nr. 477 - 2011 - Institut for Natur, Systemer og Modeller (NSM)

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176 Index of diabetes, 2 Michaelis Constant, 25, 134 Michaelis-Menten, 25, 26 Michaelis-Menten Kinetics, 133 Miracle, 133 Model A, 106, 108 and criterion II, 109 system of equations, 108 Model B, 110, 110 Model Criteria expanded model, 105 Multistability, 101 Newton-Raphson, 71, 134 initial guess, 70 iteration function, 70 method, 70 Nobel Prize, 8 NOD, 7, 18 Nonlinear System, 59 flow of, 59 Nonlinearity, 24 Normoglycemia, 14, 15 Nullcline, 54, 57, 60 Nutrient, 133 Oscillation and spirals, 67 Pancreas, 7 Parameter Sensitivity, 69 Phagocytosis, 9 Rate, 70 Phase Space, 41, 67 stable spiral, 155 Pitchfork Bifurcation, 66 Poincaré-Bendixson’s Theorem, 59 Principal Minor, 53 QSS Assumption, 74 Quasi-Steady-State Assumption (QSS), 134 Rate Constant, 22 Reaction Equation, 22 differential equation, 22 Reaction Rate, 133 Receptor, 133 Recruitment Rate, 25 Reversible Model NOD phagocytosis, 40 Routh-Hurwitz criteria, 53, 96 Saddle-Node bifurcation, 81 Saddle-Node Bifurcation, 66, 75, 89 Saddle-Point, 66, 81 Saturation, 133 Separatrix, 63, 95 and the IM, 56 in the IM, 56 Sound Model, 3 Specimen-Specific Model, 41 Spiral, 41, 66 stable, 34, 41, 67, 79 at NODf1-USB, 76 unstable, 67, 77 Sprague Dawley Rat, 120 Sprial unstable at NODf1-USB, 78 Stable Manifold of the IM, 56 Stable Manifold Theorem, 59 Stable Spiral existence of, 76 Fig. 8.3, 77 Steady State and nullclines, 54 Substrate, 35 Symptoms, 1 T Cell, 9, 18 autoreactive, 7 immature, 9 T1D, 1, 2, 13, 18, 46 and autoantibodies, 8 and environmental factors, 1 and fatality, 1 and genetic screening, 13 dendritic cell, 15 interspecimen difference in development, 41 symptoms of, 7 T2D, 1
The Intermediate Model, 45 Therapy, 13 β-cell neogenesis, 14 proliferation, 14 regeneration, 14 and DCs, 15 and progression, 13 antigen based, 13 dendritic cells, 16 diet, 13 Epidermal Growth Factor (EGF), 15 gastrin, 14 GLP-1, 14 immunotherapy, 14 Thesis Statement, 3 Topological Equivalence, 59 of flow, 65 Transcritical Bifurcation, 66 Turnover of activated macrophages, 41 of cytokine, 26 Type 1 Diabetes (T1D), 1 Type 2 Diabetes (T2D), 1 Tyrosine Phosphatase (IA-2), 8 Unstable Manifold, 79 Upper Stable Branch (USB) NODf1 NODf1 , 75 NODf2, 90 Upper Unstable Branch (UUB), 85 UUB as part of unstable limit cycle, 86 function of f1, 98 Vatican, 134 177
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- I, OM OG MED MATEMATIK OG FYSIK E
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Exploring Treatment Strategies for
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Preface iii questions that were out
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vi Contents Significance of the Apo
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List of Tables 5.1 summarizes the m
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x List of Figures 8.3 Phase space p
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xii
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2 Introduction In the following dec
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4 Introduction There are several sc
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6 Introduction because I had to mak
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8 Type 1 Diabetes and Its Etiology
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10 Type 1 Diabetes and Its Etiology
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3 Prospects for Therapy - A Mini Re
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3.3 Gastrin 15 eration in situ Urus
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4 Mathematical Modelling The langua
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5 The DuCa Model In the following w
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5.3 The DuCa Model - An Appetiser 2
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5.4 The DuCa Model - Compartment Mo
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5.6 Our Compartment Model 29 migrat
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5.6 Our Compartment Model 31 a ✓
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5.7 Discussion of Marée et al. (20
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5.7 Discussion of Marée et al. (20
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5.8 Discussion of Parameters 37 Fig
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5.8 Discussion of Parameters 39 Par
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5.8 Discussion of Parameters 41 tha
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5.8 Discussion of Parameters 43 Fig
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46 The Intermediated Model The diff
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48 The Intermediated Model expected
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50 The Intermediated Model Stabilit
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52 The Intermediated Model restrict
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54 The Intermediated Model We see t
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56 The Intermediated Model paramete
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58 The Intermediated Model ✻ Ma(t
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60 The Intermediated Model 6.2 The
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62 The Intermediated Model ✻ Ma(t
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7 A Brief Introduction to Bifurcati
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7.2 The Hopf bifurcation 67 the gen
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7.3 Biological Relevance of Bifurca
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7.5 Locating the Fixed Points 71 Ev
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74 Bifurcation Diagrams and Analysi
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98 Discussion of the Bifurcation An
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100 Discussion of the Bifurcation A
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106 Expanding and Modifying the DuC
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118 Discussion of the Expanded Mode
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120 Discussion of the Expanded Mode
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Page 140 and 141: 126 Bibliography Christen, U. and M
Page 142 and 143: 128 Bibliography Notkins, A. L. and
Page 144 and 145: 130 Bibliography Yu, J. and G. S. E
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Page 154 and 155: 140 Additional Figures Figure B.2 P
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Page 162 and 163: 148 Additional Figures Figure B.14
Page 172 and 173: 158 matlab Code w(r+1)=w(r)+dw; g=w
Page 174 and 175: 160 matlab Code end V_11(r)=E(1); V
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Page 178 and 179: 164 matlab Code M=M’; % end s_7(r
Page 180 and 181: 166 matlab Code w_7,V_34,’.b’,w
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Page 184 and 185: 170 matlab Code %options = odeset(
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Page 188 and 189: 174 Index value, 73 Bifurcation Ana
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nr. 477 - 2011 - Institut for Natur, Systemer og Modeller (NSM)

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