Inverse problem of magneto-acoustic concentration tomography for magnetic nanoparticles with magnetic induction in a saturation magnetization state based on the least squares QR factorization method-trapezoidal method

Abstract

In order to improve the imaging quality of magneto-acoustic concentration tomography for magnetic nanoparticles (MNPs) with magnetic induction (MACT-MI) and overcome the boundary singularity, this paper built a matrix model which shows the relationship between the partial derivative distribution of MNP concentration and the ultrasound signals, and focused on proposing a concentration reconstruction method based on the least squares QR factorization (LSQR) method-trapezoidal method. Firstly, simulation models with different shapes were established. Secondly, the magnetic and acoustic field simulation data was substituted into the inverse problem method based on LSQR-trapezoidal method for concentration reconstruction. Finally, the reconstructed images were analyzed and the effect of MNP cluster radius on the reconstruction was investigated. Considering the diffusely asymptotic concentration distribution of MNPs in actual biological tissue environment, an asymptotic concentration model was established and the reconstructed images were analyzed. The simulation results show that under the same conditions, compared with the reconstruction method based on the method of moments (MoM), LSQR-trapezoidal method has clearer image boundaries, more stable imaging results, and faster imaging speed. Compared with the uniform concentration model, LSQR-trapezoidal method is more applicable to the asymptotic concentration model. This study provides a basis for further reconstruction of the accuracy of experimental research.

Keywords: Least squares QR factorization (LSQR) method; Magneto-acoustic concentration tomography for magnetic nanoparticles with magnetic induction (MACT-MI); System matrix; Trapezoidal method.