Modeling and Measurement of the Nonlinear Force on Nanoparticles in Magnetomotive Techniques

Displacement Patterns in Magnetomotive Ultrasound Explored by Finite Element Analysis

Magnetomotive ultrasound is an emerging technique that enables detection of magnetic nanoparticles. This has implications for ultrasound molecular imaging, and potentially addresses clinical needs regarding determination of metastatic infiltration of the lymphatic system. Contrast is achieved by a time-varying magnetic field that sets nanoparticle-laden regions in motion. This motion is governed by vector-valued mechanical and magnetic forces. Understanding how these forces contribute to observed displacement patterns is important for the interpretation of magnetomotive ultrasound images. Previous studies have captured motion adjacent to nanoparticle-laden regions that was attributed to diamagnetism. While diamagnetism could give rise to a force, it cannot fully account for the observed displacements in magnetomotive ultrasound. To isolate explanatory variables of the observed displacements, a finite element model is set up. Using this model, we explore potential causes of the unexplained motion by comparing numerical models with earlier experimental findings. The simulations reveal motion outside particle-laden regions that could be attributed to mechanical coupling and the principle of mass conservation. These factors produced a motion that counterbalanced the time-varying magnetic excitation, and whose extent and distribution was affected by boundary conditions as well as compressibility and stiffness of the surroundings. Our findings emphasize the importance of accounting for the vector-valued magnetic force in magnetomotive ultrasound imaging. In an axisymmetric geometry, that force can be represented by a simple scalar expression, an oversimplification that rapidly becomes inaccurate with distance from the symmetry axis. Additionally, it results in an underestimation of the vertical force component by up to 30%. We therefore recommend using the full vector-valued force to capture the magnetic interaction. This study enhances our understanding of how forces govern magnetic nanoparticle displacement in tissue, contributing to accurate analysis and interpretation of magnetomotive ultrasound imaging.

Single Magnetic Particle Motion in Magnetomotive Ultrasound: An Analytical Model and Experimental Validation

Magnetomotive Ultrasound (MMUS) is an emerging imaging modality, in which magnetic nanoparticles (MNPs) are used as contrast agents. MNPs are driven by a time-varying magnetic force, and the resulting movement of the surrounding tissue is detected with a signal processing algorithm. However, there is currently no analytical model to quantitatively predict this magnetically-induced displacement. Toward the goal of predicting motion due to forces on the distribution of MNPs, in this work, a model originally derived from the Navier-Stokes equation for the motion of a single magnetic particle subject to a magnetic gradient force is presented and validated. Displacement amplitudes for a spatially inhomogeneous and temporally sinusoidal force were measured as a function of force amplitude and Young's modulus, and the predicted linear and inverse relationships were confirmed in gelatin phantoms, respectively, with three out of four data sets exhibiting R² ≥ 0.88 . The mean absolute uncertainty between the predicted displacement magnitude and experimental results was 14%. These findings provide a means by which the performance of MMUS systems may be predicted to verify that systems are working to theoretical limits and to compare results across laboratories.

Identification of static nonlinearities by sinusoidal excitation with variable DC offsets

When identifying nonlinear systems with input-output measurements, a suitable test signal must be selected. Nonlinear systems are almost always in a cascade with linear systems, i.e., a Wiener-Hammerstein type system cascade. A suitable test signal is preferably less influenced by the linear systems and is therefore sinusoidal, if time-varying signals are required for the measurement principle, e.g., for induction or vibration measurements. Then, a sinusoidal excitation with different DC offsets is a suitable signal to analyze a static nonlinear system in a Wiener-Hammerstein type cascade by measuring the cascade output at higher harmonics of the input frequency in a steady state, e.g., by using sensitive lock-in techniques. To calculate the cascade output given the input signal or to reconstruct the static nonlinear system also given the output signal, the transfer function of the DC offset at the nonlinear system input to the higher harmonics at the nonlinear system output is required. Those transfer functions are calculated here with emphasis on the first harmonic component. The reconstruction of a static nonlinear system is demonstrated in a simple simulation scenario by inverse filtering, i.e., deconvolution, with the derived transfer function. It is pointed out that a commonly made small signal assumption to the test signal is bypassed with the deconvolution method, which can lead to more precise measurements in applications due to a higher signal-to-noise ratio at the cascade output.

Implementation method for magneto-acoustic concentration tomography with magnetic induction (MACT-MI) based on the method of moments

Magneto-acoustic concentration tomography of magnetic nanoparticles with magnetic induction (MACT-MI) is a new imaging technology that combines the advantages of the high sensitivity of magnetic particle imaging and the high resolution of ultrasonic imaging. This technique has broad application prospects in the biomedical and molecular imaging fields. In this study, a reconstruction algorithm based on the method of moments (MoM) is proposed for the MACT-MI inverse problem. Image reconstructions of the acoustic source and superparamagnetic nanoparticle (SPN) concentration were performed using different shape models, and the reconstructed images were analyzed. In addition, the effect of the radius of the tissue region loaded with SPNs on the quality of the reconstructed images was evaluated. The results demonstrated that the new method could reconstruct the SPN concentration distribution well, and a negative correlation existed between the radius of the imaging model and reconstructed image quality. The finding of this research can potentially contribute to the development of MACT-MI in medicine.

Magnetomotive Ultrasound Imaging Systems: Basic Principles and First Applications

This review discusses magnetomotive ultrasound, which is an emerging technique that uses superparamagnetic iron oxide nanoparticles as a contrast agent. The key advantage of using nanoparticle-based contrast agents is their ability to reach extravascular targets, whereas commercial contrast agents for ultrasound comprise microbubbles confined to the blood stream. This also extends possibilities for molecular imaging, where the contrast agent is labeled with specific targeting molecules (e.g., antibodies) so that pathologic tissue may be visualized directly. The principle of action is that an external time-varying magnetic field acts to displace the nanoparticles lodged in tissue and thereby their immediate surrounding. This movement is then detected with ultrasound using frequency- or time-domain analysis of echo data. As a contrast agent already approved for magnetic resonance imaging (MRI) by the US Food and Drug Administration, there is a shorter path to clinical translation, although safety studies of magnetomotion are necessary, especially if particle design is altered to affect biodistribution or signal strength. The external modulated magnetic field may be generated by electromagnets, permanent magnets, or a combination of the two. The induced nanoparticle motion may also reveal mechanical material properties of tissue, healthy or diseased, one of several interesting potential future aspects of the technique.