Altered Phase Interactions between Spontaneous Blood Pressure and Flow Fluctuations in Type 2 Diabetes Mellitus: Nonlinear Assessment of Cerebral Autoregulation

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.

Application of a multicomponent model of convectional reaction-diffusion to description of glucose gradients in a neurovascular unit

A supply of glucose to a nervous tissue is fulfilled by a cerebrovascular network, and further diffusion is known to occur at both an arteriolar and a microvascular level. Despite a direct relation, a blood flow dynamic and reaction-diffusion of metabolites are usually considered separately in the mathematical models. In the present study they are coupled in a multiphysical approach which allows to evaluate the effects of capillary blood flow changes on near-vessels nutrient concentration gradients evidently. Cerebral blood flow (CBF) was described by the non-steady-state Navier-Stokes equations for a non-Newtonian fluid whose constitutive law is given by the Carreau model. A three-level organization of blood–brain barrier (BBB) is modelled by the flux dysconnectivity functions including densities and kinetic properties of glucose transporters. The velocity of a fluid flow in brain extracellular space (ECS) was estimated using Darcy’s law. The equations of reaction-diffusion with convection based on a generated flow field for continues and porous media were used to describe spatial-time gradients of glucose in the capillary lumen and brain parenchyma of a neurovascular unit (NVU), respectively. Changes in CBF were directly simulated using smoothing step-like functions altering the difference of intracapillary pressure in time. The changes of CBF cover both the decrease (on 70%) and the increase (on 50%) in a capillary flow velocity. Analyzing the dynamics of glucose gradients, it was shown that a rapid decrease of a capillary blood flow yields an enhanced level of glucose in a near-capillary nervous tissue if the contacts between astrocytes end-feet are not tight. Under the increased CBF velocities the amplitude of glucose concentration gradients is always enhanced. The introduced approach can be used for estimation of blood flow changes influence not only on glucose but also on other nutrients concentration gradients and for the modelling of distributions of their concentrations near blood vessels in other tissues as well.

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.

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.

Cerebral Autoregulation in Ischemic Stroke: From Pathophysiology to Clinical Concepts

Ischemic stroke (IS) is one of the most impacting diseases in the world. In the last decades, new therapies have been introduced to improve outcomes after IS, most of them aiming for recanalization of the occluded vessel. However, despite this advance, there are still a large number of patients that remain disabled. One interesting possible therapeutic approach would be interventions guided by cerebral hemodynamic parameters such as dynamic cerebral autoregulation (dCA). Supportive hemodynamic therapies aiming to optimize perfusion in the ischemic area could protect the brain and may even extend the therapeutic window for reperfusion therapies. However, the knowledge of how to implement these therapies in the complex pathophysiology of brain ischemia is challenging and still not fully understood. This comprehensive review will focus on the state of the art in this promising area with emphasis on the following aspects: (1) pathophysiology of CA in the ischemic process; (2) methodology used to evaluate CA in IS; (3) CA studies in IS patients; (4) potential non-reperfusion therapies for IS patients based on the CA concept; and (5) the impact of common IS-associated comorbidities and phenotype on CA status. The review also points to the gaps existing in the current research to be further explored in future trials.

COHmax: an algorithm to maximise coherence in estimates of dynamic cerebral autoregulation

OBJECTIVE

The reliability of dynamic cerebral autoregulation (dCA) parameters, obtained with transfer function analysis (TFA) of spontaneous fluctuations in arterial blood pressure (BP), require statistically significant values of the coherence function. A new algorithm (COH_max) is proposed to increase values of coherence by means of the automated, selective removal of sub-segments of data.

APPROACH

Healthy subjects were studied at baseline (normocapnia) and during 5% breathing of CO₂ (hypercapnia). BP (Finapres), cerebral blood flow velocity (CBFV, transcranial Doppler), end-tidal CO₂ (EtCO₂, capnography) and heart rate (ECG) were recorded continuously during 5 min in each condition. TFA was performed with sub-segments of data of duration (SEG_D) 100 s, 50 s or 25 s and the autoregulation index (ARI) was obtained from the CBFV response to a step change in BP. The area-under-the curve (AUC) was obtained from the receiver-operating characteristic (ROC) curve for the detection of changes in dCA resulting from hypercapnia.

