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

are not only sensitive to the biochemistry 1 of their environment but also to the physical
characteristics of the substrate they settle on. For example, the stiffness 2 , patterning 3 and
topography 4 of the adhesive surfaces are known to influence the mechanical state of the
cell and thereby to guide biological processes such as cell division 5 , differentiation 2 ,
migration, matrix synthesis 6 and apoptosis 7 . Despite this knowledge the way in which
these individual responses lead to the formation of a soft material organised at larger
length scales is still to be clarified.
This study 8 follows the work of Rumpler etal 9 and investigates how the geometrical
features of a substrate, although much larger than a single cell, control tissue formation
and organisation. The conclusions are of great interest for explaining biological
processes involving tissue production and designing scaffolds to promote tissue repair.
3. METHODS
3.1 Cell culture experiments
Hydroxyapatite (HA) scaffolds are produced following the protocol of Woesz etal 10 .
The 2mm thick scaffolds are designed to contain circular straight sided pores and semicircular
channels with the same diameter (1mm). MC3T3-E1 pre-osteoblasts are seeded
on the scaffolds and cultured for 4 weeks. Tissue growth is quantified in each pore by
measuring the projected tissue area (PTA) on phase contrast images taken every 3 to 4
days. After culture, some tissues are fixed and stained for actin and nuclei with
fluorescent dyes and imaged with a confocal microscope.
3.2 Computational description
The method proposed by Frette etal 11 was used to estimate curvature profiles on the
digital phase contrast images. We then extended the implementation to simulate
curvature-driven growth. A digital circular mask with a radius r that is scaled on the
size of a cell, is used to scan the previously binarised image. For each position of the
mask, the area A of the circle out of the pore (black) is calculated. For masks centred
on the interface, the curvature at the central pixel is proportional to the ratio:
3π
⎛ A 1 ⎞
κ =
⎜ − ⎟ (Eq.1)
r ⎝ Atot
2 ⎠
where Atot is the mask area. When the centre of the mask is located within the medium,
we define an effective curvature that represents how much of the geometrical features a
cell can feel from this position. The growth process is then simulated by applying a
conditional change in each white pixel: if the effective curvature is positive - i.e. the
surface is concave - the pixel is filled with tissue (black). If not, the pixel remains white.
The procedure is iterated over many steps to describe growth over several weeks of cell
culture. We could demonstrate that the local interfacial motion δ is proportional to
curvature and scales with the size of the mask, when the geometrical features of the
interface are large compared to cell length:
2
r
δ ( r , κ ) = κ
(Eq.2)
6
Experimental and computational techniques are further detailed in Ref 8 .