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

More documents

Recommendations

Info

42 The DuCa Model Figure 5.12 shows simulations of the irreducible model made with matlab where k = 0, f1 = 1.29 × 10 −5 ml cell −1 d −1 , f2 = 5.66 × 10 −5 ml cell −1 d −1 , and the term −cMa has been added in equation 5.7 to model turnover of active macrophages. The initial values are that of a healthy rest state. On the left we have the log-concentration versus time plots of the concentrations. On the right is a phase space plot of M versus Ma. Figure 5.13 shows a simulation made with matlab of the reversible model where a term of −cMa has been added to equation 5.7 to model turnover of active macrophages. The simulation is done with f1 = 1.31 × 10 −5 ml cell −1 d −1 , f2 = 5.18 × 10 −5 ml cell −1 d −1 and initial conditions that simulate a healthy rest state. fails to exhibit Balb/c dynamics as observed in experiments. In figure 5.14 we see the solution curves of the respective concentrations in a log-concentration versus time plot, and a phase space portrait of the resting versus active macrophages. The phase space portrait shows that a so-called limit cycle exists for (f1, f2) = (1.88, 5) in the DuCa model with Ma-efflux.
5.8 Discussion of Parameters 43 Figure 5.14 In the figures simulations of the DuCa model with turnover of the active macrophages are presented. To the right we see sustained oscillations in the concentrations of macrophages, active macrophages, apoptotic and necrotic β-cells, and to the left we have a phase space plot of macrophage versus active macrophage concentration. The phase space portrait reveals the existence of a limit cycle, which by further numerical inspection turns out to be semi-stable.
Page 1 and 2:
- I, OM OG MED MATEMATIK OG FYSIK E
Page 3 and 4:
Exploring Treatment Strategies for
Page 5: Preface iii questions that were out
Page 8 and 9: vi Contents Significance of the Apo
Page 10 and 11: List of Tables 5.1 summarizes the m
Page 12 and 13: x List of Figures 8.3 Phase space p
Page 14 and 15: xii
Page 16 and 17: 2 Introduction In the following dec
Page 18 and 19: 4 Introduction There are several sc
Page 20 and 21: 6 Introduction because I had to mak
Page 22 and 23: 8 Type 1 Diabetes and Its Etiology
Page 24 and 25: 10 Type 1 Diabetes and Its Etiology
Page 27 and 28: 3 Prospects for Therapy - A Mini Re
Page 29 and 30: 3.3 Gastrin 15 eration in situ Urus
Page 31 and 32: 4 Mathematical Modelling The langua
Page 33 and 34: 5 The DuCa Model In the following w
Page 35 and 36: 5.3 The DuCa Model - An Appetiser 2
Page 37 and 38: 5.4 The DuCa Model - Compartment Mo
Page 43 and 44: 5.6 Our Compartment Model 29 migrat
Page 45 and 46: 5.6 Our Compartment Model 31 a ✓
Page 47 and 48: 5.7 Discussion of Marée et al. (20
Page 49 and 50: 5.7 Discussion of Marée et al. (20
Page 51 and 52: 5.8 Discussion of Parameters 37 Fig
Page 53 and 54: 5.8 Discussion of Parameters 39 Par
Page 55: 5.8 Discussion of Parameters 41 tha
Page 60 and 61: 46 The Intermediated Model The diff
Page 62 and 63: 48 The Intermediated Model expected
Page 64 and 65: 50 The Intermediated Model Stabilit
Page 66 and 67: 52 The Intermediated Model restrict
Page 68 and 69: 54 The Intermediated Model We see t
Page 70 and 71: 56 The Intermediated Model paramete
Page 72 and 73: 58 The Intermediated Model ✻ Ma(t
Page 74 and 75: 60 The Intermediated Model 6.2 The
Page 76 and 77: 62 The Intermediated Model ✻ Ma(t
Page 79 and 80: 7 A Brief Introduction to Bifurcati
Page 81 and 82: 7.2 The Hopf bifurcation 67 the gen
Page 83 and 84: 7.3 Biological Relevance of Bifurca
Page 85: 7.5 Locating the Fixed Points 71 Ev
Page 88 and 89: 74 Bifurcation Diagrams and Analysi
Page 106 and 107:
92 Bifurcation Diagrams and Analysi
Page 108 and 109:
Page 110 and 111:
Page 112 and 113:
98 Discussion of the Bifurcation An
Page 114 and 115:
100 Discussion of the Bifurcation A
Page 116 and 117:
102
Page 118 and 119:
104
Page 120 and 121:
106 Expanding and Modifying the DuC
Page 122 and 123:
Page 124 and 125:
Page 126 and 127:
Page 128 and 129:
Page 130 and 131:
Page 132 and 133:
118 Discussion of the Expanded Mode
Page 134 and 135:
120 Discussion of the Expanded Mode
Page 136 and 137:
122
Page 138 and 139:
124
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
Page 152 and 153:
138
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 160 and 161:
Page 162 and 163:
148 Additional Figures Figure B.14
Page 164 and 165:
Page 166 and 167:
Page 168 and 169:
Page 170 and 171:
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(
Page 186 and 187:
172
Page 188 and 189:
174 Index value, 73 Bifurcation Ana
Page 190 and 191:
176 Index of diabetes, 2 Michaelis
show all

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

Create successful ePaper yourself

Delete template?

Save as template?