How linear tension converts to curvature: geometric control of bone tissue growth

• Published in: PloS one 2012-05, Vol.7 (5), p.e36336-e36336
• Main Authors: Bidan, Cécile M, Kommareddy, Krishna P, Rumpler, Monika, Kollmannsberger, Philip, Bréchet, Yves J M, Fratzl, Peter, Dunlop, John W C
• Format: Article
• Language: English
• Subjects: 3T3 Cells; Actin; Adaptation; Algorithms; Animals; Biocompatibility; Biology; Biomechanical Phenomena; Biomedical materials; Bone (cortical); Bone (trabecular); Bone growth; Bone remodeling; Bone Remodeling - physiology; Bone resorption; Bone Substitutes; Bones; Calcification; Cancellous bone; Channel pores; Chemical Sciences; Circularity; Cortical bone; Curvature; Durapatite; Evolution; Geometry; Growth; Hydroxyapatite; Hydroxyapatites; Hypotheses; Material chemistry; Materials Science; Mechanical properties; Medical research; Metabolism; Metallurgy; Mice; Microscopy; Microscopy, Phase-Contrast; Mimicry; Models, Biological; Muscle proteins; Osteoblasts - cytology; Osteoblasts - physiology; Osteogenesis - physiology; Osteons; Pattern formation; Phase contrast; Physics; Pores; Radius; Science; Signal Transduction; Surgical implants; Tensile Strength; Tension; Tissue engineering; Tissue Scaffolds; Tomography
• ISSN: 1932-6203; 1932-6203
• DOI: 10.1371/journal.pone.0036336

This study investigated how substrate geometry influences in-vitro tissue formation at length scales much larger than a single cell. Two-millimetre thick hydroxyapatite plates containing circular pores and semi-circular channels of 0.5 mm radius, mimicking osteons and hemi-osteons respectively, were incubated with MC3T3-E1 cells for 4 weeks. The amount and shape of the tissue formed in the pores, as measured using phase contrast microscopy, depended on the substrate geometry. It was further demonstrated, using a simple geometric model, that the observed curvature-controlled growth can be derived from the assembly of tensile elements on a curved substrate. These tensile elements are cells anchored on distant points of the curved surface, thus creating an actin "chord" by generating tension between the adhesion sites. Such a chord model was used to link the shape of the substrate to cell organisation and tissue patterning. In a pore with a circular cross-section, tissue growth increases the average curvature of the surface, whereas a semi-circular channel tends to be flattened out. Thereby, a single mechanism could describe new tissue growth in both cortical and trabecular bone after resorption due to remodelling. These similarities between in-vitro and in-vivo patterns suggest geometry as an important signal for bone remodelling.