In irradiation process, instead of traverse on the targeted cells, there is side effect happens to non-targeted cells. The targeted cells that had been irradiated with ionizing radiation emits damaging signal molecules to the surrounding and then, damage the bystander cells. The type of damage considered in this work is the number of double-strand breaks (DSBs) of deoxyribonucleic acid (DNA) in cell’s nucleus. By using mathematical approach, a mechanistic model that can describe this phenomenon is developed based on a structured population approach. Then, the accuracy of the model is validated by its ability to match the experimental data. The Particle Swarm (PS) optimization is employed for the data fitting procedure. PS optimization searches the parameter value that minimize the errors between the model simulation data and experimental data. It is obtained that the mathematical modelling proposed in this paper is strongly in line with the experimental data.

Real-life situations showed damage effects on non-targeted cells located in the vicinity of an irradiation region, due to danger signal molecules released by the targeted cells. This effect is widely known as radiation-induced bystander effects (RIBE). The purpose of this paper is to model the interaction of non-targeted cells towards bystander factors released by the irradiated cells by using a system of structured ordinary differential equations. The mathematical model and its simulations are presented in this paper. In the model, the cells are grouped based on the number of double-strand breaks (DSBs) and mis-repair DSBs because the DSBs are formed in non-targeted cells. After performing the model's simulations, the analysis continued with sensitivity analysis. Sensitivity analysis will determine which parameter in the model is the most sensitive to the survival fraction of non-targeted cells. The proposed mathematical model can explain the survival fraction of non-targeted cells affected by the bystander factors.

Radiotherapy treatment uses ionizing radiation (IR) in order to kill cancer cells. However, the IR exerted its effects outside the radiation field and causes cell death in healthy cells. This effect namely as radiation-induced bystander effects (RIBE) phenomenon. The scope of the overview of the RIBE phenomenon discussed in this paper includes the RIBE mechanism, danger signaling process, deoxyribonucleic acid (DNA) double-strand breaks (DSBs) damage and the damage repair. This paper extended with the discussion of several mathematical models used to describe the RIBE phenomenon. The discussions towards the mathematical models include the models of signals concentration, the models of bystander effects and the survival fraction model. Mathematical modelling and computer simulation are powerful tools used to understand the biological phenomenon of RIBE. The suitable mathematical model of repair and mis-repair DNA DSBs damage has been briefly reviewed in view of the relevance of this model towards RIBE phenomenon. The outcome of this paper suggested a recommendation for future research on the suitable mathematical model and simulation analysis in describing the complexity of RIBE phenomenon.

Study on the biological effects of irradiation has become important nowadays. Mathematical modeling is one of the interests among researchers due to its ability to explain the dynamics process of the irradiation. Some physical parameters cannot be evaluated from the empirical data. Therefore, the aim of this work is to estimate parameters of the model of irradiation effects on bystander cells using optimization approaches. We employ two algorithms: Nelder-Mead Simplex (NMS) (which is the local optimizer) and Particle Swarm (which is the global optimizer). We compare the ef iciency of two optimization algorithms in optimizing the parameter values of the model. 50 sets of parameters have been estimated and all sets are able to match the model simulation and the experimental data with the least Sum-Squared Error (SSE). The graph of model simulation using a set of the estimated parameters from both optimization algorithms shows a good it with the experimental data. The overall results indicate that NSM is better than Particle Swarm (PS) optimization in the aspect of time computing, while there is no signi icant difference in the score of SSE and converging iteration to the least SSE.

Mechanisms of mammalian cell killing effects produced by irradiation are complex processes and it is vitally importance to understand the phenomenon. In this research, models of survival fraction of targeted and bystander cells are employed, with modification on the signaling factors. The models are a type of two-dimensional vector that structure a population cell depends on the double-strand breaks (DSBs) and mis-repair DSBs count (k and m, respectively). Data fitting and parameter estimation are used as model calibration. Then, by using the estimated parameters, the model simulation shows a good fit against the experimental data with a sum of absolute error (SAE) of 0.0355 and 0.1542, respectively. These errors confirmed that the models are successfully depicted the actual measurement of targeted and bystander effects.