Modeling the interactions between osteoblast and osteoclast activities in bone remodeling
Catherine
Lloyd
Bioengineering Institute, University of Auckland
Model Structure
Please note that the CellML model presented here (variant 1) represents an extension of the core model (version 1) such that osteoblasts are being added at a constant rate from day 20 to day 80.
Bone is a dynamic, living tissue whose structure and shape are continually adjusting to provide a structural framework. In addition to its supporting function, bone also represents the principal site of hematopoiesis. Bone comprises a unique composite of living cells embedded within a three dimensional, mineralised, honeycomb like structure. Even after the skeletal growth is complete, bone remodelling continues. This complex process is carried out by two types of cells; osteoclasts and osteoblasts. Osteoclasts are responsible for the resorption of mineralised bone, while osteoblasts are responsible for the synthesis of bone matrix. The interaction between osteoblasts and osteoclasts is known as coupling, and it is essential for maintaining a balance between the rates of bone loss and gain. Metabolic bone diseases occur when a biochemical or cellular link in this regulated network is disrupted. One such disease is osteoporosis, characterised by rapid bone loss together with the spontaneous fracturing of the remaining bone.
In the paper described here, Lemaine et al. present a mathematical model of the interactions which occur between osteoblasts and osteoclasts in the process of bone remodelling. Using this model the authors were able to simulate skeletal disease by inserting dysfunctional connections in the coupling network to explore different disease hypotheses.
model diagram
Schematic diagram of the basic structure of the model.
The complete original paper reference is cited below:
Modeling the interactions between osteoblast and osteoclast activities in bone remodeling, Vincent Lemaire, Frank L. Tobin, Larry D. Greller, Carolyn R. Cho, and Larry J. Suva, 2004, Journal of Theoretical Biology, 229, 293-309. PubMed ID: 15234198
R
responding osteoblasts
$\frac{d R}{d \mathrm{time}}=\mathrm{DR}\mathrm{pi\_C}-\frac{\mathrm{DB}}{\mathrm{pi\_C}}R$
B
active osteoblasts
$\frac{d B}{d \mathrm{time}}=\frac{\mathrm{DB}}{\mathrm{pi\_C}}R-\mathrm{kB}B+ff=\begin{cases}0.0001 & \text{if $(\mathrm{time}> 20.0)\land (\mathrm{time}\le 80.0)$}\\ 0.0 & \text{otherwise}\end{cases}$
C
active osteoclasts
$\frac{d C}{d \mathrm{time}}=\mathrm{DC}\mathrm{pi\_L}-\mathrm{DA}\mathrm{pi\_C}C$
$\mathrm{pi\_L}=\frac{\mathrm{k3}}{\mathrm{k4}}\frac{\mathrm{KLP}\mathrm{pi\_P}B}{1.0+\frac{\mathrm{k3}K}{\mathrm{k4}}+\frac{\mathrm{k1}}{\mathrm{k2}\mathrm{ko}}(\frac{\mathrm{KOP}}{\mathrm{pi\_P}}R+\mathrm{Io})}(1.0+\frac{\mathrm{IL}}{\mathrm{rL}})$
$\mathrm{DB}=\mathrm{f0}\mathrm{dB}\mathrm{pi\_C}=\frac{C+\mathrm{f0}\mathrm{C\_s}}{C+\mathrm{C\_s}}\mathrm{pi\_P}=\frac{P+\mathrm{P\_0}}{P+\mathrm{P\_s}}P=\frac{\mathrm{IP}}{\mathrm{kP}}\mathrm{P\_0}=\frac{\mathrm{SP}}{\mathrm{kP}}\mathrm{P\_s}=\frac{\mathrm{k6}}{\mathrm{k5}}$
osteoblast
osteoclast
osteoporosis
parathyroid hormone
Larry
Suva
J
Modeling the interactions between osteoblast and osteoclast activities in bone remodeling
229
293
309
Vincent
Lemaire
keyword
The University of Auckland, Bioengineering Institute
2004-08-07
Lemaire et al's 2004 mathematical model of the interactions between osteoblast and osteoclast activities in bone remodelling.
c.lloyd@auckland.ac.nz
140
10000
0.1
This is a CellML description of Lemaire et al's 2004 mathematical model of the interactions between osteoblast and osteoclast activities in bone remodelling.
James
Lawson
Richard
2008-09-12T16:22:14+12:00
Larry
Greller
D
Frank
Tobin
L
2007-07-26T00:00:00+00:00
deleted extraneous connection
added cmeta:id's
added simulation metadata
Carolyn
Cho
R
Catherine Lloyd
15234198
Journal of Theoretical Biology
The University of Auckland
The Bioengineering Institute
Catherine
Lloyd
May