Early mechanistic vision

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Table of contents

1 Introduction to morphogenetic theories in living matter 
1.1 Early mechanistic vision
1.1.1 Wilhelm His and the \constrained expansion model
1.1.2 Wilhelm Roux and developmental mechanics
1.2 The 20th century
1.2.1 D’Arcy Thompson: arst mathematical approach to morphogenesis
1.2.2 Genetics
1.2.3 Pattern Formation
1.3 Modern approaches to morphogenesis
1.3.1 Volumetric Growth and Remodeling
1.3.2 Mixture theory
1.3.3 Morphomechanics: hyper-restoration principle
1.3.4 Mechanotransduction
1.4 Summary and conclusions
2 Morphoelasticity: theory and methods 
2.1 The thermo-mechanics of open systems
2.1.1 Kinematics
2.1.2 Mathematical theory of growth and remodeling
2.1.3 Governing equations
2.1.4 Boundary conditions
2.1.5 Constitutive relations
2.1.6 Summary of the key equations and some comments
2.2 Method of incremental deformations superposed on nite deformations
2.2.1 Incremental deformation
2.2.2 Incremental boundary value problem
2.2.3 Summary of the key incremental equations
2.3 Theories and methods for solving the incremental problem
2.3.1 Stroh formulation
2.3.2 The surface impedance method
2.3.3 Mixed boundary conditions
2.3.4 Neumann boundary conditions
2.4 Concluding remarks
3 Morphoelastic modeling of gastro-intestinal organogenesis 
3.1 Introduction to intestinal morphogenesis
3.2 State of the art of biomechanical modeling
3.2.1 Spatially constrained growth models
3.2.2 Dierential growth models
3.3 Homogeneous growth model with spatial constraints
3.3.1 Kinematics
3.3.2 Constitutive equations
3.3.3 Governing equations and basic axial-symmetric solution
3.3.4 Incremental boundary value problem
3.3.5 Stroh formulation of the BVP and numerical solution
3.3.6 Results
3.3.7 Discussion of the results
3.4 Dierential growth model without spatial constraints
3.4.1 Kinematics
3.4.2 Constitutive equations
3.4.3 Governing equations and axial-symmetric solution
3.4.4 Incremental boundary value problem
3.4.5 Stroh formulation of the BVP
3.4.6 Surface impedance method and numerical solution
3.4.7 Theoretical results of the linear stability analysis
3.4.8 Finite element simulations in the post-buckling regime
3.4.9 Numerical results
3.4.10 Validation of the model with experimental data
3.5 Concluding remarks
4 Helical buckling of pre-stressed tubular organs
4.1 Preliminary remarks
4.1.1 Introduction to the anatomy and the physiology of arteries
4.1.2 Principle of homeostasis
4.1.3 Residual stresses and stress-free state
4.1.4 Remodeling process in arteries
4.2 Kinematics of the elastic problem
4.3 Constitutive equations
4.4 Governing equations and basic axial-symmetric solutions
4.4.1 Case (a): stress-free internal and external surfaces
4.4.2 Case (b): Pressure load P at the internal surface
4.4.3 Case (c): Pressure load P at the external surface
4.5 Incremental boundary value problem
4.6 Stroh formulation of the BVP
4.7 Surface impedance method and numerical solution
4.8 Numerical results
4.8.1 Eect of the circumferential pre-stretch
4.8.2 Eect of the axial pre-stretch
4.9 Discussion of the results
4.10 Validation of the model with experimental data
4.11 Concluding remarks
5 Conclusions and perspectives