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A System Biology Approach to Bone
Remodelling
Andrew Chiu
Abstract – Often viewed as static structural supports, bone is
indeed a dynamic tissue that is capable of self-remodelling. This
process, which involves simultaneous bone resorption and bone
deposition, helps to optimize bone structure and maintain
mineral homeostasis. The bone cells that are involved in bone
remodelling include osteoblasts, osteoclasts, osteocytes, and the
bone-lining cells. Together with the various growth factors and
matrix molecules, they form a network of complex signalling
pathways. In this paper, a systematic approach is applied to the
study of bone remodelling. Two different mathematical models
are presented and discussed. By using quantitative means, the
goal of systems biology is to rationalize the relationships between
the various cells and factors, so that models can be generated to
predict system behaviour.
Index Terms – Bone remodelling, mathematical models,
mechanical stimulus, systems biology
I. INTRODUCTION
Bone is a dynamic, living tissue in that deposition and
resorption constantly take place throughout life.
It is
estimated that for a young healthy adult, over 10% of the total
bone mass is being replaced each year [1]. This process,
termed bone remodelling, plays an important role in body
mineral homeostasis. Besides, as a material, bone is subject to
continual cyclic loading, causing the accumulation of
microdefects in its crystal structure. Remodelling helps to
remove these structural damages, and thus maintaining the
mechanical strength of the skeleton [2].
Bone remodelling can be triggered by a variety of stimuli.
The most common, which is also the one most widely studied,
happens when bone is subject to some aspects of mechanical
loading, such as compression and tensile stress. In fact, the
study of bone response to mechanical stimuli began as early as
the late 19th century when a German anatomist named Julius
Wolff (1892) proposed what was later known as the Wolff’s
Law [3]. He suggested that in response to mechanical stimuli,
bone could adapt optimally, seeking to attain maximum
mechanical efficiency with minimum mass. Moreover, he
observed that the orientation of bone trabeculae were always
in alignment with the direction of principal mechanical stress.
Based on this, a German surgeon named Wilhem Roux (1905)
later suggested that bone cells were capable of sensing their
local environment, therefore optimizing their structure in
response to mechanical stress. He subsequently proposed the
idea of bone adaptation, in which he stated that the change in
bone structure as a result of mechanical stimuli was mediated
by cell-based deposition and resorption [3].
Since then, most of the studies in bone adaptation had been
focused on the structural mechanics. An example of such
research was given by John Koch, who in 1917 performed a
material strength analysis on human femur, through which he
discovered that bone density was highest in areas of highest
shear stress [3]. In fact, it was not until the 1960s when
scientists turned their attention to the physiological
mechanisms of bone adaptation. The first breakthrough came
in 1963 when Donald Enlow postulated that bone remodelling
was mediated by groups of specialized cells, which he referred
as basic multicellular units (BMUs), that resorbed and
synthesized bone at the same site [3]. A similar idea was
proposed by Harold Frost in 1966, who also suggested that
bone remodelling was a highly regulated process in that
resportion by osteoclasts was closely coupled with deposition
by osteoblasts [3].
While all these studies were good in their own, each of
them provided only a partial picture of the whole process of
bone adaptation. In order to obtain a complete and clear
understanding of it, all these findings must be integrated
together, and this is where systems biology comes in. In
general, the essence of systems biology is to investigate the
relationships and interactions between the various components
of the system, so that a model can be built to predict the output
given the values of the input parameters [4].
The application of systems biology to the study of bone
remodelling gives several advantages. First, through iterative
model predictions (hypotheses) and global experimental
observations (discoveries), new insight into the process could
be gained [4]. Second, the construction of a model would
allow scientists to predict the effects of drugs and other
environment factors (such as mechanical stress) on bone, and
thus assist the development of treatments for bone diseases
such as osteoporosis [5].
The objective of this paper is to provide a general
discussion on bone adaptation from a systematic perspective.
A brief review on bone physiology and the remodelling
process will be given; on the basis of that two different models
of bone adaptation will be presented and discussed.
