Identification of the three-dimensional gel microstructure from transmission electron micrographs

Single particle raster image analysis of diffusion

As a complement to the standard RICS method of analysing Raster Image Correlation Spectroscopy images with estimation of the image correlation function, we introduce the method SPRIA, Single Particle Raster Image Analysis. Here, we start by identifying individual particles and estimate the diffusion coefficient for each particle by a maximum likelihood method. Averaging over the particles gives a diffusion coefficient estimate for the whole image. In examples both with simulated and experimental data, we show that the new method gives accurate estimates. It also gives directly standard error estimates. The method should be possible to extend to study heterogeneous materials and systems of particles with varying diffusion coefficient, as demonstrated in a simple simulation example. A requirement for applying the SPRIA method is that the particle concentration is low enough so that we can identify the individual particles. We also describe a bootstrap method for estimating the standard error of standard RICS.

Fast two-dimensional bubble analysis of biopolymer filamentous networks pore size from confocal microscopy thin data stacks

The average pore size ξ0 of filamentous networks assembled from biological macromolecules is one of the most important physical parameters affecting their biological functions. Modern optical methods, such as confocal microscopy, can noninvasively image such networks, but extracting a quantitative estimate of ξ0 is a nontrivial task. We present here a fast and simple method based on a two-dimensional bubble approach, which works by analyzing one by one the (thresholded) images of a series of three-dimensional thin data stacks. No skeletonization or reconstruction of the full geometry of the entire network is required. The method was validated by using many isotropic in silico generated networks of different structures, morphologies, and concentrations. For each type of network, the method provides accurate estimates (a few percent) of the average and the standard deviation of the three-dimensional distribution of the pore sizes, defined as the diameters of the largest spheres that can be fit into the pore zones of the entire gel volume. When applied to the analysis of real confocal microscopy images taken on fibrin gels, the method provides an estimate of ξ0 consistent with results from elastic light scattering data.

An algorithm for extracting the network geometry of three-dimensional collagen gels

The geometric structure of a biopolymer network impacts its mechanical and biological properties. In this paper, we develop an algorithm for extracting the network architecture of three-dimensional (3d) fluorescently labeled collagen gels, building on the initial work of Wu et al., (2003). Using artificially generated images, the network extraction algorithm is then validated for its ability to reconstruct the correct bulk properties of the network, including fiber length, persistence length, cross-link density, and shear modulus.

Brownian dynamics simulations in hydrogels using an adaptive time-stepping algorithm

The adaptive time-stepping algorithm for Brownian simulation of solute diffusion in three-dimensional complex geometries previously developed by the authors of this paper was applied to heterogeneous three-dimensional polymer hydrogel structures. The simulations were performed on reconstructed three-dimensional hydrogels. The obstruction effect from the gel strands on water and diffusion of dendrimers with different sizes were determined by simulations and compared with experimental nuclear magnetic resonance diffusometry data obtained from the same material. It was concluded that obstruction alone cannot explain the observed diffusion rates, but an interaction between the dendrimers and the gel strands should be included in the simulations. The effect of a sticky-wall interaction potential with geometrically distributed residence times on the diffusion rate has been studied. It was found that sticky-wall interaction is a possible explanation for the discrepancy between simulated and experimental diffusion data for dendrimers of different sizes diffusing in hydrogels.