# A Computational Study on Magnetic Nanoparticles Hyperthermia of Ellipsoidal Tumors
## 1 Introduction  
The most well-known techniques for cancer treatment are chemotherapy, radiation, immunotherapy and targeted therapy [1; 2; 3]. These treatments suffer from various severe side effects such as hair loss, nausea, infertility, nerve damage and general discomfort to the patient [3]. Hyperthermia is a widely studied treatment with a broad spectrum of applications ranging from cardiac ablation [4; 5] to arterial low-density lipoprotein (LDL) deposition [6; 7] to drug delivery enhancement [8; 9] and thermal ablation of tumors under microwaves [10; 11; 12] and/or with magnetic nanoparticles (MNPs) [13; 14; 15]. The hyperthermia of tumors is regarded as a viable treatment provided that the tumor locations are known and have not metastasized or when it is difficult to surgically remove the tumor, such as in liver cancer [16]. The ultimate treatment goal is to raise the tumor temperature above the physiological temperature for a certain time and to damage the malignant cells through several mechanisms such as protein denaturation, apoptosis and necrosis [17], without significantly affecting the surrounding healthy tissue. In mild hyperthermia the tumor temperature usually ranges between 40-45 \({}^{\circ}\)C and typically above 50 \({}^{\circ}\)C for ablation therapy [18; 19; 20; 21; 22]. MNPs have a broad spectrum of applications such as heat exchangers, solar collectors and separation of heavy metals from water [23; 24; 25]. Hyperthermia using MNPs (magnetic hyperthermia) has received increased attention due to its ability to deliver adequate heating power to several types of tumors [26]. The therapy involves the administrationof MNPs, usually in the form of colloidal suspensions, intravenously or directly into the tumor, and subsequently exposing the MNPs loaded tumor to an external alternating magnetic field (AMF) [27; 28]. From clinical trials, it has been shown that the product of the magnetic field amplitude and field frequency must be kept below the value of approximately \(4.85\times 10^{8}\) A\(\cdot\)m\({}^{-1}\cdot\)s\({}^{-1}\) for safety purposes [29; 30]. For intravenous injection, the magnetic field may also facilitate the nanoparticles magnetic guidance towards the desired location [31; 32]. Due to the AMF, the injected nanoparticles generate heat via mainly two mechanisms, usually referred to as Neelian and Brownian relaxations. Based on this, [PERSON] [33] developed a theoretical heat generation model that takes into account the magnetic properties of the nanoparticles as well as properties associated with the applied magnetic field. The efficiency of MNPs to convert electromagnetic energy into heat may be quantified experimentally, usually by specific loss power (SLP), also referred to as specific absorption rate (SAR) [15; 34]. The most common types of MNPs used to date are superparamagnetic iron oxide nanoparticles (SPIONs) such as magnetite Fe\({}_{3}\)O\({}_{4}\) and maghemite \(\gamma\)-Fe\({}_{2}\)O\({}_{3}\)[35; 36; 37], due to their biocompatibility [38] upon injection in human tissues. Several other nanoparticle types have also been reported, such as metallic alloys [39; 40] and carbon nanotubes [41]. The distribution of the nanoparticles reaching the tumor may generally vary from approximately uniform distributions throughout the whole tumor to fully localized ones inside specific tumor regions as observed from real tumor sections [42; 43]. The distributions depend on several factors such as injection parameters, the tumor's physiological and mechanical properties, and the physicochemical properties of the nanoparticles [44; 45; 46]. According to several studies [47; 48; 49], modeling the magnetic hyperthermia plays a seminal role in the treatment. Determination of the therapeutic temperature profile and the treatment duration are key parameters frequently taken into consideration during the treatment procedure.