Complex analysis of intracranial hypertension using approximate entropy*

Predicting the Severity and Discharge Prognosis of Traumatic Brain Injury Based on Intracranial Pressure Data Using Machine Learning Algorithms

OBJECTIVE

This study aimed to explore the potential of employing machine learning algorithms based on intracranial pressure (ICP), ICP-derived parameters, and their complexity to predict the severity and short-term prognosis of traumatic brain injury (TBI).

METHODS

A single-center prospectively collected cohort of neurosurgical intensive care unit admissions was analyzed. We extracted ICP-related data within the first 6 hours and processed them using complex algorithms. To indicate TBI severity and short-term prognosis, Glasgow Coma Scale score on the first postoperative day and Glasgow Outcome Scale-Extended score at discharge were used as binary outcome variables. A univariate logistic regression model was developed to predict TBI severity using only mean ICP values. Subsequently, 3 multivariate Random Forest (RF) models were constructed using different combinations of mean and complexity metrics of ICP-related data. To avoid overfitting, five-fold cross-validations were performed. Finally, the best-performing multivariate RF model was used to predict patients' discharge Glasgow Outcome Scale-Extended score.

RESULTS

The logistic regression model exhibited limited predictive ability with an area under the curve (AUC) of 0.558. Among multivariate models, the RF model, combining the mean and complexity metrics of ICP-related data, achieved the most robust ability with an AUC of 0.815. Finally, in terms of predicting discharge Glasgow Outcome Scale-Extended score, this model had a consistent performance with an AUC of 0.822. Cross-validation analysis confirmed the performance.

CONCLUSIONS

This study demonstrates the clinical utility of the RF model, which integrates the mean and complexity metrics of ICP data, in accurately predicting the TBI severity and short-term prognosis.

Permutation Entropy Analysis to Intracranial Hypertension from a Porcine Model

Intracranial pressure (ICP) monitoring is commonly used in the follow-up of patients in intensive care units, but only a small part of the information available in the ICP time series is exploited. One of the most important features to guide patient follow-up and treatment is intracranial compliance. We propose using permutation entropy (PE) as a method to extract non-obvious information from the ICP curve. We analyzed the results of a pig experiment with sliding windows of 3600 samples and 1000 displacement samples, and estimated their respective PEs, their associated probability distributions, and the number of missing patterns (NMP). We observed that the behavior of PE is inverse to that of ICP, in addition to the fact that NMP appears as a surrogate for intracranial compliance. In lesion-free periods, PE is usually greater than 0.3, and normalized NMP is less than 90% and p(s1)>p(s720). Any deviation from these values could be a possible warning of altered neurophysiology. In the terminal phases of the lesion, the normalized NMP is higher than 95%, and PE is not sensitive to changes in ICP and p(s720)>p(s1). The results show that it could be used for real-time patient monitoring or as input for a machine learning tool.

k-Shape clustering for extracting macro-patterns in intracranial pressure signals

Background

Intracranial pressure (ICP) monitoring is a core component of neurosurgical diagnostics. With the introduction of telemetric monitoring devices in the last years, ICP monitoring has become feasible in a broader clinical setting including monitoring during full mobilization and at home, where a greater diversity of ICP waveforms are present. The need for identification of these variations, the so-called macro-patterns lasting seconds to minutes—emerges as a potential tool for better understanding the physiological underpinnings of patient symptoms.

Methods

We introduce a new methodology that serves as a foundation for future automatic macro-pattern identification in the ICP signal to comprehensively understand the appearance and distribution of these macro-patterns in the ICP signal and their clinical significance. Specifically, we describe an algorithm based on k-Shape clustering to build a standard library of such macro-patterns.

Results

In total, seven macro-patterns were extracted from the ICP signals. This macro-pattern library may be used as a basis for the classification of new ICP variation distributions based on clinical disease entities.

Conclusions

We provide the starting point for future researchers to use a computational approach to characterize ICP recordings from a wide cohort of disorders.

