XFDTD Bio-Pro now performs Ultra-Wide-Bandwidth (UWB) calculations of the interactions of transient electromagnetic fields with human bodies.

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Remcom has been the leader in providing software tools to make Bio-Electromagnetic calculations. The latest addition to XFdtd’s capabilities allows for Ultra-Wide-Bandwidth (UWB) calculations of the interactions of transient electromagnetic fields with human bodies. To accomplish this the Remcom High-Fidelity meshes have been enhanced to include the frequency-dependent behavior of the human body tissues. The frequency-dependence is based on approximating the Cole-Cole curve fits provided by Gabriel et al using multiple DeBye poles. The multiple-pole approximation was curve-fit over the frequency range 50MHz to 20GHz, but in most cases is valid beyond this range.

Using the new UWB capability is extremely easy. Either the High-Fidelity Head or Body mesh is loaded into XFdtd and the Frequency-Dependent Tissue Model is selected from the pull-down menu. This enables the XFdtd calculations to be made with the correct variation of tissue permittivity and conductivity over the bandwidth of the transient excitation.

Since these parameters vary considerably with frequency, this capability may be very important if accurate results are to be obtained. For example, consider the plots of the permittivity vs. frequency (Figure 1) and conductivity vs. frequency (Figure 2) of cortical bone. From 50 MHz to 20 GHz the relative permittivity changes from 16 to 6, and the conductivity changes from nearly 0 to almost 4 S/m. If, for example, a transient calculation over this frequency bandwidth were make for constant tissue parameters valid a 1 GHz, the tissue relative permittivity and conductivity would be approximately 12.4 and 0.15 S/m. This would be an extremely poor approximation to the actual values over most of the frequency range.

To illustrate the effects of this frequency variation two different calculations were made using the High-Fidelity Head Mesh. For both calculations an identical Gaussian-pulse plane wave was incident on the head traveling toward the face, and the induced electric field vs time in the right eye was calculated and sampled. For one calculation the tissue permittivities and conductivities were held constant at their 1 GHz values. For the other calculation the UWB variation of the tissue permittivities and conductivies was included in the calculation.

The results for the electric field vs time are shown in Figure 3 and Figure 4. The results are obviously quite different. If they are transformed to the frequency domain the corresponding plots are in Figure 5 and Figure 6. The two frequency domain results agree exactly at 1 GHz, where the single frequency tissue parameters are valid. At higher and lower frequencies the single-frequency tissue results deviate significantly from the UWB tissue results.

Transient electric field snapshots for both calculations are shown in Figures 7-9. Figure 7 shows the electric field in a mesh plane containing the right eye after 301 time steps using the UWB capability. The incident plane wave outside the head has propagated to the back of the head, while inside the head the propagation velocity is slower. The fields inside the UWB head are seen more clearly in Figure 8 with the tissue material display turned off. The corresponding results calculated for the head with 1 GHz values is shown in Figure 9. The internal fields are quite different.

It is clear from this example that the Remcom UWB body tissue capability is necessary to obtain accurate results for transient excitation.