Chemotaxis of mesenchymal stem cells within 3D biomimetic scaffolds—a modeling approach

Bone tissue engineering is a promising strategy to repair local defects by implanting biodegradable scaffolds which undergo remodeling and are replaced completely by autologous bone tissue. Here, we consider a Keller–Segel model to describe the chemotaxis of bone marrow-derived mesenchymal stem cells (BMSCs) into a mineralized collagen scaffold. Following recent experimental results in bone healing, demonstrating that a sub-population of BMSCs can be guided into 3D scaffolds by gradients of signaling molecules such as SDF‐1αSDF‐1α, we consider a population of BMSCs on the surface of the pore structure of the scaffold and the chemoattractant SDF‐1αSDF‐1α within the pores. The resulting model is a coupled bulk/surface model which we reformulate following a diffuse-interface approach in which the geometry is implicitly described using a phase-field function. We explain how to obtain such an implicit representation and present numerical results on μCT‐dataμCT‐data for real scaffolds, assuming a diffusion of SDF‐1αSDF‐1α being coupled to diffusion and chemotaxis of the cells towards SDF‐1αSDF‐1α. We observe a slowing-down of BMSC ingrowth after the scaffold becomes saturated with SDF‐1αSDF‐1α, suggesting that a slow release of SDF‐1αSDF‐1α avoiding an early saturation is required to enable a complete colonization of the scaffold. The validation of our results is possible via SDF‐1αSDF‐1α release from injectible carrier materials, and an adaption of our model to similar coupled bulk/surface problems such as remodeling processes seems attractive.