II. BONE PHYSIOLOGY
Bone is the main constituent of the adult skeletal system
that performs several basic functions. First of all, it serves as
the structural framework that helps to maintain the shape of
the body. Second, it provides protection to many internal
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organs. Third, it assists body movement by transmitting
forces of muscular contraction between different parts of the
body. Last, it serves as reservoir for ions and helps to
maintain mineral balances [6].
Bone tissue can be structually organized into two types:
cortical (compact) and trabecular (spongy). Cortical bones are
arranged in units called osteons, which are composed of rings
of hard, calcified matrix called lamellae. They form the
external layers of all bones, and make up the bulk of the
diaphyses (stem) of long bones (e.g. femur, tibia, and humeri).
On the other hand, trabecular bones are composed of irregular
latticework of thin columns of bone called trabeculae. They
make up most of the short, flat, and irregular shaped bones,
and also the inside part of long bones. Overall, the ratio of
cortical to trabecular bones by mass is around 8:2, but the
actual distribution varies greatly between individual bones [6].
Bone is a composite material that consists organic and
inorganic phases. The organic phase, which takes up around
35% of the total weight, mainly consists of collagen, which
accounts for about 90% of organic matrix, bone cells, and
other various noncollagenous proteins such as osteocalcin,
osteonectin, and some other growth factors. The functions of
most of these noncollagenous proteins remain unclear. On the
other hand, the inorganic phase, which accounts for the rest
65% of bone tissue, consists of mainly hydroxyapatite
(calcium phosphate and calcium carbonate) with small
amounts of other mineral salts such as magnesium hydroxide,
fluoride, and sulfate. The deposition of these mineral salts
into the collagen fibre matrix, a process termed mineralization,
provides bones the hardness they need to take on loads [6].
There are four major types of bone cells, namely the
osteoblasts, osteoclasts, osteocytes, and the bone lining cells
[6,7].
Osteoblasts are mononucleated cuboidal cells that originate
from local mesenchymal cells. They secrete collagen fibres
and other organic molecules needed to build the matrix of the
bone tissue, and initiate bone mineralization. They might be
involved in the process of bone resorption as well. In contrast,
osteoclasts are multinucleated giant cells derived from the
fusion of mononucleated cells from the monocyte /
macrophage lineage.
They are responsible for bone
resorption – the breakdown of bone matrix.
Osteocytes are the most abundant cell type in mature bone.
They are derived from osteoblasts that are left behind in the
mineralized bone matrix during bone formation. Osteocytes
are connected to one another, and to the cells on the bone
surface through cellular processes called canuliculi through
which they communicate. There are two main functions for
osteocytes. First, they help to maintain bone integrity.
Second, they detect and respond to mechanical stimuli,
subsequently influencing bone adaptation behaviour.
The last type of cell is the bone lining cells, which are
flattened, elongated cells that cover quiescent bone surfaces.
They serve as a barrier to regulate ionic flux between the bone
matrix and the interstitial fluids, and are involved in
osteoclastic bone resorption.
There are two ways in which bones are formed. The first
one, termed intramembranous ossification, involves the
replacement of connective membranous tissue by bony tissue.
Osteoblasts migrate to sites of ossification where they lay
down bone matrix and initiate mineralization.
In
endochondral ossification, on the other hand, bone tissue is
formed by replacing hyaline cartilage. A cartilage model,
which takes the shape of the future bone, is first formed.
Osteoblasts subsequently replace it with bony tissue.
Bone remodelling refers to the continual process of bone
formation and resorption. It differs from bone formation as
mentioned in that it is coupled process so that the formation
takes place at where the resorption has occurred, resulting no
net gain of bone. Besides, bone remodelling normally takes
place only in mature bones (with low turnover), as it helps to
maintain bone quality and mineral homeostasis.
