Multi-scale symbolic entropy analysis provides prognostic prediction in patients receiving extracorporeal life support

Abstract

Introduction: Extracorporeal life support (ECLS) can temporarily support cardiopulmonary function, and is occasionally used in resuscitation. Multi-scale entropy (MSE) derived from heart rate variability (HRV) is a powerful tool in outcome prediction of patients with cardiovascular diseases. Multi-scale symbolic entropy analysis (MSsE), a new method derived from MSE, mitigates the effect of arrhythmia on analysis. The objective is to evaluate the prognostic value of MSsE in patients receiving ECLS. The primary outcome is death or urgent transplantation during the index admission.

Methods: Fifty-seven patients receiving ECLS less than 24 hours and 23 control subjects were enrolled. Digital 24-hour Holter electrocardiograms were recorded and three MSsE parameters (slope 5, Area 6-20, Area 6-40) associated with the multiscale correlation and complexity of heart beat fluctuation were calculated.

Results: Patients receiving ECLS had significantly lower value of slope 5, area 6 to 20, and area 6 to 40 than control subjects. During the follow-up period, 29 patients met primary outcome. Age, slope 5, Area 6 to 20, Area 6 to 40, acute physiology and chronic health evaluation II score, multiple organ dysfunction score (MODS), logistic organ dysfunction score (LODS), and myocardial infarction history were significantly associated with primary outcome. Slope 5 showed the greatest discriminatory power. In a net reclassification improvement model, slope 5 significantly improved the predictive power of LODS; Area 6 to 20 and Area 6 to 40 significantly improved the predictive power in MODS. In an integrated discrimination improvement model, slope 5 added significantly to the prediction power of each clinical parameter. Area 6 to 20 and Area 6 to 40 significantly improved the predictive power in sequential organ failure assessment.

Conclusions: MSsE provides additional prognostic information in patients receiving ECLS.

Figure 1

The first operation of MSsE is coarse graining. We divide the time series {x₁, x₂ … x_M} into non-overlapping boxes of size N (scale "N"). The median of each local box is taken, thus producing a new time series . The second stage in forming the sign time series is to transform the coarse-grained series into yet another new series by taking the directions in its change. We measure the change against a threshold value and acquire the sign series , where is either +1 or -1, depending on whether the corresponding is increasing or decreasing. To quantify the complexity of the sign sequence, we sort all sequences into categories of sub-sets consist of L consecutive binary bits (L-bit; L = 8 in this study). The probability distribution of all patterns of sub-sets is recorded. To avoid over-counting similar patterns, the data sequence of total length L should be divided into multiple m-dimensional vectors; each consists of m consecutive bits {(b₁, b₂, … b_m); (b₂, b₃, … b_{m +1}); …}. The conditional probability is determined numerically by the ratio of number of each paired vectors which are of exactly same binary codes for dimension "m+1" to the number for the identical vectors of dimension "m". By identifying the patterns of the same conditional probability, it allows us to rank the m-bit patterns according to the information they imply (large rank number means lower conditional probability). The expectation value of the rank conceptually indicates the degree of uncertainty.

Figure 2

Quantification of multiscale symbolic entropy (MSsE): summation of the entropy over different scales can quantify the complexity over certain timescales. However, typical profile of MSsE in extracorporeal life support patients showed a crossover phenomenon around scale 5. Three parameters of the MSsE were assessed: (1) the linear-fitted slope between scales 1 to 5; (2) complexity between intermediate scales (Area 6-20); and (3) the overall complexity (Area 6-40).

Figure 3

Multiscale symbolic entropy (MSsE) analysis of heart rate dynamics from control subjects, patients surviving after extracorporeal life support (ECLS), and non-surviving ECLS patients. The values are represented as mean ± standard error. The MSsE profile of ECLS patients who survived differed from that of non-survivors.

Figure 4

Receiver-operator characteristic curves for models with (solid line) and without slope 5 (broken line). The area under the curve (AUC) for sequential organ failure assessment SOFA was 0.637. After adding slope 5, the AUC of the new model improved to 0.749.