3D in silico study of magnetic fluid hyperthermia of breast tumor using Fe₃O₄ magnetic nanoparticles

Highlights

• 3D in silico study of magnetic fluid hyperthermia of breast tumor is conducted.

• Infusion, diffusion, and heat transfer in breast cup are simulated on COMSOL Multiphysics.

• The backflow of nanofluid and fraction of tumor necrosis in breast cup is predicted quantitatively.

• The sensitivity of heating parameters and magnetic field arises due to current carrying coil to heat tumor is investigated.

• Mesh dependent solution of the bioheat transfer model in breast cup is analyzed.

Abstract

Modeling and simulation of the temperature distribution, the mass concentration, and the heat transfer in the breast tissue are hot issues in magnetic fluid hyperthermia treatment of cancer. The breast tissue can be visualized as a porous matrix with saturated blood. In this paper, 3D in silico study of breast cancer hyperthermia using magnetic nanoparticles (MNPs) is conducted. The 3D FEM models are incorporated to investigate the infusion and backflow of nanofluid in the breast tumor, the diffusion of nanofluid, temperature distribution during the treatment, and prediction of the fraction of tumor necrosis while dealing with the thermal therapy. All the hyperthermia procedures are simulated and analyzed on COMSOL Multiphysics. The sensitivity of frequency and amplitude of the applied magnetic field (AMF) is investigated on the heating effect of the tumor. The mesh dependent solution of Penne's bioheat model is also analyzed. The simulated results demonstrate successful breast cancer treatment using MNPs with minimum side effects. Validation of current simulations results with experimental studies existing in literature advocates the success of our therapy. The increase in the amplitude and frequency of the AMF increases of the temperature in the tumor. The variation of mesh from coarser to finer increased the temperature through small fractions. We have also simulated the magnetic induction problem where the magnetic field is generated by current-carrying coil conductors induce heat in nearby breast tumors due to excitation of MNPs by magnetic flux. This research will aid treatment protocols and real-time clinical breast cancer treatments.

Introduction

Breast cancer is a major cause of mortality worldwide. In the USA, in 2019, there were an estimated 268,600 women breast cancer cases and 2670 cancer cases identified in men. From 2006 to 2015 the women breast cancer cases were increased by 0.4% per year and estimated deaths in 2019 are 42,260 including both male and female (Gaugler et al., 2019). World Health Organization, in 2005, an estimated 7.6 million people died of breast tumor and more than 70% of all cancer affected deaths happen in underdeveloped countries due to a lack of diagnosis and treatment facilities. Prominent symptoms of breast cancer are a lump in the breast, nipple retraction, asymmetry, blood-stained nipple discharge, eczematous, and skin retraction (Organization, 2007). In 2008, 1383500 breast cancer cases and 458400 cancer affected deaths were identified and half of these deaths were in third world countries (Ferlay et al., 2008). The main risk factors for breast cancer are a family history of breast cancer, alcohol intake, physical inactivity, obesity, and smoking (Surdyka et al., 2014). Breast cancer contributes 23% to all female breast cancers. After lung cancer, it is the second most common cancer and is the fifth most frequent cause of cancer deaths carrying a mortality-to-incidence ratio of 0.35 globally. The International Agency for Research on Cancer (2002) calculated 514,000 new breast cancer cases in underdeveloped countries compared to the 636,000 cases in developed countries, but there were 221,000 deaths in third world countries compared to the 190,000 deaths in the developed countries, implying mortality-to-incidence ratio 0.43 versus 0.30, respectively (Parkin et al., 2005).

Hyperthermia is a heating procedure where the tumor temperature is raised above normal temperature (37 °C) of the body. It is elevated to 42–45 °C in mild hyperthermia and above 50 °C for ablation therapy. Moderate hyperthermia may also range from 41 to 46 °C and thermal ablation from 46 to 56 °C that causes tumor cells to go under coagulation, direct necrosis of tissue or carbonization and causes protein denaturation and aggregation (Goldstein et al., 2003). The traditional cancer treatment includes chemotherapy, radiotherapy, immunotherapy, and surgery but each of these treatment modalities carries drawbacks of killing normal cells of the body as well. Here magnetic fluid hyperthermia (MFH) offers a solution to the problem based on selective heating for the destruction of the tumor. In hyperthermia, heat can be produced by microwave, laser beam, ultrasound, or MNPs (Moroz et al., 2002).

