A nonlinear dynamic approach reveals a long-term stroke effect on cerebral blood flow regulation at multiple time scales

Exploring neurovascular coupling in stroke patients: insights on linear and nonlinear dynamics using transfer entropy

Objective.The study of neurovascular coupling (NVC), the relationship between neuronal activity and cerebral blood flow, is essential for understanding brain physiology in both healthy and pathological states. Current methods to study NVC include neuroimaging techniques with limited temporal resolution and indirect neuronal activity measures. Methods including electroencephalographic (EEG) data are predominantly linear and display limitations that nonlinear methods address. Transfer entropy (TE) explores linear and nonlinear relationships simultaneously. This study hypothesizes that complex NVC interactions in stroke patients, both linear and nonlinear, can be detected using TE.Approach.TE between simultaneously recorded EEG and cerebral blood flow velocity (CBFV) signals was computed and analyzed in three settings: ipsilateral (EEG and CBFV from same hemisphere) stroke and nonstroke, and contralateral (EEG from stroke hemisphere, CBFV from nonstroke hemisphere). A surrogate analysis was performed to evaluate the significance of TE values and to identify the nature of the interactions.Main results.The results showed that EEG generally influenced CBFV. There were more linear+nonlinear interactions in the ipsilateral nonstroke setting and in the delta band in ipsilateral stroke and contralateral settings. Interactions between EEG and CBFV were stronger on the nonstroke side for linear+nonlinear dynamics. The strength and nature of the interactions were weakly correlated with clinical outcomes (e.g. delta band (p<0.05): infarct growth linear = -0.448, linear+nonlinear = -0.339; NIHSS linear = -0.473, linear+nonlinear = -0.457).Significance.This study exemplifies the benefits of using TE in linear and nonlinear NVC analysis to better understand the implications of these dynamics in stroke severity.

Time-domain methods for quantifying dynamic cerebral blood flow autoregulation: Review and recommendations. A white paper from the Cerebrovascular Research Network (CARNet)

Cerebral Autoregulation (CA) is an important physiological mechanism stabilizing cerebral blood flow (CBF) in response to changes in cerebral perfusion pressure (CPP). By maintaining an adequate, relatively constant supply of blood flow, CA plays a critical role in brain function. Quantifying CA under different physiological and pathological states is crucial for understanding its implications. This knowledge may serve as a foundation for informed clinical decision-making, particularly in cases where CA may become impaired. The quantification of CA functionality typically involves constructing models that capture the relationship between CPP (or arterial blood pressure) and experimental measures of CBF. Besides describing normal CA function, these models provide a means to detect possible deviations from the latter. In this context, a recent white paper from the Cerebrovascular Research Network focused on Transfer Function Analysis (TFA), which obtains frequency domain estimates of dynamic CA. In the present paper, we consider the use of time-domain techniques as an alternative approach. Due to their increased flexibility, time-domain methods enable the mitigation of measurement/physiological noise and the incorporation of nonlinearities and time variations in CA dynamics. Here, we provide practical recommendations and guidelines to support researchers and clinicians in effectively utilizing these techniques to study CA.

Lower middle cerebral artery blood velocity during low-volume high-intensity interval exercise in chronic stroke

High-intensity interval training (HIIE) may present unique challenges to the cerebrovascular system in individuals post-stroke. We hypothesized lower middle cerebral artery blood velocity (MCAv) in individuals post-stroke: 1) during 10 minutes of HIIE, 2) immediately following HIIE, and 3) 30 minutes after HIIE, compared to age- and sex-matched controls (CON). We used a recumbent stepper submaximal exercise test to determine workloads for high-intensity and active recovery. Our low volume HIIE protocol consisted of 1-minute intervals for 10 minutes. During HIIE, we measured MCAv, mean arterial pressure (MAP), heart rate (HR), and end tidal carbon dioxide (PETCO2). We assessed carotid-femoral pulse wave velocity as a measure of arterial stiffness. Fifty participants completed the study (25 post-stroke, 76% ischemic, 32% moderate disability). Individuals post-stroke had lower MCAv during HIIE compared to CON (p = 0.03), which remained 30 minutes after HIIE. Individuals post-stroke had greater arterial stiffness (p = 0.01) which was moderately associated with a smaller MCAv responsiveness during HIIE (r = -0.44). No differences were found for MAP, HR, and PETCO2. This study suggests individuals post-stroke had a lower MCAv during HIIE compared to their peers, which remained during recovery up to 30 minutes. Arterial stiffness may contribute to the lower cerebrovascular responsiveness post-stroke.