Bone remodelling consists of 2 phases: resorption and
formation. Upon activation, osteoclasts migrate to the site of
resorption. Each osteoclast subsequently forms a ring-shaped
seal to the bone surface, between which a bone-resorbing
compartment is created. The attached osteoclasts then secret
acids and other protein digesting enzymes into the
compartment. The acids dissolve the bone minerals whereas
the enzymes help to digest the organic components. After
resorbing the bone to a certain depth, the osteoclasts detach,
leaving collagen fibrils protruding from the surface, which are
later removed by the bone lining cells. The whole process of
resorption takes about 1 to 3 weeks.
Bone formation comes about a week or two after the
completion of resorption. It consists of two stages. In first,
osteoblasts proliferate and migrate to the sites of resorption,
where they synthesize and deposit a layer of bone matrix.
After that, mineralization takes place, which takes another 3 to
6 months to complete.
In general, bone remodelling is a complicated process that
involves complex interactions between bone cells and various
signalling factors. Therefore, it is important not just to
identify the elements playing in the process, but also to
understand the relationships between them, from a systematic
perspective.
III. MATHEMATICAL MODELLING
Two different mathematical models are presented. The first
one, which was proposed by S. J. Hazelwood et al. in 2000,
was a mechanistic model that related mechanical stimuli to
bone strength [8]. In contrast, the second model, which was
proposed by M. J. Martin et al. in 2004, focused on the
cellular mechanism of bone remodelling [5].
In Hazelwood’s model [8], bone remodelling was activated
whenever the bone was being disused or overloaded. In the
disuse mode, the bone experienced a lower-than-normal strain
state. Since bone always worked to optimize its structure in
relation to its mechanical needs, this triggered the remodelling
process to remove the ‘excess’ bone. Conversely, in the
overload mode, the bone experienced a higher-than-normal
strain rate, subsequently causing the formation of
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microdamages. Remodelling was hence stimulated to repair
these damages.
Modulus, E
overload
Damage
Formation
Rate, Df
remodelling
Load,Ф / Geometry
Strain, s
disuse
Damage, D
Activation
Frequency, fa
Porisity, P
Damage
Removal
Rate, Dr
Surface
Area, Sa
Fig. 1 – Schematic representation of the bone remodelling algorithm
by S.J. Hazelwood et al. [8]
Maximum Activity x Amount of Substrate
Amount of Substrate + constant K
where K is the Michaelis-Menten constant, which is equal to
the amount of substrate when the activity is half of its
maximum.
During phase I, the activity of osteoclast resorption was
assumed to be limited by the amount of ‘ligand for receptor
activator for nuclear factor κB’ (RANKL). RANKL was
expressed by osteoblasts and bound to osteoclasts during bone
resorption. Another factor that was also considered in the
model was the macrophage colony stimulating factor (M-CSF),
which was produced by the marrow stromal cell. Both
Amax, osteoclast[ RANKL]
[ FM CSF ]
[ RANKL]  K RANKL
Note that M-CSF was not a limiting reagent, so MichaelisMenten did not apply to it.
During Phase II, the collagen fibres that were left by the
osteoclasts became the substrate for the bone-lining cells.
Since the amount of collagen decreased as the process was
going on, it became the limiting reagent:
ActivityBoneLining 
Amax, BoneLining[collagen ]
[collagen ]  K collagen
The following figure illustrated the relationships between
various elements of the model:
Substrate limited by
effective [RANKL]
OPG
M-CSF
Rate of osteoclast
activity
apoptosis TGFβ
TGFβ1
collagen fibrils
Rate of bone-lining
cell activity
Phase II
Activity =
Activityosteoclast 
Phase I
As figure 1 illustrated, this model consisted of 2 feedback
loops. To the right, remodelling resulted in damage removal,
therefore lowering the remodelling activation frequency
(negative feedback). To the left, in contrast, remodelling led
to changes in porosity and elasticity, which in turn affected the
strain state of the bone. Both feedback mechanisms helped to
regulate the process so that homeostasis could be maintained.
In addition, since bone remodelling must start on a bone
surface, the activation frequency was taken to be a function of
the bone surface area (Sa) as well.
