Evaluating selection criteria for optimized excitation coils in magnetorelaxometry imaging

Abstract

Objective. Magnetorelaxometry imaging (MRXI) is an experimental imaging technique applicable for noninvasive, qualitative and quantitative imaging of magnetic nanoparticles (MNPs). Accurate reconstructions of nanoparticle distributions are crucial for several novel treatment methods employing MNPs such as magnetic drug targeting or magnetic hyperthermia therapy. Hence, it is desirable to design MRXI setups such that the reconstruction accuracy is maximized for a given set of design parameters. Several attempts exist in literature that focus on the improvement of MRXI and other related linear inverse problems with respect to various figures of merit. However, to date it remains unclear, which approach leads to the largest benefit for the reconstruction accuracy. Thus, the aim of this study is to compare the different figures of merit, thereby determining the most reliable and effective optimization approach for magnetorelaxometry setups. Approach. In the present simulation study, we translate these figures of merit to various cost functions, allowing us to optimize the electromagnetic coil positions and radii of two distinct MRXI setups with an adapted tabu search algorithm. Multiple artificial MNP phantoms are reconstructed employing the optimized setups and the resulting imaging qualities are subsequently compared. Main results. The extensive amount of generated synthetic data unprecedented in previous MRXI studies identifies the condition number as the most reliable indicator for good imaging results. This is the case for both the qualitative as well as the quantitative reconstruction accuracies. Significance. The results of this study show that optimized coil configurations increase the reconstruction quality compared to the state-of-the-art. The insights obtained here can also be extended to other design parameters of MRXI setups, thus enabling more reliable reconstructions of MNP ensembles which will ultimately render the aforementioned treatment methods safer and more efficient.

Experimental demonstration of improved magnetorelaxometry imaging performance using optimized coil configurations

“…Initially, a large number of coils with different positions and radii were placed around the cuboidal as well as the cylindrical ROIs in our MRXI simulation environment. The first part of the optimization process involved the selection of a subset of $$N_\mathrm{c}=32$$ coils with minimal $$\kappa (\mathbf {L})$$ out of these large coil configurations by means of global tabu search optimization 35 . According to the results shown in this study, a coil count of $$N_\mathrm{c}=32$$ is suitable for ROIs of this size and the PTB sensor system.…”

“…The condition number is calculated by $$\begin{align} \kappa {\left(\mathbf {L}\right)} = {\left\Vert \mathbf {L}\right\Vert} _2 {\left\Vert \mathbf {L}^+\right\Vert} _2, \end{align}$$where $$\Vert \cdot \Vert _2$$ represents the spectral matrix norm and $$\mathbf {L}^+$$ denotes the Moore–Penrose inverse of the system matrix. The condition number is an indicator for the stability of linear inverse problems 40,41 and it was shown in a simulation study that the minimization of $$\kappa (\mathbf {L})$$ is an effective approach to optimize the reconstruction quality of MRXI setups 35 …”

“…The condition number is an indicator for the stability of linear inverse problems 40,41 and it was shown in a simulation study that the minimization of 𝜅(L) is an effective approach to optimize the reconstruction quality of MRXI setups. 35 Typically, 𝜅(L) exhibits a vast amount of local minima when the excitation coil positions and radii are varied. Thus, the optimization was conducted in two consecutive steps to determine an objective function value close to the global minimum of 𝜅(L).…”

“…The experiments in the present study shall be based upon the cuboidal and cylindrical ROIs investigated in our earlier work. We will determine initial coil configurations for both ROIs by means of the presented discrete global optimization approach 35 . The initial coil configurations shall then be continuously optimized with a subsequent constrained local optimization approach allowing for the design of technically feasible coil configurations.…”

Perspective: magnetic nanoparticles in theranostic applications

“…Other MNP imaging techniques, still in their infancy compared to MPI, have in the last years mainly focused on improving their imaging performance [46][47][48][49][50] . Nevertheless, they might also contribute in advancing theranostic applications, as each technique has its distinct advantages.…”