Mathematical Modeling of Mitochondrial Swelling. ([2018])

• Record Type: Book
• Further Information: Note: Messoud Efendiev.
• Authors: Efendiev, Messoud
• Contents: Intro; Preface; Contents; 1 Functional Spaces; 1.1 Sobolev Spaces and Embeddings Theorem; 1.2 Poincaré, Wirtinger, and Friedrichs Inequalities; 1.3 Nemytski Operators; 1.4 Subdifferential; Monotonicity of Subdifferentials; Subdifferentials and PDEs; Subdifferential in Hilbert Spaces; References; 2 Biological Background; 2.1 The Mitochondrion; Structure; 2.2 Apoptosis; Pathways; 2.3 Mitochondrial Permeability Transition (MPT); Permeability Transition Pore (PTP); Ca2+ Release; Pharmaceutical Background; Experimental Procedure; References; 3 Model Description; 3.1 Existing Models; Microscale MacroscaleFirst Order Kinetics; Several Steps of Calcium Uptake; Second Order Kinetics; 3.2 Spatial Effects; In Vitro Swelling; 3.3 The Mitochondria Model: In Vitro; The Variables; Initial Conditions; Boundary Conditions; Model Function f; Model Function g; Calcium Evolution; References; 4 Mathematical Analysis of Vitro Models; 4.1 Neumann Boundary Conditions; Existence and Uniqueness of Global Solutions; Asymptotic Behavior of Solutions; 4.2 Classification of Partial and Complete Swelling; Convergence Rate; 4.3 Numerical Analysis: In Vitro; The In Vitro Model; Model Parameters DiscretizationNumerical Approximation; Initial Values; Simulation; Comparison with Experimental Data; Conclusion; 4.4 Dirichlet Boundary Conditions; Hopf's Maximum Principle; Corresponding Eigenvalue Problem; Wirtinger's Inequality; 4.5 Numerical Simulation; Discussion and Conclusion; References; 5 The Swelling of Mitochondria: In Vivo; 5.1 Increase of Intracellular Ca2+; 5.2 The Cell Membrane; 5.3 Summary; 5.4 Mathematical Analysis of an Vivo Model of Mitochondria Swelling; Well Posedness and Asymptotic Behavior of Solutions; Uniform Convergence of u; Partial Swelling; Complete Swelling 5.5 Numerical IllustrationsConclusion; References; 6 The Swelling of Mitochondria: Degenerate Diffusion; 6.1 Mathematical Analysis of Mitochondria Swelling in Porous Medium; Finite Propagation Speed; Degeneracy; Well Posedness and Asymptotic Behavior of Solutions; 6.2 Numerical Simulation; References; 7 The Spatial Evolution of Mitochondria: PDE-PDE Systems; 7.1 Well Posedness; 7.2 Asymptotic Behavior of Solutions; 7.3 Numerical Simulations; Conclusion; References
• Publisher Details: Cham, Switzerland : Springer
• Publication Date: 2018
• Extent: 1 online resource, illustrations (some colour)
• Subjects: 616.39; Mathematics; Mitochondrial pathology -- Mathematical models; HEALTH & FITNESS / Diseases / General; MEDICAL / Clinical Medicine; MEDICAL / Diseases; MEDICAL / Evidence-Based Medicine; MEDICAL / Internal Medicine; Mathematics -- Mathematical Analysis; Science -- Life Sciences -- Cytology; Nonlinear science; Cellular biology (cytology); Physiology_xMathematics; Differentiable dynamical systems; Cell physiology; Mathematics -- Applied; Applied mathematics; Electronic books
• Languages: English
• ISBNs: 9783319991009; 3319991000
• Related ISBNs: 9783319990996; 3319990993
• Notes: Note: Includes bibliographical references.; Note: Online resource; title from PDF title page (EBSCO, viewed October 5, 2018).; Note: Vendor-supplied metadata.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
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