The aim of this thesis was to investigate some methods for quantitative analysis of bone structure, particularly techniques which might ultimately be applied post-operatively following orthopaedic reconstruction operations. Initially it was decided to explore the efficacy of MRI in quantifying the bone structure at high resolution by comparing high resolution MRI against 'gold standards' such as Scanning Electron Microscopy (SEM) and optical histology. This basic study provided a measure of the distortions in the morphological bone parameters derived from MR images due to susceptibility artefacts and partial volume effects. The study of bone architecture was then extended to a model of advanced renal osteodystrophy in a growing rat. For this study, high-resolution micro computed tomography (microCT) was used and as a result of the high resolution images obtained, three new bone morphological parameters were introduced to characterise the bone structure. The desire to study bone architecture post-operatively in hip replacements led to a preliminary study on ex-vivo sheep acetabulae following total hip replacement, to determine the extent that the bone architecture could be investigated around the acetabulum. The motivation for studying the acetabulum was based on the high occurrence of debonding at the bone / prosthesis interface. This study demonstrated the superior nature of 3D MRI over conventional x-ray radiographs in early quantitation of fibrous membranes located between the host bone and the non-metallic implant and/or the bone cement. The presence of such fibrous membranes is strongly indicative of failure of the prosthesis. When using clinical MRI to image post-operative hip replacement, the image quality is severely affected by the presence of the metallic implant. The head of the prosthesis is shaped like a metal sphere and is located in the acetabular cup. This problem was investigated by performing simulations of MR images in the presence of the field perturbation induced by the presence of a metal sphere, with the effects of slice excitation and frequency encoding incorporated into the simulations. The simulations were compared with experimental data obtained by imaging a phantom comprising a stainless steel ball bearing immersed in agarose gel. The simulations were used to predict the effects of changing imaging parameters that influence artefact size and also to show how current metal artefact reduction techniques such as view angle tilting (VAT) work and to identify their limitations. It was shown that 2D SE and VAT imaging techniques should not be used when metallic prosthesis are present due to extreme slice distortion, whereas 3D MRI provided a method that has no slice distortion, although the effects of using a frequency encoding gradient still remain.