1. Home
  2. Journals
  3. Biomedical Research and Clinical Advancements
  4. Articles In Press
  Submit Manuscript

Research Article | DOI: https://doi.org/BRCA-25-RA-23

Analysis and Control of a Drug Delivery Model

Lakshmi. N. Sridhar *

Chemical Engineering Department University of Puerto Rico Mayaguez,United States of America

*Corresponding Author: Lakshmi. N. Sridhar, Chemical Engineering Department University of Puerto Rico Mayaguez ,United States of America

Citation: Lakshmi. N. Sridhar (2025). Analysis and Control of a Drug Delivery Model, J Biomedical Research and Clinical Advancements . 2 (3) 23, DOI: BRCA-25-RA-23.

Copyright: Lakshmi. N. Sridhar, et al © (2025). This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Received: 24 May 2025 | Accepted: 31 May 2025 | Published: 21 June 2025

Keywords: Bifurcation, optimization, control, drug-delivery

Abstract

 Many chronic diseases require continuous treatment, and the interaction between drug exposure and pharmacological response is very complex and nonlinear. It is important to understand the nonlinear complexity and use this nonlinearity effectively to obtain the best advantage. Several factors must be considered, and multiple objectives must be achieved simultaneously. Bifurcation analysis and multi-objective nonlinear model predictive control (MNLMPC) calculations are performed on a dynamic model involving drug delivery. The MATLAB program MATCONT was used to perform the bifurcation analysis. The MNLMPC calculations were carried out using the optimization language PYOMO in conjunction with the advanced global optimization solvers IPOPT and BARON. The bifurcation analysis revealed the existence of a branch point in the system. These branch point (which causes multiple steady-state solutions from a single point) is beneficial because it enables the multi-objective nonlinear model predictive control calculations to converge to the Utopia point, which is the best possible solution. It has been demonstrated (with computational validation) that the branch point results from the presence of two distinct separable functions in one of the equations of the dynamic model. A theorem was developed to prove this fact for any dynamic model..

