Modelling and Control of Mutation Dynamics of the Cancer Cells Employing Chemotherapy

ADMT Journal

دوره 15، شماره 1، خرداد 2022، صفحه 73-83   

نوع مقاله: Original Article

شناسه دیجیتال (DOI): 10.30486/admt.2021.1920220.1240

نویسندگان

Hami Tourajizadeh^{* 1}؛ zahra goorkani zarandi¹؛ zakie farbodi¹؛ ehsan sadeghi²

¹Department of Mechanical Engineering, Faculty of engineering, University of Kharazmi, Tehran, Iran

²Departeman of Electrical Engineering, Sistan and Baluchestan University, Zahedan, Iran

چکیده

In this paper, the analytic model of the mutation dynamics related to the cancer cells which is under the control of chemotherapy is developed and its corresponding metastasis is controlled using chemotherapy method.  The progress of a cancer tumours is contributed to two main factors including metastasis and mutation. It is observed that controlling the metastasis dynamic without considering the mutation phenomenon is doomed to fail. In this paper, the mathematical model of the cancer dynamic is improved considering the mutation of the stem cells and the effect of chemotherapy injection as the corresponding controlling signal is investigated in the extracted state space. Controlling the cancer growth and its mutation process is accomplished here using PID controller and State Feedback Control (SVFC) method. It is shown that by the aid of the proposed model of this paper, not only the number of the cancer cells can be converted to zero, but also the mutation process can be blocked since the feedback of the mutated cells are also engaged in the state space of the system. Verification of the model is conducted by the aid of simulation in the MATLAB and comparing the results with previous studies.

