Abstract Book

S1081

ESTRO 37

Purpose or Objective To investigate the form of a population TCP distribution presuming that the radiosensitivity parameters of the LQ model of cell kill are normally distributed among a population. Material and Methods The case of spread only in parameter α is investigated. Parameter β is presumed related to parameter α through a fixed α/β ratio. The TCP distributions are calculated using a Monte-Carlo method. In case when only α varies over the population, an analytical formula can also be derived describing the TCP probability density:

Here b is the cell birth rate, d is the natural cell death rate, N is the initial number of tumor cells, n is the number of fractions, T k-1 is the time until after the k th fraction, p s ( T k-1 ) is the cell survival probability after the k th fraction, T n-1 is the total treatment time, p s ( T n-1 ) is the final cell survival probability. A Monte-Carlo (MC) code which was initially developed to model radiation induced cell kill and cell repopulation [3] is modified to include natural cell death as well. Results We present in figure 1 distributions of the surviving cells before and after (bold lines) an irradiation for the last four fractions of a six-fraction regime characterized with cell survival probability per fraction p s =0.4 (p s ( T n-1 ) = (p s ) n ), b =0.16d -1 , d =0.06 d -1 , N= 30. Dotted lines represent the case when only cell repopulation is considered, solid lines correspond to the case of both cell repopulation and natural cell death being taken into account. The analytically calculated TCP is 14.74% and the one obtained using the MC method based on 1.5x10 5 simulations is 14.68%. If there is no natural cell death the TCP calculated via both methods is 2.88% and 2.91% correspondingly.

where all the tumor clonogens receive identical total dose D=nd . Results A TCP distribution when parameter α is normally distributed and α/β is constant is shown in the Figure; the parameter values employed in the calculations are also shown. The black dots represent values calculated using the above analytical expression, showing excellent agreement with the Monte-Carlo simulated distribution.

Conclusion The results from the MC simulations show perfect agreement with the TCP values calculated using the derived analytical expression for various values of the model parameters and various fractionation regimes. The difference between the distributions obtained with and without accounting for natural cell death implies that natural cell death may have a positive impact on the tumour treatment outcome depending on the values of cell birth and natural cell death rates. A future analysis of TCP experimental animal data would help to estimate the impact of natural cell death. 1. Zaider M, Minerbo GN. Phys Med Biol 2000;45(2):279-93. 2. Stavreva N, Stavrev P, Warkentin B, Fallone BG. Med Phys 2003;30(5):735-42. 3. Stavreva N, Stavrev P, Fallone GB. Physica Medica (2009) 25, 181-191 EP-1989 Linear model for salivary gland dose dose response M. Tenhunen 1 , L. Tuomikoski 1 , J. Collan 1 , V. Loimu 1 , K. Saarilahti 1 1 Helsinki University Central Hospital, Cancer centre- Department of Radiotherapy, Helsinki, Finland Purpose or Objective A linear dose response model is tested for stimulated total salivary flow and individual parotid gland function. Parotid glands are considered the main source of stimulated salivary flow (60 – 70 %) and at least one parotid gland can usually be restricted to a mean dose level < 25 Gy during radical radiotherapy of head and neck tumours.

Conclusion The rather unexpected form of the TCP distribution is due to the steepness of the individual TCP as a function of α and the particular values of α, σα and D chosen for this study. The dependence of the form of the TCP distribution on the values of these parameters will be further investigated. EP-1988 Impact of natural tumor cell death on TCP N. Stavreva 1 , P. Stavrev 1 , D. Penev 1 1 Sofia University “St. Kliment Ohridski”, Faculty of Physics, Sofia, Bulgaria Purpose or Objective To investigate the effect of including natural tumor cell death in TCP modeling and to derive a corresponding analytical TCP expression based on Zaider-Minerbo model [1] for the case of different time intervals between fractions and dose per fraction. Material and Methods The corresponding analytical TCP, an upgrade of a TCP expression previously derived in [2], is obtained and is as follows: