A Review of Wavelet Transform Time-Frequency Methods for NIRS-Based Analysis of Cerebral Autoregulation

Dynamic cerebral autoregulation is preserved during orthostasis and intrathoracic pressure regulation in healthy subjects: A pilot study

Resistance breathing may restore cardiac output (CO) and cerebral blood flow (CBF) during hypovolemia. We assessed CBF and cerebral autoregulation (CA) during tilt, resistance breathing, and paced breathing in 10 healthy subjects. Blood velocities in the internal carotid artery (ICA), middle cerebral arteries (MCA, four subjects), and aorta were measured by Doppler ultrasound in 30° and 60° semi-recumbent positions. ICA blood flow and CO were calculated. Arterial blood pressure (ABP, Finometer), and end-tidal CO2 (ETCO2) were recorded. ICA blood flow response was assessed by mixed-models regression analysis. The synchronization index (SI) for the variable pairs ABP-ICA blood velocity, ABP-MCA velocities in 0.005-0.08 Hz frequency interval was calculated as a measure of CA. Passive tilting from 30° to 60° resulted in 12% decrease in CO (p = 0.001); ICA blood flow tended to fall (p = 0.04); Resistance breathing restored CO and ICA blood flow despite a 10% ETCO2 drop. ETCO2 and CO contributed to ICA blood flow variance (adjusted R2: 0.9, p < 0.0001). The median SI was low (<0.2) indicating intact CA, confirmed by surrogate date testing. The peak SI was transiently elevated during resistance breathing in the 60° position. Resistance breathing may transiently reduce CA efficiency. Paced breathing did not restore CO or ICA blood flow.

Near-Infrared Spectroscopy Regional Oxygen Saturation Based Cerebrovascular Reactivity Assessments in Chronic Traumatic Neural Injury versus in Health: A Prospective Cohort Study

Near-infrared spectroscopy (NIRS) regional cerebral oxygen saturation (rSO2)-based cerebrovascular reactivity (CVR) monitoring has enabled entirely non-invasive, continuous monitoring during both acute and long-term phases of care. To date, long-term post-injury CVR has not been properly characterized after acute traumatic neural injury, also known as traumatic brain injury (TBI). This study aims to compare CVR in those recovering from moderate-to-severe TBI with a healthy control group. A total of 101 heathy subjects were recruited for this study, along with 29 TBI patients. In the healthy cohort, the arterial blood pressure variant of the cerebral oxygen index (COx_a) was not statistically different between males and females or in the dominant and non-dominant hemispheres. In the TBI cohort, COx_a was not statistically different between the first and last available follow-up or by the side of cranial surgery. Surprisingly, CVR, as measured by COx_a, was statistically better in those recovering from TBI than those in the healthy cohort. In this prospective cohort study, CVR, as measured by NIRS-based methods, was found to be more active in those recovering from TBI than in the healthy cohort. This study may indicate that in individuals that survive TBI, CVR may be enhanced as a neuroprotective measure.

Dynamic cerebral autoregulation in postpartum individuals with and without preeclampsia

BACKGROUND

Changes in dynamic cerebral autoregulation (DCA) may contribute to postpartum maternal cerebrovascular complications after preeclampsia. We hypothesized that DCA is impaired in the first week postpartum after diagnosis of preeclampsia with severe features (PSF), compared with normotensive postpartum individuals and healthy non-pregnant female volunteers.

METHODS

We measured DCA within seven days after delivery in individuals with and without PSF, using transcranial Doppler and continuous arterial blood pressure monitoring with finger plethysmography. Historical data from 28 healthy female non-pregnant volunteers, collected using the same methods, were used for comparison. We used generalized harmonic wavelets to estimate autoregulation parameters (phase shift and gain) in very low frequency and low frequency bands, with lower phase shift and higher gain indicating impaired DCA function. We compared DCA parameters between the three groups using the Kruskal Wallis test.

RESULTS

A total of 69 postpartum participants contributed data, of whom 49 had preeclampsia with severe features. Median phase shifts in both postpartum groups were higher compared with historical controls across all frequency ranges (p = 0.001), indicating faster autoregulatory response. Gain was higher in both postpartum groups than in historical controls across all frequency ranges (p = 0.04), indicating impaired dampening effect.

CONCLUSION

We found that postpartum individuals, regardless of preeclampsia diagnosis, had higher phase shifts and higher gain than healthy non-pregnant/postpartum female volunteers. Our results suggest hyperdynamic DCA with impaired dampening effect in the first week postpartum, regardless of preeclampsia diagnosis.

Reduced-order modeling and analysis of dynamic cerebral autoregulation via diffusion maps

Objective.A data-driven technique for parsimonious modeling and analysis of dynamic cerebral autoregulation (DCA) is developed based on the concept of diffusion maps. Specifically, first, a state-space description of DCA dynamics is considered based on arterial blood pressure, cerebral blood flow velocity, and their time derivatives. Next, an eigenvalue analysis of the Markov matrix of a random walk on a graph over the dataset domain yields a low-dimensional representation of the intrinsic dynamics. Further dimension reduction is made possible by accounting only for the two most significant eigenvalues. The value of their ratio indicates whether the underlying system is governed by active or hypoactive dynamics, indicating healthy or impaired DCA function, respectively. We assessed the reliability of the technique by considering healthy individuals and patients with unilateral internal carotid artery (ICA) stenosis or occlusion. We computed the sensitivity of the technique to detect the presumed side-to-side difference in the DCA function of the second group (assuming hypoactive dynamics on the occluded or stenotic side), using McNemar's chi square test. The results were compared with transfer function analysis (TFA). The performance of the two methods was also compared under the assumption of missing data.Main results.Both diffusion maps and TFA suggested a physiological side-to-side difference in the DCA of ICA stenosis or occlusion patients with a sensitivity of 81% and 71%, respectively. Further, both two methods suggested the difference between the occluded or stenotic side and any two sides of the healthy group. However, the diffusion maps captured additional difference between the unoccluded side and the healthy group, that TFA did not. Furthermore, compared to TFA, diffusion maps exhibited superior performance when subject to missing data.Significance.The eigenvalues ratio derived using the diffusion maps technique can be potentially used as a reliable and robust biomarker for assessing how active the intrinsic dynamics of the autoregulation is and for indicating healthy versus impaired DCA function.