MAIN RESULTS

In 120 healthy subjects (69 male, age range 20-77 years), CO₂ breathing was effective in changing mean EtCO₂ and CBFV (p < 0.001). For SEG_D = 100 s, ARI changed from 5.8 ± 1.4 (normocapnia) to 4.0 ± 1.7 (hypercapnia, p < 0.0001), with similar differences for SEG_D = 50 s or 25 s. Depending on the value of SEG_D, in normocapnia, 15.8% to 18.3% of ARI estimates were rejected due to poor coherence, with corresponding rates of 8.3% to 13.3% in hypercapnia. With increasing coherence, 36.4% to 63.2% of these could be recovered in normocapnia (p < 0.001) and 50.0% to 83.0% in hypercapnia (p < 0.005). For SEG_D = 100 s, ROC AUC was not influenced by the algorithm, but it was superior to corresponding values for SEG_D = 50 s or 25 s.

SIGNIFICANCE

COH_max has the potential to improve the yield of TFA estimates of dCA parameters, without introducing a bias or deterioration of their ability to detect impairment of autoregulation. Further studies are needed to assess the behaviour of the algorithm in patients with different cerebrovascular conditions.

[Prediction of syncope with nonlinear dynamic analysis during head-up tilt in vasovagal syncope patients]

OBJECTIVE

To quantify the relationship between cerebral blood flow velocity and peripheral blood pressure during hypotension period, aiming to predict the brain hypotension before symptomatic occurrence.

METHODS

Twenty vasovagal syncope (VVS) patients who had a previous clinical history were selected in groups and 20 pair-matched control subjects underwent 70° tilt-up test. The subjects remained supine for 30 minutes before recordings when Doppler probes, electrodes and Finapres device were prepared. After continuous baseline recordings for 10 min, the subjects underwent head up tilt (HUT) test (70°), and were standing upright for 30 minutes or until syncope was imminent. For ethical reasons, the subjects were turned back to supine position immediately after SBP dropped to ≥20 mmHg, when their consciousness persisted. The point of syncope was synchronized for all the subjects by the point SBP reached the minima. Their beat-to-beat blood pressures (BP) were recorded continuously and bilateral middle cerebral artery (MCA) flow velocities were obtained with two 2 MHz Doppler probes from a transcranial Doppler ultrasonography (TCD) system. A nonlinear dynamic method--multimodal pressure flow (MMPF) analysis was introduced to access cerebral autoregulation during different time intervals. We introduced a new indicator--syncope index (SI), which was extracted from blood flow velocity (BFV) signal to evaluate the variation of cerebral vascular tension, and could reflect the deepness of dicrotic notch in BFV signal.

RESULTS

Compared with the syncope index of the baseline value at the beginning of the tilt test, SI in VVS group showed significantly lower when the VVS occurred (0.16±0.10 vs.0.27±0.10,P<0.01),while there was no significant difference in syncope index between the control group at the end of the tilt test and the baseline value at the beginning of the tilt test. For those VVS patients, pulse index and resistance index had no significant change. Syncope index decreased significantly 3 minutes before the point of syncope (0.23±0.07 vs.0.29±0.07,P<0.01).

CONCLUSION

Dynamic regulation is exhausted when vasovagal syncope occurred. Tension decrease of small vessels could have some relationship with loss of the cerebral autoregulation capability. The proposed syncope index could be a useful parameter in predicting syncope of VVS patients since it decreased significantly up to 3 minutes earlier from the point of syncope.

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.

