Quantitative Approaches to Microcirculation : Mathematical Models, Computational Methods and Data Analysis

• Autore: Linninger Andreas
• Pubblicazione: Cham : , : Springer International Publishing AG, , 2024; ©2024
• Edizione: 1st ed.
• Descrizione fisica: 1 online resource (0 pages)
• Altri autori: MardalKent-Andre ZuninoPaolo
• Nota di contenuto: Intro -- Preface -- Contents -- Mathematical Models of the Cerebral Microcirculation in Health and Pathophysiology -- 1 Introduction -- 2 Methodology -- 3 Applications -- 4 Future Directions -- 5 Conclusions -- References -- A Computational Model of the Tumor Microenvironment Applied to Fractionated Radiotherapy -- 1 Introduction -- 2 An Oxygen Transport Model Coupled to Radiotherapy -- 2.1 A Mixed-Dimensional Oxygen Transport Model -- 2.2 Constitutive Laws of the Oxygen Transport Model -- 2.3 The Linear-Quadratic Radiobiological Model -- 2.4 Coupling the Oxygen Transport and the Radiobiological Models -- 2.5 Numerical Methods -- 3 Numerical Simulations of the Interaction of Radiotherapy and the Tumor Microenvironment -- 3.1 The Effect of Fractionated Radiotherapy -- 3.2 The Effect of Reoxygenation After Radiotherapy -- 3.3 The Effect of Vascular Modifications Due to Radiotherapy -- 4 Discussion and Conclusions -- References -- Microvascular Modeling for Medical Imaging and ToxicityAssessment -- 1 Introduction -- 2 Methods: Key Concepts and Equations -- 2.1 Continuum Mechanics of Fluids: The Balance of Mass and Momentum -- 2.1.1 Mass Balance -- 2.1.2 Momentum Balance -- 2.1.3 System of Equations of a Continuum -- 2.2 Hemodynamics Modeling -- 2.2.1 The Navier-Stokes Equations -- 2.2.2 The (Hagen-)Poiseuille Flow Model -- 2.3 Viscosity Law -- 2.4 Transport in a Vascularized Tissue -- 2.4.1 Multi-Components, Single Phase Models -- 2.4.2 Multi-Components, Multi-Phases Models -- 2.4.3 Compartment Models -- 2.5 Vascular Networks -- 2.5.1 Geometry -- 2.5.2 Hemodynamics in Vessel Networks -- 2.5.3 Transport -- 3 Results -- 3.1 Case 1: Vascularized Tumor -- 3.1.1 Motivations -- 3.1.2 Specific Equations and Boundary Conditions -- 3.1.3 Numerical Methods -- 3.1.4 Results -- 3.2 Case 2: Lobule -- 3.2.1 Specific Equations and Boundary Conditions. ; 3.2.2 Results -- 3.3 Case 3: Toxicity -- 3.3.1 Specific Equations and Boundary Conditions -- 3.3.2 Results -- 4 Discussion -- 4.1 Strengths and Limitations of These Approaches -- 4.2 Similarities and Differences in the Three Cases -- 5 Conclusion and Perspectives -- Appendix -- References -- Finite Element Software and Performance for Network Models with Multipliers -- 1 Introduction -- 2 A Minimal Mixed-Dimensional Model: Hydraulic Networks with Multipliers -- 2.1 Mathematical Model -- 2.2 A Mixed Finite Element Method -- 3 Software Components and Implementation -- 3.1 Mixed-Domain Abstractions and Algorithms in FEniCS and FEniCSx -- 3.1.1 Submeshes -- 3.1.2 Mixed-Domain Finite Element Kernel Generation -- 3.1.3 Mixed-Domain Assembly -- 3.2 Implementation of the Hydraulic Network Solver -- 4 Results -- 4.1 Network Code Generation and Assembly in FEniCS vs FEniCSx -- 4.2 FEniCSx Performance on Larger Networks -- 5 Conclusions, Limitations, and Further Work -- References -- A Fast-Fourier Preconditioned Schur Complement Method for the Simulation of Cerebrocortical Oxygen Supply -- 1 Introduction -- 2 Models and Methods -- 2.1 Overview -- 2.2 Graph Representation and Discretization