# Revisiting the Analysis of Radiative Mid-Range Wireless Link for Pacemakers
## 4 Discussion  
This paper presents biomedical applications of the formulas to compute the mid-range wireless link in the radiative near-field region. The radiation characteristics of the implanted antennas in the radiative near-field region are studied, and the related gain reduction factor is derived. The step by step procedures from the radiation characteristics to the analysis of the wireless link are presented. The formulas require the far-field information to compute the coupling between two antennas in the radiative near-field region. An overview of the different formulations is summarized in Table 3. The important aspects of the formulas are presented in terms of scenarios, computing time, input data, and effective regions. The case of the full-wave simulation FEKO is classified into the MoM method. The formulas were used to successfully compute the power transmission for the implanted patch antennas immersed with different depths of the human skin. A good agreement with the results obtained from the full-wave simulation FEKO is observed, and an enhancement of 1.7-2.5 dB, with respect to the Friis formula, was obtained. For the rotational scenario, a reasonable agreement with the results obtained from full-wave simulation FEKO was obtained. The validity of the evaluation was verified using the indoor measurement, and a good agreement between the simulated and the measured results was obtained. This work presents effective methods in the radiating near-field region; however, an uncovered proximity distance still exists, especially at lower frequency bands. In order to include the inductive coupling in the reactive near-field region, an example of the coupling at 400 MHz between a coil outside the human body and a loop antenna inside the human body is presented in Appendix A. The effective region of the proposed formulas implies that the (physical) minimum range can be reduced at a higher frequency band, such as 2.4 GHz, for body area communication. Conceptualization, I.K. and J.-H.L. ; methodology, I.K. ; software, I.K. and B.-H.C.; validation, I.K. ; formal analysis, I.K. ; investigation, I.K. ; resources, I.K. ; data curation, I.K. and B.-H.C.; writing--original draft preparation, I.K. ; writing--review and editing, I.K. and J.-H.L. ; visualization, I.K. ; supervision, J.-H.L. ; project administration, J.-H.L. ; funding acquisition, J.-H.L. ; All authors have read and agreed to the published version of the manuscript. This work was supported in part by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (No. 2015R1A6A1A03031833) and in part by the MSIT (Ministry of Science and ICT), Korea, under the ITRC (Information Technology Research Center) support program (IITP-2021-2016-0-00291) supervised by the IITP (Institute for Information & Communications Technology Planning & Evaluation). Not applicable. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Scenarios** &
\begin{tabular}{c} **Computing Time** \\ **(One Position)** \\ \end{tabular} & **Input Data** & **Effective Region** \\ \hline Asymptotic Friis formula & On-axis scenario & Instant & Far-field gain & Fresnel region \\ Chu formula & On-axis scenario & Instant & Far-field gain & Fresnel region \\ Integral coupling formula & On-axis, off-axis, and rotational scenarios & few seconds & 3D vector far-field & Radiative near-field \\ The method of moments & On-axis, off-axis, and rotational scenarios & 20\(\sim\)25 min & EM antenna designs & Radiative and \\ (MoM) & On-axis, off-axis, and rotational scenarios & 20\(\sim\)25 min & and geometries & non-radiative near-field \\ Finite-difference & On-axis, off-axis, and rotational scenarios & 40\(\sim\)45 min & EM antenna designs & Radiative and \\  & & & and geometries & non-radiative near-field \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Overview of the different techniques for the radiative near-field regions. **Informed Consent Statement:** Not applicable. **Data Availability Statement:** Not applicable.