Aged mice; BMC, bone mineral content; BS, bone surface; BV, bone volume; CF, control-fed; CTX-1, C-terminal telopeptide of type 1 collagen; Conn.Dn., connectivity density; FGF21, fibroblast growth factor-21; HFD, high-fat diet; HHCy, hyperhomocysteinemia; IDI, indentation depth increase; IGF-1, insulin-like growth factor-1; Imax, maximal MOI; Imin, minimal MOI; LPD, low protein diet; MC3T3-E1 subclone 4; MOI, moment of inertia; MR, methionine restriction; Methionine restriction; Micro-computed tomography; Nanoindentation; OC, osteocalcin; OPG, osteoprotegerin; P1NP, N-terminal propeptide of type 1 procollagen; RANKL, receptor activator for nuclear factor κB ligand; SMI, structure model index; TV, total volume; Tb.N, trabecular number; Tb.Sp, trabecular separation; Tb.Th, trabecular thickness; pMOI, polar MOI; vBMD, volumetric bone mass density; µCT, micro-computed tomography