The Fourier decomposition method for nonlinear and non-stationary time series analysis

for many decades, there has been a general perception in the literature that Fourier methods are not suitable for the analysis of nonlinear and non-stationary data. In this paper, we propose a novel and adaptive Fourier decomposition method (FDM), based on the Fourier theory, and demonstrate its efficacy for the analysis of nonlinear and non-stationary time series. The proposed FDM decomposes any data into a small number of 'Fourier intrinsic band functions' (FIBFs). The FDM presents a generalized Fourier expansion with variable amplitudes and variable frequencies of a time series by the Fourier method itself. We propose an idea of zero-phase filter bank-based multivariate FDM (MFDM), for the analysis of multivariate nonlinear and non-stationary time series, using the FDM. We also present an algorithm to obtain cut-off frequencies for MFDM. The proposed MFDM generates a finite number of band-limited multivariate FIBFs (MFIBFs). The MFDM preserves some intrinsic physical properties of the multivariate data, such as scale alignment, trend and instantaneous frequency. The proposed methods provide a time-frequency-energy (TFE) distribution that reveals the intrinsic structure of a data. Numerical computations and simulations have been carried out and comparison is made with the empirical mode decomposition algorithms.

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.

Cerebrovascular effects of the thigh cuff maneuver

Arterial hypotension can be induced by sudden release of inflated thigh cuffs (THC), but its effects on the cerebral circulation have not been fully described. In nine healthy subjects [aged 59 (9) yr], bilateral cerebral blood flow velocity (CBFV) was recorded in the middle cerebral artery (MCA), noninvasive arterial blood pressure (BP) in the finger, and end-tidal CO2 (ETCO2) with nasal capnography. Three THC maneuvers were performed in each subject with cuff inflation 20 mmHg above systolic BP for 3 min before release. Beat-to-beat values were extracted for mean CBFV, BP, ETCO2 , critical closing pressure (CrCP), resistance-area product (RAP), and heart rate (HR). Time-varying estimates of the autoregulation index [ARI(t)] were also obtained using an autoregressive-moving average model. Coherent averages synchronized by the instant of cuff release showed significant drops in mean BP, CBFV, and RAP with rapid return of CBFV to baseline. HR, ETCO2 , and ARI(t) were transiently increased, but CrCP remained relatively constant. Mean values of ARI(t) for the 30 s following cuff release were not significantly different from the classical ARI [right MCA 5.9 (1.1) vs. 5.1 (1.6); left MCA 5.5 (1.4) vs. 4.9 (1.7)]. HR was strongly correlated with the ARI(t) peak after THC release (in 17/22 and 21/24 recordings), and ETCO2 was correlated with the subsequent drop in ARI(t) (19/22 and 20/24 recordings). These results suggest a complex cerebral autoregulatory response to the THC maneuver, dominated by myogenic mechanisms and influenced by concurrent changes in ETCO2 and possible involvement of the autonomic nervous system and baroreflex.

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.

Time-varying modeling of cerebral hemodynamics

The scientific and clinical importance of cerebral hemodynamics has generated considerable interest in their quantitative understanding via computational modeling. In particular, two aspects of cerebral hemodynamics, cerebral flow autoregulation (CFA) and CO2 vasomotor reactivity (CVR), have attracted much attention because they are implicated in many important clinical conditions and pathologies (orthostatic intolerance, syncope, hypertension, stroke, vascular dementia, mild cognitive impairment, Alzheimer's disease, and other neurodegenerative diseases with cerebrovascular components). Both CFA and CVR are dynamic physiological processes by which cerebral blood flow is regulated in response to fluctuations in cerebral perfusion pressure and blood CO2 tension. Several modeling studies to date have analyzed beat-to-beat hemodynamic data in order to advance our quantitative understanding of CFA-CVR dynamics. A confounding factor in these studies is the fact that the dynamics of the CFA-CVR processes appear to vary with time (i.e., changes in cerebrovascular characteristics) due to neural, endocrine, and metabolic effects. This paper seeks to address this issue by tracking the changes in linear time-invariant models obtained from short successive segments of data from ten healthy human subjects. The results suggest that systemic variations exist but have stationary statistics and, therefore, the use of time-invariant modeling yields "time-averaged models" of physiological and clinical utility.

