Modeling and Bias-Robust Estimation of the Acoustic Release of Chemotherapeutics from Liposomes

Abstract

This paper models the acoustic drug release of chemotherapeutics from liposomes using a kinetic model that accounts for systematic biases affecting the drug delivery process. An optimal stochastic filter is then proposed to provide robust estimates of the percent drug released. Optimality is guaranteed by accurately identifying the underlying statistical noise characteristics in experimental data. The estimator also quantifies the bias in the release, exhibited by the experimental data. Drug release is experimentally measured as a change in fluorescence upon the application of ultrasound. First, a first-order kinetic model is proposed to model the release, which is aided by a bias term to account for the fact that full release is not achieved under the conditions explored in this study. The noise structure affecting the process dynamics and the measurement process is then identified in terms of the statistical covariance of the measured quantities. The identified covariance magnitudes are then utilized to estimate the dynamics of drug release as well as the bias term. The identified a priori knowledge is used to implement an optimal Kalman filter, which was initially tested in a simulation environment. The experimental datasets are then fed into the filter to estimate the state and identify the bias. Experiments span a number of ultrasonic power densities for liposomes. The results suggest that the proposed algorithm, the optimal Kalman filter, performs well in modeling acoustically activated drug release from liposomes.