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  1. Book: Mathematical methods and models in biomedicine

    Ledzewicz, Urszula

    (Lecture notes on mathematical modelling in the life sciences)

    2013  

    Author's details Urszula Ledzewicz
    Series title Lecture notes on mathematical modelling in the life sciences
    Keywords Medical sciences--Mathematics ; Medical sciences--Mathematical models
    Language English
    Size XI, 427 S. : Ill., graph. Darst., Kt., 24 cm
    Publisher Springer
    Publishing place New York u.a.
    Publishing country United States
    Document type Book
    HBZ-ID HT017461295
    ISBN 978-1-4614-4177-9 ; 1-4614-4177-3 ; 9781461441786 ; 1461441781
    Database Catalogue ZB MED Medicine, Health

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    In stock of ZB MED Cologne/Königswinter

    Shelf markLoan statusLocation
    2012 A 5756 order for loan Magazin

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  2. Article ; Online: Optimal dosage protocols for mathematical models of synergy of chemo- and immunotherapy.

    Ledzewicz, Urszula / Schättler, Heinz

    Frontiers in immunology

    2024  Volume 14, Page(s) 1303814

    Abstract: The release of tumor antigens during traditional cancer treatments such as radio- or chemotherapy leads to a stimulation of the immune response which provides synergistic effects these treatments have when combined with immunotherapies. A low-dimensional ...

    Abstract The release of tumor antigens during traditional cancer treatments such as radio- or chemotherapy leads to a stimulation of the immune response which provides synergistic effects these treatments have when combined with immunotherapies. A low-dimensional mathematical model is formulated which, depending on the values of its parameters, encompasses the 3 E's (elimination, equilibrium, escape) of tumor immune system interactions. For the escape situation, optimal control problems are formulated which aim to revert the process to the equilibrium scenario. Some numerical results are included.
    MeSH term(s) Humans ; Neoplasms/therapy ; Models, Theoretical ; Immunotherapy/methods
    Language English
    Publishing date 2024-01-19
    Publishing country Switzerland
    Document type Journal Article
    ZDB-ID 2606827-8
    ISSN 1664-3224 ; 1664-3224
    ISSN (online) 1664-3224
    ISSN 1664-3224
    DOI 10.3389/fimmu.2023.1303814
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  3. Article ; Online: Introduction to the special collection in honor of Avner Friedman.

    Othmer, Hans / Lou, Yuan / Maini, Philip / Ledzewicz, Urszula

    Journal of mathematical biology

    2023  Volume 86, Issue 3, Page(s) 33

    Language English
    Publishing date 2023-01-25
    Publishing country Germany
    Document type Journal Article
    ZDB-ID 187101-8
    ISSN 1432-1416 ; 0303-6812
    ISSN (online) 1432-1416
    ISSN 0303-6812
    DOI 10.1007/s00285-022-01864-7
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  4. Article: On the Role of the Objective in the Optimization of Compartmental Models for Biomedical Therapies.

    Ledzewicz, Urszula / Schättler, Heinz

    Journal of optimization theory and applications

    2020  Volume 187, Issue 2, Page(s) 305–335

    Abstract: We review and discuss results obtained through an application of tools of nonlinear optimal control to biomedical problems. We discuss various aspects of the modeling of the dynamics (such as growth and interaction terms), modeling of treatment ( ... ...

    Abstract We review and discuss results obtained through an application of tools of nonlinear optimal control to biomedical problems. We discuss various aspects of the modeling of the dynamics (such as growth and interaction terms), modeling of treatment (including pharmacometrics of the drugs), and give special attention to the choice of the objective functional to be minimized. Indeed, many properties of optimal solutions are predestined by this choice which often is only made casually using some simple ad hoc heuristics. We discuss means to improve this choice by taking into account the underlying biology of the problem.
    Keywords covid19
    Language English
    Publishing date 2020-09-30
    Publishing country United States
    Document type Journal Article
    ZDB-ID 1468244-8
    ISSN 1573-2878 ; 0022-3239
    ISSN (online) 1573-2878
    ISSN 0022-3239
    DOI 10.1007/s10957-020-01754-2
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  5. Book: Mathematical methods and models in biomedicine

    Ledzewicz, Urszula

    (Lecture notes on mathematical modelling in the life sciences,)

    2013  

    Abstract: Mathematical biomedicine is a rapidly developing interdisciplinary field of research that connects the natural and exact sciences in an attempt to respond to the modeling and simulation challenges raised by biology and medicine. There exist a large ... ...

