Study of phase estimation methods to analyse cardiorespiratory synchronization in OSA patients

Obstructive Sleep Apnea (OSA) is a sleep disorder highly prevalent in the general population. Cardiorespiratory Phase Synchronization (CRPS) is a form of non-linear interaction between respiratory and cardiovascular systems that was found to be reduced in severe OSA patients. The Hilbert Transform (HT) method was the recommended choice for estimating the respiratory phase in CRPS studies. But we have noticed that HT provides a phase that is aligned to the transition between the exhalation and the inhalation parts of different breathing cycles, instead of being aligned to the breathing onsets. In this work we proposed a Realigned HT phase estimation method (RHT) and we compared it to the conventional HT and to the Linear Phase (LP) approximation for estimating CRPS in a database of 28 patients with different OSA severity levels. RHT provided similar synchronization percentages (%Sync) as HT, and it enhanced the significant differences in %Sync between mild and severe OSA patients. %Sync showed the highest negative correlation with the Apnea-Hypopnea Index (AHI) when using RHT (r_AHI=-0.692, p<;0.001), which only had an 10% extra computational cost. On the other hand, LP method significantly overestimated %Sync especially in the more severe patients, because it was unable to track the phase non-linearities that can be observed during sleep disordered breathing. Therefore, the newly proposed RHT can be the preferred alternative over the conventional HT or the LP approximation for estimating CRPS in OSA patients.