Simulation of a Microsolenoid for the Detection of Magnetical Captured Beads
Authors: Struk Daniel , Lee Hoseon , Hesketh Peter J. 
Published: November 2022

Low-cost, fast and accurate antibody detection is important for viral infection testing, especially for in cases of epidemics or pandemics. Currently, most rapid antibody detection methods are based on lateral flow immunoassay tests. [1] Beads offer a convenient way to capture and concentrate antigens, antibodies, and other biological molecules but determining the concentration or number can be a challenge, in particular at lower concentration levels. What we would like to achieve is the ability to detect much lower concentration levels, and in principle count individual molecules or a bound complex labelled with the magnetic bead using a micro-solenoid.
In this paper, a three-dimensional, hollow channel, micro-solenoid is investigated to improve sensitivity, with antibody testing using magnetic microbeads bound to the target antigen. Previous work has shown the use of magnetic microbeads for microfluidic devices [2]. The micro-solenoid is simulated using COMSOL multiphysics to test various geometric parameters such as bead size, coil size, and bead velocity for the goal of detecting and counting antibodies bound to the beads.
A time dependent model was constructed in COMSOL using the magnetic fields and moving mesh modules. In order to simplify the simulation, a 2D axisymmetric model was used and the model was first solved using a stationary step. The bead is represented by a short cylinder, and the solenoid as a uniform diameter annular cylinder, 390 um in length. The coil was simulated through the coil interface under the magnetic fields module allowing it to be represented as single uniform object with variable number of turns, conductivity, and cross-sectional area.
For several sets of constant bead size, coil size, and bead magnetization, the maximum voltage reached was found to be a linear function with respect to velocity. In terms of coil radius, the simulated voltage response decreased quadratically with increasing radius however this was only significant when the bead size was appreciable to the coil size for simulations featuring coil radii of 15, 25, 35, and 50 um with 2, 5, 10, and 12.5 um radii beads. The data is presented in figure 1A and 1B. The results for 10 and 12.5 um radius bead are the only ones with appreciable curvature. The simulated voltage response increased quadratically with increasing bead size and the curvature of the underlying quadratic fit increased with decreased coil radius. Future avenues of study include 3 dimensional designs and simulations and fabrication using microfabricated coils.
[1] D. A. Mistry, J. Y. Wang, M.-E. Moeser, T. Starkey, and L. Y. W. Lee, “A systematic review of the sensitivity and specificity of lateral flow devices in the detection of SARS-CoV-2.,” BMC Infect. Dis., vol. 21, no. 1, p. 828, Aug. 2021, doi: 10.1186/s12879-021-06528-3.
[2] Kyu Sung Kim and Je-Kyun Park, “Magnetic force-based immunoassay using superparamagnetic nanoparticles in microfluidic channel,” in The 13th International Conference on Solid-State Sensors, Actuators and Microsystems, 2005. Digest of Technical Papers. TRANSDUCERS ’05., Jun. 2005, vol. 1, pp. 81-84 Vol. 1. doi: 10.1109/SENSOR.2005.1496364.

Figure 1