EMF Power Absorption in Bone and Bone Marrow: Mathematical Model

A deterministic mathematical method is adopted to evaluate the power absorption due to EMF radiation in bone and bone marrow. The specific absorption rate (SAR), in both anatomic structures, is computed according to the present mathematical model, is represented spatially in the bone-marrow-bone layers under study. The effect of exposure to electric field of strengths ranging from 1 V/m to 1 kV/m is investigated for a wide frequency spectrum in each layer of the proposed model. The frequency dependence of the SAR, through these layers, is illustrated for frequencies ranging from 1 kHz to1GHz. The present results are in agreement with international safety standards for applied filed strengths of maximum value; 10 V/m for bone and 100 V/m for bone marrow. Moreover the present model shows that oblique incidence results in higher SAR values than with normal incidence, highly evident for low frequency.

Aim: Evaluation of the EMF power absorption and distribution, in bone and bone marrow, due to EMF radiation.

Study Design: Mathematical analysis followed by computer simulation of the problem.

Place and Duration of Study: Department of Engineering Physics & Math., Faculty of Engineering, Cairo University, between May 2014 and Dec.2015.

Methodology: The author employs a bone-marrow-bone model to investigate the effect of incident EMF. The equations governing the total electric and magnetic field distributions in each layer are deduced, considering its biological electromagnetic properties. The model is simulated by a computer program using Maple V. The computed values of specific absorption rate (SAR) in bone and bone marrow are graphically represented to show spatial distribution in each one. The exposure to electric field of strength ranging from 1V/m to 1kV/m is investigated using the proposed method. The frequency dependence of the SAR through the bone-marrow-bone layers under study is illustrated for a frequency range of 1 kHz-1GHz.

Results: Electromagnetic radiation of 1 MHz-10MHz induce absorbed power within the safety limits for all applied field strengths. The 1 GHz incident radiation induces SAR values higher than permissible ranges for field strengths above 400V/m whereas the same occurs for a low frequency range at 100 V/m. Moreover, the present results are in agreement with international safety standards for applied filed strengths till 10 V/m for bone and till 100 V/m for bone marrow, covering the applied frequencies (1 kHz -1 GHz). Except for exposure to electric field of strength higher than 100 V/m, the SAR acquired by the bone marrow is within the safety levels.

Conclusion: The results obtained are in agreement with international safety standards for filed strengths of maximum value 10 V/m for bone and 100 V/m for bone marrow. Oblique incidence results in higher SAR values than normal incidence, especially for low frequency (1 kHz).