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

A Finite Element Analysis Model for Magnetomotive Ultrasound Elastometry Magnet Design with Experimental Validation

Objective

Magnetomotive ultrasound (MMUS) using magnetic nanoparticle contrast agents has shown promise for thrombosis imaging and quantitative elastometry via magnetomotive resonant acoustic spectroscopy (MRAS). Young's modulus measurements of smaller, stiffer thrombi require an MRAS system capable of generating forces at higher temporal frequencies. Solenoids with fewer turns, and thus less inductance, could improve high frequency performance, but the reduced force may compromise results. In this work, a computational model capable of predicting improved MRAS magnet configurations optimized for elastometry is presented and validated.

Approach

Finite element analysis (FEA) was used to model the force and inductance of MRAS systems. The simulations incorporated both solenoid electromagnets and permanent magnets in three-dimensional steady-state, frequency domain, and time domain studies.

Main results

The model successfully predicted a configuration in which permanent magnets could be used to increase the force supplied by an existing MRAS system. Accordingly, the displacement measured in a magnetically labeled validation phantom increased by a factor of 2.2 ± 0.3 when the force was predicted to increase by a factor of 2.2 ± 0.2. The model additionally identified a new solenoid configuration consisting of four smaller coils capable of providing sufficient force at higher driving frequencies.

Significance

These results indicate two methods by which MRAS systems could be designed to deliver higher frequency magnetic forces without the need for experimental trial and error. Either the number of turns within each solenoid could be reduced while permanent magnets are added at precise locations, or a larger number of smaller solenoids could be used. These findings overcome a key challenge toward the goal of thrombosis elastometry via MMUS.

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.

Modelling of magnetic microbubbles to evaluate contrast enhanced magnetomotive ultrasound in lymph nodes - a pre-clinical study

OBJECTIVES

Despite advances in MRI the detection and characterisation of lymph nodes in rectal cancer remains complex, especially when assessing the response to neoadjuvant treatment. An alternative approach is functional imaging, previously shown to aid characterisation of cancer tissues. We report proof of concept of the novel technique Contrast-Enhanced Magneto-Motive Ultrasound (CE-MMUS) to recover information relating to local perfusion and lymphatic drainage, and interrogate tissue mechanical properties through magnetically induced deformations.

METHODS

The feasibility of the proposed application was explored using a combination of experimental animal and phantom ultrasound imaging, along with finite element analysis. First, contrast-enhanced ultrasound imaging on one wild type mouse recorded lymphatic drainage of magnetic microbubbles after bolus injection. Second, tissue phantoms were imaged using MMUS to illustrate the force- and elasticity dependence of the magnetomotion. Third, the magnetomechanical interactions of a magnetic microbubble with an elastic solid were simulated using finite element software.

RESULTS

Accumulation of magnetic microbubbles in the inguinal lymph node was verified using contrast enhanced ultrasound, with peak enhancement occurring 3.7 s post-injection. The magnetic microbubble gave rise to displacements depending on force, elasticity, and bubble radius, indicating an inverse relation between displacement and the latter two.

CONCLUSION

Combining magnetic microbubbles with MMUS could harness the advantages of both techniques, to provide perfusion information, robust lymph node delineation and characterisation based on mechanical properties.

ADVANCES IN KNOWLEDGE

(a) Lymphatic drainage of magnetic microbubbles visualised using contrast-enhanced ultrasound imaging and (b) magnetomechanical interactions between such bubbles and surrounding tissue could both contribute to (c) robust detection and characterisation of lymph nodes.

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.