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value: 0.025
name: k3
type: Parameter

217247
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value: 0.1
name: epsilon
type: Parameter

217251
constant: true
value: 0.009
name: a2
type: Parameter

217266
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value: 0.5
name: kp
type: Parameter

217250
constant: true
value: 0.05
name: a1
type: Parameter

993339
unit: 993351
name: time
type: SBMLUnitsDef

217259
constant: true
value: 0.3
name: b2
type: Parameter

217257
constant: true
value: 0.1
name: b1
type: Parameter

217256
constant: true
value: 0.005
name: a5
type: Parameter

459609
constant: false
boundary condition: false
has only substance units: false
initial concentration: 1.0
initial amount: NaN
in compartment: 217240
name: active osteoclasts
type: Species

993327
exponent: 1.0
scale: 0
multipler: 60.0
kind: SECOND
type: SBMLUnit

217260
constant: true
value: 0.01
name: b3
type: Parameter

217240
constant: true
units: litre
size: 1.0
spatial dimensions: 3.0
type: Compartment

993315
unit: 993327
name: minute
type: SBMLUnitsDef

993351
exponent: 1.0
scale: 0
multipler: 60.0
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459610
constant: false
boundary condition: false
has only substance units: false
initial concentration: 0.15
initial amount: NaN
in compartment: 217240
name: active osteoblasts
type: Species

459607
constant: false
boundary condition: false
has only substance units: false
initial concentration: 2.0
initial amount: NaN
in compartment: 217240
name: PTH
type: Species

217253
constant: true
value: 0.675
name: a3
type: Parameter

217254
constant: true
value: 0.01
name: a4
type: Parameter

MODEL1012140000
parameter: 217254
type: SBMLModel
parameter: 217263
parameter: 217250
parameter: 217256
species: 459607
is described by: http://identifiers.org/pubmed/12753937
volume units: volume
species: 459610
area units: area
length unit: length
parameter: 217266
rule: 217246
rule: 217243
parameter: 217259
units def: 993315
parameter: 217265
parameter: 217251
parameter: 217257
parameter: 217248
species: 459609
units def: 993339
parameter: 217247
notes: This a model from the article: Modeling of bone formation and resorption mediated by parathyroid hormone: response to estrogen/PTH therapy. Rattanakul C, Lenbury Y, Krishnamara N, Wollkind DJ. Biosystems 2003:70(1):55-72. 12753937 , Abstract: Bone, a major reservoir of body calcium, is under the hormonal control of the parathyroid hormone (PTH). Several aspects of its growth, turnover, and mechanism, occur in the absence of gonadal hormones. Sex steroids such as estrogen, nonetheless, play an important role in bone physiology, and are extremely essential to maintain bone balance in adults. In order to provide a basis for understanding the underlying mechanisms of bone remodeling as it is mediated by PTH, we propose here a mathematical model of the process. The nonlinear system model is then utilized to study the temporal effect of PTH as well as the action of estrogen replacement therapy on bone turnover. Analysis of the model is done on the assumption, supported by reported clinical evidence, that the process is characterized by highly diversified dynamics, which warrants the use of singular perturbation arguments. The model is shown to exhibit limit cycle behavior, which can develop into chaotic dynamics for certain ranges of the system's parametric values. Effects of estrogen and PTH administrations are then investigated by extending on the core model. Analysis of the model seems to indicate that the paradoxical observation that intermittent PTH administration causes net bone deposition while continuous administration causes net bone loss, and certain other reported phenomena may be attributed to the highly diversified dynamics which characterizes this nonlinear remodeling process. About this model: This model represents the second model from the published paper (eqs 35-37). The model has been built on the core model (which describes changes in the concentration of PTH, the number of osteoclasts and the number of osteoblasts) by considering the effects of exogeno…
curated: false
parameter: 217262
rule: 217244
time units: 993339
name: Rattanakul2003_BoneFormation_PTHadministration
compartment: 217240
substance units: substance
parameter: 217260
parameter: 217253

217262
constant: true
value: 0.1
name: k1
type: Parameter

217263
constant: true
value: 0.5
name: k2
type: Parameter

217248
constant: true
value: 0.9
name: delta
type: Parameter