Cerebral blood flow response to cardiorespiratory oscillations in healthy humans

Dynamic cerebral autoregulation (CA) characterizes the cerebral blood flow (CBF) response to abrupt changes in arterial blood pressure (ABP). CA operates at frequencies below 0.15 Hz. ABP regulation and probably CA are modified by autonomic nervous activity. We investigated the CBF response and CA dynamics to mild increase in sympathetic activity. Twelve healthy volunteers underwent oscillatory lower body negative pressure (oLBNP), which induced respiratory-related ABP oscillations at an average of 0.22 Hz. We recorded blood velocity in the internal carotid artery (ICA) by Doppler ultrasound and ABP. We quantified variability and peak wavelet power of ABP and ICA blood velocity by wavelet analysis at low frequency (LF, 0.05-0.15 Hz) and Mayer waves (0.08-0.12 Hz), respectively. CA was quantified by calculation of the wavelet synchronization gamma index for the pair ABP-ICA blood velocity in the LF and Mayer wave band. oLBNP increased ABP peak wavelet power at the Mayer wave frequency. At the Mayer wave, ABP peak wavelet power increased by >70 % from rest to oLBNP (p < 0.05), while ICA blood flow velocity peak wavelet power was unchanged, and gamma index increased (from 0.49 to 0.69, p < 0.05). At LF, variability in both ABP and ICA blood velocity and gamma index were unchanged from rest to oLBNP. Despite an increased gamma index at Mayer wave, ICA blood flow variability was unchanged during increased ABP variability. The increased synchronization during oLBNP did not cause less stable CBF or less active CA. Sympathetic activation seems to improve the mechanisms of CA.

Identifying Cognitive Impairment in Elderly Using Coupling Functions Between Cerebral Oxyhemoglobin and Arterial Blood Pressure

Background

This study aimed to assess brain oxygenation status and cerebral autoregulation function in subjects with cognitive dysfunction.

Methods

The Montreal Cognitive Assessment (MoCA) was applied to divide the subjects into three groups: cognitive impairment (Group CI, 72.50 ± 10.93 y), mild cognitive impairment (Group MCI, 72.02 ± 9.90 y), and normal cognition (Group NC, 70.72 ± 7.66 y). Near-infrared spectroscopy technology and a non-invasive blood pressure device were used to simultaneously measure changes in cerebral tissue oxygenation signals in the bilateral prefrontal lobes (LPFC/RPFC) and arterial blood pressure (ABP) signals from subjects in the resting state (15 min). The coupling between ABP and cerebral oxyhemoglobin concentrations (Δ [O2Hb]) was calculated in very-low-frequency (VLF, 0.02-0.07 Hz) and low-frequency (LF, 0.07-0.2 Hz) bands based on the dynamical Bayesian inference approach. Pearson correlation analyses were used to study the relationships between MoCA scores, tissue oxygenation index, and strength of coupling function.

Results

In the interval VLF, Group CI (p = 0.001) and Group MCI (p = 0.013) exhibited significantly higher coupling strength from ABP to Δ [O2Hb] in the LPFC than Group NC. In the interval LF, coupling strength from ABP to Δ [O2Hb] in the LPFC was significantly higher in Group CI than in Group NC (p = 0.001). Pearson correlation results showed that MoCA scores had a significant positive correlation with the tissue oxygenation index and a significant negative correlation with the coupling strength from ABP to Δ [O2Hb].

Conclusion

The significantly increased coupling strength may be evidence of impaired cerebral autoregulation function in subjects with cognitive dysfunction. The Pearson correlation results suggest that indicators of brain oxygenation status and cerebral autoregulation function can reflect cognitive function. This study provides insights into the mechanisms underlying the pathophysiology of cognitive impairment and provides objective indicators for screening cognitive impairment in the elderly population.

The INfoMATAS project: Methods for assessing cerebral autoregulation in stroke

Cerebral autoregulation refers to the physiological mechanism that aims to maintain blood flow to the brain approximately constant when blood pressure changes. Impairment of this protective mechanism has been linked to a number of serious clinical conditions, including carotid stenosis, head trauma, subarachnoid haemorrhage and stroke. While the concept and experimental evidence is well established, methods for the assessment of autoregulation in individual patients remains an open challenge, with no gold-standard having emerged. In the current review paper, we will outline some of the basic concepts of autoregulation, as a foundation for experimental protocols and signal analysis methods used to extract indexes of cerebral autoregulation. Measurement methods for blood flow and pressure are discussed, followed by an outline of signal pre-processing steps. An outline of the data analysis methods is then provided, linking the different approaches through their underlying principles and rationale. The methods cover correlation based approaches (e.g. Mx) through Transfer Function Analysis to non-linear, multivariate and time-variant approaches. Challenges in choosing which method may be 'best' and some directions for ongoing and future research conclude this work.