Time-Series Modeling and Forecasting of Cerebral Pressure-Flow Physiology: A Scoping Systematic Review of the Human and Animal Literature

The modeling and forecasting of cerebral pressure-flow dynamics in the time-frequency domain have promising implications for veterinary and human life sciences research, enhancing clinical care by predicting cerebral blood flow (CBF)/perfusion, nutrient delivery, and intracranial pressure (ICP)/compliance behavior in advance. Despite its potential, the literature lacks coherence regarding the optimal model type, structure, data streams, and performance. This systematic scoping review comprehensively examines the current landscape of cerebral physiological time-series modeling and forecasting. It focuses on temporally resolved cerebral pressure-flow and oxygen delivery data streams obtained from invasive/non-invasive cerebral sensors. A thorough search of databases identified 88 studies for evaluation, covering diverse cerebral physiologic signals from healthy volunteers, patients with various conditions, and animal subjects. Methodologies range from traditional statistical time-series analysis to innovative machine learning algorithms. A total of 30 studies in healthy cohorts and 23 studies in patient cohorts with traumatic brain injury (TBI) concentrated on modeling CBFv and predicting ICP, respectively. Animal studies exclusively analyzed CBF/CBFv. Of the 88 studies, 65 predominantly used traditional statistical time-series analysis, with transfer function analysis (TFA), wavelet analysis, and autoregressive (AR) models being prominent. Among machine learning algorithms, support vector machine (SVM) was widely utilized, and decision trees showed promise, especially in ICP prediction. Nonlinear models and multi-input models were prevalent, emphasizing the significance of multivariate modeling and forecasting. This review clarifies knowledge gaps and sets the stage for future research to advance cerebral physiologic signal analysis, benefiting neurocritical care applications.

NONAN GaitPrint: An IMU gait database of healthy young adults

An ongoing thrust of research focused on human gait pertains to identifying individuals based on gait patterns. However, no existing gait database supports modeling efforts to assess gait patterns unique to individuals. Hence, we introduce the Nonlinear Analysis Core (NONAN) GaitPrint database containing whole body kinematics and foot placement during self-paced overground walking on a 200-meter looping indoor track. Noraxon Ultium MotionTM inertial measurement unit (IMU) sensors sampled the motion of 35 healthy young adults (19-35 years old; 18 men and 17 women; mean ± 1 s.d. age: 24.6 ± 2.7 years; height: 1.73 ± 0.78 m; body mass: 72.44 ± 15.04 kg) over 18 4-min trials across two days. Continuous variables include acceleration, velocity, position, and the acceleration, velocity, position, orientation, and rotational velocity of each corresponding body segment, and the angle of each respective joint. The discrete variables include an exhaustive set of gait parameters derived from the spatiotemporal dynamics of foot placement. We technically validate our data using continuous relative phase, Lyapunov exponent, and Hurst exponent-nonlinear metrics quantifying different aspects of healthy human gait.

Daily rhythm of dynamic cerebral autoregulation in patients after stroke

Dynamic cerebral autoregulation (dCA) in healthy young adults displays a daily variation. Whether the rhythm exists in patients with stroke is unknown. We studied 28 stroke patients (age: 26-83 years, 7 females) within 48 hours after thrombolysis. dCA was assessed 54 times in these patients during supine rest (twice in 26 and once in 2 patients): 9 assessments between 0-9AM, 12 between 9AM-2PM, 20 between 2-7PM, and 13 between 7PM-12AM. To estimate dCA, phase shifts between spontaneous oscillations of cerebral blood flow velocity (CBFV) in the middle cerebral artery and arterial blood pressure (BP) were obtained in four frequency bands: <0.05 Hz, 0.05-0.1 Hz, 0.1-0.2 Hz, and >0.2 Hz. CBFV-BP phase shifts at <0.05 Hz were significantly larger between 2-7PM, suggesting better dCA, than those at other times (p < 0.0001), and the daily rhythm was consistent for stroke and non-stroke sides. No significant rhythms were observed at higher frequencies (all p > 0.2). All results were independent of age, sex, stroke type and severity, and other cardiovascular conditions. dCA after stroke showed a daily rhythm, leading to a better regulation of CBFV at <0.05 Hz during the afternoon. The finding may have implications for daily activity management of stroke patients.

