Biosensor arrays for collaborative detection of analytes

In this paper, we address the problem of estimating the concentration of target molecules in a fluid which flows past multiple biosensors. The main goal is to evaluate the estimation improvement that can be obtained by using multiple biosensors. The dynamics of the flow is described by an advection-diffusion partial differential equation. Exploiting the multiple time-scale behaviour of the system, a lumped parameter description of the system is derived which describes the dynamics of the system by a system of ordinary differential equations. Estimating the concentration is then equivalent to the solution of a nonlinear least squares problem using the derived model. Furthermore, an expression is derived for the asymptotic variance of the estimation error. We examine our method on a biosensor built out of protein molecules as a case study. According to the expression for the variance, the achievable improvement in the estimate based on the number of biosensors is evaluated.