Structural formation during bread baking in a combined microwave-convective oven determined by sub-second in-situ synchrotron X-ray microtomography.

A new concept has been developed for characterizing the real-time evolution of the three-dimensional pore and lamella microstructure of bread during baking using synchrotron X-ray microtomography (SRµCT). A commercial, combined microwave-convective oven was modified and installed at the TOMCAT synchrotron tomography beamline at the Swiss Light Source (SLS), to capture the 3D dough-to-bread structural development in-situ at the micrometer scale with an acquisition time of 400 ms. This allowed characterization and quantitative comparison of three baking technologies: (1) convective heating, (2) microwave heating, and (3) a combination of convective and microwave heating. A workflow for automatic batchwise image processing and analysis of 3D bread structures (1530 analyzed volumes in total) was established for porosity, individual pore volume, elongation, coordination number and local wall thickness, which allowed for evaluation of the impact of baking technology on the bread structure evolution. The results showed that the porosity, mean pore volume and mean coordination number increase with time and that the mean local cell wall thickness decreases with time. Small and more isolated pores are connecting with larger and already more connected pores as function of time. Clear dependencies are established during the whole baking process between the mean pore volume and porosity, and between the mean local wall thickness and the mean coordination number. This technique opens new opportunities for understanding the mechanisms governing the structural changes during baking and discern the parameters controlling the final bread quality.

Controlling the structure of spin-coated multilayer ethylcellulose/hydroxypropylcellulose films for drug release.

Porous phase-separated ethylcellulose/hydroxypropylcellulose (EC/HPC) films are used to control drug transport out of pharmaceutical pellets. Water-soluble HPC leaches out and forms a porous structure that controls the drug transport. Industrially, the pellets are coated using a fluidized bed spraying device, and a layered film exhibiting varying porosity and structure after leaching is obtained. A detailed understanding of the formation of the multilayered, phase-separated structure during production is lacking. Here, we have investigated multilayered EC/HPC films produced by sequential spin-coating, which was used to mimic the industrial process. The effects of EC/HPC ratio and spin speed on the multilayer film formation and structure were investigated using advanced microscopy techniques and image analysis. Cahn-Hilliard simulations were performed to analyze the mixing behavior. A gradient with larger structures close to the substrate surface and smaller structures close to the air surface was formed due to coarsening of the layers already coated during successive deposition cycles. The porosity of the multilayer film was found to vary with both EC/HPC ratio and spin speed. Simulation of the mixing behavior and in situ characterization of the structure evolution showed that the origin of the discontinuities and multilayer structure can be explained by the non-mixing of the layers.

Sodium reduction in foods: Challenges and strategies for technical solutions.

In many parts of the world, sodium consumption is higher than recommended levels, representing one of the most important food-related health challenges and leading to considerable economical costs for society. Therefore, there is a need to find technical solutions for sodium reduction that can be implemented by food producers and within food services. The aims of this review are to discuss the barriers related to sodium reduction and to highlight a variety of technical solutions. The barriers relate to consumer perception, microbiology, processing, and physicochemistry. Existing technical solutions include inhomogeneous salt distribution, coated salt particles, changing particle sizes and forms, surface coating, multisensory combinations, sodium replacements, double emulsions, adapted serum release by microstructure design, and adapted brittleness by microstructure design. These solutions, their implementation and the associated challenges, and applicable product categories are described. Some of these solutions are ready for use or are in their early development stages. Many solutions are promising, but in most cases, some form of adaptation or optimization is needed before application in specific products, and care must always be taken to ensure food safety. For instance, further research and innovation are required in the dynamic evolution of saltiness perception, consumer acceptance, the binding and migration of sodium, juiciness, microbiological safety, and the timing of salt addition during processing. Once implemented, these solutions will undoubtedly support food producers and food services in reducing sodium content and extend the application of the solutions to different foods.

Cross-sectional structure evolution of phase-separated spin-coated ethylcellulose/hydroxypropylcellulose films during solvent quenching.