Assessing rheoencephalography dynamics through analysis of the interactions among brain and cardiac networks during general anesthesia

Cerebral blood flow (CBF) reflects the rate of delivery of arterial blood to the brain. Since no nutrients, oxygen or water can be stored in the cranial cavity due to space and pressure restrictions, a continuous perfusion of the brain is critical for survival. Anesthetic procedures are known to affect cerebral hemodynamics, but CBF is only monitored in critical patients due, among others, to the lack of a continuous and affordable bedside monitor for this purpose. A potential solution through bioelectrical impedance technology, also known as rheoencephalography (REG), is proposed, that could fill the existing gap for a low-cost and effective CBF monitoring tool. The underlying hypothesis is that REG signals carry information on CBF that might be recovered by means of the application of advanced signal processing techniques, allowing to track CBF alterations during anesthetic procedures. The analysis of REG signals was based on geometric features extracted from the time domain in the first place, since this is the standard processing strategy for this type of physiological data. Geometric features were tested to distinguish between different anesthetic depths, and they proved to be capable of tracking cerebral hemodynamic changes during anesthesia. Furthermore, an approach based on Poincaré plot features was proposed, where the reconstructed attractors form REG signals showed significant differences between different anesthetic states. This was a key finding, providing an alternative to standard processing of REG signals and supporting the hypothesis that REG signals do carry CBF information. Furthermore, the analysis of cerebral hemodynamics during anesthetic procedures was performed by means of studying causal relationships between global hemodynamics, cerebral hemodynamics and electroencephalogram (EEG) based-parameters. Interactions were detected during anesthetic drug infusion and patient positioning (Trendelenburg positioning and passive leg raise), providing evidence of the causal coupling between hemodynamics and brain activity. The provided alternative of REG signal processing confirmed the hypothesis that REG signals carry information on CBF. The simplicity of the technology, together with its low cost and easily interpretable outcomes, should provide a new opportunity for REG to reach standard clinical practice. Moreover, causal relationships among the hemodynamic physiological signals and brain activity were assessed, suggesting that the inclusion of REG information in depth of anesthesia monitors could be of valuable use to prevent unwanted CBF alterations during anesthetic procedures.

Characterisation of the complexity of intracranial pressure signals measured from idiopathic and secondary normal pressure hydrocephalus patients

Hydrocephalus is a condition characterised by enlarged cerebral ventricles, which in turn affects intracranial pressure (ICP); however, the mechanisms regulating ICP are not fully understood. A nonlinear signal processing approach was applied to ICP signals measured during infusion studies from patients with two forms of hydrocephalus, in a bid to compare the differences. This is the first study of its kind. The two forms of hydrocephalus were idiopathic normal pressure hydrocephalus (iNPH) and secondary normal pressure hydrocephalus (SH). Following infusion tests, the Lempel-Ziv (LZ) complexity was calculated from the iNPH and SH ICP signals. The LZ complexity values were averaged for the baseline, infusion, plateau and recovery stages of the tests. It was found that as the ICP increased from basal levels, the LZ complexities decreased, reaching their lowest during the plateau stage. However, the complexities computed from the SH ICP signals decreased to a lesser extent when compared with the iNPH ICP signals. Furthermore, statistically significant differences were found between the plateau and recovery stage complexities when comparing the iNPH and SH results (p = 0.05). This Letter suggests that advanced signal processing of ICP signals with LZ complexity can help characterise different types of hydrocephalus in more detail.

Cerebrovascular Signal Complexity Six Hours after Intensive Care Unit Admission Correlates with Outcome after Severe Traumatic Brain Injury

