Wood pulp fibres are an important component of environmentally sound and renewable fibre-reinforced composite materials. The high aspect ratio of pulp fibres is an essential property with respect to the mechanical properties a given composite material can achieve. The length of pulp fibres is affected by composite processing operations. This thus emphasizes the importance of assessing the pulp fibre length and how this may be affected by a given process for manufacturing composites. In this work a new method for measuring the length distribution of fibres and fibre fragments has been developed. The method is based on; (i) dissolving the composites, (ii) preparing the fibres for image acquisition and (iii) image analysis of the resulting fibre structures. The image analysis part is relatively simple to implement and is based on images acquired with a desktop scanner and a new ImageJ plugin. The quantification of fibre length has demonstrated the fibre shortening effect because of an extrusion process and subsequent injection moulding. Fibres with original lengths of >1 mm where shortened to fibre fragments with length of <200 μm. The shortening seems to be affected by the number of times the fibres have passed through the extruder, the amount of chain extender and the fraction of fibres in the polymer matrix.

A new framework for the estimation of diffusion coefficients from data on fluorescence recovery after photobleaching (FRAP) with confocal laser scanning microscopy (CLSM) is presented. It is a pixel-based statistical methodology that efficiently utilizes all information about the diffusion process in the available set of images. The likelihood function for a series of images is maximized which gives both an estimate of the diffusion coefficient and a corresponding error. This framework opens up possibilities (1) to obtain localized diffusion coefficient estimates in both homogeneous and heterogeneous materials, (2) to account for time differences between the registrations at the pixels within each image, and (3) to plan experiments optimized with respect to the number of replications, the number of bleached regions for each replicate, pixel size, the number of pixels, the number of images in each series etc. To demonstrate the use of the new framework, we have applied it to a simple system with polyethylene glycol (PEG) and water where we find good agreement with diffusion coefficient estimates from NMR diffusometry. In this experiment, it is also shown that the effect of the point spread function is negligible, and we find fluorochrome-concentration levels that give a linear response function for the fluorescence intensity. © 2008 The Authors.

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.

Recently we complemented the raster image correlation spectroscopy (RICS) method of analysing raster images via estimation of the image correlation function with the method single particle raster image analysis (SPRIA). In SPRIA, individual particles are identified and the diffusion coefficient of each particle is estimated by a maximum likelihood method. In this paper, we extend the SPRIA method to analyse mixtures of particles with a finite set of diffusion coefficients in a homogeneous medium. In examples with simulated and experimental data with two and three different diffusion coefficients, we show that SPRIA gives accurate estimates of the diffusion coefficients and their proportions. A simple technique for finding the number of different diffusion coefficients is also suggested. Further, we study the use of RICS for mixtures with two different diffusion coefficents and investigate, by plotting level curves of the correlation function, how large the quotient between diffusion coefficients needs to be in order to allow discrimination between models with one and two diffusion coefficients. We also describe a minor correction (compared to published papers) of the RICS autocorrelation function. Lay description Diffusion is a key mass transport mechanism for small particles. Efficient methods for estimating diffusion coefficients are crucial for analysis of microstructures, for example in soft biomaterials. The sample of interest may consist of a mixture of particles with different diffusion coefficients. Here, we extend a method called Single Particle Raster Image Analysis (SPRIA) to account for particle mixtures and estimation of the diffusion coefficients of the mixture components. SPRIA combines elements of classical single particle tracking methods with utilizing the raster scan with which images obtained by using a confocal laser scanning microscope. In particular, single particles are identified and their motion estimated by following their center of mass. Thus, an estimate of the diffusion coefficient will be obtained for each particle. Then, we analyse the distribution of the estimated diffusion coefficients of the population of particles, which allows us to extract information about the diffusion coefficients of the underlying components in the mixture. On both simulated and experimental data with mixtures consisting of two and three components with different diffusion coefficients, SPRIA provides accurate estimates and, with a simple criterion, the correct number of mixture components is selected in most cases.