Machine Learning Models and Statistical Complexity to Analyze the Effects of Posture on Cerebral Hemodynamics

The mechanism of cerebral blood flow autoregulation can be of great importance in diagnosing and controlling a diversity of cerebrovascular pathologies such as vascular dementia, brain injury, and neurodegenerative diseases. To assess it, there are several methods that use changing postures, such as sit-stand or squat-stand maneuvers. However, the evaluation of the dynamic cerebral blood flow autoregulation (dCA) in these postures has not been adequately studied using more complex models, such as non-linear ones. Moreover, dCA can be considered part of a more complex mechanism called cerebral hemodynamics, where others (CO2 reactivity and neurovascular-coupling) that affect cerebral blood flow (BF) are included. In this work, we analyzed postural influences using non-linear machine learning models of dCA and studied characteristics of cerebral hemodynamics under statistical complexity using eighteen young adult subjects, aged 27 ± 6.29 years, who took the systemic or arterial blood pressure (BP) and cerebral blood flow velocity (BFV) for five minutes in three different postures: stand, sit, and lay. With models of a Support Vector Machine (SVM) through time, we used an AutoRegulatory Index (ARI) to compare the dCA in different postures. Using wavelet entropy, we estimated the statistical complexity of BFV for three postures. Repeated measures ANOVA showed that only the complexity of lay-sit had significant differences.

Regulation of cerebral blood flow in humans: physiology and clinical implications of autoregulation

Brain function critically depends on a close matching between metabolic demands, appropriate delivery of oxygen and nutrients, and removal of cellular waste. This matching requires continuous regulation of cerebral blood flow (CBF), which can be categorized into four broad topics: 1) autoregulation, which describes the response of the cerebrovasculature to changes in perfusion pressure; 2) vascular reactivity to vasoactive stimuli [including carbon dioxide (CO2)]; 3) neurovascular coupling (NVC), i.e., the CBF response to local changes in neural activity (often standardized cognitive stimuli in humans); and 4) endothelium-dependent responses. This review focuses primarily on autoregulation and its clinical implications. To place autoregulation in a more precise context, and to better understand integrated approaches in the cerebral circulation, we also briefly address reactivity to CO2 and NVC. In addition to our focus on effects of perfusion pressure (or blood pressure), we describe the impact of select stimuli on regulation of CBF (i.e., arterial blood gases, cerebral metabolism, neural mechanisms, and specific vascular cells), the interrelationships between these stimuli, and implications for regulation of CBF at the level of large arteries and the microcirculation. We review clinical implications of autoregulation in aging, hypertension, stroke, mild cognitive impairment, anesthesia, and dementias. Finally, we discuss autoregulation in the context of common daily physiological challenges, including changes in posture (e.g., orthostatic hypotension, syncope) and physical activity.

Time-evolving coupling functions for evaluating the interaction between cerebral oxyhemoglobin and arterial blood pressure with hypertension

PURPOSES

This study aimed to investigate the network coupling between arterial blood pressure (ABP) and changes in cerebral oxyhemoglobin concentration (Δ [O₂ Hb]/Δ [HHb]) oscillations based on dynamical Bayesian inference in hypertensive subjects.

METHODS

Two groups of subjects, consisting of 30 healthy (Group Control, 55.1 ± 10.6 y), and 32 hypertensive individuals (Group AH, 58.9 ± 8.7 y), participated in this study. A functional near-infrared spectroscopy system was used to measure the Δ [O₂ Hb] and Δ [HHb] signals in the bilateral prefrontal cortex (LPFC/RPFC), motor cortex (LMC/RMC), and occipital lobe (LOL/ROL) during the resting state (12 min). Based on continuous wavelet analysis and coupling functions, the directed coupling strength (CS) between ABP and cerebral hemoglobin was identified and analyzed in three frequency intervals (I: 0.6-2 Hz, II: 0.145-0.6 Hz, III: 0.01-0.08 Hz). The Pearson correlations between the CS and blood pressure parameters were calculated in the hypertension group.