Disease states are associated with a breakdown in healthy interactions and are often characterized by reduced signal complexity. We applied approximate entropy (ApEn) analysis to investigate the correlation between the complexity of heart rate (ApEn-HR), mean arterial pressure (ApEn-MAP), intracranial pressure (ApEn-ICP), and a combined ApEn-product (product of the three individual ApEns) and outcome after traumatic brain injury. In 174 severe traumatic brain injured patients, we found significant differences across groups classified by the Glasgow Outcome Score in ApEn-HR (p = 0.007), ApEn-MAP (p = 0.02), ApEn-ICP (p = 0.01), ApEn-product (p = 0.001), and pressure reactivity index (PRx) (p = 0.004) in the first 6 h. This relationship strengthened in a 24 h and 72 h analysis (ApEn-MAP continued to correlate with death but was not correlated with favorable outcome). Outcome was dichotomized as survival versus death, and favorable versus unfavorable; the ApEn-product achieved the strongest statistical significance at 6 h (F = 11.0; p = 0.001 and F = 10.5; p = 0.001, respectively) and was a significant independent predictor of mortality and favorable outcome (p < 0.001). Patients in the lowest quartile for ApEn-product were over four times more likely to die (39.5% vs. 9.3%, p < 0.001) than those in the highest quartile. ApEn-ICP was inversely correlated with PRx (r = -0.39, p < 0.000001) indicating unique information related to impaired cerebral autoregulation. Our results demonstrate that as early as 6 h into monitoring, complexity measures from easily attainable vital signs, such as HR and MAP, in addition to ICP, can help triage those who require more intensive neurological management at an early stage.

Intracranial pressure for the characterization of different types of hydrocephalus: A Permutation Entropy study

Hydrocephalus is a condition characterized by altered cerebrospinal fluid (CSF) dynamics and chronic rises in intracranial pressure (ICP). However, the reason why hydrocephalic physiologies fail to inhibit dangerously high ICP levels is not known. Infusion studies are used to raise ICP and evaluate CSF circulation disorders. In this pilot study, ICP signals recorded during infusion tests from 33 patients with normal pressure hydrocephalus and 36 patients having developed a secondary form of normal pressure hydrocephalus were characterized using Permutation Entropy (PE), a symbolic non-linear method to quantify complexity. Each ICP signal was divided into four epochs--baseline (before infusion begins), infusion, plateau, and recovery (after infusion has stopped)--and the mean PE was calculated for each epoch. Statistically significant differences were found between PE for most epochs (p<;0.00833, Bonferroni-corrected Wilcoxon tests), with a significant decrease in the plateau phase. However, differences between PE for normal pressure and secondary hydrocephalus were not significant. Results suggest that the increase in ICP during infusion studies is associated with a significant decrease in PE. PE analysis of ICP signals could be useful for increasing our understanding of CSF dynamics in normal pressure hydrocephalus.

Selection of entropy-measure parameters for knowledge discovery in heart rate variability data

Background

Heart rate variability is the variation of the time interval between consecutive heartbeats. Entropy is a commonly used tool to describe the regularity of data sets. Entropy functions are defined using multiple parameters, the selection of which is controversial and depends on the intended purpose. This study describes the results of tests conducted to support parameter selection, towards the goal of enabling further biomarker discovery.

Methods

This study deals with approximate, sample, fuzzy, and fuzzy measure entropies. All data were obtained from PhysioNet, a free-access, on-line archive of physiological signals, and represent various medical conditions. Five tests were defined and conducted to examine the influence of: varying the threshold value r (as multiples of the sample standard deviation σ, or the entropy-maximizing r_Chon), the data length N, the weighting factors n for fuzzy and fuzzy measure entropies, and the thresholds r_F and r_L for fuzzy measure entropy. The results were tested for normality using Lilliefors' composite goodness-of-fit test. Consequently, the p-value was calculated with either a two sample t-test or a Wilcoxon rank sum test.

Results

The first test shows a cross-over of entropy values with regard to a change of r. Thus, a clear statement that a higher entropy corresponds to a high irregularity is not possible, but is rather an indicator of differences in regularity. N should be at least 200 data points for r = 0.2 σ and should even exceed a length of 1000 for r = r_Chon. The results for the weighting parameters n for the fuzzy membership function show different behavior when coupled with different r values, therefore the weighting parameters have been chosen independently for the different threshold values. The tests concerning r_F and r_L showed that there is no optimal choice, but r = r_F = r_L is reasonable with r = r_Chon or r = 0.2σ.

Conclusions

Some of the tests showed a dependency of the test significance on the data at hand. Nevertheless, as the medical conditions are unknown beforehand, compromises had to be made. Optimal parameter combinations are suggested for the methods considered. Yet, due to the high number of potential parameter combinations, further investigations of entropy for heart rate variability data will be necessary.

