Computer Simulation in Cell Radiobiology

The search for ways to overcome tumour radioresistance is a major problem of experimental and clinical radiation oncology. The difficulties involved in the attempts to solve this problem are a matter of common knowledge. In many a laboratory extensive studies are underway of factors determining tumour tissue response to irradiation and of methods for exerting directional effect upon those factors. Such studies have revealed that, at least at the cellular level, a considerable number of factors manifest themselves which are responsible for radiation effect [1]. Among those are: spatial heterogeneity of tumour cell population producing radioresistant cell reserves (hypoxic cells of solid tumours); differing radiosensitivities of cell life cycle phases; intrinsic dynamics of the processes of radiation damage and postradiation cell recovery; induction of proliferative processes in response to the death of some cells within the population; the stochastic nature of cell kinetics and complicated interaction between individual cell subpopulations corresponding to different tumour loci.

Methods for mathematical modelling of the processes of cell proliferation and differentiation in normal and tumour tissues and their practical utilization are the subject of a considerable body of works. The theory of cell population dynamics and its applications has now become a full-fledged division of mathematical biology. The fundamentals of the mathematical theory of cell systems have been more comprehensively covered in monographs [13, 25, 70]. According to some authors [12, 13, 20, 67] the following are among the currently central problems of mathematical modelling in that field:

The model proposed here simulates development in time of a cell population which, depending on a chosen model structure and initial values of the parameters, may correspond to either an exponentially growing or stationary culture of normal or tumour cells, as well as to a stem-cell population from embryonal or somatic definitive renewing tissues. It is designed primarily for studying the effect of radiation on the kinetics of cell populations following a single or fractionated exposure. Radiation effect is assessed from the clonogenic capacity of cells. The computer realization of the model was accomplished with the aid of the GPSS/36O language. The individual blocks of the model will be described and substantiated from the standpoint of present-day radiobiological concepts.

In the preceding chapter we proposed a simulation model of the effect of ionizing radiation on in vitro cell systems. The adequacy of a multiparameter model to the actual processes for whose description it has been developed may be reliably established only when it proves instrumental in reproducing a whole set of results obtained in biological experiments.

Cell population homeostasis of renewing tissues is maintained by the dynamic balance between the processes of proliferation of cells and their subsequent death following the fulfillment by each cell of its specialized tissue function. The cell acquires its tissue function competence as a result of the maturation or differentiation processes associated with the mechanisms of its ageing and death. It is taken for granted that the cell composition of such “organized” tissues is regulated on the principle of negative feedback. Many of the existing simulation models of cell systems e.g. [7, 8, 12, 13] contain formalized descriptions of feedback. Their authors, however, made no attempts to study the concrete role of the mechanisms of tissue homeostasis in ensuring the functioning of the cell system under normal conditions and after exposure to damaging agents. In the works by Gusev and Yakovlev [3, 4, 5] a stochastic simulation model was developed designed for studying specific responses of controlled cell systems to external factors. By means of that model some of the possible ways of simulating tumour growth were explored [4] as well as the reaction of the cell system to hydroxyurea [3].

The problems considered below demonstrate the efficacy of employing computer simulation wherever analytical approaches of the mathematical theory to the investigation of the statistical properties of processes come up against certain technical difficulties. Getting over these difficulties often appears to be the most important stage both in substantiating theoretically the limits of applicability of a particular mathematical model and in elaborating requirements on the accuracy of evaluating from experimental evidence the proposed kinetic indicators.

In recent years simulation techniques have been used to an increasing extent in describing a variety of biological processes, cell population kinetics in particular. This tendency is easily explicable. Indeed, creation of efficient means for interpreting experimental observations is inexorably associated with the development of models meeting stringent requirements for realistic description of the processes under study. Simulation modelling offers possibilities for conceptual analysis and prediction of reactions of complex systems with the minimum of limitations on the structure of the model and, in some cases, with replacing labour consuming biological experiments by their simulation on a computer.