Intermittent Sequential Pneumatic Compression Improves Coupling between Cerebral Oxyhaemoglobin and Arterial Blood Pressure in Patients with Cerebral Infarction

This study aims to explore the effect of intermittent sequential pneumatic compression (ISPC) intervention on the coupling relationship between arterial blood pressure (ABP) and changes in oxyhaemoglobin (Δ [O₂Hb]). The coupling strength between the two physiological systems was estimated using a coupling function based on dynamic Bayesian inference. The participants were 22 cerebral infarction patients and 20 age- and sex-matched healthy controls. Compared with resting state, the coupling strength from ABP to Δ [O₂Hb] oscillations was significantly lower in the bilateral prefrontal cortex (PFC), sensorimotor cortex (SMC), and temporal lobe cortex (TLC) during the ISPC intervention in cerebral infarction patients in interval II. Additionally, the coupling strength was significantly lower in the bilateral SMC in both groups in interval III. These findings indicate that ISPC intervention may facilitate cerebral circulation in the bilateral PFC, SMC, and TLC in cerebral infarction patients. ISPC may promote motor function recovery through its positive influences on motor-related networks. Furthermore, the coupling between Δ [O₂Hb] and ABP allows non-invasive assessments of autoregulatory function to quantitatively assess the effect of rehabilitation tasks and to guide therapy in clinical situations.

A Novel Cognitive Function Scale Using Functional Near-Infrared Spectroscopy for Evaluating Cognitive Dysfunction

Background:

Maintaining cognitive function is integral to a healthy social life in the aged. Although neuropsychological tests and brain imaging methods can assess cognitive dysfunction, these techniques are subjective, psychologically burdensome, and cannot be conducted easily.

Objective:

We sought to develop an objective, low-burden novel cognitive function scale based on functional near-infrared spectroscopy (fNIRS) of hemodynamic changes in the cerebral cortex during daily task performance.

Methods:

A total of 63 participants (aged 60–80 years) identified as non-dementia controls (NDC) or with mild cognitive impairment (MCI) were recruited and randomly assigned to training and test data sets. Explanatory variables were hemodynamic responses during low-burden sensory and simple tasks without higher-order brain functioning.

Results:

A logistic regression analysis of the fNIRS index in NDCs and MCI patients revealed area under the curve, sensitivity, specificity, and holdout results of 0.98, 94%, 88%, and 62% respectively. Correlation between fNIRS index and MCI odds showed positive linearity (R² = 0.96).

Conclusion:

Positive correlation between the fNIRS index and MCI odds indicated effectiveness of this fNIRS measurement. Although additional experiments are necessary, the fNIRS index representing degree of cognitive decline can be an onsite monitoring tool to assess cognitive status.

Spectral Analysis of Muscle Hemodynamic Responses in Post-Exercise Recovery Based on Near-Infrared Spectroscopy

Spectral analysis of blood flow or blood volume oscillations can help to understand the regulatory mechanisms of microcirculation. This study aimed to explore the relationship between muscle hemodynamic response in the recovery period and exercise quantity. Fifteen healthy subjects were required to perform two sessions of submaximal plantarflexion exercise. The blood volume fluctuations in the gastrocnemius lateralis were recorded in three rest phases (before and after two exercise sessions) using near-infrared spectroscopy. Wavelet transform was used to analyze the total wavelet energy of the concerned frequency range (0.005–2 Hz), which were further divided into six frequency intervals corresponding to six vascular regulators. Wavelet amplitude and energy of each frequency interval were analyzed. Results showed that the total energy raised after each exercise session with a significant difference between rest phases 1 and 3. The wavelet amplitudes showed significant increases in frequency intervals I, III, IV, and V from phase 1 to 3 and in intervals III and IV from phase 2 to 3. The wavelet energy showed similar changes with the wavelet amplitude. The results demonstrate that local microvascular regulators contribute greatly to the blood volume oscillations, the activity levels of which are related to the exercise quantity.

Measuring the Frequency-Specific Functional Connectivity Using Wavelet Coherence Analysis in Stroke Rats Based on Intrinsic Signals

Optical intrinsic signal imaging (OISi) method is an optical technique to evaluate the functional connectivity (FC) of the cortex in animals. Already, using OISi, the FC of the cortex has been measured in time or frequency domain separately, and at frequencies below 0.08 Hz, which is not in the frequency range of hemodynamic oscillations which are able to track fast cortical events, including neurogenic, myogenic, cardiac and respiratory activities. In the current work, we calculated the wavelet coherence (WC) transform of the OISi time series to evaluate the cerebral response changes in the stroke rats. Utilizing WC, we measured FC at frequencies up to 4.5 Hz, and could monitor the time and frequency dependency of the FC simultaneously. The results showed that the WC of the brain diminished significantly in ischemic motor and somatosensory cortices. According to the statistical results, the signal amplitude, responsive area size, correlation, and wavelet coherence of the motor and the somatosensory cortices for stroke hemisphere were found to be significantly lower compared to the healthy hemisphere. The obtained results confirm that the OISi-based WC analysis is an efficient method to diagnose the relative severity of infarction and the size of the infarcted region after ischemic stroke.

Joint time-frequency analysis of dynamic cerebral autoregulation using generalized harmonic wavelets

OBJECTIVE

To develop a joint time-frequency analysis technique based on generalized harmonic wavelets (GHWs) for dynamic cerebral autoregulation (DCA) performance quantification.

