Losing the sensation of touch: Mathematical modeling of diabetic neuropathy using spatial point processes
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Diabetes has led to an epidemic of complications associated with this disease. Diabetic neuropathy, which causes pain and loss of sensation due to degeneration of nerve fibers, is one of the most common complications of diabetes. Confocal microscopy made it possible to observe that the nerve endings in the outer skin of sick patients tend to be more clustered than in healthy subjects. Therefore, it is imperative to understand the process of degeneration and the spatial thinning of nerve fibers to detect diabetic neuropathy at an early stage. The two main hypotheses were tested are whether the nerve thinning occurs randomly and independently of other points and whether the nerve thinning is conditional on the other points. Three mathematical models were developed based on spatial thinning. The first is an independent random thinning model, the second is a deterministic thinning model and the third is a Gaussian thinning model. The second and third models are conditional on the location of the base point and the distance from it. When evaluating the spatial statistics, we used the centered L-function as a summary function when conducting a global envelope test with N = 500 simulations, where we tested the hypothesis under the empirical mild data. We also evaluated the different models based on non-spatial statistics which were compared to the mild data. The spatial results from the first model showed that nerve thinning does not occur randomly and independently (p = 0.01), thus rejected the null-hypothesis for significance level α = 0.05. The second model could not be rejected under the null-hypothesis (p = 0.624) as well as the third model (p = 0.056) for significance level α = 0.05. The non-spatial results showed that the first model sufficed if the desired outcome is to observe just non-spatial characteristics of the data whilst the second and third model lacked in this area. A likely explanation as to why the second and third models performed worse in the non-spatial regard, may be that spatial thinning isn’t a sufficient explanation behind the underlying mechanisms.