References

  1. Coldman AJ, Murray JM. Optimal control for a stochastic model of cancer chemotherapy. Math Biosci.2000; 168(2):187±200. https://doi.org/10.1016/S0025-5564(00)00045-6 PMID: 11121565
    View at Publisher | View at Google Scholar
  2. Oefelein MG, Feng A, Scolieri MJ, Ricchiutti D, Resnick MI. Reassessment of the definition of castrate levels of testosterone: implications for clinical decision making. Urology. 2000; 56(6):1021±1024. https://doi.org/10.1016/S0090-4295(00)00793-7 PMID: 11113751
    View at Publisher | View at Google Scholar
  3. Stengel RF, Ghigliazza RM, Kulkarni NV. Optimal enhancement of immune response. Bioinformatics.2002; 18(9):1227±1235. https://doi.org/10.1093/bioinformatics/18.9.1227 PMID: 12217914
    View at Publisher | View at Google Scholar
  4. Oefelein MG, Resnick MI. Effective testosterone suppression for patients with prostate cancer: is there a best castration? Urology. 2003; 62(2):207±213. https://doi.org/10.1016/S0090 4295(03)00331-5 PMID: 12893320
    View at Publisher | View at Google Scholar
  5. Kimmel M, Swierniak A. Control Theory Approach to Cancer Chemotherapy: Benefiting from Phase Dependence and Overcoming Drug Resistance. In: Tutorials in Mathematical Biosciences III. Lecture Notes in Mathematics. Springer, Berlin, Heidelberg; 2006. p. 185±221.
    View at Publisher | View at Google Scholar
  6. Gu W, Moore H. Optimal therapy regimens for treatment-resistant mutations of HIV; 2006.
    View at Publisher | View at Google Scholar
  7. Tornøe CW, Agersø H, Senderovitz T, Nielsen HA, Madsen H, Karlsson MO, et al. Population pharmacokinetic/pharmacodynamic (PK/PD) modelling of the
    View at Publisher | View at Google Scholar
  8. hypothalamic±pituitary±gonadal axis following treatment with GnRH analogues. Br J Clin Pharmacol. 2007; 63(6):648±664. https://doi.org/10.1111/j.1365-2125.2006.02820.x PMID: 17096678
    View at Publisher | View at Google Scholar
  9. Scher HI, Halabi S, Tannock I, Morris M, Sternberg CN, Carducci MA, et al. Design and End Points of Clinical Trials for Patients With Progressive Prostate Cancer and Castrate Levels of Testosterone: Recommendations of the Prostate Cancer Clinical Trials Working Group. J Clin Oncol. 2008; 26(7):1148±1159. https://doi.org/10.1200/JCO.2007.12.4487 PMID: 18309951
    View at Publisher | View at Google Scholar
  10. Woodcock J, Woosley R. The FDA Critical Path Initiative and Its Influence on New Drug Development. Annu Rev Med. 2008;
    View at Publisher | View at Google Scholar
  11. 59(1):1±12.doi.org/10.1146/annurev.med.59.090506.155819 PMID: 18186700
    View at Publisher | View at Google Scholar
  12. De Pillis LG, Fister KR, Gu W, Head T, Maples K, Neal T, et al. Optimal Control of Mixed Immunotherapy and Chemotherapy of Tumors. J Biol Syst. 2008; 16(01):51±80. https://doi.org/10.1142/S0218339008002435
    View at Publisher | View at Google Scholar
  13. Engelhart M, Lebiedz D, Sager S. Optimal control for selected cancer chemotherapy ODE models: a view on the potential of optimal schedules and choice of objective function. Math Biosci. 2011; 229 (1):123±134. https://doi.org/10.1016/j.mbs.2010.11.007 PMID: 21129386
    View at Publisher | View at Google Scholar
  14. Romero E, VeÂlez de Mendizabal N, CendroÂs JM, Peraire C, Bascompta E, Obach R, et al. Pharmacokinetic/pharmacodynamic model of the testosterone effects of triptorelin administered in sustained release formulations in patients with prostate cancer. J Pharmacol Exp Ther. 2012; 342(3):788±798.https://doi.org/10.1124/jpet.112.195560 PMID: 22691297
    View at Publisher | View at Google Scholar
  15. Shi J, Alagoz O, Erenay FS, Su Q. A survey of optimization models on cancer chemotherapy treatment planning. Ann Oper Res. 2014; 221(1):331±356. https://doi.org/10.1007/s10479-011-0869-4
    View at Publisher | View at Google Scholar
  16. Buil-Bruna N, Garrido MJ, Dehez M, Manon A, Nguyen TXQ, Gomez-Panzani EL, et al. Population Pharmacokinetic Analysis of Lanreotide Autogel/Depot in the Treatment of Neuroendocrine Tumors:Pooled Analysis of Four Clinical Trials. Clin Pharmacokinet. 2016; 55(4):461±473. https://doi.org/10.1007/s40262-015-0329-4 PMID: 26416534
    View at Publisher | View at Google Scholar
  17. Ledzewicz U, Moore H. Dynamical Systems Properties of a Mathematical Model for the Treatment ofCML. NATO Adv Sci Inst Ser E Appl Sci. 2016; 6(10):291.
    View at Publisher | View at Google Scholar
  18. Almeida J, MendoncËa T, Rocha P. A simplified control scheme for the Depth of Anesthesia. IFACPapersOnLine. 2016; 49(5):230±235. https://doi.org/10.1016/j.ifacol.2016.07.118
    View at Publisher | View at Google Scholar
  19. Almeida J, MendoncËa T, Rocha P. A Simplified Control Approach for the Neuromuscular Blockade Level. In: CONTROLO 2016. Lecture Notes in Electrical Engineering. Springer, Cham; 2017. p. 37±44.
    View at Publisher | View at Google Scholar
  20. He Q, Zhu J, Dingli D, Foo J, Leder KZ. Optimized Treatment Schedules for Chronic Myeloid Leukemia.PLoS Comput Biol. 2016; 12(10):e1005129.
    View at Publisher | View at Google Scholar
  21. Irurzun-Arana I, Janda A, Ardanza-Trevijano S, TrocoÂniz IF (2018) Optimal dynamic control approach in a multi-objective therapeutics cenario: Application to drug delivery in the treatment of prostate cancer. PLoS Comput Biol14(4): e1006087.https://doi.org/10.1371/journal.pcbi.1006087
    View at Publisher | View at Google Scholar
  22. Dhooge, A., Govearts, W., and Kuznetsov, A. Y., MATCONT: “A Matlab package for numerical bifurcation analysis of ODEs”, ACM transactions on Mathematical software 29(2) pp. 141-164, 2003.
    View at Publisher | View at Google Scholar
  23. Dhooge, A.,W. Govaerts; Y. A. Kuznetsov, W. Mestrom, and A. M. Riet , “CL_MATCONT”; A continuation toolbox in Matlab, 2004.
    View at Publisher | View at Google Scholar
  24. Kuznetsov,Y.A. “Elements of applied bifurcation theory” .Springer,NY, 1998.
    View at Publisher | View at Google Scholar
  25. Kuznetsov,Y.A.(2009).”Five lectures on numerical bifurcation analysis” ,Utrecht University,NL., 2009.
    View at Publisher | View at Google Scholar
  26. Govaerts, w. J. F., “Numerical Methods for Bifurcations of Dynamical Equilibria”, SIAM, 2000.
    View at Publisher | View at Google Scholar
  27. Flores-Tlacuahuac, A. Pilar Morales and Martin Riveral Toledo; “Multiobjective Nonlinear model predictive control of a class of chemical reactors” . I & EC research; 5891-5899, 2012.
    View at Publisher | View at Google Scholar
  28. Hart, William E., Carl D. Laird, Jean-Paul Watson, David L. Woodruff, Gabriel A. Hackebeil, Bethany L. Nicholson, and John D. Siirola. “Pyomo – Optimization Modeling in Python” Second Edition. Vol. 67.
    View at Publisher | View at Google Scholar
  29. Wächter, A., Biegler, L. “On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming”. Math. Program. 106, 25–57 (2006). https://doi.org/10.1007/s10107-004-0559-y
    View at Publisher | View at Google Scholar
  30. Tawarmalani, M. and N. V. Sahinidis, “A polyhedral branch-and-cut approach to global optimization”, Mathematical Programming, 103(2), 225-249, 2005
    View at Publisher | View at Google Scholar
  31. Sridhar LN. (2024) Coupling Bifurcation Analysis and Multiobjective Nonlinear Model Predictive Control. Austin Chem Eng. 2024; 10(3): 1107.
    View at Publisher | View at Google Scholar
  32. Upreti, Simant Ranjan(2013); Optimal control for chemical engineers. Taylor and Francis.
    View at Publisher | View at Google Scholar
img

