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A mathematical modeling approach toward magnetic fluid hyperthermia of cancer and unfolding heating mechanism

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Abstract

Magnetic nanoparticles (MNPs)-induced hyperthermia is capable of heating the tumor without side effects. In this technique, the tumor temperature is elevated to 41–43 °C from a normal temperature of 37 °C of the body. The Pennes' bio-heat transfer equation is widely used to transfer heat in living organs with blood perfusion rate. The elevated temperature destroys cancer cells and keeps normal cells harmless. This state-of-the-art review describes the basic physical mechanisms behind this treatment modality and recent advances in the mathematical modeling approach toward this therapy. Firstly, we throw light on different MNPs applicable in hyperthermia, heat generation mechanism, basic parameters affecting the efficiency of heating, thermophysical properties of MNPs, in vivo studies, and clinical studies. Secondly, we have discussed in detail the mathematical modeling of hyperthermia including analytical solutions, computational modeling, and prominent optimization techniques applied in thermotherapy. We shortly discuss hyperthermia integrated with chemotherapy, laser therapy, radiotherapy, and immunotherapy. In the end, we narrate some major challenges and opportunities for hyperthermia and discussed future directions.

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References

  1. Society AC. Global cancer facts & figures. American Cancer Society Atlanta; 2011.

  2. Cancer IAfRo. IARC: outdoor air pollution a leading environmental cause of cancer deaths: International Agency for Research on Cancer; 2011.

  3. EJ H. Physical and biologic basis of radiation therapy. Moss’ Radiat Oncol Ration Tech Res. 1994:3–66.

  4. Dewey W, Hopwood L, Sapareto S, Gerweck L. Cellular responses to combinations of hyperthermia and radiation. Radiology. 1977;123:463–74.

    Article  CAS  PubMed  Google Scholar 

  5. Overgaard J. Hyperthermic oncology 1984: summary papers. London: Taylor & Francis; 1984.

    Google Scholar 

  6. Christophi C, Winkworth A, Muralihdaran V, Evans P. The treatment of malignancy by hyperthermia. Surg Oncol. 1998;7:83–90.

    Article  CAS  PubMed  Google Scholar 

  7. Fagnoni FF, Zerbini A, Pelosi G, Missale G. Combination of radiofrequency ablation and immunotherapy. Front Biosci. 2008;13:369–81.

    Article  CAS  PubMed  Google Scholar 

  8. Goldstein L, Dewhirst M, Repacholi M, Kheifets L. Summary, conclusions and recommendations: adverse temperature levels in the human body. Int J Hyperth. 2003;19:373–84.

    Article  CAS  Google Scholar 

  9. Habash RW, Bansal R, Krewski D, Alhafid HT. Thermal therapy, part 2: hyperthermia techniques. Crit Rev Biomed Eng. 2006;34:491–542.

    Article  PubMed  Google Scholar 

  10. Robins HI, Woods JP, Schmitt CL, Cohen JD. A new technological approach to radiant heat whole body hyperthermia. Cancer Lett. 1994;79:137–45.

    Article  CAS  PubMed  Google Scholar 

  11. Nielsen OS, Horsman M, Overgaard J. A future for hyperthermia in cancer treatment? Eur J Cancer. 2001;37:1587–9.

    Article  CAS  PubMed  Google Scholar 

  12. Lin JC, Wang Y-J. Interstitial microwave antennas for thermal therapy. Int J Hyperth. 1987;3:37–47.

    Article  CAS  Google Scholar 

  13. Kobayashi T. Cancer hyperthermia using magnetic nanoparticles. Biotechnol J. 2011;6:1342–7.

    Article  CAS  PubMed  Google Scholar 

  14. van der Zee J, González D, van Rhoon GC, van Dijk JD, van Putten WL, Hart AA. Comparison of radiotherapy alone with radiotherapy plus hyperthermia in locally advanced pelvic tumours: a prospective, randomised, multicentre trial. The Lancet. 2000;355:1119–25.

    Article  Google Scholar 

  15. Overgaard J, Bentzen S, Gonzalez DG, Hulshof M, Arcangeli G, Dahl O, et al. Randomised trial of hyperthermia as adjuvant to radiotherapy for recurrent or metastatic malignant melanoma. The Lancet. 1995;345:540–3.

    Article  CAS  Google Scholar 

  16. Group ICH, Vernon CC, Hand JW, Field SB, Machin D, Whaley JB, et al. Radiotherapy with or without hyperthermia in the treatment of superficial localized breast cancer: results from five randomized controlled trials. Int J Radiat Oncol Biol Phys. 1996;35:731–44.

    Article  Google Scholar 

  17. Issels RD, Lindner LH, Verweij J, Wust P, Reichardt P, Schem B-C, et al. Neo-adjuvant chemotherapy alone or with regional hyperthermia for localised high-risk soft-tissue sarcoma: a randomised phase 3 multicentre study. Lancet Oncol. 2010;11:561–70.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  18. Colombo R, Salonia A, Leib Z, Pavone-Macaluso M, Engelstein D. Long-term outcomes of a randomized controlled trial comparing thermochemotherapy with mitomycin-C alone as adjuvant treatment for non-muscle-invasive bladder cancer (NMIBC). BJU Int. 2011;107:912–8.

    Article  CAS  PubMed  Google Scholar 

  19. Dennis C, Jackson A, Borchers J, Ivkov R, Foreman A, Hoopes P, et al. The influence of magnetic and physiological behaviour on the effectiveness of iron oxide nanoparticles for hyperthermia. J Phys D Appl Phys. 2008;41:134020.

    Article  CAS  Google Scholar 

  20. Kawai N, Futakuchi M, Yoshida T, Ito A, Sato S, Naiki T, et al. Effect of heat therapy using magnetic nanoparticles conjugated with cationic liposomes on prostate tumor in bone. Prostate. 2008;68:784–92.

    Article  PubMed  Google Scholar 

  21. Suto M, Hirota Y, Mamiya H, Fujita A, Kasuya R, Tohji K, et al. Heat dissipation mechanism of magnetite nanoparticles in magnetic fluid hyperthermia. J Magn Magn Mater. 2009;321:1493–6.

    Article  CAS  Google Scholar 

  22. Lévy M, Wilhelm C, Siaugue J-M, Horner O, Bacri J-C, Gazeau F. Magnetically induced hyperthermia: size-dependent heating power of γ-Fe2O3 nanoparticles. J Phys: Condens Matter. 2008;20:204133.

    Google Scholar 

  23. Blonska-Tabero A, Bosacka M, Filipek E, Piz M, Kochmanski P. High-temperature synthesis and unknown properties of M3Cr4 (PO4)6, where M = Zn or Mg and a new solid solution Zn 1.5 Mg 1.5 Cr 4 (PO 4) 6. J Therm Anal Calorim 2019:1–7.

  24. Kim D-H, Lee S-H, Kim K-N, Kim K-M, Shim I-B, Lee Y-K. Temperature change of various ferrite particles with alternating magnetic field for hyperthermic application. J Magn Magn Mater. 2005;293:320–7.

