Main description:

This book concerns the mathematical modeling and computer simulation of the human stomach. It follows the four modern P's (prevention, prediction, personalization, and precision in medicine) approach in addressing the highly heterogeneous nature of processes underlying gastric motility disorders manifested as gastroparesis, functional dyspepsia, myenteric enteropathy etc. The book comprehensively guides readers through the fundamental theoretical concepts to complex physiological models of the organ. This requires a deep and thorough understanding of driving pathophysiological mechanisms as well as the collaborative effort of specialists working in fundamental and biological science. Such a multidisciplinary partnership is vital because it upholds gnostic capabilities and provides the exchange of thoughts and ideas thus offering broad perspectives into the evolution and management of diseases. The book is a valuable resource for applied mathematicians, computational biologists, bioengineers, physicians, physiologists and researchers working in various fields of biomedicine.

Contents:

Preface

Notations

Abbreviations

Introduction

Chapter 1. Biological Preliminaries

1.1 Anatomy and physiological background

1.2 Smooth muscle syncytia

1.3 Regulatory system

1.4 Electrophysiology of the stomach

1.5 Neuroendocrine modulators

1.6 Coupling phenomenon

1.7 Biomechanics of the human stomach

Chapter 2. Biomechanics of the Human Stomach

2.1 Constitutive relations for the tissue

2.2 Models of the human stomach

2.3 Models of myoelectrical activity

Chapter 3. Geometry of the Surface

3.1 Intrinsic geometry

3.2 Extrinsic geometry

3.3 Equations of Gauss and Codazzi

3.4 General curvilinear coordinates

3.5 Deformation of the surface

3.6 Equations of compatibility

Chapter 4. Parameterization of Shells of Complex Geometry

4.1 Fictitious deformations

4.2 Parameterization of the equidistant surface

4.3 A single function variant of the method of fictitious deformation

4.4 Parameterization of a complex surface in preferred coordinates

4.5 Parameterization of complex surfaces on plane

Chapter 5. Nonlinear Theory of Thin Shells

5.1 Deformation of the shell

5.2 Forces and moments

5.3 Equations of equilibrium

Chapter 6. Continuum Model of the Biological Tissue

6.1 Biocomposite as a mechanochemical continuum

6.2 Biological factor

6.3 Mechanical properties of the human stomach

6.3.1 Uniaxial loading

6.3.2 Biaxial loading

6.3.3 Histomorphological changes in the tissue under loading

6.3.4 Active forces

Chapter 7. Boundary Conditions

7.1 Geometry of the boundary

7.2 Stresses on the boundary

7.3 Static boundary conditions

7.4 Deformations of the edge

7.5 Equations of Gauss-Codazzi for the boundary

Chapter 8. Soft Shells

8.1 Deformations of soft shell

8.2 Principal deformations

8.3 Membrane forces

8.4 Principal membrane forces

8.5 Corollaries of the fundamental assumptions

8.6 Nets

8.7 Equations of motion in general curvilinear coordinates

8.8 Governing equations in orthogonal Cartesian coordinates

8.9 Governing equations in cylindrical coordinates

Chapter 9. The Intrinsic Regulatory Pathways

9.1 Biological preliminaries

9.2 Topographical neuronal assemblies in the human stomach

9.3 A model of a neuron

9.4 Inhibitory neural circuit

9.5 Planar neuronal network

Chapter 10. The synapse

10.1System compartmentalization

10.2cAMP-dependent pathway

10.3PLC pathway

10.4Variations in synaptic neurotransmission

Chapter 11. Multiple co-transmission and receptor polymodality

11.1Co-localization and co-transmission by multiple neurotransmitters

11.2Co-transmission by VIP and nitric oxide

11.3Co-transmission by acetylcholine, VIP and nitric oxide

11.4Co-transmission by SP, acetylcholine, VIP and nitric oxide

11.5Co-transmission by serotonin, VIP and nitric oxide

11.6Co-transmission by NPY, acetylcholine and nitric oxide

Chapter 12. A Model of Gastric Smooth Muscle

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12.1

12.2Response of SIP/ganglion to stimulation

12.3The vagal external input

12.4Self-oscillatory dynamics of SIP

12.5Gastric arrhythmia

12.6Effects of co-transmission on the SIP/ganglion unit

Chapter 13. Human Stomach as a Soft Biological Shell

13.2 Basic assumptions

13.3 The stomach as a soft biological shell

13.4 Stress-strain analysis in anatomically variable stomach

13.5 Electromechanical wave phenomenon

13.6 Motility patterns in the physiological stomach

13.7 A model of gastroparesis

13.8 A model of myenteric neuropathy

13.9 A model of gastric arrythmia

Chapter 14. Pharmacology of Gastric Contractility

14.1Classes of drugs

14.2Current therapies of gastric dysfunction

14.3Model of competitive antagonist action

14.4Model of allosteric interaction

14.5Allosteric modulation of competitive agonist/antagonist action

14.6Model of PDE-4 inhibitor

14.7Effects of existing and prospective drugs on gastric motility

Chapter 15. Biomechanics of the Human Stomach after Surgery

15.1 Sleeve gastectomy

15.2 Billroth I and II

15.3 Truncal, partial and selective vagotomy

Chapter 16. Biomechanics of the Human Stomach in Perspective

16.1Reliability of models

16.2The Brain-stomach interaction

16.3Applications, pitfalls and future problems

Addendum

Chapter 17. Existence of solutions

Chapter 18. Dynamics of waves in solid deformable structures

References

Index