    Author's details Urszula Ledzewicz ... [et al.], editors
    Series title Lecture notes on mathematical modelling in the life sciences,
    Abstract Mathematical biomedicine is a rapidly developing interdisciplinary field of research that connects the natural and exact sciences in an attempt to respond to the modeling and simulation challenges raised by biology and medicine. There exist a large number of mathematical methods and procedures that can be brought in to meet these challenges and this book presents a palette of such tools ranging from discrete cellular automata to cell population based models described by ordinary differential equations to nonlinear partial differential equations representing complex time- and space-dependent continuous processes. Both stochastic and deterministic methods are employed to analyze biological phenomena in various temporal and spatial settings. This book illustrates the breadth and depth of research opportunities that exist in the general field of mathematical biomedicine by highlighting some of the fascinating interactions that continue to develop between the mathematical and biomedical sciences. It consists of five parts that can be read independently, but are arranged to give the reader a broader picture of specific research topics and the mathematical tools that are being applied in its modeling and analysis. The main areas covered include immune system modeling, blood vessel dynamics, cancer modeling and treatment, and epidemiology. The chapters address topics that are at the forefront of current biomedical research such as cancer stem cells, immunodominance and viral epitopes, aggressive forms of brain cancer, or gene therapy. The presentations highlight how mathematical modeling can enhance biomedical understanding and will be of interest to both the mathematical and the biomedical communities including researchers already working in the field as well as those who might consider entering it. Much of the material is presented in a way that gives graduate students and young researchers a starting point for their own work.
    MeSH term(s) Models, Theoretical ; Biomedical Research
    Language English
    Size xi, 427 p. :, ill. (some col.) ;, 23 cm.
    Publisher Springer
    Publishing place New York
    Document type Book
    ISBN 9781461441779 ; 1461441773 ; 9781461441786 ; 1461441781
    Database Catalogue of the US National Library of Medicine (NLM)

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  6. Article ; Online: Determining optimal combination regimens for patients with multiple myeloma.

    Aghaee, Mahya / Ledzewicz, Urszula / Robbins, Michael / Bezman, Natalie / Jay Cho, Hearn / Moore, Helen

    European journal of pharmaceutical sciences : official journal of the European Federation for Pharmaceutical Sciences

    2023  Volume 187, Page(s) 106492

    Abstract: While many novel therapies have been approved in recent years for treating patients with multiple myeloma, there is still no established curative regimen, especially for patients with high-risk disease. In this work, we use a mathematical modeling ... ...

    Abstract While many novel therapies have been approved in recent years for treating patients with multiple myeloma, there is still no established curative regimen, especially for patients with high-risk disease. In this work, we use a mathematical modeling approach to determine combination therapy regimens that maximize healthy lifespan for patients with multiple myeloma. We start with a mathematical model for the underlying disease and immune dynamics, which was presented and analyzed previously. We add the effects of three therapies to the model: pomalidomide, dexamethasone, and elotuzumab. We consider multiple approaches to optimizing combinations of these therapies. We find that optimal control combined with approximation outperforms other methods, in that it can quickly produce a combination regimen that is clinically-feasible and near-optimal. Implications of this work can be used to optimize doses and advance the scheduling of drugs.
    MeSH term(s) Humans ; Multiple Myeloma/drug therapy ; Dexamethasone/therapeutic use ; Antineoplastic Combined Chemotherapy Protocols/therapeutic use ; Combined Modality Therapy
    Chemical Substances Dexamethasone (7S5I7G3JQL)
    Language English
    Publishing date 2023-06-09
    Publishing country Netherlands
    Document type Journal Article
    ZDB-ID 1154366-8
    ISSN 1879-0720 ; 0928-0987
    ISSN (online) 1879-0720
    ISSN 0928-0987
    DOI 10.1016/j.ejps.2023.106492
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    Zs.A 3705: Show issues Location:
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  7. Article ; Online: Application of mathematical models to metronomic chemotherapy: What can be inferred from minimal parameterized models?