Overall, this model consisted of 8 state variables: elastic
modulus (E), porisity (p), damage (D), strain (s), activation
frequency (fa), bone surface area (Sa), and the number of
resorbing (Nr) and refilling (Nf) BMUs. The last two
variables did not show up on the schematic diagram since they
were hidden in the remodelling process. Given an initial
mechanical stimulus (the input), the goal was to numerically
determine the time response of these variables.
In Martin’s model [5], the author broke down the resorption
process into two phases: the digestion of the bone matrix by
osteoclasts, followed by the collagen fibril removal by bonelining cells. In each phase, the cellular activity was modelled
by Michaelis-Menten equation, assuming both ‘reactions’
were regulated by limited ‘substrates’. The general form of
Michaelis-Menten equation is as follow:
promote the differentiation of osteoclasts, and thus the activity
of osteoclast resorption:
amino acids
Fig. 2 – Schematic representation of the bone remodelling algorithm
by M.J. Martin et al. [5]
Notice that this model contained two negative feedback
loops to regulate the osteoclast resorption. In first, the break
down of bone matrix released transforming growth factor β
(TGFβ), which in high concentration triggered the apoptosis
of the osteoclasts. Second, the release of TGFβ1, an isoform
of TGFβ, induced the production of osteoprotegerin (OPG),
which inhibited the binding of RANKL to osteoclasts.
Overall, this model consisted of 6 state variables, namely
the concentrations of RANKL, TGFβ, collagen, and the rates
of activity of the osteoclasts and the bone-lining cells during
phase I and phase II respectively. The aim was to determine
the amount of bone that would be resorbed (output), which
was determined from the amount of amino acids produced,
given the initial concentrations of RANKL and M-CSF.
IV. DISCUSSION
The two mathematical models presented above represent
two different levels of study in systems biology. At the global
level, the model by Hazelwood measured parameters that were
associated with the entire bone, such as porosity, extent of
microdamges, and elastic modulus. It described the effects of
mechanical stimuli on the structural properties of bone on the
basis of the whole organ. On the other hand, the model by
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Martin portrayed the cellular mechanism of bone remodelling
at local bone site. The term ‘local’ is used here because bone
remodelling is usually only confined to a small region. In
particular, depending on the distribution of stress and / or
other factors, a bone could have resorption at one site while
deposition at another site [2].
While both models demonstrated certain successes in
accordance to their results, their scopes were limited. It is
therefore necessary to develop models that would allow the
interactions of local adaptation mechanism with the overall
structural response, which could be accomplished by using a
combination of global and local models. In this scenario, the
global model is used to determine the changes in the overall
stress distribution. The local model then takes on this data to
determine the extent of local remodelling. Subsequently, the
results of the local analysis are fed back to the global model to
determine the changes in structural parameters.
One major challenge in applying systems biology to the
study of bone remodelling currently is the lack of emprical
data to test against the models. This is primarily due to the
fact that bone remodelling normally takes up to a year in
human, therefore making the generation of data difficult. To
overcome this problem, scientists now are using animal
models such as rats, rabbits, and dogs for experimental testing.
Remodelling generally takes faster in these animals, but it
poses another issue in that how should the results from them
be correlated with human.
Another problem that comes up frequently is system
identification. In fact, in addition to mechanical stimuli,
certain chemical factors such as hormones and steriods could
affect bone remodelling as well. Furthermore, there have been
studies [2,9] suggesting that external applied electircal and
magnetic fields could have impacts on bone remodelling too.
Therefore, the question here is to determine which of these
factors should be included in the system, since some of them
might not act directly on bone remodelling.
V. CONCLUSION
In summary, bone remodelling involves the complex
interactions between bone cells and the various signalling
molecules. A system-level of study would be beneficial as it
helps to elucidate the relationships among them, thus giving a
more comprehensive understanding of the whole process. The
mechanistic and the cellular models reviewed in this paper
represent a global and a local level approaches, though not
perfect, provide a basis of the application of systems biology
to the study of bone remodelling. The ultimate goal is to
combine studies at multiple levels so as to construct an
integrated model that could make accurate predictions.
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