Vertebral trabecular main direction can be determined from clinical CT datasets using the gradient structure tensor and not the inertia tensor - A case study

Osteoporosis is a wide spread disease with one-third of all women beyond their menopause and a fifth of men above the age of 50 years suffering from it. Patient specific finite element models would be a great improvement for the diagnosis of vertebral fracture risk. Different material models have been proposed, which incorporate information about the anisotropy of trabecular bone in addition to bone mineral density (BMD) using a second rank structure tensor. Two alternative structure measurement methods, gradient structure tensor (GST) and inertia tensor (IT), were investigated. Structure was determined from in situ scans. This was compared to structure computed with the mean intercept length (MIL) tensor from μ CT scans at the same locations. GST delivered information comparable to MIL regarding the structural main direction even at normal dose standard clinical settings (median of the scalar products of up to ≈ 0.98). IT was not comparable to MIL (median ≈ 0.4). Neither of the alternatives could determine eigenvalues comparable to these determined from MIL (p > 0.5). In conclusion, this study could show that the measurement of the structural main direction is possible for in situ scans in a clinical setting. It was shown that the method of choice to determine trabecular main direction in situ is GST. Knowing the main direction a transverse isotropic fabric tensor can be constructed.