Modelling and Bayesian adaptive prediction of individual patients’ tumour volume change during radiotherapy

Abstract

The aim of this study was to develop a mathematical modelling method that can predict individual patients' response to radiotherapy, in terms of tumour volume change during the treatment. The main idea was to start from a population-average model, which is subsequently updated from an individual's tumour volume measurement; therefore the model becomes more and more personalised and so is the prediction. This idea of adaptive prediction was realised by using a Bayesian approach for updating the model parameters. The feasibility of the developed method was demonstrated on the data from 25 nonsmall cell lung cancer patients treated with helical Tomotherapy, during which tumour volume was measured from daily imaging as part of the image-guided radiotherapy. The method could provide useful information for adaptive treatment planning and dose scheduling based on the patient's personalised response.

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

“…1B). As in the Tariq study (Tariq et al 2016) the best fit to individual patient's data was achieved for patient 9 (R 2 =0.98, Fig. 1C).…”

“…However, despite its simplicity or maybe because of its simplicity, the PSI model may be able to derive patient-specific cancer and cancer response properties that could be predictive and prognostic. We set out to re-evaluate the radiation response of twenty-five NSCLC patients with the simple PSI model (Prokopiou et al 2015) and compare its adaptive Bayesian prediction power to the more complex model introduced by Tariq (Tariq et al 2016). In our simple logistic growth and radiation response model, the model parameters tumor growth rate, carrying capacity, and radiation sensitivity are not independent.…”

“…Twenty-five non-small cell lung cancer patients were treated for NSCLC with standard of care radiation treatment over an 8-week period on the Hi-Art Helical Tomotherapy unit at the London Regional Cancer Program, Ontario, Canada, from 2005 to 2007 (Tariq et al 2016). Volumetric tumor measurements were collected at each treatment fraction.…”

“…The chosen model was a two-variable, coupled differential equation model simulating total tumor volume as the sum of living and dead cancer cells (V=Vl+Vd). To best fit the model to the data, parameters were derived that would kill all living cancer cells after 4-6 Gy in 2-3 days (of the conventional 45 days schedule), and the modeled exponential decay of the dead cell compartment mimicked the overall tumor volume regression (Tariq et al 2016). Whilst mathematically elegant with excellent fits to the clinical data, the model implications are clinically unrealistic and yield to predictions that cannot be trusted.…”

Mathematical Modeling in Radiation Oncology

“…The most common approach is to fit a model to patient data by adjusting parameters in a fixed model. This can be done through a variety of methods, with Bayesian inference Tariq et al 2016) and model-data fitting procedures (Rockne et al 2010;Hathout et al 2015a;Colombo et al 2015) being two of the most prevalent methods in recent years. For model-fitting algorithms, the most common forms of input are tumor volume and shape characteristics obtained from magnetic resonance imaging (MRI) (Rockne et al 2010;Neal et al 2013;Hathout et al 2015b), positron emission tomography (PET) Mz et al 2013), or computed tomography (CT) (Prokopiou et al 2015;Belfatto et al 2015).…”