Extended Spherical Diffusion Theory: Electrochemiluminescence Imaging Analysis of Diffusive Molecules from Spherical Biosamples.

Spherical biosamples such as immunobeads, cells, and cell aggregates have been widely used in bioapplications. The bioactivity of individual spherical biosamples in highly sensitive assays and individual analyses must be evaluated in a high-throughput manner. Electrochemiluminescence (ECL) imaging was recently proposed for the high-throughput analysis of diffusive molecules from spherical biosamples. ECL imaging involves the placing of spherical biosamples on a flat electrode filled with a solution. The biosamples produce (or consume) biological/chemical molecules such as H₂O₂ and O₂, which diffuse to form a concentration gradient at the electrode. The ECL signals from the molecules are then measured to obtain the concentration profile, which allows the flux to be estimated, from which their bioactivities can be successfully calculated. However, no studies on theoretical approaches for spherical biosamples on flat surfaces have been conducted using ECL imaging. Therefore, this paper presents a novel spherical diffusion theory for spherical biosamples on a flat surface, which is based on the common spherical diffusion theory and was designated as the extended spherical diffusion theory. First, the concepts behind this theory are discussed. The theory is then validated by comparison with a simulated analysis. The resulting equation successfully expresses the concentration profile for the entire area. The glucose oxidase activity in the hydrogel beads is subsequently visualized using ECL imaging, and the enzymatic product flux is calculated using the proof-of-concept theory. Finally, a time-dependent simulation is conducted to fill the gap between the theoretical and experimental data. This paper presents novel guidelines for this analysis.