Analysis of Intracranial Pressure

The monitoring of intracranial pressure (ICP) is an important tool in medicine for its ability to portray the brain’s compliance status. The bedside monitor displays the ICP waveform and intermittent mean values to guide physicians in the management of patients, particularly those having sustained a traumatic brain injury. Researchers in the fields of engineering and physics have investigated various mathematical analysis techniques applicable to the waveform in order to extract additional diagnostic and prognostic information, although they largely remain limited to research applications. The purpose of this review is to present the current techniques used to monitor and interpret ICP and explore the potential of using advanced mathematical techniques to provide information about system perturbations from states of homeostasis. We discuss the limits of each proposed technique and we propose that nonlinear analysis could be a reliable approach to describe ICP signals over time, with the fractal dimension as a potential predictive clinically meaningful biomarker. Our goal is to stimulate translational research that can move modern analysis of ICP using these techniques into widespread practical use, and to investigate to the clinical utility of a tool capable of simplifying multiple variables obtained from various sensors.

Reduced complexity of intracranial pressure observed in short time series of intracranial hypertension following traumatic brain injury in adults

Physiological parameters, such as intracranial pressure (ICP), are regulated by interconnected feedback loops, resulting in a complex time course. According to the decomplexification theory, disease is characterised by a loss of feedback loops resulting in a reduced complexity of the time course of physiological parameters. We hypothesized that complexity of the ICP time series is decreased during periods of intracranial hypertension (IHT) following adult traumatic brain injury. In an observational retrospective cohort study, ICP was continuously monitored using intraparenchymally implanted probes and stored using ICM + -software. Periods of IHT (ICP > 25 mmHg for at least 1,024 s), were compared with preceding periods of intracranial normotension (ICP < 20 mmHg) and analysed at 1 s-intervals. ICP data (length = 1,024 s) were normalised (mean = 0, SD = 1) and complexity was estimated using the scaling exponent α (as derived from detrended fluctuation analysis), sample entropy (SampEn, m = 1, r = 0.2 × SD) and multiscale entropy. 344 episodes were analysed in 22 patients. During IHT (ICP = 31.7 ± 7.8 mmHg, mean ± SD), α was significantly elevated (α = 1.02 ± 0.22, p < 0.001) and SampEn significantly reduced (SampEn = 1.45 ± 0.46, p = 0.004) as compared to before IHT (ICP = 15.7 ± 3.2 mmHg, α = 0.81 ± 0.14, SampEn = 1.81 ± 0.24). In addition, MSE revealed a significantly (p < 0.05) decreased entropy at scaling factors ranging from 1 to 10. Both the increase in α as well as the decrease in SampEn and MSE indicate a loss of ICP complexity. Therefore following traumatic brain injury, periods of IHT seem to be characterised by a decreased complexity of the ICP waveform.

Characterisation of the intracranial pressure waveform during infusion studies by means of central tendency measure

OBJECTIVE

In the present study an attempt was made to quantify and characterise the changes in the intracranial pressure (ICP) waveform over the wide pressure range covered during infusion studies by means of the central tendency measure (CTM). CTM is a non-linear approach using continuous chaotic modelling that summarises the degree of variability in a signal.

METHODS

CTM of the ICP wave in the lumbar subarachnoid space was analysed in 77 infusion studies performed in patients with idiopathic and secondary forms of normal pressure hydrocephalus (median age 74 years, range 22-88). Four artefact-free epochs were selected during the baseline, infusion, plateau and relaxation stages of every infusion study. The average pressure, pulse amplitude and CTM were determined for each epoch. Correlations among these parameters were explored.

RESULTS

CTM of the ICP waveform decreases, i.e. variability increases, as infusion studies progress from baseline pressure to the plateau stage. Significant correlations were found during all phases of infusion testing, except at baseline, between CTM and pressure, CTM and amplitude and pressure and amplitude. Partial correlations emphasised the relationship between CTM and amplitude. When pulse amplitude is held constant, CTM and the pressure range do not correlate.

CONCLUSIONS

Volume loading leads to increased variability of the ICP signal measured by means of CTM. This finding summarises numerically the long-established phenomenon of increasing amplitude and rounding of ICP pulses associated with ICP elevation during infusion studies. CTM could be a suitable approach to quantify and characterise the pulsatile nature of the ICP wave.

