Discrete-time MPC for switched systems with applications to biomedical problems

Switched systems in which the manipulated control action is the time-dependingswitching signal describe many engineering problems, mainly related to biomedical applications. In such a context, to control the system means to select an autonomous system - at each time step - among a given finite family. Even when this selection can be done by solving a Dynamic Programming (DP) problem, such a solution is often difficult to apply, and state/control constraints cannot be explicitly considered. In this work a new set-based Model Predictive Control (MPC) strategy is proposed to handle switched systems in a tractable form. The optimization problem at the core of the MPC formulation consists in an easy-to-solve mixed-integer optimization problem, whose solution is applied in a receding horizon way. Two biomedical applications are simulated to test the controller: (i) the drug schedule to attenuate the effect of viralmutation and drugs resistance on the viral load, and (ii) the drug schedule for Triple Negative breast cancer treatment. The numerical results suggest that the proposed strategy outperform the schedule for available treatments.Fil: Anderson, Alejandro Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; ArgentinaFil: González, Alejandro Hernán. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; ArgentinaFil: Ferramosca, Antonio. Universidad Tecnológica Nacional; ArgentinaFil: Hernandez Vargas, Esteban Abelardo. Frankfurt Institute For Advanced Studies-fias; Alemani

Discrete-time switching MPC with applications to mitigate resistance in viral infections

Many engineering applications can be described as switched linear systems, in which the manipulated control action is the time-dependent switching signal. In such a case, the control strategy must select a linear autonomous system at each time step, among a finite number of them. Even when this selection can be done by solving a Dynamic Programming (DP) problem, the implementation of such a solution is often difficult and state/control constraints cannot be explicitly accounted for. In this paper, a new set-based Model Predictive Control (MPC) strategy is presented to handle switched linear systems in a tractable form. The optimization problem at the core of the MPC formulation consists of an easy-to-solve mixed-integer optimization problem, whose solution is applied in a receding horizon way. The medical application of viral mutation and its respective drug resistance is addressed to acute and chronic infections. The objective is to attenuate the effect of mutations on the total viral load, and the numerical results suggested that the proposed strategy outperforms the schedule for available treatments.Fil: Anderson, Alejandro Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; ArgentinaFil: González, Alejandro Hernán. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; ArgentinaFil: Ferramosca, Antonio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; ArgentinaFil: Hernandez Vargas, Esteban Abelardo. Frankfurt Institute For Advanced Studies-fias; Alemani

Optimal control strategies to tailor antivirals for acute infectious diseases in the host

Several mathematical models in SARS-CoV-2 have shown how target-cell model can help to understand the spread of the virus in the host and how potential candidates of antiviral treatments can help to control the virus. Concepts as equilibrium and stability show to be crucial to qualitative determine the best alternatives to schedule drugs, according to effectivity in inhibiting the virus infection and replication rates. Important biological events such as rebounds of the infections (when antivirals are incorrectly interrupted) can also be explained by means of a dynamic study of the target-cell model. In this work a full characterization of the dynamical behavior of the target-cell models under control actions is made and, based on this characterization, the optimal fixeddose antiviral schedule that produces the smallest amount of dead cells (without viral load rebounds) is computed. Several simulation results - performed by considering real patient data - show the potential benefits of both, the model characterization and the control strategy.Fil: Perez, Mara Isabel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; ArgentinaFil: Abuin, Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; ArgentinaFil: Actis, Marcelo Jesús. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe; Argentina. Universidad Nacional del Litoral. Facultad de Ingeniería Química; ArgentinaFil: Ferramosca, Antonio. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Università Degli Studi Di Bergamo; ItaliaFil: Hernandez Vargas, Esteban Abelardo. Universidad Nacional Autónoma de México; MéxicoFil: González, Alejandro Hernán. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; Argentin

