Mathematical modeling is the art of judicious
oversimplification.
H. H. Barrett &W.Swindell
The use of single photon emission computed tomography (SPECT) in the investigation of cerebral disorders such as epilepsy has generally been limited to its utilisation as an aid in the gross lateralization of the epileptogenic focus [HMDD92][Jac93][BR91]. The combination of SPECT's continuously improving resolution capabilities and very attractive cost benefit ratio as compared to positron emission tomography (PET) has served to increase its use in the investigation of more finely localized functional studies. For example, the introduction of the use of intracarotid sodium amobarbital in conjunction with SPECT in the assessment of hippocampal inactivation for the neuropsychological evaluation of memory performance in pre-surgical studies of seizure foci resection have been greatly aided by the improved resolution of multi-detector SPECT systems [JG91][JGBD+87][LDL+94][MDJG+94]. The advent of more finely localised investigations with SPECT was simply not possible with the resolution capabilities of systems from just a decade ago. Due to coarse resolution and the functional nature of the information provided by SPECT, such studies require the anatomical information and very fine resolution provided by magnetic resonance (MR) or external source X-ray computed tomography (CT) images (figure 1.1 shows regsitered MR and SPECT volumes). Simple visual alignment is insufficient for proper study because the underlying errors in a resultant diagnosis based on registered data are quantitatively unknown. More robust mathematical methods of image re-positioning and alignment, registration, and knowledge of the errors associated with the procedure are clearly required. The internal landmark matching (ILM) technique was first implemented for the registration of multi-modality brain volumes by Evans et al [EBM+88][EMT+91] to provide for such procedures. The transformation errors arising from the use of the ILM technique for registration will be investigated in this thesis by using point simulations and real scan studies based on 3-D brain phantom with external fiducials. The results of previous validations of the use of the ILM technique in PET/MR registrations may not be extended directly to SPECT/MR registrations because of the anisotropic nature of SPECT's spatial resolution and differences in the methods used to measure error.
The ILM technique incorporates user chosen homologous point pairs from the SPECT and MR volumes with Procrustes analysis for the anatomical/functional volumetric registrations. The reasons for the existence of this study are clear. The premise of error measurements is that the true value is known or may reasonably be approximated with the mean. Errors in clinical registrations may only be measured by comparing with correct registrations, but a basis for correct registrations is usually unavailable in real scan registrations using retrospective techniques like ILM unless imaging was performed within a stereotactic environment or with some other external marking system. As such, only likewise retrospective investigations may be performed to indirectly measure and study the registration error in a statistical context. Point simulations provide an implicit knowledge of the correct registration. These simulations will be performed within bound spherically symmetric objects in 3-D space so that the point configurations are more realistic (not just random generations in Cartesian space) and to allow the study of the radial dependence of rotation error (because of simple geometrical considerations regarding the rotation of the configurations about a centered reference system). Shells will be used to exaggerate the dependence of the rotational error on radius. Point simulations alone are insufficient because the homology error is not homogeneous in reality and the point configurations are not totally random and spherically symmetric in registrations of clinical scans. The anthropomorphic phantom is offered to avoid the imposition of the additional morbidity associated with requesting external marker systems on real patients, and yet allowing the provision of data with anisotropic homology error and realistically distributed point pair configurations. Results from point simulations with spheres of different radii, homology error, and number of point pairs will therefore be compared to results from real scans with the brain phantom to allow a more effective study of the translation and rotation errors which arise in transformations required for clinical registrations.
This thesis is concerned with the assessment of the registration errors
associated with the implementation of the ILM technique in registering
SPECT and MR brain volumes. A brief overview of brain SPECT with
Tc-HMPAO will be presented in the next chapter to discuss some of the
factors which hamper the selection of exactly corresponding points and
therefore contribute to the magnitude of the similarity or homology error
between the chosen point pairs in the context of linear systems theory.
The basic principles of registration with the ILM technique based on
Procrustes analysis and the theory behind the assessment of the
registration error is presented in the third chapter. The remaining
chapters are concerned with the presentation of the study, its results,
and general discussions. The more salient points presented in this thesis
are summarised in the concluding chapter.