RESULTS

In interval I, Group AH exhibited a significantly higher CS for the coupling from ABP to Δ [O₂ Hb] than Group Control in LMC, RMC, LOL, and ROL. In interval III, the CS from ABP to Δ [O₂ Hb] in LPFC, RPFC, LMC, RMC, LOL, and ROL was significantly higher in Group AH than in Group Control. For the patients with hypertension, diastolic blood pressure was negatively and pulse pressure was positively related to the CS from ABP to Δ [O₂ Hb] oscillations in interval III.

CONCLUSIONS

The higher CS from ABP to Δ [O₂ Hb] in interval I indicated that the components of cardiac activity in cerebral hemoglobin oscillations were more directly responsive to the changes in systematic ABP in patients with hypertension than in healthy subjects. Meanwhile, the higher CS from ABP to Δ [O₂ Hb] in interval III indicated that the cerebral hemoglobin oscillations were susceptible to changes in blood pressure in hypertensive subjects. The results may serve as evidence of impairment in cerebral autoregulation after hypertension. The Pearson correlation results showed that diastolic blood pressure and pulse pressure might be regarded as predictors of cerebral autoregulation function in patients with hypertension, and may be useful for hypertension stratification. This study provides novel insights into the interaction mechanism between ABP and cerebral hemodynamics and could help in the development of new assessment techniques for cerebral vascular disease.

New insights and best practices for the successful use of Empirical Mode Decomposition, Iterative Filtering and derived algorithms

Algorithms based on Empirical Mode Decomposition (EMD) and Iterative Filtering (IF) are largely implemented for representing a signal as superposition of simpler well-behaved components called Intrinsic Mode Functions (IMFs). Although they are more suitable than traditional methods for the analysis of nonlinear and nonstationary signals, they could be easily misused if their known limitations, together with the assumptions they rely on, are not carefully considered. In this work, we examine the main pitfalls and provide caveats for the proper use of the EMD- and IF-based algorithms. Specifically, we address the problems related to boundary errors, to the presence of spikes or jumps in the signal and to the decomposition of highly-stochastic signals. The consequences of an improper usage of these techniques are discussed and clarified also by analysing real data and performing numerical simulations. Finally, we provide the reader with the best practices to maximize the quality and meaningfulness of the decomposition produced by these techniques. In particular, a technique for the extension of signal to reduce the boundary effects is proposed; a careful handling of spikes and jumps in the signal is suggested; the concept of multi-scale statistical analysis is presented to treat highly stochastic signals.

Causal decomposition in the mutual causation system

Inference of causality in time series has been principally based on the prediction paradigm. Nonetheless, the predictive causality approach may underestimate the simultaneous and reciprocal nature of causal interactions observed in real-world phenomena. Here, we present a causal-decomposition approach that is not based on prediction, but based on the covariation of cause and effect: cause is that which put, the effect follows; and removed, the effect is removed. Using empirical mode decomposition, we show that causal interaction is encoded in instantaneous phase dependency at a specific time scale, and this phase dependency is diminished when the causal-related intrinsic component is removed from the effect. Furthermore, we demonstrate the generic applicability of our method to both stochastic and deterministic systems, and show the consistency of causal-decomposition method compared to existing methods, and finally uncover the key mode of causal interactions in both modelled and actual predator–prey systems.

Causality inference in time series analysis based on temporal precedence principle between cause and effect fails to detect mutual causal interactions. Here, Yang et al. introduce a causal decomposition approach based on the covariation principle of cause and effect that overcomes this limitation.

Improving forecasting accuracy for stock market data using EMD-HW bagging

Many researchers documented that the stock market data are nonstationary and nonlinear time series data. In this study, we use EMD-HW bagging method for nonstationary and nonlinear time series forecasting. The EMD-HW bagging method is based on the empirical mode decomposition (EMD), the moving block bootstrap and the Holt-Winter. The stock market time series of six countries are used to compare EMD-HW bagging method. This comparison is based on five forecasting error measurements. The comparison shows that the forecasting results of EMD-HW bagging are more accurate than the forecasting results of the fourteen selected methods.