A control theoretic approach to mitigate viral escape in HIV

A very important scientific advance was the identification of HIV as a causative agent for AIDS. HIV infection typically involves three main stages: a primary acute infection, a long asymptomatic period and a final increase in viral load with a simultaneous collapse in healthy CD4+T cell count during which AIDS appears. Motivated by the worldwide impact of HIV infection on health and the difficulties to test in vivo or in vitro the different hypothesis which help us to understand the infection, we study the problem from a control theoretic perspective. We present a deterministic ordinary differential equation model that is able to represent the three main stages in HIV infection. The mechanism behind this model suggests that macrophages could be long-term latent reservoirs for HIV and may be important in the progression to AIDS. To avoid or slow this progression to AIDS, antiretroviral drugs were introduce in the late eighties. However, these drugs are not always successful causing a viral rebound in the patient. This rebound is associated with the emergence of resistance mutations resulting in genotypes with reduced susceptibility to one or more of the drugs. To explore antiretroviral effects in HIV, we extend the mathematical model to include the impact of therapy and suggest different mutation models. Under some additional assumptions the model can be seen to be a positive switched dynamic system. Consequently we test clinical treatments and allow preliminary control analysis for switching treatments. After introducing the biological background and models, we formulate the problem of treatment scheduling to mitigate viral escape in HIV. The goal of this therapy schedule is to minimize the total viral load for the period of treatment. Using optimal control theory a general solution in continuous time is presented for a particular case of switched positive systems with a specific symmetry property. In this case the optimal switching rule is on a sliding surface. For the discrete-time version several algorithms based on linear programming are proposed to reduce the computational burden whilst still computing the optimal sequence. Relaxing the demand of optimality, we provide a result on state-feedback stabilization of autonomous positive switched systems through piecewise co-positive Lyapunov functions in continuous and discrete time. The performance might not be optimal but provides a tractable solution which guarantees some level of performance. Model predictive control (MPC) has been considered as an important suboptimal technique for biological applications, therefore we explore this technique to the viral escape mitigation problem

Observers for biological systems

Cell counts and viral load serve as major clinical indicators to provide treatment in the course of a viral infection. Monitoring these markers in patients can be expensive and some of them are not feasible to perform. An alternative solution to this problem is the observer based estimation. Several observer schemes require the previous knowledge of the model and parameters, such condition is not achievable for some applications. A linear output assumption is required in the majority of the current works. Nevertheless, the output of the system can be a nonlinear combination of the state variables. This paper presents a discrete-time neural observer for non-linear systems with a non-linear output; the mathematical model is assumed to be unknown. The observer is trained on-line with the extended Kalman filter (EKF)-based algorithm and the respective stability analysis based on the Lyapunov approach is addressed. We applied different observers to the estimation problem in HIV infection; that is state estimation of the viral load, and the number of infected and non-infected CD4+ T cells. Simulation results suggest a good performance of the proposed neural observer and the applicability to biological systems. © 2013 Elsevier B.V. All rights reserved

High-resolution epidemic simulation using within-host infection and contact data

Abstract Background Recent epidemics have entailed global discussions on revamping epidemic control and prevention approaches. A general consensus is that all sources of data should be embraced to improve epidemic preparedness. As a disease transmission is inherently governed by individual-level responses, pathogen dynamics within infected hosts posit high potentials to inform population-level phenomena. We propose a multiscale approach showing that individual dynamics were able to reproduce population-level observations. Methods Using experimental data, we formulated mathematical models of pathogen infection dynamics from which we simulated mechanistically its transmission parameters. The models were then embedded in our implementation of an age-specific contact network that allows to express individual differences relevant to the transmission processes. This approach is illustrated with an example of Ebola virus (EBOV). Results The results showed that a within-host infection model can reproduce EBOV’s transmission parameters obtained from population data. At the same time, population age-structure, contact distribution and patterns can be expressed using network generating algorithm. This framework opens a vast opportunity to investigate individual roles of factors involved in the epidemic processes. Estimating EBOV’s reproduction number revealed a heterogeneous pattern among age-groups, prompting cautions on estimates unadjusted for contact pattern. Assessments of mass vaccination strategies showed that vaccination conducted in a time window from five months before to one week after the start of an epidemic appeared to strongly reduce epidemic size. Noticeably, compared to a non-intervention scenario, a low critical vaccination coverage of 33% cannot ensure epidemic extinction but could reduce the number of cases by ten to hundred times as well as lessen the case-fatality rate. Conclusions Experimental data on the within-host infection have been able to capture upfront key transmission parameters of a pathogen; the applications of this approach will give us more time to prepare for potential epidemics. The population of interest in epidemic assessments could be modelled with an age-specific contact network without exhaustive amount of data. Further assessments and adaptations for different pathogens and scenarios to explore multilevel aspects in infectious diseases epidemics are underway

