# Parametric analysis of electromagnetic wave interactions with layered biological tissues for varying frequency, polarization, and fat thickness

## TL;DR

This paper studies how electromagnetic waves interact with layered biological tissues at different frequencies and angles, revealing how fat thickness and polarization affect heating and reflection.

## Contribution

A novel MATLAB framework integrating transmission line theory, dielectric modeling, and bioheat simulations to analyze EM wave interactions with layered tissues across ISM bands.

## Key findings

- Significant superficial heating (up to 3.5°C) occurs at 5.8 GHz due to reduced penetration depth.
- Subcutaneous fat modulates the balance between reflection and absorption depending on its thickness.
- Polarization and angle influence the shape of reflection curves, including TM Brewster-like minima.

## Abstract

Electromagnetic wave interaction with biological tissue is frequency-, angle-, and polarization-dependent, influencing both dosimetric parameters and resultant thermal effects. This work presents a comprehensive analysis across the major ISM bands (433, 915, 2450, and 5800 MHz) for transverse electric (TE) and transverse magnetic (TM) polarizations incident on a three-layer tissue model (skin–fat–muscle). A custom MATLAB code was developed to integrate the multilayer transmission line formalism, polarization-specific wave impedance modeling, Cole–Cole dielectric parameterization, and a finite difference method (FDM) solution of the Pennes bioheat equation. Simulations were performed for incident power density 50 W/\documentclass[12pt]{minimal}
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\begin{document}$$\hbox {m}^2$$\end{document} and fat thicknesses from 0.005 m to 0.03 m, over incidence angles 0 °C– 80 °C. Throughout the manuscript, reflection is reported strictly as a power quantity \documentclass[12pt]{minimal}
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\begin{document}$$R=|\Gamma |^2$$\end{document} rather than a field-amplitude coefficient. The thermal pipeline solves the steady-state Pennes equation in its direct \documentclass[12pt]{minimal}
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\begin{document}$$\Delta T$$\end{document} form with consistent surface (Robin) and deep (Dirichlet) boundary conditions, and simulations are audited by an energy-conservation budget. Results indicate that while temperature increases remain below 0.4 °C at lower frequencies (433–915 MHz), significant superficial heating (up to 3.5 °C) occurs at 5.8 GHz due to reduced penetration depth, even at moderate exposure levels. The results demonstrate that subcutaneous fat acts as a low-loss impedance transformer whose thickness strongly modulates the balance between reflection and internal absorption, while polarization and angle primarily tune the detailed shape of angular reflection curves (including TM Brewster-like minima) at a given incident power. The analytical framework therefore complements voxel-based full-wave numerical models by providing fast, physically transparent trends across ISM bands that are directly relevant for preliminary assessment of wearable devices, implanted sensors, and compliance with radiofrequency safety limits.