Modeling the interactions between osteoblast and osteoclast activities in bone remodeling
Catherine
Lloyd
Auckland Bioengineering Institute, The University of Auckland
Model Status
This CellML model represents an extension of the core model such that responding osteoclasts are being added at a constant rate from day 20 to day 80. The model runs in both OpenCell and COR to recreate the published results. The units are consistent throughout.
Model Structure
ABSTRACT: We propose a mathematical model explaining the interactions between osteoblasts and osteoclasts, two cell types specialized in the maintenance of the bone integrity. Bone is a dynamic, living tissue whose structure and shape continuously evolves during life. It has the ability to change architecture by removal of old bone and replacement with newly formed bone in a localized process called remodeling. The model described here is based on the idea that the relative proportions of immature and mature osteoblasts control the degree of osteoclastic activity. In addition, osteoclasts control osteoblasts differentially depending on their stage of differentiation. Despite the tremendous complexity of the bone regulatory system and its fragmentary understanding, we obtain surprisingly good correlations between the model simulations and the experimental observations extracted from the literature. The model results corroborate all behaviors of the bone remodeling system that we have simulated, including the tight coupling between osteoblasts and osteoclasts, the catabolic effect induced by continuous administration of PTH, the catabolic action of RANKL, as well as its reversal by soluble antagonist OPG. The model is also able to simulate metabolic bone diseases such as estrogen deficiency, vitamin D deficiency, senescence and glucocorticoid excess. Conversely, possible routes for therapeutic interventions are tested and evaluated. Our model confirms that anti-resorptive therapies are unable to partially restore bone loss, whereas bone formation therapies yield better results. The model enables us to determine and evaluate potential therapies based on their efficacy. In particular, the model predicts that combinations of anti-resorptive and anabolic therapies provide significant benefits compared with monotherapy, especially for certain type of skeletal disease. Finally, the model clearly indicates that increasing the size of the pool of preosteoblasts is an essential ingredient for the therapeutic manipulation of bone formation. This model was conceived as the first step in a bone turnover modeling platform. These initial modeling results are extremely encouraging and lead us to proceed with additional explorations into bone turnover and skeletal remodeling.
model diagram
Schematic diagram of the basic structure of the model.
The 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
B
active osteoblasts
C
active osteoclasts
osteoblast
osteoclast
osteoporosis
parathyroid hormone
Carolyn
Cho
R
Main Model + Adding Responding Osteoclasts
The University of Auckland, Bioengineering Institute
Journal of Theoretical Biology
The University of Auckland
The Bioengineering Institute
Larry
Greller
D
Larry
Suva
J
Vincent
Lemaire
Catherine Lloyd
140
10000
0.1
15234198
Catherine
Lloyd
May
Frank
Tobin
L
2007-07-26T00:00:00+00:00
keyword
Modeling the interactions between osteoblast and osteoclast activities in bone remodeling
229
293
309
This is a CellML description of Lemaire et al's 2004 mathematical model of the interactions between osteoblast and osteoclast activities in bone remodelling.
Lemaire et al's 2004 mathematical model of the interactions between osteoblast and osteoclast activities in bone remodelling.
2004-08-07
c.lloyd@auckland.ac.nz
$\frac{d R}{d \mathrm{time}}=\mathrm{DR}\mathrm{pi\_C}-\frac{\mathrm{DB}}{\mathrm{pi\_C}}R$
$\frac{d B}{d \mathrm{time}}=\frac{\mathrm{DB}}{\mathrm{pi\_C}}R-\mathrm{kB}B$
$\frac{d C}{d \mathrm{time}}=\mathrm{DC}\mathrm{pi\_L}-\mathrm{DA}\mathrm{pi\_C}C+ff=\begin{cases}0.0001 & \text{if $(\mathrm{time}> 20)\land (\mathrm{time}\le 80)$}\\ 0 & \text{otherwise}\end{cases}$
$\mathrm{pi\_L}=\frac{\frac{\frac{\mathrm{k3}}{\mathrm{k4}}\mathrm{KLP}}{1}\mathrm{pi\_P}B}{1+\frac{\mathrm{k3}K}{\mathrm{k4}}+\frac{\mathrm{k1}}{\mathrm{k2}\mathrm{ko}}(\frac{\frac{\mathrm{KOP}}{1}}{\mathrm{pi\_P}}R+\mathrm{Io})}(1+\frac{\mathrm{IL}}{\mathrm{rL}})$
$\mathrm{DB}=\mathrm{f0}\mathrm{dB}\mathrm{pi\_C}=\frac{C+\mathrm{f0}\mathrm{C\_s}}{C+\mathrm{C\_s}}\mathrm{pi\_P}=\frac{P+\mathrm{P\_0}}{P+\mathrm{P\_s}}P=\frac{\mathrm{IP}}{\mathrm{kP}}\mathrm{P\_0}=\frac{\mathrm{SP}}{\mathrm{kP}}\mathrm{P\_s}=\frac{\mathrm{k6}}{\mathrm{k5}}$