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'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.

Ämnesord

NATURVETENSKAP  -- Data- och informationsvetenskap -- Annan data- och informationsvetenskap (hsv//swe)

NATURAL SCIENCES  -- Computer and Information Sciences -- Other Computer and Information Science (hsv//eng)

TEKNIK OCH TEKNOLOGIER  -- Annan teknik -- Mediateknik (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Other Engineering and Technologies -- Media Engineering (hsv//eng)

NATURVETENSKAP  -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Probability Theory and Statistics (hsv//eng)

Nyckelord

point process

cylindrical K function

Markov random field

anisotropy

Markov chain Monte Carlo

pseudo-likelihood

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