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

Gastrin, 14, 15
Global Bifurcation, 71, 83
GLP-1, 121
anti-apoptosis, 14
Glucagon-Like Peptide 1 (GLP-1), 2, 14
Glutamic Acid Decarboxylase (GAD), 8
Growth Rate, 133
Hartman-Grobman’s Theorem, 59, 132
Healthy β-Cells
linear depletion of, 106
simulation of, 108
Healthy Rest State(HRS), 75
Heteroclinic Orbit, 83
figure 8.7, 83
Hill Function, 34
Hill function, 26
Homeomorphism, 59
Homeostasis, 7
Hopf Bifurcation, 71
degenerate, 68
on the USBf1-NOD, 77
point, 75
subcritical, 87
supercritical, 68
value, 87
Hopf Bifurcation Theorem, 77
Hyperbolic, 59
Hyperglycemia, 1, 7
Hypoglycemia, 2
Hysteresis, 69, 87
IDDM, 1, 2
IM
including crowding terms
flow equivalence to the DuCa, 81
Immune System
Adaptive, 15
Implicit Function Theorem, 55, 132
Incretin Concept, 2, 8
Inflammation
upper bound of, 81
Influx
of macrophages, 25
Initial Condition, 66
Insulin, 1
first bolus of, 1
175
Insulin Dependent Diabetes Mellitus (IDDM),
1
Insulitis, 9, 106
Interferon (IFN), 10
Interleukin (IL)
1, 10, 120
2, 10
Intermediate Model (IM), 21
Irreversible Model
NOD phagocytosis, 40
phase space
M versus Ma, 42
Islet of Langerhans, 7, 9
Jacobian, 50, 59, 71
and general solution of ODE, 66
in Newton-Raphson, 70
La Barre, 2
Limit Cycle, 67, 77
detection of, 77
semi-stable, 43
Linear Differential Equation
general solution of, 67
Lipschitz, 131
Lipschitz Continuity, 131
Lower Unstable Branch (LUB)
NODf2, 90
NODf1 , 75
Macrophage, 9, 18
volume of, 99
Manifold, 59
stable, 94
stable, 79
NODf1-USB, 76
unstable, 79
of the NODf1-LUB, 83
of the NODf1-USB, 83
Mass Action Kinetics, 30
Mathematical Model, 16
Mathematical Modelling, 17
and etiology of T1D, 2
and medical sciences, 17
construction of, 17
GLP-1, 15
guidelines, 17