Iranian Journal of Biomedical Engineering (IJBME)
نشریه علمی مهندسی پزشکی زیستی

Nonlinear Adaptive Control of Mathematical Model of Lung Cancer Tumor Growth using Angiogenic Inhibition

Document Type : Full Research Paper

Authors

Mehdi Ghasemi 1
Adel Akbarimajd 2
Solmaz Kia 3

1 M.Sc. Student, Department of Electrical and Computer Engineering, University of Mohaghegh Ardabili, Ardabil, Iran

2 Professor, Department of Electrical and Computer Engineering, University of Mohaghegh Ardabili, Ardabil, Iran

3 Assistant Professor, Department of Advanced Technology, University of Mohaghegh Ardabili,, Namin, Iran

https://doi.org/10.22041/ijbme.2024.2034314.1910
Abstract
The primary target of high-dose chemotherapy is the rapidly proliferating tumor cells. Chemotherapy, while beneficial in cancer treatment, also comes with significant side effects. In recent decades, in addition to classical treatment methods, new targeted molecular therapies have emerged, some of which are designed based on mathematical models. Metronomic chemotherapy is a method in which low doses of chemotherapy drugs are given continuously and regularly to treat cancer. This method specifically targets active endothelial cells in new blood vessels. These cells play a supportive role in the tumor and are therefore a suitable target for this therapy. Therefore, biomedical control engineering, based on mathematical modeling, can be a powerful tool for optimizing the treatment process and controlling tumor growth. By providing treatment protocols and adjusting and minimizing the dosage of chemotherapeutic drugs during patient treatment, treatment outcomes can be improved. In this paper, a nonlinear adaptive method for determining the chemotherapy dosage to control the considered model is proposed, relying on the validated mathematical model of lung cancer tumor growth developed by Hahnfeldt et al. The proposed model describes the interactions between endothelial cells, which form the inner lining of blood vessels, and tumor cells in a two-dimensional nonlinear dynamical system. The proposed approach in this research, utilizing a nonlinear model reference adaptive controller, has successfully achieved a significant reduction in both endothelial cell volume and tumor volume while substantially decreasing drug consumption. Simulation results demonstrate that the system variables converged to a safe range within approximately 19 days and continued to decrease until day 24. Ultimately, the volume of variables was reduced to approximately 1 mm3.

Keywords

Adaptive Control
Nonlinear Control
Cancer Treatment
Anti Angiogenic
Chemotherapy
Metronomic Therapy

