Impulsive zone model predictive control (iZMPC) for therapeutic treatments: Application to HIV dynamics

Rivadeneira, Pablo S.; Caicedo, Michelle A.; Ferramosca, Antonio; González, Alejandro H.

doi:10.1109/cdc.2017.8264260

Cited by 13 publications

(27 citation statements)

References 21 publications

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“…Mathematical description of IL-2 therapy After intravenous administration of a drug, instantaneous jumps are observed in the drug concentration in plasma and target organ (22). In the framework of mathematical modeling, systems with discontinuities in their dynamics can be categorized as impulsive systems and allows for application of control engineering design tools (19,20,(23)(24)(25)(26)(27)(28)(29)(30)(31). Among these methods, model predictive control (MPC) techniques have been widely used (19,20,(23)(24)(25)(26)(27)(28) due to their ability to consider systemic constraints, which confine the dynamics of the system variables or the external control input.…”

Section: Methodsmentioning

confidence: 99%

“…This process is repeated at each next drug administration time point. In this study, we employed the iZMPC algorithm (19,20), an advanced version of MPC, in which system dynamics are moved toward a desired equilibrium set or space (instead to an equilibrium point) no matter which point inside the set.…”

Section: Methodsmentioning

confidence: 99%

“…In what follows, we delineate the preliminary steps toward using iZMPC. A detailed description, the mathematical basis of the steps and some other biological application of iZMPC can be found in (19,20,24,25).…”

Section: Supplemental Information (Si)mentioning

confidence: 99%

“…control scheme to calculate a time-resolved adaptive IL-2 dosing for each individual in silico patient. This scheme is based on the "impulsive zone model predictive control (iZMPC)" algorithm (19,20). The adaptive algorithm calculates proper IL-2 doses at each injection episode based on (1) feedback from the current status of the patient's immune response, (2) prediction of how the immune response progresses according to the mathematical model for a limited time horizon, and (3) predefined desired range and constraints for the immune variables (Tconvs, Tregs and IL-2).…”

Section: Introductionmentioning

confidence: 99%

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An adaptive control scheme for Interleukin-2 therapy

Khailaie

Montaseri

Meyer‐Hermann

2020

Preprint

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Regulatory T cells (Treg) are suppressor cells that control self-reactive and excessive effector conventional helper T cell (Tconv) responses. Breakdown of the balance between Tregs and Tconvs is a hallmark of autoimmune and inflammatory diseases. Due to the positive dependency of both populations on Interleukin-2 (IL-2), it is subtle leverage to restore the healthy immune balance. By employing a mechanistic mathematical model, we studied the IL-2 therapy in order to increase and stabilize Treg population and restrict inflammatory Tconv response. We introduced an adaptive control strategy to design the minimal IL-2 dosage. This adaptive strategy allows for an individualized therapy based on the feedback of immune kinetics of the patient. Our in silico results suggest that a minimal Treg population is required to restrict the transient side-effect of IL-2 injections on the effector Tconv response. The combination of IL-2 and adoptive Treg transfer therapies is able to limit this side effect in our simulations. Implications of our in silico results are discussed in the context of autoimmunity and transplantation.

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Supplemental Information (Si)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

An adaptive control scheme for Interleukin-2 therapy

Khailaie

Montaseri

Meyer‐Hermann

2020

Preprint

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“…Between-hosts models have helped to propose new vaccination strategies or support public health strategies [34,16,32]. On the other hand, for within-host infection, mathematical modeling has been used to capture the dynamics of different infectious diseases inside the host to understand the interaction of the pathogen and the immune system, as well as scheduling of therapies [2,22,11,9,33]. Most mathematical models to represent microbes dynamics are shown to be based on variations of the classical Verhulst logistic growth equation.…”

Section: Introductionmentioning

confidence: 99%

Switching Logistic Maps to Design Cycling Approaches Against Antimicrobial Resistance

Hernandez‐Vargas

Parra‐Rojas

Olaru

2020

Preprint

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Antimicrobial resistance is a major threat to global health and food security today. Scheduling cycling therapies by targeting phenotypic states associated to specific mutations can help us to eradicate pathogenic variants in chronic infections. In this paper, we introduce a logistic switching model in order to abstract mutation networks of collateral resistance. We found particular conditions for which unstable zero-equilibrium of the logistic maps can be stabilized through a switching signal. That is, persistent populations can be eradicated through tailored switching regimens.Starting from an optimal-control formulation, the switching policies show their potential in the stabilization of the zero-equilibrium for dynamics governed by logistic maps. However, employing such switching strategies, deserve a specific characterization in terms of limit behaviour. Ultimately, we use evolutionary and control algorithms to find either optimal and sub-optimal switching policies. Simulations results show the applicability of Parrondo's Paradox to design cycling therapies against drug resistance.

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Inverse optimal control for positive impulsive systems toward personalized therapeutic regimens

Hernandez‐Vargas¹,

Hernández-Mejía

Hernández‐González

2022

Optim Control Appl Methods

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Infectious diseases are latent threats to humankind. Control theoretical approaches can help practitioners to advance the scheduling of drugs. For the case of infectious diseases, it is not possible to keep continuous flow of drug administration over all time-steps, thus the action of the control input has to be restricted at some of the kth instants. This paper presents the adaptation of inverse optimal control to positive impulsive systems in discrete-time to schedule therapies. The properties of positive systems are used to simplify the control design. Thus, the problem of scheduling therapies in infectious diseases is illustrated with influenza and COVID-19. Numerical results show the applicability of the control algorithms.

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Impulsive zone model predictive control (iZMPC) for therapeutic treatments: Application to HIV dynamics

Cited by 13 publications

References 21 publications

An adaptive control scheme for Interleukin-2 therapy

An adaptive control scheme for Interleukin-2 therapy

Switching Logistic Maps to Design Cycling Approaches Against Antimicrobial Resistance

Inverse optimal control for positive impulsive systems toward personalized therapeutic regimens

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