Mathematical modeling of the dynamics and production of biosensors.

摘要

The central theme of this dissertation is the analysis of biosensors and biosensor platforms by mathematical modeling of mass-transport processes. More efficient operation and production of biosensors is achieved through theoretical analyses of the physical processes that are involved in measurement and production of biosensors.;In this thesis I mathematically model the mass-transport processes that occur outside the glucose biosensor itself to improve the precision of biosensor measurements. The biosensor measures glucose concentrations in the subcutaneous tissue while measurements of blood glucose concentrations are desired. Classical regularization allows the real-time prediction of blood glucose concentrations based on the biosensor measurements of subcutaneous glucose. The optimal parameters for the application of the regularization method, including the sampling rate and smoothing condition, are found by a Monte-Carlo type simulation study. ELISA is also used to test the continuous glucose sensors for leaching of glucose oxidase, which is the enzyme employed in the transduction layer.;For the manufacture of microarray-type biosensors, I apply mathematical analysis to understand how sensor platforms, or microwell chips, can be optimally produced using two new lithographic techniques: imprint lithography and thermocapillary lithography. In imprint lithography a squeeze flow that occurs between a sinusoidally corrugated plate and a flat plate is studied to evaluate the effect of corrugations on compression rate. Asymptotic analysis and simulations were used to solve two- and three-dimensional squeeze flow problems. I conclude that the compression rate of plates with fewer than 50 corrugations is qualitatively different from that of flat plates. Finally, I explore the production of microwell chips using thermocapillary lithography. This technique takes advantage of instabilities in thin films caused by the motion of the film surface due to temperature gradients on the surface. Numerical simulations, linear analysis and scaling analysis are used to explore the stability map of thin film flow that is subject to thermocapillary, capillary and van der Waals forces. The analysis predicts that thermocapillary lithography can effectively produce simple micron-scale patterns on surfaces. Potential applications for these lithographic techniques include the manufacture of microelectronic devices, photonic devices, controlled-release microchips and biosensor platforms.