Adapting source grid parameters to improve the condition of the magnetostatic linear inverse problem of estimating nanoparticle distributions

Abstract

The problem of estimating magnetic nanoparticle distributions from magnetorelaxometric measurements is addressed here. The objective of this work was to identify source grid parameters that provide a good condition for the related linear inverse problem. The parameters investigated here were the number of sources, the extension of the source grid, and the source direction. A new measure of the condition, the ratio between the largest and mean singular value of the lead field matrix, is proposed. Our results indicated that the source grids should be larger than the sensor area. The sources and, consequently, the magnetic excitation field, should be directed toward the Z-direction. For underdetermined linear inverse problems, such as in our application, the number of sources affects the condition to a relatively small degree. Overdetermined magnetostatic linear inverse problems, however, benefit from a reduction in the number of sources, which considerably improves the condition. The adapted source grids proposed here were used to estimate the magnetostatic dipole from simulated data; the L2-norm, residual, and distances between the estimated and simulated sources were significantly reduced.

Quantitative model selection for enhanced magnetic nanoparticle imaging in magnetorelaxometry

“…The forward model is adapted with the intention to receive the maximum amount of information while keeping measurement data to a minimum. Previous adaptations include the investigation of different noise models, 24 use of multiple time points, 25 different inverse solution methods, 26 grid and sensors adaptations, 27,28 and different activation patterns and configurations of the coil array. [29][30][31][32][33][34][35] The difficulty lies in determining the information content of the forward model and comparing different forward models with each other.…”

Real-Time MEG Source Localization Using Regional Clustering

“…, the inverse problem using a better conditioned gain matrix (Eq. 11) is less influenced by low SNRs [9]. The optimal cluster size was found by evaluating the condition of different sized gain matrices, see Eq.…”

Robustness Assessment of 1-D Electron Paramagnetic Resonance for Improved Magnetic Nanoparticle Reconstructions

“…ρ is defined in [29] as the ratio between the largest eigenvalue of F and the mean singular value size of F. Smaller ρ signifies a better numerical stability. The conventional condition measure (σ 1 · σ −1 L ) depends to a great extent on the smaller eigenvalues which make it difficult to compare different matrix sizes.…”