Non-linear models for the detection of impaired cerebral blood flow autoregulation

The ability to discriminate between normal and impaired dynamic cerebral autoregulation (CA), based on measurements of spontaneous fluctuations in arterial blood pressure (BP) and cerebral blood flow (CBF), has considerable clinical relevance. We studied 45 normal subjects at rest and under hypercapnia induced by breathing a mixture of carbon dioxide and air. Non-linear models with BP as input and CBF velocity (CBFV) as output, were implemented with support vector machines (SVM) using separate recordings for learning and validation. Dynamic SVM implementations used either moving average or autoregressive structures. The efficiency of dynamic CA was estimated from the model's derived CBFV response to a step change in BP as an autoregulation index for both linear and non-linear models. Non-linear models with recurrences (autoregressive) showed the best results, with CA indexes of 5.9 ± 1.5 in normocapnia, and 2.5 ± 1.2 for hypercapnia with an area under the receiver-operator curve of 0.955. The high performance achieved by non-linear SVM models to detect deterioration of dynamic CA should encourage further assessment of its applicability to clinical conditions where CA might be impaired.

Transcranial Doppler in autonomic testing: standards and clinical applications

When cerebral blood flow falls below a critical limit, syncope occurs and, if prolonged, ischemia leads to neuronal death. The cerebral circulation has its own complex finely tuned autoregulatory mechanisms to ensure blood supply to the brain can meet the high metabolic demands of the underlying neuronal tissue. This involves the interplay between myogenic and metabolic mechanisms, input from noradrenergic and cholinergic neurons, and the release of vasoactive substrates, including adenosine from astrocytes and nitric oxide from the endothelium. Transcranial Doppler (TCD) is a non-invasive technique that provides real-time measurements of cerebral blood flow velocity. TCD can be very useful in the work-up of a patient with recurrent syncope. Cerebral autoregulatory mechanisms help defend the brain against hypoperfusion when perfusion pressure falls on standing. Syncope occurs when hypotension is severe, and susceptibility increases with hyperventilation, hypocapnia, and cerebral vasoconstriction. Here we review clinical standards for the acquisition and analysis of TCD signals in the autonomic laboratory and the multiple methods available to assess cerebral autoregulation. We also describe the control of cerebral blood flow in autonomic disorders and functional syndromes.

Applying time-frequency analysis to assess cerebral autoregulation during hypercapnia

OBJECTIVE

Classic methods for assessing cerebral autoregulation involve a transfer function analysis performed using the Fourier transform to quantify relationship between fluctuations in arterial blood pressure (ABP) and cerebral blood flow velocity (CBFV). This approach usually assumes the signals and the system to be stationary. Such an presumption is restrictive and may lead to unreliable results. The aim of this study is to present an alternative method that accounts for intrinsic non-stationarity of cerebral autoregulation and the signals used for its assessment.

METHODS

Continuous recording of CBFV, ABP, ECG, and end-tidal CO2 were performed in 50 young volunteers during normocapnia and hypercapnia. Hypercapnia served as a surrogate of the cerebral autoregulation impairment. Fluctuations in ABP, CBFV, and phase shift between them were tested for stationarity using sphericity based test. The Zhao-Atlas-Marks distribution was utilized to estimate the time-frequency coherence (TFCoh) and phase shift (TFPS) between ABP and CBFV in three frequency ranges: 0.02-0.07 Hz (VLF), 0.07-0.20 Hz (LF), and 0.20-0.35 Hz (HF). TFPS was estimated in regions locally validated by statistically justified value of TFCoh. The comparison of TFPS with spectral phase shift determined using transfer function approach was performed.

RESULTS

The hypothesis of stationarity for ABP and CBFV fluctuations and the phase shift was rejected. Reduced TFPS was associated with hypercapnia in the VLF and the LF but not in the HF. Spectral phase shift was also decreased during hypercapnia in the VLF and the LF but increased in the HF. Time-frequency method led to lower dispersion of phase estimates than the spectral method, mainly during normocapnia in the VLF and the LF.

CONCLUSION

The time-frequency method performed no worse than the classic one and yet may offer benefits from lower dispersion of phase shift as well as a more in-depth insight into the dynamic nature of cerebral autoregulation.