    Article  CAS  Google Scholar 

  25. Hergt R, Andra W, d’Ambly CG, Hilger I, Kaiser WA, Richter U, et al. Physical limits of hyperthermia using magnetite fine particles. IEEE Trans Magn. 1998;34:3745–54.

    Article  CAS  Google Scholar 

  26. Koch CM, Winfrey AL. FEM optimization of energy density in tumor hyperthermia using time-dependent magnetic nanoparticle power dissipation. IEEE Trans Magn. 2014;50:1–7.

    Article  Google Scholar 

  27. Pankhurst QA, Connolly J, Jones S, Dobson J. Applications of magnetic nanoparticles in biomedicine. J Phys D Appl Phys. 2003;36:R167.

    Article  CAS  Google Scholar 

  28. Branquinho LC, Carrião MS, Costa AS, Zufelato N, Sousa MH, Miotto R, et al. Effect of magnetic dipolar interactions on nanoparticle heating efficiency: implications for cancer hyperthermia. Sci Rep. 2013;3:2887.

    Article  PubMed  PubMed Central  Google Scholar 

  29. Berry CC, Curtis AS. Functionalisation of magnetic nanoparticles for applications in biomedicine. J Phys D Appl Phys. 2003;36:R198.

    Article  CAS  Google Scholar 

  30. Wang X, Gu H, Yang Z. The heating effect of magnetic fluids in an alternating magnetic field. J Magn Magn Mater. 2005;293:334–40.

    Article  CAS  Google Scholar 

  31. Habib A, Ondeck C, Chaudhary P, Bockstaller M, McHenry M. Evaluation of iron-cobalt/ferrite core-shell nanoparticles for cancer thermotherapy. J Appl Phys. 2008;103:07A307.

    Article  CAS  Google Scholar 

  32. Kappiyoor R, Liangruksa M, Ganguly R, Puri IK. The effects of magnetic nanoparticle properties on magnetic fluid hyperthermia. J Appl Phys. 2010;108:094702.

    Article  CAS  Google Scholar 

  33. Iravani S. Green synthesis of metal nanoparticles using plants. Green Chem. 2011;13:2638–50.

    Article  CAS  Google Scholar 

  34. Obaidat I, Issa B, Haik Y. Magnetic properties of magnetic nanoparticles for efficient hyperthermia. Nanomaterials. 2015;5:63–89.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  35. Bergs JW, Wacker MG, Hehlgans S, Piiper A, Multhoff G, Roedel C, et al. The role of recent nanotechnology in enhancing the efficacy of radiation therapy. Biochim Biophys Acta BBA Rev Cancer. 2015;1856:130–43.

    Article  CAS  Google Scholar 

  36. Maeda H, Nakamura H, Fang J. The EPR effect for macromolecular drug delivery to solid tumors: improvement of tumor uptake, lowering of systemic toxicity, and distinct tumor imaging in vivo. Adv Drug Deliv Rev. 2013;65:71–9.

    Article  CAS  PubMed  Google Scholar 

  37. Hilger I, Rapp A, Greulich K-O, Kaiser WA. Assessment of DNA damage in target tumor cells after thermoablation in mice. Radiology. 2005;237:500–6.

    Article  PubMed  Google Scholar 

  38. van Landeghem FK, Maier-Hauff K, Jordan A, Hoffmann K-T, Gneveckow U, Scholz R, et al. Post-mortem studies in glioblastoma patients treated with thermotherapy using magnetic nanoparticles. Biomaterials. 2009;30:52–7.

    Article  PubMed  CAS  Google Scholar 

  39. Ng EYK, Kumar SD. Physical mechanism and modeling of heat generation and transfer in magnetic fluid hyperthermia through Néelian and Brownian relaxation: a review. Biomed Eng Online. 2017;16:36.

    Article  PubMed  PubMed Central  Google Scholar 

  40. Kumar CS, Mohammad F. Magnetic nanomaterials for hyperthermia-based therapy and controlled drug delivery. Adv Drug Deliv Rev. 2011;63:789–808.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  41. Datta N, Krishnan S, Speiser D, Neufeld E, Kuster N, Bodis S, et al. Magnetic nanoparticle-induced hyperthermia with appropriate payloads: Paul Ehrlich’s “magic (nano) bullet” for cancer theranostics? Cancer Treat Rev. 2016;50:217–27.

    Article  CAS  PubMed  Google Scholar 

  42. Dutz S, Hergt R. Magnetic nanoparticle heating and heat transfer on a microscale: basic principles, realities and physical limitations of hyperthermia for tumour therapy. Int J Hyperth. 2013;29:790–800.

    Article  Google Scholar 

  43. Kneller E. Theory of the magnetization curve of small crystals. Encycl Phys. 1966;18:2.

    Google Scholar 

  44. Wang Z, Mao N, Jiang F. Study on the effect of spacing on thermal runaway propagation for lithium-ion batteries. J Therm Anal Calorim. 2019;140:1–15.

    Google Scholar 

  45. Leszczyński J, Mizera A, Nieroda J, Nieroda P, Drożdż E, Sitarz M, et al. Application of TPO/TPR methods in oxidation investigations of CoSb3 and Mg2 Si thermoelectrics with and without a protective coating of “black glass”. J Therm Anal Calorim. 2019;140:1–10.

    Google Scholar 

  46. Néel L. Théorie du traînage magnétique des substances massives dans le domaine de Rayleigh. J Phys Radium. 1950;11:49–61.

    Article  Google Scholar 

  47. Brown WF Jr. Thermal fluctuations of a single-domain particle. Phys Rev. 1963;130:1677.

    Article  Google Scholar 

  48. Rosensweig RE. Heating magnetic fluid with alternating magnetic field. J Magn Magn Mater. 2002;252:370–4.

    Article  CAS  Google Scholar 

  49. Sapareto SA, Dewey WC. Thermal dose determination in cancer therapy. Int J Radiat Oncol Biol Phys. 1984;10:787–800.

    Article  CAS  PubMed  Google Scholar 

  50. Haines P, Reading M, Wilburn F. Differential thermal analysis and differential scanning calorimetry. Handbook of thermal analysis and calorimetry. Amsterdam: Elsevier; 1998. p. 279–361.

    Google Scholar 

  51. Khachani M, El Hamidi A, Halim M, Arsalane S. Non-isothermal kinetic and thermodynamic studies of the dehydroxylation process of synthetic calcium hydroxide Ca (OH)2. J Mater Environ Sci. 2014;5:615–24.

    CAS  Google Scholar 

  52. Silva AC, Oliveira TR, Mamani JB, Malheiros SM, Malavolta L, Pavon LF, et al. Application of hyperthermia induced by superparamagnetic iron oxide nanoparticles in glioma treatment. Int J Nanomed. 2011;6:591.

    CAS  Google Scholar 

  53. Brezovich IA. Low frequency hyperthermia: capacitive and ferromagnetic thermoseed methods. Med Phys Monogr. 1988;16:82–111.