of Vascular and Tissue Domains -- 2.3 Simulation of Blood Flow in the Vascular Network -- 2.4 Oxygen Convection and Mass Transfer in the Vascular Domain -- 2.4.1 The Connectivity Matrix of a Graph -- 2.4.2 The Convection Matrices -- 2.4.3 Fast Inversion of the Convection Matrices -- 2.4.4 Dissociation of Oxygen from RBCs to Plasma -- 2.4.5 The Connectivity Matrix of the Domain Coupling -- 2.5 Oxygen Metabolism and Diffusion in the Tissue Domain -- 2.5.1 The Graph Laplacian -- 2.5.2 Fast Inversion of the Graph Laplacian with Dirichlet Boundary Conditions -- 2.5.3 Metabolism in the Tissue -- 2.6 Steady-State: Schur Complement of the Linearized System -- 2.6.1 The Newton Step. ; 2.6.2 The Schur Complement System -- 2.6.3 Preconditioning the Schur Complement System -- 2.7 The Dynamic Case -- 2.7.1 The Newton Step -- 2.7.2 The Preconditioned Schur Complement System -- 2.7.3 Summary of Method -- 3 Application to Massive Steady-State Oxygen Exchange Simulation in the Cerebral Cortex -- 3.1 Pure Diffusion of an Ideal Solute -- 3.2 Idealized Exchange of Oxygen Across the Blood Brain Barrier (Linear Mass Transfer) -- 3.3 Cortical Oxygen Extraction with Nonlinear Dissociation Kinetics -- 4 Discussion -- 5 Conclusions -- Appendix 1: Discretization of the Continuous Problem -- Appendix 2: Dependence of the DST on Domain Side Length -- Appendix 3: Dynamic Oxygen Simulation for a Single Capillary -- References -- Robust Preconditioning of Mixed-Dimensional PDEs on 3d-1d Domains Coupled with Lagrange Multipliers -- 1 Introduction -- 2 Mathematical Formulation of the 3d-1d Coupled Problem -- 2.1 The Stability of the Continuous Problem -- 2.2 Numerical Evidence About Preconditioning the Mixed-Dimensional Problems -- 3 Definition of a Preconditioner for the 3d-1d Problem: Performances and Drawbacks -- 4 The Role of the Inner Radius on Mixed-Dimensional Problems -- 4.1 The 2d-1d Formulation for the Perforated Domain Problem -- 4.2 Numerical Results About the 2d-1d Formulation -- 4.3 The 2d-0d Formulation for the Perforated Domain Problem -- 5 Conclusion -- Appendix -- Numerical Experiments for Square-Shaped Inclusion -- Numerical Experiments for Layered Mesh -- Numerical Experiments for P2-P1 Discretization -- References -- Numerical Approaches for Multiphase Microfluids -- 1 Introduction -- 2 Fluid/Fluid Interaction -- 2.1 Tangent of Hyperbola Interface Capturing (THINC) Method -- 2.2 Pressure Poisson Equation -- 2.3 Applications in Microfluidics -- 2.4 Emulsions Effective Viscosity -- 3 Fluid/Structure Interaction: The dynamic-IB Approach. ; 3.1 Fluid Evolution on Ω -- 3.2 Dirichlet Boundary Condition on ∂Ω -- 3.3 Evolution of M(t) -- 3.4 Dirichlet Boundary Conditions on M(t) -- 3.5 Strength and Limitations of the Dynamic-IB Approach -- 4 Conclusive Remarks -- References -- Application of the Zenger Correction to an Elliptic PDE with Dirac Source Term -- 1 Introduction -- 2 Model Problem -- 3 Iterative Solution Scheme -- 4 Application of the Zenger Correction -- 5 Numerical Tests -- 5.1 Local Convergence Behavior -- 5.2 Accurate Computation of the Exchange Term -- 5.3 Convergence of the Iterative Solution Scheme -- 6 Conclusions and Outlook -- References.
• Titolo autorizzato: Quantitative Approaches to Microcirculation
• ISBN: 3-031-58519-4
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910874675503321
• Lo trovi qui: Univ. Federico II
• Serie: SEMA SIMAI Springer Series