Investigating the effect of cell repopulation on the tumor response to fractionated external radiotherapy

Abstract

In this work we study the descriptive power of the main tumor control probability (TCP) models based on the linear quadratic (LQ) mechanism of cell damage with cell recovery. The Poisson, binomial, and a dynamic TCP model, developed recently by Zaider and Minerbo are considered. The Zaider-Minerbo model takes cell repopulation into account. It is shown that the Poisson approximation incorporating cell repopulation is conceptually incorrect. Based on the Zaider-Minerbo model, an expression for the TCP for fractionated treatments with varying intervals between two consecutive fractions and with cell survival probability that changes from fraction to fraction is derived. The models are fitted to an experimental data set consisting of dose response curves that correspond to different fractionation regimes. The binomial TCP model based on the LQ mechanism of cell damage solely was unable to fit the fractionated response data. It was found that the Zaider-Minerbo model, which takes tumor cell repopulation into account, best fits the data.

Relating the proton relative biological effectiveness to tumor control and normal tissue complication probabilities assuming interpatient variability in α/β

“…We followed the formalism outlined by Warkentin et al [21], originally published by Zaider and Minerbo [22] and subsequently extended for fractionated delivery by Stavreva et al [23]. The model includes linear-quadratic (LQ) cell kill and repopulation and is based on the following input parameters: …”

A TCP‐NTCP estimation module using DVHs and known radiobiological models and parameter sets

“…Since the number of FSUs is always quite large, the cumulative binomial distribution in Eq. (4) can be approximated by a cumulative normal distribution (14) : $\text{NTCP}=\mathrm{\Phi }\left(\frac{\sqrt{N}(p_{\text{FSU}}(D)-{\mathrm{normal\mu }}_{\text{cr}})}{\sqrt{p_{\text{FSU}}(D)\hspace{0.17em}(1-p_{\text{FSU}}(D))}}\right),$ where the Φ (probit) function is as defined in Eq. (2).…”

Mathematical Ecology of Cancer

“…In a recent PhD thesis, Gong [21] included cancer stem cells into the TCP models and she confirmed that it is critical to control the stem cells for treatment to be successful. First studies have shown that the above TCP models are powerful tools in the prediction and planning of radiation treatments ( [22,61]), however, further studies of their qualitative properties and further data analysis is needed.…”

“…The mathematical framework comes directly from ecological applications, but the interpretations, and some of the details are specific to cancer modelling. This direction of research has blossomed in beautiful theories on brith-death processes and branching processes, which are able to include cell cycle dynamics and differential radiosensitivities depending on the cell cycle state (see [22,25,26,31,43,61,66]). In a recent PhD thesis, Gong [21] included cancer stem cells into the TCP models and she confirmed that it is critical to control the stem cells for treatment to be successful.…”