Switching strategies to mitigate HIV mutation

HIV mutates rapidly and may develop resistance to specific drug therapies. There is no general agreement on how to optimally schedule the available treatments for mitigating the effects of mutations. With a switched positive linear system, we examined different control strategies applied to a higher order nonlinear mutation model. Simulation results suggest that model predictive control could outperform the common clinical treatment recommendations. This brief is a step forward to develop further tools for helping the practitioners to find the optimal treatment schedule

Computational Study to Determine When to Initiate and Alternate Therapy in HIV Infection.

HIV is a widespread viral infection without cure. Drug treatment has transformed HIV disease into a treatable long-term infection. However, the appearance of mutations within the viral genome reduces the susceptibility of HIV to drugs. Therefore, a key goal is to extend the time until patients exhibit resistance to all existing drugs. Current HIV treatment guidelines seem poorly supported as practitioners have not achieved a consensus on the optimal time to initiate and to switch antiretroviral treatments. We contribute to this discussion with predictions derived from a mathematical model of HIV dynamics. Our results indicate that early therapy initiation (within 2 years postinfection) is critical to delay AIDS progression. For patients who have not received any therapy during the first 3 years postinfection, switch in response to virological failure may outperform proactive switching strategies. In case that proactive switching is opted, the switching time between therapies should not be larger than 100 days. Further clinical trials are needed to either confirm or falsify these predictions

Oseltamivir PK/PD Modeling and Simulation to Evaluate Treatment Strategies against Influenza-Pneumococcus Coinfection.

Influenza pandemics and seasonal outbreaks have shown the potential of Influenza A virus (IAV) to enhance susceptibility to a secondary infection with the bacterial pathogen Streptococcus pneumoniae (Sp). The high morbidity and mortality rate revealed the poor efficacy of antiviral drugs and vaccines to fight IAV infections. Currently, the most effective treatment for IAV is by antiviral neuraminidase inhibitors. Among them, the most frequently stockpiled is Oseltamivir which reduces viral release and transmission. However, effectiveness of Oseltamivir is compromised by the emergence of resistant IAV strains and secondary bacterial infections. To date, little attention has been given to evaluate how Oseltamivir treatment strategies alter Influenza viral infection in presence of Sp coinfection and a resistant IAV strain emergence. In this paper we investigate the efficacy of current approved Oseltamivir treatment regimens using a computational approach. Our numerical results suggest that the curative regimen (75 mg) may yield 47% of antiviral efficacy and 9% of antibacterial efficacy. An increment in dose to 150 mg (pandemic regimen) may increase the antiviral efficacy to 49% and the antibacterial efficacy to 16%. The choice to decrease the intake frequency to once per day is not recommended due to a significant reduction in both antiviral and antibacterial efficacy. We also observe that the treatment duration of 10 days may not provide a clear improvement on the antiviral and antibacterial efficacy compared to 5 days. All together, our in silico study reveals the success and pitfalls of Oseltamivir treatment strategies within IAV-Sp coinfection and calls for testing the validity in clinical trials