ARUP; ISBN: 978-0-9562121-5-3 - CMBBE 2012 - Cardiff University

A COMPUTATIONAL MODEL OF THE GROWTH PLATE
INCLUDING THE EFFECT OF MECHANICAL LOADING ON THE
FINAL CHONDROCYTIC HEIGHT IN THE HYPERTROPHIC ZONE
1. ABSTRACT
C.A. Narváez-Tovar 1,2 and D.A. Garzón-Alvarado 2
The growth plate is a cartilaginous structure with embedded chondrocytes that cause the
endochondral growth of long bones due to their proliferation and hypertrophy. There are
two main factors that modulate the growth plate activity: biochemical signals, like the
PTHrP-Ihh feedback loop, and sustained or variable mechanical loads. It is known that
mechanical loading modulates the rate of growth, according with the ‘Hueter-Volkmann
Law’, and it has been demonstrated that mechanical loading has a larger effect on
chondrocytes in the hypertrophic zone than it does on the proliferative zone. From a
computational point of view, the existing models describe the mechanical modulation of
the growth plate from the phenomenological aspect. They do not model the change of
the final chondrocytic height due to mechanical modulation and they ignore the
differentiation of chondrocytes from the proliferative to the hypertrophic phenotype.
This work proposes a new computational model that describes the growth plate activity
and its mechanical regulation from a biological aspect, taking into account the
chondrocytic enlargement as the main contribution to the modulated growth rate. The
model was implemented on a finite element code using a UEL subroutine for ABAQUS
and it was validated on a two-dimensional domain based on the histology for a 2-year
old male distal femoral growth plate.
2. INTRODUCTION
The growth of long bones depends on the proliferation and hypertrophy of the
chondrocytes that are embedded in the growth plates [1]. These cellular processes are
regulated by systemic and local factors [2]. The most important local biochemical factor
governing the behavior of the growth plate is the PThrP-Ihh negative loop [3]. On the
other hand, it is known that mechanical loads regulate the proliferation and hypertrophy
of the chondrocytes [4]. Several studies [5-7] had quantified the effects of the
mechanical modulation on the growth plate activity and it can be stated that mechanical
loading has a greater effect on the hypertrophic zone than in the proliferative zone [6].
The behavior of the growth plate has been modeled using the finite element method.
There are biochemical regulation models, like the proposed by Brouwers et al [8] or
Garzón-Alvarado et al [9], that take into account the PTHrP-Ihh regulatory loop and its
effect on the cellular differentiation process. Furthermore, there are mechanical
1
Professor, Mechanical Engineering Applications and Research Group, Universidad Santo Tomás, Cra 9
No. 51-11, Bogotá, Colombia.
2
Professor, Engineering Modeling and Numerical Methods Group, Universidad Nacional de Colombia,
Cra 30 No. 45-03, Bogotá, Colombia.