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. 2008 Oct 6;5(27):1173-80.
doi: 10.1098/rsif.2008.0064.

The effect of geometry on three-dimensional tissue growth

Monika Rumpler  1 , Alexander Woesz, John W C Dunlop, Joost T van Dongen, Peter Fratzl
Affiliations
Free PMC article

The effect of geometry on three-dimensional tissue growth

Monika Rumpler et al. J R Soc Interface. .
Free PMC article

Abstract

Tissue formation is determined by uncountable biochemical signals between cells; in addition, physical parameters have been shown to exhibit significant effects on the level of the single cell. Beyond the cell, however, there is still no quantitative understanding of how geometry affects tissue growth, which is of much significance for bone healing and tissue engineering. In this paper, it is shown that the local growth rate of tissue formed by osteoblasts is strongly influenced by the geometrical features of channels in an artificial three-dimensional matrix. Curvature-driven effects and mechanical forces within the tissue may explain the growth patterns as demonstrated by numerical simulation and confocal laser scanning microscopy. This implies that cells within the tissue surface are able to sense and react to radii of curvature much larger than the size of the cells themselves. This has important implications towards the understanding of bone remodelling and defect healing as well as towards scaffold design in bone tissue engineering.

Figures

Figure 1
Figure 1
(a) New tissue formed in three-dimensional matrix channels. Actin stress fibres are stained with phalloidin-FITC and visualized under a confocal laser scanning microscope. Here, the tissue formation is shown (i–iii) after 21 days and (iv) after 30 days of cell culture in the channels of a (i) triangular, (ii) square, (iii) hexagonal and (iv) round shape introduced into a HA plate in vitro. (b) Numerical simulation of tissue formation within channels of various shapes: (i) triangular, (ii) square, (iii) hexagonal and (iv) round. The lines (early time point 1, ongoing times 2 and 3) mark the simulated development of tissue formation due to ongoing culture time, which corresponds closely to the observed development of new tissue formation in vitro.
Figure 2
Figure 2
Three-dimensional fluorescence images. The cytoskeleton of the cells within the tissue is visualized by FITC staining and serial two-dimensional sections were obtained with a confocal laser scanning microscope. Three-dimensional pictures were then stacked from all single pictures. In (a–c) three examples of the serial pictures obtained from the tissue formed in a square channel are shown at depth (c) 0, (b) −135 μm and (a) −470 μm, as well as (d) the combination of all single pictures. In (e–g) three examples of the serial pictures obtained from the tissue formed in a hexagonal channel are shown at depth (e) −485 μm, (f) −260 μm and (g) 0, as well as (h) the combination of all single pictures.
Figure 3
Figure 3
Sketch of two channels in a HA plate (dark grey). The figure illustrates the definition of the initial perimeter of the channel cross-section P and of the projected tissue area A (light grey) with transmission light microscopy in each channel, which was used to calculate quantitative data for tissue formation kinetics.
Figure 4
Figure 4
Quantitative tissue formation and kinetics. (a) Mean tissue layer thickness (calculated by the normalization of the projected tissue area to the perimeter) as a function of culture time in different shapes (illustrated by the appropriate symbols) and different channel perimeter P=3.14 mm (black), 4.71 mm (grey) and 6.28 mm (white). Data represent the mean value+s.e.; n=10. (b) Projected tissue area as a function of culture time minus lag time, which is the time that is needed until cells start curvature-driven growth. In the inset, the lag time is given as a function of initial channel perimeter.
Figure 5
Figure 5
pO2 measurements. MC3T3-E1 cells were seeded onto the HA and tissue formation was running over a time period of 43 days. At distinct time points, 25 days (black), 32 days (dark grey) and 43 days (light grey), the oxygen concentration inside the central channel was measured in the direct vicinity of the growing tissue. These values, expressed as percentage of air-saturated buffer, were plotted against the free area of the central channel. The size of the triangle indicates the hole size (small, P=3.14 mm; medium, P=4.71 mm; and large, P=6.28 mm); n=5.
Figure 6
Figure 6
Fluorescence microscopic images of the stained cytoskeletal stress fibres within the new formed tissue. (a) A zoom into the corner of a triangular HA channel shows a strong orientation of the stress fibres parallel to the tissue surface. (b) An image of the cell network on the external flat surface at regions between the channels shows a completely random orientation.
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