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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

A rigorous full-wave solution, via the Finite-Difference-Time-Domain (FDTD) method, is performed in an attempt to obtain realistic communication channel models for on-body wireless transmission in Body-Area-Networks (BANs), which are local data networks using the human body as a propagation medium. The problem of modeling the coupling between body mounted antennas is often not amenable to attack by hybrid techniques owing to the complex nature of the human body. For instance, the time-domain Green's function approach becomes more involved when the antennas are not conformal. Furthermore, the human body is irregular in shape and has dispersion properties that are unique. One consequence of this is that we must resort to modeling the antenna network mounted on the body in its entirety, and the number of degrees of freedom (DoFs) can be on the order of billions. Even so, this type of problem can still be modeled by employing a parallel version of the FDTD algorithm running on a cluster. Lastly, we note that the results of rigorous simulation of BANs can serve as benchmarks for comparison with the abundance of measurement data.

As wireless technologies continue to evolve, the development of personalized devices which exchange data with unprecedented ease and efficiency is certain to grow unabated. Recently, such technologies have garnered much attention from those interested in biomedical sensing and Body-Area-Networks (BANs). These technologies, which are data networks that operate through wireless transmission using the human body as a propagation medium, continue to be an active area of research in fields such as remote health monitoring and medical biosensors. However, the complexity of integrating efficient communication systems in the human body environment poses many challenges to the future of this emerging technology. The excitation of surface and space waves from radiating antennas mounted on the body can have a large impact on the performance of co-site body-centric antenna systems. Moreover, the presence of multiple antennas on the body can lead to unexpected coupling due to creeping wave interaction. Fortunately, recent developments in powerful numerical methods, such as the Finite-Difference-Time-Domain (FDTD) method running on parallel platforms, has made it feasible for us to carry out a detailed study of these body-centric antenna systems.

For many years researchers have used simplified geometries to model the interaction of electromagnetic energy with biological tissue. Such geometries typically lend themselves to simple shapes, such as cylinders, ellipses and spheres for which past research has typically treated these as perfectly conducting objects, low loss high dielectrics, and surface impedance models. This type of treatment was convenient due to the availability of well-known analytical methods used solve these problems, such as the uniform theory of diffraction (UTD), ray tracing (RT), creeping waves, and eigenfunction analysis [

In this section we provide the results of a simplified model for the human body torso. The proposed model is a 3-layer elliptical structure having major and minor axis of 150 cm and 120 cm, respectively. This model has been used in [

The 3-layer ellipse model incorporates the skin, fat, and muscle layers. In [

Although the FDTD method enjoys a significant advantage over MoM in terms of its ability to simulate complex structures and lossy inhomogeneous materials, it has been known to require far more computational resources than are usually available to accurately model, simultaneously, the fine features of the radiating element, the layered structure of the geometry and the electrically large size of the entire structure typically encountered in the study of BANs. To circumvent this problem, most research done on BANs by utilizing the FDTD have been carried out using a point source approximation. While such an approximation may be adequate for directly estimating the path loss associated with the body, it does not rigorously account for a number of crucial antenna factors that affect the antenna performance, such as finite ground size, radiation pattern and efficiency. Furthermore, any field behavior in either the near or the intermediate region is inherently neglected in the point source approximation, whereas the physical structure of the radiating element must be included to properly model the physical system.

In this paper we have used a parallel version of FDTD that can handle such electrically large geometries as well as the fine features of the radiating element. To this end, we have used quarter-wave monopoles resonant at 2.45 GHz with a 75 mm × 75 mm square ground plane located at tangent points one to two FDTD cells away from the models analyzed in this study. Although other antennas could be used, the choice of the monopole antenna has the distinct advantage in that the radiation pattern in the plane azimuthal to the monopole is inherently stable across the bandwidth of interest. However, the monopoles used in this study do not have an impedance matching bandwidth wide enough to cover the frequencies of interest, and, therefore, the channel path loss data between observation points should be considered relative to one another for a given frequency. Nevertheless, the polarization and radiation pattern deviations of the transmitter and receivers across the frequency band can more or less be neglected when performing coupling calculations, which make these antennas useful for studying channel characteristics of the on-body propagation medium.

