Multiphysics 5.3a

A commercial software package (COMSOL Multiphysics 5.3a) is used to simulate the kinetics reaction of the proposed microfluidic immunoassay. The electric field distribution, flow pattern, transportation of antigen, and surface reaction under different conditions are simulated in detail.

Numerical simulations were performed using COMSOL Multiphysics 5.3a using the base and microfluidics modules. A hybrid mesh solution was used for all simulations: coarse mesh in the areas of least interest (e.g. the connection tubes), fine mesh for the 200 µm channel and super fine mesh for the whole sphere and the hydrodynamic focusing area. Boundary conditions were set to no-slip condition for the walls of the entire chip, while different pressures were applied to the inlets to simulate behavior under different circumstances. To correctly visualize (Fig. 3c) the cross section of two identical fluids (buffer and sample) under flow conditions, a suitable simulation strategy was used: the two flows (sample and buffer) were mimic as a set of small spheres of 50 nm (red for buffer molecules—blue for sample molecules) starting from their respective inlets and propagating through the device. For each inlet 10′000 beads were released, imposing the pressures reported in the capture (P_{inlet sample} = 80 mbar; P_{inlet sheath} = 110 mbar). The particles were set as not interacting with each other (bringing to excess a non-viscous fluid) while for the walls we impose non-slip conditions. Once stationary, the cross section was observed hundreds of microns away from the focusing zone.

The numerical calculations were performed with commercial finite-element-methods based software (Comsol Multiphysics 5.3a). The cross-section and the axial direction of the microrods were treated as two-dimensional objects with an effective refractive index. The openness of the system was simulated with a perfectly matched layer to absorb the outgoing waves without reflection. Thus the calculated frequencies of quasi-bound states were complex numbers. Then the calculated frequencies and field patterns of modes were used as inputs in SALT^{49 (link)–54 (link)} to study their lasing actions. Similar to the experiments, only TE (E in plane) field was considered in the numerical calculations.

The finite element analysis (FEA) simulation was conducted by using COMSOL Multiphysics 5.3a (Stockholm, Sweden). An acoustic module and bioheat transfer module were used in this study. In the simulation setup, the eyeball was simplified to four main parts: cornea, lens, vitreous body, and retina where the shape and size of each part were preset [56 (link), 57 (link)]. The acoustic and thermodynamic properties of each part were set based on the previous literature [54 (link)]. Detailed parameters are listed in Supplementary Table 3.

To validate our finite element analysis, we used our 3D-aortic wall model to reproduce published simulation results according to the boundary conditions of respective studies. Our model using COMSOL Multiphysics 5.3a was able to replicate results published by Roccabianca et al.^{18 (link)}, Baek et al.^{28 (link)} and de Gelidi et al.^{29 (link)}. Markers in Fig. 5 represent data reported in Roccabianca’s study^{18 (link)}. The authors simulated biaxial loading protocols of the descending thoracic aorta (material test data by García-Herrera et al.^{30 (link)} with circumferential to axial stress ratio of 1:2, 1:1 and 2:1. Reproduced values using our aortic wall model are plotted as solid lines (Fig. 5), showing averages of circumferential and axial Cauchy stresses across representative central cut planes. Our validation provided good overall correlation with slight deviations for minimal aortic wall strains.Figure 5

Model validation via biaxial Cauchy stress–stretch data evaluated for three different loading protocols (ratio circumferential to axial stress). Markers represent results reported in Roccabianca et al.^{18 (link)}. Solid lines were obtained by inflation tests of aortic wall model employing the identical constitutive equation and concomitant best-fit parameters.