Quantitative and binding-specific imaging of magnetic nanoparticle distributions

Abstract

Fig. 1. left: Phantom support containing an MNP distribution of unbound (1 ml MNP suspension with 12 mg Fe) and bound (9 MNP loaded gypsum cubes with 6 mg Fe/cube) MNPs. right: estimated MNP distributions for unbound and bound MNPs. The chosen voxel grid exceeds the dimension of the mount as indicated by the black square to compensate for possible edge effects in the reconstructions. Physical non-plausible negative MNP content (< 1mg) is not shown in the reconstructions. INTRODUCTION:Magnetic nanoparticles (MNPs) are intensively tested in novel cancer treatment approaches where they act as drug carriers in magnetic drug targeting or as heat generators in magnetic hyperthermia. For these applications the quantitative knowledge of the MNP distribution side the body is essential. In addition to the location of the MNP, information about the interaction of the MNPs with the biological matrix would be extremely useful. Here, we demonstrate a quantitative imaging experiment for MNPs where in addition to the distribution of MNP concentration also the binding state of the MNPs is visualized. In magnetorelaxometry (MRX) the magnetic relaxation of an MNP ensemble after changing an external magnetization field is utilized for their specific and quantitative detection. The relaxation time is determined by the superposition of Brownian and Néel relaxation processes within the MNP ensemble. Thus, it contains information about the binding state of the MNPs. Recently, we experimentally demonstrated quantitative imaging of an MNP distribution by sequential MRX measurements using spatially varying magnetization field patterns [1]. Here, we extend this approach by a phenomenological data model [2] in order to identify different binding states of the MNPs in the images of the MNP distribution. METHODS:For the relaxation measurements we assembled in the top layer (1) of a mount (10x10x6cm 3 ) a suspension of unbound MNPs (Berlin Heart GmbH, Germany) and in the lower layer (2) 9 MNP loaded cubes (edge length of 12 mm) of bound MNPs immobilized in gypsum as depicted in fig. 1 (left). Magnetizing field patterns were sequentially generated for 1s from 30 planar excitation coils (d=36mm) and relaxation signals were detected by 304 SQUID magnetometers after switching off the magnetizing field. We modeled each signal B(t) by B(t)= B b,norm (t)+ B ub,norm (t)+B offs, where B b,norm (t) and B ub,norm (t) were previously measured reference signals of bound and unbound MNP and B offs was an arbitrary offset. Each of the resulting two vectors of relaxation amplitudes B b =[α i B b,norm ] and B ub =[β i B ub,norm ] was modeled by a linear equation system B=LX with X being the unknown voxel concentrations of bound or unbound MNP, respectively, and L the vector of a priori known transfer functions from voxels to sensors for each magnetizing coil. The inverse problem was solved for X b and X ub by calculating the pseudoinverse of L using a truncated SVD method. RESULTS:We could reconstruct the MNP distributions for X b for bound and X ub for unboun...