title: Are mineralized tissues open crystal foams reinforced by crosslinked collagen? Some energy arguments.
abstract: Which of the elementary components (hydroxyapatite (HA) crystals, collagen, non-collagenous organic matter, water) do significantly contribute to the ultrastructural elastic stiffness magnitude and anisotropy of mineralized tissues; and how, i.e. through which shapes and assemblages (which micromechanical morphology)? We suggest answers to these questions by analyzing stiffness-volume fraction relationships of wet and dry tissue specimens in the framework of strain energy considerations. Radial stiffness values of both isotropic and anisotropic tissues are found to depend linearly to quadratically on only the mineral volume fraction. This suggests the isotropic contribution of HA to the ultrastructural stiffness. An energy-based analysis of the difference between the axial and radial stiffness values of anisotropic, collagen-rich tissues allows us to assess the collagen elasticity contribution, which is found to depend linearly on the extra-collagenous mineral concentration. These results suggest that collagen and hydroxyapatite are the elementary components governing the ultrastructural elastic stiffness magnitude and anisotropy of bone and mineralized tendons. The elastic stiffness of water and non-collagenous organic matter does not play a significant role. As for the morphological issue, we suggest that mineralized tissues are isotropic open crystal foams; and that these foams are reinforced unidirectionally by collagen molecules which are mechanically activated through tight links between these molecules and HA-crystals. The HA crystals are mechanically activated through stretching and bending in long bone tissues, they are predominantly stretched in mineralized tendons, and bent in hyperpycnotic tissues.
authors.affiliation: Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Building 1-280, Cambridge, MA 02139, USA. hellmich@mit.edu
authors.forename: Ch
authors.initials: Ch
authors.lastname: Hellmich
authors.forename: F-J
authors.initials: FJ
authors.lastname: Ulm
mesh_terms: D000818:Animals; D016880:Anisotropy; D015519:Bone Density / Q000502:physiology; D001857:Bone Matrix / Q000737:chemistry / Q000000981:diagnostic imaging / Q000502:physiology* / Q000648:ultrastructure*; D001842:Bone and Bones; D002113:Calcification, Physiologic; D003094:Collagen / Q000737:chemistry*; D003198:Computer Simulation; D003460:Crystallization; D017886:Durapatite / Q000737:chemistry*; D004548:Elasticity; D004734:Energy Metabolism / Q000502:physiology; D006801:Humans; D008322:Mammals; D008832:Microchemistry; D008903:Minerals / Q000737:chemistry; D008954:Models, Biological; D008956:Models, Chemical; D036103:Nanotechnology / Q000379:methods; D013045:Species Specificity; D013223:Statistics as Topic; D013314:Stress, Mechanical; D014463:Ultrasonography; D014867:Water / Q000737:chemistry*; D016474:Weight-Bearing / Q000502:physiology
chemical_list: D008903:Minerals; D014867:Water; D003094:Collagen; D017886:Durapatite