Iranian Journal of Biomedical Engineering (IJBME)

کنترل تطبیقی ​​غیرخطی مدل ریاضی رشد تومور سرطان ریه با استفاده از مهار رگ‌زایی

نوع مقاله : مقاله کامل پژوهشی

نویسندگان

1 دانشجوی کارشناسی ارشد، گروه مهندسی برق و کامپیوتر، دانشکده‌ی فنی و مهندسی، دانشگاه محقق اردبیلی، اردبیل، ایران

2 استاد، گروه مهندسی برق و کامپیوتر، دانشکده‌ی فنی و مهندسی، دانشگاه محقق اردبیلی، اردبیل، ایران

3 استادیار، گروه فناوری‌های نوین، دانشکده‌ی فناوری‌های نوین نمین، دانشگاه محقق اردبیلی، نمین، ایران

چکیده
هدف اصلی شیمی‌درمانی با دوزهای بالا عمدتا سلول‌های تکثیری تومور است. روش­های شیمی‌درمانی در کنار مزایایی که دارند، دارای عوارض جانبی قابل توجهی نیز می‌باشند. در دهه‌های اخیر روش‌های درمانی مولکولی هدفمند جدیدی بر پایه‌ی مدل‌های ریاضی ظهور یافته است. شیمی‌درمانی مترونومیک روشی است که در آن از دوزهای کم داروهای شیمی‌درمانی به طور مداوم و منظم برای درمان سرطان استفاده می‌شود. این روش به طور خاص سلول‌های اندوتلیال فعال در رگ‌های خونی جدید که سلول‌ها نقش حمایتی از تومور دارند را هدف قرار می‌دهد. در این میان مهندسی کنترل زیست‌پزشکی با تکیه بر مدل‌سازی‌های ریاضی می‌تواند ابزاری قدرتمند برای بهینه‌سازی روند درمان و کنترل رشد تومور باشد و با ارائه‌ی پروتکل‌های درمانی و تنظیم و حداقل‌سازی دوز داروهای شیمی‌درمانی، به بهبود نتایج درمان کمک کند. در این مقاله بر مبنای مدل ریاضی معتبر هانفلد برای رشد تومور سرطان ریه، یک روش تطبیقی غیرخطی برای تعیین دوز شیمی‌درمانی ارائه شده است. مدل هانفلد اثرات متقابل بین سلول‌های اندوتلیال که لایه‌ی داخلی رگ‌های خونی را تشکیل می‌دهد و سلول‌های تومور را در یک سیستم دینامیکی غیرخطی توصیف می‌کند. رویکرد پیشنهادی در این پژوهش با بهره‌گیری از یک کنترل کننده‌ی تطبیقی غیرخطی مدل مرجع، توانسته است ضمن کاهش چشم‌گیر مصرف دارو، حجم سلول‌های اندوتلیال و حجم تومور را به طور قابل توجهی کاهش دهد. نتایج شبیه‌سازی نشان می‌دهد که متغیرهای سیستم در مدت زمان تقریبی 19 روز به محدوده‌ی امن رسیده و این روند کاهشی تا روز 24 ادامه یافته است. در نهایت، حجم متغیرها به حدود 1 میلی‌مترمکعب کاهش پیدا کرده است.

کلیدواژه‌ها

موضوعات


عنوان مقاله English

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

نویسندگان English

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
چکیده English

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.

کلیدواژه‌ها English

Adaptive Control
Nonlinear Control
Cancer Treatment
Anti Angiogenic
Chemotherapy
Metronomic Therapy
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.
دوره 18، شماره 1
بهار 1403
صفحه 51-64

  • تاریخ دریافت 11 تیر 1403
  • تاریخ بازنگری 06 آبان 1403
  • تاریخ پذیرش 08 آبان 1403