Proceedings of the ASME 2011 Summer Bioengineering Conference
SBC2011
June 22-25, Nemacolin Woodlands Resort, Famington, Pennsylvania, USA
SBC2011-53714
SIMULATION OF THE EMERGENCE OF THE ENDOCHONDRAL OSSIFICATION
PROCESS IN EVOLULTION
Hanifeh Khayyeri, Patrick J. Prendergast
Trinity Centre for Bioengineering
Trinity College Dublin
Dublin, Ireland
INTRODUCTION
periosteum and outer callus, migrated and proliferated in to the
fracture site and differentiated into osteoblasts, chondrocytes or
fibroblasts depending on a biophysical stimulus (S). Based on fluid
flow and shear strain (4), MSC fate was determined according to the
following scheme:
The ability of tissues to adapt to the mechanical environment is a
remarkable feature of the skeleton. Although the mechano-regulation
process is very complex, several mechano-regulation theories for
musculo-skeletal tissues have successfully predicted the tissue
differentiation and remodelling process in various scenarios with
reasonable accuracy (1,2); but how did mechano-regulated bone
differentiation emerge in evolution? Early vertebrates, like
cartilaginous fishes, could modulate their tissues to the mechanical
environment and it is likely that evolution worked with the regulatory
genes for skeletal tissues, rather than changes in structural genes, i.e.
adapting skeletal tissues to the local conditions rather than involving
major changes in cells or tissue types (3).
In this study, we hypothesised that mechano-regulated
endochondral ossification has emerged in evolution by being favoured
by natural selection. In particular, we investigate if a combination of a
mechano-regulated tissue differentiation model and a genetic
algorithm describing evolutionary change can simulate the emergence
of the mechano-regulated endochondral ossification process similar to
that reported in animal experiments.
Healing was assumed to be reached when the entire fracture gap had
been replaced with osteoblasts. Tissue differentiation simulations with
variations of the endochondral boundary (m) – n is kept constant –
were performed to generate a fitness function.
Fitness Function
The fitness function depended on the healing time (HT), where
shorter healing time represented a better fitness and gave higher
probability of mating. As endochondral ossification would emerge
(m>0) in evolution, the fracture healing time changed and therefore the
fitness. The probability of surviving depended on the fitness of the
individual, i.e. HT, and a hazard rate (HR), which increased the
probability of dying linearly with healing time (Eq. 1).
MATERIALS AND METHODS
Tissue Differentiation Model
Pr(survival) = 1 – HT(m)*HR(t)
As the ability to heal fractures could have a profound effect on
the survival rate of vertebrates a 3D finite element model of a mouse
fracture was developed to simulate the mechano-regulation
endochondral ossification process. The fracture gap was 0.4 mm and
was loaded with 2 BWs daily. The tissues were modelled as
poroelastic and Abaqus soils analysis was used to compute the
mechanical environment. To model the stochastic cellular activities of
migration, proliferation, apoptosis and differentiation a lattice
modelling approach was adopted, which mapped the mechanical
environment computed for each finite element onto a grid of lattice
points representing positions for cell activity (2).
The time course of healing was simulated in a series of time
increments, where one increment represented one day. During each
increment, mesenchymal stem cells, originating from the marrow,
(1)
Genetic Algorithm
The evolution process was modelled using a genetic algorithm
developed by Nowlan and Prendergast (2005), with mutations. A
hypothetical population of 1000 diploid individuals were equipped
with 5 loci (5). The loci were filled with genes that were selected at
random from a gene pool. The m-value, i.e. the endochondral response
to mechanical loading, was determined by the normalised sum of the
average of the genes.
Each generation was assumed to have only one mating
opportunity with no overlaps between the generations. Random
selection and recombination determined the genes of the next
generation, see Fig. 1. Natural selection affected the evolutionary
process such that individuals with low fitness would have low
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Copyright © 2011 by ASME
DISCUSSION
probability to survive a fracture (Eq. 1) and mate whereas individuals
with higher fitness would have a better chance of surviving, therefore
mating and passing their genes on to the next generation. The
evolution process was simulated for 20 000 years, i.e. 1000
generations.
Despite several limitations, the genetic simulation result was in
agreement with experimental studies that show how osteoblast
differentiation is a response to relatively low mechanical stimulus (6).
Furthermore, the results converged not to a single mechano-regulated
boundary value but to a distribution (Fig. 3); this variability represents
the inter-population variation in response to loading, also often
reported in animal experiments. The simulated distribution, Fig. 3, is
capturing the physiological limitations of osteoblast formation and
maintenance during high mechanical loading (7). Also, the simulations
arrived at a realistic and probabilistic boundary value for a mechanoregulation algorithm.
In conclusion, this study corroborated the hypothesis as the
results showed that mechano-regulation of osteoblast differentiation,
when favoured in natural selection, could lead to the emergence of the
endochondral ossification process. Finally, the variable endochondral
ossification process derived from the model is a step towards
developing probabilistic tissue differentiation simulations for a
population.
Figure 1. The process of recombination (5)
RESULTS
The fracture healing simulations generated a fitness function such
that lower values of m predict longer healing times, which decreases as
m emerges in evolution (Fig. 2). No endochondral boundary (m=0)
resulted expectedly in non-union (because no bone was formed at
m=0) and as the endochondral boundary emerged in the process
(m>0), healing was observed within a finite time.
ACKNOWLEDGMENTS
The authors would like to thank Dr. Niamh Nowlan for many
helpful discussions. This project was funded by Science Foundation
Ireland, Principal Investigator Award No. [SFI/06/IN.1/B86].
REFERENCES
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Figure 2. The fitness function derived from the results of
the fracture healing simulations
5.
After evolution of 1000 generations, the model showed an evolved
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and a distribution as seen in Fig. 3. Although each run of the genetic
algorithm gave different results, the final outcome and distribution
were very similar in 10 runs of identical simulations.
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Figure 3. Histology of the m-values (mean=1.1) obtained for
the population after 20 000 years
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Copyright © 2011 by ASME