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

4. COMPUTATIONAL IMPLEMENTATION
As illustrated in Figure 1, we employed an 8 mm × 8 mm square domain, horizontally
divided into six regions: the upper and lower regions correspond to the epiphyseal and
metaphyseal trabecular bone, respectively, while the inner regions correspond to the
inert cartilage and the hypertrophic and proliferative areas of the columnar cartilage [1].
To simulate the growth produced by mitosis, we have included a thin strip of cartilage
between the proliferative columnar cartilage and the inert cartilage zones.
Figure 1: Square domain inspired on the quantitative histology of a 2-years old male
distal femoral growth plate.
The width of each cartilage zone is presented in Table 1. Based on the quantitative
histology reported for a 2-years old male distal femoral plate [1], 104 choncrocyte
columns were modeled with a separation of of 76.29 μm. Each column had 49
proliferative cells with an average size of 10 μm and 6 hypertrophic cells ( N CH = 6 )
with an average size of 30 μm.
Table 1: Width of cartilage zones, according to Kember y Sissons [2]
CartilageZone Width [mm]
columnar 0.7
Proliferative 0.52
Hypertrophic 0.18
Inert 0.9
Following a similar approach to the proposed by Piszczatowski [15], all tissues were
treated as linear isotropic materials and their mechanical properties are summarized in
Table 2. The model takes into account the change of mechanical properties for each of
the cartilage zones, according to the study of Sergerie et al [16].
Table 2: Tissue Mechanical properties
Tissue E [MPa] ν Reference
Trabecular bone 2000 0.3 [17]
Inert cartilage 0.48 0.07 [16]
Proliferative columnar cartilage 0.25 0.13 [16]