Mass transport in gels depends crucially on local properties of the gel network. We propose a method for identifying the three-dimensional (3D) gel microstructure from statistical information in transmission electron micrographs. The gel strand network is modelled as a random graph with nodes and edges (branches). The distribution of edge length, the number of edges at nodes and the angles between edges at a node are estimated from transmission electron micrographs by image analysis methods. The 3D network is simulated by Markov chain Monte Carlo, with a probability function based on the statistical information found from the micrographs. The micrographs are projections of stained gel strands in slices, and we derive a formula for estimating the thickness of the stained gel slice based on the total projected gel strand length and the number of times that gel strands enter or exit the slice. © 2007 The Authors.

We implement a massively parallel population Monte Carlo approximate Bayesian computation (PMC-ABC) method for estimating diffusion coefficients, sizes and concentrations of diffusing nanoparticles in liquid suspension using confocal laser scanning microscopy and particle tracking. The method is based on the joint probability distribution of diffusion coefficients and the time spent by a particle inside a detection region where particles are tracked. We present freely available central processing unit (CPU) and graphics processing unit (GPU) versions of the analysis software, and we apply the method to characterize mono- and bidisperse samples of fluorescent polystyrene beads.

We study the microstructure of a granular amorphous silica ceramic material synthesized by spark plasma sintering. Using monodisperse spherical silica particles as precursor, spark plasma sintering yields a dense granular material with distinct granule boundaries. We use selective etching to obtain nanoscopic pores along the granule borders. We interrogate this highly interesting material structure by combining scanning electron microscopy, X-ray computed nanotomography and simulations based on random close packed spherical particles. We determine the degree of anisotropy caused by the uni-axial force applied during sintering, and our analysis shows that our synthesis method provides a means to avoid significant granule growth and to fabricate a material with well-controlled microstructure.

Combined focused ion beam and scanning electron microscope (FIB-SEM) tomography is a well-established technique for high resolution imaging and reconstruction of the microstructure of a wide range of materials. Segmentation of FIB-SEM data is complicated due to a number of factors; the most prominent is that for porous materials, the scanning electron microscope image slices contain information not only from the planar cross-section of the material but also from underlying, exposed subsurface pores. In this work, we develop a segmentation method for FIB-SEM data from ethyl cellulose porous films made from ethyl cellulose and hydroxypropyl cellulose (EC/HPC) polymer blends. These materials are used for coating pharmaceutical oral dosage forms (tablets or pellets) to control drug release. We study three samples of ethyl cellulose and hydroxypropyl cellulose with different volume fractions where the hydroxypropyl cellulose phase has been leached out, resulting in a porous material. The data are segmented using scale-space features and a random forest classifier. We demonstrate good agreement with manual segmentations. The method enables quantitative characterization and subsequent optimization of material structure for controlled release applications. Although the methodology is demonstrated on porous polymer films, it is applicable to other soft porous materials imaged by FIB-SEM. We make the data and software used publicly available to facilitate further development of FIB-SEM segmentation methods. Lay Description: For imaging of very fine structures in materials, the resolution limits of, e.g. X-ray computed tomography quickly become a bottleneck. Scanning electron microscopy (SEM) provides a way out, but it is essentially a two-dimensional imaging technique. One manner in which to extend it to three dimensions is to use a focused ion beam (FIB) combined with a scanning electron microscopy and acquire tomography data. In FIB-SEM tomography, ions are used to perform serial sectioning and the electron beam is used to image the cross section surface. This is a well-established method for a wide range of materials. However, image analysis of FIB-SEM data is complicated for a variety of reasons, in particular for porous media. In this work, we analyse FIB-SEM data from ethyl cellulose porous films made from ethyl cellulose and hydroxypropyl cellulose (EC/HPC) polymer blends. These films are used as coatings for controlled drug release. The aim is to perform image segmentation, i.e. to identify which parts of the image data constitute the pores and the solid, respectively. Manual segmentation, i.e. when a trained operator manually identifies areas constituting pores and solid, is too time-consuming to do in full for our very large data sets. However, by performing manual segmentation on a set of small, random regions of the data, we can train a machine learning algorithm to perform automatic segmentation on the entire data sets. The method yields good agreement with the manual segmentations and yields porosities of the entire data sets in very good agreement with expected values. The method facilitates understanding and quantitative characterization of the geometrical structure of the materials, and ultimately understanding of how to tailor the drug release. © 2020 The Authors.

