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Table of 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
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
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
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
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
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
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
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