Porous phase-separated ethylcellulose/hydroxypropylcellulose (EC/HPC) films are used to control drug transport out of pharmaceutical pellets. The films are applied on the pellets using fluidized bed spraying. The drug transport rate is determined by the structure of the porous films that are formed as the water-soluble HPC leaches out. However, a detailed understanding of the evolution of the phase-separated structure during production is lacking. Here, we have investigated EC/HPC films produced by spin-coating, which mimics the industrial manufacturing process. This work aimed to understand the structure formation and film shrinkage during solvent evaporation. The cross-sectional structure evolution was characterized using confocal laser scanning microscopy (CLSM), profilometry and image analysis. The effect of the EC/HPC ratio on the cross-sectional structure evolution was investigated. During shrinkage of the film, the phase-separated structure undergoes a transition from 3D to nearly 2D structure evolution along the surface. This transition appears when the typical length scale of the phase-separated structure is on the order of the thickness of the film. This was particularly pronounced for the bicontinuous systems. The shrinkage rate was found to be independent of the EC/HPC ratio, while the initial and final film thickness increased with increasing HPC fraction. A new method to estimate part of the binodal curve in the ternary phase diagram for EC/HPC in ethanol has been developed. The findings of this work provide a good understanding of the mechanisms responsible for the morphology development and allow tailoring of thin EC/HPC films structure for controlled drug release.

Inverse design of anisotropic spinodoid materials with prescribed diffusivity.

The three-dimensional microstructure of functional materials determines its effective properties, like the mass transport properties of a porous material. Hence, it is desirable to be able to tune the properties by tuning the microstructure accordingly. In this work, we study a class of spinodoid i.e. spinodal decomposition-like structures with tunable anisotropy, based on Gaussian random fields. These are realistic yet computationally efficient models for bicontinuous porous materials. We use a convolutional neural network for predicting effective diffusivity in all three directions. We demonstrate that by incorporating the predictions of the neural network in an approximate Bayesian computation framework for inverse problems, we can in a computationally efficient manner design microstructures with prescribed diffusivity in all three directions.

Structure formation and coarsening kinetics of phase-separated spin-coated ethylcellulose/hydroxypropylcellulose films.

Porous phase-separated ethylcellulose/hydroxypropylcellulose (EC/HPC) films are used to control drug transport from pharmaceutical pellets. The drug transport rate is determined by the structure of the porous films that are formed as water-soluble HPC leaches out. However, a detailed understanding of the evolution of the phase-separated structure in the films is lacking. In this work, we have investigated EC/HPC films produced by spin-coating, mimicking the industrial fluidized bed spraying. The aim was to investigate film structure evolution and coarsening kinetics during solvent evaporation. The structure evolution was characterized using confocal laser scanning microscopy and image analysis. The effect of the EC:HPC ratio (15 to 85 wt% HPC) on the structure evolution was determined. Bicontinuous structures were found for 30 to 40 wt% HPC. The growth of the characteristic length scale followed a power law, L(t) ∼ t(n), with n ∼ 1 for bicontinuous structures, and n ∼ 0.45-0.75 for discontinuous structures. The characteristic length scale after kinetic trapping ranged between 3.0 and 6.0 µm for bicontinuous and between 0.6 and 1.6 µm for discontinuous structures. Two main coarsening mechanisms could be identified: interfacial tension-driven hydrodynamic growth for bicontinuous structures and diffusion-driven coalescence for discontinuous structures. The 2D in-plane interface curvature analysis showed that the mean curvature decreased as a function of time for bicontinuous structures, confirming that interfacial tension is driving the growth. The findings of this work provide a good understanding of the mechanisms responsible for morphology development and open for further tailoring of thin EC/HPC film structures for controlled drug release.

Convolutional neural networks for segmentation of FIB-SEM nanotomography data from porous polymer films for controlled drug release.

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.