Complexity of intracranial pressure correlates with outcome after traumatic brain injury

This study applied multiscale entropy analysis to investigate the correlation between the complexity of intracranial pressure waveform and outcome after traumatic brain injury. Intracranial pressure and arterial blood pressure waveforms were low-pass filtered to remove the respiratory and pulse components and then processed using a multiscale entropy algorithm to produce a complexity index. We identified significant differences across groups classified by the Glasgow Outcome Scale in intracranial pressure, pressure-reactivity index and complexity index of intracranial pressure (P < 0.0001; P = 0.001; P < 0.0001, respectively). Outcome was dichotomized as survival/death and also as favourable/unfavourable. The complexity index of intracranial pressure achieved the strongest statistical significance (F = 28.7; P < 0.0001 and F = 17.21; P < 0.0001, respectively) and was identified as a significant independent predictor of mortality and favourable outcome in a multivariable logistic regression model (P < 0.0001). The results of this study suggest that complexity of intracranial pressure assessed by multiscale entropy was significantly associated with outcome in patients with brain injury.

Clinical applications of heart rate variability in the triage and assessment of traumatically injured patients

Heart rate variability (HRV) is a method of physiologic assessment which uses fluctuations in the RR intervals to evaluate modulation of the heart rate by the autonomic nervous system (ANS). Decreased variability has been studied as a marker of increased pathology and a predictor of morbidity and mortality in multiple medical disciplines. HRV is potentially useful in trauma as a tool for prehospital triage, initial patient assessment, and continuous monitoring of critically injured patients. However, several technical limitations and a lack of standardized values have inhibited its clinical implementation in trauma. The purpose of this paper is to describe the three analytical methods (time domain, frequency domain, and entropy) and specific clinical populations that have been evaluated in trauma patients and to identify key issues regarding HRV that must be explored if it is to be widely adopted for the assessment of trauma patients.

Complexity analysis of the cerebrospinal fluid pulse waveform during infusion studies

PURPOSE

Nonlinear dynamics has enhanced the diagnostic abilities of some physiological signals. Recent studies have shown that the complexity of the intracranial pressure waveform decreases during periods of intracranial hypertension in paediatric patients with acute brain injury. We wanted to assess changes in the complexity of the cerebrospinal fluid (CSF) pressure signal over the large range covered during the study of CSF circulation with infusion studies.

METHODS

We performed 37 infusion studies in patients with hydrocephalus of various types and origin (median age 71 years; interquartile range 60-77 years). After 5 min of baseline measurement, infusion was started at a rate of 1.5 ml/min until a plateau was reached. Once the infusion finished, CSF pressure was recorded until it returned to baseline. We analysed CSF pressure signals using the Lempel-Ziv (LZ) complexity measure. To characterise more accurately the behaviour of LZ complexity, the study was segmented into four periods: basal, early infusion, plateau and recovery.

RESULTS

The LZ complexity of the CSF pressure decreased in the plateau of the infusion study compared to the basal complexity (p=0.0018). This indicates loss of complexity of the CSF pulse waveform with intracranial hypertension. We also noted that the level of complexity begins to increase when the infusion is interrupted and CSF pressure drops towards the initial values.

CONCLUSIONS

The LZ complexity decreases when CSF pressure reaches the range of intracranial hypertension during infusion studies. This finding provides further evidence of a phenomenon of decomplexification in the pulsatile component of the pressure signal during intracranial hypertension.

Detrended fluctuation analysis is considered to be useful as a new indicator for short-term glucose complexity

BACKGROUND

This study clarified whether detrended fluctuation analysis (DFA) can evaluate how to advance the loss of complexity from impaired glucose tolerance (IGT) through mild diabetes mellitus (DM) to overt DM.

METHODS

Continuous glucose monitoring (CGM) was done during a 48-h interval for 59 subjects from multiple centers. Subjects were divided according to CGM data into those with impaired glucose tolerance (IGT) (n = 20), mild DM (n = 13), and overt DM (n = 26). The short-term (α1) and long-term (α2) range exponentials by DFA were compared among the three groups.

