Toward estimating concentration fields in biological hydrogels using point sensors

This paper is motivated by problems from biology involving estimation of concentration fields in a tissue sample using point measurements given by optical contactless biosensors. Due to biological constraints, the sensors may only be sparsely distributed and intermittently monitored. This paper proposes a nonbiological experimental platform, based on hydrogel and dye diffusion, for studying the problem of concentration field estimation using point sensors. A reduced order model for the diffusion system is derived using Karhunen-Loéve-Galerkin method and a discrete time Kalman filter is used to estimate the concentration field. The estimator is then applied to experimental data consisting of subsampled images from a diffusion process. Performance is evaluated by comparing the state estimates to the original images. Future work will use the experimental platform to study the effects of spatial distribution and timing of sensor measurements, to examine the effects of additional dynamics such as advection and reaction, and to perform online identification of process parameters.