    Ledzewicz, Urszula / Schättler, Heinz

    Cancer letters

    2017  Volume 401, Page(s) 74–80

    Abstract: Metronomic chemotherapy refers to the frequent administration of chemotherapy at relatively low, minimally toxic doses without prolonged treatment interruptions. Different from conventional or maximum-tolerated-dose chemotherapy which aims at an ... ...

    Abstract Metronomic chemotherapy refers to the frequent administration of chemotherapy at relatively low, minimally toxic doses without prolonged treatment interruptions. Different from conventional or maximum-tolerated-dose chemotherapy which aims at an eradication of all malignant cells, in a metronomic dosing the goal often lies in the long-term management of the disease when eradication proves elusive. Mathematical modeling and subsequent analysis (theoretical as well as numerical) have become an increasingly more valuable tool (in silico) both for determining conditions under which specific treatment strategies should be preferred and for numerically optimizing treatment regimens. While elaborate, computationally-driven patient specific schemes that would optimize the timing and drug dose levels are still a part of the future, such procedures may become instrumental in making chemotherapy effective in situations where it currently fails. Ideally, mathematical modeling and analysis will develop into an additional decision making tool in the complicated process that is the determination of efficient chemotherapy regimens. In this article, we review some of the results that have been obtained about metronomic chemotherapy from mathematical models and what they infer about the structure of optimal treatment regimens.
    MeSH term(s) Administration, Metronomic ; Antineoplastic Agents/administration & dosage ; Antineoplastic Agents/adverse effects ; Computer Simulation ; Decision Support Techniques ; Dose-Response Relationship, Drug ; Drug Resistance, Neoplasm ; Humans ; Models, Statistical ; Models, Theoretical ; Neoplasms/drug therapy ; Neoplasms/pathology ; Numerical Analysis, Computer-Assisted ; Patient Selection ; Time Factors ; Treatment Outcome ; Tumor Microenvironment
    Chemical Substances Antineoplastic Agents
    Language English
    Publishing date 2017-08-10
    Publishing country Ireland
    Document type Journal Article ; Review
    ZDB-ID 195674-7
    ISSN 1872-7980 ; 0304-3835
    ISSN (online) 1872-7980
    ISSN 0304-3835
    DOI 10.1016/j.canlet.2017.03.021
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    Zs.A 1177: Show issues Location:
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  8. Book: Geometric optimal control

    Ledzewicz, Urszula / Schättler, Heinz

    theory, methods and examples

    (Interdisciplinary Applied Mathematics ; 38)

    2012  

    Author's details Heinz Schättler; Urszula Ledzewicz
    Series title Interdisciplinary Applied Mathematics ; 38
    Keywords Control theory ; Control theory/Mathematical models
    Language English
    Size XIX, 640 S, Ill., graph. Darst.
    Publisher Springer
    Publishing place New York u.a.
    Document type Book
    Note Literaturverz. S. [625] - 635
    ISBN 9781461438335 ; 9781461438342 ; 1461438330 ; 1461438349
    Database Library catalogue of the German National Library of Science and Technology (TIB), Hannover

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  9. Article: Optimizing Chemotherapeutic Anti-cancer Treatment and the Tumor Microenvironment: An Analysis of Mathematical Models.

    Ledzewicz, Urszula / Schaettler, Heinz

    Advances in experimental medicine and biology

    2016  Volume 936, Page(s) 209–223

    Abstract: We review results about the structure of administration of chemotherapeutic anti-cancer treatment that we have obtained from an analysis of minimally parameterized mathematical models using methods of optimal control. This is a branch of continuous-time ... ...