APPROACH

We considered two groups of human subjects to develop and validate the method: 55 healthy volunteers and 35 stroke-free subjects with unilateral internal carotid artery stenosis (CAS). We determined the mean and coherence-weighted average of the phase shift (PS) of appropriately defined GHW-based transfer functions, based on data points over the joint time-frequency domain. We compared agreement of standard transfer function analysis (TFA) and GHW analyses in healthy subjects using Bland-Altman plots. We assessed sensitivity of each metric to detect the presumed side-to-side difference in DCA function in CAS subjects (with decreased PS on the occluded side), using McNemar's chi square test to compare each metric to the standard TFA approach. An alternative Morlet wavelet-based approach was also considered.

MAIN RESULTS

The GHW and TFA methods exhibited strong agreement in healthy subjects. Among CAS subjects, GHW metrics outperformed TFA and Morlet wavelet-based approaches in identifying expected side-to-side differences: TFA sensitivity was 40.0% (95%CI 23.9-57.9), Morlet 60.0% (95%CI 42.1-76.1), and GHW  >70% for both metrics (GHW mean PS sensitivity 74.3, 95%CI 56.7-87.5, p   =  0.0027 versus TFA; GHW coherence-weighted PS sensitivity 71.4, 95%CI 53.7-85.4, p   =  0.0009 versus TFA).

SIGNIFICANCE

In comparison to the widely used stationary Fourier transform-based TFA and to Morlet wavelet-based analysis, our data suggest that the GHW-based analysis performs better in identifying DCA asymmetry between the two cerebral hemispheres in patients with high grade unilateral carotid stenosis. Our method may provide enhanced confidence in employing DCA metrics as a sensitive diagnostic tool for detecting impaired DCA function in a variety of pathological settings.

Dynamic Tracking Algorithm for Time-Varying Neuronal Network Connectivity using Wide-Field Optical Image Video Sequences

Propagation of signals between neurons and brain regions provides information about the functional properties of neural networks, and thus information transfer. Advances in optical imaging and statistical analyses of acquired optical signals have yielded various metrics for inferring neural connectivity, and hence for mapping signal intercorrelation. However, a single coefficient is traditionally derived to classify the connection strength between two cells, ignoring the fact that neural systems are inherently time-variant systems. To overcome these limitations, we utilized a time-varying Pearson's correlation coefficient, spike-sorting, wavelet transform, and wavelet coherence of calcium transients from DIV 12-15 hippocampal neurons from GCaMP6s mice after applying various concentrations of glutamate. Results provide a comprehensive overview of resulting firing patterns, network connectivity, signal directionality, and network properties. Together, these metrics provide a more comprehensive and robust method of analyzing transient neural signals, and enable future investigations for tracking the effects of different stimuli on network properties.

An on-line processing strategy for head movement interferences removal of dynamic brain electrical impedance tomography based on wavelet decomposition

BACKGROUND

Head movement interferences are a common problem during prolonged dynamic brain electrical impedance tomography (EIT) clinical monitoring. Head movement interferences mainly originate from body movements of patients and nursing procedures performed by medical staff, etc. These body movements will lead to variation in boundary voltage signals, which affects image reconstruction.

METHODS

This study employed a data preprocessing method based on wavelet decomposition to inhibit head movement interferences in brain EIT data. Mixed Gaussian models were applied to describe the distribution characteristics of brain EIT data. We identified head movement signal through the differences in distribution characteristics of corresponding wavelet decomposition coefficients between head movement artifacts and normal signals, and then managed the contaminated data with improved on-line wavelet processing methods.

RESULTS

To validate the efficacy of the method, simulated signal experiments and human data experiments were performed. In the simulation experiment, the simulated movement artifact was significantly reduced and data quality was improved with indicators' increase in PRD and correlation coefficient. Human data experiments demonstrated that this method effectively suppressed head movement in signals and reduce artifacts resulting from head movement artifacts in images.

CONCLUSION

In this paper, we proposed an on-line strategy to manage the head movement interferences from the brain EIT data based on the distribution characteristics of wavelet coefficients. Our strategy is capable of reducing the movement interference in the data and improving the reconstructed images. This work would improve the clinical practicability of brain EIT and contribute to its further promotion.

Frequency-resolved analysis of coherent oscillations of local cerebral blood volume, measured with near-infrared spectroscopy, and systemic arterial pressure in healthy human subjects

We report a study on twenty-two healthy human subjects of the dynamic relationship between cerebral hemoglobin concentration ([HbT]), measured with near-infrared spectroscopy (NIRS) in the prefrontal cortex, and systemic arterial blood pressure (ABP), measured with finger plethysmography. [HbT] is a measure of local cerebral blood volume (CBV). We induced hemodynamic oscillations at discrete frequencies in the range 0.04-0.20 Hz with cyclic inflation and deflation of pneumatic cuffs wrapped around the subject's thighs. We modeled the transfer function of ABP and [HbT] in terms of effective arterial (K(a)) and venous (K(v)) compliances, and a cerebral autoregulation time constant (τ(AR)). The mean values (± standard errors) of these parameters across the twenty-two subjects were K(a) = 0.01 ± 0.01 μM/mmHg, K(v) = 0.09 ± 0.05 μM/mmHg, and τ(AR) = 2.2 ± 1.3 s. Spatially resolved measurements in a subset of eight subjects reveal a spatial variability of these parameters that may exceed the inter-subject variability at a set location. This study sheds some light onto the role that ABP and cerebral blood flow (CBF) play in the dynamics of [HbT] measured with NIRS, and paves the way for new non-invasive optical studies of cerebral blood flow and cerebral autoregulation.

