Ionizing Radiation Effects Modelling in Cells Population with Gold Nanoparticles


  • Normah Maan
  • Wan Nordiana W Abd Rahman



Ionizing Radiation, Nanoparticle, Double-Strand Breaks (DSBs), Parameter Estimation, Sensitivity Analysis


Radiosensitizer such as gold nanoparticle is a promising agent to be used in radiotherapy to increase the number of cancer cell death. Gold nanoparticle increases the production of the secondary electron after being hit by primary radiation that will cause DNA damage. The gold nanoparticle can be targeted to specific cancer cells and therefore reduce damage to the healthy nearby cell. Thus, nanoparticles will elevate the efficacy of radiation treatment without delivering a high radiation dose that will damage the organ at risk. Therefore, this paper aimed to study the effects of radiosensitizer on radiation therapy. The study was done by incorporating the function of dose deposited by gold nanoparticles into the existing model of ionizing radiation effects. The model was mathematically described using Ordinary Differential Equations (ODEs). The simulation results were fitted to the Linear Quadratic (LQ) formulation to give the ratio for a/b. Next, the parameter estimation and sensitivity analysis of the model are carried out using experimental data of HeLa cell with the aid of the MATLAB programming. The estimated parameter values can explain the radiobiology process, which can support the result of the experimental design. The result showed that the sum-squared error (SSE) between simulation data and experimental data obtained is 0.015 which indicates an excellent fit to the experimental data. Thus, this model is in line with the experimental result. The model is able to explain the dynamics process of ionizing radiation effects with gold nanoparticles on the cell population.


S. Penninckx, A.C. Heuskin, C. Michiels, S. Lucas, Gold nanoparticles as a potent radiosensitizer: a transdisciplinary approach from physics to patient. Cancers, vol. 12, no. 8, pp. 2021.2020.

S. H. Lim, C. H. Li, Y. I. Jeong et al., Enhancing radiotherapeutic effect with nanoparticle-mediated radiosensitizer delivery guided by focused gamma rays in lewis lung carcinoma-bearing mouse brain tumor models. International Journal of Nanomedicine, vol. 14, pp. 8861, 2019.

S. Yang, G. Han, Q. Chen et al., Au-Pt Nanoparticle Formulation as a Radiosensitizer for Radiotherapy with Dual Effects. International Journal of Nanomedicine, vol. 16, pp. 239, 2021.

C. Yang, K. Bromma, Di Ciano-Oliveira et al., Gold nanoparticle-mediated combined cancer therapy, Cancer Nanotechnology, vol. 9, no. 1, pp. 4,2018.

F. Khan, S. Akhtar, S. Almofty et al., MSP-nanoparticles induced cell death on human breast adenocarcinoma cell line (MCF-7 Cells): morphometric analysis, Biomolecules, vol. 8, no. 2, pp. 32, 2018.

T. Cardilin, J. Almquist, M. Jirstrand et al., Model‐Based Evaluation of Radiation and Radiosensitizing Agents in Oncology, CPT: Pharmacometrics & Systems Pharmacology, vol. 7, no. 1, pp. 51-58.2018.

B. Sah and MP. Antosh, Effect of size on gold nanoparticles in radiation therapy: Uptake and survival effects. Journal of Nanomedicine, vol. 2, no. 1, pp. 1013, 2019.

S.M. Siam, M. Grinfeld, A. Bahar et al., A mechanistic model of high dose irradiation damage, Mathematics and Computers in Simulation, vol.151, pp. 156- 168, 2016.

J. Gao and Y. Zheng, Monte Carlo study of secondary electron production from gold nanoparticle in proton beam irradiation. International Journal of Cancer Therapy and Oncology, vol 2, pp. 2025, 2014.

K. Huang, H. Ma, J. Liu et al., Size-Dependent Localization and Penetration of Ultrasmall Gold Nanoparticles in Cancer Cells, Multicellular Spheroids, and Tumors in Vivo. ACS Nano, vol. 6, no. 5, pp. 4483-4493,2012.

J. F. Hillyer and R. M. Albrecht, Gastrointestinal prescription and tissue distribution of differently sized colloidal gold nanoparticles. Journal of Pharmaceutical Sciences, vol. 90, no. 12, pp. 1927-1936, 2001.

E. Saion, E. Gharibshahi, K. Naghavi, Size-controlled and optical properties of monodispersed silver nanoparticles synthesized by the radiolytic reduction method. International Journal of Molecular Sciences, vol. 14, no. 4, pp. 7880-7896, 2013.

M. K. Leung, J. C. Chow, B. D. Chithrani et al, Irradiation of gold nanoparticles by x‐rays: Monte Carlo simulation of dose enhancements and the spatial properties of the secondary electrons production, Medical Physics, vol. 38, no. 2, pp. 624-631, 2011.

J. M. Wentz, V. Vainstein, D. Oldson et al., Mathematical model of radiation effects on thrombopoiesis in rhesus macaques and humans, Journal of Theoretical Biology, vol. 383, pp. 44-60, 2015.

T. Wada, Y. Manabe and M. Bando, A mathematical model for the effects of radiation to the induced cancer in mice, In APS March Meeting Abstracts, pp. Y6-012, 2017.

Y. Watanabe, E. L. Dahlman, K.Z. Leder & S. K. Hui, A mathematical model of tumor growth and its response to single irradiation , Theoretical Biology and Medical Modelling, vol. 13, no. 1, pp.1-20, 2016.

J. C. Chow, M. K. Leung, S. Fahey et al., Monte Carlo simulation on low-energy electrons from gold nanoparticle in radiotherapy, In Journal of physics: Conference series, vol. 341, no. 1, pp. 012012. IOP Publishing. 2012.

M. Simkó, D. Nosske W. and Kreyling, Metrics, dose, and dose concept: the need for a proper dose concept in the risk assessment of nanoparticles. International Journal of Environmental Research and Public Health, vol. 11, no. 4, pp. 4026-4048, 2014.

L. Štefančíková, S. Lacombe, D. Salado et al., Effect of gadolinium based nanoparticles on nuclear DNA damage and repair in glioblastoma tumor cells. Journal of nanobiotechnology, vol. 14, no. 1, pp. 1-15, 2016.

R. A. Rashid, K. A. Razak, M. Geso et al., Radiobiological Characterization of the Radiosensitization Effects by Gold Nanoparticles for Megavoltage Clinical Radiotherapy Beams. BioNanoScience, vol. 8, no. 3, pp.713-722, 2018.

P. Bajpai and M. Kumar, Genetic algorithm–an approach to solve global optimization problems. Indian Journal of Computer Science and Engineering, vol. 1, no. 3, pp. 199-206,2010.

J. Morio, Global and local sensitivity analysis methods for a physical system, European Journal of Physics, vol. 32, no. 6, pp. 1577,2011.

M.H. Nasir and F. M. Siam, Simulation and Sensitivity Analysis on the Parameter of Non-Targeted Irradiation Effects Model, Jurnal Teknologi , vol. 81, no.1, pp. 133-142.2019.

C. M. Van Leeuwen, A. L. Oei, J. Crezee et al., The alfa and beta of tumours: a review of parameters of the linear-quadratic model, derived from clinical radiotherapy studies, Radiation Oncology, vol. 13, no. 1, pp. 96, 2018.

T. Mori and T. Hegmann, Determining the composition of gold nanoparticles: a compilation of shapes, sizes, and calculations using geometric considerations, Journal of Nanoparticle Research, vol. 18. no. 10, pp. 1-36, 2016.