RESULTS

The value of α1 within 1h was significantly lower in the IGT group than in either of the other two groups (IGT vs. mild DM vs. overt DM, 1.53 ± 0.22 vs. 1.71 ± 0.17 vs. 1.77 ± 0.13, P<0.0001), and α1 within 2h differed significantly among the three groups (1.49 ± 0.13 vs. 1.57 ± 0.10 vs. 1.72 ± 0.10, P<0.0001). The α1 within 3h was significantly higher in overt DM than in either of the other two groups but did not change between IGT and mild DM (1.44 ± 0.12 vs. 1.52 ± 0.11 vs. 1.67 ± 0.09, P<0.0001). All short-term exponents decreased gradually but significantly as the window widened in all groups (P<0.0001). The α2 over 1h was significantly higher in overt DM but was unchanged in IGT and mild DM (1.22 ± 0.11 vs. 1.27 ± 0.12 vs. 1.36 ± 0.13, P = 0.0010). The α2 over 3h did not differ among the three groups.

CONCLUSIONS

Progressive loss of complexity in the glycemic profile occurred from the short-term range and spread to the long-term range concomitantly with the progression of the DM state.

Differences in complexity of glycemic profile in survivors and nonsurvivors in an intensive care unit: a pilot study

OBJECTIVE

To investigate glycemic dynamics and its relation with mortality in critically ill patients. We searched for differences in complexity of the glycemic profile between survivors and nonsurvivors in patients admitted to a multidisciplinary intensive care unit.

DESIGN

Prospective, observational study, convenience sample.

SETTINGS

Multidisciplinary intensive care unit of a teaching hospital in Madrid, Spain.

PATIENTS

A convenience sample of 42 patients, aged 29 to 86 yrs, admitted to an intensive care unit with an Acute Physiology and Chronic Health Evaluation II score of >or=14 and with an anticipated intensive care unit stay of >72 hrs.

INTERVENTIONS

A continuous glucose monitoring system was used to measure subcutaneous interstitial fluid glucose levels every 5 mins for 48 hrs during the first days of intensive care unit stay. A 24-hr period (n = 288 measurements) was used as time series for complexity analysis of the glycemic profile.

MEASUREMENTS

Complexity of the glycemic profile was evaluated by means of detrended fluctuation analysis. Other conventional measurements of variability (range, sd, and Mean Amplitude of Glycemic Excursions) were also calculated.

MAIN RESULTS

Ten patients died during their intensive care unit stay. Glycemic profile was significantly more complex (lower detrended fluctuation analysis) in survivors (mean detrended fluctuation analysis, 1.49; 95% confidence interval, 1.44-1.53) than in nonsurvivors (1.60; 95% confidence interval, 1.52-1.68). This difference persisted after accounting for the presence of diabetes. In a logistic regression model, the odds ratio for death was 2.18 for every 0.1 change in detrended fluctuation analysis.Age, gender, Simplified Acute Physiologic Score 3 or Acute Physiologic and Chronic Health Evaluation II scores failed to explain differences in survivorship. Conventional variability measurements did not differ between survivors and nonsurvivors.

CONCLUSIONS

Complexity of the glycemic profile of critically ill patients varies significantly between survivors and nonsurvivors. Loss of complexity in glycemia time series, evaluated by detrended fluctuation analysis, is associated with higher mortality.

The Fourth National Institutes of Health Symposium on the Functional Genomics of Critical Injury: Surviving stress from organ systems to molecules

Recent strides in computational biology and high-throughput technologies have generated considerable interest in understanding complex biological systems. The application of these technologies to critical illness and injury offers the potential to define adaptive and maladaptive programs of gene expression induced by infection, shock, trauma, or other inflammatory triggers, and to detect biomarkers and genetic polymorphisms linked to these responses and outcome. A systems biology approach is timely because despite substantial effort, treatment approaches directed at a single mediator or inflammatory pathway have met with little success in altering outcomes of critically ill or injured patients. Highlights from the Fourth National Institute of Health Functional Genomics of Critical Illness and Injury Symposium are described herein, in addition to deliverables for the field identified during panel discussions. Next steps for the community and suggestions for future research are presented.

