# Phase Compensation Technique for Effective Heat Focusing in Microwave Hyperthermia Systems
## 1 Introduction  
Breast cancer treatments have been investigated throughout the past decade, and thermal treatments for breast cancer using microwaves are being rapidly developed to reduce the dangerous side effects associated with conventional methods [1]. Primary breast cancer treatments include surgical operations, radiotherapy, chemotherapy, and hyperthermia. Among these, microwave hyperthermia is an effective treatment that uses a beneficial heating effect. Because cancerous tissues are highly vascularized, and it is harder to remove excess heat from them than from healthy tissues, thermal damages are sensitive to the cancer [2]. A non-invasive microwave hyperthermia system for cancer treatment is reliable, cost effective, and painless compared with surgical operations. Furthermore, hyperthermia has a synergistic effect when used in combination with radiation oncology or chemotherapy [3; 4; 5; 6]. In hyperthermic systems, tumor cells are damaged under the temperature range of 43-47 \({}^{\circ}\)C, while normal cells are not damaged [7]. Non-invasive microwave hyperthermia employing an antenna array is a reliable treatment method that can achieve effective breast tumor necrosis [8]. In this procedure, electromagnetic (EM) energy is radiated from array elements and concentrated on the tumor region, where heating is applied for treatment [9; 10; 11]. Microwave hyperthermia for deep-seated tumors inside the human breast should be designed so that EM energy can be transferred well into the interior of the body. The human body is composed of various dielectric tissues that make it difficult to provide a suitable EM energy concentration because of dielectric losses [12]. One of the challenges of this treatment method is to design microwave hyperthermia systems that, while focusing the EM energy into the human body, heat only malignant tissues, without overheating normal tissues [13]. Mathematically, accurate EM energy focusing methods are essential for optimal accumulation. Many techniques, such as the time reversal method, specific absorption rate(SAR) optimization, temperature optimization, and phased array, have been researched to prove the efficacy of hyperthermia treatments [14; 15; 16; 17; 18; 19]. The SAR optimization technique can assume the correlation between SAR and temperature to anticipate deviations in thermal boundary conditions [14; 15; 16]. Temperature-based optimization seeks to optimize the temperature distribution; however, this method is dependent on the properties of the thermal tissue, which results in very large uncertainty and higher computational costs than the SAR-based optimization technique [14; 19]. Therefore, the SAR optimization method for effective energy focusing using a phased array is a very attractive technique due to the practicality of its implementation and its simple procedure [14; 15; 16; 17; 19; 20; 21]. To deliver microwaves inside the breast, the input phase of each antenna should differ depending on the location of the tumor cells. Strong constructive interference in the target area can be achieved with accurate phase control. Narrowband phased-array antenna systems for treating single targets that operate on a single frequency best suited for healing superficial and single tumor locations are presented in [18; 20; 21]. However, these systems have some issues, such as the relatively large number of hot spots, poor resolutions, and their limitation to unicentric breast cancers. Multifocal/multicentric breast cancers, which occur when there is more than one distinct type of tumor cell in a single quadrant, are more aggressive and are associated with worse outcomes than unifocal cancers [22]. Hyperthermia therapy for multiple tumor locations has been studied by [23; 24]. In [23], iron oxide nanoparticle-loaded nanocapsules were injected into different tumor positions to be used with magnetic hyperthermia therapy. In [24], a multi-frequency excitation approach for multiple tumor locations was proposed for enhanced EM energy penetration and the resolution of its localization.