Approximate entropy as indication of goodness-of-fit

Interrelationship between blood and tissue lactate in a general intensive care unit: a subcutaneous adipose tissue microdialysis study on 162 critically ill patients

PURPOSE

The aim of the study was to study the interrelationship between blood and tissue lactate in critically ill patients with or without shock admitted in a general intensive care unit.

MATERIALS AND METHODS

We studied 162 mechanically ventilated patients: 106 with shock (septic shock, 97; cardiogenic shock, 9) and 56 without shock (severe sepsis, 38; systemic inflammatory response syndrome, 18). A microdialysis catheter was inserted in the subcutaneous adipose tissue of the upper thigh, and interstitial fluid was collected every 4 hours for a maximum of 6 days. We assessed the relationship between tissue and blood lactate using cross-approximate entropy and cross-correlation analysis.

RESULTS

Patients with shock had higher area under the curve for blood (261 vs 175 mmol/L*hours, P < .0001) and tissue lactate (386 vs 281 mmol/L*hours, P < .0001) compared with patients without shock. The interrelationship of tissue-blood lactate, as assessed with cross-approximate entropy, was more regular in patients with shock compared with patients without shock. Cross-correlation of tissue vs blood lactate yielded higher correlation coefficients in patients with shock compared with those without shock, being higher when tissue lactate preceded blood lactate by 4 hours compared with tissue vs blood lactate with no lag time.

CONCLUSIONS

In critical illness, the detailed dynamics between blood and tissue lactate are affected by the presence of shock. In patients with shock, microdialysis-assessed tissue lactate is higher compared with those without shock and may detect metabolic disturbances before these become evident in the systemic circulation.

The use of regularity as estimated by approximate entropy to distinguish saltatory growth

A nonlinear dynamics metric, approximate entropy (ApEn), is investigated as a diagnostic method for distinguishing between mathematical models, and the underlying mechanistic hypotheses that purport to describe the same time series experimental observations. ApEn measures the occurrence of pattern regularity within a time series, and is used here to investigate growth patterns in daily length growth. The notion investigated is that ApEn distributions for competing time series patterns expressed as mathematical formulations can be modelled by Monte Carlo and bootstrap methods and compared to the ApEn values for an original experimental data series. If the ApEn values for the different models do not overlap, then it is expected that ApEn can be utilized to distinguish these models and hypotheses, and to provide statistical assessment for the underlying biological patterns in experimental data. The conclusion is that the ApEn metric is successful as a time series diagnostic tool. It is a model-independent statistic that clearly differentiates saltatory growth from slowly varying continuous models of growth and serves to further document the saltatory nature of growth. This is a unique application of approximate entropy, illustrating the broad applicability of ApEn to biological time series, with the specific example of discriminating a saltatory growth process in longitudinal growth data. Future investigations of regularity in longitudinal time series in human biology with ApEn statistics are suggested.