Continuous monitoring of cerebrovascular reactivity through pulse transit time and intracranial pressure

OBJECTIVE

Cerebrovascular reactivity (CR) is a mechanism that maintains stable blood flow supply to the brain. Pressure reactivity index (PRx), the correlation coefficient between slow waves of invasive arterial blood pressure (ABP) and intracranial pressure (ICP) has been validated for CR assessment. However, in clinical ward, not every subarachnoid hemorrhage (SAH) patient has invasive ABP monitoring. Pulse transit time (PTT), the propagation time of a pulse wave travelling from the heart to peripheral arteries, has been suggested as a surrogate measure of ABP. In this study, we proposed to use PTT instead of invasive ABP to monitor CR.

APPROACH

Forty-five SAH patients with simultaneous recordings of invasive ABP, ICP, oxygen saturation level (SpO2) and electrocardiograph (ECG) were included. PTT was calculated as the time from the ECG R-wave peak to the onset of SpO2. PTT based pressure reactivity index (tPRx) was calculated as the correlation coefficient between slow waves of PTT and ICP. Wavelet tPRx (wtRx) was calculated as the cosine of wavelet phase shift between PTT and ICP. Meanwhile, PRx and wPRx were also calculated using invasive ABP and ICP as input.

MAIN RESULTS

The result showed a negative relationship between PTT and ABP (r  =  -0.58, p   <  0.001). tPRx negatively correlated with PRx (r  =  -0.51, p   =  0.003). Wavelet method correlated well with correlation method demonstrated through positive relationship between wPRx and PRx (r  =  0.82, p   <  0.001) as well as wtPRx and tPRx (r  =  0.84, p   <  0.001).

SIGNIFICANCE

PTT demonstrates great potential as a useful tool for CR assessment when invasive ABP is unavailable. Key points • Pulse transit time (PTT), defined as the propagation time of a pulse wave travelling from the heart to the peripheral arteries, has been proposed as a surrogate measure of ABP. The relationship between PTT and ABP in SAH patients remains unknown. • Cerebrovascular reactivity (CR) assessment through PTT has advantages over invasive ABP, as it avoids bleeding and infection risk, and can be used outside of the ICU. • We introduced a new method to assess CR using PTT and ICP through correlation based method and wavelet based method. • We found that beat-to-beat PTT was negatively related with invasive ABP in SAH patients. A significant linear relationship exists between PTT-based CR parameter and a well validated method, PRx. PTT demonstrates great potential as a useful tool for CR assessment when invasive ABP is unavailable in SAH patients.

The meaning of "coherent" and its quantification in coherent hemodynamics spectroscopy

We have recently introduced a new technique, coherent hemodynamics spectroscopy (CHS), which aims at characterizing a specific kind of tissue hemodynamics that feature a high level of covariation with a given physiological quantity. In this study, we carry out a detailed analysis of the significance of coherence and phase synchronization between oscillations of arterial blood pressure (ABP) and total hemoglobin concentration ([Hbt]), measured with near-infrared spectroscopy (NIRS) during a typical protocol for CHS, based on a cyclic thigh cuff occlusion and release. Even though CHS is based on a linear time invariant model between ABP (input) and NIRS measurands (outputs), for practical reasons in a typical CHS protocol, we induce finite "groups" of ABP oscillations, in which each group is characterized by a different frequency. For this reason, ABP (input) and NIRS measurands (output) are not stationary processes, and we have used wavelet coherence and phase synchronization index (PSI), as a metric of coherence and phase synchronization, respectively. PSI was calculated by using both the wavelet cross spectrum and the Hilbert transform. We have also used linear coherence (which requires stationary process) for comparison with wavelet coherence. The method of surrogate data is used to find critical values for the significance of covariation between ABP and [Hbt]. Because we have found similar critical values for wavelet coherence and PSI by using five of the most used methods of surrogate data, we propose to use the data-independent Gaussian random numbers (GRNs), for CHS. By using wavelet coherence and wavelet cross spectrum, and GRNs as surrogate data, we have found the same results for the significance of coherence and phase synchronization between ABP and [Hbt]: on a total set of 20 periods of cuff oscillations, we have found 17 coherent oscillations and 17 phase synchronous oscillations. Phase synchronization assessed with Hilbert transform yielded similar results with 14 phase synchronous oscillations. Linear coherence and wavelet coherence overall yielded similar number of significant values. We discuss possible reasons for this result. Despite the similarity of linear and wavelet coherence, we argue that wavelet coherence is preferable, especially if one wants to use baseline spontaneous oscillations, in which phase locking and coherence between signals might be only temporary.

