TY - JOUR
T1 - Surface curvatures of trabecular bone microarchitecture
AU - Jinnai, H.
AU - Watashiba, H.
AU - Kajihara, T.
AU - Nishikawa, Y.
AU - Takahashi, M.
AU - Ito, M.
N1 - Funding Information:
H. J. was supported by the Japan Society of Promotion of Science (Grant-in-Aid for Encouragement of Young Scientists [No. 12750799] and Scientific Research of Priority Area [A] and Dynamic Control of Strongly Correlated Soft Materials [No. 13031057]).
PY - 2002
Y1 - 2002
N2 - Microstructure of trabecular bone has been examined with a particular emphasis on surface curvatures in two-phase (trabecular and intertrabecular space- i.e., marrow space) structures. Three trabecular bone samples, quantified as 'plate-like,' 'rod-like,' and a mixture of these two structural elements according to the structure model index (SMI), were subjected to analysis based on (differential) geometry. A correspondence between the SMI and the mean curvature was found. A method to measure surface curvatures is proposed. The gaussian curvatures averaged over the surfaces for the three analyzed bone structures were all found to be negative, demonstrating their surfaces to be, on average, hyperbolic. In addition, the Euler-Poincaré characteristics and the genus, both characterizing topological features of bone connectivity, were estimated from integral gaussian curvature (Gauss-Bonnet theorem). The three bone microstructures were found to be topologically analogous to spheres with one to three handles.
AB - Microstructure of trabecular bone has been examined with a particular emphasis on surface curvatures in two-phase (trabecular and intertrabecular space- i.e., marrow space) structures. Three trabecular bone samples, quantified as 'plate-like,' 'rod-like,' and a mixture of these two structural elements according to the structure model index (SMI), were subjected to analysis based on (differential) geometry. A correspondence between the SMI and the mean curvature was found. A method to measure surface curvatures is proposed. The gaussian curvatures averaged over the surfaces for the three analyzed bone structures were all found to be negative, demonstrating their surfaces to be, on average, hyperbolic. In addition, the Euler-Poincaré characteristics and the genus, both characterizing topological features of bone connectivity, were estimated from integral gaussian curvature (Gauss-Bonnet theorem). The three bone microstructures were found to be topologically analogous to spheres with one to three handles.
KW - Differential geometry
KW - Hyperbolic surface
KW - Parallel surface method
KW - Surface curvatures
KW - Three-dimensional (3D) image analysis
KW - Trabecular bone microstructure
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U2 - 10.1016/S8756-3282(01)00672-X
DO - 10.1016/S8756-3282(01)00672-X
M3 - Article
C2 - 11792584
AN - SCOPUS:0036139781
SN - 8756-3282
VL - 30
SP - 191
EP - 194
JO - Bone
JF - Bone
IS - 1
ER -
