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Khalili P, Vatankhah R. Optimal control design for drug delivery of immunotherapy in chemoimmunotherapy treatment. Comput Methods Programs Biomed 2023; 229:107248. [PMID: 36463673 DOI: 10.1016/j.cmpb.2022.107248] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/17/2022] [Revised: 11/04/2022] [Accepted: 11/15/2022] [Indexed: 06/17/2023]
Abstract
BACKGROUND AND OBJECTIVE There are various approaches to control a mathematical dynamic of cancer, each of which is suitable for a special goal. Optimal control is considered as an applicable method to calculate the minimum necessary drug delivery in such systems. METHODS In this paper, a mathematical dynamic of cancer is proposed considering tumor cells, natural killer cells, CD8+T cells, circulating lymphocytes, IL-2 cytokine and Regulatory T cells as the system states, and chemotherapy, IL-2 and activated CD8+T cells injection rate as the control signals. After verifying the proposed mathematical model, the importance of the drug delivery timing and the effect of cancer cells initial condition are discussed. Afterwards, an optimal control is designed by defining a proper cost function with the goal of minimizing the number of tumor cells, and two immunotherapy drug amounts during treatment CONCLUSIONS: Results show that inappropriate injection of immunotherapy time schedule and the number of initial conditions of cancer cells might result in chemoimmunotherapy failure and auxiliary treatment must be prescribed to decrease tumor size before any treatment takes place. The obtained optimal control signals show that with lower amount of drug delivery and a suitable drug injection time schedule, tumor cells can be eliminated while a fixed immunotherapy time schedule protocol fails with larger amount of drug injection. This conclusion can be utilized with the aim of personalizing drug delivery and designing more accurate clinical trials based on the improved model simulations in order to save cost and time.
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Affiliation(s)
- Pariya Khalili
- PhD Candidate, School of Mechanical Engineering, Shiraz University, Shiraz, Iran
| | - Ramin Vatankhah
- Associated Professor, School of Mechanical Engineering, Shiraz University, Shiraz, Iran.
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Tallon J, Browning B, Couenne F, Bordes C, Venet F, Nony P, Gueyffier F, Moucadel V, Monneret G, Tayakout-Fayolle M. Dynamical modeling of pro- and anti-inflammatory cytokines in the early stage of septic shock. In Silico Biol 2020; 14:101-121. [PMID: 32597796 PMCID: PMC7505012 DOI: 10.3233/isb-200474] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Abstract
A dynamical model of the pathophysiological behaviors of IL18 and IL10 cytokines with their receptors is tested against data for the case of early sepsis. The proposed approach considers the surroundings (organs and bone marrow) and the different subsystems (cells and cyctokines). The interactions between blood cells, cytokines and the surroundings are described via mass balances. Cytokines are adsorbed onto associated receptors at the cell surface. The adsorption is described by the Langmuir model and gives rise to the production of more cytokines and associated receptors inside the cell. The quantities of pro and anti-inflammatory cytokines present in the body are combined to give global information via an inflammation level function which describes the patient’s state. Data for parameter estimation comes from the Sepsis 48 H database. Comparisons between patient data and simulations are presented and are in good agreement. For the IL18/IL10 cytokine pair, 5 key parameters have been found. They are linked to pro-inflammatory IL18 cytokine and show that the early sepsis is driven by components of inflammatory character.
