# Revisiting the Analysis of Radiative Mid-Range Wireless Link for Pacemakers
## 1 Introduction  
The use of implantable medical devices (IMD) has led to the advancement of various medical treatments and diagnostic methodologies. In particular, pacemakers have received a considerable amount of interest for the patients suffering from abnormal heart rhythms. They have been used to successfully recover heart rhythms for the patients. The implantable medical devices, such as pacemakers, typically require wireless power transfer (WPT) as well as wireless data transfer [1]. The use of wireless devices is advantageous in contrast to the wire-based devices where battery life time and replacement are the biggest issues [2, 3, 4, 5]. In spite of apparent benefits of the wireless devices, the implanted devices must meet strict requirements to provide the continuous wireless link with external devices. Considering low available power for the implanted devices, an accurate estimating method of the wireless link is required [6, 7, 8]. A variety of techniques based on inductive, capacitive, magnetic, mid-field, far-field, acoustic, and optical link have been investigated for WPT applications [9, 10, 11, 12]. In particular, mid-range applications made in the radiative near-field or far-field region have gained significant attention. The traditional WPT operating in the VHF band has focused on a non-radiative near-field region, and the use of high-frequency applications in recent years permits the use of WPT systems realized in a radiative near-field region, which are known as \"radiative mid-range\" [13, 14, 15, 16, 17, 18, 19, 20, 21]. The mid-range applications allow the device to communicate through using the radiation characteristics of two antennas. Several techniques have been studied for the electromagnetic characteristics of various implanted antennas, including an interaction between the implanted antenna and the external antenna [22, 23, 24, 25, 26]. The ray tracing methods, such as geometrical optics (GO) and uniform theory of diffraction (UTD), are suitable for computing the electrically largeobjects. The methods have been used for the investigation on the outdoor point-to-point link, and have recently demonstrated their applicability to the case of body centric wireless link [22]. A finite-difference time-domain (FDTD) is useful for the study on electromagnetic problems with inhomogeneous media [23; 24]. The accuracy and efficiency of the method has been investigated for the diverse biomedical devices. However, the FDTD method has been limited to the short wireless link in order to meet the specific discretization of unit cell with allowed computing capability. Meanwhile, the method of moment (MoM) provides a degree of freedom to diverse locations of biomedical devices [25; 26]. The method has been applied to the calculation of the on-body wireless link; however, for the case with inhomogeneous and lossy media, the use of the MoM might be less efficient than using other methods. Even though those methods have been widely used in the study of the mid-range wireless link in biomedical areas, electromagnetic analysis of antennas in the human body usually requires intensive computation. Therefore, an efficient method needs to be employed in order to study diverse cases of wireless links in a limited time. The Friis formula, based on plane-wave characteristics, is computationally advantageous for the wireless link in the far-field region [27]. A variant of the Friis formula and integral coupling formula have been introduced to compute the wireless link in the radiative near-field region [28; 29; 30; 31]. In the radiative near-field region, in contrast to the far-field region, broadened radiation patterns with reduced gains are observed. The ability to accurately estimate the changes of the radiation in a proximity distance is becoming more critical. The Friis formula with correction terms has been successfully utilized to estimate the wireless link in the Fresnel region [27; 28; 29].