Prediction of Treatment Response for Combined Chemo- and Radiation Therapy for Non-Small Cell Lung Cancer Patients Using a Bio-Mathematical Model

Abstract

The goal of this work was to develop a mathematical model to predict Kaplan–Meier survival curves for chemotherapy combined with radiation in Non-Small Cell Lung Cancer patients for use in clinical trial design. The Gompertz model was used to describe tumor growth, radiation effect was simulated by the linear-quadratic model with an α/β-ratio of 10, and chemotherapy effect was based on the log-cell kill model. To account for repopulation during treatment, we considered two independent methods: 1) kickoff-repopulation using exponential growth with a decreased volume doubling time, or 2) Gompertz-repopulation using the gradually accelerating growth rate with tumor shrinkage. The input parameters were independently estimated by fitting to the SEER database for untreated tumors, RTOG-8808 for radiation only, and RTOG-9410 for sequential chemo-radiation. Applying the model, the benefit from concurrent chemo-radiation comparing to sequential for stage III patients was predicted to be a 6.6% and 6.2% improvement in overall survival for 3 and 5-years respectively, comparing well to the 5.3% and 4.5% observed in RTOG-9410. In summary, a mathematical model was developed to model tumor growth over extended periods of time, and can be used for the optimization of combined chemo-radiation scheduling and sequencing.

Proliferation Saturation Index in an adaptive Bayesian approach to predict patient-specific radiotherapy responses

“…Whilst the field is still in its infancy, most work is focused on analyzing retrospective data to build mathematical models and evaluate their predictive potential for patient-specific treatment responses (Rockne et al 2010;Yankeelov et al 2015;Geng et al 2017). The art of the trade is to balance and synergize available data, model complexity and model usefulness.…”

Modeling Resistance and Recurrence Patterns of Combined Targeted-Chemoradiotherapy Predicts Benefit of Shorter Induction Period

“…simulated patient) of the tumor progression model, yielding a histogram of times to events, which in turn was used to create simulated Kaplan-Meier (K-M) curves for the distributed population (see Methods). The model parameter distributions were then optimized such that the model predicted K-M curves matched clinically reported K-M curves, as was done in Geng et al (21). In this work, the growth and radiosensitivity distributions were fitted to literature K-M curves of freedom from local and distant failure (FFLF and FFDF) in wildtype (WT) and EGFR+ locally advanced NSCLC populations receiving definitive concurrent CRT (22,26,27).…”

“…While older reports suggested could be higher than 10 for lung cancer (57), our results were insensitive to the exact value of as different fractionation schema were not considered. The initial local cell number was based on tumor volume distributions for each stage of NSCLC and an assumed cell density of 5.8x10 8 cells/cm 3 estimated from previous model based work of NSCLC tumor growth (21,58,59). The initial distant cell number was assumed to be a scalar fraction of the initial local cell number (Eq.…”

“…12) and TKI plasma concentrations ( ./0 , Eq. 14) used in our model were fully described in previous publications (11,21). The state equations were implemented with 0.1 day resolution (∆ ) with the differential effect of each term calculated independently.…”

“…The log-normal model parameter distributions published by Geng et al (21) were used, with the growth and radiosensitivity distributions recalibrated to three single institutional reports of freedom from local and distant failure (FFLF and FFDF) rates in wildtype (WT) and EGFR mutant locally advanced (LA) NSCLC populations receiving definitive concurrent CRT (22,26,27). In this analysis, WT specifically refers to a randomly sample from the general population not screened for EGFR status, with reported incidences of EGFR mutations of 24/118 (20%, US) (27), 26/95 (27%, Japan) (22), 29/184 (16%, South Korea) (26) and a mean of 79/397 (20%).…”