Harry Brooks

journal of Clinical Case Studies and Review Reports. I would be very delighted to submit my testimonial regarding the reviewer board and the editorial office.the reviewer board were accurate and helpful regarding anu modifications for my manuscript,and the editorial office were very helpful and supportive in contacting and monitoring with any update and offering help.it was my pleasure to contribute with your promising journal and i am looking forward for more collaboration.

img

Mark

My testimonial covering : the peer review process is qucick and effective,the support from the editorial office is very professional and friendly, quality of the Clinical Case Studies and Review Reports is scientific and publishers research.

img

Sinisa franjic

i would like to thank the editorial team for their timely responses and consideration in the publication of my paper . I would encourage to publish there research in ScienceFrontier.

img

Ritu Tiwari

I am pleased to submit my testimonials regarding the reviewer board and the editorial office. As a peer reviewer for the manuscript titled “A Novel Dissolution Method for Simultaneous Estimation of sennoside A and Sennoside B in Senna Tablet,” I was consistently impressed by the reviewers’ thorough analysis, insightful feedback, and unwavering commitment to enhancing the quality of the work. Their reviews were comprehensive and characterized by a respectful and collaborative approach, providing valuable suggestions that significantly improved the paper's outcome. Their dedication to the peer review process demonstrated their expertise and steadfast pursuit of excellence.

img

Qader Bawerdi

With all due respect, I would like to express my opinion on the peer review, editorial support, and the quality of the journal as follows: The peer review was conducted quickly and with great care, and my article was accepted for publication in less than a week. The editorial support regarding the status of the article process was excellent, and they informed me every day until the acceptance of the current status of the article version, and regarding how to answer questions, the editorial support was excellent, timely, and friendly, and they answered questions as soon as possible and did not hesitate. The quality of the journal was excellent and it made me proud to be acquainted with the journal, and I sincerely look forward to extensive scientific collaborations in any field. I hope for increasing success and pride for the International Journal of Social Science Research and Review and all scientific and knowledge-based communities. Thank you

img

Bhuvanagiri Sathya Sindhuja

"I would like to express my sincere appreciation for the opportunity to contribute to this esteemed journal. The publication process was smooth, well-coordinated, and the peer reviewers deemed highly professional. The editorial team demonstrated exceptional diligence and support at every stage, ensuring a seamless experience from submission to final publication. I am truly honored to be featured in such a reputable platform and look forward to future collaborations."

img

Safana Abdullah Algutaini

Testimonial for the Journal of Biomedical Research and Clinical Advancements It was a truly rewarding experience publishing our study, "Single-Surgeon Outcomes of Left Ventricular Aneurysm Repair in Wartime Syria: A 10-Year Retrospective Study at Damascus University Cardiac Surgery Hospital," with the Journal of Biomedical Research and Clinical Advancements. The editorial and peer-review process was both rigorous and efficient, demonstrating a high standard of academic integrity and scientific scrutiny. The journal’s commitment to open access and global health equity is evident in its support of research emerging from conflict-affected and resource-limited settings—making our work not only visible but impactful. The professionalism of the editorial team, the speed of communication, and the clarity of submission guidelines all contributed to a smooth publication process. We were particularly impressed by the quality of the publication layout and the prompt indexing of our article, which enhances its accessibility to clinicians, researchers, and policymakers worldwide. We are proud to have contributed to this journal and highly recommend it to fellow researchers seeking a reputable platform to disseminate clinically significant and globally relevant findings.