Continuous wavelet transform in the study of the time-scale properties of intracranial pressure in hydrocephalus

Normal pressure hydrocephalus (NPH) encompasses a heterogeneous group of disorders generally characterized by clinical symptoms, ventriculomegaly and anomalous cerebrospinal fluid (CSF) dynamics. Lumbar infusion tests (ITs) are frequently performed in the preoperatory evaluation of patients who show NPH features. The analysis of intracranial pressure (ICP) signals recorded during ITs could be useful to better understand the pathophysiology underlying NPH and to assist treatment decisions. In this study, 131 ICP signals recorded during ITs were analysed using two continuous wavelet transform (CWT)-derived parameters: Jensen divergence (JD) and spectral flux (SF). These parameters were studied in two frequency bands, associated with different components of the signal: B₁(0.15-0.3 Hz), related to respiratory blood pressure oscillations; and B₂ (0.67-2.5 Hz), related to ICP pulse waves. Statistically significant differences (p < 1.70 × 10^-3, Bonferroni-corrected Wilcoxon signed-rank tests) in pairwise comparisons between phases of ITs were found using the mean and standard deviation of JD and SF. These differences were mainly found in B₂, where a lower irregularity and variability, together with less prominent time-frequency fluctuations, were found in the hypertension phase of ITs. Our results suggest that wavelet analysis could be useful for understanding CSF dynamics in NPH.This article is part of the theme issue 'Redundancy rules: the continuous wavelet transform comes of age'.

Wavelet pressure reactivity index: a validation study

KEY POINTS

The brain is vulnerable to damage from too little or too much blood flow. A physiological mechanism termed cerebral autoregulation (CA) exists to maintain stable blood flow even if cerebral perfusion pressure (CPP) is changing. A robust method for assessing CA is not yet available. There are still some problems with the traditional measure, the pressure reactivity index (PRx). We introduce a new method, the wavelet transform method (wPRx), to assess CA using data from two sets of controlled hypotension experiments in piglets: one set had artificially manipulated arterial blood pressure (ABP) oscillations; the other group were spontaneous ABP waves. A significant linear relationship was found between wPRx and PRx in both groups, with wPRx providing a more stable result for the spontaneous waves. Although both methods showed similar accuracy in distinguishing intact and impaired CA, it seems that wPRx tends to perform better than PRx, although not significantly so.

ABSTRACT

We present a novel method to monitor cerebral autoregulation (CA) using the wavelet transform (WT). The new method is validated against the pressure reactivity index (PRx) in two piglet experiments with controlled hypotension. The first experiment (n = 12) had controlled haemorrhage with artificial stationary arterial blood pressure (ABP) and intracranial pressure (ICP) oscillations induced by sinusoidal slow changes in positive end-expiratory pressure ('PEEP group'). The second experiment (n = 17) had venous balloon inflation during spontaneous, non-stationary ABP and ICP oscillations ('non-PEEP group'). The wavelet transform phase shift (WTP) between ABP and ICP was calculated in the frequency range 0.0067-0.05 Hz. Wavelet semblance, the cosine of WTP, was used to make the values comparable to PRx, and the new index was termed wavelet pressure reactivity index (wPRx). The traditional PRx, the running correlation coefficient between ABP and ICP, was calculated. The result showed a significant linear relationship between wPRx and PRx in the PEEP group (R = 0.88) and non-PEEP group (R = 0.56). In the non-PEEP group, wPRx showed better performance than PRx in distinguishing cerebral perfusion pressure (CPP) above and below the lower limit of autoregulation (LLA). When CPP was decreased below LLA, wPRx increased from 0.43 ± 0.28 to 0.69 ± 0.12 (P = 0.003) while PRx increased from 0.07 ± 0.21 to 0.27 ± 0.37 (P = 0.04). Moreover, wPRx provided a more stable result than PRx (SD of PRx was 0.40 ± 0.07, and SD of wPRx was 0.28 ± 0.11, P = 0.001). Assessment of CA using wavelet-derived phase shift between ABP and ICP is feasible.

Alterations in the coupling functions between cerebral oxyhaemoglobin and arterial blood pressure signals in post-stroke subjects

Cerebral autoregulation (CA) is the complex homeostatic regulatory relationship between blood pressure (BP) and cerebral blood flow (CBF). This study aimed to analyze the frequency-specific coupling function between cerebral oxyhemoglobin concentrations (delta [HbO₂]) and mean arterial pressure (MAP) signals based on a model of coupled phase oscillators and dynamical Bayesian inference. Delta [HbO₂] was measured by 24-channel near-infrared spectroscopy (NIRS) and arterial BP signals were obtained by simultaneous resting-state measurements in patients with stroke, that is, 9 with left hemiparesis (L–H group), 8 with right hemiparesis (R–H group), and 17 age-matched healthy individuals as control (healthy group). The coupling functions from MAP to delta [HbO₂] oscillators were identified and analyzed in four frequency intervals (I, 0.6–2 Hz; II, 0.145–0.6 Hz; III, 0.052–0.145 Hz; and IV, 0.021–0.052 Hz). In L–H group, the CS from MAP to delta [HbO₂] in interval III in channel 8 was significantly higher than that in healthy group (p = 0.003). Compared with the healthy controls, the coupling in MAP→delta [HbO₂] showed higher amplitude in interval I and IV in patients with stroke. The increased CS and coupling amplitude may be an evidence of impairment in CA, thereby confirming the presence of impaired CA in patients with stroke. In interval III, the CS in L–H group from MAP to delta [HbO₂] in channel 16 (p = 0.001) was significantly lower than that in healthy controls, which might indicate the compensatory mechanism in CA of the unaffected side in patients with stroke. No significant difference in region-wise CS between affected and unaffected sides was observed in stroke groups, indicating an evidence of globally impaired CA. These findings provide a method for the assessment of CA and will contribute to the development of therapeutic interventions in stroke patients.

