arXiv subjects

Shannon E. Foley

Publications and source records attributed to Shannon E. Foley.

5 recordsLinked to original sources

arXiv2026

Accurate Computation of Activated Volume in Electromagnetic Heating

In electromagnetic heating and other applications, we need to compute the volume enclosed by an isosurface of the 3D temperature distribution that is numerically represented on a rectangular grid. This situation arises naturally when the temperature distribution is obtained by solving a partial differential equation numerically using a finite difference method. Given the temperature distribution on the 3D grid, the isosurface of a prescribed value is represented approximately by a triangulation, a collection of triangles with vertices on the grid lines. The vertices are determined by a linear interpolation to approximate the locations where the temperature is at the prescribed level. The region enclosed by the isosurface is approximated by that enclosed by the triangulation, which is a set of tetrahedrons. The enclosed volume is approximated by summing those of tetrahedrons. This volume approximation is analogous to approximating a curve using line segments and is limited in accuracy. In this study, we combine extrapolation with the triangulation approximation to develop a more accurate method for computing the volume enclosed by an isosurface of the 3D temperature distribution on a rectangular grid.

math-ph↗

arXiv2026

An Analytical Framework for Frequency-Dependent Electromagnetic Power Absorption in Biological Tissues

As exposure to electromagnetic waves becomes increasingly widespread, it is important to quantify how incident fields couple into biological tissue and where absorbed energy is deposited. This work presents an analytical, physics based framework derived from Maxwell's equations to model the propagation of a normally incident electromagnetic plane wave within homogeneous, lossy dielectric biological tissues. Closed-form expressions for the electric and magnetic fields are derived, enabling the determination of frequency-dependent power reflectance and transmittance at the air-tissue interface, as well as the power absorption coefficient and penetration depth within the medium. Using complex relative permittivity data from the literature, we examine six tissue types across a broad frequency range (1 MHz to 100 GHz). The results demonstrate that higher water content significantly increases dielectric loss and reduces penetration depth. Conversely, low-water tissues (e.g., non-infiltrated fat) exhibit lower attenuation and deeper penetration. Frequency is shown to be a dominant driver of this behavior, with higher frequencies shifting the power budget from reflection-limited coupling toward highly superficial absorption. These findings provide a foundation basis for exposure assessments and the design of emerging electromagnetic technologies.

physics.bio-ph↗

arXiv2026

Asymptotic Effects of Incident Angle and Lateral Conduction in Electromagnetic Skin Heating

Previously we derived the leading term asymptotic solution of temperature distribution in skin heating by an electromagnetic beam at an arbitrary incident angle. The asymptotic analysis is based on that the penetration depth of the beam into skin is much smaller than the size of beam cross-section. It allows arbitrary incident angle. We expand the temperature in powers of the small depth to lateral scale ratio. The incident angle affects all terms in the expansion while the lateral heat conduction appears only in terms of positive even powers. The previously obtained leading term solution captures only the main effect of incident angle. The main effect of lateral heat conduction is contained in the second order term, which is mathematically negligible in the limit of small depth to lateral scale ratio. At a moderate length scale ratio (e.g., 0.1), however, the contribution from lateral conduction is quite significant and needs to be included in a meaningful approximate solution. In this study, we derive closed form analytical expressions for the first order and the second order terms in the asymptotic expansion. The resulting asymptotic solution is capable of predicting the temperature distribution accurately including the effects of both incident angle and lateral heat conduction even at a moderate length scale ratio.

physics.class-ph↗

arXiv2025

Asymptotic Solution for Skin Heating by an Electromagnetic Beam at an Incident Angle

We investigate the temperature evolution in the three-dimensional skin tissue exposed to a millimeter-wave electromagnetic beam that is not necessarily perpendicular to the skin surface. This study examines the effect of the beam's incident angle. The incident angle influences the thermal heating in two aspects: (i) the beam spot projected onto the skin is elongated compared to the intrinsic beam spot in a perpendicular cross section, resulting in a lower power per skin area; and (ii) within the tissue, the beam propagates at the refracted angle relative to the depth direction. At millimeter-wavelength frequencies, the characteristic penetration depth is sub-millimeter, whereas the lateral extent of the beam spans at least several centimeters in applications. We explore the small ratio of the penetration depth to the lateral length scale in a non-dimensional formulation and derive a leading-term asymptotic solution for the temperature distribution. This analysis does not rely on a small incident angle and is therefore applicable to arbitrary angles of incidence. Based on the asymptotic solution, we establish scaling laws for the three-dimensional skin temperature, the skin surface temperature, and the skin volume in which thermal nociceptors are activated.

physics.optics↗

arXiv2024

Assessing skin thermal injury risk in exposure tests of heating until flight

We assess the skin thermal injury risk in the situation where a test subject is exposed to an electromagnetic beam until the occurrence of flight action. The physical process is modeled as follows. The absorbed electromagnetic power increases the skin temperature. Wherever it is above a temperature threshold, thermal nociceptors are activated and transduce an electrical signal. When the activated skin volume reaches a threshold, the flight signal is initiated. After the delay of human reaction time, the flight action is materialized when the subject moves away or the beam power is turned off. The injury risk is quantified by the thermal damage parameter calculated in the Arrhenius equation. It depends on the beam power density absorbed into the skin, which is not measurable. In addition, the volume threshold for flight initiation is unknown. To circumference these difficulties, we normalize the formulation and write the thermal damage parameter in terms of the occurrence time of flight action, which is reliably observed in exposure tests. This thermal injury formulation provides a viable framework for investigating the effects of model parameters.

cs.CE↗