Mathematical Foundations and Biomechanics of the Digestive System

Half-title......Page 3
Title......Page 5
Copyright......Page 6
Dedication......Page 7
Contents......Page 9
Preface......Page 13
Notation......Page 17
Introduction......Page 23
Exercises......Page 26
1.1 Intrinsic geometry......Page 28
1.2 Extrinsic geometry......Page 30
1.3 The equations of Gauss and Codazzi......Page 35
1.4 General curvilinear coordinates......Page 37
1.5 Deformation of the surface......Page 40
1.6 Equations of compatibility......Page 44
Exercises......Page 48
2.1 Fictitious deformations......Page 50
2.2 Parameterization of the equidistant surface......Page 53
2.3 A single-function variant of the method of fictitious deformation......Page 55
2.4 Parameterization of a complex surface in preferred coordinates......Page 59
2.5 Parameterization of complex surfaces on a plane......Page 64
Exercises......Page 68
3.1 Deformation of the shell......Page 69
3.2 Forces and moments......Page 72
3.3 Equations of equilibrium......Page 77
Exercises......Page 82
4.1 Structure of the tissue......Page 83
4.2 Biocomposite as a mechanochemical continuum......Page 84
4.3 The biological factor......Page 93
Exercises......Page 96
5.1 The geometry of the boundary......Page 98
5.2 Stresses on the boundary......Page 100
5.3 Static boundary conditions......Page 103
5.4 Deformations of the edge......Page 106
5.5 Gauss–Codazzi equations for the boundary......Page 109
Exercises......Page 110
6.1 Deformation of soft shell......Page 111
6.2 Principal deformations......Page 117
6.3 Membrane forces......Page 119
6.4 Principal membrane forces......Page 122
6.5 Corollaries of the fundamental assumptions......Page 123
6.6 Nets......Page 127
6.7 Equations of motion in general curvilinear coordinates......Page 128
6.8 Governing equations in orthogonal Cartesian coordinates......Page 131
6.9 Governing equations in cylindrical coordinates......Page 133
Exercises......Page 135
7.1 Anatomical and physiological background......Page 137
7.2 Constitutive relations for the tissue......Page 141
7.3 A one-dimensional model of gastric muscle......Page 152
7.3.1 Myoelectrical activity......Page 154
7.3.2 Decrease in external Ca2+ concentration......Page 155
7.3.3 Effects of T- and L-type Ca2+ -channel antagonists......Page 156
7.3.4 Acetylcholine-induced myoelectrical responses......Page 157
7.3.6 Effect of selective K+-channel antagonist......Page 158
7.4 The stomach as a soft biological shell......Page 159
7.4.1 Inflation of the stomach......Page 162
7.4.2 The electromechanical wave phenomenon......Page 164
7.4.3 The chronaxiae of pacemaker discharges......Page 167
7.4.4 Multiple pacemakers......Page 169
Exercises......Page 177
8.1 Anatomical and physiological background......Page 179
8.2 A one-dimensional model of intestinal muscle......Page 180
8.2.1 Myoelectrical activity......Page 181
8.2.3 Effects of Ca2+-activated K+-channel agonist......Page 182
8.2.4 Response to a selective K+-channel agonist......Page 183
8.2.5 Effect of selective K+-channel antagonist......Page 185
8.2.6 Conjoint effect of changes in Ca2thinsp+ dynamics and extracellular K+ concentrations......Page 186
8.3 The small intestine as a soft cylindrical shell......Page 187
8.3.1 Pendular movements......Page 188
8.3.2 Segmentation......Page 190
8.3.4 Self-sustained periodic activity......Page 195
8.3.5 Effect of lidocaine......Page 199
Exercises......Page 202
9.1 Anatomical and physiological background......Page 204
9.2 The colon as a soft shell......Page 206
9.2.2 Contractions of the teniae coli......Page 209
9.3.1 Effect of Lotronex......Page 214
Exercises......Page 216
10.1 Biomechanics of hollow abdominal viscera......Page 218
10.2 Future developments and applications......Page 223
Exercises......Page 230
References......Page 232
Index......Page 239