MODEL1006230083
type: SBMLModel
modified:
  W3 CDTF: Fri Jun 25 14:40:08 BST 2010
name: Kroll2000_PTH_BoneFormationDesorption
parameter: 607628
created:
  W3 CDTF: Fri Jun 25 14:40:08 BST 2010
length unit: 493212
parameter: 607617
rule: 607607
curated: false
parameter: 607627
units def: 570425
parameter: 607632
modified:
  W3 CDTF: Fri Jun 25 14:40:08 BST 2010
is described by: http://identifiers.org/pubmed/10824426
parameter: 607613
parameter: 607622
compartment: 607602
parameter: 607619
parameter: 607618
rule: 607606
volume units: 290956
creator:
  ORG:
    orgname: University of Auckland
  n:
    given: Catherine
    family: Lloyd
rule: 607611
substance units: 178797
modified:
  W3 CDTF: Fri Jun 25 14:40:08 BST 2010
units def: 570449
rule: 607609
parameter: 607633
units def: 570473
creator:
  ORG:
    orgname: University of Auckland
  n:
    given: Catherine
    family: Lloyd
parameter: 607615
parameter: 607614
parameter: 607624
parameter: 607623
parameter: 607620
creator:
  ORG:
    orgname: University of Auckland
  n:
    given: Catherine
    family: Lloyd
parameter: 607629
area units: 237671
parameter: 607630
rule: 607610
parameter: 607634
notes: This a model from the article: Parathyroid hormone temporal effects on bone formation and resorption. Kroll MH. Bull Math Biol 2000 Jan;62(1):163-88 10824426 , Abstract: Parathyroid hormone (PTH) paradoxically causes net bone loss (resorption) when administered in a continuous fashion, and net bone formation (deposition) when administered intermittently. Currently no pharmacological formulations are available to promote bone formation, as needed for the treatment of osteoporosis. The paradoxical behavior of PTH confuses endocrinologists, thus, a model bone resorption or deposition dependent on the timing of PTH administration would de-mystify this behavior and provide the basis for logical drug formulation. We developed a mathematical model that accounts for net bone loss with continuous PTH administration and net bone formation with intermittent PTH administration, based on the differential effects of PTH on the osteoblastic and osteoclastic populations of cells. Bone, being a major reservoir of body calcium, is under the hormonal control of PTH. The overall effect of PTH is to raise plasma levels of calcium, partly through bone resorption. Osteoclasts resorb bone and liberate calcium, but they lack receptors for PTH. The preosteoblastic precursors and preosteoblasts possess receptors for PTH, upon which the hormone induces differentiation from the precursor to preosteoblast and from the preosteoblast to the osteoblast. The osteoblasts generate IL-6; IL-6 stimulates preosteoclasts to differentiate into osteoclasts. We developed a mathematical model for the differentiation of osteoblastic and osteoclastic populations in bone, using a delay time of 1 hour for differentiation of preosteoblastic precursors into preosteoblasts and 2 hours for the differentiation of preosteoblasts into osteoblasts. The ratio of the number of osteoblasts to osteoclasts indicates the net effect of PTH on bone resorption and deposition; the timing of events producing the maximum ratio would…
time units: 570473
parameter: 607625

607628
type: Parameter
constant: true
value: 0.01
name: ky

607617
type: Parameter
constant: false
value: 200.0
name: Z

607627
type: Parameter
constant: true
value: 0.02
name: k6

570425
type: SBMLUnitsDef
unit: 570437
name: hour

570437
type: SBMLUnit
exponent: 1.0
scale: 0
multipler: 3600.0
kind: SECOND

607632
type: Parameter
constant: true
value: 1.0
name: C1

607613
type: Parameter
constant: false
value: 10.0
name: Y

607622
type: Parameter
constant: true
value: 1.3
name: k2

607602
type: Compartment
constant: true
units: litre
size: 1.0
spatial dimensions: 3.0

607619
type: Parameter
constant: true
value: 50.0
name: C

607618
type: Parameter
constant: false
value: 1.9
name: IL6

570449
type: SBMLUnitsDef
unit: 570461
name: first_order_rate_constant

570461
type: SBMLUnit
exponent: -1.0
scale: 0
multipler: 3600.0
kind: SECOND

607633
type: Parameter
constant: true
value: 1.0
name: C2

570473
type: SBMLUnitsDef
unit: 570485
name: time

570485
type: SBMLUnit
exponent: 1.0
scale: 0
multipler: 3600.0
kind: SECOND

607615
type: Parameter
constant: false
value: 10.0
name: P

607614
type: Parameter
constant: false
value: 500.0
name: X

607624
type: Parameter
constant: true
value: 0.9
name: k4

607623
type: Parameter
constant: true
value: 0.05
name: k3

607620
type: Parameter
constant: true
value: 1.0
name: k1

607629
type: Parameter
constant: true
value: 5.0
name: K

607630
type: Parameter
constant: true
value: 2.0
name: K2

607634
type: Parameter
constant: true
value: 1.0
name: C3

607625
type: Parameter
constant: true
value: 5.0
name: k5