Provides a better understanding of the physiological and mechanical behaviour of the human body and the design of tools for their realistic numerical simulations, including concrete examples of such computational models. This book covers a large range of methods and an illustrative set of applications.
| CHAPTER I |
|
7 | (10) |
|
|
|
7 | (1) |
|
2. A brief description of the human vascular system |
|
|
8 | (3) |
|
3. The main variables for the mathematical description of blood flow |
|
|
11 | (1) |
|
|
|
11 | (6) |
| CHAPTER II |
|
17 | (18) |
|
5. The derivation of the equations for the flow field |
|
|
17 | (1) |
|
|
|
17 | (1) |
|
7. The motion of continuous media |
|
|
18 | (7) |
|
8. The derivation of the basic equations of fluid mechanics |
|
|
25 | (6) |
|
9. The Navier-Stokes equations |
|
|
31 | (4) |
| CHAPTER III |
|
35 | (22) |
|
10. The incompressible Navier-Stokes equations and their approximation |
|
|
35 | (2) |
|
11. Weak form of Navier-Stokes equations |
|
|
37 | (4) |
|
12. An energy inequality for the Navier-Stokes equations |
|
|
41 | (2) |
|
|
|
43 | (1) |
|
14. Numerical approximation of Navier-Stokes equations |
|
|
44 | (13) |
| CHAPTER IV |
|
57 | (14) |
|
15. Mathematical modelling of the vessel wall |
|
|
57 | (2) |
|
16. Derivation of 1D models of vessel wall mechanics |
|
|
59 | (9) |
|
17. Analysis of vessel wall models |
|
|
68 | (3) |
| CHAPTER V |
|
71 | (16) |
|
18. The coupled fluid structure problem |
|
|
71 | (9) |
|
19. An iterative algorithm to solve the coupled fluid-structure problem |
|
|
80 | (7) |
| CHAPTER VI |
|
87 | (24) |
|
20. One-dimensional models of blood flow in arteries |
|
|
87 | (24) |
| CHAPTER VII |
|
111 | (11) |
|
21. Some numerical results |
|
|
111 | (11) |
|
|
|
122 | (1) |
| Acknowledgements |
|
122 | (3) |
| REFERENCES |
|
125 | |
Nicolas Ayache is Research Director at INRIA, Le Chesnay, France.
