Near an interface, the distribution of swimming microorganisms such as bacteria is distinguished from inert colloidal particles because of the interfacial hydrodynamics induced by swimming. In this work, we use nontumbling flagellated bacteria, Escherichia coli, to study cell distribution near gas and liquid interfaces and compare it to the case of a solid wall. For low-viscosity ratios such as gas interfaces, we observe a stronger cell accumulation compared to that near liquid and solid surfaces. This contradicts known theoretical predictions. Therefore, we develop a model based on Brownian dynamics, including hydrodynamic effects and short-range physiochemical interactions between bacteria and interfaces. This model explains our experimental findings and can predict cell distribution near clean and surfactant-contaminated interfaces. By considering higher order singularities, this study helps explain bacteria orientation, trajectories, and cell density.

Implantable, bioresorbable drug delivery systems offer an alternative to current drug administration techniques; allowing for patient‐tailored drug dosage, while also increasing patient compliance. Mechanistic mathematical modeling allows for the acceleration of the design of the release systems, and for prediction of physical anomalies that are not intuitive and may otherwise elude discovery. This study investigates short‐term drug release as a function of water‐mediated polymer phase inversion into a solid depot within hours to days, as well as long‐term hydrolysis‐mediated degradation and erosion of the implant over the next few weeks. Finite difference methods are used to model spatial and temporal changes in polymer phase inversion, solidification, and hydrolysis. Modeling reveals the impact of non‐uniform drug distribution, production and transport of H⁺ ions, and localized polymer degradation on the diffusion of water, drug, and hydrolyzed polymer byproducts. Compared to experimental data, the computational model accurately predicts the drug release during the solidification of implants over days and drug release profiles over weeks from microspheres and implants. This work offers new insight into the impact of various parameters on drug release profiles, and is a new tool to accelerate the design process for release systems to meet a patient specific clinical need.

We present a novel approach to estimate the uncertainty in ensemble particle image velocimetry (PIV) measurements. The ensemble PIV technique is widely used when the cross-correlation signal-to-noise ratio is insufficient to perform a reliable instantaneous velocity measurement. Despite the utility of ensemble PIV, uncertainty quantification for this type of measurement has not been studied. Here, we propose a method for estimating the uncertainty directly from the probability density function of displacements found by deconvolving the ensemble cross-correlation from the ensemble autocorrelation. We then find the second moment of the probability density function and apply a scaling factor to report the uncertainty in the velocity measurement. We call this method the moment of probability of displacement (MPD). We assess MPD’s performance with synthetic and experimental images. We show that predicted uncertainties agree well with the expected root mean square (RMS) of the error in the velocity measurements over a wide range of image and flow conditions. MPD shows good sensitivity to various PIV error sources with around 86% accuracy in matching the RMS of the error in the baseline data sets. So, MPD establishes itself as a reliable uncertainty quantification algorithm for ensemble PIV. We compared the results of MPD against one of the existing instantaneous PIV uncertainty approaches, moment of correlation (MC). We adapted the MC approach for ensemble PIV, however, its primary limitations remain the assumption of the Gaussian probability density function of displacements and the Gaussian particles’ intensity profile. In addition, our analysis shows that ensemble MC consistently underestimates the uncertainty, while MPD outperforms that and removes the limiting Gaussian assumption for the particle and probability density function, thus overcoming the limitations of MC.

We introduce an image-based algorithm to find the probability density function (PDF) of particle displacements from a sequence of images. Conventionally methods based on cross correlation (CC) of image ensembles estimate the standard deviation of an assumed Gaussian PDF from the width of the CC peak. These methods are subject to limiting assumptions that the particle intensity profile and distribution of particle displacements are both Gaussian. Here, we introduce an approach to image-based probability estimation of displacement (iPED) without making any assumptions about the shape of particles’ intensity profile or the PDF of the displacements. In addition, we provide a statistical convergence criterion for iPED to achieve an accurate estimate of the underlying PDF. We compare iPED's performance with the previous CC method for both Gaussian and non-Gaussian particle intensity profiles undergoing Gaussian or non-Gaussian processes. We validate iPED using synthetic images and show that it accurately resolves the PDF of particle displacements with no underlying assumptions. Finally, we demonstrate the application of iPED to real experimental data sets and evaluate its performance. In conclusion, this work presents a method for the estimation of the probability density function of random displacements from images. This method is generalized and independent of any assumptions about the underlying process and is applicable to any moving objects of any arbitrary shape.

We introduce a method to measure the concentration-dependent diffusion coefficient from a sequence of images of molecules diffusing from a source toward a sink. Generally, approaches measuring the diffusion coefficient, such as fluorescence recovery after photobleaching (FRAP), assume that the diffusion coefficient is constant. Hence, these methods cannot capture the concentration dependence of the diffusion coefficient if present. Other approaches measure the concentration-dependent diffusion coefficient from an instantaneous concentration profile and lose the temporal information. These methods make unrealistic assumptions, are not robust, and lead to 100% error. We introduce an image analysis framework that utilizes spatial and temporal information in a sequence of concentration images and numerically solves the general form of Fick's second law using radial basis functions (RBF) to measure the concentration-dependent diffusion coefficient. We term this approach as concentration image diffusimetry (CID). Our method makes no assumptions about the sink and source size and the diffusion dependence on concentration. CID is superior to existing methods in estimating spatiotemporal changes and concentration-dependent diffusion. CID also provides a statistical uncertainty quantification on the measurements using a bootstrapping approach, improving the reliability of the diffusion measurement. We assessed CID's performance using synthetically generated images. Our analysis suggests that CID accurately measures the diffusion coefficient with less than 2% error for most cases. We validated CID with FRAP experimental images and showed that CID agrees with established FRAP algorithms for samples with a constant diffusion coefficient. Finally, we demonstrate the application of CID to experimental datasets of a concentration gradient-driven protein diffusion into a tissue replicate. In conclusion, this work presents an image-based methodology that uses the spatial and temporal changes of concentration fields to measure the concentration-dependent diffusion coefficient.