Transfer Entropy Characterization of TBI Cases

Abstract

Traumatic brain injury (TBI) is an important public health problem worldwide. This paper introduces transfer entropy as a measure to identify any standard between arterial blood pressure and electrocardiogram signal for patients diagnosed with TBI. Therefore, we will review the basic definitions of information theory and transfer entropy, which interpretation is influenced not only by the Kullback-Leibler divergence, but also by conditioned mutual information. For transfer entropy measurement we used Kraskov-Stögbauer-Grassberger (KSG) technique. It is observed that directionality in transfer entropy can provide clinical decision support for TBI cases.

Estimation of Transfer Entropy for Capturing Connectivity and Causality in Industrial Processes

“…The analytical study of causality and connectivity of the three-dimensional autoregressive system, combined with simulations that disregard any statistical knowledge of the processes, is essential to demonstrate, in these cases, the reliability of the estimators based on distances of neighbors, (8) and (9).…”

“…For computational reasons, the embedding dimension of random variables sequences in equations (4) and (5) were considered equal to 1. Furthermore, for equations (8) and 9, we considered k = 4. The choice is based on [16] which suggests that in practical applications, one should choose k > 1 to reduce statistical errors, avoid high values of k and typically use k = 2, 3, or 4.…”

“…To analyze the convergence of the estimators, 8000 samples of each process were simulated, among which the first 3000 were discarded to guarantee the stationarity of the autoregressive processes [5]. The causal relationships were identified by the estimator of equation (8). The Figure 2 shows the convergence of estimated values to analytical values, when the estimates are greater than zero, as a function of the increasing number of samples analyzed (after discarding the 3000 samples).…”

“…They have one important advantage: quantifies the directional causal influence between two processes. This analysis can support the diagnosis of abnormalities and disorders throughout the plant [1], [2], [3], [4], [5] and it has been recently used in different scientific fields, such as neuroscience [6], [7] and biomedical data [8], [9].…”

“…Although the concepts in information theory are relatively simple and mathematical formulations are objective, in practice, their estimation can be a complex process. For continuous variables, techniques that use nearest neighbors distances have been used for transfer entropy estimates [8], [10].…”