Proliferation saturation index in an adaptive Bayesian approach to predict patient-specific radiotherapy responses

Int J Radiat Biol. 2019 Oct;95(10):1421-1426. doi: 10.1080/09553002.2019.1589013. Epub 2019 Mar 19.


Purpose: Radiotherapy prescription dose and dose fractionation protocols vary little between individual patients having the same tumor grade and stage. To personalize radiotherapy a predictive model is needed to simulate radiation response. Previous modeling attempts with multiple variables and parameters have been shown to yield excellent data fits at the cost of non-identifiability and clinically unrealistic results. Materials and methods: We develop a mathematical model based on a proliferation saturation index (PSI) that is a measurement of pre-treatment tumor volume-to-carrying capacity ratio that modulates intrinsic tumor growth and radiation response rates. In an adaptive Bayesian approach, we utilize an increasing number of data points for individual patients to predict patient-specific responses to subsequent radiation doses. Results: Model analysis shows that using PSI as the only patient-specific parameter, model simulations can fit longitudinal clinical data with high accuracy (R2=0.84). By analyzing tumor response to radiation using daily CT scans early in the treatment, response to the remaining treatment fractions can be predicted after two weeks with high accuracy (c-index = 0.89). Conclusion: The PSI model may be suited to forecast treatment response for individual patients and offers actionable decision points for mid-treatment protocol adaptation. The presented work provides an actionable image-derived biomarker prior to and during therapy to personalize and adapt radiotherapy.

Keywords: Radiotherapy; mathematical model; non-small cell lung cancer; proliferation saturation index; response prediction.

Publication types

  • Research Support, N.I.H., Extramural
  • Research Support, Non-U.S. Gov't

MeSH terms

  • Algorithms
  • Bayes Theorem
  • Biomarkers
  • Carcinoma, Non-Small-Cell Lung / radiotherapy*
  • Cell Proliferation
  • Dose Fractionation, Radiation
  • Humans
  • Lung Neoplasms / radiotherapy*
  • Models, Theoretical
  • Radiation Dosage
  • Radiotherapy / methods*
  • Radiotherapy Dosage
  • Radiotherapy Planning, Computer-Assisted / methods*
  • Reproducibility of Results
  • Tomography, X-Ray Computed
  • Tumor Burden


  • Biomarkers