Modeling tumor growth using fractal calculus: Insights into tumor dynamics

Golmankhaneh A. K., TUNÇ S., Schlichtinger A. M., Asanza D. M., Golmankhaneh A. K.

BioSystems, vol.235, 2024 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 235
  • Publication Date: 2024
  • Doi Number: 10.1016/j.biosystems.2023.105071
  • Journal Name: BioSystems
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aquatic Science & Fisheries Abstracts (ASFA), BIOSIS, CAB Abstracts, EMBASE, Geobase, INSPEC, Veterinary Science Database
  • Keywords: Fractal analysis, Fractal calculus, Fractal cancer growth models, Fractal Gompertz growth model, Fractal Richards growth model, Fractal temporal
  • Istanbul Medipol University Affiliated: Yes


Important concepts like fractal calculus and fractal analysis, the sum of squared residuals, and Aikaike's information criterion must be thoroughly understood in order to correctly fit cancer-related data using the proposed models. The fractal growth models employed in this work are classified in three main categories: Sigmoidal growth models (Logistic, Gompertz, and Richards models), Power Law growth model, and Exponential growth models (Exponential and Exponential-Lineal models)”. We fitted the data, computed the sum of squared residuals, and determined Aikaike's information criteria using Matlab and the web tool WebPlotDigitizer. In addition, the research investigates “double-size cancer” in the fractal temporal dimension with respect to various mathematical models.