Generalisation of continuous time random walk to anomalous diffusion MRI models with an age-related evaluation of human corpus callosum.

Diffusion MRI measures of the human brain provide key insight into microstructural variations across individuals and into the impact of central nervous system diseases and disorders. One approach to extract information from diffusion signals has been to use biologically relevant analytical models to link millimetre scale diffusion MRI measures with microscale influences. The other approach has been to represent diffusion as an anomalous transport process and infer microstructural information from the different anomalous diffusion equation parameters. In this study, we investigated how parameters of various anomalous diffusion models vary with age in the human brain white matter, particularly focusing on the corpus callosum. We first unified several established anomalous diffusion models (the super-diffusion, sub-diffusion, quasi-diffusion and fractional Bloch-Torrey models) under the continuous time random walk modelling framework. This unification allows a consistent parameter fitting strategy to be applied from which meaningful model parameter comparisons can be made. We then provided a novel way to derive the diffusional kurtosis imaging (DKI) model, which is shown to be a degree two approximation of the sub-diffusion model. This link between the DKI and sub-diffusion models led to a new robust technique for generating maps of kurtosis and diffusivity using the sub-diffusion parameters ßSUB and DSUB. Superior tissue contrast is achieved in kurtosis maps based on the sub-diffusion model. 7T diffusion weighted MRI data for 65 healthy participants in the age range 19-78 years was used in this study. Results revealed that anomalous diffusion model parameters α and ß have shown consistent positive correlation with age in the corpus callosum, indicating α and ß are sensitive to tissue microstructural changes in ageing.

Reducing Myosin II and ATP-Dependent Mechanical Activity Increases Order and Stability of Intracellular Organelles.

Organization of intracellular content is affected by multiple simultaneous processes, including diffusion in a viscoelastic and structured environment, intracellular mechanical work and vibrations. The combined effects of these processes on intracellular organization are complex and remain poorly understood. Here, we studied the organization and dynamics of a free Ca++ probe as a small and mobile tracer in live T cells. Ca++, highlighted by Fluo-4, is localized in intracellular organelles. Inhibiting intracellular mechanical work by myosin II through blebbistatin treatment increased cellular dis-homogeneity of Ca++-rich features in length scale < 1.1 µm. We detected a similar effect in cells imaged by label-free bright-field (BF) microscopy, in mitochondria-highlighted cells and in ATP-depleted cells. Blebbistatin treatment also reduced the dynamics of the Ca++-rich features and generated prominent negative temporal correlations in their signals. Following Guggenberger et al. and numerical simulations, we suggest that diffusion in the viscoelastic and confined medium of intracellular organelles may promote spatial dis-homogeneity and stability of their content. This may be revealed only after inhibiting intracellular mechanical work and related cell vibrations. Our described mechanisms may allow the cell to control its organization via balancing its viscoelasticity and mechanical activity, with implications to cell physiology in health and disease.

Multi-term time fractional diffusion equations and novel parameter estimation techniques for chloride ions sub-diffusion in reinforced concrete.

In this paper, searching for a better chloride ions sub-diffusion system, a multi-term time-fractional derivative diffusion model is proposed for the description of the time-dependent chloride ions penetration in reinforced concrete structures exposed to chloride environments. We prove the stability and convergence of the model. We use the modified grid approximation method (MGAM) to estimate the fractional orders and chloride ions diffusion coefficients in the reinforced concrete for the multi-term time fractional diffusion system. And then to verify the efficiency and accuracy of the proposed methods in dealing with the fractional inverse problem, two numerical examples with real data are investigated. Meanwhile, we use two methods of fixed chloride ions diffusion coefficient and variable diffusion coefficient with diffusion depth to simulate chloride ions sub-diffusion system. The result shows that with the new fractional orders and parameters, our multi-term fractional order chloride ions sub-diffusion system is capable of providing numerical results that agree better with the real data than other models. On the other hand, it is also noticed from the numerical solution of the chloride ions sub-diffusion system that setting the variable diffusion coefficient with diffusion depth is more reasonable. And it is also found that chloride ions diffusion coefficients in reinforced concrete should be decreased with diffusion depth which is completely consistent with the theory. In addition, the model can be used to predict the chloride profiles with a time-dependent property. This article is part of the theme issue 'Advanced materials modelling via fractional calculus: challenges and perspectives'.

Circle scanning STED fluorescence correlation spectroscopy to quantify membrane dynamics and compartmentalization.

