Conformity Magazine - August 2008 - (Page 54)

Numerical Solution of Bioheat Equation The thermal increase distribution inside the EM exposed tissues can be calculated by the solution of a parabolic PDE known as the bioheat equation [11]: Equation 2 H=20 W/(m2 °C), respectively, and the air temperature is assumed to be Te=23 °C[5], [6]. Equation 2 can be solved numerically by a forward finitedifference scheme using a structured grid with 0.25 mm cell size, as: where T is the unknown temperature, C the specific heat of the tissue, K the thermal conductivity of the tissue, SAR the specific absorption rate, A the basal metabolic rate, B the term associated with blood perfusion, and Tb the blood temperature. Solution of (2) in the computational domain Ω coinciding with the only human head requires adequate boundary conditions on the body-air interface ∂Ωe (i.e. on the skin and cornea) taking into account the radiative, convective and evaporative heat exchange [5], [6]. These convective boundary conditions are given by: Equation 3 Equation 4 where H is the convection coefficient that takes into account the radiative, convective and evaporative effects, and Te is the fluid temperature. On the skin-air and cornea-air interfaces weassume a convective coefficient H=10.5 and where ∆t is the time step, ∆ the spatial discretization. NINT and NEXT are respectively the number of internal and external cells adjacent to the considered cell identified by pedices i, j, k using the standard finite difference notation. It should be noted that, in order to simplify the notation, pedices i, j, k are not reported in the quantities C, ρ, K, A, B even if they also are depending on the position inside the computational domain. To avoid numerical instabilities, the time step ∆t of the explicit finite difference scheme (4) must satisfy the following criterion [12]: Equation 5 The application of the stability criterion on the discretized thermal model leads to a maximum usable time step of about ∆t = 0.07 s for the most critical condition (5). This gives rise to a long computational time when considering the thermal steady-state condition that occurs after about ten minutes for this kind of exposures. Numerical Computational Aspects Equation 2 is solved by the finite difference procedure (4) using a structured grid with cell size of 0.25 mm and time step ∆t = 0.07 s. The numerical analysis of the whole human head exposed to a wireless handheld source leads to a heavy computation that cannot be carried out by using a normal PC. To overcome this problem, the idea is to reduce the dimensions of the thermal computational domain since the main scientific interest of this study is focused on the temperature increase in the eye, especially in the lens, which is the most critical zone for any eventual thermal damage. The problem then consists in how to reduce the computational domain Ω and, above all, in finding the adequate boundary conditions in the new truncation boundary surfaces ∂Ωi located inside the human head. For the first problem, there Figure 2. Eye model with 0.5 mm cell size as in [6] (a) and with the proposed 0.25 mm cell size (b). 5 Conformity AUGUSt 2008

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Conformity Magazine - August 2008 Contents Editor’s Note FCC Seeks Comment on Reauction of 700 MHz D Block Commission Cracks Down (Again!) on Junk Fax Marketer Canada Levies Fees for Public Safety Radio Spectrum FDA Issues Guidance on Medical Device Tracking Greenpeace Challenges Video Game Manufacturers The IEEE EMC Society: A Proud History of Accomplishments ESD Open Forum An Update on Changes to the Automotive ESD Standard, ISO 10605 Modeling of Radiated Electromagnetic Disturbances in Automotive Applications Design Issues in Automotive Radio Frequency Systems IEEE EMC Symposium IEEE 2008 Show Preview Exhibitors Buyer’s Guide Product News Most Eco-Friendly Companies Updated Standards List For the EU’s Pressure Equipment Directive Commission Issues Updated Standards List For Directive on Gas-Fired Appliances HHS Releases Fact Sheet on U.S. Imports from China Customs Agents Seize Holiday Lights IEEE PSES Symposium Set for October CPSC Actions in the News IEC Standards Update UL Standards Update Telcordia Standards Update From Our “You Can’t Make This Stuff Up” Department Looking Back: Items from Past Issues of Conformity Product Reviews Advertisers

Conformity Magazine - August 2008

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