Dynamic cerebral autoregulation is preserved during isometric handgrip and head-down tilt in healthy volunteers

In healthy humans, cerebral blood flow (CBF) is autoregulated against changes in arterial blood pressure. Spontaneous fluctuations in mean arterial pressure (MAP) and CBF can be used to assess cerebral autoregulation. We hypothesized that dynamic cerebral autoregulation is affected by changes in autonomic activity, MAP, and cardiac output (CO) induced by handgrip (HG), head‐down tilt (HDT), and their combination. In thirteen healthy volunteers, we recorded blood velocity by ultrasound in the internal carotid artery (ICA), HR, MAP and CO‐estimates from continuous finger blood pressure, and end‐tidal CO₂. Instantaneous ICA beat volume (ICABV, mL) and ICA blood flow (ICABF, mL/min) were calculated. Wavelet synchronization index γ (0–1) was calculated for the pairs: MAP–ICABF, CO–ICABF and HR–ICABV in the low (0.05–0.15 Hz; LF) and high (0.15–0.4 Hz; HF) frequency bands. ICABF did not change between experimental states. MAP and CO were increased during HG (+16% and +15%, respectively, P < 0.001) and during HDT + HG (+12% and +23%, respectively, P < 0.001). In the LF interval, median γ for the MAP–ICABF pair (baseline: 0.23 [0.12–0.28]) and the CO–ICABF pair (baseline: 0.22 [0.15–0.28]) did not change with HG, HDT, or their combination. High γ was observed for the HR–ICABV pair at the respiratory frequency, the oscillations in these variables being in inverse phase. The unaltered ICABF and the low synchronization between MAP and ICABF in the LF interval suggest intact dynamic cerebral autoregulation during HG, HDT, and their combination.

Autoregulation in paediatric TBI-current evidence and implications for treatment

BACKGROUND

Children who survive acute traumatic brain injury are at risk of death from subsequent brain swelling and secondary injury. Strict physiologic management in the ICU after traumatic brain injury is believed to be key to survival, and cerebral perfusion pressure is a prominent aspect of post brain injury care. However, optimal cerebral perfusion pressure targets for children are not known. Autoregulation monitoring has been used to delineate individualized optimal perfusion pressures for patients with traumatic brain injury. The methods to do so are diverse, confusing, and not universally validated.

METHODS

In this manuscript, we discuss the history of autoregulation monitoring, outline and categorize the methods used to measure autoregulation, and review the available validation data for methods used to monitor autoregulation.

CONCLUSIONS

Impaired autoregulation after traumatic brain injury is associated with a poor prognosis. Observational data suggests that optimal neurologic outcome and survival are associated with optimal perfusion pressure defined by autoregulation monitoring. No randomized, controlled, interventional data is available to assess autoregulation monitoring after pediatric traumatic brain injury.

Calibration transfer of near-infrared spectroscopy by canonical correlation analysis coupled with wavelet transform

Calibration model transfer has played a prominent role in the practical application of NIR spectral analysis. The change of instruments and sample physical states may lead to variation of the NIR spectrum, which results in the applicability of the model in judicatory practice being unsatisfactory. Therefore, a transfer for the calibration model considering both the variation of instruments and sample states is a necessity to ensure its availability. In this paper, a novel approach, namely canonical correlation analysis coupled with wavelet transform (WTCCA), was proposed for calibration transfer between two near infrared spectrometers (a portable and a laboratory instrument), and simultaneously, among three physical states (tobacco powder, tobacco filament and intact leaf) to determine the content of total sugars, reducing sugars, and nicotine in tobacco leaf samples, respectively. Wavelet transform (WT) is introduced to reduce noise and deduct background shifts from the spectra by compression, and then, calibration transfer by canonical correlation analysis (CTCCA) extracts the compressed spectral similarities using canonical scores for spectra correction. Three similar standardization algorithms, including piecewise direct standardization (PDS), piecewise direct standardization with wavelet transform (WTPDS), and CTCCA were compared with WTCCA to evaluate its relative performance. The obtained results showed that the employment of WTCCA yielded the lowest root mean standard error of prediction (RMSEP) on the three analytes in three physical states. For the tobacco powder dataset, the RMSEP values had a reduction of 25.83%, 13.96%, and 14.22% compared with the values of direct prediction without spectra transfer, respectively. For the tobacco filament dataset, the corresponding values were decreased by 18.06%, 14.90%, and 13.61% and for the intact leaf dataset, the values had dropped by 10.70%, 18.21%, and 28.21%, respectively. In summary, the comprehensive investigation carried out in the present work shows that WTCCA is very appropriate for correcting the variations caused by the change of machines and sample states. Furthermore, WTCCA is a promising calibration transfer method which can be recommended for on-line/in-line application.

Bifurcation in Blood Oscillatory Rhythms for Patients with Ischemic Stroke: A Small Scale Clinical Trial using Laser Doppler Flowmetry and Computational Modeling of Vasomotion

We describe application of spectral analysis of laser Doppler flowmetry (LDF) signals to investigation of cerebrovascular haemodynamics in patients with post-acute ischemic stroke (AIS) and cerebrovascular insufficiency. LDF was performed from 3 to 7 days after the onset of AIS on forehead in the right and left supraorbital regions in patients. Analysis of LDF signals showed that perfusion in the microvasculature in AIS patients was lower than that in patients with cerebrovascular insufficiency. As a result of wavelet analysis of the LDF signals we obtained activation of the vasomotion in the frequency range of myogenic oscillation of 0.1 Hz and predominantly nutritive regime microcirculation after systemic thrombolytic therapy of the AIS patients. In case of significant stroke size, myogenic activity, and nutritive pattern microhaemodynamics were reduced, in some cases non-nutritive pattern and/or venular stasis was revealed. Wavelet analysis of the LDF signals also showed asymmetry in wavelet spectra of the LDF signals obtained in stroke-affected and unaffected hemispheres in the AIS patients. A mechanism underlying the observed asymmetry was analyzed by computational modeling of vasomotion developed in Arciero and Secomb (2012). We applied this model to describe relaxation oscillation of arteriole diameter which is forced by myogenic oscillation induced by synchronous calcium oscillation in vascular smooth muscle cells. Calculation showed that vasomotion frequency spectrum at the low-frequency range (0.01 Hz) is reciprocally modulated by myogenic oscillation (0.1 Hz) that correlates with experimental observation of inter-hemispheric variation in the LDF spectrum.