Drug release from pharmaceutical tablets or pellets is often controlled by applying a phase-separated polymer film coating. Ethyl cellulose and hydroxypropyl cellulose (EC/HPC) polymer blends are commonly used. The HPC phase leaches out when in contact with water and the result is a porous EC matrix coating, with mass transport properties that can be controlled by tailoring the structure of the porous network. High-resolution 3D imaging is necessary to characterize such materials, and the resolution of e.g. X-ray computed tomography is simply insufficient. Combined focused ion beam and scanning electron microscope (FIB-SEM) tomography on the other hand is a suitable technique, but segmentation of FIB-SEM data, in this case to separate the solid matrix and the porous network, is challenging. In this work, we develop a method for segmentation of FIB-SEM image data acquired from three different EC porous films where the HPC phases have been leached out. The segmentation is based on convolutional neural networks (CNNs). CNNs is a well-established machine learning paradigm and has demonstrated state-of-the-art performance in many image analysis and segmentation tasks. CNNs are inspired from biological processes in the visual cortex and act similarly, at least conceptually. In contrast to most conventional machine learning algorithms, CNNs learn by themselves which features to extract from the images. The features are extracted at different spatial scales and may constitute e.g. edge and contrast detectors. These features are subsequently used for classification. In this work, CNNs are used for image segmentation. The goal is to identify which regions in the images that contain either pore (empty space) or solid (material), hence a binary classification task. For the CNN to learn how to perform such a task, a ground truth is needed. This is achieved by letting an expert manually segment parts of the data. This is a very time-consuming endeavor, hence only a small random subset of the full dataset is manually segmented. The CNN is trained for the task using the manually segmented data, after which automatic segmentation of the full dataset is performed. We obtain very good agreement with manual segmentations in terms of accuracy and porosity, and a clear improvement in comparison to an earlier developed random forest classifier trained on Gaussian scale-space features on the same data. The development of accurate segmentation methods is a crucial step toward better understanding and tailoring of coatings for controlled drug release.

Structure evolution during phase separation in spin-coated ethylcellulose/hydroxypropylcellulose films.

Porous phase-separated films made of ethylcellulose (EC) and hydroxypropylcellulose (HPC) are commonly used for controlled drug release. The structure of these thin films is controlling the drug transport from the core to the surrounding liquids in the stomach or intestine. However, detailed understanding of the time evolution of these porous structures as they are formed remains elusive. In this work, spin-coating, a widely applied technique for making thin uniform polymer films, was used to mimic the industrial manufacturing process. The focus of this work was on understanding the structure evolution of phase-separated spin-coated EC/HPC films. The structure evolution was determined using confocal laser scanning microscopy (CLSM) and image analysis. In particular, we determined the influence of spin-coating parameters and EC : HPC ratio on the final phase-separated structure and the film thickness. The film thickness was determined by profilometry and it influences the ethanol solvent evaporation rate and thereby the phase separation kinetics. The spin speed was varied between 1000 and 10 000 rpm and the ratio of EC : HPC in the polymer blend was varied between 78 : 22 wt% and 40 : 60 wt%. The obtained CLSM micrographs showed phase separated structures, typical for the spinodal decomposition phase separation mechanism. By using confocal laser scanning microscopy combined with Fourier image analysis, we could extract the characteristic length scale of the phase-separated final structure. Varying spin speed and EC : HPC ratio gave us precise control over the characteristic length scale and the thickness of the film. The results showed that the characteristic length scale increases with decreasing spin speed and with increasing HPC ratio. The thickness of the spin-coated film decreases with increasing spin speed. It was found that the relation between film thickness and spin speed followed the Meyerhofer equation with an exponent close to 0.5. Furthermore, good correlations between thickness and spin speed were found for the compositions 22 wt% HPC, 30 wt% HPC and 45 wt% HPC. These findings give a good basis for understanding the mechanisms responsible for the morphology development and increase the possibilities to tailor thin EC/HPC film structures.

New Characterization Measures of Pore Shape and Connectivity Applied to Coatings used for Controlled Drug Release.

Pore geometry characterization-methods are important tools for understanding how pore structure influences properties such as transport through a porous material. Bottlenecks can have a large influence on transport and related properties. However, existing methods only catch certain types of bottleneck effects caused by variations in pore size. We here introduce a new measure, geodesic channel strength, which captures a different type of bottleneck effect caused by many paths coinciding in the same pore. We further develop new variants of pore size measures and propose a new way of visualizing 3-D characterization results using layered images. The new measures together with existing measures were used to characterize and visualize properties of 3-D FIB-SEM images of three leached ethyl-cellulose/hydroxypropyl-cellulose films. All films were shown to be anisotropic, and the strongest anisotropy was found in the film with lowest porosity. This film had very tortuous paths and strong geodesic channel-bottlenecks, while the paths through the other two films were relatively straight with well-connected pore networks. The geodesic channel strength was shown to give important new visual and quantitative insights about connectivity, and the new pore size measures provided useful information about anisotropies and inhomogeneities in the pore structures. The methods have been implemented in the freely available software MIST.

DeepFRAP: Fast fluorescence recovery after photobleaching data analysis using deep neural networks.

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.