The MFH is better than the conventional noninvasive treatment techniques due to heat generation in deep-seated tumors with minimum normal tissue damage. Different researchers have attempted to treat breast cancer using MFH. The prominent approaches include the work by (Miaskowski et al., 2010) who used the magnetite MNPs to treat female breast cancer. They proposed a theoretical formula based on specific absorption rate to determine the temperature increase in breast cancer. This formula agrees well with the experiments conducted on female breast cancer phantom. In another study (Miaskowski and Sawicki, 2013), treated numerically the MFH of female breast cancer. They developed an artificial female breast phantom and transform the experimental results on anatomically breast models. The study (Guiot et al., 1998) dealt with the hyperthermia differently; they studied the recurrence of tumor in the chest wall experimentally by inserting probes at different locations in the recurrence region. The perfusion effect on the thermal map was investigated along with thermal conductivity through the solution of Penne's bioheat equation. Despite these prominent approaches of MFH towards breast cancer, some authors dealt with MFH in the presence of blood vessels. The study by (Yue et al., 2014) dealt with hyperthermia and injection position on blood vessel bifurcation. They researched that the size, structure, and position of the bifurcation blood vessel greatly affect the injection parameters concentration of nanofluid, injection volume, arrangement of injections in tissue, and distance between bifurcation and injection site. They suggested that high concentration nanofluid and high injection density must be administered in the region near the blood vessel to reduce the cooling function of blood flow. In the study (Tungjitkusolmun et al., 2002), the authors used a radiofrequency probe for ablation therapy of liver tumors. They predicted the tissue temperature distribution during the hyperthermia. They investigated that the temperature in the hepatic tissue between the blood vessel and electrode rises due to the joule effect because of the higher electrical conductivity of the blood. The blood flow acts as a heat sink and absorbs the heat from nearby tissue. In the study by (Rodrigues et al., 2013), the authors discussed briefly the convective effect of the blood vessel in the brain while dealing with a multilayered solution bioheat equation. They investigated that the presence of large blood vessels causes the temperature nears the walls of 0.3 °C of the white matter brain. In the study (Adhikary and Banerjee, 2016) the authors also dealt with hyperthermia of skin cancer while blood vessel was present. The temperature is minimum where the blood vessel was present. High blood velocity causes an abrupt rise in the cooling effect and low blood velocity maintains the therapeutic temperature range within the tumor. In the study (Attar et al., 2014) the temperature distribution inside the tumor was investigated where the distribution of MNPs was investigated. They also experimentally investigated the hyperthermia of porcine liver tissue and their time-dependent solution agreed well with experimental results. Heating effect of MNPs on human cells lines was investigated by (Attar and Haghpanahi, 2016) where they concluded that dose of MNPs of 80 μg/mL with a diameter size of 8 nm at the resonant coil frequency during 30 min time duration was sufficient to kill all the cancer cells in the flask. Thermal visco elastics behavior of tumor tissue was investigated by (Attar et al., 2016a, Attar et al., 2016b) where they predicted the stress and displacement fields using the FEM method, again they validated their numerical results with the experimental tests in good agreement. In another study (Attar et al., 2017) used 20 nm size MNPs for hyperthermia of dead liver kidneys with blood perfusion. Their simulation studies and experiential results both concluded that the blood flow rate in the tissue almost 70% decreases the temperature. In another prominent study (Attar et al., 2016a, Attar et al., 2016b) the MFH of human HCT-116 colon cancer cell lines. They concluded from their study that a thermal dose of 4.5 ± 0.5 °C/30 min initiating from temperature 37 °C, death of HCT-116 starts when the external magnetic field was applied.

The above literature concludes that most of the authors dealt with MFH on different body organs besides the breast organ and among those who treated breast cancer they have not discussed the details of models dealing with processes of infusion, backflow, diffusion, and prediction of fractions of tumor damage. Also, their work carries limitations through whole work in 2D geometry. None of them investigated the sensitivity of parameters involved in such complex problems which are much sensitive to the heating effect. The literature also has a lack of mesh dependent analysis of the heat dissipation by the MNPs. These limitations in the previous studies motivated us to address such issues. Our objective in this study is to simulate and analyze all the processes in MFH with a 3D FEM numerical model analysis of female breast cancer using biocompatible iron oxide Fe₃O₄ MNPs and to analyze the sensitivity of main parameters on heating tumor involved in this treatment modality. Another objective is to simulate the magnetic induction problem where the magnetic field generated by current-carrying coil conductors will induce heat in nearby breast tumors due to the excitation of MNPs by magnetic flux.