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

Abstract

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
• response prediction
• mathematical model
• proliferation saturation index
• non-small cell lung cancer

Disclosure statement

The authors declare no conflicts of interest.

Additional information

Funding

This project was supported in part by a pilot award from the NIH/NCI U54CA143970-05 (Physical Science Oncology Network (PSON)) “Cancer as a complex adaptive system”. DT and NJ were supported by the High school Internship Program in Integrated Mathematical Oncology (HIP IMO) at Moffitt Cancer Center.

Notes on contributors

Enakshi D. Sunassee

Enakshi D. Sunassee, is a senior undergraduate student in Chemical Engineering, and a research intern in Dr. Enderling's research group at Moffitt Cancer Center, Tampa, FL, USA.

Dean Tan

Dean Tan, was a HIP IMO high school intern in the Integrated Mathematical Oncology department at Moffitt Cancer Center when he contributed to this study, and is currently a freshman at Northwestern University, Chicago, IL, USA.

Nathan Ji

Nathan Ji, was a HIP IMO high school intern in the Integrated Mathematical Oncology department at Moffitt Cancer Center when he contributed to this study, and is currently a freshman at Johns Hopkins University, Baltimore, MD, USA.

Renee Brady

Renee Brady, Ph.D. in applied mathematics, works as a mathematical oncologist in the Integrated Mathematical Oncology department at Moffitt Cancer Center, Tampa, FL, USA

Eduardo G. Moros

Eduardo G. Moros, Ph.D. in mechanical engineering, is chief of medical physics in the department of Radiation Oncology at Moffitt Cancer Center, Tampa, FL, USA.

Jimmy J. Caudell

Jimmy J. Caudell, M.D., Ph.D. in molecular biology, is director of research as well as the section chief of head and neck in the department of Radiation Oncology at Moffitt Cancer Center, Tampa, FL, USA.

Slav Yartsev

Slav Yartsev, Ph.D., D.Sc., works as a medical physicist in the London Regional Cancer Program at the University of Western Ontario, London, ON, CA.

Heiko Enderling

Heiko Enderling, Ph.D. in mathematical biology, directs a research group on Quantitative Personalized Oncology at the Integrated Mathematical Oncology department, and is Director for Education and Outreach at the Physical Sciences in Oncology Center at Moffitt Cancer Center, Tampa, FL, USA.