کلیدواژه‌ها

Cancer Modelling؛ Dynamics of Mutation؛ Metastasis Controlling؛ Stem-cells

مراجع

• Kolch, W., Halasz, M., Granovskaya, M., and Kholodenko, B. N., The Dynamic Control of Signal Transduction Networks in Cancer Cells, Nature Reviews Cancer Vol. 15, No. 9, 2015, pp. 515-527.
• Andasari, V., Gerisch, A., Lolas, G., South, A. P., and Chaplain, M. A., Mathematical Modeling of Cancer Cell Invasion of Tissue: Biological Insight from Mathematical Analysis and Computational Simulation, Journal of mathematical biology, Vol. 63, No. 1, 2011, pp. 141-171.
• Ghaffari, P., Mardinoglu, A., Asplund, A., Shoaie, S., Kampf, C., Uhlen, M., and Nielsen, J., Identifying Anti-Growth Factors for Human Cancer Cell Lines Through Genome-Scale Metabolic Modeling, Scientific Reports, Vol. 5, No. 1, 2015, pp. 1-10.
• Jackson, T. L., A Mathematical Investigation of the Multiple Pathways to Recurrent Prostate Cancer: Comparison with Experimental Data, Neoplasia, Vol. 6, No. 6, 2004, pp. 697-704.
• Kohandel, M., Sivaloganathan, S., and Oza, A., Mathematical Modeling of Ovarian Cancer Treatments: Sequencing of Surgery and Chemotherapy, Journal of Theoretical Biology, Vol. 242, No. 2, 2006, pp. 62-68.
• Fassoni, A. C., Yang, H. M., Modeling Dynamics for Oncogenesis Encompassing Mutations and Genetic Instability, Mathematical Medicine and Biology: A Journal of the IMA, Vol. 36, No. 2, 2019, pp.241-267.
• Wang, S., Schättler, H., Optimal Control of a Mathematical Model for Cancer Chemotherapy Under Tumor Heterogeneity, Mathematical Biosciences & Engineering, Vol. 13, No. 6, 2016 pp. 1223
• El-Garawany, A. H., Karar, M. E., and El-Brawany, M. A., Embedded Drug Delivery Controller for Cancer Chemotherapy Under Treatment Constrains, In 2017 Intl Conf on Advanced Control Circuits Systems (ACCS) Systems & 2017 Intl Conf on New Paradigms in Electronics & Information Technology (PEIT), 2017, pp. 264-271.
• Kozusko, F., Chen, P. H., Grant, S. G., Day, B. W., and Panetta, J. C., A Mathematical Model of in Vitro Cancer Cell Growth and Treatment with The Antimitotic Agent Curacin A, Mathematical biosciences, Vol. 170, No. 1, 2001, pp. 1-16.
• Swierniak, A., Polanski, A., and Kimmel, M., Optimal Control Problems Arising in Cell‐Cycle‐Specific Cancer Chemotherapy, Cell Proliferation, Vol. 29, No. 3, 1996, pp. 117-139.
• Dingli, D., Cascino, M. D., Josić, K., Russell, S. J., and Bajzer, Ž, Mathematical Modeling of Cancer Radiovirotherapy, Mathematical Biosciences, Vol. 199, No. 1, 2006, pp. 55-78.
• Vivek, P., Nikhil, P., Asha, R., and Vijander, S. Optimal ISA-PID-Based Drug Concentration Control in Cancer Chemotherapy, In Intelligent Communication, Control and Devices, 2018, pp. 165-171.
• Kimmel, M., Swierniak, A., Control Theory Approach to Cancer Chemotherapy: Benefiting from Phase Dependence and Overcoming Drug Resistance, Tutorials in Mathematical Biosciences III, Springer, Berlin, Heidelberg, Vol. 1872, 2006, pp. 185-221.
• Oke, S. I., Matadi, M. B., and Xulu, S. S., Optimal Control Analysis of a Mathematical Model for Breast Cancer, Mathematical and Computational Applications, Vol. 23, No. 2, 2018 pp. 21.
• Bajger, P., Bodzioch, M., and Foryś, U., Singularity of Controls in A Simple Model of Acquired Chemotherapy Resistance, Discrete & Continuous Dynamical Systems-B, Vol. 24, No. 5, 2019, pp. 2039.
• Panjwani, B., Mohan, V., Rani, A., and Singh, V., Optimal Drug Scheduling for Cancer Chemotherapy Using Two Degree of Freedom Fractional Order PID Scheme, Journal of Intelligent & Fuzzy Systems, Vol. 36, No. 3, 2019, pp. 2273-2284.
• Dunne, L. W., Huang, Z., Meng, W., Fan, X., Zhang, N., Zhang, Q., and An, Z., Human Decellularized Adipose Tissue Scaffold as a Model for Breast Cancer Cell Growth and Drug Treatments, Biomaterials, Vol. 35, No. 18, 2014, pp. 4940-4949.
• Khalili, P., Zolatash, S., and Vatankhah, R., Fuzzy Control for Drug Delivery in Cancerous Tumors Chemotherapy. Modares Mechanical Engineering, Vol. 19, No. 6, 2019, pp. 1467-1473.
• Wodarz, D., Effect of Stem Cell Turnover Rates On Protection Against Cancer and Aging, Journal of Theoretical Biology, Vol. 245, No. 3, 2007, pp. 449-458.
• Samuels, Y., Diaz Jr, L. A., Schmidt-Kittler, O., Cummins, J. M., DeLong, L., Cheong, I., Rago, C., Huso, D. L., Lengauer, C., Kinzler, K. W., and Vogelstein, B., Mutant PIK3CA Promotes Cell Growth and Invasion of Human Cancer Cells, Cancer Cell, Vol. 7, No. 6, 2005, pp. 561-573.
• Ashkenazi, R., Gentry, S. N., and Jackson, T. L., Pathways to Tumorigenesis—Modeling Mutation Acquisition in Stem Cells and Their Progeny, Neoplasia, Vol. 10, No, 11, 2008, pp. 1170-IN6.
• Sameen, S., Barbuti, R., Milazzo, P., Cerone, A., Del Re, M., and Danesi, R., Mathematical Modeling of Drug Resistance Due to KRAS Mutation in Colorectal Cancer, Journal of Theoretical Biology, Vol. 389, 2016, pp. 263-273.
• Stiehl, T., Marciniak-Czochra, A., Stem Cell Self-Renewal in Regeneration and Cancer: Insights from Mathematical Modeling, Current Opinion in Systems Biology, Vol. 5, 2017, pp. 112-120.
• Ascolani, G., Liò, P., Modeling Breast Cancer Progression to Bone: How Driver Mutation Order and Metabolism Matter, BMC Medical Genomics, Vol. 12, No. 6, 2019, pp. 106.
• Ascolani, G., Liò, P., Modeling Breast Cancer Progression to Bone: How Driver Mutation Order and Metabolism Matter, BMC Medical Genomics, Vol. 12, No. 6, 2019, pp. 106.
• Owolabi, K. M., Shikongo, A., Mathematical Modelling of Multi-Mutation and Drug Resistance Model with Fractional Derivative, Alexandria Engineering Journal, 2020.
• Lee, M., Vasioukhin, V., Cell Polarity and Cancer–Cell and Tissue Polarity as A Non-Canonical Tumor Suppressor, Journal of Cell Science, Vol. 121, No. 8, 2008, pp. 1141-1150.
• Wu, M., Kwon, H. Y., Rattis, F., Blum, J., Zhao, C., Ashkenazi, R., Jackson, T. L., Gaiano, N., Oliver, T., and Reya, T., Imaging Hematopoietic Precursor Division in Real Time, Cell Stem Cell, Vol. 1, No. 5, 2007, pp. 541-554.
• Michor, F., Hughes, T. P., Iwasa, Y., Branford, S., Shah, N. P., Sawyers, C. L., and Nowak, M. A., Dynamics of Chronic Myeloid Leukaemia, Nature, Vol. 435, No. 7046, 2005, pp. 1267-1270.