Time evolution of interhemispheric coupling in a model of focal neocortical epilepsy in mice

Epilepsy is characterized by substantial network rearrangements leading to spontaneous seizures and little is known on how an epileptogenic focus impacts on neural activity in the contralateral hemisphere. Here, we used a model of unilateral epilepsy induced by injection of the synaptic blocker tetanus neurotoxin (TeNT) in the mouse primary visual cortex (V1). Local field potential (LFP) signals were simultaneously recorded from both hemispheres of each mouse in acute phase (peak of toxin action) and chronic condition (completion of TeNT effects). To characterize the neural electrical activities the corresponding LFP signals were analyzed with several methods of time series analysis. For the epileptic mice, the spectral analysis showed that TeNT determines a power redistribution among the different neurophysiological bands in both acute and chronic phases. Using linear and nonlinear interdependence measures in both time and frequency domains, it was found in the acute phase that TeNT injection promotes a reduction of the interhemispheric coupling for high frequencies (12-30 Hz) and small time lag (<20 ms), whereas an increase of the coupling is present for low frequencies (0.5-4 Hz) and long time lag (>40 ms). On the other hand, the chronic period is characterized by a partial or complete recovery of the interhemispheric interdependence level. Granger causality test and symbolic transfer entropy indicate a greater driving influence of the TeNT-injected side on activity in the contralateral hemisphere in the chronic phase. Lastly, based on experimental observations, we built a computational model of LFPs to investigate the role of the ipsilateral inhibition and exicitatory interhemispheric connections in the dampening of the interhemispheric coupling. The time evolution of the interhemispheric coupling in such a relevant model of epilepsy has been addressed here.

Spurious cross-frequency amplitude-amplitude coupling in nonstationary, nonlinear signals

Recent studies of brain activities show that cross-frequency coupling (CFC) play an important role in memory and learning. Many measures have been proposed to investigate the CFC phenomenon, including the correlation between the amplitude envelopes of two brain waves at different frequencies - cross-frequency amplitude-amplitude coupling (AAC). In this short communication, we describe how nonstationary, nonlinear oscillatory signals may produce spurious cross-frequency AAC. Utilizing the empirical mode decomposition, we also propose a new method for assessment of AAC that can potentially reduce the effects of nonlinearity and nonstatonarity and, thus, help to avoid the detection of artificial AACs. We compare the performances of this new method and the traditional Fourier-based AAC method. We also discuss the strategies to identify potential spurious AACs.

Non-Linear Characterisation of Cerebral Pressure-Flow Dynamics in Humans

Cerebral metabolism is critically dependent on the regulation of cerebral blood flow (CBF), so it would be expected that vascular mechanisms that play a critical role in CBF regulation would be tightly conserved across individuals. However, the relationships between blood pressure (BP) and cerebral blood velocity fluctuations exhibit inter-individual variations consistent with heterogeneity in the integrity of CBF regulating systems. Here we sought to determine the nature and consistency of dynamic cerebral autoregulation (dCA) during the application of oscillatory lower body negative pressure (OLBNP). In 18 volunteers we recorded BP and middle cerebral artery blood flow velocity (MCAv) and examined the relationships between BP and MCAv fluctuations during 0.03, 0.05 and 0.07Hz OLBNP. dCA was characterised using project pursuit regression (PPR) and locally weighted scatterplot smoother (LOWESS) plots. Additionally, we proposed a piecewise regression method to statistically determine the presence of a dCA curve, which was defined as the presence of a restricted autoregulatory plateau shouldered by pressure-passive regions. Results show that LOWESS has similar explanatory power to that of PPR. However, we observed heterogeneous patterns of dynamic BP-MCAv relations with few individuals demonstrating clear evidence of a dCA central plateau. Thus, although BP explains a significant proportion of variance, dCA does not manifest as any single characteristic BP-MCAv function.

Neurovascular regulation in the ischemic brain

SIGNIFICANCE

The brain has high energetic requirements and is therefore highly dependent on adequate cerebral blood supply. To compensate for dangerous fluctuations in cerebral perfusion, the circulation of the brain has evolved intrinsic safeguarding measures.

RECENT ADVANCES AND CRITICAL ISSUES

The vascular network of the brain incorporates a high degree of redundancy, allowing the redirection and redistribution of blood flow in the event of vascular occlusion. Furthermore, active responses such as cerebral autoregulation, which acts to maintain constant cerebral blood flow in response to changing blood pressure, and functional hyperemia, which couples blood supply with synaptic activity, allow the brain to maintain adequate cerebral perfusion in the face of varying supply or demand. In the presence of stroke risk factors, such as hypertension and diabetes, these protective processes are impaired and the susceptibility of the brain to ischemic injury is increased. One potential mechanism for the increased injury is that collateral flow arising from the normally perfused brain and supplying blood flow to the ischemic region is suppressed, resulting in more severe ischemia.

