Optimal Impulsive Control for Cancer Therapy

Belfo, João P.; Lemos, João M.

doi:10.1007/978-3-030-50488-5

Cited by 6 publications

(10 citation statements)

References 19 publications

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“…Nonetheless, two issues arise in this case, it is not biologically feasible to constantly applied an immunotherapy treatment to a cancer patient and it is evident that the solution of the effector T cells

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256,596 cells/μL (a concentration close to that of the the maximum carrying capacity of the CML cancer cells) which could produce adverse events in the patient’s health [ 36 ]. Hence, in order to avoid the latter, numerous authors have proposed different treatment strategies to apply therapies such as chemotherapy, radiotherapy and immunotherapy by time intervals or in the form of periodic oscillations, one can see [ 14 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 ]. Thus, our hypothesis is as follows: Daily applications for a finite period of time of the immunotherapy treatment will decrease the CML cancer cells concentration below a critical threshold under which it is possible to ensure the complete eradication of the disease.…”

Section: Discussion and In Silico Experimentationmentioning

confidence: 99%

Personalized Immunotherapy Treatment Strategies for a Dynamical System of Chronic Myelogenous Leukemia

Valle

Coria

Plata

2021

Cancers

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This paper is devoted to exploring personalized applications of cellular immunotherapy as a control strategy for the treatment of chronic myelogenous leukemia described by a dynamical system of three first-order ordinary differential equations. The latter was achieved by applying both the Localization of Compact Invariant Sets and Lyapunov’s stability theory. Combination of these two approaches allows us to establish sufficient conditions on the immunotherapy treatment parameter to ensure the complete eradication of the leukemia cancer cells. These conditions are given in terms of the system parameters and by performing several in silico experimentations, we formulated a protocol for the therapy application that completely eradicates the leukemia cancer cells population for different initial tumour concentrations. The formulated protocol does not dangerously increase the effector T cells population. Further, complete eradication is considered when solutions go below a finite critical value below which cancer cells cannot longer persist; i.e., one cancer cell. Numerical simulations are consistent with our analytical results.

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Section: Discussion and In Silico Experimentationmentioning

confidence: 99%

Personalized Immunotherapy Treatment Strategies for a Dynamical System of Chronic Myelogenous Leukemia

Valle

Coria

Plata

2021

Cancers

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“…Furthermore, we have fixed the chances to execute the impulsive interventions, while they can also become additional variables to be optimized. Theoretically, the adaptive timing approach that has been employed for impulse control problems of ordinary differential equations arising in cancer therapy [15] can be extended to our case. However, its computational cost needs to be carefully evaluated.…”

Section: Discussionmentioning

confidence: 99%

“…In summary, to compute the optimal control * u , what we should do is to solve the adjoint equation(s) (12) backward in time starting from the terminal condition (15) with the internal boundary conditions (32) and (38). The optimal control is given by (36) as a quantity determined from the adjoint variables ( ) i p .…”

Section: Optimality Conditionmentioning

confidence: 99%

A simple PDE-constrained Optimization Problem to Evaluate the Strategy for Fishery Resource Transportation

Yoshioka

Tanaka

Horinouchi

et al. 2021

Stochastic Systems Theory and its Applications (SSS)

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We present a new impulse control problem of degenerate parabolic Fokker-Planck equations that govern stochastic growth dynamics of biological resource from the viewpoint of probability density functions of the body weight. The problem we focus on is impulsively transporting a resource population from a habitat to other habitat(s), which stems from a recent engineering problem in a river in Japan. A formula of the optimal control is theoretically derived with the help of an adjoint equation method. A remarkable point is simplicity of the problem such that finding the optimal control can be achieved by only solving an adjoint equation. We present a demonstrative computational example of Ayu sweetfish Plecoglossus altivelis altivelis utilizing a very recent Weighted Essentially Non-Oscillatory method.

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“…Various schemes have been proposed in the literature, which aim to optimize the time instants of the treatment, the amount of drug administered to the patient, or even both [1,2]. Some recent results involve impulsive systems, reinforcement learning, or other model-based approaches [3][4][5][6]. e proper mathematical treatment of the problem often involves impulsive control actions, which has been researched extensively [7,8] and has vast importance in cases where the drug is administered by injections.…”

Section: Introductionmentioning

confidence: 99%

“…e main contribution of our work is that we show the viability of model-based metronomic therapy in in vivo using mice experiments. Since the vast majority of current research in model-based chemotherapy optimization mostly demonstrates in silico results [2,3,10], an experimental validation showing the feasibility of the approach can bring more attention to this field from other researchers.…”

Section: Introductionmentioning

confidence: 99%

Experimental Closed‐Loop Control of Breast Cancer in Mice

et al. 2022

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Cancer therapy optimization is an issue that can be solved using the control engineering approach. An optimal therapy generation algorithm is presented and tested using a tractable mouse model of breast cancer. The optimized therapeutic protocol is calculated in a closed-loop manner at fixed time instants, twice in a week. The controller consists of a nonlinear model predictive controller which uses the state estimation of a moving horizon estimator. The estimator also computes parameter estimates of the prediction model such that the time varying nature of tumor evolution can be captured. Results show that remission can be induced in a 28-day interval using the algorithm.

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Optimal Impulsive Control for Cancer Therapy

Cited by 6 publications

References 19 publications

Personalized Immunotherapy Treatment Strategies for a Dynamical System of Chronic Myelogenous Leukemia

Personalized Immunotherapy Treatment Strategies for a Dynamical System of Chronic Myelogenous Leukemia

A simple PDE-constrained Optimization Problem to Evaluate the Strategy for Fishery Resource Transportation

Experimental Closed‐Loop Control of Breast Cancer in Mice

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