More Than Just a Number: Complexity of Intracranial Pressure Correlates with Outcome After Traumatic Brain Injury

Abstract & Commentary

By Halinder S. Mangat, MD, Assistant Professor of Clinical Neurology, Weill Cornell Medical College. Dr. Mangat reports no financial relationships relevant to this field of study.

Synopsis: Analysis of intracranial pressure complexity using a non-linear method of multiscale entropy shows that it correlates with outcome after traumatic brain injury.

Source: Lu C-W, et al. Complexity of intracranial pressure correlates with outcome after traumatic brain injury. Brain 2012;135:2399-2408.

Due to their complexity, data analysis of physiological signals using linear models may not accurately represent such systems. Therefore, non-linear models are gaining application in understanding the complex behavior of physiological variables such as intracranial pressure (ICP).1 Approximate entropy2 and wavelet entropy3 have been applied to understand ICP changes in different clinical scenarios.

In this article, the authors apply multiscale entropy to study the correlation of ICP complexity with outcome after traumatic brain injury (TBI).4 Briefly, entropy relates to the predictability of a variable based on previously recorded values; the higher the entropy, the more unpredictable the variable.

The authors used data from 325 patients admitted to the neurosciences critical care unit after TBI. Time series were evolved by a graining procedure, which involved averaging consecutive data values for comparison. Averaging increasing number of consecutive data points up to 20 values created multiple time series. For each time series, sample entropy analysis was calculated, i.e., the likelihood of two similar sequences of two data points that would remain similar if a third data point was included (computed as the negative logarithm of the ratio of number of three data point pattern to the number of two data point patterns). Multiscale entropy was plotted as sample entropy for each time series against its time scale and the area under the curve was the complexity index.

There was a decrease in entropy of ICP signal and ICP complexity index across all measured scales during plateau ICP waves. ICP complexity index was significantly higher in patients who had good outcome compared with those with moderate-to-severe disability. In the multivariate logistic regression model, adding the complexity index identified it as a strong predictor of mortality. In pooled data analysis, ICP complexity index showed an inverse relationship with ICP.


This is the first study using multiscale entropy to study the relationship of ICP and outcome. In the comparison of data between baseline low ICP and high ICP in plateau waves, the entropy decreases as does complexity index of ICP. This supports the idea that worsening ICP changes the dynamics of ICP and at high ICP there is decomplexification of the dynamics. However, one must consider that treatment of high ICP in itself is directed to change ICP dynamics, and the effect of sedation or removing CSF may also reduce complexity of ICP signal. This is also highlighted by the fact that during plateau waves autoregulation may be severely impaired and its dynamic effect lost.5

Whether the loss of complexity is an exhaustion of regulatory mechanisms leading up to high ICP or this is a hallmark of high ICP remains to be determined. As the authors mention, it is difficult clinically to determine physiological interpretation of these findings. Further work using non-linear models studying one variable at a time may help to understand these.

Overall, this is an eloquent study that delves into the dynamic state and complexity of ICP, once more highlighting that ICP is much more than just a number.


1. Santamarta D, et al. Pulse amplitude and Lempel-Ziv complexity of the cerebrospinal fluid pressure signal. Acta Neurochir Suppl 2012;114:23-27.

2. Hornero R, et al. Interpretation of approximate entropy: Analysis of intracranial pressure approximate entropy during intracranial hypertension. IEEE Trans Biomed Eng 2005;52:1671-1680.

3. Xu P, et al. Wavelet entropy characterization of elevated intracranial pressure. Conf Proc IEEE Eng Med Biol Soc 2008;2008:2924-2927.

4. Lu C-W, et al. Complexity of intracranial pressure correlates with outcome after traumatic brain injury. Brain 2012;135:2399-2408.

5. Czosnyka M, et al. Continuous assessment of the cerebral vasomotor reactivity in head injury. Neurosurgery 1997;41:11-17.