Understanding Raynaud’s Phenomenon through a Hierarchical Model Based on Splines

Raynaud's Phenomenon (RP) is a vasospastic disorder of some specific arteries, typically induced by cold exposure and emotional stress, causing discoloration of the fingers, toes, ears, and niples. RP can be classified as primary (PRP), with no identifiable underlying pathological disorder, and secondary which is frequently associated with systemic sclerosis (SS). Patients who are classified as primary RP might evolve to secondary RP.

Thermal infrared (IR) imaging is a technique providing the map of the superficial temperature of a given body by measuring the infrared energy emitted, providing important indirect information on circulation, thermal properties and thermoregulatory functionality of the cutaneous tissue. PRP, SS and healthy controls (HC) groups show different thermal recoveries in consequence of the same standardized functional stimulation. In this study patients from HC, PRP and SS groups underwent a standard cold challenge, and temperatures of the 10 fingers of each patient, before and after the cold stress, were recorded. Temperatures of each finger of each person were measured every 30 seconds, 2.5 minutes before the cold stress and 20 minutes after it, resulting on $T=46$ temperature measurements for each individual. We aim to estimate the mean temperature as a function of time for each finger of each patient.
We also aim to obtain an overall mean function for each patient. This will provide us with tools to understand better the temperature behaviour
of each patient from each group. For this, we propose a hierarchical model based on B-splines. Inference procedure is performed under the Bayesian paradigm, therefore we are able to clearly describe the uncertainty of our estimates.