Figure 1.
Tissue differentiation regulated by substrate stiffness and oxygen tension.
The oxygen tension axis extends radially from the centre of the circle, low oxygen tension in the centre of the circle increasing towards the periphery. The substrate stiffness axis extends circumferentially in a clockwise direction from the right side of the dotted line at the top of the circle. The presence of a blood supply is also a prerequisite for formation of bone and marrow. (CC: Calcified Cartilage).
Table 1.
Model parameters.
Figure 2.
Finite element, cell and angiogenic models.
(a): Finite element model with loading and boundary conditions. (b): boundary conditions for angiogenic and cell models. Radial displacement, axial displacement and fluid velocity are shown as ur, uz, and vf respectively.
Table 2.
Material properties.
Figure 3.
Iterative procedure for tissue differentiation hypothesis testing.
Figure 4.
(a): Model predictions compared to experimental data for oxygen tension readings in the periosteal callus adjacent to the fracture gap (Image adapted from Epari et al (2008) with permission). (b): Predictions of oxygen tension in the callus at early, middle and late Stages of healing.
Figure 5.
Model predictions for substrate stiffness and oxygen tension
. Locations chosen as characteristic of the periosteal callus, fracture gap and endosteal callus respectively. It should be noted that substrate stiffness here refers to the macroscale stiffness of the regenerating tissue, where it is noted (as discussed in the manuscript) that the elasticity of the microenvironment of the cell is most likely different.
Figure 6.
Model predictions versus experimental data.
Model A: Model predictions for Stages III to VI of fracture healing when tissue differentiation is regulated by substrate stiffness and oxygen tension. Model B: Model predictions for Stages III to VI of fracture healing when tissue differentiation is regulated tissue shear strain and relative fluid velocity [6], [7]. Experimental Data: Averaged histological images obtained from an extensive study of fracture healing in sheep (Images adapted from Vetter et al (2010) with permission).
Figure 7.
Effect on healing Time of parameter variations.
(a): Healing time versus angiogenic strain threshold, γangio (X signifies the prediction of non-union) (b): Healing time versus tissue formation rate, TFR. (c): Healing time versus angiogenic diffusion coefficient, H.
Figure 8.
Tissue differentiation regulated by proximity and oxygen tension.
The oxygen tension axis extends radially from the centre of the circle, low oxygen tension in the centre of the circle increasing towards the periphery. Bone and adipose tissue formation occur when there is sufficient oxygen tension “in proximity” to existing adipose tissue or bone fronts. The presence of a blood supply is also a prerequisite for formation of bone and adipose tissue. (CC: Calcified Cartilage).