The process of developing an end-to-end model of a magneto-immunoassay is described, simulating the agglutination effect due to the specific binding of bacteria to paramagnetic particles. After establishing the properties of the dose-specific agglutination through direct imaging, a microfluidic assay was used to demonstrate changes in the magnetophoretic transport dynamics of agglutinated clusters via transient inductive magentometer measurements. End-to-end mathematical modelling is used to establish the physical processes underlying the assay. First, a modified form of Becker-Döring nucleation kinetic equations is used to establish a relationship between analyte dose and average cluster size. Next, Stokes flow equations are used to establish a relationship between cluster size and speed of motion within the fluid chamber. This predicts a cluster-size dynamic profile of concentration of PMPs versus time when the magnetic field is switched between the two actuated magnets. Finally, inductive modelling is carried out to predict the response of the magnetometer circuit in response to the dynamics of magnetic clusters. The predictions of this model are shown to agree well with the results of experiments, and to predict the shape of the dose-response curve.
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