Pairwise interaction Markov model for 3D epidermal nerve fibre endings

In this paper, the spatial arrangement and possible interactions between epidermal nerve fibre endings are investigated and modelled by using confocal microscopy data. We are especially interested in possible differences between patterns from healthy volunteers and patients suffering from mild diabetic neuropathy. The locations of the points, where nerves enter the epidermis, the first branching points and the points where the nerve fibres terminate, are regarded as realizations of spatial point processes. We propose an anisotropic point process model for the locations of the nerve fibre endings in three dimensions, where the points interact in cylindrical regions. First, the locations of end points in (Formula presented.) are modelled as clusters around the branching points and then, the model is extended to three dimensions using a pairwise interaction Markov field model with cylindrical neighbourhood for the z-coordinates conditioned on the planar locations of the points. We fit the model to samples taken from healthy subjects and subjects suffering from diabetic neuropathy. In both groups, after a hardcore radius, there is some attraction between the end points. However, the range and strength of attraction are not the same in the two groups. Performance of the model is evaluated by using a cylindrical version of Ripley\u27s K function due to the anisotropic nature of the data. Our findings suggest that the proposed model is able to capture the 3D spatial structure of the end\ua0points

Spatial modeling of epidermal nerve fiber patterns

Peripheral neuropathy is a condition associated with poor nerve functionality. Epidermal nerve fiber (ENF) counts per epidermal surface are dramatically reduced and the two-dimensional (2D) spatial structure of ENFs tends to become more clustered as neuropathy progresses. Therefore, studying the spatial structure of ENFs is essential to fully understand the mechanisms that guide those morphological changes. In this article, we compare ENF patterns of healthy controls and subjects suffering from mild diabetic neuropathy by using suction skin blister specimens obtained from the right foot. Previous analysis of these data has focused on the analysis and modeling of the spatial ENF patterns consisting of the points where the nerves enter the epidermis, base points, and the points where the nerve fibers terminate, end points, projected on a 2D plane, regarding the patterns as realizations of spatial point processes. Here, we include the first branching points, the points where the nerve trees branch for the first time, and model the three-dimensional (3D) patterns consisting of these three types of points. To analyze the patterns, spatial summary statistics are used and a new epidermal active territory that measures the volume in the epidermis that is covered by the individual nerve fibers is constructed. We developed a model for both the 2D and the 3D patterns including the branching points. Also, possible competitive behavior between individual nerves is examined. Our results indicate that changes in the ENFs spatial structure can more easily be detected in the later parts of the ENFs

What we look at in paintings: A comparison between experienced and inexperienced art viewers

How do people look at art? Are there any differences between how experienced and inexperienced art viewers look at a painting? We approach these questions by analyzing and modeling eye movement data from a cognitive art research experiment, where the eye movements of twenty test subjects, ten experienced and ten inexperienced art viewers, were recorded while they were looking at paintings. Eye movements consist of stops of the gaze as well as jumps between the stops. Hence, the observed gaze stop locations can be thought of as a spatial point pattern, which can be modeled by a spatio-temporal point process. We introduce some statistical tools to analyze the spatio-temporal eye movement data, and compare the eye movements of experienced and inexperienced art viewers. In addition, we develop a stochastic model, which is rather simple but fits quite well to the eye movement data, to further investigate the differences between the two groups through functional summary statistics

Detecting anisotropy in spatial point patterns - a comparison of statistical indices

Isotropy of a point process, defined as invariance of the distribution\ua0under rotation, is often assumed in spatial statistics. Formal\ua0tests for the hypothesis of isotropy can be created by comparing\ua0directional summary statistics in different directions. In this paper,\ua0the statistical powers of tests based on a variety of summary\ua0statistics and several choices of deviance measures are compared\ua0in a simulation study. Four models for anisotropic point processes\ua0are considered covering both regular and clustered cases.\ua0We discuss the robustness of the results to changes of the tuning\ua0parameters, and highlight the strengths and limitations of the\ua0methods

Statistical modeling of diabetic neuropathy: Exploring the dynamics of nerve mortality

Diabetic neuropathy is a disorder characterized by impaired nerve function and reduction of the number of epidermal nerve fibers per epidermal surface. Additionally, as neuropathy related nerve fiber loss and regrowth progresses over time, the two-dimensional spatial arrangement of the nerves becomes more clustered. These observations suggest that with development of neuropathy, the spatial pattern of diminished skin innervation is defined by a thinning process which remains incompletely characterized. We regard samples obtained from healthy controls and subjects suffering from diabetic neuropathy as realisations of planar point processes consisting of nerve entry points and nerve endings, and propose point process models based on spatial thinning to describe the change as neuropathy advances. Initially, the hypothesis that the nerve removal occurs completely at random is tested using independent random thinning of healthy patterns. Then, a dependent parametric thinning model that favors the removal of isolated nerve trees is proposed. Approximate Bayesian computation is used to infer the distribution of the model parameters, and the goodness-of-fit of the models is evaluated using both non-spatial and spatial summary statistics. Our findings suggest that the nerve mortality process changes as neuropathy advances

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

Tessellation-based stochastic modelling of 3D coating structures imaged with FIB-SEM tomography

To facilitate printing, coatings are typically applied to paperboard used for packaging to provide a good surface for application. To optimise the performance of the coating, it is important to understand the relationship between the microstructure of the material and its mass transport properties. In this work, three samples of paperboard coating are imaged using combined focused ion beam and scanning electron microscope (FIB-SEM) tomography data appropriately segmented to characterise the internal microstructure. These images are used to inform a parametric, tessellation-based stochastic three-dimensional model intended to mimic the irregular geometry of the particles that can be seen in the coating. Parameters for the model are estimated from the FIB-SEM image data, and we demonstrate good agreement between the real and virtual structures both in terms of geometrical measures and mass transport properties. The development of this model facilitates exploration of the relationship between the structure and its properties

Correlating 3D porous structure in polymer films with mass transport properties using FIB-SEM tomography

Porous polymer coatings are used to control drug release from pharmaceutical products. The coating covers a drug core and depending on the porous structure, different drug release rates are obtained. This work presents mass transport simulations performed on porous ethyl cellulose films with different porosities. The simulations were performed on high spatial resolution 3D data obtained using a focused ion beam scanning electron microscope. The effective diffusion coefficient of water was determined using a diffusion chamber. Lattice Boltzmann simulations were used to simulate water diffusion in the 3D data. The simulated coefficient was in good agreement with the measured coefficient. From the results it was concluded that the tortuosity and constrictivity of the porous network increase with decreasing amount of added hydroxypropyl cellulose, resulting in a sharp decrease in effective diffusion. This work shows that high spatial resolution 3D data is necessary, and that 2D data is insufficient, in order to predict diffusion through the porous structure with high accuracy

Stochastic modelling of 3D fiber structures imaged with X-ray microtomography

Many products incorporate into their design fibrous material with particular levels of permeability as a way to control the retention and flow of liquid. The production and experimental testing of these materials can be expensive and time consuming, particularly if it needs to be optimised to a desired level of absorbency. We consider a parametric virtual fiber model as a replacement for the real material to facilitate studying the relationship between structure and properties in a cheaper and more convenient manner. 3D image data sets of a sample fibrous material are obtained using X-ray microtomography and the individual fibers isolated. The segmented fibers are used to estimate the parameters of a 3D stochastic model for generating softcore virtual fiber structures. We use several spatial measures to show the consistency between the real and virtual structures, and demonstrate with lattice Boltzmann simulations that our virtual structure has good agreement with respect to the permeability of the physical material