Subjects

1.      H. Sung et al., “Global cancer statistics 2020: GLOBOCAN estimates of incidence and mortality worldwide for 36 cancers in 185 countries,” CA Cancer J Clin, vol. 71, no. 3, pp. 209–249, 2021.
2.      D. T. Debela et al., “New approaches and procedures for cancer treatment: Current perspectives,” SAGE Open Med, vol. 9, p. 20503121211034370, 2021.
3.      L. Kovács et al., “Model-based angiogenic inhibition of tumor growth using modern robust control method,” Comput Methods Programs Biomed, vol. 114, no. 3, pp. e98–e110, 2014.
4.      E. Pérez-Herrero and A. Fernández-Medarde, “Advanced targeted therapies in cancer: Drug nanocarriers, the future of chemotherapy,” European journal of pharmaceutics and biopharmaceutics, vol. 93, pp. 52–79, 2015.
5.      S. K. De, Fundamentals of Cancer Detection, Treatment, and Prevention. John Wiley & Sons, 2022.
6.      U. Ledzewicz and H. Schättler, “Application of optimal control to a system describing tumor anti-angiogenesis,” in Proceedings of the 17th International Symposium on Mathematical Theory of Networks and Systems (MTNS), Kyoto, Japan, 2006, pp. 478–484.
7.      S. C. Shah, V. Kayamba, R. M. Peek Jr, and D. Heimburger, “Cancer control in low-and middle-income countries: is it time to consider screening?,” J Glob Oncol, vol. 5, pp. 1–8, 2019.
8.      L. Kovács et al., “Model-based angiogenic inhibition of tumor growth using modern robust control method,” Comput Methods Programs Biomed, vol. 114, no. 3, pp. e98–e110, 2014.
9.      A.-M. Tsimberidou, “Targeted therapy in cancer,” Cancer Chemother Pharmacol, vol. 76, pp. 1113–1132, 2015.
10.   A. A. Secord and S. Siamakpour-Reihani, “Chapter 5 - Angiogenesis,” M. J. Birrer and L. B. T.-T. A. in G. C. Ceppi, Eds., Boston: Academic Press, 2017, pp. 79–109. doi: https://doi.org/10.1016/B978-0-12-803741-6.00005-7.
11.   D.-B. Chen and J. Zheng, “Regulation of placental angiogenesis,” Microcirculation, vol. 21, no. 1, pp. 15–25, Jan. 2014, doi: 10.1111/micc.12093.
12.   U. Ledzewicz and H. Schättler, “Application of optimal control to a system describing tumor anti-angiogenesis,” in Proceedings of the 17th International Symposium on Mathematical Theory of Networks and Systems (MTNS), Kyoto, Japan, 2006, pp. 478–484.
13.   I. Zuazo-Gaztelu and O. Casanovas, “Unraveling the role of angiogenesis in cancer ecosystems,” Front Oncol, vol. 8, p. 248, 2018.
14.   M. J. Ansari et al., “Cancer combination therapies by angiogenesis inhibitors; a comprehensive review,” Cell Communication and Signaling, vol. 20, no. 1, pp. 1–23, 2022.
15.   S. Sadhukhan and S. K. Basu, “Avascular tumour growth models based on anomalous diffusion,” J Biol Phys, vol. 46, pp. 67–94, 2020.
16.   R. Lugano, M. Ramachandran, and A. Dimberg, “Tumor angiogenesis: causes, consequences, challenges and opportunities,” Cellular and Molecular Life Sciences, vol. 77, pp. 1745–1770, 2020.
17.   J. Ma and D. J. Waxman, “Combination of antiangiogenesis with chemotherapy for more effective cancer treatment,” Mol Cancer Ther, vol. 7, no. 12, pp. 3670–3684, 2008.
18.   J. Sápi, D. A. Drexler, I. Harmati, Z. Sápi, and L. Kovács, “Linear state-feedback control synthesis of tumor growth control in antiangiogenic therapy,” in 2012 IEEE 10th International Symposium on Applied Machine Intelligence and Informatics (SAMI), 2012, pp. 143–148. doi: 10.1109/SAMI.2012.6208945.
19.   J. Enderle and J. Bronzino, Introduction to biomedical engineering. Academic press, 2012.
20.   A. A. Alexander-Bryant, W. S. Vanden Berg-Foels, and X. Wen, “Bioengineering strategies for designing targeted cancer therapies,” Adv Cancer Res, vol. 118, pp. 1–59, 2013.
21.   M. Kuznetsov, J. Clairambault, and V. Volpert, “Improving cancer treatments via dynamical biophysical models,” Phys Life Rev, vol. 39, pp. 1–48, 2021.
22.   I. Lasheras Bujanda, “Theoretical and computational study of a mathematical model for cancer tumor growth, including chemotherapy,” 2023.
23.   O. Y. Basar, S. Mohammed, M. W. Qoronfleh, and A. Acar, “Optimizing cancer therapy: a review of the multifaceted effects of metronomic chemotherapy,” Front Cell Dev Biol, vol. 12, p. 1369597, 2024.
24.   P. Hahnfeldt, D. Panigrahy, J. Folkman, and L. Hlatky, “Tumor development under angiogenic signaling: a dynamical theory of tumor growth, treatment response, and postvascular dormancy,” Cancer Res, vol. 59, no. 19, pp. 4770–4775, 1999.
