Renormalization of radiobiological response functions by energy loss fluctuations and complexities in chromosome aberration induction: deactivation theory for proton therapy from cells to tumor control

Abstract

We employ a multi-scale mechanistic approach built upon our recent phenomenological / computational methodologies (Ref. [42]) to investigate radiation induced cell toxicities and deactivation mechanisms as a function of linear energy transfer in hadron therapy. Our theoretical model consists of a system of Markov chains in microscopic and macroscopic spatio-temporal landscapes, i.e., stochastic birth-death processes of cells in millimeter-scale colonies that incorporates a coarsegrained driving force to account for microscopic radiation induced damage. The coupling, hence the driving force in this process, stems from a nano-meter scale radiation induced DNA damage that incorporates the enzymatic end-joining repair and mis-repair mechanisms. We use this model for global fitting of the high-throughput and high accuracy clonogenic cell-survival data acquired under exposure of the therapeutic scanned proton beams, the experimental design that considers γ-H2AX as the biological endpoint and exhibits maximum observed achievable dose and LET, beyond which the majority of the cells undergo collective biological deactivation processes. An estimate to optimal dose and LET calculated from tumor control probability by extension to 10 6 cells per mm-size voxels is presented. We attribute the increase in degree of complexity in chromosome aberration to variabilities in the observed biological responses as the beam linear energy transfer (LET) increases, and verify consistency of the predicted cell death probability with the in-vitro cell survival assay of approximately 100 non-small cell lung cancer (NSCLC) cells. The present model provides an interesting interpretation to variabilities in α and β indices via perturbative expansion of the cell survival fraction (SF) in terms of specific and lineal energies, z and y, corresponding to continuous transitions in pair-wise to ternary, quaternary and more complex recombination of broken chromosomes from the entrance to the end of the range of proton beam.PACS numbers:

A new approach to modeling the microdosimetry of proton therapy beams

“…We now turn to present RBE of in-vitro clonogenic cell survival assay of H460 cell lines, a type of non-small cell lung cancer (NSCLC). The dependence of SF on dose and LET were measured experimentally in our group [30] and fitted by 3D global fitting method by the present authors [16][17][18][19]. Shown RBE calculated using variable l (red dots) and constant chord length equal to 5µm (black dots), as recommended by ICRU 36.…”

“…In our recent study [19], we demonstrated that the linear density of DNA DSBs, ∆ l , a fundamental biological response function in a radiation field, is a variable of linear density of the collisions. To this ends, we recall the following relation derived in our first principle multi-scale study [19]…”

A DNA damage multiscale model for NTCP in proton and hadron therapy

“…The steps involving these algebra is cumbersome, but it is straightforward to show 11 P½nðtÞ ¼ 1 À SF eff ½nðtÞ ð Þ N 0 :…”

“…As discussed in Ref. 11, L fits a linear-quadratic type-relation in dose with a and b, polynomial functions of stochastic lineal energy, y, or its deterministic counterpart, LET, that is,…”

“…Our model calculation starts from a recently developed multiscale computational platform that calculates a probability in tissue toxicity, P, as a function of dose and LET for scanning beam of protons. 10,11 In this model, we derived an analytical expression for P based on a system of Markov chains in vastly different spatiotemporal landscapes. The model starts from the time evolution of DNA lethal lesions that is the driving force, and an input to P. Computationally, we simulate the initial DNA damage in nanometer (nm) from event-by-event energy loss processes that leads to chromosome aberration and subsequently transfer the results to the cell deactivation in micrometer (lm) and tumor response in millimeter (mm).…”