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 nonidentifiability 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 for predicting response 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 (R 2 =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 offer 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. 3

WAM to SeeSaw model for cancer therapy – overcoming LQM difficulties –

“…In Figure 1 of the PSI model (Sunassee et al 2019), two cases are shown with detailed measurements of the volume of cancers using largely different k p and c D : For these patients, the agreements are very good. In Figure 2 of this paper (Sunassee et al 2019), they show comparisons of the PSI model with the common values of k p and c D by changing slightly the PSI values. The agreements are good.…”

“…Especially in the field of radiotherapy, it is remarkable to see various models trying to accommodate the biological radiation effect using the LQ model, which is expressed in terms of the total dose D to the t dependent dynamics due to the proliferation of tumor. These models are the ZM model and related works (Zaider and Minerbo 2000), the clinical model using the proliferation saturation index (PSI) (Rockne et al 2010;Prokopiou et al 2015;Tariq et al 2016;Sunassee et al 2019), and the clinical model using the biological effective dose (BED) (Fowler 1989(Fowler , 2010, together with many related works (Tobias 1985;Sottoriva et al 2010;Borasi 2016;Borasi & Nahum 2016).…”

“…The most serious point is how to connect the LQ model with the differential equation to account for the growth effects. They have to assume the instantaneous approximation using the LQ model (Harpold et al 2007;Prokopiou et al 2015;Sunassee et al 2019), or to derive the differentiated LQM form, of which the reaction rate is divided into the time-dependent and time independent parts. Although the latter term can be identified as the growth factor together with an additional constant, which corresponds to k in the SS model, the time dependent term is inevitably left unknown, and had to be replaced with another information of so-called TCP (Millar and Canney 1993;Zaider and Minerbo 2000;Keinj et al 2011;Watanabe et al 2016;Ponce Bobadilla et al 2018;Nuraini and Widita 2019).…”

“…We here pick up non-small cell lung cancer (NSCLC) (in Figure 2 of their paper), which has been analyzed by the PSI model (Prokopiou et al 2015). Further comparisons are made in their recent publications (Sunassee et al 2019). In Figure 1 of the PSI model (Sunassee et al 2019), two cases are shown with detailed measurements of the volume of cancers using largely different k p and c D : For these patients, the agreements are very good.…”

Are all models wrong?

“…For clinical purpose, predictive models may not need to accurately describe the complex biology of cancer, but to provide a trigger for decision making, often upon binary endpoints. For many years, we have set ourselves the lofty goal of predicting the tumor burden evolution during treatment with ever decreasing error to the actual data [14–16]; yet the clinical endpoint for patients is often not the actual tumor volume dynamics but binary endpoints such as continuous response or cancer progression, tumor control or treatment failure. Machine learning approaches (or simple statistics) can identify threshold values for tumor burden at different time points during therapy that stratify patients into the different outcomes [17–19].…”