Optimization of FIB-SEM Tomography and Reconstruction for Soft, Porous, and Poorly Conducting Materials.

Tomography using a focused ion beam (FIB) combined with a scanning electron microscope (SEM) is well-established for a wide range of conducting materials. However, performing FIB­SEM tomography on ion- and electron-beam-sensitive materials as well as poorly conducting soft materials remains challenging. Some common challenges include cross-sectioning artifacts, shadowing effects, and charging. Fully dense materials provide a planar cross section, whereas pores also expose subsurface areas of the planar cross-section surface. The image intensity of the subsurface areas gives rise to overlap between the grayscale intensity levels of the solid and pore areas, which complicates image processing and segmentation for three-dimensional (3D) reconstruction. To avoid the introduction of artifacts, the goal is to examine porous and poorly conducting soft materials as close as possible to their original state. This work presents a protocol for the optimization of FIB­SEM tomography parameters for porous and poorly conducting soft materials. The protocol reduces cross-sectioning artifacts, charging, and eliminates shadowing effects. In addition, it handles the subsurface and grayscale intensity overlap problems in image segmentation. The protocol was evaluated on porous polymer films which have both poor conductivity and pores. 3D reconstructions, with automated data segmentation, from three films with different porosities were successfully obtained.

Raster Image Correlation Spectroscopy Performance Evaluation.

Raster image correlation spectroscopy (RICS) is a fluorescence image analysis method for extracting the mobility, concentration, and stoichiometry of diffusing fluorescent molecules from confocal image stacks. The method works by calculating a spatial correlation function for each image and analyzing the average of those by model fitting. Rules of thumb exist for RICS image acquisitioning, yet a rigorous theoretical approach to predict the accuracy and precision of the recovered parameters has been lacking. We outline explicit expressions to reveal the dependence of RICS results on experimental parameters. In terms of imaging settings, we observed that a twofold decrease of the pixel size, e.g., from 100 to 50 nm, decreases the error on the translational diffusion constant (D) between three- and fivefold. For D = 1 µm2 s-1, a typical value for intracellular measurements, ∼25-fold lower mean-squared relative error was obtained when the optimal scan speed was used, although more drastic improvements were observed for other values of D. We proposed a slightly modified RICS calculation that allows correcting for the significant bias of the autocorrelation function at small (≪50 × 50 pixels) sizes of the region of interest. In terms of sample properties, at molecular brightness E = 100 kHz and higher, RICS data quality was sufficient using as little as 20 images, whereas the optimal number of frames for lower E scaled pro rata. RICS data quality was constant over the nM-µM concentration range. We developed a bootstrap-based confidence interval of D that outperformed the classical least-squares approach in terms of coverage probability of the true value of D. We validated the theory via in vitro experiments of enhanced green fluorescent protein at different buffer viscosities. Finally, we outline robust practical guidelines and provide free software to simulate the parameter effects on recovery of the diffusion coefficient.

A Highly Accurate Pixel-Based FRAP Model Based on Spectral-Domain Numerical Methods.

We introduce a new, to our knowledge, numerical model based on spectral methods for analysis of fluorescence recovery after photobleaching data. The model covers pure diffusion and diffusion and binding (reaction-diffusion) with immobile binding sites, as well as arbitrary bleach region shapes. Fitting of the model is supported using both conventional recovery-curve-based estimation and pixel-based estimation, in which all individual pixels in the data are utilized. The model explicitly accounts for multiple bleach frames, diffusion (and binding) during bleaching, and bleaching during imaging. To our knowledge, no other fluorescence recovery after photobleaching framework incorporates all these model features and estimation methods. We thoroughly validate the model by comparison to stochastic simulations of particle dynamics and find it to be highly accurate. We perform simulation studies to compare recovery-curve-based estimation and pixel-based estimation in realistic settings and show that pixel-based estimation is the better method for parameter estimation as well as for distinguishing pure diffusion from diffusion and binding. We show that accounting for multiple bleach frames is important and that the effect of neglecting this is qualitatively different for the two estimation methods. We perform a simple experimental validation showing that pixel-based estimation provides better agreement with literature values than recovery-curve-based estimation and that accounting for multiple bleach frames improves the result. Further, the software developed in this work is freely available online.

Heterogeneity of Network Structures and Water Dynamics in κ-Carrageenan Gels Probed by Nanoparticle Diffusometry.