Quantifying molecular dynamics of cell membrane constituents is required to understand organization and function of biological membranes. Because of its complex structure unambiguous interpretation of molecular membrane dynamics requires high spatial and temporal resolution measurements. In this paper, we provide a comprehensive description of circle scanning fluorescence correlation spectroscopy and its combination with stimulated emission depletion microscopy (CS-STED-FCS). This method allows quantification of sub-diffusion processes and direct mapping of heterogeneities in membranes with high spatiotemporal resolution. We show how to use model membranes to calibrate and test the technique and how to apply it in the context of living cells to quantify membrane dynamics with high spatiotemporal resolution and good statistics.

Fluorescence Correlation Spectroscopy with Photobleaching Correction in Slowly Diffusing Systems.

Fluorescence correlation spectroscopy (FCS) is a powerful tool to quantitatively study the diffusion of fluorescently labeled molecules. It allows in principle important questions of macromolecular transport and supramolecular aggregation in living cells to be addressed. However, the crowded environment inside the cells slows diffusion and limits the reservoir of labeled molecules, causing artifacts that arise especially from photobleaching and limit the utility of FCS in these applications. We present a method to compute the time correlation function from weighted photon arrival times, which compensates computationally during the data analysis for the effect of photobleaching. We demonstrate the performance of this method using numerical simulations and experimental data from model solutions. Using this technique, we obtain correlation functions in which the effect of photobleaching has been removed and in turn recover quantitatively accurate mean-square displacements of the fluorophores, especially when deviations from an ideal Gaussian excitation volume are accounted for by using a reference calibration correlation function. This allows quantitative FCS studies of transport processes in challenging environments with substantial photobleaching like in living cells in the future.

The bimolecular reactive transport in heterogeneous porous media: Sub-diffusion in interpretation of laboratory experiment.

This present work consists of investigating the effects of particle size heterogeneity and flow rates on transport-reaction kinetics of CuSO4 and Na2EDTA2- in porous media, via the combination of a bimolecular reaction experiment and model simulations. In the early stages of transport, a peak is observed in the concentration breakthrough curve of the reactant CuSO4, related to the delayed mixing and reaction of the reactants. The numerical results show that an increase in flow rate promotes the mixing processes between the reactants, resulting in a larger peak concentration and a slighter tail of breakthrough curves, while an increase in medium heterogeneity leads to a more significant heavy tail. The apparent anomalous diffusion and heavy-tailing behavior can be effectively quantified by a novel truncated fractional derivative bimolecular reaction model. The truncated fractional-order model, taking into account the incomplete mixing, offers a satisfactory reproduction of the experimental data.

Robust, fast and accurate mapping of diffusional mean kurtosis.

Diffusional kurtosis imaging (DKI) is a methodology for measuring the extent of non-Gaussian diffusion in biological tissue, which has shown great promise in clinical diagnosis, treatment planning, and monitoring of many neurological diseases and disorders. However, robust, fast, and accurate estimation of kurtosis from clinically feasible data acquisitions remains a challenge. In this study, we first outline a new accurate approach of estimating mean kurtosis via the sub-diffusion mathematical framework. Crucially, this extension of the conventional DKI overcomes the limitation on the maximum b-value of the latter. Kurtosis and diffusivity can now be simply computed as functions of the sub-diffusion model parameters. Second, we propose a new fast and robust fitting procedure to estimate the sub-diffusion model parameters using two diffusion times without increasing acquisition time as for the conventional DKI. Third, our sub-diffusion-based kurtosis mapping method is evaluated using both simulations and the Connectome 1.0 human brain data. Exquisite tissue contrast is achieved even when the diffusion encoded data is collected in only minutes. In summary, our findings suggest robust, fast, and accurate estimation of mean kurtosis can be realised within a clinically feasible diffusion-weighted magnetic resonance imaging data acquisition time.

Transient Anomalous Diffusion MRI Measurement Discriminates Porous Polymeric Matrices Characterized by Different Sub-Microstructures and Fractal Dimension.