25.   U. Ledzewicz and H. Schättler, “Antiangiogenic therapy in cancer treatment as an optimal control problem,” SIAM J Control Optim, vol. 46, no. 3, pp. 1052–1079, 2007.
26.   B. Czako, J. Sápi, and L. Kovács, “Model-based optimal control method for cancer treatment using model predictive control and robust fixed point method,” in 2017 IEEE 21st International Conference on Intelligent Engineering Systems (INES), IEEE, 2017, pp. 271–276.
27.   P. Yazdjerdi, N. Meskin, M. Al-Naemi, A.-E. Al Moustafa, and L. Kovács, “Reinforcement learning-based control of tumor growth under anti-angiogenic therapy,” Comput Methods Programs Biomed, vol. 173, pp. 15–26, 2019.
28.   U. Ledzewicz and H. Schattler, “A synthesis of optimal controls for a model of tumor growth under angiogenic inhibitors,” in Proceedings of the 44th IEEE Conference on Decision and Control, IEEE, 2005, pp. 934–939.
29.   D. A. Drexler, J. Sápi, A. Szeles, I. Harmati, A. Kovács, and L. Kovács, “Flat control of tumor growth with angiogenic inhibition,” in 2012 7th IEEE International Symposium on Applied Computational Intelligence and Informatics (SACI), IEEE, 2012, pp. 179–183.
30.   D. A. Drexler, L. Kovács, J. Sápi, I. Harmati, and Z. Benyó, “Model-based analysis and synthesis of tumor growth under angiogenic inhibition: a case study*,” IFAC Proceedings Volumes, vol. 44, no. 1, pp. 3753–3758, 2011, doi: https://doi.org/10.3182/20110828-6-IT-1002.02107.
31.   D. A. Drexler, J. Sápi, and L. Kovács, “Positive nonlinear control of tumor growth using angiogenic inhibition,” IFAC-PapersOnLine, vol. 50, no. 1, pp. 15068–15073, 2017.
32.   I. Lasheras Bujanda, “Theoretical and computational study of a mathematical model for cancer tumor growth, including chemotherapy,” 2023.
33.   I. Alimirzaei and A. Malek, “Optimal Control of Anti‐Angiogenesis and Radiation Treatments for Cancerous Tumor: Hybrid Indirect Solver,” Journal of Mathematics, vol. 2023, no. 1, p. 5554420, 2023.
34.   J.-J. E. Slotine, “Applied Nonlinear Control,” PRENTICE-HALL google schola, vol. 2, pp. 1123–1131, 1991.
35.   K. J. Åström and B. Wittenmark, Adaptive Control. in Dover Books on Electrical Engineering. Dover Publications, 2008. [Online]. Available: https://books.google.com/books?id=L0m_CR-IK24C
36.   E. Lavretsky, “Adaptive control: Introduction, overview, and applications,” in Lecture notes from IEEE Robust and Adaptive Control Workshop, 2008.
37.   S. Ziyad and M. L. Iruela-Arispe, “Molecular Mechanisms of Tumor Angiogenesis,” Genes Cancer, vol. 2, no. 12, pp. 1085–1096, Dec. 2011, doi: 10.1177/1947601911432334.
38.   B. Czakó and L. Kovács, “Nonlinear Model Predictive Control Using Robust Fixed Point Transformation-Based Phenomena for Controlling Tumor Growth,” Machines, vol. 6, no. 4, 2018, doi: 10.3390/machines6040049.
39.   I. D. Landau, R. Lozano, M. M’Saad, and A. Karimi, Adaptive control: algorithms, analysis and applications. Springer Science & Business Media, 2011.
40.   A. Shekhar and A. Sharma, “Review of model reference adaptive control,” in 2018 international conference on information, communication, engineering and technology (ICICET), IEEE, 2018, pp. 1–5.
41.   E. Lavretsky, “Adaptive control: Introduction, overview, and applications,” in Lecture notes from IEEE Robust and Adaptive Control Workshop, 2008.
42.   B. G. Czakó, J. Sápi, and L. Kovács, “Optimal PID based computed torque control of tumor growth models,” IFAC-PapersOnLine, vol. 51, no. 4, pp. 900–905, 2018.
43.   D. A. Drexler, J. Sápi, A. Szeles, I. Harmati, A. Kovács, and L. Kovács, “Flat control of tumor growth with angiogenic inhibition,” in 2012 7th IEEE International Symposium on Applied Computational Intelligence and Informatics (SACI), IEEE, 2012, pp. 179–183.
44.   D. A. Drexler, L. Kovács, J. Sápi, I. Harmati, and Z. Benyó, “Model-based analysis and synthesis of tumor growth under angiogenic inhibition: a case study*,” IFAC Proceedings Volumes, vol. 44, no. 1, pp. 3753–3758, 2011, doi: https://doi.org/10.3182/20110828-6-IT-1002.02107.
45.   P. Yazdjerdi, N. Meskin, M. Al-Naemi, A.-E. Al Moustafa, and L. Kovács, “Reinforcement learning-based control of tumor growth under anti-angiogenic therapy,” Comput Methods Programs Biomed, vol. 173, pp. 15–26, 2019.
Iranian Journal of Biomedical Engineering (IJBME)
Volume 18, Issue 1
Spring 2024
Pages 51-64

  • Receive Date 01 July 2024
  • Revise Date 27 October 2024
  • Accept Date 29 October 2024

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