The setup used in the simulation is shown in _{21} is recorded. The mode of propagation is known to be a creeping wave and the direct ray paths are shown. For each observation plane the _{21} was calculated along the elliptical path in the level plane and plotted for frequencies between 0.8–6 GHz as shown in

For BANs it is typically assumed that the wave propagation through the body is so attenuated that its contribution can be ignored. To verify this we have plotted the fields for the cross-section of the ellipse in the source plane as well as a vertical cross-section along the extent of the ellipse model. The electric field plots are shown in

In

Although simplified geometries have their use in analyzing body-centric communication networks, the availability of realistic human body models enables us to use a more rigorous approach to understand how the irregular shape of the body affects the performance of BANs. One of the most commonly used body models is shown in

Additionally, the resolution of the original voxel data set, which is 1 mm × 1 mm × 1 mm, was down-sampled to 3 mm × 3 mm × 3 mm. Even at this lower resolution the computational resources needed are high, specifically 8 hours on 16 Pentium 4 CPUs. Although this may seem too coarse for the conventional λ/20 cell size, the fields couple on or near the surface of the body, where the mesh can be coarser, and we are interested in separation distance well into the asymptotic region of the transmitting antenna. To demonstrate that the loss of accuracy is negligible in doing so, we have performed a simple experiment by computing the difference in field magnitude at 3 GHz—far away from the transmitting antenna on the same plane as shown in

It is commonly claimed in the literature that a good approximation for the body can be made by using a full muscle phantom or a two-thirds muscle equivalent phantom, the latter being more commonly used in EMC analysis for SAR [_{n}_{n}_{n}_{n} <

The difficulty in this model lies in the fact that there are not any simple closed-form expressions amenable to the FDTD algorithm. Specifically, this is due to the fact that the inverse Fourier transform is non-trivial.

In this Section we will introduce a technique that can be used to implement the Cole-Cole model into the desired frequency band of interest for simple geometries relevant to BANs (e.g., planar human tissue phantoms) in FDTD. Since the static conductivity term can be handled easily in the FDTD update equations we turn our attention to the term containing _{n}

Then the expression for the electric field density follows as:

Therefore, if it is possible to find a time domain representation for the Laplace transform of the unknown spectrum _{i}

The problem at hand is to determine a suitable function for which we can derive the Laplace transform. To do this we first rewrite the Debye integral representation as:

To find

Now we use the Laplace transform relation given by:

Of course, we could have used

Next, we can apply the method of least squares to find the coefficients _{n}_{n}^{+}̿b̄

In common with most over-constrained inverse problems, we must use the Moore-Penrose pseudoinverse for ^{+}̿

As an illustrative example of this approach, the 4-term Cole-Cole model was taken for the tissue corresponding to the muscle. Although the preceding formulation corresponds to a single Cole-Cole term, the postulated Debye spectrum can equally well be applied to the entire summation of Cole-Cole terms. The parameters given by Gabriel [

Using the proposed algorithm we have obtained the following coefficients for an 11th-order expansion that are listed in

As an example, the calculated coefficients along with the fitting parameter were used to model the frequency response in a muscle medium. Using the convolution sum of

The problem with incorporating the spectral approximation algorithm proposed in the previous section is that FDTD requires a record-keeping of all past time values of the electric field components. If either the problem size is small, or reflection properties from an infinite planar slab are of interest then this approach may be feasible. However, for practical problems, the computational domain can become exceedingly large (e.g., upward of 1 billion unknowns for realistic human body phantoms), and other approximation methods must be used. Often times, the dispersion properties of biological tissue can be approximated by a Debye model over a finite frequency bandwidth. In this case it is possible to formulate an FDTD updating scheme for dispersive materials that does not require keeping all past histories of the fields.