    Google Scholar 

  54. Mehdaoui B, Meffre A, Lacroix L-M, Carrey J, Lachaize S, Gougeon M, et al. Large specific absorption rates in the magnetic hyperthermia properties of metallic iron nanocubes. J Magn Magn Mater. 2010;322:L49–52.

    Article  CAS  Google Scholar 

  55. Pradhan P, Giri J, Samanta G, Sarma HD, Mishra KP, Bellare J, et al. Comparative evaluation of heating ability and biocompatibility of different ferrite-based magnetic fluids for hyperthermia application. J Biomed Mater Res Part B Appl Biomater Off J Soc Biomater Jpn Soc Biomater Aust Soc Biomater Korean Soc Biomater. 2007;81:12–22.

    Article  CAS  Google Scholar 

  56. Ito A, Nakahara Y, Tanaka K, Kuga Y, Honda H, Kobayashi T. Time course of biodistribution and heat generation of magnetite cationic liposomes in mouse model. Therm Med (Jpn J Hypertherm Oncol). 2003;19:151–9.

    Article  Google Scholar 

  57. Johannsen M, Gneveckow U, Eckelt L, Feussner A, Waldoefner N, Scholz R, et al. Clinical hyperthermia of prostate cancer using magnetic nanoparticles-preliminary experience with a new interstitial technique. 2005.

  58. Kawai N, Ito A, Nakahara Y, Honda H, Kobayashi T, Futakuchi M, et al. Complete regression of experimental prostate cancer in nude mice by repeated hyperthermia using magnetite cationic liposomes and a newly developed solenoid containing a ferrite core. Prostate. 2006;66:718–27.

    Article  CAS  PubMed  Google Scholar 

  59. Wust P, Gneveckow U, Wust P, Gneveckow U, Johannsen M, Böhmer D, et al. Magnetic nanoparticles for interstitial thermotherapy–feasibility, tolerance and achieved temperatures. Int J Hyperth. 2006;22:673–85.

    Article  CAS  Google Scholar 

  60. Rast L, Harrison JG. Computational modeling of electromagnetically induced heating of magnetic nanoparticle materials for hyperthermic cancer treatment. PIERS Online. 2010;6:690–4.

    Article  Google Scholar 

  61. Candeo A, Dughiero F. Numerical FEM models for the planning of magnetic induction hyperthermia treatments with nanoparticles. IEEE Trans Magn. 2009;45:1658–61.

    Article  CAS  Google Scholar 

  62. Guardia P, Di Corato R, Lartigue L, Wilhelm C, Espinosa A, Garcia-Hernandez M, et al. Water-soluble iron oxide nanocubes with high values of specific absorption rate for cancer cell hyperthermia treatment. ACS Nano. 2012;6:3080–91.

    Article  CAS  PubMed  Google Scholar 

  63. Cervadoro A, Giverso C, Pande R, Sarangi S, Preziosi L, Wosik J, et al. Design maps for the hyperthermic treatment of tumors with superparamagnetic nanoparticles. PLoS ONE. 2013;8:e57332.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  64. Bellizzi G, Bucci OM, Chirico G. Numerical assessment of a criterion for the optimal choice of the operative conditions in magnetic nanoparticle hyperthermia on a realistic model of the human head. Int J Hyperth. 2016;32:688–703.

    Article  CAS  Google Scholar 

  65. Deatsch AE, Evans BA. Heating efficiency in magnetic nanoparticle hyperthermia. J Magn Magn Mater. 2014;354:163–72.

    Article  CAS  Google Scholar 

  66. Khandhar AP, Ferguson RM, Simon JA, Krishnan KM. Enhancing cancer therapeutics using size-optimized magnetic fluid hyperthermia. J Appl Phys. 2012;111:07B306.

    Article  PubMed Central  CAS  Google Scholar 

  67. Bakoglidis K, Simeonidis K, Sakellari D, Stefanou G, Angelakeris M. Size-dependent mechanisms in AC magnetic hyperthermia response of iron-oxide nanoparticles. IEEE Trans Magn. 2012;48:1320–3.

    Article  CAS  Google Scholar 

  68. Gonzales-Weimuller M, Zeisberger M, Krishnan KM. Size-dependant heating rates of iron oxide nanoparticles for magnetic fluid hyperthermia. J Magn Magn Mater. 2009;321:1947–50.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  69. Purushotham S, Ramanujan R. Modeling the performance of magnetic nanoparticles in multimodal cancer therapy. J Appl Phys. 2010;107:114701.

    Article  CAS  Google Scholar 

  70. Guimarães AP, Guimaraes AP. Principles of nanomagnetism. Berlin: Springer; 2009.

    Book  Google Scholar 

  71. Berkowitz A, Lahut J, Jacobs I, Levinson LM, Forester D. Spin pinning at ferrite-organic interfaces. Phys Rev Lett. 1975;34:594.

    Article  CAS  Google Scholar 

  72. Di Corato R, Espinosa A, Lartigue L, Tharaud M, Chat S, Pellegrino T, et al. Magnetic hyperthermia efficiency in the cellular environment for different nanoparticle designs. Biomaterials. 2014;35:6400–11.

    Article  PubMed  CAS  Google Scholar 

  73. Bødker F, Mørup S, Linderoth S. Surface effects in metallic iron nanoparticles. Phys Rev Lett. 1994;72:282.

    Article  PubMed  Google Scholar 

  74. Kalambur VS, Han B, Hammer BE, Shield TW, Bischof JC. In vitro characterization of movement, heating and visualization of magnetic nanoparticles for biomedical applications. Nanotechnology. 2005;16:1221.

    Article  CAS  Google Scholar 

  75. Chen S, Chiang C-L, Hsieh S. Simulating physiological conditions to evaluate nanoparticles for magnetic fluid hyperthermia (MFH) therapy applications. J Magn Magn Mater. 2010;322:247–52.

    Article  CAS  Google Scholar 

  76. Davari H, Goshayeshi HR, Öztop HF, Chaer I. Experimental investigation of oscillating heat pipe efficiency for a novel condenser by using Fe3O4 nanofluid. J Therm Anal Calorim 2019;140:1–10.

    Google Scholar 

  77. Petryk AA, Misra A, Mazur CM, Petryk JD, Hoopes PJ. Magnetic nanoparticle hyperthermia cancer treatment efficacy dependence on cellular and tissue level particle concentration and particle heating properties. Energy-based Treatment of Tissue and Assessment VIII: International Society for Optics and Photonics; 2015. p. 93260L.

  78. Pavel M, Stancu A. Study of the optimum injection sites for a multiple metastases region in cancer therapy by using MFH. IEEE Trans Magn. 2009;45:4825–8.

    Article  CAS  Google Scholar 

  79. Gupta M, Singh V, Kumar R, Said Z. A review on thermophysical properties of nanofluids and heat transfer applications. Renew Sustain Energy Rev. 2017;74:638–70.

    Article  CAS  Google Scholar 

  80. Nakhchi M, Esfahani J. Numerical investigation of turbulent CuO–water nanofluid inside heat exchanger enhanced with double V-cut twisted tapes. J Ther Anal Calorim. 2020;1–11.

