Magnetic Particle Imaging (MPI) is a new method of medical imaging with great promise for rapid angiography, cell tracking, and cancer detection. In this thesis, we approach the development of MPI theory and hardware from two perspectives, frequency space and x- space.

We begin our analysis of MPI in frequency space by developing a new theory for narrow- band MPI using intermodulation. MPI, as originally envisioned, requires a high-bandwidth receiver coil and preamplifier, which are difficult to optimally noise match. Narrowband MPI dramatically reduces bandwidth requirements and increases the signal-to-noise ratio for a fixed specific absorption rate. We employ a two-tone excitation (called intermodulation) that can be tailored for a high-Q, narrowband receiver coil. We demonstrate a new MPI instrument capable of full 3D tomographic imaging of SPIO particles by imaging acrylic and tissue phantoms.

Using the principles of narrowband MPI, we describe the construction of a system capable of imaging a mouse without requiring movement of the mouse using a moving stage. The system has a high field 6500 mT/m permanent magnet NdFeB gradient, and intermodulation excitation and slow FFP movement in the X, Y, and Z axes. The system excites with a HF field in the Z axis at approximately 250 kHz.

Narrowband MPI produces multiple images at intermodulation products of the funda- mental frequency. It is necessary to convert these multiple harmonic images into a single composite image. We describe an efficient method to combine multiple harmonic images in frequency space that scales as O(Nlog(N)), readily scaling to reconstruction of whole-body 3D data sets in real time.

We then develop the x-Space theory of MPI. In x-Space theory, we no longer consider signal excitation and reception as a frequency space process, but instead as occurring in real space. We derive the one-dimensional MPI signal, resolution, bandwidth requirements, SNR, specific absorption rate, and slew rate limitations. We follow with experimental data measuring the point spread function for commercially available SPIO nanoparticles and a demonstration of the principles behind one-d imaging using a static offset field. We conclude by generalizing x-Space MPI to multiple dimensions, where we discover that MPI imaging occurs on a reference frame aligned with the FFP velocity vector. We briefly discuss pulse sequences, and finish by presenting experimental results demonstrating the three-dimensional point spread function of the MPI experiment.