Table 1.

Definitions for tibial bone and muscle mechanical parameters. SM = section modulus, L_tib = length of tibia, pCSMI = polar cross-sectional moment of inertia, vBMD_i = volumetric BMD, d_i = distance of individual voxel from torsional (z) or bending (x,y) axis, d_max = maximum distance among all voxels from torsional (z) or bending (x,y) axis, A_i = area of individual bone pixel, vBMD_max = maximum bone density (1.2 g/cm³), MCSA = muscle cross-sectional area.

Bone & muscle mechanical indices	Equation	Definition	Units
CSMI (cross-sectional moment of inertia	Σ(di2*A)	Resistance of bone to bending and torsional force as a result of inertial properties of mass distributed around the torsional or bending axis (4)	mm4
SM (section modulus)	Σ(di2*A)/dmax	The ratio of the bone's resistance to bending and torsion to its maximally distributed distance about the bending or torsional axis (37)	mm3
BSI (bending strength index)	SM/(Ltib*0.66)	A more reliable predictor of bone strength in bending and torsion related to SM – dependent on length of lever arm (8)	mm2
SSIp (polar stress strain index)	pCSMI·cortical vBMDi dmax · vBMDmax	Estimates bone strength in bending and torsion based on distribution of density-weighted bone voxels from polar axis	mm3
MSS (muscle-specific strength)	(Grip strength (kg) × 9.81 (N/kg))/MCSA (mm2)	Muscular strength as defined by muscular force over a given cross-sectional area	N/mm2
MBM (muscle bending moment)	MCSA × Ltib × 66% × tension of muscle acting on bone (9.5 N/mm2)*	The work implicated by the muscle acting to bend bone, related to the length of the moment arm and muscle cross-sectional area	N.mm

^*Tension of muscle acting on bone was estimated by Rittweger et al (13) based on a peak muscle tension measured at 650 kPa at the calf muscles, assuming 60% of the total MCSA is effective during peak force production, with the force concentrated over 4.1% of the tibia = 650 kPa × 60%/4.1% = 9500 kPa × 0.001 N/mm² / kPa = 9.5 N/mm².