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

Abstract

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.

Figure 1.

Cross-sectional view of model geometry after deformation of spherical shell with radius $r_0$ , internal pressure $p_{in}$ and a solid cylinder with Young’s modulus $E_1$ and Poisson’s ratio ${\nu }_1$ . Total deformation is $d$ and the contact area covers an indent with a radius of $a$ , that describes a circle perpendicular to the vertical symmetry axis. The bottom surface of the solid is fixed and its remaining boundaries are free. A spring foundation applied to the shell boundary prevented rigid motion of the sphere and was incrementally, non-linearly decreased while the force and pressure were ramped up. Regarding the bubble, only the shell was modelled explicitly using shell elements with a thickness of 2 nm. The internal pressure was applied on the boundary and was ramped up. Due to rotational symmetry, the geometry was created as a semicircle and a rectangle. Symmetry boundary conditions were applied on the axis of symmetry.

Figure 2.

Ultrasound B-mode (panels A and C) and contrast mode images (B and D) of lymph node pre-contrast administration and at peak enhancement on the top and second row respectively. The lymph node, indicated by an oval in panels A through D, is distinguishable from the background in the B-mode images (left), as a hypoechoic region. The same region is clearly void of non-linear signal in the absence of contrast agent, see panel B, but shows a strong signal post-injection, panel D. The filling of the region of interest outlining the lymph node is shown in panel E, showing peak enhancement 3.7 s post-injection.

Figure 3.

MMUS imaging: MMUS displacements were detected predominately in the insert containing magnetic nanoparticles, see image in panel A of 5% PVAc phantom at high excitation current, 3 V peak-peak amplified by 20 dB. The size and approximate position of the insert is indicated by a circle. B shows the maximum displacement in six phantoms with PVA concentrations, 5 and 10%, for two excitation settings, such that the magnetic flux density at the centre of the insert was approximately 0.017 T and 0.026 T respectively. Magnetic flux density, or more precisely magnetisation field, is an important factor in determining the magnetic force, see Equation 1, and the different concentrations of PVA produce cryogels with distinctly different stiffnesses, or Young’s modulus of 8.3 and 30 kPa respectively. Each box represents six measurements taken on three phantoms in two image planes. The centre line represents the median, box edges are 25th and 75th percentile and whiskers show the full range of values recorded. MMUS, magnetomotive ultrasound; PVA, polyvinyl alcohol.

Figure 4.

Field measurements along the symmetry axis of the solenoid for two amplification settings, 20 dB (top) and 16 dB (below). Each point represents the mean of three measurements, and error bars indicate standard deviation. The first derivative was obtained from a cubic spline interpolant in the piecewise polynomial form, shown as a dashed line.

Figure 5.

Finite element modelling of tissue deformation due to magnetic microbubble motion: normalised contact pressure (asterisk) and solid displacement (solid line) occurring due to a magnetic microbubble moving under a magnetic field. The analytical contact pressure according to Hertz contact theory is shown as a dashed line. Each variable was normalised to its maximum value.

Figure 6.

Contact area radius (A), midpoint displacement (B) and midpoint contact pressure (C) outputs for a magnetic microbubble contacting an elastic solid with Young’s moduli ranging from 8 to 30 kPa. Bubble radius was 1.05 µm, and force was 1.0 pN. Curves fitted based on the Hertz contact theory.

Figure 7.

Contact area radius (A), midpoint displacement (B) and midpoint contact pressure (C) outputs for bubble radii ranging from 1 to 1.5 µm. Young’s modulus of the solid was 24 kPa, and force magnitude was 1.0 pN. Fitted curves based on the Hertz contact theory.

Figure 8.

Contact area radius (A), midpoint displacement (B) and contact pressure (C) outputs for total force magnitude ranging from 0.75 to 1.75 pN. Bubble radius was 1.05 µm, and Young’s modulus of the solid was 24 kPa. Fitted curves are based on the Hertz contact theory.