.16±0.04) and the equivalent ɛ_{m} (23±9). The resulting estimates of the volume fraction of fat tissue are in good correlation with arm skinfold thickness (fat volume fraction of arm=2.42×10^{−3}×arm skinfold thickness (mm)+0.099, R=0.756, p<0.0001). Therefore it is concluded that the newly derived cell suspension model is well suited for the description of the dielectric properties of human tissues and thus the derivation of the ECF volume fraction and equivalent ɛ_{m}.

### Keywords

Dielectric property Human body Modelling Cell suspension Dielectric constant Cell membrane### List of symbols Major abbreviations are listed in order of appearance in the text

*R*resistance

*X*reactance

- ω
angular frequency (=2π

*f*)*f*measuring frequency

- κ
electrical conductivity which is the reciprocal of resistivity

- ε
dielectric constant

- ε
_{v} absolute dielectric constant of a vacuum

- ε
^{*} complex dielectric constant\(\left( { = \varepsilon - j\frac{\kappa }{{\omega \varepsilon _\nu }}} \right)\)

- β
a distribution parameter of the relaxation time of a dielectric dispersion

- ϕ
volume fraction of cells in suspension

*d*thickness of the cell membrane

*D*diameter of the inner phase of a cell

*r*relative thickness of the cell membrane to the diameter of the inner phase of a cell

- ε
_{m} dielectric constant of the cell membrane

*q*volume fraction of fat-free mass in the whole tissue

*j*imaginary unit

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