Deconvolution of Concentration Recordings at Live Cell Preparations via Shape Error Optimization

Abstract

In many fields of science and engineering including several areas in analytical chemistry, deconvolution needs to be performed on measured data to extract meaningful information. This situation arises when a variable of interest has to be indirectly estimated from a measurable quantity that depends on this variable in some known manner. This dependence, called the "forward problem", has to be computationally undone to obtain the information sought from the experimental results. Solving this "inverse problem" requires deconvolution whenever the forward problem involves convolution. Despite its ubiquitous importance, however, performance of the methodologies used for deconvolution remains often unsatisfactory. An example is in bioanalytical applications where microsensing at live preparations is performed to obtain information on biological transport. It is in this context that a novel approach to solve inverse problems, shape error optimization, is proposed and tested in this work. The experimental paradigm addressed is in the area of multidrug resistance (MDR) in cancer that gives rise to passive and active drug efflux from cells. Doxorubicin (DOX) concentration is monitored with a carbon fiber microelectrode in vitro at close proximity to a monolayer of cells expressing MDR. The measured local concentration is the result of convolution of cellular efflux with the impulse response of diffusion in the extracellular medium. Hence, estimating DOX efflux, which is the biologically meaningful information, leads to a deconvolution problem. Performance of deconvolution via shape error optimization is compared with that of two conventional techniques: discrete Fourier transform and square error optimization. The results obtained are also applicable to other areas of science and engineering where deconvolution is commonly used for processing experimental data.