Nonlinear Adaptive Optimal Controller Design for Anti-Angiogenic Tumor Treatment
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Updated: Aug 9, 2025
Transfer of Manipulated Tumor-associated Neutrophils into Tumor-Bearing Mice to Study their Angiogenic Potential In Vivo
Published on: July 20, 2019
Nitendra Nath1, Irfan Kil2, Ugur Hasirci3
1Ford Motor Company, Dearborn, MI 48126, USA.
Abstract:
Angiogenesis is an important process in tumor growth as it represents the regime when the tumor recruits blood vessels from the surrounding tissue to support further tumor growth. Anti-angiogenic treatments aim to shrink the tumor by interrupting the vascularization of the tumor; however, the anti-angiogenic agents are costly and the tumor response to these agents is nonlinear. Simple dosing schemes, e.g., a constant dose, may yield higher cost or lower efficacy than an approach that considers the tumor system dynamics. Hence, in this study, the administration of anti-angiogenic treatment is considered as a nonlinear control problem. The main aim of the controller design is to optimize the anti-angiogenic tumor therapy, specifically, to minimize the tumor volume and drug dose. Toward this aim, two nonlinear optimal controllers are presented. The first controller ensures exponential tracking of a desired, optimal tumor volume profile under the assumption that all parameters in the system model are known. The second controller, on the other hand, assumes all the parameters are unknown and provides asymptotic tracking. Both controllers take pharmacokinetics and pharmacodynamics into account, as well as the carrying capacity of the vascular network. Lyapunov based arguments are used to design the controllers, using stability arguments, and numerical simulation results are presented to demonstrate the effectiveness of the proposed method.
Insights
This study optimizes anti-angiogenic therapy for cancer by developing nonlinear controllers to minimize tumor volume and drug dosage. These controllers account for tumor dynamics, improving treatment efficacy and reducing costs.
Area of Science:
- Oncology
- Control Theory
- Pharmacology
Background:
- Tumor growth relies on angiogenesis, the formation of new blood vessels.
- Anti-angiogenic therapies aim to inhibit tumor vascularization but face challenges with cost and nonlinear responses.
- Optimizing drug delivery is crucial for effective cancer treatment.
Purpose of the Study:
- To design nonlinear optimal controllers for anti-angiogenic tumor therapy.
- To minimize both tumor volume and the required drug dose.
- To develop adaptive control strategies for unknown system parameters.
Main Methods:
- Formulating anti-angiogenic treatment as a nonlinear control problem.
- Designing two nonlinear optimal controllers: one for known parameters and one for unknown parameters.
- Utilizing Lyapunov-based stability arguments for controller design.
- Incorporating pharmacokinetics, pharmacodynamics, and vascular capacity into the models.
Main Results:
- Demonstrated the effectiveness of proposed controllers through numerical simulations.
- Achieved exponential tracking of optimal tumor volume profiles with known parameters.
- Provided asymptotic tracking for systems with unknown parameters.
- Showcased optimized tumor volume and drug dose reduction.
Conclusions:
- Nonlinear optimal control offers a promising approach to enhance anti-angiogenic cancer therapy.
- Adaptive controllers can effectively manage treatment when system parameters are uncertain.
- Optimized dosing strategies can improve treatment efficacy and cost-effectiveness.
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