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.

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.

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.

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

Magnetomotive ultrasound (MMUS) contrasts superparamagnetic iron-oxide nanoparticles (SPIOs) that undergo submicrometer-scale displacements in response to a magnetic gradient force applied to an imaging sample. Typically, MMUS signals are defined in a way that is proportional to the medium displacement, rendering an indirect measure of the density distribution of SPIOs embedded within. Displacement-based MMUS, however, suffers from 'halo effects' that extend into regions without SPIOs due to their inherent mechanical coupling with the medium. To reduce such effects and to provide a more accurate representation of the SPIO density distribution, we propose a model-based inversion of MMUS displacement fields by reconstructing the body force distribution. Displacement fields are modelled using the static Navier-Cauchy equation for linear, homogeneous, and isotropic media, and the body force fields are, in turn, reconstructed by minimizing a regularized least-squares error functional between the modelled and the measured displacement fields. This reconstruction, when performed on displacement fields of two tissue-mimicking phantoms with cuboidal SPIO-laden inclusions, improved the range of errors in measured heights and widths of the inclusions from 54%-282% pre-inversion to-15%-20%. Likewise, the post-inversion contrast to noise ratios (CNRs) of the images were significantly larger than displacement-derived CNRs alone (p  = 0.0078, Wilcoxon signed rank test). Qualitatively, it was found that inversion ameliorates halo effects and increases overall detectability of the inclusion. These findings highlight the utility of model-based inversion as a tool for both signal processing and accurate characterization of the number density distribution of SPIOs in magnetomotive imaging.

Blind Source Separation-Based Motion Detector for Imaging Super-Paramagnetic Iron Oxide (SPIO) Particles in Magnetomotive Ultrasound Imaging.

In magnetomotive ultrasound (MMUS) imaging, an oscillating external magnetic field displaces tissue loaded with super-paramagnetic iron oxide (SPIO) particles. The induced motion is on the nanometer scale, which makes its detection and its isolation from background motion challenging. Previously, a frequency and phase locking (FPL) algorithm was used to suppress background motion by subtracting magnetic field off ( -off) from on ( -on) data. Shortcomings to this approach include long tracking ensembles and the requirement for -off data. In this paper, a novel blind source separation-based FPL (BSS-FPL) algorithm is presented for detecting motion using a shorter ensemble length (EL) than FPL and without -off data. MMUS imaging of two phantoms containing an SPIO-laden cubical inclusion and one control phantom was performed using an open-air MMUS system. When background subtraction was used, contrast and contrast to noise ratio (CNR) were, respectively, 1.20±0.20 and 1.56±0.34 times higher in BSS-FPL as compared to FPL-derived images for EL < 3.5 s. However, contrast and CNR were similar for BSS-FPL and FPL for EL ≥ 3.5 s. When only -on data was used, contrast and CNR were 1.94 ± 0.21 and 1.56 ± 0.28 times higher, respectively, in BSS-FPL as compared to FPL-derived images for all ELs. Percent error in the estimated width and height was 39.30% ± 19.98% and 110.37% ± 6.5% for FPL and was 7.30% ± 7.6% and 16.21% ± 10.29% for BSS-FPL algorithm. This paper is an important step toward translating MMUS imaging to in vivo application, where long tracking ensembles would increase acquisition time and -off data may be misaligned with -on due to physiological motion.

Effect of Model Thrombus Volume and Elastic Modulus on Magnetomotive Ultrasound Signal Under Pulsatile Flow.

Direct ultrasonic imaging of arterial and venous thrombi could aid in diagnosis and treatment planning by providing rapid and cost-effective measurements of thrombus volume and elastic modulus. Toward this end, it was demonstrated that open-air magnetomotive ultrasound (MMUS) provides specific contrast to superparamagnetic iron oxide-labeled model thrombi embedded in gelatin-based blood vessel-mimicking flow phantoms. MMUS was performed on model thrombi in the presence of pulsatile flow that mimics cardiac-induced motion found in real vasculature. The MMUS signal and contrast-to-noise ratio (CNR) were measured across a range of physiologically relevant thrombus volumes and elastic moduli. Model thrombus volumes as small as 0.5 ml were shown to be detectable (CNR > 1) over the entire range of elastic moduli tested (3.5-40 kPa). It was also found that MMUS signal and CNR are increased with increasing thrombus volume ( ) and decreasing elastic modulus ( ), while variations in pulsatile flow rate had little effect. These findings demonstrate that MMUS has promise as a direct in vivo thrombosis imaging modality for quantifying thrombus volume and stiffness.

Comparison of 1,4-distyrylfluorene and 1,4-distyrylbenzene analogues: synthesis, structure, electrochemistry and photophysics.

A series of nine 1,4-distyrylfluorene derivatives (2) functionalized with substituents of variable electrondonating or -accepting capabilities was synthesised. The photophysical properties of the molecules were investigated, including UV/vis absorption, photoluminescence emission, and fluorescence quantum yields. Photophysical properties of chromophores 2 were found to exhibit significant solvatochromic effects, especially in the Stokes shift and photoluminescence maxima. The electrochemical properties of series 2 were also assessed by cyclic voltammetry and differential pulse voltammetry. Results of photophysical and electrochemical analyses were further supported by DFT calculations (B3LYP/6-31G*) and single crystal X-ray diffraction on select molecules. The contributions of intermolecular π-stacking and hydrogen bonding to crystal packing are discussed. A series of nine 1,4-distyrylphenylene derivatives (3) were also synthesised and similarly characterized for comparison to photophysical and solvatochromic effects observed in series 2. Properties of similarly-substituted molecules in series 2 and 3 were compared to one another in order to assess the influence of the 1,4-fluorenylene unit.