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Affiliation(s)
- J Tallon
- Université Claude Bernard Lyon 1, CNRS, LAGEPP UMR 5007, Villeurbanne, France
| | - B Browning
- Université Claude Bernard Lyon 1, CNRS, LAGEPP UMR 5007, Villeurbanne, France
| | - F Couenne
- Université Claude Bernard Lyon 1, CNRS, LAGEPP UMR 5007, Villeurbanne, France
| | - C Bordes
- Université Claude Bernard Lyon 1, CNRS, LAGEPP UMR 5007, Villeurbanne, France
| | - F Venet
- Hospices Civils de Lyon, LYON Cedex 03 - France
| | - P Nony
- Université Claude Bernard Lyon 1, CNRS, LBBE UMR 5558, Lyon, France
| | - F Gueyffier
- Université Claude Bernard Lyon 1, CNRS, LBBE UMR 5558, Lyon, France
| | | | - G Monneret
- Hospices Civils de Lyon, LYON Cedex 03 - France
| | - M Tayakout-Fayolle
- Université Claude Bernard Lyon 1, CNRS, LAGEPP UMR 5007, Villeurbanne, France
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Angaroni F, Graudenzi A, Rossignolo M, Maspero D, Calarco T, Piazza R, Montangero S, Antoniotti M. An Optimal Control Framework for the Automated Design of Personalized Cancer Treatments. Front Bioeng Biotechnol 2020; 8:523. [PMID: 32548108 PMCID: PMC7270334 DOI: 10.3389/fbioe.2020.00523] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/06/2020] [Accepted: 05/01/2020] [Indexed: 12/17/2022] Open
Abstract
One of the key challenges in current cancer research is the development of computational strategies to support clinicians in the identification of successful personalized treatments. Control theory might be an effective approach to this end, as proven by the long-established application to therapy design and testing. In this respect, we here introduce the Control Theory for Therapy Design (CT4TD) framework, which employs optimal control theory on patient-specific pharmacokinetics (PK) and pharmacodynamics (PD) models, to deliver optimized therapeutic strategies. The definition of personalized PK/PD models allows to explicitly consider the physiological heterogeneity of individuals and to adapt the therapy accordingly, as opposed to standard clinical practices. CT4TD can be used in two distinct scenarios. At the time of the diagnosis, CT4TD allows to set optimized personalized administration strategies, aimed at reaching selected target drug concentrations, while minimizing the costs in terms of toxicity and adverse effects. Moreover, if longitudinal data on patients under treatment are available, our approach allows to adjust the ongoing therapy, by relying on simplified models of cancer population dynamics, with the goal of minimizing or controlling the tumor burden. CT4TD is highly scalable, as it employs the efficient dCRAB/RedCRAB optimization algorithm, and the results are robust, as proven by extensive tests on synthetic data. Furthermore, the theoretical framework is general, and it might be applied to any therapy for which a PK/PD model can be estimated, and for any kind of administration and cost. As a proof of principle, we present the application of CT4TD to Imatinib administration in Chronic Myeloid leukemia, in which we adopt a simplified model of cancer population dynamics. In particular, we show that the optimized therapeutic strategies are diversified among patients, and display improvements with respect to the current standard regime.
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Affiliation(s)
- Fabrizio Angaroni
- Department of Informatics, Systems and Communication, University of Milan-Bicocca, Milan, Italy
| | - Alex Graudenzi
- Department of Informatics, Systems and Communication, University of Milan-Bicocca, Milan, Italy.,Institute of Molecular Bioimaging and Physiology, Consiglio Nazionale delle Ricerche (IBFM-CNR), Segrate, Milan, Italy
| | - Marco Rossignolo
- Center for Integrated Quantum Science and Technologies, Institute for Quantum Optics, Universitat Ulm, Ulm, Germany.,Istituto Nazionale di Fisica Nucleare (INFN), Padova, Italy
| | - Davide Maspero
- Department of Informatics, Systems and Communication, University of Milan-Bicocca, Milan, Italy.,Institute of Molecular Bioimaging and Physiology, Consiglio Nazionale delle Ricerche (IBFM-CNR), Segrate, Milan, Italy.,Fondazione IRCCS Istituto Nazionale dei Tumori, Milan, Italy
| | - Tommaso Calarco
- Forschungszentrum Jülich, Institute of Quantum Control (PGI-8), Jülich, Germany
| | - Rocco Piazza
- Department of Medicine and Surgery, University of Milano-Bicocca, Monza, Italy.,Hematology and Clinical Research Unit, San Gerardo Hospital, Monza, Italy
| | - Simone Montangero
- Istituto Nazionale di Fisica Nucleare (INFN), Padova, Italy.,Department of Physics and Astronomy "G. Galilei", University of Padova, Padova, Italy
| | - Marco Antoniotti
- Department of Informatics, Systems and Communication, University of Milan-Bicocca, Milan, Italy.,Bicocca Bioinformatics Biostatistics and Bioimaging Centre - B4, Milan, Italy
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Ewald J, Sieber P, Garde R, Lang SN, Schuster S, Ibrahim B. Trends in mathematical modeling of host-pathogen interactions. Cell Mol Life Sci 2020; 77:467-480. [PMID: 31776589 PMCID: PMC7010650 DOI: 10.1007/s00018-019-03382-0] [Citation(s) in RCA: 28] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/05/2019] [Revised: 11/05/2019] [Accepted: 11/12/2019] [Indexed: 12/18/2022]
Abstract
Pathogenic microorganisms entail enormous problems for humans, livestock, and crop plants. A better understanding of the different infection strategies of the pathogens enables us to derive optimal treatments to mitigate infectious diseases or develop vaccinations preventing the occurrence of infections altogether. In this review, we highlight the current trends in mathematical modeling approaches and related methods used for understanding host-pathogen interactions. Since these interactions can be described on vastly different temporal and spatial scales as well as abstraction levels, a variety of computational and mathematical approaches are presented. Particular emphasis is placed on dynamic optimization, game theory, and spatial modeling, as they are attracting more and more interest in systems biology. Furthermore, these approaches are often combined to illuminate the complexities of the interactions between pathogens and their host. We also discuss the phenomena of molecular mimicry and crypsis as well as the interplay between defense and counter defense. As a conclusion, we provide an overview of method characteristics to assist non-experts in their decision for modeling approaches and interdisciplinary understanding.