  81. Gautam RK, Seth D. Thermal conductivity of deep eutectic solvents. J Ther Anal Calorim. 2019;140:1–8.

    Google Scholar 

  82. Hamilton RL, Crosser O. Thermal conductivity of heterogeneous two-component systems. Ind Eng Chem Fundam. 1962;1:187–91.

    Article  CAS  Google Scholar 

  83. Brinkman H. The viscosity of concentrated suspensions and solutions. J Chem Phys. 1952;20:571.

    Article  CAS  Google Scholar 

  84. Buongiorno J. Convective transport in nanofluids. J Heat Transf. 2006;128:240–50.

    Article  Google Scholar 

  85. Jimbow K, Takada T, Sato M, Sato A, Kamiya T, Ono I, et al. Keynote-4 Melanin biology and translational research strategy; melanogenesis and nanomedicine as the basis for melanoma-targeted Dds and chemo-thermo-immunotherapy. Pigment Cell Melanoma Res. 2008;21:243–4.

    Article  Google Scholar 

  86. Gordon R, Hines J, Gordon D. Intracellular hyperthermia a biophysical approach to cancer treatment via intracellular temperature and biophysical alterations. Med Hypoth. 1979;5:83–102.

    Article  CAS  Google Scholar 

  87. LeBrun A, Joglekar T, Bieberich C, Ma R, Zhu L. Identification of infusion strategy for achieving repeatable nanoparticle distribution and quantification of thermal dosage using micro-CT Hounsfield unit in magnetic nanoparticle hyperthermia. Int J Hyperth. 2016;32:132–43.

    Article  CAS  Google Scholar 

  88. Kong G, Braun RD, Dewhirst MW. Characterization of the effect of hyperthermia on nanoparticle extravasation from tumor vasculature. Can Res. 2001;61:3027–32.

    CAS  Google Scholar 

  89. Balivada S, Rachakatla RS, Wang H, Samarakoon TN, Dani RK, Pyle M, et al. A/C magnetic hyperthermia of melanoma mediated by iron (0)/iron oxide core/shell magnetic nanoparticles: a mouse study. BMC Cancer. 2010;10:119.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  90. Zhao Q, Wang L, Cheng R, Mao L, Arnold RD, Howerth EW, et al. Magnetic nanoparticle-based hyperthermia for head & neck cancer in mouse models. Theranostics. 2012;2:113.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  91. Verde EL, Landi GT, Gomes JDA, Sousa MH, Bakuzis AF. Magnetic hyperthermia investigation of cobalt ferrite nanoparticles: comparison between experiment, linear response theory, and dynamic hysteresis simulations. J Appl Phys. 2012;111:123902.

    Article  CAS  Google Scholar 

  92. Jordan A, Scholz R, Maier-Hauff K, van Landeghem FK, Waldoefner N, Teichgraeber U, et al. The effect of thermotherapy using magnetic nanoparticles on rat malignant glioma. J Neurooncol. 2006;78:7–14.

    Article  CAS  PubMed  Google Scholar 

  93. Jordan A, Scholz R, Wust P, Fähling H, Krause J, Wlodarczyk W, et al. Effects of magnetic fluid hyperthermia (MFH) on C3H mammary carcinoma in vivo. Int J Hyperth. 1997;13:587–605.

    Article  CAS  Google Scholar 

  94. Shinkai M, Ueda K, Ohtsu S, Honda H, Kohri K, Kobayashi T. Effect of functional magnetic particles on radiofrequency capacitive heating: an in vivo study. Jpn J Cancer Res. 2002;93:103–8.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  95. Yanase M, Shinkai M, Honda H, Wakabayashi T, Yoshida J, Kobayashi T. Intracellular hyperthermia for cancer using magnetite cationic liposomes: an in vivo study. Jpn J Cancer Res. 1998;89:463–70.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  96. Kennedy LC, Bickford LR, Lewinski NA, Coughlin AJ, Hu Y, Day ES, et al. A new era for cancer treatment: gold-nanoparticle-mediated thermal therapies. Small. 2011;7:169–83.

    Article  CAS  PubMed  Google Scholar 

  97. Salloum M, Ma R, Zhu L. An in-vivo experimental study of temperature elevations in animal tissue during magnetic nanoparticle hyperthermia. Int J Hyperth. 2008;24:589–601.

    Article  CAS  Google Scholar 

  98. Kabashin A, Tamarov K, Ryabchikov YV, Osminkina L, Zinovyev S, Kargina J, et al. Si nanoparticles as sensitizers for radio frequency-induced cancer hyperthermia. Synthesis and Photonics of Nanoscale Materials XIII: International Society for Optics and Photonics; 2016. p. 97370A.

  99. Brusentsov NA, Nikitin LV, Brusentsova TN, Kuznetsov AA, Bayburtskiy FS, Shumakov LI, et al. Magnetic fluid hyperthermia of the mouse experimental tumor. J Magn Magn Mater. 2002;252:378–80.

    Article  CAS  Google Scholar 

  100. Elsherbini AA, Saber M, Aggag M, El-Shahawy A, Shokier HA. Magnetic nanoparticle-induced hyperthermia treatment under magnetic resonance imaging. Magn Reson Imaging. 2011;29:272–80.

    Article  PubMed  Google Scholar 

  101. Shinkai M, Yanase M, Suzuki M, Honda H, Wakabayashi T, Yoshida J, et al. Intracellular hyperthermia for cancer using magnetite cationic liposomes. J Magn Magn Mater. 1999;194:176–84.

    Article  CAS  Google Scholar 

  102. Johannsen M, Gneveckow U, Taymoorian K, Thiesen B, Waldöfner N, Scholz R, et al. Morbidity and quality of life during thermotherapy using magnetic nanoparticles in locally recurrent prostate cancer: results of a prospective phase I trial. Int J Hyperth. 2007;23:315–23.

    Article  CAS  Google Scholar 

  103. Maier-Hauff K, Ulrich F, Nestler D, Niehoff H, Wust P, Thiesen B, et al. Efficacy and safety of intratumoral thermotherapy using magnetic iron-oxide nanoparticles combined with external beam radiotherapy on patients with recurrent glioblastoma multiforme. J Neurooncol. 2011;103:317–24.

    Article  PubMed  Google Scholar 

  104. Johannsen M, Thiesen B, Wust P, Jordan A. Magnetic nanoparticle hyperthermia for prostate cancer. Int J Hyperth. 2010;26:790–5.

    Article  Google Scholar 

  105. Mahmoudi K, Hadjipanayis CG. The application of magnetic nanoparticles for the treatment of brain tumors. Frontiers in chemistry. 2014;2:109.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  106. Patterson J, Strang R. The role of blood flow in hyperthermia. Int J Radiat Oncol Biol Phys. 1979;5:235–41.

    Article  CAS  PubMed  Google Scholar 

  107. Miaskowski A, Sawicki B. Magnetic fluid hyperthermia modeling based on phantom measurements and realistic breast model. IEEE Trans Biomed Eng. 2013;60:1806–13.

