Abstract

The advancement of micro-total analysis systems is increasing the ability to perform multiple functions in one microfluidic device. These systems have several advantages in biomedical applications, including lower equipment and personnel costs, reduced power requirements, faster separations, and smaller sample and reagent volume requirements. Because of this, there has been a growing interest in the study of particle motion in micro- and nanochannels. The ACBA device (see below for definition) labels, sorts, and analyzes cancer cells in an enriched blood sample. This paper focuses on the labeling step of this device and the objective is to determine the probability that an antibody will bind with an antigen on a circulating tumor cell (CTC), a process that we term labeling. A stochastic model using the Fokker-Planck equation to predict the transition probability of an antibody that is assumed to follow a stochastic trajectory is developed. The analysis is carried out for a single antibody that is imbedded in a fully developed Poiseuille flow. The transition probability is then integrated to obtain the probability density. One more integration of the probability density associated with the antibody over a region in the neighborhood of the cell surface is required to predict the probability of binding to the cell.