title: Quantitative model selection for enhanced magnetic nanoparticle imaging in magnetorelaxometry.
abstract: OBJECTIVE
  The performance of an increasing number of biomedical applications is dependent on the accurate knowledge of the spatial magnetic nanoparticle (MNP) distribution in the body. Magnetorelaxometry (MRX) imaging is a promising and noninvasive technique for the reconstruction of this distribution. To date, no accurate and quantitative measure is available to compare and optimize different MRX imaging models and setups independent of the MNP distribution. In this paper, the authors employ statistical parameters to develop quantitative MRX imaging models. Using these models, a straightforward optimization of setups and models is possible resulting in improved MNP reconstructions.
  
  
  METHODS
  A MRX imaging setup is considered with different coil configurations, each corresponding to a MRX imaging model. The models can be represented by a sensitivity matrix. These are compared by employing the matrices as inputs to statistical parameters such as conditional entropy and mutual information (MI). These parameters determine the best model to reconstruct the MNP amount for each volume-element (voxel) in the sample. The matrix is transformed by multiplying the columns with different weightings depending on the performance of the MRX imaging model with respect to the other models. This transformed matrix is compared to the original sensitivity matrix without weightings.
  
  
  RESULTS
  Compared to the original sensitivity matrix, an increased numerical stability and improved noise robustness for the transformed sensitivity matrix are observed. The reconstruction of the MNP shows improvements: a correlation to the actual MNP distribution of 99.2%, whereas the original matrix only had 82.5%. By selecting the MRX models with the smallest MI, the authors are able to reduce the measurement time by 65% and still obtain an improved imaging accuracy and noise robustness. The statistical parameters allow a direct measure of the relative information content within the setup such that the optimal voxel size for the MRX setup is determined to be between 5 and 15 mm, while other sizes show a significant change in the statistical parameters.
  
  
  CONCLUSIONS
  The use of statistical parameters in MRX imaging models results in quantitative models which can optimize MRX setups in a very fast and elegant way such that improved MNP imaging can be realized. Finally, the presented measure allows to quantitatively and accurately compare different MRX models and setups independent of the MNP distribution.
authors.affiliation: Department of Electrical Energy, Systems and Automation, Ghent University, Zwijnaarde 9052, Belgium.
authors.forename: Annelies
authors.initials: A
authors.lastname: Coene
authors.affiliation: Department of Electrical Energy, Systems and Automation, Ghent University, Zwijnaarde 9052, Belgium and Department of Solid State Sciences, Ghent University, Ghent 9000, Belgium.
authors.forename: Jonathan
authors.initials: J
authors.lastname: Leliaert
authors.affiliation: Department of Electrical Energy, Systems and Automation, Ghent University, Zwijnaarde 9052, Belgium.
authors.forename: Luc
authors.initials: L
authors.lastname: Dupré
authors.affiliation: Department of Electrical Energy, Systems and Automation, Ghent University, Zwijnaarde 9052, Belgium.
authors.forename: Guillaume
authors.initials: G
authors.lastname: Crevecoeur
mesh_terms: D003198:Computer Simulation; D003952:Diagnostic Imaging / Q000295:instrumentation / Q000379:methods*; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D007257:Information Theory; D058185:Magnetite Nanoparticles; D060306:Magnetometry / Q000295:instrumentation / Q000379:methods*; D019047:Phantoms, Imaging
chemical_list: D058185:Magnetite Nanoparticles