    Article  PubMed  Google Scholar 

  108. Pennes HH. Analysis of tissue and arterial blood temperatures in the resting human forearm. J Appl Physiol. 1948;1:93–122.

    Article  CAS  PubMed  Google Scholar 

  109. Wulff W. The energy conservation equation for living tissue. IEEE Trans Biomed Eng. 1974;BME-21:494–5.

    Article  Google Scholar 

  110. Chen MM, Holmes KR. Microvascular contributions in tissue heat transfer. Ann N Y Acad Sci. 1980;335:137–50.

    Article  CAS  PubMed  Google Scholar 

  111. Jiji L, Weinbaum S, Lemons D. Theory and experiment for the effect of vascular microstructure on surface tissue heat transfer—part II: model formulation and solution. J Biomech Eng. 1984;106:331–41.

    Article  CAS  PubMed  Google Scholar 

  112. Weinbaum S, Jiji L. A new simplified bioheat equation for the effect of blood flow on local average tissue temperature. ASME J Biomech Eng. 1985;107:131–9.

    Article  CAS  Google Scholar 

  113. Balidemaj E, Kok HP, Schooneveldt G, van Lier AL, Remis RF, Stalpers LJ, et al. Hyperthermia treatment planning for cervical cancer patients based on electrical conductivity tissue properties acquired in vivo with EPT at 3 T MRI. Int J Hyperth. 2016;32:558–68.

    Article  CAS  Google Scholar 

  114. Deuflhard P, Seebass M, Stalling D, Beck R. Hege H-C. Hyperthermia treatment planning in clinical cancer therapy: modelling, simulation and visualization. ZIB-Report, 1997;3:9–17.

    Google Scholar 

  115. Nguyen PT, Abbosh A, Crozier S. Three-dimensional microwave hyperthermia for breast cancer treatment in a realistic environment using particle swarm optimization. IEEE Trans Biomed Eng. 2017;64:1335–44.

    Article  PubMed  Google Scholar 

  116. Arkin H, Xu L, Holmes K. Recent developments in modeling heat transfer in blood perfused tissues. IEEE Trans Biomed Eng. 1994;41:97–107.

    Article  CAS  PubMed  Google Scholar 

  117. Baish J, Ayyaswamy P, Foster K. Heat transport mechanisms in vascular tissues: a model comparison. J Biomech Eng. 1986;108:324–31.

    Article  CAS  PubMed  Google Scholar 

  118. Charny C, Levin R. Bioheat transfer in a branching countercurrent network during hyperthermia. J Biomech Eng. 1989;111:263–70.

    Article  CAS  PubMed  Google Scholar 

  119. Wissler E. Comments on the new bioheat equation proposed by Weinbaum and Jiji. J Biomech Eng. 1987;109:226.

    Article  CAS  PubMed  Google Scholar 

  120. Jamil M, Ng EY-K. To optimize the efficacy of bioheat transfer in capacitive hyperthermia: a physical perspective. J Therm Biol. 2013;38:272–9.

    Article  Google Scholar 

  121. Tzou D. Transfer M-tMH. Washington, DC: Taylor & Francis; 1997. p. 138–46.

    Google Scholar 

  122. Rubio MFJC, Hernández AV, Salas LL. High temperature hyperthermia in breast cancer treatment. Istanbul: Hyperthermia: IntechOpen; 2013.

    Google Scholar 

  123. Majchrzak E, Turchan Ł. Numerical analysis of tissue heating using the bioheat transfer porous model. Comput Assist Methods Eng Sci. 2017;20:123–31.

    Google Scholar 

  124. Gilchrist R, Medal R, Shorey WD, Hanselman RC, Parrott JC, Taylor CB. Selective inductive heating of lymph nodes. Ann Surg. 1957;146:596.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  125. Kobayashi T, Kakimi K, Nakayama E, Jimbow K. Antitumor immunity by magnetic nanoparticle-mediated hyperthermia. Nanomedicine. 2014;9:1715–26.

    Article  CAS  PubMed  Google Scholar 

  126. LeBrun A, Manuchehrabadi N, Attaluri A, Wang F, Ma R, Zhu L. MicroCT image-generated tumour geometry and SAR distribution for tumour temperature elevation simulations in magnetic nanoparticle hyperthermia. Int J Hyperth. 2013;29:730–8.

    Article  Google Scholar 

  127. LeBrun A, Ma R, Zhu L. MicroCT image based simulation to design heating protocols in magnetic nanoparticle hyperthermia for cancer treatment. J Therm Biol. 2016;62:129–37.

    Article  PubMed  Google Scholar 

  128. Eagle S, Wadsworth S, Wnorowski A. Modeling an injection profile of nanoparticles to optimize tumor treatment time with magnetic hyperthermia. BEE 4530-2015 (Student paper) 2015.

  129. Sankar S, Zhang M. Optimization of combined radiation and gold nanoparticle hyperthermia therapy for treating cutaneous squamous carcinoma. BEE 4530-2015 (Student paper) 2015.

  130. Hainfeld JF, Lin L, Slatkin DN, Dilmanian FA, Vadas TM, Smilowitz HM. Gold nanoparticle hyperthermia reduces radiotherapy dose. Nanomed Nanotechnol Biol Med. 2014;10:1609–17.

    Article  CAS  Google Scholar 

  131. Kim B, Han G, Toley BJ, Kim C-K, Rotello VM, Forbes NS. Tuning payload delivery in tumour cylindroids using gold nanoparticles. Nat Nanotechnol. 2010;5:465.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  132. Javidi M, Heydari M, Karimi A, Haghpanahi M, Navidbakhsh M, Razmkon A. Evaluation of the effects of injection velocity and different gel concentrations on nanoparticles in hyperthermia therapy. J Biomed Phys Eng. 2014;4:151.

    CAS  PubMed  PubMed Central  Google Scholar 

  133. Salloum M, Ma R, Zhu L. Enhancement in treatment planning for magnetic nanoparticle hyperthermia: optimization of the heat absorption pattern. Int J Hyperth. 2009;25:309–21.

    Article  CAS  Google Scholar 

  134. Hall M, Yanga D, Yi K, Zhou J. Optimized injection site location for magnetic nanoparticle induced hyperthermia cancer treatment. BEE 4530-2012 (Student paper) 2012.

  135. Perigo EA, Hemery G, Sandre O, Ortega D, Garaio E, Plazaola F, et al. Fundamentals and advances in magnetic hyperthermia. Applied Physics Reviews. 2015;2:041302.

    Article  CAS  Google Scholar 

  136. Liangruksa M, Ganguly R, Puri IK. Parametric investigation of heating due to magnetic fluid hyperthermia in a tumor with blood perfusion. J Magn Magn Mater. 2011;323:708–16.

    Article  CAS  Google Scholar 

  137. Maenosono S, Saita S. Theoretical assessment of FePt nanoparticles as heating elements for magnetic hyperthermia. IEEE Trans Magn. 2006;42:1638–42.