FUTURE DIRECTIONS

Approaches to support collateral flow may ameliorate the outcome of focal cerebral ischemia by rescuing cerebral perfusion in potentially viable regions of the ischemic territory.

Identification of under-detected periodicity in time-series microarray data by using empirical mode decomposition

Detecting periodicity signals from time-series microarray data is commonly used to facilitate the understanding of the critical roles and underlying mechanisms of regulatory transcriptomes. However, time-series microarray data are noisy. How the temporal data structure affects the performance of periodicity detection has remained elusive. We present a novel method based on empirical mode decomposition (EMD) to examine this effect. We applied EMD to a yeast microarray dataset and extracted a series of intrinsic mode function (IMF) oscillations from the time-series data. Our analysis indicated that many periodically expressed genes might have been under-detected in the original analysis because of interference between decomposed IMF oscillations. By validating a protein complex coexpression analysis, we revealed that 56 genes were newly determined as periodic. We demonstrated that EMD can be used incorporating with existing periodicity detection methods to improve their performance. This approach can be applied to other time-series microarray studies.

Detecting phase-amplitude coupling with high frequency resolution using adaptive decompositions

BACKGROUND

Phase-amplitude coupling (PAC)--the dependence of the amplitude of one rhythm on the phase of another, lower-frequency rhythm - has recently been used to illuminate cross-frequency coordination in neurophysiological activity. An essential step in measuring PAC is decomposing data to obtain rhythmic components of interest. Current methods of PAC assessment employ narrowband Fourier-based filters, which assume that biological rhythms are stationary, harmonic oscillations. However, biological signals frequently contain irregular and nonstationary features, which may contaminate rhythms of interest and complicate comodulogram interpretation, especially when frequency resolution is limited by short data segments.

NEW METHOD

To better account for nonstationarities while maintaining sharp frequency resolution in PAC measurement, even for short data segments, we introduce a new method of PAC assessment which utilizes adaptive and more generally broadband decomposition techniques - such as the empirical mode decomposition (EMD). To obtain high frequency resolution PAC measurements, our method distributes the PAC associated with pairs of broadband oscillations over frequency space according to the time-local frequencies of these oscillations.

COMPARISON WITH EXISTING METHODS

We compare our novel adaptive approach to a narrowband comodulogram approach on a variety of simulated signals of short duration, studying systematically how different types of nonstationarities affect these methods, as well as on EEG data.

CONCLUSIONS

Our results show: (1) narrowband filtering can lead to poor PAC frequency resolution, and inaccuracy and false negatives in PAC assessment; (2) our adaptive approach attains better PAC frequency resolution and is more resistant to nonstationarities and artifacts than traditional comodulograms.

Impaired cerebral autoregulation is associated with brain atrophy and worse functional status in chronic ischemic stroke

Dynamic cerebral autoregulation (dCA) is impaired following stroke. However, the relationship between dCA, brain atrophy, and functional outcomes following stroke remains unclear. In this study, we aimed to determine whether impairment of dCA is associated with atrophy in specific regions or globally, thereby affecting daily functions in stroke patients.

We performed a retrospective analysis of 33 subjects with chronic infarctions in the middle cerebral artery territory, and 109 age-matched non-stroke subjects. dCA was assessed via the phase relationship between arterial blood pressure and cerebral blood flow velocity. Brain tissue volumes were quantified from MRI. Functional status was assessed by gait speed, instrumental activities of daily living (IADL), modified Rankin Scale, and NIH Stroke Score.

Compared to the non-stroke group, stroke subjects showed degraded dCA bilaterally, and showed gray matter atrophy in the frontal, parietal and temporal lobes ipsilateral to infarct. In stroke subjects, better dCA was associated with less temporal lobe gray matter atrophy on the infracted side ( = 0.029), faster gait speed ( = 0.018) and lower IADL score (0.002). Our results indicate that better dynamic cerebral perfusion regulation is associated with less atrophy and better long-term functional status in older adults with chronic ischemic infarctions.