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# Contents

Preface vii
1 PDE Model Formulation 1
2 Model Implementation 3
2.1 Introduction .......................... 3
2.2 ProgrammingofMBPDEModel ............... 3
2.2.1 MainProgram ..................... 3
2.2.2 ODE/MOLRoutine .................. 13
2.3 SummaryandConclusions .................. 16
References ............................... 16
3 Model Output 17
3.1 Introduction .......................... 17
3.2 Fixed Boundary Output .................... 17
3.3 Constant Rate Moving Boundary Output .......... 23
3.4 Variable Rate Moving Boundary Output .......... 29
3.5 SummaryandConclusions .................. 43
4 Tumor Growth 45
4.1 Introduction .......................... 45
4.2 PDEsinCoordinate-freeFormat ............... 45
4.3 Vector Operators in Spherical Coordinates ......... 46
4.4 1D PDE Model, Spherical Coordinates ........... 47
4.4.1 MainProgram ..................... 51
4.4.2 ODE/MOLRoutine .................. 64
4.4.3 ModelOutput...................... 69
4.5 SummaryandConclusions .................. 86
References ............................... 86
5 Plaque Formation in Atherosclerosis 89
5.1 Introduction .......................... 89
5.2 PDEModel ........................... 89
5.2.1 MainProgram ..................... 93
5.2.2 ODE/MOLRoutine .................. 108
5.2.3 ModelOutput...................... 115

5.3 SummaryandConclusions .................. 130
References ............................... 130
ppendix A1: Test of Spline Regridding 131
A1.1 Fixed Boundary Analysis ................... 131
A1.2 Moving Boundary Analysis .................. 144
ppendix A2: Test of Moving Boundary Algorithm
Spline Formulation 159
A2.1 MainProgram ......................... 159
A2.2 ODE/MOLRoutine ...................... 163
A2.3 ModelOutput ......................... 164
ppendix A3: Test of Moving Boundary Algorithm Finite
Difference Formulation 167
A3.1 MainProgram ......................... 167
A3.2 ODE/MOLRoutine ...................... 169
A3.3 ModelOutput ......................... 172
Reference ................................ 176
Index  177