A Lumped Element Method for Acoustoelectric Imaging Reconstruction: A Numerical Study

Acoustoelectric impedance tomography (AET) is a new non-invasive medical imaging procedure used to map the electrical properties of biological tissues with higher spatial resolution than traditional electrical impedance tomography (EIT). It exploits the acoustoelectric effect where modulated ultrasonic pressure changes the local tissue conductivity. This provides additional information to reconstruct a tomographic image, and has a stabilizing effect on an otherwise highly unstable inverse problem.In this paper, a novel approach to solving the AET inverse problem for image reconstruction is proposed. In the algorithm, the acoustoelectric effect is assumed to create small perturbations in the local resistance of the medium under observation. A lumped model consisting of a finite mesh of resistors approximates the medium under observation, through which boundary voltage differences between the excited and unexcited medium are calculated. A variation of the Modified Newton Raphson (MNR) algorithm is then proposed, where each pattern in the algorithm is created from small perturbations of the tissue conductivity. A total of eight simulation scenarios are evaluated, where the conductivity perturbations are in the order of 1%, 2.5% to 5% of the nominal tissue conductivity. The algorithm can successfully reconstruct the images in the presence of random noise. The obtained images are compared against traditional EIT where the percentage error is calculated for each simulated tomographic image. The simulation results indicate that the proposed approach is superior to traditional EIT as it constructs more distinct and high contrasting images with less percentage error.