Interacting cluster point process model for epidermal nerve fibers

Garcia, Nancy L.; Guttorp, Peter; Ludwig, Guilherme

doi:10.1016/j.spasta.2020.100414

Cited by 3 publications

(9 citation statements)

References 17 publications

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“…Instead of modelling the planar coordinates first, we could find a 3D model with interaction within and between base points, branching points and end points. For instance, the interaction cluster point process model introduced in Garcia et al 8 . for the planar point patterns could be a good starting point.…”

Section: Discussionmentioning

confidence: 99%

“…Instead of modelling the planar coordinates first, we could find a 3D model with interaction within and between base points, branching points and end points. For instance, the interaction cluster process model introduced in Garcia et al 8 for the planar point patterns could be a good starting point. Furthermore, the 2D model for the branching points could be improved by taking into account not only the closest base point but all base point.…”

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…In the NOC model, end point clusters favour directions towards open space, that is, away from the closest other base point, while in the UCC model no specific direction was preferred. For data from thighs from four healthy subjects, Garcia et al 8 introduced a continuous time birth and death process, where there is interaction between the base points and within the points in each end point cluster. Furthermore, Ghorbanbour et al 3 modelled interaction between the entire nerve trees, each consisting of an ENF base point and the end points connected to it, by a sequential marked point process model.…”

Section: Introductionmentioning

confidence: 99%

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Pairwise interaction Markov model for 3D epidermal nerve fibre endings

Konstantinou

Särkkä

2022

Journal of Microscopy

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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 ℝ 2 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's 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 points.

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Section: Discussionmentioning

confidence: 99%

“…Instead of modelling the planar coordinates first, we could find a 3D model with interaction within and between base points, branching points and end points. For instance, the interaction cluster process model introduced in Garcia et al 8 for the planar point patterns could be a good starting point. Furthermore, the 2D model for the branching points could be improved by taking into account not only the closest base point but all base point.…”

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Pairwise interaction Markov model for 3D epidermal nerve fibre endings

Konstantinou

Särkkä

2022

Journal of Microscopy

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“…suggested a Poisson cluster model, more specifically a Thomas process, for the base point patterns. Garcia et al 7 . introduced an interacting cluster point process, where the base points are modelled first and then, end points given the base points, allowing interaction within the base points and within the end points.…”

Section: Introductionmentioning

confidence: 99%

Marked point process analysis of epidermal nerve fibres

Ghorbanpour

Särkkä

Pourtaheri

2021

Journal of Microscopy

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Epidermal nerve fibre (ENF) density and summed length of ENFs per epidermal surface area are reduced, and ENFs may appear more clustered within the epidermis in subjects suffering from diabetic neuropathy compared to healthy subjects. Therefore, it is important to understand the spatial behaviour of ENFs in healthy and neuropathy subjects. By using confocal microscopy data , we study the spatial structure of epidermal nerves by regarding the nerve tree locations as realizations of marked point processes . The termination points of the fibres of a nerve tree are used to define a reactive territory which is taken as a mark for the nerve tree location. We study the differences in the spatial pattern of ENFs between healthy subjects and subjects suffering from mild diabetic neuropathy by using Ripley's K function and the mark correlation function. In addition, we propose a marked sequential point process model for the nerve tree locations. Data are replicated point patterns, where we have several patterns from each subject and from each group.

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

Konstantinou

Ghorbanpour

Picchini

et al. 2023

Statistics in Medicine

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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.

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Interacting cluster point process model for epidermal nerve fibers

Cited by 3 publications

References 17 publications

Pairwise interaction Markov model for 3D epidermal nerve fibre endings

Pairwise interaction Markov model for 3D epidermal nerve fibre endings

Marked point process analysis of epidermal nerve fibres

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

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