Amore realistic simulation approach is used to study the behavior of the Compton camera in this thesis than previous studies to date. The Compton camera differs from gamma cameras in that the collimator is replaced by a detector known as the ‘scatterer’. Gamma rays may be Compton scattered in the scatterer and subsequently detected by an ‘absorber’ which is the equivalent of the detector in a gamma camera. By measuring the energies and the positions of the points on the scatterer and the absorber where the incident and scattered gamma rays interacted with the detectors, an image of the source can be reconstructed. Because there is no collimator present, the potential sensitivity of the Compton camera is much higher than the gamma camera, resulting in reduced acquisition times. Most of the work described in this thesis was done with the GEANT4 Monte Carlo simulation software. GEANT4 has been proven to be very robust and efficient in modelling physics problems of radiation transport and interactions with matter in complex geometries. Four major studies are carried out to estimate and optimize the performance of this novel equipment. The first study takes a look at the scatterer’s imaging parameters with the aim of prescribing an optimal scatterer material and geometry. In the second study, the contribution of the absorber to the overall Compton camera performance is evaluated, considering detector material, interaction type and geometry. The third study explores the limitations imposed by the detector energy threshold and dead time on the Compton camera performance, using a simplified model of the general electronic architecture. An evaluation of Compton camera for scintimammography was performed in the fourth study. For this study, three dual-head Compton camera models (Si/CZT, Si/LaBr₃:Ce and Si/NaI(Tl) Compton cameras) were simulated, and the effect of scintillation photons’ interactions with the photomultipliers was implemented. The results show that silicon of about 1 cm thickness would be adequate as the Compton camera scatterer. Analyses suggest however, that the choice of silicon is not completely flawless. Doppler broadening for this detector material contributes as much as 7.3 mm and 2.4 mm to full-width-at-half-maximum (FWHM) image resolution at 140.5 keV and 511 keV respectively. On the other hand, detector spatial resolution which accounts for the least image degradation at 140.5 keV is found to be the dominant degrading factor at 511 keV, suggesting that the absorber parameters play major roles in image resolution at higher diagnostic energies. Findings further suggest that cadmium zinc telluride (CZT) would be themost suitable detector as the absorber since thematerial demonstrated the highest efficiency and least positioning error due to multiple interactions as well as good spatial resolution. The inclusion of the energy threshold and detector dead time at 140.5 keV, reduced the Compton camera detection efficiency by 48% and 17% respectively, but improved the image resolution from 10.7 mm to 9.5 mm at the source-to-scatterer distance of 5 cm. At 511 keV, the inclusion of these parameters reduced the efficiency by 6% and 13% respectively, but made no significant difference on the camera resolution. For a challenging detection case in scintimammography, 5 mm breast tumours of tumour/background uptakes of 10:1 and 6:1 at 511 keV were used. The best signal-to-noise ratio (SNR) was attained for the Si/CZT Compton camera model, with the SNR values of 12.2 and 5.3. It is therefore envisioned that with an optimal camera geometry, improved reconstruction technique and adequate filter algorithm, the combination of Si and CZT as the scatterer and the absorber of the Compton camera would make a very promising imaging system for nuclear medicine studies at higher gamma ray energies where the collimated SPECT systems perform very poorly due to increased septal penetration. It is equally evident from the studies that with improved technology, new detectors such as LaBr₃:Ce could replace the traditional NaI(Tl) detector as imaging detectors.