Electrical Impedance Mammography (EIM) offers the potential for early detection of breast cancer in ways that conventional methods such as x-ray mammography and ultrasound mammography fail. EIM involves passing low level alternating currents through the breast tissues via a number of surface electrodes placed on the skin, and monitoring the surface voltages produced as a result. Images of the complex impedance of the internal tissues are formed by solving the mathematical equations governing the relationships between current, voltage and impedance in a volume conductor. However, due to inherent ill-conditioning within these equations the image formation process is inefficient and leads to poor resolution images. The work presented here is a simulation study aimed at investigating the factors that affect the conditioning of the underlying equations in order to gain a better understanding of how the image resolution might be maximised. The first part of the investigation focuses on 2-dimensional EIM, and in particular the effect of increasing the number of electrodes used. The second part explores 3-dimensional imaging and concentrates on the interrelated effects on image quality of breast shape, electrode placement and the current and voltage patterns applied to the electrodes. In doing so an algorithm for modelling breast imaging in 3-dimensions is developed and a number of original approaches to data collection strategies are proposed and tested. As well as optimising image performance, one of the key considerations throughout the study is the spatial variance of the resolution, since it is desirable to have an imaging modality which is not biased to any particular region of the breast. In conclusion, a new electrode placement methodology is proposed which promises an improvement in resolution over any of the existing ElM systems, and has the added benefit of easily adapting to a wide range of breast shapes and sizes