Webpage: www.ijaret.org Volume 3, Issue VIII, Aug 2015 ISSN 2320-6802 INTERNATIONAL JOURNAL FOR ADVANCE RESEARCH IN ENGINEERING AND TECHNOLOGY WINGS TO YOUR THOUGHTS….. Page 37 OPTIMIZATION OF MULTI-POLE DEBYE MODELS OF TISSUE DIELECTRIC PROPERTIES USING GENETIC ALGORITHM Ch. Rajani Chandra 1 , Y. Ratna Kumar 2 1 PG Scholar [BME], Dept. of ECE, Andhra University College of Engineering (A), Andhra Pradesh, India 1 rajanichandra91@gmail.com 2 Assistant professor (c), Dept. of ECE, Andhra University College of Engineering (A), Andhra Pradesh, India 2 rkratnabio@gmail.com Abstract: In the past few decades many researchers have studied regarding the dielectric properties. Models of the dielectric properties of body tissues enable us to simulate the interactions of these tissues with electromagnetic fields. These properties are the permittivity and conductivity which vary many orders of the magnitude at frequencies after the microwave bands. To calculate the dielectric properties over broad frequency range, any different parametric models have been developed. Parametric formulae are available based on a multi-pole model of tissue dispersions, but although they give the dielectric properties over a wide frequency range, they do not convert easily to the time domain. An alternative is the multi pole Debye model which works well in both time and frequency domains. Optimization is needed to find the parameters that give the best fit to measured data, or to previously validated models. Genetic algorithms are an evolutionary approach to optimization and it is found that this technique is effective at finding the best values of the multi Debye parameters. Thus genetic algorithm optimizes these parameters to fit to Cole-Cole model and working well over wide frequency ranges. Keywords: Genetic Algorithm (GA), Debye model, Cole-Cole model. 1. INTRODUCTION In electromagnetism, absolute permittivity is the measure of the resistance that is encountered when forming an electric field in a medium. In other words, permittivity is a measure of how an electric field affects, and is affected by, a dielectric medium. The permittivity of a medium describes how much electric field is 'generated' per unit charge in that medium. More electric flux exists in a medium with a high permittivity because of polarization effects. Permittivity is directly related to electric susceptibility, which is a measure of how easily a dielectric polarizes in response to an electric field. Thus, permittivity relates to a material's ability to transmit an electric field. In SI units, permittivity ε is measured in farads per meter (F/m); electric susceptibility χ is dimensionless. They are related to each other through (1) Where ε r is the relative permittivity of the material, and = 8.8541878176… × 10 −12 F/m is the vacuum permittivity. The (relative) complex permittivity is defined as: (2) where is the dielectric constant, is the loss factor and σ is the conductivity of the tissue;the angular frequency where is frequency, and is the permittivity of free space. Owing to the complex cellular structure and the presence of numerous internal interfaceswithin typical tissues such as muscle, bone or fat, the parameters, , and all vary stronglywith frequency from static fields up to microwaves at tens of GHz [1].This is because there are several different mechanisms contributing to the polarization of thetissue in an electric field, each of which responds in a different timescale. This leads to anumber of ‘dispersions’ or ‘relaxations’ which can be seen in a plot against frequency as a fallin between two steady values, and a corresponding increase in . The -dispersion is dueto counter-ion flow in bulk tissues which has a time constant of milliseconds. Charging/discharging ofcell membranes at s timescale is responsible for the -dispersion. Finally the –dispersionis caused by the fastest process considered here, rotation of polar water molecules with time constant of picoseconds (ps). 2. PARAMETRIC MODELS Some simplemolecules such as methanol have a single time constant and the frequency dependence of their dielectric properties can be described by an equation introduced by Debye (1929): (3)