A set of functionalized nanoparticles (PEGylated dendrimers, d = 2.8-11 nm) was used to probe the structural heterogeneity in Na+/K+ induced κ-carrageenan gels. The self-diffusion behavior of these nanoparticles as observed by 1H pulsed-field gradient NMR, fluorescence recovery after photobleaching, and raster image correlation spectroscopy revealed a fast and a slow component, pointing toward microstructural heterogeneity in the gel network. The self-diffusion behavior of the faster nanoparticles could be modeled with obstruction by a coarse network (average mesh size <100 nm), while the slower-diffusing nanoparticles are trapped in a dense network (lower mesh size limit of 4.6 nm). Overhauser dynamic nuclear polarization-enhanced NMR relaxometry revealed a reduced local solvent water diffusivity near 2,2,6,6-tetramethylpiperidin-1-oxyl (TEMPO)-labeled nanoparticles trapped in the dense network, showing that heterogeneity in the physical network is also reflected in heterogeneous self-diffusivity of water. The observed heterogeneity in mesh sizes and in water self-diffusivity is of interest for understanding and modeling of transport through and release of solutes from heterogeneous biopolymer gels.

Computational high-throughput screening of fluid permeability in heterogeneous fiber materials.

We explore computational high-throughput screening as a design strategy for heterogeneous, isotropic fiber materials. Fluid permeability, a key property in the design of soft porous materials, is systematically studied using a multi-scale lattice Boltzmann framework. After characterizing microscopic permeability as a function of solid volume fraction in the microstructure, we perform high-throughput computational screening of in excess of 35 000 macrostructures consisting of a continuous bulk interrupted by spherical/elliptical domains with either lower or higher microscopic permeability (hence with two distinct microscopic solid volume fractions and therefore two distinct microscopic permeabilities) to assess which parameters determine macroscopic permeability for a fixed average solid volume fraction. We conclude that the fractions of bulk and domains and the distribution of solid volume fraction between them are the primary determinants of macroscopic permeability, and that a substantial increase in permeability compared to the corresponding homogenous material is attainable.

Interplay between flow and diffusion in capillary alginate hydrogels.

Alginate gels with naturally occurring macroscopic capillaries have been used as a model system to study the interplay between laminar flow and diffusion of nanometer-sized solutes in real time. Calcium alginate gels that contain homogeneously distributed parallel-aligned capillary structures were formed by external addition of crosslinking ions to an alginate sol. The effects of different flow rates (0, 1, 10, 50 and 100 µl min(-1)) and three different probes (fluorescein, 10 kDa and 500 kDa fluorescein isothiocyanate-dextran) on the diffusion rates of the solutes across the capillary wall and in the bulk gel in between the capillaries were investigated using confocal laser scanning microscopy. The flow in the capillaries was produced using a syringe pump that was connected to the capillaries via a tube. Transmission electron microscopy revealed an open aggregated structure close to the capillary wall, followed by an aligned network layer and the isotropic network of the bulk gel. The most pronounced effect was observed for the 1 nm-diameter fluorescein probe, for which an increase in flow rate increased the mobility of the probe in the gel. Fluorescence recovery after photobleaching confirmed increased mobility close to the channel, with increasing flow rate. Mobility maps derived using raster image correlation spectroscopy showed that the layer with the lowest mobility corresponded to the anisotropic layer of ordered network chains. The combination of microscopy techniques used in the present study elucidates the flow and diffusion behaviors visually, qualitatively and quantitatively, and represents a promising tool for future studies of mass transport in non-equilibrium systems.

Fluorescence recovery after photobleaching in material and life sciences: putting theory into practice.