Wavelet entropy characterization of elevated intracranial pressure

Intracranial Hypertension (ICH) often occurs for those patients with traumatic brain injury (TBI), stroke, tumor, etc. Pathology of ICH is still controversial. In this work, we used wavelet entropy and relative wavelet entropy to study the difference existed between normal and hypertension states of ICP for the first time. The wavelet entropy revealed the similar findings as the approximation entropy that entropy during ICH state is smaller than that in normal state. Moreover, with wavelet entropy, we can see that ICH state has the more focused energy in the low wavelet frequency band (0-3.1 Hz) than the normal state. The relative wavelet entropy shows that the energy distribution in the wavelet bands between these two states is actually different. Based on these results, we suggest that ICH may be formed by the re-allocation of oscillation energy within brain.

Characterization of interdependency between intracranial pressure and heart variability signals: a causal spectral measure and a generalized synchronization measure

Causal coherence and generalized synchronization (GS) index were extracted from beat-to-beat mean intracranial pressure (ICP) and intervals between consecutive normal sinus heart beats (RR interval) that were recorded from 12 patients undergoing normal pressure hydrocephalus diagnosis. Data were organized into two groups including an ICP B-Wave group and a baseline control group. Maximal classic coherence (CC) between ICP and RR interval within [0.04, 0.15] Hz was found to be significantly greater than zero for both B-Wave and control groups with B-Wave CC greater than that of the baseline group. Causal coherence analysis further revealed that feedforward coherence due to RR interval's effect on ICP always exists for both B-Wave and baseline ICP state and no significant difference exists between two groups. On the other hand, feedback coherence from ICP to RR interval was enhanced during the occurrence of B-Wave. This finding regarding the enhanced directional, from ICP to RR interval, coupling between ICP and RR interval was also confirmed by a modified GS measure.

Adaptive computation of approximate entropy and its application in integrative analysis of irregularity of heart rate variability and intracranial pressure signals

The present study introduces an adaptive calculation of approximate entropy (ApEn) by exploiting sample-by-sample construction and update of nearest neighborhoods in an n-dimensional space. The algorithm is first validated with a standard numerical test set. It is then applied to electrocardiogram R wave interval (RR) and beat-to-beat intracranial pressure signals recorded from 12 patients undergoing normal pressure hydrocephalus diagnosis. The ApEn time series are further processed using the causal coherence analysis to study the interaction between ICP and RR interval. Numerical validation demonstrates that the proposed algorithm reproduces the known time-varying patterns in the test set and better tracks abrupt signal changes. It is also demonstrated that occurrences of large-amplitude ICP oscillation are associated with decreased ICP ApEn and RR ApEn for all 12 patients. The causal coherence analysis of ApEn time series shows that coherence between RR ApEn and ICP ApEn, after mathematically decoupling RR effect on ICP, is enhanced for the oscillatory ICP state and so is the amplitude of transfer function between ICP and RR interval. However, no enhanced coherence is observed after mathematically decoupling ICP effect on RR interval. In conclusion, the adaptive ApEn algorithm can be used to track nonstationary signal characteristics. Furthermore, interactions between dynamic systems could be studied by using ApEn time series of the direct observations of systems.

Predicting survival in critical patients by use of body temperature regularity measurement based on approximate entropy

Body temperature is a classical diagnostic tool for a number of diseases. However, it is usually employed as a plain binary classification function (febrile or not febrile), and therefore its diagnostic power has not been fully developed. In this paper, we describe how body temperature regularity can be used for diagnosis. Our proposed methodology is based on obtaining accurate long-term temperature recordings at high sampling frequencies and analyzing the temperature signal using a regularity metric (approximate entropy). In this study, we assessed our methodology using temperature registers acquired from patients with multiple organ failure admitted to an intensive care unit. Our results indicate there is a correlation between the patient's condition and the regularity of the body temperature. This finding enabled us to design a classifier for two outcomes (survival or death) and test it on a dataset including 36 subjects. The classifier achieved an accuracy of 72%.

