Uncertainty Quantification and Estimation in Differential Dynamic Microscopy

Mengyang Gu, Matthew Helgeson, Megan Valentine


DDM is a technique that exploits optical microscopy to obtain local, multi-scale quantitative information about dynamic samples, such as liquid suspensions, soft materials, cells, and tissues. In DDM, image sequences are analyzed via a combination of image differences and spatial Fourier transforms to obtain information such as the dynamic structure function which elucidates inter-particle correlations and their time evolution. Through Gaussian process regression, it was shown that predictive samples of the image structure function require only around 0.5%–5% of the Fourier transforms of the observed quantities, leading to a statistical analysis that reduces computational times by 25-120 times. The approach, named DDM with uncertainty quantification (DDM-UQ), was validated using both simulations and experiments with respect to accuracy and computational efficiency, as compared with conventional DDM and multiple particle tracking.

 Importance of the Achievement

Despite DDM’s broad usefulness in determining dynamical properties, it has not been fully adopted as a routine characterization tool, largely due to computational cost and lack of algorithmic robustness. DDM-UQ quantifies the noise, reduces the computational order and enhances the robustness of DDM analysis, laying the foundation for important new applications of DDM, as well as to high-throughput characterization. Moreover, with the potential to carry out real-time analysis via down-sampling, the proposed method can be extended to map out an entire phase space of material composition or physicochemical conditions in a high-throughput manner. DDM-UQ-powered software package will significantly improve the performance of BioPACIFIC MIP's micro-rheology tool and will become available to all its users as well as for any non-profit use.

 Unique Features of BioPACIFIC MIP that Enabled this Achievement

Financial support was provided for one female postdoctoral scholar and one female graduate student through the Fellows program, as well as funds for the materials and development of a state-of-the-art DDM-based high-throughput micro-rheometer.