A compressed sensing approach to immobilized nanoparticle localization for superparamagnetic relaxometry

Superparamagnetic relaxometry (SPMR) exploits the unique magnetic properties of targeted superparamagnetic iron oxide nanoparticles (SPIOs) to detect small numbers of cancer cells. Reconstruction of the spatial distribution of cancer-bound nanoparticles requires solving an ill-posed inverse problem. The current method, multiple source analysis (MSA), uses a least-squares fit to determine the strength and location of a pre-determined number of magnetic dipoles. In this proof-of-concept study, we propose the application of a sparsity averaged reweighting algorithm (SARA) for volumetric reconstruction of immobilized nanoparticle distributions. We first calibrate the parameters that define the location of the sensors in the forward model of measurement physics. Using this optimized model, we evaluated the performance of the algorithms on various configurations of single and multiple point-source phantoms. We investigated the effect of the data fidelity parameter, voxel size, and iterative reweighting on the reconstruction produced by SARA. We found that the calibrated physics model can predict the detected field values within 5% of the measured data. When only a single source was present, both algorithms were able to detect as little as 0.5 µg of immobilized particles. However, when two sources were measured simultaneously, MSA failed to detect sources containing as much as 10 µg of particles, while SARA detected all of the sources containing at least 5 µg of particles. We show that a suitable data fidelity parameter can be selected objectively, and the total magnitude and location of a point source reconstructed by SARA is not sensitive to voxel size. Detection and localization of multiple small clusters of nanoparticles is a crucial step in SPMR-based diagnostic applications. Our algorithm overcomes the need to know the number of dipoles before reconstruction and improves the sensitivity of the reconstruction when multiple sources are present.