Fast detection and data compensation for electrodes disconnection in long-term monitoring of dynamic brain electrical impedance tomography

Background

Electrode disconnection is a common occurrence during long-term monitoring of brain electrical impedance tomography (EIT) in clinical settings. The data acquisition system suffers remarkable data loss which results in image reconstruction failure. The aim of this study was to: (1) detect disconnected electrodes and (2) account for invalid data.

Methods

Weighted correlation coefficient for each electrode was calculated based on the measurement differences between well-connected and disconnected electrodes. Disconnected electrodes were identified by filtering out abnormal coefficients with discrete wavelet transforms. Further, previously valid measurements were utilized to establish grey model. The invalid frames after electrode disconnection were substituted with the data estimated by grey model. The proposed approach was evaluated on resistor phantom and with eight patients in clinical settings.

Results

The proposed method was able to detect 1 or 2 disconnected electrodes with an accuracy of 100%; to detect 3 and 4 disconnected electrodes with accuracy of 92 and 84% respectively. The time cost of electrode detection was within 0.018 s. Further, the proposed method was capable to compensate at least 60 subsequent frames of data and restore the normal image reconstruction within 0.4 s and with a mean relative error smaller than 0.01%.

Conclusions

In this paper, we proposed a two-step approach to detect multiple disconnected electrodes and to compensate the invalid frames of data after disconnection. Our method is capable of detecting more disconnected electrodes with higher accuracy compared to methods proposed in previous studies. Further, our method provides estimations during the faulty measurement period until the medical staff reconnects the electrodes. This work would improve the clinical practicability of dynamic brain EIT and contribute to its further promotion.

Effect of infusion tests on the dynamical properties of intracranial pressure in hydrocephalus

BACKGROUND AND OBJECTIVE

Hydrocephalus comprises a number of conditions characterised by clinical symptoms, dilated ventricles and anomalous cerebrospinal fluid (CSF) dynamics. Infusion tests (ITs) are usually performed to study CSF circulation and in the preoperatory evaluation of patients with hydrocephalus. The study of intracranial pressure (ICP) signals recorded during ITs could be useful to gain insight into the underlying pathophysiology of this condition and to further support treatment decisions. In this study, two wavelet parameters, wavelet turbulence (WT) and wavelet entropy (WE), were analysed in order to characterise the variability, irregularity and similarity in spectral content of ICP signals in hydrocephalus.

METHODS

One hundred and twelve ICP signals were analysed using WT and WE. These parameters were calculated in two frequency bands: B1 (0.15-0.3 Hz) and B2 (0.67-2.5 Hz). Each signal was divided into four artefact-free epochs corresponding to the basal, early infusion, plateau and recovery phases of the IT. We calculated the mean and standard deviation of WT and WE and analysed whether these parameters revealed differences between epochs of the IT.

RESULTS

Statistically significant differences (p < 1.70⋅10(-3), Bonferroni-corrected Wilcoxon signed-rank tests) in pairwise comparisons between phases of ITs were found using the mean and standard deviation of WT and WE. These differences were mainly found in B2.

CONCLUSIONS

Wavelet parameters like WT and WE revealed changes in the signal time-scale representation during ITs. Statistically significant differences were mainly found in B2, associated with ICP pulse waves, and included a higher degree of similarity in the spectral content, together with a lower irregularity and variability in the plateau phase with respect to the basal phase.

Identifying stable phase coupling associated with cerebral autoregulation using the synchrosqueezed cross-wavelet transform and low oscillation morlet wavelets

A novel method of identifying stable phase coupling behavior of two signals within the wavelet transform time-frequency plane is presented. The technique employs the cross-wavelet transform to provide a map of phase coupling followed by synchrosqueezing to collect the stable phase regime information. The resulting synchrosqueezed cross-wavelet transform method (Synchro-CrWT) is illustrated using a synthetic signal and then applied to the analysis of the relationship between biosignals used in the analysis of cerebral autoregulation function.

Modular continuous wavelet processing of biosignals: extracting heart rate and oxygen saturation from a video signal

A novel method of extracting heart rate and oxygen saturation from a video-based biosignal is described. The method comprises a novel modular continuous wavelet transform approach which includes: performing the transform, undertaking running wavelet archetyping to enhance the pulse information, extraction of the pulse ridge time-frequency information [and thus a heart rate (HRvid) signal], creation of a wavelet ratio surface, projection of the pulse ridge onto the ratio surface to determine the ratio of ratios from which a saturation trending signal is derived, and calibrating this signal to provide an absolute saturation signal (SvidO2). The method is illustrated through its application to a video photoplethysmogram acquired during a porcine model of acute desaturation. The modular continuous wavelet transform-based approach is advocated by the author as a powerful methodology to deal with noisy, non-stationary biosignals in general.