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

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13 Conclusion 2 The primary objective of this thesis was to find out if i we could add a natural expansion to the DuCa model ii the expansion induced a more realistic behavior iii the (natural) expansion would agree with experimental data Based on Model C we conclude that: we were able to expand the DuCa model in a way that yielded more realistic simulations, and did not disagree with experimental data. Furthermore we hypothesize that Model C can easily be modified/expanded to investigate different treatment strategies; as outlined in the discussion (chapter 12). 123
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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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Page 88 and 89: 74 Bifurcation Diagrams and Analysi
Page 112 and 113: 98 Discussion of the Bifurcation An
Page 114 and 115: 100 Discussion of the Bifurcation A
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Page 120 and 121: 106 Expanding and Modifying the DuC
Page 132 and 133: 118 Discussion of the Expanded Mode
Page 134 and 135: 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
Page 146 and 147: 132 Mathematical Appendices the com
Page 148 and 149: 134 Mathematical Appendices in that
Page 150 and 151: 136 Mathematical Appendices A.6 Dim
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Page 154 and 155: 140 Additional Figures Figure B.2 P
Page 156 and 157: 142 Additional Figures B.2 Eigenval
Page 158 and 159: 144 Additional Figures Figure B.8 P
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
Page 176 and 177: 162 matlab Code n=675; w_5=0; dw_5=
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
Page 182 and 183: 168 matlab Code M=M’; % M must be
Page 184 and 185: 170 matlab Code %options = odeset(
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172
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174 Index value, 73 Bifurcation Ana
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176 Index of diabetes, 2 Michaelis
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nr. 477 - 2011 - Institut for Natur, Systemer og Modeller (NSM)

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