Abstract: A method of calculating derived variables comprises selecting a model equation, generating Monte Carlo paths and constructing a lattice of state variables, then calculating derived variables on the lattice. Derived variables for each Monte Carlo path are then calculated from the derived variables on the lattice, wherein the Monte Carlo path state variables are not restricted to the lattice node values.

Abstract: Methods are provided for detecting and diagnosing osteoporosis using high-resolution NMR imaging of trabecular bone. One such method comprises the steps of obtaining high-resolution NMR imaging data indicative of the trabecular microstructure of a mass of bone, analyzing the imaging data to determine the density of the trabeculae of the bone, comparing the density thus obtained with reference trabecular density data, and determining on the basis of the comparison whether the subject is osteoporotic or normal. To determine trabecular density, bone volume can be computed as the area fraction of those pixels that by virtue of their characteristic pixel intensity can be assigned to bone. Trabecular thickness can be computed from the relative bone area in a region of interest divided by half the perimeter length, the perimeter length being the circumference of all bone islands observed in the region of interest.