Phase-separated polymer films are commonly used as coatings around pharmaceutical oral dosage forms (tablets or pellets) to facilitate controlled drug release. A typical choice is to use ethyl cellulose and hydroxypropyl cellulose (EC/HPC) polymer blends. When an EC/HPC film is in contact with water, the leaching out of the water-soluble HPC phase produces an EC film with a porous network through which the drug is transported. The drug release can be tailored by controlling the structure of this porous network. Imaging and characterization of such EC porous films facilitates understanding of how to control and tailor film formation and ultimately drug release. Combined focused ion beam and scanning electron microscope (FIB-SEM) tomography is a well-established technique for high-resolution imaging, and suitable for this application. However, for segmenting image data, in this case to correctly identify the porous network, FIB-SEM is a challenging technique to work with. In this work, we implement convolutional neural networks for segmentation of FIB-SEM image data. The data are acquired from three EC porous films where the HPC phases have been leached out. The three data sets have varying porosities in a range of interest for controlled drug release applications. We demonstrate very good agreement with manual segmentations. In particular, we demonstrate an improvement in comparison to previous work on the same data sets that utilized a random forest classifier trained on Gaussian scale-space features. Finally, we facilitate further development of FIB-SEM segmentation methods by making the data and software used open access. © 2021 The Authors.

Conventional analysis of fluorescence recovery after photobleaching (FRAP) data for diffusion coefficient estimation typically involves fitting an analytical or numerical FRAP model to the recovery curve data using non-linear least squares. Depending on the model, this can be time consuming, especially for batch analysis of large numbers of data sets and if multiple initial guesses for the parameter vector are used to ensure convergence. In this work, we develop a completely new approach, DeepFRAP, utilizing machine learning for parameter estimation in FRAP. From a numerical FRAP model developed in previous work, we generate a very large set of simulated recovery curve data with realistic noise levels. The data are used for training different deep neural network regression models for prediction of several parameters, most importantly the diffusion coefficient. The neural networks are extremely fast and can estimate the parameters orders of magnitude faster than least squares. The performance of the neural network estimation framework is compared to conventional least squares estimation on simulated data, and found to be strikingly similar. Also, a simple experimental validation is performed, demonstrating excellent agreement between the two methods. We make the data and code used publicly available to facilitate further development of machine learning-based estimation in FRAP. Lay description: Fluorescence recovery after photobleaching (FRAP) is one of the most frequently used methods for microscopy-based diffusion measurements and broadly used in materials science, pharmaceutics, food science and cell biology. In a FRAP experiment, a laser is used to photobleach fluorescent particles in a region. By analysing the recovery of the fluorescence intensity due to the diffusion of still fluorescent particles, the diffusion coefficient and other parameters can be estimated. Typically, a confocal laser scanning microscope (CLSM) is used to image the time evolution of the recovery, and a model is fit using least squares to obtain parameter estimates. In this work, we introduce a new, fast and accurate method for analysis of data from FRAP. The new method is based on using artificial neural networks to predict parameter values, such as the diffusion coefficient, effectively circumventing classical least squares fitting. This leads to a dramatic speed-up, especially noticeable when analysing large numbers of FRAP data sets, while still producing results in excellent agreement with least squares. Further, the neural network estimates can be used as very good initial guesses for least squares estimation in order to make the least squares optimization convergence much faster than it otherwise would. This provides for obtaining, for example, diffusion coefficients as soon as possible, spending minimal time on data analysis. In this fashion, the proposed method facilitates efficient use of the experimentalist's time which is the main motivation to our approach. The concept is demonstrated on pure diffusion. However, the concept can easily be extended to the diffusion and binding case. The concept is likely to be useful in all application areas of FRAP, including diffusion in cells, gels and solutions. © 2020 The Authors.