Description |
1 online resource (viii, 257 pages) : illustrations (some color) |
Series |
SEMA SIMAI Springer series, 2199-305X ; volume 33 |
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SEMA SIMAI Springer series ; v.33. 2199-305X
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Contents |
Intro -- Preface -- Contents -- An Application of the Grünwald-Letinkov Fractional Derivative to a Study of Drug Diffusion in Pharmacokinetic CompartmentalModels -- 1 Introduction -- 2 Pharmacokinetic Two Compartmental Model -- 2.1 Grünwald-Letinkov Approximation for Bicompartmental Model (14) -- 2.2 Non-standard Discretization of Bicompartmental Model (14) -- 2.3 Fractional Bicompartmental Model -- 3 Bicompartmental Model with NPs Infusion -- 4 Applications of Fractional Calculus to Model Drug Diffusion in a Three Compartmental Pharmacokinetic Model -- 5 Discussion -- References |
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Merging On-chip and In-silico Modelling for Improved Understanding of Complex Biological Systems -- 1 Introduction -- 2 The Organs-on-Chip Technology -- 2.1 Setting of the Laboratory Experiments -- 3 Mathematical Modeling of OoC -- 3.1 Macroscopic Model for CoC Experiment BBN -- 3.1.1 Interface Between 2D-1D Models in (1)-(4) -- 3.2 Hybrid Macro-Micro Model for CoC Experiment BDNPR -- 3.2.1 Function F1: Chemotactic Term -- 3.2.2 Function F2: ICs/TCs Repulsion -- 3.2.3 Function F3: ICs Adhesion/Repulsion -- 3.2.4 Friction -- 3.2.5 Function F4: Production of Chemical Signal |
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3.2.6 Initial Conditions -- 3.2.7 Boundary Conditions -- 3.2.8 Stochastic Model -- 3.3 Future Directions: Mean-Field Limits and Nonlocal Models NP2022 -- 4 Numerical Approximation -- 4.1 Numerical Schemes for the Approximation of the Models (1)-(4) -- 4.1.1 Stability at Interfaces -- 4.2 Numerical Schemes for the Approximation of the Model (7)-(8) -- 4.2.1 Discretization of the PDE (Eq.(7)) -- 4.2.2 Boundary Conditions -- 4.2.3 Discretization of the ODE (8) -- 4.3 Discretization of the SDE (20) -- 5 Simulation Results -- 5.1 Simulation Results Obtained by Macroscopic Model |
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5.1.1 Time Evolution of Macroscopic Densities -- 5.2 Simulation Results Obtained by Hybrid Macro-Micro Model -- 5.2.1 Scenario 1: Deterministic Motion -- 5.2.2 Scenario 2: Deterministic Motion Including Cell Death -- 5.2.3 Scenario 3: Stochastic Motion -- 6 Conclusions -- References -- A Particle Model to Reproduce Collective Migrationand Aggregation of Cells with Different Phenotypes -- 1 Introduction -- 2 Mathematical Framework and Representative Simulations -- 2.1 Cell Proliferation -- 2.2 Cell Movement -- 2.2.1 Cell Repulsive Behavior and Random Movement |
Summary |
Mathematical modelling and computer simulations are playing a crucial role in the solution of the complex problems arising in the field of biomedical sciences and provide a support to clinical and experimental practices in an interdisciplinary framework. Indeed, the development of mathematical models and efficient numerical simulation tools is of key importance when dealing with such applications. Moreover, since the parameters in biomedical models have peculiar scientific interpretations and their values are often unknown, accurate estimation techniques need to be developed for parameter identification against the measured data of observed phenomena. In the light of the new challenges brought by the biomedical applications, computational mathematics paves the way for the validation of the mathematical models and the investigation of control problems. The volume hosts high-quality selected contributions containing original research results as well as comprehensive papers and survey articles including prospective discussion focusing on some topical biomedical problems. It is addressed, but not limited to: research institutes, academia, and pharmaceutical industries |
Notes |
Online resource; title from PDF title page (SpringerLink, viewed August 24, 2023) |
Subject |
Biomedical engineering -- Mathematical models
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Biomedical engineering -- Computer simulation
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Mathematical models -- Industrial applications
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Computer simulation -- Industrial applications
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Biomedical engineering -- Computer simulation
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Biomedical engineering -- Mathematical models
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Form |
Electronic book
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Author |
Bretti, Gabriella, editor
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Natalini, R., editor.
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Palumbo, Pasquale, editor
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Preziosi, Luigi, editor.
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ISBN |
9783031357152 |
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3031357159 |
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