Mathematical Models and Computer Simulations for Biomedical Applications

✍ Scribed by Gabriella Bretti, Roberto Natalini, Pasquale Palumbo, Luigi Preziosi

• Publisher: Springer
• Year: 2023
• Tongue: English
• Leaves: 261
• Series: SEMA SIMAI Springer Series, Volume 33
• Category: Library

✦ Table of Contents

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
2.2.2 Phenotypic-Related Cell Behavior
3 Model Application: Wound Healing Assay
4 Conclusions
References
Modelling HIF-PHD Dynamics and Related Downstream Pathways
1 Introduction
2 HIFs and PHDs
2.1 Equilibrium States
2.2 The Limit ζ→0
2.3 The Anoxic Limit
2.4 HIF-PHD Dynamics
3 Hypoxia and Inflammation
3.1 HIF-Alarmin-NFkB Dynamics
3.2 HIF-Interleukine Dynamics
4 Modelling Other HIF-Related Downstream Pathways
4.1 HIF and Metabolism
4.2 HIF and pH
4.3 HIF and Cell Cycle
4.4 HIF and ECM-Stiffening
4.5 HIF and VEGF
4.6 HIF and High Altitude
References
An Imaging-Informed Mechanical Framework to Providea Quantitative Description of Brain Tumour Growthand the Subsequent Deformation of White Matter Tracts
1 Introduction
2 A Multiphase Model for Brain Tumour Growth
2.1 Eulerian Formulation
2.1.1 Balance Equations
2.1.2 Stress Tensor and Constitutive Equations
2.1.3 Nutrients
2.1.4 Diffusion Tensor D and Preferential Directions Tensor A
2.1.5 Interface Conditions at the Boundary Between the Tumour and the Healthy Tissue
2.2 Lagrangian Formulation of the Model
3 Numerical Implementation
3.1 Weak Formulation of the Lagrangian Model
3.2 Discrete Formulation of the Continuous Variational Problems
3.3 Parameters Estimation
3.4 Mesh Preparation
4 Numerical Simulations in the Brain
5 Conclusions and Future Developments
References
A Multi-Scale Immune System Simulator for the Onset of Type2 Diabetes
1 Introduction
2 Mathematical Models
2.1 The Model of Metabolism
2.2 The Hormonal Glucagon/Insulin Model
2.3 The Model of the Physical Exercise
2.4 The Model of Food Intake, Stomach Emptying and Macronutrient Absorption
2.5 Modeling Total Daily Energy Balance and Body Weight
2.6 Modeling the Effect of a Calorie Excess on the Adipocytes
2.7 The Model of IL-6 Release
2.8 The Model of Inflammation
3 Results
3.1 Setting the Parameters for the Glucagon/Insulin Model
3.2 Simulating Different Lifestyle Scenarios
4 Discussion and Conclusions
References
Molecular Fingerprint Based and Machine Learning Driven QSAR for Bioconcentration Pathways Determination
1 Introduction
2 Materials and Methods
2.1 Data Processing
2.2 Machine Learning Models
2.2.1 Extreme Gradient Boosting
2.2.2 Support Vector Machines
2.2.3 Neural Networks
2.2.4 Spiking Neural Networks
3 Results
4 Discussion
5 Conclusions
Appendix
Author contributions
References
Advanced Models for COVID-19 Variant Dynamicsand Pandemic Waves
1 Introduction
2 Description of Data
3 Drivers of Case Count
4 Data Analysis
4.1 Computation of ``Switching Time''
4.2 Days Between Variants Dominance and Cases Peak
4.3 Comparing the Trend of Variant Progression with Cases Progression
5 Modeling a Virus with Mutation
5.1 Epidemiological Modeling
5.2 Definition of MC-ODE System
5.3 Simulations
6 Discussion
References
Multifractal Spectrum Based Classification for Breast Cancer
1 Introduction
2 Related Work
3 Dataset
4 Patient-Based Breast Cancer Identification
4.1 Image Processing
4.2 Fractal Dimension
4.3 Multifractal Spectrum
5 Experiments and Results
5.1 The Extended Dataset: Structure and Preprocessing
5.2 Classification Results
5.3 Discussion
6 Conclusions
References