Photon Absorptiometry in Three Component Systems; Bone Mineral at the Spine and in the Presence of a Hip Prosthesis

Abstract

The non-invasive measurement of the mass of bone is a clinically relevant problem. The bone is one component of a composite system. At the spine it may include fat, lean and bone mineral. At a hip prosthesis it may include soft tissue, bone mineral and metal. The measurement of the attenuation of photons of different energies can be used to determine the mass of one or all of the components of the composite system. The first system is currently measured using only two photon energies by assuming that it is a two component system. A model was developed which predicts the effect of the third component, fat, and was validated using phantom measurements. Typical parameters for the volume and spatial distribution of fat 𝘪𝘯 𝘷𝘪𝘷𝘰 were determined using CT scans. In combination with the model a median error of 8% is introduced by the third component. The feasibility of using a third energy to correct for the error was investigated. A model for the variance of the bone measurement normalized to emitted photon flux was developed. The optimal set of photon energies yielded a minimum value for the variance. However, this variance was excessively high, requiring a radiation dose 3000 times that for dual photon absortiometry. For the second system a triple photon absorptiometry technique was developed using the isotopes 203-Hg and 141-Ce. The technique was shown to be valid, but the variance was high due to cross-over of high energy photons in the detector and by scattering. In order to make measurements with a precision of 1%, counting times of 70 hours are required. Monte Carlo simulations were performed to determine the optimal geometry to reduce cross-over from scattering. However, cross-over cannot be reduced sufficiently with 203-Hg and 141-Ce. A three isotope source is required to make clinical bone measurements at a prosthesis.