MODEL1201140002
type: SBMLModel
name: Lenbury2001_InsulinKineticsModel_A
volume units: 122997
compartment: 194319
parameter: 194453
parameter: 194417
parameter: 194381
curated: false
parameter: 194477
rule: 194538
notes: This a model from the article: Modeling insulin kinetics: responses to a single oral glucose administration or ambulatory-fed conditions. Lenbury Y, Ruktamatakul S, Amornsamarnkul S. Biosystems. 2001 Jan;59(1):15-25. 11226623 , Abstract: This paper presents a nonlinear mathematical model of the glucose-insulin feedback system, which has been extended to incorporate the beta-cells' function on maintaining and regulating plasma insulin level in man. Initially, a gastrointestinal absorption term for glucose is utilized to effect the glucose absorption by the intestine and the subsequent release of glucose into the bloodstream, taking place at a given initial rate and falling off exponentially with time. An analysis of the model is carried out by the singular perturbation technique in order to derive boundary conditions on the system parameters which identify, in particular, the existence of limit cycles in our model system consistent with the oscillatory patterns often observed in clinical data. We then utilize a sinusoidal term to incorporate the temporal absorption of glucose in order to study the responses in the patients under ambulatory-fed conditions. A numerical investigation is carried out in this case to construct a bifurcation diagram to identify the ranges of parametric values for which chaotic behavior can be expected, leading to interesting biological interpretations. This model was taken from the CellML repository and automatically converted to SBML. The original model was: lenbury_ruktamatakul_amornsamarnkul_2001_A The original CellML model was created by: Catherine Lloyd c.lloyd@aukland.ac.nz The University of Auckland The Bioengineering Institute This model originates from BioModels Database: A Database of Annotated Published Models (http://www.ebi.ac.uk/biomodels/). It is copyright (c) 2005-2011 The BioModels.net Team. To the extent possible under law, all copyright and related or neighbouring rights to this encoded model have been dedicated to the pu…
rule: 194550
parameter: 194331
is described by: http://identifiers.org/pubmed/11226623
area units: 802883
rule: 194526
length unit: 802859
time units: 152087
parameter: 194356
parameter: 194441
parameter: 194405
parameter: 194514
parameter: 194393
parameter: 194368
parameter: 194489
parameter: 194344
parameter: 194465
parameter: 194429
parameter: 194502
substance units: 163161

194319
type: Compartment
constant: true
size: 1.0
spatial dimensions: 3.0

194453
type: Parameter
constant: true
value: 0.1
name: r_5

194417
type: Parameter
constant: true
value: 0.1
name: r_4

194381
type: Parameter
constant: true
value: 0.1
name: c_1

194477
type: Parameter
constant: true
value: 0.05
name: r_7

194331
type: Parameter
constant: true
value: NaN
name: time

194356
type: Parameter
constant: true
value: 0.2
name: r_1

194441
type: Parameter
constant: false
value: 1.0
name: z

194405
type: Parameter
constant: true
value: 0.1
name: r_3

194514
type: Parameter
constant: true
value: 0.1
name: epsilon

194393
type: Parameter
constant: false
value: 0.0
name: y

194368
type: Parameter
constant: true
value: 0.1
name: r_2

194489
type: Parameter
constant: true
value: 2.0
name: z_hat

194344
type: Parameter
constant: false
value: 4.0
name: x

194465
type: Parameter
constant: true
value: 0.1
name: r_6

194429
type: Parameter
constant: true
value: 0.1
name: c_2

194502
type: Parameter
constant: true
value: 1.24
name: y_hat