Considering the current development of new nanostructured and complex materials and gels, it is critical to develop a sub-micro-scale sensitivity tool to quantify experimentally new parameters describing sub-microstructured porous systems. Diffusion NMR, based on the measurement of endogenous water's diffusion displacement, offers unique information on the structural features of materials and tissues. In this paper, we applied anomalous diffusion NMR protocols to quantify the subdiffusion of water and to measure, in an alternative, non-destructive and non-invasive modality, the fractal dimension dw of systems characterized by micro and sub-micro geometrical structures. To this end, three highly heterogeneous porous-polymeric matrices were studied. All the three matrices composed of glycidylmethacrylate-divynilbenzene porous monoliths obtained through the High Internal Phase Emulsion technique were characterized by pores of approximately spherical symmetry, with diameters in the range of 2-10 µm. Pores were interconnected by a plurality of window holes present on pore walls, which were characterized by size coverings in the range of 0.5-2 µm. The walls were characterized by a different degree of surface roughness. Moreover, complementary techniques, namely Field Emission Scanning Electron Microscopy (FE-SEM) and dielectric spectroscopy, were used to corroborate the NMR results. The experimental results showed that the anomalous diffusion α parameter that quantifies subdiffusion and dw = 2/α changed in parallel to the specific surface area S (or the surface roughness) of the porous matrices, showing a submicroscopic sensitivity. The results reported here suggest that the anomalous diffusion NMR method tested may be a valid experimental tool to corroborate theoretical and simulation results developed and performed for describing highly heterogeneous and complex systems. On the other hand, non-invasive and non-destructive anomalous subdiffusion NMR may be a useful tool to study the characteristic features of new highly heterogeneous nanostructured and complex functional materials and gels useful in cultural heritage applications, as well as scaffolds useful in tissue engineering.

Sliding Dynamics of Ring Chains on Two Asymmetric/Symmetric Chains in a Simple Slide-Ring Gel.

The sliding dynamics along two asymmetric/symmetric axial chains of ring chains linked by a linear chainis investigated using molecular dynamics (MD) simulations. A novel sub-diffusion behavior is observed for ring chains sliding along eithera fixed rod-like chain or fluctuating axial chain on asymmetric/symmetric axial chainsat the intermediate time range due to their strongly interplay between two ring chains. However, two ring chains slide in the normal diffusion at along time range because their sliding dynamics can be regarded as an overall motion of two ring chains. For ring chains sliding on two symmetric/asymmetricaxial chains, the diffusion coefficient D of ring chains relies on the bending energy of axial chains (Kb) as well as the distance of two axial chains (d). There exists a maximum diffusion coefficient Dmax at d = d* in which ring chains slide at the fastest velocity due to the maximum conformational entropy for the linking chain between two ring chainsat d = d*. Ring chain slide on fixed rod-like axial chainsfaster in the symmetric axial chain case than that in the asymmetric axial chain case. However, ring chains slide on fluctuatingaxial chainsslower in the symmetric axial chain case than that in the asymmetric axial chain case. This investigation can provide insights into the effects of the linked chain conformation on the sliding dynamics of ring chains in a slide-ring gel.

Molecular simulations of cellular processes.

It is, nowadays, possible to simulate biological processes in conditions that mimic the different cellular compartments. Several groups have performed these calculations using molecular models that vary in performance and accuracy. In many cases, the atomistic degrees of freedom have been eliminated, sacrificing both structural complexity and chemical specificity to be able to explore slow processes. In this review, we will discuss the insights gained from computer simulations on macromolecule diffusion, nuclear body formation, and processes involving the genetic material inside cell-mimicking spaces. We will also discuss the challenges to generate new models suitable for the simulations of biological processes on a cell scale and for cell-cycle-long times, including non-equilibrium events such as the co-translational folding, misfolding, and aggregation of proteins. A prominent role will be played by the wise choice of the structural simplifications and, simultaneously, of a relatively complex energetic description. These challenging tasks will rely on the integration of experimental and computational methods, achieved through the application of efficient algorithms. Graphical abstract.

Peclet number as affected by molecular diffusion controls transient anomalous transport in alluvial aquifer-aquitard complexes.

This study evaluates the role of the Peclet number as affected by molecular diffusion in transient anomalous transport, which is one of the major knowledge gaps in anomalous transport, by combining Monte Carlo simulations and stochastic model analysis. Two alluvial settings containing either short- or long-connected hydrofacies are generated and used as media for flow and transport modeling. Numerical experiments show that 1) the Peclet number affects both the duration of the power-law segment of tracer breakthrough curves (BTCs) and the transition rate from anomalous to Fickian transport by determining the solute residence time for a given low-permeability layer, 2) mechanical dispersion has a limited contribution to the anomalous characteristics of late-time transport as compared to molecular diffusion due to an almost negligible velocity in floodplain deposits, and 3) the initial source dimensions only enhance the power-law tail of the BTCs at short travel distances. A tempered stable stochastic (TSS) model is then applied to analyze the modeled transport. Applications show that the time-nonlocal parameters in the TSS model relate to the Peclet number, Pe. In particular, the truncation parameter in the TSS model increases nonlinearly with a decrease in Pe due to the decrease of the mean residence time, and the capacity coefficient increases with an increase in molecular diffusion which is probably due to the increase in the number of immobile particles. The above numerical experiments and stochastic analysis therefore reveal that the Peclet number as affected by molecular diffusion controls transient anomalous transport in alluvial aquifer-aquitard complexes.