Modellering av nervmönster med spatiala punktprocesser
Examensarbete för kandidatexamen
People with diabetes can sometimes develop diabetic neuropathy, a nerve disease which can infuse numbness and pain. It has been observed that the end points of nerve fibers in the epidermis, which is the outermost living layer of the skin, appear more clustered on patients with diabetic neuropathy . Attempts to model the fiber patterns have been made in the hope that at an early stage distinguish patients with risk of developing diabetic neuropathy. These nerve fibers can be described by spatial point processes.The unknown parameters of such a process can be estimated using the minimum contrast method (MCM) where the main goal of this project is to investigate how the choice of upper integration limit in MCM affects the parameter estimates. The Thomas process was chosen for this project where in addition to the examination of the integration limit in MCM we also examine if this process is a suitable choice to describe nerve fibers from patients associated with two groups. The first acts as a control group whith healthy subjects without symptoms of diabetic neuropathy. The second group consist of subjects with diabetes and mild symtombs of the disease. This is done by means of simulation and the R-package spatstat . It turns out that the choice of integration limit is important and that there are some guidelines of how to make this choice to avoid the variance of the parameter estimations getting to large. Likewise, complications in selecting too large of a integration limit are present although their importance are not as prominent. Lastly we show that we can not reject that the Thomas process describes nerve fibers from the two groups.
Grundläggande vetenskaper , Matematik , Basic Sciences , Mathematics