    Article  CAS  Google Scholar 

  138. Liu K-C, Chen H-T. Analysis for the dual-phase-lag bio-heat transfer during magnetic hyperthermia treatment. Int J Heat Mass Transf. 2009;52:1185–92.

    Article  CAS  Google Scholar 

  139. Wu J, Ma X, Wang Y. Hyperthermia cancer therapy by magnetic nanoparticles. BENG 221, 2013 (Student paper) 2013.

  140. Feng Y, Rylander M, Bass J, Oden J, Diller K. Optimal design of laser surgery for cancer treatment through nanoparticle-mediated hyperthermia therapy. NSTI-Nanotech2005. pp. 39–42.

  141. Pearce JA, Petyk AA, Hoopes PJ. FEM numerical model analysis of magnetic nanoparticle tumor heating experiments. In: 2014 36th annual international conference of the IEEE engineering in medicine and biology society: IEEE; 2014. pp. 5312–5.

  142. Bhowmick S, Coad J, Swanlund D, Bischof J. In vitro thermal therapy of AT-1 dunning prostate tumours. Int J Hyperth. 2004;20:73–92.

    Article  CAS  Google Scholar 

  143. Huang H-C, Rege K, Heys JJ. Spatiotemporal temperature distribution and cancer cell death in response to extracellular hyperthermia induced by gold nanorods. ACS Nano. 2010;4:2892–900.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  144. Moritz AR, Henriques F Jr. Studies of thermal injury: II. The relative importance of time and surface temperature in the causation of cutaneous burns. Am J Pathol. 1947;23:695.

    CAS  PubMed  PubMed Central  Google Scholar 

  145. Elliott A, Schwartz J, Wang J, Shetty A, Hazle J, Stafford JR. Analytical solution to heat equation with magnetic resonance experimental verification for nanoshell enhanced thermal therapy. Lasers Surg Med Off J Am Soc Laser Med Surg. 2008;40:660–5.

    Google Scholar 

  146. Huang X, Jain PK, El-Sayed IH, El-Sayed MA. Determination of the minimum temperature required for selective photothermal destruction of cancer cells with the use of immunotargeted gold nanoparticles. Photochem Photobiol. 2006;82:412–7.

    Article  CAS  PubMed  Google Scholar 

  147. Xu R, Zhang Y, Ma M, Xia J, Liu J, Guo Q, et al. Measurement of specific absorption rate and thermal simulation for arterial embolization hyperthermia in the maghemite-gelled model. IEEE Trans Magn. 2007;43:1078–85.

    Article  Google Scholar 

  148. Nabil M, Zunino P. A computational study of cancer hyperthermia based on vascular magnetic nanoconstructs. R Soc Open Sci. 2016;3:160287.

    Article  PubMed  PubMed Central  Google Scholar 

  149. Nabil M, Decuzzi P, Zunino P. Modelling mass and heat transfer in nano-based cancer hyperthermia. R Soc Open Sci. 2015;2:150447.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  150. Pearce J, Giustini A, Stigliano R, Hoopes PJ. Magnetic heating of nanoparticles: the importance of particle clustering to achieve therapeutic temperatures. J Nanotechnol Eng Med. 2013;4:011005.

    Article  CAS  Google Scholar 

  151. Sulman MM, Miller DF, Kozlowski G. Nonlinear model for magnetic nanoparticle-based hyperthermia. Int J Math Modell Numer Optim. 2015;6:223–34.

    Google Scholar 

  152. Wang H, Wu J, Zhuo Z, Tang J. A three-dimensional model and numerical simulation regarding thermoseed mediated magnetic induction therapy conformal hyperthermia. Technol Health Care. 2016;24:S827–39.

    Article  PubMed  Google Scholar 

  153. Andrä W, d’Ambly C, Hergt R, Hilger I, Kaiser W. Temperature distribution as function of time around a small spherical heat source of local magnetic hyperthermia. J Magn Magn Mater. 1999;194:197–203.

    Article  Google Scholar 

  154. Sawyer CA, Habib AH, Miller K, Collier KN, Ondeck CL, McHenry ME. Modeling of temperature profile during magnetic thermotherapy for cancer treatment. J Appl Phys. 2009;105:07B320.

    Article  CAS  Google Scholar 

  155. Bagaria H, Johnson D. Transient solution to the bioheat equation and optimization for magnetic fluid hyperthermia treatment. Int J Hyperth. 2005;21:57–75.

    Article  CAS  Google Scholar 

  156. Durkee J Jr, Antich P, Lee C. Exact solutions to the multiregion time-dependent bioheat equation I: solution development. Phys Med Biol. 1990;35:847.

    Article  PubMed  Google Scholar 

  157. Di Michele F, Pizzichelli G, Mazzolai B, Sinibaldi E. On the preliminary design of hyperthermia treatments based on infusion and heating of magnetic nanofluids. Math Biosci. 2015;262:105–16.

    Article  PubMed  Google Scholar 

  158. Hayat T, Ahmed B, Abbasi F, Ahmad B. Mixed convective peristaltic flow of carbon nanotubes submerged in water using different thermal conductivity models. Comput Methods Programs Biomed. 2016;135:141–50.

    Article  CAS  PubMed  Google Scholar 

  159. Hayat T, Ahmed B, Alsaedi A, Abbasi F. Numerical study for peristalsis of Carreau–Yasuda nanomaterial with convective and zero mass flux condition. Res Phys. 2018;8:1168–77.

    Google Scholar 

  160. Ahmed B, Hayat T, Alsaedi A, Abbasi F. Entropy generation analysis for peristaltic motion of Carreau–Yasuda nanomaterial. Phys Scr. 2020;95:055804.

    Article  CAS  Google Scholar 

  161. Hayat T, Ahmed B, Abbasi F, Alsaedi A. Flow of carbon nanotubes submerged in water through a channel with wavy walls with convective boundary conditions. Colloid Polym Sci. 2017;295:1905–14.

    Article  CAS  Google Scholar 

  162. Hayat T, Ahmed B, Abbasi F, Alsaedi A. Hydromagnetic peristalsis of water based nanofluids with temperature dependent viscosity: a comparative study. J Mol Liq. 2017;234:324–9.

    Article  CAS  Google Scholar 

  163. Hayat T, Ahmed B, Abbasi F, Alsaedi A. Peristalsis of nanofluid through curved channel with Hall and Ohmic heating effects. J Cent S Univers. 2019;26:2543–53.

    Article  CAS  Google Scholar 

  164. Hayat T, Ahmed B, Abbasi F, Alsaedi A. Numerical investigation for peristaltic flow of Carreau–Yasuda magneto-nanofluid with modified Darcy and radiation. J Therm Anal Calorim. 2019;137:1359–67.

    Article  CAS  Google Scholar 

  165. Khan MI, Qayyum S, Hayat T, Khan MI, Alsaedi A, Khan TA. Entropy generation in radiative motion of tangent hyperbolic nanofluid in presence of activation energy and nonlinear mixed convection. Phys Lett A. 2018;382:2017–26.

    Article  CAS  Google Scholar 

  166. Kaddi CD, Phan JH, Wang MD. Computational nanomedicine: modeling of nanoparticle-mediated hyperthermal cancer therapy. Nanomedicine. 2013;8:1323–33.

