MVEX01-22-04 Point processes and nerve fibers

​Data in the form of a set of points, irregularly distributed within a region in space, can arise in many different contexts, for example locations of trees in a forest, locations of bird nests, locations of cells, or locations of stars. Such a data set is called a spatial point pattern. A point pattern in this project is a collection of locations of nerve base points in the outmost part of your skin. The project is related to a larger project where we study how the nerve pattern is affected by some small fiber neuropathy, e.g. diabetic neuropathy.

Spatial point processes describing how points are located with respect to each other are used as models for point patterns. Often, point patterns are divided into three groups, completely spatially random (no obvious structure), clustered, and regular, and point process models have been introduced for each group. Point pattern data consisting of the nerve base point locations obtained from healthy volunteers and mild diabetic subjects are available. It is well established that the nerve fiber counts decrease with the progression of the neuropathy. Current clinical practices for the diagnosis of the disease are based on this observation.

The aim of this project is to model the biological process that guides the morphological changes that occur in the nerve fibers. For this purpose, point process models based on spatial thinning will be developed. An independent random thinning model will initially be tested. If time allows, more sophisticated thinning schemes might be suggested. The models will be tested using nerve base point data from healthy controls and subjects suffering from mild diabetic neuropathy and the goodness of fit will be evaluated using some summary statistics from spatial point process theory as well as some non-spatial summary statistics. A simulation study might also be included in the project.

After having completed the project you
•    have learned some basic theory of point processes
•    have learned how to apply the theory to point pattern data
•    have used the R package spatstat

The report will be written in English.

 

Projektkod: MVEX01-22-04
Gruppstorlek: 3-4 studenter
Målgrupp:
GU- och Chalmersstudenter. För GU-studenter räknas projektet som ett projekt i Matematisk statistik (MSG900/MSG910).
Projektspecifika förkunskapskrav:
An introductory course in mathematical statistics, good programming skills.
Se respektive kursplan för allmänna förkunskapskrav. Utöver de allmänna förkunskapskraven i MVEX01 ska Chalmersstudenter ha avklarat kurser i en- och flervariabelanalys, linjär algebra och matematisk statistik.
Handledare: Konstantinos Konstantinou, konkons@chalmers.se
Examinator: Maria Roginskaya, Ulla Dinger
Institution: Matematiska vetenskaper

 

Sidansvarig Publicerad: må 11 okt 2021.