Biomedical Engineering Reference
In-Depth Information
due to the complexity of the bone regulation system, which involves numerous
factors and interactions, systemic understanding is still incomplete.
Mathematical modeling provides a powerful tool for testing and analyz-
ing various hypotheses in complex systems that are very difficult (such as
those that consume time or resources) or just impossible to apply in vivo
or in vitro. However, relatively few mathematical models have so far been
proposed regarding bone remodeling. In addition to the model mentioned
in Chapter 6 for describing the effects of PTH on the bone remodeling pro-
cess, trabecular bone remodeling has been extensively studied in aspects
ranging from prediction of the development of trabecular architecture [14] to
the effects of mechanical forces on the maintenance and adaptation of form
in trabecular bone [15,16]. Based on the trabecular bone remodeling theory
developed by Weinans, Huiskes, and Grootenboer [17], Li [18] developed a
new trabecular bone remodeling model that could simulate both the under-
load and overload resorptions that often occur in dental implant treatments.
However, compared with trabecular bone that represents 20% of the
skeletal mass [19], even less theoretical work has been done on cortical bone,
which comprises 80% of the skeleton and has high resistance to bending and
torsion [19]. The following five representative papers that mathematically
analyzed cortical bone remodeling were published in the last decade. The
first two [20,21] presented a mathematical model at the cellular level, intro-
ducing magnitude of force and number of osteocytes to consider produc-
tion of NO and PGE
2
. The third paper [22] proposed a macroscopic model to
describe the time-dependent characteristics of the bone remodeling process.
Based on the work of Lemaire et al. [23], the last two papers [3,4] developed
an extended bone-cell population model by incorporating the following sig-
nificant modifications:
a rate equation describing changes in bone volume
a rate equation describing TGF-β concentration as a function of resorbed
bone volume
RANKL and OPG expression on osteoblastic cells at different stages of
maturation
new activator/repressor functions based on enzyme kinetics
Inspired by current advances in bone biology experiments and based on
the work of Pivonka et al. [3] as well as the model presented in Wang, Qin,
and Kalyanasundaram [24], Qin and Wang [2] developed a cell population
dynamics model incorporating the following features, which provide deeper
understanding of the mechanical bone remodeling mechanism at the cel-
lular level:
1. The interstitial fluid shear stress rate
R
IFSS
in the lacuno-canalicular
porosity structure is proposed as the physical mediator of mechano-
transduction by osteocytes in mathematical formulation.