    Article  CAS  PubMed  Google Scholar 

  167. Loulou T, Scott EP. Thermal dose optimization in hyperthermia treatments by using the conjugate gradient method. Numer Heat Transf Part A Appl. 2002;42:661–83.

    Article  Google Scholar 

  168. Pearce JA, Cook JR, Hoopes PJ, Giustini A. FEM numerical model study of heating in magnetic nanoparticles. Energy-based Treatment of Tissue and Assessment VI: International Society for Optics and Photonics; 2011. pp. 79010B

  169. Pavel M, Stancu A. Ferromagnetic nanoparticles dose based on tumor size in magnetic fluid hyperthermia cancer therapy. IEEE Trans Magn. 2009;45:5251–4.

    Article  CAS  Google Scholar 

  170. Jeyadevan B. Present status and prospects of magnetite nanoparticles-based hyperthermia. J Ceram Soc Jpn. 2010;118:391–401.

    Article  CAS  Google Scholar 

  171. Yue K, Yu C, Lei Q, Luo Y, Zhang X. Numerical simulation of effect of vessel bifurcation on heat transfer in the magnetic fluid hyperthermia. Appl Therm Eng. 2014;69:11–8.

    Article  Google Scholar 

  172. Sawicki B, Miaskowski A. Nonlinear higher-order transient solver for magnetic fluid hyperthermia. J Comput Appl Math. 2014;270:143–51.

    Article  Google Scholar 

  173. Chen Z, Miller W, Roemer R, Cetas T. Errors between two-and three-dimensional thermal model predictions of hyperthermia treatments. Int J Hyperth. 1990;6:175–91.

    Article  Google Scholar 

  174. Craciun V, Calugaru G, Badescu V. Accelerated simulation of heat transfer in magnetic fluid hyperthermia. Czech J Phys. 2002;52:725–8.

    Article  Google Scholar 

  175. Zhang C, Johnson DT, Brazel CS. Numerical study on the multi-region bio-heat equation to model magnetic fluid hyperthermia (MFH) using low Curie temperature nanoparticles. IEEE Trans Nanobiosci. 2008;7:267–75.

    Article  Google Scholar 

  176. Paruch M. Hyperthermia process control induced by the electric field in order to cancer destroying. Acta Bioeng Biomech. 2014;16:123–30.

    PubMed  Google Scholar 

  177. Sawicki B, Miaskowski A. Numerical model of magnetic fluid hyperthermia. Przeglad Elektrotechniczny. 2013;89:86–8.

    Google Scholar 

  178. Majchrzak E, Paruch M. Numerical modelling of the cancer destruction during hyperthermia treatment. In: 19th international conference on computer methods in mechanics CMM-2011, Warsaw, Poland, Short Papers2001. pp. 333–4.

  179. Gooneratne CP, Kurnicki A, Yamada S, Mukhopadhyay SC, Kosel J. Analysis of the distribution of magnetic fluid inside tumors by a giant magnetoresistance probe. PLoS ONE. 2013;8:e81227.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  180. Reis RF, dos Santos Loureiro F, Lobosco M. 3D numerical simulations on GPUs of hyperthermia with nanoparticles by a nonlinear bioheat model. J Comput Appl Math. 2016;295:35–47.

    Article  Google Scholar 

  181. Rodrigues DB, Hurwitz MD, Maccarini PF, Stauffer PR. Optimization of chest wall hyperthermia treatment using a virtual human chest model. In: 2015 9th European conference on antennas and propagation (EuCAP): IEEE; 2015. pp. 1–5.

  182. Mital M, Tafreshi HV. A methodology for determining optimal thermal damage in magnetic nanoparticle hyperthermia cancer treatment. Int J Numer Methods Biomed Eng. 2012;28:205–13.

    Article  Google Scholar 

  183. Faktorová D, Pápežová M. Optimization of mild microwave hyperthermia interconnection with targeted delivery of nanoparticles. Przegląd Elektrotechniczny. 2014;90:117–9.

    Google Scholar 

  184. Tsuda N, Kuroda K, Suzuki Y. An inverse method to optimize heating conditions in RF-capacitive hyperthermia. IEEE Trans Biomed Eng. 1996;43:1029–37.

    Article  CAS  PubMed  Google Scholar 

  185. Di Barba P, Dughiero F, Sieni E. Field synthesis for the optimal treatment planning in magnetic fluid hyperthermia. Arch Electr Eng. 2012;61:57–67.

    Article  Google Scholar 

  186. Wolf M, Rath K, Ruiz AER, Kühnicke E. Ultrasound thermometry for optimizing heat supply during a hyperthermia therapy of cancer tissue. Phys Proc. 2015;70:888–91.

    Article  Google Scholar 

  187. Hu G, Li Y, Yang S, Bai Y, Huang J. Temperature field optimization and magnetic nanoparticles optimal approximation of MFH for cancer therapy. IEEE Trans Magn. 2015;51:1–4.

    Google Scholar 

  188. Lalonde RJ, Hunt JW. Optimizing ultrasound focus distributions for hyperthermia. IEEE Trans Biomed Eng. 1995;42:981–90.

    Article  CAS  PubMed  Google Scholar 

  189. Hassan S, Yoon J. Nano carriers based targeted drug delivery path planning using hybrid particle swarm optimizer and artificial magnetic fields. In: 2012 12th international conference on control, automation and systems: IEEE; 2012. pp. 1700–5.

  190. Nguyen PT. Focusing microwave hyperthermia in realistic environment for breast cancer treatment: Ph.D. Thesis, University of Queensland; 2015.

  191. Jagt TZ. Improving the tumor coverage by dynamic steering in Hyperthermia. Part of collection (Student paper) 2011.

  192. Siauve N, Nicolas L, Vollaire C, Nicolas A, Vasconcelos JA. Optimization of 3-D SAR distribution in local RF hyperthermia. IEEE Trans Magn. 2004;40:1264–7.

    Article  Google Scholar 

  193. Aldhaeebi M, Alzabidi M, Elshafiey I. Genetic algorithm optimization of SAR distribution in hyperthermia treatment of human head. In: 2013 1st international conference on artificial intelligence, modelling and simulation: IEEE; 2013. pp. 92–7.

  194. Nizam-Uddin N, Elshafiey I. Enhanced energy localization in hyperthermia treatment based on hybrid electromagnetic and ultrasonic system: proof of concept with numerical simulations. BioMed Res Int 2017;2017.

  195. Chakraborty A, Neogi K, Banerjee A, Sadhu PK. Switching frequency optimization in Hyperthermia treatment using BSD 2000. In: 2015 international conference on energy, power and environment: towards sustainable growth (ICEPE): IEEE; 2015. pp. 1–8.

  196. Rylander MN, Feng Y, Bass J, Diller KR. Heat shock protein expression and injury optimization for laser therapy design. Lasers Surg Med Off J Am Soc Laser Med Surg. 2007;39:731–46.