    Abstract We review results about the structure of administration of chemotherapeutic anti-cancer treatment that we have obtained from an analysis of minimally parameterized mathematical models using methods of optimal control. This is a branch of continuous-time optimization that studies the minimization of a performance criterion imposed on an underlying dynamical system subject to constraints. The scheduling of anti-cancer treatments has all the features of such a problem: treatments are administered in time and the interactions of the drugs with the tumor and its microenvironment determine the efficacy of therapy. At the same time, constraints on the toxicity of the treatments need to be taken into account. The models we consider are low-dimensional and do not include more refined details, but they capture the essence of the underlying biology and our results give robust and rather conclusive qualitative information about the administration of optimal treatment protocols that strongly correlate with approaches taken in medical practice. We describe the changes that arise in optimal administration schedules as the mathematical models are increasingly refined to progress from models that only consider the cancerous cells to models that include the major components of the tumor microenvironment, namely the tumor vasculature and tumor-immune system interactions.
    MeSH term(s) Angiogenesis Inhibitors/pharmacokinetics ; Angiogenesis Inhibitors/therapeutic use ; Computer Simulation ; Cytotoxins/pharmacokinetics ; Cytotoxins/therapeutic use ; Drug Administration Schedule ; Drug Combinations ; Drug Dosage Calculations ; Endothelial Cells/drug effects ; Endothelial Cells/immunology ; Endothelial Cells/pathology ; Humans ; Models, Statistical ; Neoplasms/blood supply ; Neoplasms/drug therapy ; Neoplasms/immunology ; Neoplasms/metabolism ; Neovascularization, Pathologic/drug therapy ; Neovascularization, Pathologic/immunology ; Neovascularization, Pathologic/metabolism ; Neovascularization, Pathologic/pathology ; Tumor Microenvironment/drug effects ; Tumor Microenvironment/immunology
    Chemical Substances Angiogenesis Inhibitors ; Cytotoxins ; Drug Combinations
    Language English
    Publishing date 2016
    Publishing country United States
    Document type Journal Article ; Research Support, U.S. Gov't, Non-P.H.S. ; Review
    ISSN 2214-8019 ; 0065-2598
    ISSN (online) 2214-8019
    ISSN 0065-2598
    DOI 10.1007/978-3-319-42023-3_11
    Database MEDical Literature Analysis and Retrieval System OnLINE

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  10. Article ; Online: Optimization of combination therapy for chronic myeloid leukemia with dosing constraints.

    Moore, Helen / Strauss, Lewis / Ledzewicz, Urszula

    Journal of mathematical biology

    2018  Volume 77, Issue 5, Page(s) 1533–1561

    Abstract: In this work, we demonstrate a mathematical technique for optimizing combination regimens with constraints. We apply the technique to a mathematical model for treatment of patients with chronic myeloid leukemia. The in-host model includes leukemic cell ... ...

    Abstract In this work, we demonstrate a mathematical technique for optimizing combination regimens with constraints. We apply the technique to a mathematical model for treatment of patients with chronic myeloid leukemia. The in-host model includes leukemic cell and immune system dynamics during treatment with tyrosine kinase inhibitors and immunomodulatory compounds. The model is minimal (semi-mechanistic) with just enough detail that all relevant therapeutic effects can be represented. The regimens are optimized to yield the highest possible reduction in disease burden, taking into account dosing constraints and side effect risks due to drug exposure. We compare the following three types of regimens: (1) regimens that are restricted to certain discrete dose levels, which can only change every three months; (2) optimal regimens determined using optimal control; and (3) regimens that are piecewise-constant like the first type of regimen, but are obtained as approximations to the optimal control regimens. All three types of regimens result in similar outcomes, but the last one is easy to compute in addition to being clinically feasible.
    MeSH term(s) Antineoplastic Agents/administration & dosage ; Antineoplastic Agents, Immunological/administration & dosage ; Antineoplastic Combined Chemotherapy Protocols/administration & dosage ; Computer Simulation ; Fusion Proteins, bcr-abl/antagonists & inhibitors ; Humans ; Immunologic Factors/administration & dosage ; Immunotherapy/methods ; Immunotherapy/statistics & numerical data ; Leukemia, Myelogenous, Chronic, BCR-ABL Positive/drug therapy ; Leukemia, Myelogenous, Chronic, BCR-ABL Positive/therapy ; Mathematical Concepts ; Models, Biological ; Protein Kinase Inhibitors/administration & dosage
    Chemical Substances Antineoplastic Agents ; Antineoplastic Agents, Immunological ; BCR-ABL1 fusion protein, human ; Immunologic Factors ; Protein Kinase Inhibitors ; Fusion Proteins, bcr-abl (EC 2.7.10.2)
    Language English
    Publishing date 2018-07-10
    Publishing country Germany
    Document type Journal Article
    ZDB-ID 187101-8
    ISSN 1432-1416 ; 0303-6812
    ISSN (online) 1432-1416
    ISSN 0303-6812
    DOI 10.1007/s00285-018-1262-6
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