The recursive convolution FDTD is one such method and is discussed in [

After some extensive manipulations the final form of the FDTD updating equations for the electric field become:

The formulation given in _{i}_{r}

Using the muscle and the two-thirds muscle equivalent human body phantom, the CFDTD algorithm was used to simulate the setup previously shown in

For each model, the network configuration was simulated and the _{21} was calculated. Additionally, the network was also simulated in the absence of the body in order to understand the influence of its presence. The free-space case (body absent) is shown in

However, for the non-line-of-sight (NLOS) there is a noticeable difference in the path loss, especially at frequencies above 1 GHz, where the difference is approximately 35 dB compared to the free-space case.

To determine the accuracy of the elliptical model, we compare two cases, namely when the receiver is located on the back of the body and on the shoulder-side. Additionally, in order to improve the elliptical model from the previous section, two muscle tissue arms, composed of cylinders and spheres, were placed alongside the elliptical torso model and are shown superimposed on the actual physical model in

Despite the capability of FDTD to model the complex human body in its original form, it is often desirable to seek out good geometrical approximations to simply the computational cost. This has been documented in the literature for both measurement and simulation purposes. However, to-date a quantitative study that demonstrates the accuracy of the results using simplified models has not yet been reported. A detailed characterization of this comparison has been carried out and presented in this paper. It has been shown that the rigorous FDTD phantom model yielded results that are consistent with the measurements found in the literature, and they provide valuable information into potential cosite BAN antenna systems. In addition, we have shown simple models can give reasonably accurate results for some antenna configurations, but they can fail to reproduce the mutual coupling results when the antennas are not in line-of-sight. Therefore, it is highly desirable to carry out an in-depth study of these approximations and to see how well the results based on these approximations compare to the rigorous simulation of the human body.

3-layer ellipse model of the human torso with transmitting antenna at the front and receiving antenna at the back.

Path loss around the cylindrical human trunk model at the source plane.

Path loss around the cylindrical human trunk model 210 mm above source plane.

Path loss around the cylindrical human trunk model 400 mm above source plane.

Electric field distribution in the source plane.

Electric field distribution on a vertical cut plane bisecting the cylindrical model.

Path loss

Path loss

Path loss

Numerical human body phantom based on 3D CT scan voxel set with transmitting and receiving antennas in typical BAN scenario.

Experiment to determine if the down-sampled human body voxel set causes numerical inaccuracies (

Magnitude spectrum of the relative permittivity for the 4 term Cole-Cole model and the spectrum approximation.

Phase spectrum of the relative permittivity for the 4 term Cole-Cole model and the spectrum approximation.

Magnitude and Phase relative errors of the spectrum approximation and the 4 Cole-Cole model.

Normalized time-domain response of the electric flux density using the spectral approximation.

_{21} of the BAN network scenario with body absent.

_{21} of the BAN network scenario with muscle phantom.

_{21} of the BAN network scenario with 2/3-muscle phantom.

Electric field distributions (dB) on a vertical cut plane bisecting the body.

Simplified model superimposed on the human body numerical phantom.

Comparison of the path loss for different phantom models with receiving antenna on the back of the body and transmitting antenna at the waist.

Comparison of the path loss for different phantom models with receiving antenna on the shoulder side of the body and transmitting antenna at the waist.

4 term Cole-Cole model parameters for muscle.

Δ_{1} = 50 |
_{1} = 7.23 |
_{1} = 0.1 |

Δ_{2} = 7000 |
_{2} = 353.68 |
_{2} = 0.1 |

Δ_{3} = 1.2 |
_{3} = 318.31 |
_{3} = 0.1 |

Δ_{4} = 2.5 |
_{4} = 2.27 |
_{4} = 0 |

Calculated coefficients from the spectral approximation method.

C1 | 0.0002e6 |

C2 | −0.0032e6 |

C3 | 0.0394e6 |

C4 | −0.2759e6 |

C5 | 1.1027e6 |

C6 | −2.4578e6 |

C7 | 2.7137e6 |

C8 | −0.5489e6 |

C9 | −1.7652e6 |

C10 | 1.6288e6 |

C11 | −0.4334e6 |