Biophysical Reviews

, Volume 11, Issue 2, pp 183–189 | Cite as

Mathematical models applied to thyroid cancer

  • Jairo Gomes da SilvaEmail author
  • Rafael Martins de Morais
  • Izabel Cristina Rodrigues da Silva
  • Paulo Fernando de Arruda Mancera


Thyroid cancer is the most prevalent endocrine neoplasia in the world. The use of mathematical models on the development of tumors has yielded numerous results in this field and modeling with differential equations is present in many papers on cancer. In order to know the use of mathematical models with differential equations or similar in the study of thyroid cancer, studies since 2006 to date was reviewed. Systems with ordinary or partial differential equations were the means most frequently adopted by the authors. The models deal with tumor growth, effective half-life of radioiodine applied after thyroidectomy, the treatment with iodine-131, thyroid volume before thyroidectomy, and others. The variables usually employed in the models includes tumor volume, thyroid volume, amount of iodine, thyroglobulin and thyroxine hormone, radioiodine activity, and physical characteristics such as pressure, density, and displacement of the thyroid molecules. In conclusion, the mathematical models used so far with differential equations approach several aspects of thyroid cancer, including participation in methods of execution or follow-up of treatments. With the development of new models, an increase in the current understanding of the detection, evolution, and treatment of diseases is a step that should be considered.


Thyroid cancer Differential equations Mathematical modeling Systematic review 


Compliance with Ethical Standards

Conflict of interests

Jairo Gomes da Silva declares that he has no conflict of interest. Rafael Martins de Morais declares that he has no conflict of interest. Izabel Cristina Rodrigues da Silva declares that she has no conflict of interest. Paulo Fernando de Arruda Mancera declares that he has no conflict of interest.


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Copyright information

© International Union for Pure and Applied Biophysics (IUPAB) and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Instituto de BiociênciasPrograma de Pós-Graduação em Biometria, Universidade Estadual Paulista (UNESP)BotucatuBrazil
  2. 2.Faculdade de Ceilândia, Campus UniversitárioPrograma de Pós-Graduação em Ciências Médicas, Universidade de Brasília (UnB)Ceilândia SulBrazil
  3. 3.Faculdade de Ceilândia, Campus UniversitárioUniversidade de Brasília (UnB)Ceilândia SulBrazil
  4. 4.Instituto de BiociênciasUniversidade Estadual Paulista (UNESP)BotucatuBrazil

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