# Field-Based Optimal Placement of Antennas for Body-Worn Wireless Sensors
## 2 Methods  
### The Numerical Human Body Model  
An analysis of WBANs and sensor network operating in the proximity of a human body is often carried out with the use of full-wave electromagnetic simulation software which also implements a numerical model of the human body. The Finite Difference Time Domain (FDTD) method is widely used for this type of studies [10]. In our research we use the XFdtd(r) FDTD implementation from REMOOM, Inc. (State College, PA, USA) [11]. This package supports a scripting language which allows the user to execute customized functions, including real-time data exchange with external software. A number of numerical human body models have been developed for the purpose of calculating the amount of electromagnetic power absorbed by the human body [12; 13] (_i.e._, Specific Absorption Rate) which can be also used for WBAN design. Currently, complex heterogeneous models which represent the inner structure of the human body reflecting electric properties of various tissue types are widely used. Those models are available in many contemporary electromagnetic CAD packages. A limitation of the multi-tissue, heterogeneous numerical models is the lack of their physical phantom equivalents because representations of the various internal organs would be very difficult to manufacture. Such models also require a lot of computer resources as the spatial discretization has to be dense to represent structural details of inner organs. Experiments have been reported with the use of Specific Anthropomorphic Mannequin (SAM) which is a homogenous human body phantom [14; 15]. The inner structure of the body is represented with homogenous tissue stimulant liquid with electromagnetic properties similar to the average value for the human body. Such models have a shape, proportions and general dimensions similar to an average human body. Those phantoms are expensive and difficult in use in the laboratory practice because they have to be filled with a liquid of precisely controlled electric properties which tend to vary with time and temperature. Simplified human body models have been also proposed for experimental studies e.g., [16] and for numerical simulation of WBANs [17; 18]. They simplify a human body shape with cylinders filled with a homogenous tissue stimulant liquid but still are difficult to be re-created and require a careful control of dielectric properties of the liquid. This motivated us to propose an even more reduced complexity model which makes it very easy both for numerical implementation and manufacturing. The simplified cylindrical model was also simulated with XFdtd(r). Its geometry was optimized to approximate the proportion of the heterogeneous, anthropomorphic NMR Hershey model with six cylinders [19; 20]. In Figure 3a, a reference NMR Hershey model is presented. The six cylinder model is presented in Figure 3b. Both the reference and the simplified models have the same height, H = 1800 mm. Other dimensions of the simplified model were fixed to fit the geometry of thereference model best, and to preserve the diameters of standard PVC pipes. The arm length is equal to A = 500 mm and the length of the legs is L = 790 mm, while the torso length is equal to T = 836 mm. The simplified model was designed in the way which makes it easy to manufacture. In order to be able to use the standard pipes available on the market, the following diameters of the cylinders were used in the model (see Figure 3): \(\phi_{1}\) = 110 mm, \(\phi_{2}\) = 160 mm, \(\phi_{3}\) = 315 mm. The pipe wall thickness varies from 3 to 6 mm depending on the pipe diameter. All pipes were filled with liquid (a water solution of sucrose and kitchen salt) of electrical properties similar to the human tissue. The electric constant and the conductivity of the liquid were examined with Di-Line measurement unit from the IndexSar (Newdigate, UK). It employs a slot transmission line which is filled with the liquid under test. Material parameters are then identified from network parameters measured with a vector network analyzer.