Polysomnography (PSG) is the recording during sleep of multiple physiological parameters enabling to diagnose sleep disorders and to characterize sleep fragmentation. From PSG several sleep characteristics such as the micro arousal rate (MAR), the number of sleep stages shifts (SSS) and the rate of intra sleep awakenings (ISA) can be deduced each having its own fragmentation threshold value and each being more or less important (weight) in the clinician's diagnosis according to his specialization (pulmonologist, neurophysiologist and technical expert). In this work we propose a mathematical model of sleep fragmentation diagnosis based on these three main sleep characteristics (MAR, SSS, ISA) each having its own threshold and weight values for each clinician. Then, a database of 111 PSG consisting of 55 healthy adults and 56 adult patients with a suspicion of obstructive sleep apnoea syndrome (OSAS), has been diagnosed by nine clinicians divided into three groups (three pulmonologists, three neurophysiologists and three technical experts) representing a panel of polysomnography experts usually working in a hospital. This has enabled to determine statistically the thresholds and weights values which characterize each clinician's diagnosis. Thus, we show that the agreement between each clinician's diagnosis and each corresponding mathematical model goes from substantial (κ >61%) to almost perfect (κ >81%), according to their specialization and so, that the mean value of the agreements of each group is also substantial (κ >73%) despite the existing variability between clinicians. It follows from this result that our mathematical model of sleep fragmentation diagnosis is a posteriori validated for each clinician. 
Mathematical modelling of sleep fragmentation diagnosis