## 1 Introduction  
Magnetic resonance imaging (MRI) is an important technique in medical diagnostics with continuously increasing applications. Nevertheless, many patients with active implanted medical devices (AIMDs) in their bodies are excluded from this procedure. The reason for this exclusion is the interaction of AIMDs with the radiofrequency (RF) fields of the MRI scanner, leading to unwanted and potentially dangerous tissue heating at the tip of leads [1]. However, the growing number of implanted medical devices and MRI scans led to the necessity of assessing the MRI safety of AIMDs [2; 3; 4]. Several previous studies have presented in vitro measurements of the induced heating at the tip of an implanted lead, as well as in vivo measurements for specific electrodes, MR systems and conditions [5; 6; 7; 8; 9; 10]. In addition, previous works have studied several factors that influence the amount of heating at the lead tip, such as lead geometry, conductivity of the medium at the lead tip, location of the implant inside the body, position of the phantom inside the coil and the MR system used [11; 12; 13; 14; 15; 16; 17]. In order to calculate the temperature rise in tissue caused by an AIMD during an MRI session, a technical specification has been developed by the International Organization for Standardization (ISO) [18]. This specification contains a four-tier approach with increasing complexity and accuracy of estimation between successive tiers. The lower tiers are based on simplifications of the exposure situation, producing an overestimation of the temperature increase and, therefore, resulting in a larger safety margin. On the contrary, the higher tiers involve the realistic implant placement of AIMDs in the human body and the accurate calculation of the incident fields, reducing the overestimation and resulting in a more realistic evaluation of the temperature rise. In particular, the Tier 3 approach uses the concept of the transfer function (TF) of an implant and correlates the incident tangential electric field along a trajectory to the deposited power in the tissue surrounding the lead tip, which leads to the temperature increase [19]. The above-described process refers to a single lead. However, many implants, such as conventional pacemakers, deep brain stimulators, spinal fusion and nerve cuff stimulators, have multiple leads resulting in a mutual coupling between their currents induced by the RF field inside an MRI scanner [20; 21; 22; 23; 24]. Aside from these multiple-lead implants, there are cases, where, due to a technical failure, an implant should be extracted and replaced by a new device. The incomplete lead extraction could result in abandoned or retained leads inside the patient running in proximity to newly implanted leads [25; 26]. A dedicated approach to assess the potential coupling impact arising from devices with multiple leads or the presence of multiple leads, such as those found in instances of either abandoned or retained implants, has not been established to date. However, the presence of a second wire changes the TF of the single wire, causing either an increase or decrease in the current amplitude along the wire [27]. Moreover, ref. [28] concluded that the presence of an abandoned lead modified the heating profile of an MR-conditional implant, resulting either in an increase or a decrease in the induced heating, depending on the relative position of the two leads. Similarly, previous studies showed that the presence of abandoned or retained leads could pose an additional risk to the patient [25; 26]. In [29], it was reported that a broken lead enhanced the deposited power at the tip compared to the intact lead, whereas the proximity of an intact wire or even a nearby broken wire reduced the enhancement factor. In another study, the mutual coupling of the wires was used to minimize the RF heating through the addition of one or more coupled fillers to the lead [30].