Fluorescence recovery after photobleaching (FRAP) is a versatile tool for determining diffusion and interaction/binding properties in biological and material sciences. An understanding of the mechanisms controlling the diffusion requires a deep understanding of structure-interaction-diffusion relationships. In cell biology, for instance, this applies to the movement of proteins and lipids in the plasma membrane, cytoplasm and nucleus. In industrial applications related to pharmaceutics, foods, textiles, hygiene products and cosmetics, the diffusion of solutes and solvent molecules contributes strongly to the properties and functionality of the final product. All these systems are heterogeneous, and accurate quantification of the mass transport processes at the local level is therefore essential to the understanding of the properties of soft (bio)materials. FRAP is a commonly used fluorescence microscopy-based technique to determine local molecular transport at the micrometer scale. A brief high-intensity laser pulse is locally applied to the sample, causing substantial photobleaching of the fluorescent molecules within the illuminated area. This causes a local concentration gradient of fluorescent molecules, leading to diffusional influx of intact fluorophores from the local surroundings into the bleached area. Quantitative information on the molecular transport can be extracted from the time evolution of the fluorescence recovery in the bleached area using a suitable model. A multitude of FRAP models has been developed over the years, each based on specific assumptions. This makes it challenging for the non-specialist to decide which model is best suited for a particular application. Furthermore, there are many subtleties in performing accurate FRAP experiments. For these reasons, this review aims to provide an extensive tutorial covering the essential theoretical and practical aspects so as to enable accurate quantitative FRAP experiments for molecular transport measurements in soft (bio)materials.

Probe diffusion in phase-separated bicontinuous biopolymer gels.

Probe diffusion was determined in phase separated bicontinuous gels prepared by acid-induced gelation of the whey protein isolate-gellan gum system. The topological characterization of the phase-separated gel systems is achieved by confocal microscopy and the diffusion measurements are performed using pulsed field gradient (PFG) NMR and fluorescence recovery after photo-bleaching (FRAP). These two techniques gave complementary information about the mass transport at different time- and length scales, PFG NMR provided global diffusion rates in the gel systems, while FRAP enabled the measurements of diffusion in different phases of the phase-separated gels. The results revealed that the phase-separated gel with the largest characteristic wavelength had the fastest diffusion coefficient, while the gel with smaller microstructures had a slower probe diffusion rate. By using the diffusion data obtained by FRAP and the structural data from confocal microscopy, modelling through the lattice-Boltzmann framework was carried out to simulate the global diffusion and verify the validity of the experimental measurements. With this approach it was found that discrepancies between the two experimental techniques can be rationalized in terms of probe distribution between the different phases of the system. The combination of different techniques allowed the determination of diffusion in a phase-separated biopolymer gel and gave a clearer picture of this complex system. We also illustrate the difficulties that can arise if precautions are not taken to understand the system-probe interactions.

Microstructural, mechanical and mass transport properties of isotropic and capillary alginate gels.

Macroscopically homogeneous and inhomogeneous calcium alginate gels are formed via internal or external addition of various amounts of calcium to an alginate solution. The externally formed gels contain parallel aligned capillary structures. The mechanical and mass transport properties and the microstructure of the differently set gels were characterized by rheological measurements, fluorescence recovery after photobleaching (FRAP) and transmission electron microscopy (TEM). TEM images show a zone of distorted anisotropic gel structure in the vicinity of the capillaries as well as indications of a lower degree of void connectivity. The diffusion rates of dextran at large distances from the capillaries were fast and capillary gels showed a plastic behaviour in comparison to the internally set gels. The results presented show large functional differences between the internally and externally set gels, which cannot be explained by the presence of capillaries alone.

Interactions and diffusion in fine-stranded ß-lactoglobulin gels determined via FRAP and binding.

The effects of electrostatic interactions and obstruction by the microstructure on probe diffusion were determined in positively charged hydrogels. Probe diffusion in fine-stranded gels and solutions of ß-lactoglobulin at pH 3.5 was determined using fluorescence recovery after photobleaching (FRAP) and binding, which is widely used in biophysics. The microstructures of the ß-lactoglobulin gels were characterized using transmission electron microscopy. The effects of probe size and charge (negatively charged Na2-fluorescein (376Da) and weakly anionic 70kDa FITC-dextran), probe concentration (50 to 200 ppm), and ß-lactoglobulin concentration (9% to 12% w/w) on the diffusion properties and the electrostatic interaction between the negatively charged probes and the positively charged gels or solutions were evaluated. The results show that the diffusion of negatively charged Na2-fluorescein is strongly influenced by electrostatic interactions in the positively charged ß-lactoglobulin systems. A linear relationship between the pseudo-on binding rate constant and the ß-lactoglobulin concentration for three different probe concentrations was found. This validates an important assumption of existing biophysical FRAP and binding models, namely that the pseudo-on binding rate constant equals the product of the molecular binding rate constant and the concentration of the free binding sites. Indicators were established to clarify whether FRAP data should be analyzed using a binding-diffusion model or an obstruction-diffusion model.