Substrate stiffness and oxygen as regulators of stem cell differentiation during skeletal tissue regeneration: a mechanobiological model

Abstract

Extrinsic mechanical signals have been implicated as key regulators of mesenchymal stem cell (MSC) differentiation. It has been possible to test different hypotheses for mechano-regulated MSC differentiation by attempting to simulate regenerative events such as bone fracture repair, where repeatable spatial and temporal patterns of tissue differentiation occur. More recently, in vitro studies have identified other environmental cues such as substrate stiffness and oxygen tension as key regulators of MSC differentiation; however it remains unclear if and how such cues determine stem cell fate in vivo. As part of this study, a computational model was developed to test the hypothesis that substrate stiffness and oxygen tension regulate stem cell differentiation during fracture healing. Rather than assuming mechanical signals act directly on stem cells to determine their differentiation pathway, it is postulated that they act indirectly to regulate angiogenesis and hence partially determine the local oxygen environment within a regenerating tissue. Chondrogenesis of MSCs was hypothesized to occur in low oxygen regions, while in well vascularised regions of the regenerating tissue a soft local substrate was hypothesised to facilitate adipogenesis while a stiff substrate facilitated osteogenesis. Predictions from the model were compared to both experimental data and to predictions of a well established computational mechanobiological model where tissue differentiation is assumed to be regulated directly by the local mechanical environment. The model predicted all the major events of fracture repair, including cartilaginous bridging, endosteal and periosteal bony bridging and bone remodelling. It therefore provides support for the hypothesis that substrate stiffness and oxygen play a key role in regulating MSC fate during regenerative events such as fracture healing.

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).

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 u_r, u_z, and v^f respectively.

Figure 3. Iterative procedure for tissue differentiation hypothesis testing.

Figure 4. Oxygen model predictions.

(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 , . 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, γ ^angio (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).