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Affiliation(s)
- Jan Ewald
- Matthias Schleiden Institute, Bioinformatics, Friedrich Schiller University Jena, Ernst-Abbe-Platz 2, 07743, Jena, Germany
| | - Patricia Sieber
- Matthias Schleiden Institute, Bioinformatics, Friedrich Schiller University Jena, Ernst-Abbe-Platz 2, 07743, Jena, Germany
| | - Ravindra Garde
- Matthias Schleiden Institute, Bioinformatics, Friedrich Schiller University Jena, Ernst-Abbe-Platz 2, 07743, Jena, Germany
- Max Planck Institute for Chemical Ecology, Hans-Knöll-Str. 8, 07745, Jena, Germany
| | - Stefan N Lang
- Matthias Schleiden Institute, Bioinformatics, Friedrich Schiller University Jena, Ernst-Abbe-Platz 2, 07743, Jena, Germany
| | - Stefan Schuster
- Matthias Schleiden Institute, Bioinformatics, Friedrich Schiller University Jena, Ernst-Abbe-Platz 2, 07743, Jena, Germany.
| | - Bashar Ibrahim
- Matthias Schleiden Institute, Bioinformatics, Friedrich Schiller University Jena, Ernst-Abbe-Platz 2, 07743, Jena, Germany.
- Centre for Applied Mathematics and Bioinformatics, Gulf University for Science and Technology, 32093, Hawally, Kuwait.
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Rigatos G, Busawon K, Abbaszadeh M. Nonlinear optimal control of the acute inflammatory response. Biomed Signal Process Control 2020. [DOI: 10.1016/j.bspc.2019.101631] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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Bara O, Fliess M, Join C, Day J, Djouadi SM. Toward a model-free feedback control synthesis for treating acute inflammation. J Theor Biol 2018; 448:26-37. [PMID: 29625206 DOI: 10.1016/j.jtbi.2018.04.003] [Citation(s) in RCA: 34] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/18/2017] [Revised: 03/03/2018] [Accepted: 04/02/2018] [Indexed: 01/22/2023]
Abstract
An effective and patient-specific feedback control synthesis for inflammation resolution is still an ongoing research area. A strategy consisting of manipulating a pro and anti-inflammatory mediator is considered here as used in some promising model-based control studies. These earlier studies, unfortunately, suffer from the difficultly of calibration due to the heterogeneity of individual patient responses even under similar initial conditions. We exploit a new model-free control approach and its corresponding "intelligent" controllers for this biomedical problem. A crucial feature of the proposed control problem is as follows: the two most important outputs which must be driven to their respective desired states are sensorless. This difficulty is overcome by assigning suitable reference trajectories to the other two outputs that do have sensors. A mathematical model, via a system of ordinary differential equations, is nevertheless employed as a "virtual" patient for in silico testing. We display several simulation results with respect to the most varied situations, which highlight the effectiveness of our viewpoint.
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Affiliation(s)
- Ouassim Bara
- Department of Electrical Engineering and Computer Science University of Tennessee, Knoxville, TN 37996, USA.
| | - Michel Fliess
- LIX (CNRS, UMR 7161), École polytechnique, Palaiseau 91128, France; AL.I.E.N. (ALgèbre pour Identification & Estimation Numériques) 7 rue Maurice Barrès, Vézelise 54330, France.
| | - Cédric Join
- CRAN (CNRS, UMR 7039), Université de Lorraine BP 239, Vandœuvre-lès-Nancy 54506, France; Projet NON-A, INRIA Lille - Nord-Europe, France; AL.I.E.N. (ALgèbre pour Identification & Estimation Numériques) 7 rue Maurice Barrès, Vézelise 54330, France.
| | - Judy Day
- Department of Mathematics, University of Tennessee, Knoxville, TN 37996, USA.
| | - Seddik M Djouadi
- Department of Electrical Engineering and Computer Science University of Tennessee, Knoxville, TN 37996, USA.
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