Bulletin of Mathematical Biology

, Volume 80, Issue 5, pp 1195–1206 | Cite as

Predicting Patient-Specific Radiotherapy Protocols Based on Mathematical Model Choice for Proliferation Saturation Index

  • Jan Poleszczuk
  • Rachel Walker
  • Eduardo G. Moros
  • Kujtim Latifi
  • Jimmy J. Caudell
  • Heiko Enderling
Special Issue : Mathematical Oncology


Radiation is commonly used in cancer treatment. Over 50% of all cancer patients will undergo radiotherapy (RT) as part of cancer care. Scientific advances in RT have primarily focused on the physical characteristics of treatment including beam quality and delivery. Only recently have inroads been made into utilizing tumor biology and radiobiology to design more appropriate RT protocols. Tumors are composites of proliferating and growth-arrested cells, and overall response depends on their respective proportions at irradiation. Prokopiou et al. (Radiat Oncol 10:159, 2015) developed the concept of the proliferation saturation index (PSI) to augment the clinical decision process associated with RT. This framework is based on the application of the logistic equation to pre-treatment imaging data in order to estimate a patient-specific tumor carrying capacity, which is then used to recommend a specific RT protocol. It is unclear, however, how dependent clinical recommendations are on the underlying tumor growth law. We discuss a PSI framework with a generalized logistic equation that can capture kinetics of different well-known growth laws including logistic and Gompertzian growth. Estimation of model parameters on the basis of clinical data revealed that the generalized logistic model can describe data equally well for a wide range of the generalized logistic exponent value. Clinical recommendations based on the calculated PSI, however, are strongly dependent on the specific growth law assumed. Our analysis suggests that the PSI framework may best be utilized in clinical practice when the underlying tumor growth law is known, or when sufficiently many tumor growth models suggest similar fractionation protocols.


Proliferation saturation index Radiation protocol Generalized logistic equation 



This work is supported in part by the Personalized Medicine Award 09-33000-15-03 from the DeBartolo Family Personalized Medicine Institute Pilot Research Awards in Personalized Medicine (PRAPM).


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Copyright information

© Society for Mathematical Biology 2017

Authors and Affiliations

  1. 1.Department of Integrated Mathematical OncologyH. Lee Moffitt Cancer Center and Research InstituteTampaUSA
  2. 2.Department of Radiation OncologyH. Lee Moffitt Cancer Center and Research InstituteTampaUSA
  3. 3.Nalecz Institute of Biocybernetics and Biomedical EngineeringPolish Academy of SciencesWarsawPoland

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