Model of Steady-state Temperature Rise in Multilayer Tissues Due to Narrow-beam Millimeter-wave Radiofrequency Field Exposure.

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The assessment of health effects due to localized exposures from radiofrequency fields is facilitated by characterizing the steady-state, surface temperature rise in tissue. A closed-form analytical model was developed that relates the steady-state, surface temperature rise in multilayer planar tissues as a function of the spatial-peak power density and beam dimensions of an incident millimeter wave. Model data was derived from finite-difference solutions of the Pennes bioheat transfer equation for both normal-incidence plane waves and for narrow, circularly symmetric beams with Gaussian intensity distribution on the surface. Monte Carlo techniques were employed by representing tissue layer thicknesses at different body sites as statistical distributions compiled from human data found in the literature. The finite-difference solutions were validated against analytical solutions of the bioheat equation for the plane wave case and against a narrow-beam solution performed using a commercial multiphysics simulation package. In both cases, agreement was within 1-2%. For a given frequency, the resulting analytical model has four input parameters, two of which are deterministic, describing the level of exposure (i.e., the spatial-peak power density and beam width). The remaining two are stochastic quantities, extracted from the Monte Carlo analyses. The analytical model is composed of relatively simple functions that can be programmed in a spreadsheet. Demonstration of the analytical model is provided in two examples: the calculation of spatial-peak power density vs. beam width that produces a predefined maximum steady-state surface temperature, and the performance evaluation of various proposed spatial-averaging areas for the incident power density.