Inversion of displacement fields to quantify the magnetic particle distribution in homogeneous elastic media from magnetomotive ultrasound

Magneto-Acoustic Theranostic Approach: Integration of Magnetomotive Ultrasound Shear Wave Elastography and Magnetic Hyperthermia

OBJECTIVES

Although magnetically induced hyperthermia has shown great efficiency in the treatment of solid tumors, it is still a challenge to avoid incomplete ablation or overtreatment. In this study, we applied magnetomotive ultrasound shear wave elastography (MMUS-SWE) as a tool for real-time image guidance and feedback in the magnetic hyperthermia (MH) process. We called this new method as magneto-acoustic theranostic approach (MATA).

METHODS

In MATA, a ferromagnetic particle (fMP) was simultaneously used as a thermoseed for MH and a shear wave source for MMUS-SWE. The fMP was excited by a high-frequency magnetic field to induce the heating effect for MH. Meanwhile, the fMP was stimulated by a pulsed magnetic field to generate shear wave propagation for MMUS-SWE. Thus, the changes in elastic modulus surrounding fMP can be used to estimate the therapy effect of MH.

RESULTS

The phantom and in vitro experiments were conducted to verify the feasibility of MATA, which has good performance in magnetothermal conversion and treatment efficacy feedback. The shear wave speed of the isolated pork liver changed significantly after the MH process, which varied from about 1.36 to 4.85 m/s.

CONCLUSIONS

Preliminary results proved that changes in elastic modulus could be useful to estimate the therapy effect of MH. We expect that MATA, which is the integration of MMUS-SWE and MH, will be a novel theranostic method for clinical translation.

Elastometry of clot phantoms via magnetomotive ultrasound-based resonant acoustic spectroscopy

Objective. An ultrasound-based system capable of both imaging thrombi against a dark field and performing quantitative elastometry could allow for fast and cost-effective thrombosis diagnosis, staging, and treatment monitoring. This study investigates a contrast-enhanced approach for measuring the Young’s moduli of thrombus-mimicking phantoms. Approach. Magnetomotive ultrasound (MMUS) has shown promise for lending specific contrast to thrombi by applying a temporally modulated force to magnetic nanoparticle (MNP) contrast agents and measuring resulting tissue displacements. However, quantitative elastometry has not yet been demonstrated in MMUS, largely due to difficulties inherent in measuring applied magnetic forces and MNP densities. To avoid these issues, in this work magnetomotive resonant acoustic spectroscopy (MRAS) is demonstrated for the first time in ultrasound. Main results. The resonance frequencies of gelatin thrombus-mimicking phantoms are shown to agree within one standard deviation with finite element simulations over a range of phantom sizes and Young’s moduli with less than 16% error. Then, in a proof-of-concept study, the Young’s moduli of three phantoms are measured using MRAS and are shown to agree with independent compression testing results. Significance. The MRAS results were sufficiently precise to differentiate between thrombus phantoms with clinically relevant Young’s moduli. These findings demonstrate that MRAS has potential for thrombus staging.

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.

Quantitative Determination of Local Density of Iron Oxide Nanoparticles Used for Drug Targeting Employing Inverse Magnetomotive Ultrasound

Numerous medical applications make use of magnetic nanoparticles, which increase the demand for imaging procedures that are capable of visualizing this kind of particle. Magnetomotive ultrasound (MMUS) is an ultrasound-based imaging modality that can detect tissue, which is permeated by magnetic nanoparticles. However, currently, MMUS can only provide a qualitative mapping of the particle density in the particle-loaded tissue. In this contribution, we present an enhanced MMUS procedure, which enables an estimation of the quantitative level of the local nanoparticle concentration in tissue. The introduced modality involves an adjustment of simulated data to measurement data. To generate these simulated data, the physical processes that arise during the MMUS imaging procedure have to be emulated which can be a computing-intensive proceeding. Since this considerable calculation effort may handicap clinical applications, we further present an efficient approach to calculate the decisive physical quantities and a suitable way to adjust these simulated quantities to the measurement data with only moderate computational effort. For this purpose, we use the result data of a conventional MMUS measurement and the knowledge on the magnetic field quantities and on the mechanical parameters describing the biological tissue, namely, the density, the longitudinal wave velocity, and the shear wave velocity. Experiments on tissue-mimicking phantoms demonstrate that the presented technique can indeed be utilized to determine the local nanoparticle concentration in tissue quantitatively in the correct order of magnitude. By investigating test phantoms of simple geometry, the mean particle concentration of the particle-laden area could be determined with less than 22% deviation to the nominal value.