Analysis of intracranial pressure during acute intracranial hypertension using Lempel-Ziv complexity: further evidence

We analyzed intracranial pressure (ICP) signals during periods of acute intracranial hypertension (ICH) using the Lempel-Ziv (LZ) complexity measure. Our results indicate the LZ complexity of ICP decreases during periods of ICH. The mean LZ complexity before ICH was 0.20+/-0.04, while the mean LZ complexity during ICH was 0.16+/-0.03 (p<0.05). The mean decrease of the LZ complexity values during the ICH episodes was 19.5%. Additionally, we present preliminary evidence suggesting that periods of ICH may be detectable from non-invasive signals coupled with ICP, such as pulse oximetry (SpO2).

Loss of complexity characterizes the heart rate response to experimental hemorrhagic shock in swine

OBJECTIVE

To improve our ability to identify physiologic deterioration caused by critical illness, we applied nonlinear and frequency-domain analytical methods to R-to-R interval (RRI) and systolic arterial pressure (SAP) time series during hemorrhagic shock.

DESIGN

Prospective, randomized, controlled trial.

SETTING

Animal laboratory of a government research institute.

SUBJECTS

Twenty swine (weight 36.4+/-0.11 kg).

INTERVENTIONS

Fixed-volume hemorrhage followed by resuscitation; off-line analysis of RRI and SAP data.

MEASUREMENTS AND MAIN RESULTS

Anesthetized swine (shock group, n=12) underwent withdrawal of 30 mL/kg blood in 10 mL/kg decrements. A control group (n=8) received maintenance fluids only. Electrocardiogram and arterial pressure waveforms were acquired at 500 Hz. Eight hundred-beat data sets were analyzed at six time points: at baseline, after each blood withdrawal, after lactated Ringer's resuscitation, and after infusion of shed blood. Nonlinear methods were used to estimate the complexity (approximate entropy, sample entropy, Lempel-Ziv entropy, normalized entropy of symbol dynamics), RRI bits per word, and fractal dimension by curve lengths and by dispersion analysis of the RRI and SAP time series. Fast Fourier transformation was used to measure the high-frequency and low-frequency powers of RRI and SAP. Baroreflex sensitivity was assessed in the time domain with the sequence method. Hemorrhagic shock caused decreases in RRI complexity as quantified by approximate entropy, sample entropy, and symbol dynamics; these changes were reversed by resuscitation. Similar but statistically insignificant changes in fractal dimension by curve lengths were seen. RRI high-frequency power decreased with hemorrhagic shock-indicating withdrawal of vagal cardiac input-and was restored by resuscitation. Similar changes in baroreflex sensitivity were seen. Hemorrhagic shock did not affect SAP complexity.

CONCLUSIONS

Hemorrhagic shock caused a reversible decrease in RRI complexity; these changes may be mediated by changes in vagal cardiac control. Assessment of RRI complexity may permit identification of casualties with hemorrhagic shock.

Interpretation of the Lempel-Ziv complexity measure in the context of biomedical signal analysis

Lempel-Ziv complexity (LZ) and derived LZ algorithms have been extensively used to solve information theoretic problems such as coding and lossless data compression. In recent years, LZ has been widely used in biomedical applications to estimate the complexity of discrete-time signals. Despite its popularity as a complexity measure for biosignal analysis, the question of LZ interpretability and its relationship to other signal parameters and to other metrics has not been previously addressed. We have carried out an investigation aimed at gaining a better understanding of the LZ complexity itself, especially regarding its interpretability as a biomedical signal analysis technique. Our results indicate that LZ is particularly useful as a scalar metric to estimate the bandwidth of random processes and the harmonic variability in quasi-periodic signals.

Integrative analysis of intracranial pressure and R-R interval signals: a study of ICP B-wave using causal coherence

Causal coherence analysis was applied to beat-to-beat mean intracranial pressure (ICP) and RR interval signals that were recorded from twelve normal pressure hydrocephalus patients. Data were organized into two groups including an ICP B-Wave group and a control baseline group. Maximal classic coherence between ICP and RR interval within [0.04-0.15] Hz was found to be significantly greater than zero for both B-wave and control groups. Causal coherence analysis further revealed that feedforward coherence due to RR interval's effect on ICP always exists for both B-wave and baseline ICP state while feedback coherence from ICP to RR interval was enhanced during the occurrence of B-wave.