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.
Professor Dr. Roustem Miftahof, MD, PhD, DSc is the Chair of Computational Biology and Medicine Centre in the College of Medicine and Medical Sciences at Arabian Gulf University in Manama, Bahrain. He earned the Doctor of Medicine degree with Honors in 1980 and the degree in Applied Mathematics with Honors in 1981. His PhD in Mathematical and Physical Sciences was related to Numerical simulation of stress-strain distribution in the human stomach and his DSc in Technical Sciences (post-habilitation dissertation) was on Peristaltic waves in biological shells.
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 < 12.112.2Response 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