    Google Scholar 

  197. Gayzik FS, Scott EP, Loulou T. Experimental validation of an inverse heat transfer algorithm for optimizing hyperthermia treatments. J Biomech Eng. 2006;128:505–15.

    Article  PubMed  Google Scholar 

  198. Fenn AJ, King GA. Adaptive radiofrequency hyperthermia-phased array system for improved cancer therapy: phantom target measurements. Int J Hyperth. 1994;10:189–208.

    Article  CAS  Google Scholar 

  199. Schenk O, Manguoglu M, Sameh A, Christen M, Sathe M. Parallel scalable PDE-constrained optimization: antenna identification in hyperthermia cancer treatment planning. Comput Sci Res Dev. 2009;23:177–83.

    Article  Google Scholar 

  200. Liontas CA, Knott P. An Alternating Projections Algorithm for optimizing electromagnetic fields in regional hyperthermia. In: 2016 10th European conference on antennas and propagation (EuCAP): IEEE; 2016. pp. 1–5.

  201. Canters RR. Optimization and control in deep hyperthermia: clinical implementation of hyperthermia treatment planning in cervical cancer treatment to obtain a higher treatment quality. 2013.

  202. Dewhirst M. Thermal dosimetry: thermo-radiotherapy and thermochemotherapy. Berlin: Springer; 1995.

    Book  Google Scholar 

  203. Klemmer T, Hoydick D, Okumura H, Zhang B, Soffa W. Magnetic hardening and coercivity mechanisms in L10 ordered FePd ferromagnets. Scr Metall Mater. 1995;33:1793–805.

    Article  CAS  Google Scholar 

  204. Pankhurst Q, Thanh N, Jones S, Dobson J. Progress in applications of magnetic nanoparticles in biomedicine. J Phys D Appl Phys. 2009;42:224001.

    Article  CAS  Google Scholar 

  205. Inomata K, Sawa T, Hashimoto S. Effect of large boron additions to magnetically hard Fe-Pt alloys. J Appl Phys. 1988;64:2537–40.

    Article  CAS  Google Scholar 

  206. Fortin J-P, Wilhelm C, Servais J, Ménager C, Bacri J-C, Gazeau F. Size-sorted anionic iron oxide nanomagnets as colloidal mediators for magnetic hyperthermia. J Am Chem Soc. 2007;129:2628–35.

    Article  CAS  PubMed  Google Scholar 

  207. Vassiliou JK, Mehrotra V, Russell MW, Giannelis EP, McMichael R, Shull R, et al. Magnetic and optical properties of γ-Fe2O3 nanocrystals. J Appl Phys. 1993;73:5109–16.

    Article  CAS  Google Scholar 

  208. Sato T, Iijima T, Seki M, Inagaki N. Magnetic properties of ultrafine ferrite particles. J Magn Magn Mater. 1987;65:252–6.

    Article  CAS  Google Scholar 

  209. Ito A, Tanaka K, Kondo K, Shinkai M, Honda H, Matsumoto K, et al. Tumor regression by combined immunotherapy and hyperthermia using magnetic nanoparticles in an experimental subcutaneous murine melanoma. Cancer Sci. 2003;94:308–13.

    Article  CAS  PubMed  Google Scholar 

  210. Terentyuk GS, Maslyakova GN, Suleymanova LV, Khlebtsov NG, Khlebtsov BN, Akchurin GG, et al. Laser-induced tissue hyperthermia mediated by gold nanoparticles: toward cancer phototherapy. J Biomed Opt. 2009;14:021016.

    Article  PubMed  CAS  Google Scholar 

  211. Guibert C, Dupuis V, Peyre V, Fresnais J. Hyperthermia of magnetic nanoparticles: experimental study of the role of aggregation. J Phys Chem C. 2015;119:28148–54.

    Article  CAS  Google Scholar 

  212. Jiang P-S, Tsai H-Y, Drake P, Wang F-N, Chiang C-S. Gadolinium-doped iron oxide nanoparticles induced magnetic field hyperthermia combined with radiotherapy increases tumour response by vascular disruption and improved oxygenation. Int J Hyperth. 2017;33:770–8.

    CAS  Google Scholar 

  213. Petryk AA, Giustini AJ, Gottesman RE, Trembly BS, Hoopes PJ. Comparison of magnetic nanoparticle and microwave hyperthermia cancer treatment methodology and treatment effect in a rodent breast cancer model. Int J Hyperth. 2013;29:819–27.

    Article  CAS  Google Scholar 

  214. Sturesson C, Andersson-Engels S. A mathematical model for predicting the temperature distribution in laser-induced hyperthermia Experimental evaluation and applications. Phys Med Biol. 1995;40:2037.

    Article  CAS  PubMed  Google Scholar 

  215. Cheng L, Yang K, Chen Q, Liu Z. Organic stealth nanoparticles for highly effective in vivo near-infrared photothermal therapy of cancer. ACS Nano. 2012;6:5605–13.

    Article  CAS  PubMed  Google Scholar 

  216. Xu X, Meade A, Bayazitoglu Y. Numerical investigation of nanoparticle-assisted laser-induced interstitial thermotherapy toward tumor and cancer treatments. Lasers Med Sci. 2011;26:213–22.

    Article  PubMed  Google Scholar 

  217. Quinto CA, Mohindra P, Tong S, Bao G. Multifunctional superparamagnetic iron oxide nanoparticles for combined chemotherapy and hyperthermia cancer treatment. Nanoscale. 2015;7:12728–36.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  218. Kossatz S, Ludwig R, Dähring H, Ettelt V, Rimkus G, Marciello M, et al. High therapeutic efficiency of magnetic hyperthermia in xenograft models achieved with moderate temperature dosages in the tumor area. Pharm Res. 2014;31:3274–88.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  219. Bauer LM, Situ SF, Griswold MA, Samia ACS. Magnetic particle imaging tracers: state-of-the-art and future directions. J Phys Chem Lett. 2015;6:2509–17.

    Article  CAS  PubMed  Google Scholar 

  220. Krishnan KM. Biomedical nanomagnetics: a spin through possibilities in imaging, diagnostics, and therapy. IEEE Trans Magn. 2010;46:2523–58.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  221. Ito A, Shinkai M, Honda H, Kobayashi T. Medical application of functionalized magnetic nanoparticles. J Biosci Bioeng. 2005;100:1–11.

    Article  CAS  PubMed  Google Scholar 

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  1. Department of Mathematics, University of Engineering and Technology, Lahore, 54890, Pakistan

    Muhammad Suleman & Samia Riaz

  2. Department of Computer Sciences and Information Technology, Superior University, 17-KM Raiwind Road, Lahore, 54000, Pakistan

    Muhammad Suleman

  3. Department of Physics, University of Engineering and Technology, Lahore, 54890, Pakistan

    Rashid Jalil

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Suleman, M., Riaz, S. & Jalil, R. A mathematical modeling approach toward magnetic fluid hyperthermia of cancer and unfolding heating mechanism. J Therm Anal Calorim 146, 1193–1219 (2021). https://doi.org/10.1007/s10973-020-10080-8

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