Magnetic nanoparticle imaging by random and maximum length sequences of inhomogeneous activation fields Daniel Baumgarten 1,2 , Roland Eichardt 1 , Guillaume Crevecoeur 3 , Eko Supriyanto 2 and Jens Haueisen 1 Abstract— Biomedical applications of magnetic nanoparticles require a precise knowledge of their biodistribution. From multi-channel magnetorelaxometry measurements, this distri- bution can be determined by means of inverse methods. It was recently shown that the combination of sequential inho- mogeneous excitation fields in these measurements is favor- able regarding the reconstruction accuracy when compared to homogeneous activation . In this paper, approaches for the determination of activation sequences for these measurements are investigated. Therefor, consecutive activation of single coils, random activation patterns and families of m-sequences are examined in computer simulations involving a sample measure- ment setup and compared with respect to the relative condition number of the system matrix. We obtain that the values of this condition number decrease with larger number of mea- surement samples for all approaches. Random sequences and m-sequences reveal similar results with a significant reduction of the required number of samples. We conclude that the ap- plication of pseudo-random sequences for sequential activation in the magnetorelaxometry imaging of magnetic nanoparticles considerably reduces the number of required sequences while preserving the relevant measurement information. I. INTRODUCTION Magnetic nanoparticles offer a large variety of promising biomedical applications, among them magnetic drug target- ing, magnetic hyperthermia. All these applications share the need for a quantitative and precise detection of the particles with respect to monitoring their safety and efficiency. We presented a method for the spatially resolved quantification of magnetic nanoparticles in tissue based on magnetic relax- ation measurements [1]. From multichannel measurements of the decay of the particles’ magnetization after being exposed to a homogeneous magnetic excitation field, their distribution can be reconstructed using a minimum norm estimation technique [2]. It could be shown that combining the recon- struction results of sequential inhomogeneous magnetization fields considerably improves the spatial resolution of this technique [3] and is favorable when compared to homoge- neous activation regarding the reconstruction accuracy [4]. However, a consecutive activation of one single coil per mea- surement sample is too time consuming and not practicable in experimental measurements. In this paper, we address the problem of defining activation patterns for sequential inhomogeneous stimulations. It aims at finding suitable and 1 Institute of Biomedical Engineering and Informatics, Ilmenau Uni- versity of Technology, Ilmenau, Germany (email: daniel.baumgarten@tu- ilmenau.de) 2 Department of Clinical Engineering, Universiti Teknologi Malaysia, Johor Bahru, Malaysia 3 Department of Electrical Energy, Systems and Automation, Ghent University, Ghent, Belgium effective excitation sequences. For this purpose, random and pseudo-random sequences are employed and compared to the sequential activation of single coils. The evaluation is based on the condition of the system matrix. II. METHODS A. Setup The setup employed for the simulations in this paper comprises 45 excitation coils (diameter 40 mm) arranged in regular arrays positioned around the region of interest. As figure 1 illustrates, 9 coils were placed in the X-, X+, Y-, Y+ and Z- plane, respectively. Fig. 1. Schematic representation of the simulation setup with the excitation coils positioned in 5 planes around the source region containing 16 by 16 by 16 voxels and one plane of sensors above the sources. A total of 97 magnetic sensors are modeled to sit on regular grids in two planes above the source space. 81 sensors are oriented normal to the z-direction (see figure 1). 16 sensors are positioned in a second plane above, 8 oriented in x and 8 oriented in y direction (these sensors are not shown in figure 1 for clarity). The source space consists of 4096 cubic voxels with an edge length of 6 mm. B. Forward / Inverse Model The contribution of the volume elements at location ~ r i containing magnetic nanoparticles with a concentration n i to the magnetic field ~ B in the sensor point ~ r s can be expressed by 35th Annual International Conference of the IEEE EMBS Osaka, Japan, 3 - 7 July, 2013 978-1-4577-0216-7/13/$26.00 ©2013 IEEE 3258