Synchronization of respiratory, heartbeat and blood pressure signals: 3D plots and indices

In this paper we study the correlation of respiration, heartbeat and blood pressure signals in 3D space using phase coupling. To the best of our knowledge, it is the first time that the correlation of these signals is investigated in 3D space. We produce 2D and 3D phase plots and examine phase coupling in all cases. We calculate the mutual information which is a widely used metric for estimating such correlations between two signals and the slopes of the 2D phase plots. For examining signals in 3D space we compute the multivariate mutual information. The multivariate mutual information is not a simple generalization of mutual information and reveals different information detecting the correlation among all three examined signals. Additionally to the common metrics for signal synchronization, we examined the use of the gradient, in order to extract and quantify the relations as depicted in the 3D plots. Results showed us a stronger correlation between blood pressure and heartbeat signals and a relatively small correlation between respiratory and heartbeat signals, as well as between respiratory and blood pressure signals. Also, a very interesting observation is the strong correlation among all three signals which is very clear from the 3D phase plots and is also verified from both multivariate mutual information and the gradient.