PROTRACTION EFFECTS IN A STOCHASTIC CELL-CYCLE TUMOR MODEL EXPOSED TO FRACTIONATED RADIOTHERAPY Zehra Kalkan and Waldemar Zylka Westfälische Hochschule Gelsenkirchen, Germany zehrakalkan@hotmail.de Abstract: The response of repair kinetics of an avascu- lar tumor during and between fractionated irradiation and the influence on the effectiveness of radiotherapy is inves- tigated using a model of irradiated cell survival with cell- cycle regulation. Tissue response to irradiation is defined by the linear-quadratic (LQ) model in which fractionation and dose-protraction are included through the Lea-Catchside function. It is shown that the cell survival increases by pro- traction in multifractionation regimes. Keywords: tumor model, protraction, tissue response, ra- diotherapy, multifractionation, repair rate Introduction Radiation imposes cell death caused by interaction between cells’ chromosomes and radiation particle. Chromosomal double-strand-break (DSB) is one of the most interesting injuries. Two DSB’s, produced by two different radiation tracks, are able to create a lethal lesion through chromoso- mal aberration. In fractionation treatments protraction al- lows the first lesion to be repaired until the second lesion is generated [1]. The linear-quadratic (LQ) model quan- tifies this effect, by introducing the Lea-Catchside time- factor denoted by G. This factor was generalized from the incomplete-repair (IR) model and represents the n-fraction version of the lethal-potential-lethal (LPL) model [2, 3]. The purpose of this work is to analyze the time-dose re- sponse of repair kinetics during and also between fraction- ated irradiation and their influence on the effectiveness of radiotherapy. To this end, the protraction factor for dif- ferent radiation schedules and a generalized equation for acute multifractionated radiation is derived. The result is incorporated into a previously developed stochastic multi– scale model with cell cycle regulations which models the growth and treatment of avascular tumor [4, 5]. Within this model the cell survival probability S(D) is calculated for an applied total dose D using the LQ- model. This re- search investigates three different tumor cell types: prostate cells, non-small-cells of lung carcinoma (NSCLC) and hu- man general cells (HCGV). Methods The previously developed stochastic tumor model includes cell-cycle dynamics with proliferating cells. Check points in the cycle allow check for DNA damage. Cells damaged by radiation do not proliferate and will die (apoptosis). De- pending upon the oxygen conditions are hypoxic or nor- moxic [4]. These conditions are calculated for every time step Δt =1min. Proliferation and spread of cells are de- fined stochastically [4, 5]. Protraction and fraction effects in cell survival are modeled using the LQ-model: ln[S(D)] = -(αD + GβD 2 ) , (1) where D is the delivered total dose. The tissue dependent parameters α and β represent lethal lesion caused by one– track action and by two-track action, respectively [6]. The definition of the generalized Lea-Catchside function G is [1]: G(μ, τ )= 2 D 2  ∞ -∞ ˙ D(t)  t -∞ ˙ D(t ′ )e -μ(t-t ′ ) dt ′ dt, (2) where the total Dose D is given at variable dose-rate ˙ D(t) in the irradiation period [0,t max ] [2]. The repair-rate μ is defined by μ = ln(2)/T 1/2 where T 1/2 represents the cells’ repair half-time. The inner integral in Eq.(2) corresponds to an accumulated effective dose [2]. Equation (2) applies for all fractionation schemes. The range of the Lea-Catchside function is 0 ≤ G ≤ 1, where G =0 indicates the repair of all potential DSB’s and G =1 being the opposite. For G =1 cells are able to induce a lethal lesion. The protrac- tion factor has been developed for some special treatment schedules such as the continuous and acute fractionated ir- radiation. A single continuous irradiation is represented by a constant dose–rate ˙ D(t) and limited to the period of [0,τ ]. From this, it follows: G(μτ )= 2 (μτ ) 2 ( μτ - 1+ e -μτ ) , (3) which is identical to the function g(x) with x = μτ of the IR-model as defined in [3]. In case of n fractions of duration τ and separated by the time interval Δτ , we get: G(n, x, q)= 1 n (g(x)+ f (x)e x h n (q)) , (4) f (x)=  1 - e x x  2 ,h n (q)= 2 n  q 1 - q  n - 1 - q n 1 - q  with q = exp(-μ(τ +Δτ )), which determines the rate of repair kinetics [3]. To analyze the effect of protraction during radiation, based on clinical treatments, we simulated the cell-survival with parameters collected in Tab.1: Δτ the interfraction interval, d the dose per fraction and n the total number of fractions (D = nd). An acute irradiation, i.e. τ =0min is chosen. Biomed Tech 2013; 58 (Suppl. 1) © 2013 by Walter de Gruyter · Berlin · Boston. DOI 10.1515/bmt-2013-4340 Unauthenticated Download Date | 7/19/18 7:48 AM