State Estimation of the Time-Varying and Spatially Localized Concentration of Signal Molecules from the Stochastic Adsorption Dynamics on the Carbon Nanotube-Based Sensors and Its Application to Tumor Cell Detection

Abstract

This paper addresses a problem of estimating time-varying, local concentrations of signal molecules with a carbon-nanotube (CNT)-based sensor array system, which sends signals triggered by monomolecular adsorption/desorption events of proximate molecules on the surfaces of the sensors. Such sensors work on nano-scale phenomena and show inherently stochastic non-Gaussian behavior, which is best represented by the chemical master equation (CME) describing the time evolution of the probabilities for all the possible number of adsorbed molecules. In the CME, the adsorption rate on each sensor is linearly proportional to the local concentration in the bulk phase. State estimators are proposed for these types of sensors that fully address their stochastic nature. For CNT-based sensors motivated by tumor cell detection, the particle filter, which is nonparametric and can handle non-Gaussian distributions, is compared to a Kalman filter that approximates the underlying distributions by Gaussians. In addition, the second-order generalized pseudo Bayesian estimation (GPB2) algorithm and the Markov chain Monte Carlo (MCMC) algorithm are incorporated into KF and PF respectively, for detecting latent drift in the concentration affected by different states of a cell.