A Bayesian hierarchical point process model for epidermal nerve fiber patterns.

We introduce the Thomas process in a Bayesian hierarchical setting as a model for point pattern data with a nested structure. This model is applied to a nerve fiber data set which consists of several point patterns of nerve entry points from 47 subjects divided into 3 groups, where the grouping is based on the diagnosed severity of a certain nerve disorder. The modeling assumption is that each point pattern is a realization of a Thomas process, with parameter values specific to the subject. These parameter values are in turn assumed to come from distributions that depend on which group the subject belongs to. To fit the model, we construct an MCMC algorithm, which is evaluated in a simulation study. The results of the simulation study indicate that the group level mean of each parameter is well estimated, but that the estimation of the between subject variance is more challenging. When fitting the model to the nerve fiber data, we find that the structure within clusters appears to be the same in all groups, but that the number of clusters decreases with the progression of the nerve disorder.

Single particle raster image analysis of diffusion for particle mixtures.

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.

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.

From static micrographs to particle aggregation dynamics in three dimensions.

Studies on colloidal aggregation have brought forth theories on stability of colloidal gels and models for aggregation dynamics. Still, a complete link between developed frameworks and obtained laboratory observations has to be found. In this work, aggregates of silica nanoparticles (20 nm) are studied using diffusion limited cluster aggregation (DLCA) and reaction limited cluster aggregation (RLCA) models. These processes are driven by the probability of particles to aggregate upon collision. This probability of aggregation is one in the DLCA and close to zero in the RLCA process. We show how to study the probability of aggregation from static micrographs on the example of a silica nanoparticle gel at 9 wt%. The analysis includes common summary functions from spatial statistics, namely the empty space function and Ripley's K-function, as well as two newly developed summary functions for cluster analysis based on graph theory. One of the new cluster analysis functions is related to the clustering coefficient in communication networks and the other to the size of a cluster. All four topological summary statistics are used to quantitatively compare in plots and in a least-square approach experimental data to cluster aggregation simulations with decreasing probabilities of aggregation. We study scanning transmission electron micrographs and utilize the intensity-mass thickness relation present in such images to create comparable micrographs from three-dimensional simulations. Finally, a characterization of colloidal silica aggregates and simulated structures is obtained, which allows for an evaluation of the cluster aggregation process for different aggregation scenarios. As a result, we find that the RLCA process fits the experimental data better than the DLCA process.

Self-calibrated concentration measurements of polydisperse nanoparticles.

Quantitative characterization of nanoparticles, e.g. accurate estimation of concentration distributions, is critical to many pharmaceutical and biological applications. We present a method that enables for the first time highly accurate size and absolute concentration measurements of polydisperse nanoparticles in solution, based on fluorescence single particle tracking, that are self-calibrated in the sense that the detection region volume is estimated based on the tracking data. The method is evaluated using simulations and experimental data of polystyrene nanospheres in water/sucrose solution. In addition, the method is used to quantify aggregation and clearance of different types of liposomes after intravenous injection in rats, where additional and more accurate information can be obtained that was previously unavailable, which can help elucidate their usefulness as drug carriers.

Analysis of spatial structure of epidermal nerve entry point patterns based on replicated data.

Epidermal nerve fiber (ENF) density and morphology are used to diagnose small fiber involvement in diabetic, HIV, chemotherapy induced, and other neuropathies. ENF density and summed length of ENFs per epidermal surface area are reduced, and ENFs may appear clustered within the epidermis in subjects with small fiber neuropathy compared to healthy subjects. Therefore, it is important to understand the spatial behaviour of ENFs in healthy and diseased subjects. This work investigates the spatial structure of ENF entry points, which are locations where the nerves enter the epidermis (the outmost living layer of the skin). The study is based on suction skin blister specimens from two body locations of 25 healthy subjects. The ENF entry points are regarded as a realization of a spatial point process and a second-order characteristic, namely Ripley's K function, is used to investigate the effect of covariates (e.g. gender) on the degree of clustering of ENF entry points. First, the effects of covariates are evaluated by means of pooled K functions for groups and, secondly, the statistical significance of the effects and individual variation are characterized by a mixed model approach. Based on our results the spatial pattern of ENFs in samples taken from calf is affected by the covariates but not in samples taken from foot.

An additive edge correction for the influence potential of trees.

The influence potential on a quadrat (IPQ) is an index for measuring the ecological effect that trees have on understory vegetation observed in a quadrat of a plot. IPQ is defined as the sum of the effect of every trees in the plot, where the effect depends on the size of the tree and the distance between the tree and the quadrat. Since only the trees in the plot have been observed and not the trees outside the plot, the true IPQ may be underestimated. Existing edge corrections are not appropriate for this case. We propose a correction that consists of adding the expected IPQ due to effects of trees outside the plot to the observed IPQ. The expectation is obtained by applying the Campbell theorem for stationary marked point processes. Data from the 1985-86 National Forest Inventory of Finland was used to calculate IPQ for six quadrats systematically allocated to each of 1240 plots. The implementation of the correction for this data is described. The distributions of IPQ with and without the correction proved the existence of edge effects and the effectiveness of the correction to eliminate the bias. This method has the potential to be applied to other additive functions.