MODEL1012140001
type: SBMLModel
rule: 201260
species: 459609
parameter: 201287
parameter: 201305
parameter: 201270
parameter: 201302
parameter: 201273
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 third model from the published paper (eqs 38-40). 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 exogenou…
parameter: 201308
parameter: 201267
length unit: length
is described by: http://identifiers.org/pubmed/12753937
units def: 997987
parameter: 201278
time units: 997987
rule: 201263
name: Rattanakul2003_BoneFormation_Estrogenadministration
area units: area
species: 459610
compartment: 201256
parameter: 201290
volume units: volume
rule: 201266
parameter: 201296
units def: 997963
parameter: 201284
species: 459607
curated: false
parameter: 201277
substance units: substance
parameter: 201299
parameter: 201293

459609
type: Species
constant: false
boundary condition: false
has only substance units: false
initial concentration: 1.0
initial amount: NaN
in compartment: 201256
name: active osteoclasts

201256
type: Compartment
constant: true
units: litre
size: 1.0
spatial dimensions: 3.0

201287
type: Parameter
constant: true
value: 0.005
name: a5

201305
type: Parameter
constant: true
value: 0.025
name: k3

201270
type: Parameter
constant: true
value: 0.9
name: delta

201302
type: Parameter
constant: true
value: 0.5
name: k2

201273
type: Parameter
constant: true
value: 0.05
name: a1

201308
type: Parameter
constant: true
value: 0.2
name: kc

201267
type: Parameter
constant: true
value: 0.1
name: epsilon

997987
type: SBMLUnitsDef
unit: 997999
name: time

997999
type: SBMLUnit
exponent: 1.0
scale: 0
multipler: 60.0
kind: SECOND

201278
type: Parameter
constant: true
value: 0.675
name: a3

459610
type: Species
constant: false
boundary condition: false
has only substance units: false
initial concentration: 0.15
initial amount: NaN
in compartment: 201256
name: active osteoblasts

201290
type: Parameter
constant: true
value: 0.1
name: b1

201296
type: Parameter
constant: true
value: 0.01
name: b3

997963
type: SBMLUnitsDef
unit: 997975
name: minute

997975
type: SBMLUnit
exponent: 1.0
scale: 0
multipler: 60.0
kind: SECOND

201284
type: Parameter
constant: true
value: 0.01
name: a4

459607
type: Species
constant: false
boundary condition: false
has only substance units: false
initial concentration: 2.0
initial amount: NaN
in compartment: 201256
name: PTH

201277
type: Parameter
constant: true
value: 0.009
name: a2

201299
type: Parameter
constant: true
value: 0.1
name: k1

201293
type: Parameter
constant: true
value: 0.3
name: b2