Detection of impaired cerebral autoregulation improves by increasing arterial blood pressure variability

Although the assessment of dynamic cerebral autoregulation (CA) based on measurements of spontaneous fluctuations in arterial blood pressure (ABP) and cerebral blood flow (CBF) is a convenient and much used method, there remains uncertainty about its reliability. We tested the effects of increasing ABP variability, provoked by a modification of the thigh cuff method, on the ability of the autoregulation index to discriminate between normal and impaired CA, using hypercapnia as a surrogate for dynamic CA impairment. In 30 healthy volunteers, ABP (Finapres) and CBF velocity (CBFV, transcranial Doppler) were recorded at rest and during 5% CO(2) breathing, with and without pseudo-random sequence inflation and deflation of bilateral thigh cuffs. The application of thigh cuffs increased ABP and CBFV variabilities and was not associated with a distortion of the CBFV step response estimates for both normocapnic and hypercapnic conditions (P=0.59 and P=0.96, respectively). Sensitivity and specificity of CA impairment detection were improved with the thigh cuff method, with the area under the receiver-operator curve increasing from 0.746 to 0.859 (P=0.031). We conclude that the new method is a safe, efficient, and appealing alternative to currently existing assessment methods for the investigation of the status of CA.

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.

Cognition and Hemodynamics

The relationship between cerebral hemodynamics and cognitive performance has increasingly become recognized as a major challenge in clinical practice for older adults. Both diabetes and hypertension worsen brain perfusion and are major risk factors for cerebrovascular disease, stroke and dementia. Cerebrovascular reserve has emerged as a potential biomarker for monitoring pressure-perfusion-cognition relationships. Endothelial dysfunction and inflammation, microvascular disease, and mascrovascular disease affect cerebral hemodynamics and play an important role in pathohysiology and severity of multiple medical conditions, presenting as cognitive decline in the old age. Therefore, the identification of cerebrovascular vascular reactivity as a new therapeutic target is needed for prevention of cognitive decline late in life.

Investigating properties of the cardiovascular system using innovative analysis algorithms based on ensemble empirical mode decomposition

Cardiovascular system is known to be nonlinear and nonstationary. Traditional linear assessments algorithms of arterial stiffness and systemic resistance of cardiac system accompany the problem of nonstationary or inconvenience in practical applications. In this pilot study, two new assessment methods were developed: the first is ensemble empirical mode decomposition based reflection index (EEMD-RI) while the second is based on the phase shift between ECG and BP on cardiac oscillation. Both methods utilise the EEMD algorithm which is suitable for nonlinear and nonstationary systems. These methods were used to investigate the properties of arterial stiffness and systemic resistance for a pig's cardiovascular system via ECG and blood pressure (BP). This experiment simulated a sequence of continuous changes of blood pressure arising from steady condition to high blood pressure by clamping the artery and an inverse by relaxing the artery. As a hypothesis, the arterial stiffness and systemic resistance should vary with the blood pressure due to clamping and relaxing the artery. The results show statistically significant correlations between BP, EEMD-based RI, and the phase shift between ECG and BP on cardiac oscillation. The two assessments results demonstrate the merits of the EEMD for signal analysis.

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

Cerebral autoregulation (CA) is an important vascular control mechanism responsible for relatively stable cerebral blood flow despite changes of systemic blood pressure (BP). Impaired CA may leave brain tissue unprotected against potentially harmful effects of BP fluctuations. It is generally accepted that CA is less effective or even inactive at frequencies >∼0.1 Hz. Without any physiological foundation, this concept is based on studies that quantified the coupling between BP and cerebral blood flow velocity (BFV) using transfer function analysis. This traditional analysis assumes stationary oscillations with constant amplitude and period, and may be unreliable or even invalid for analysis of nonstationary BP and BFV signals. In this study we propose a novel computational tool for CA assessment that is based on nonlinear dynamic theory without the assumption of stationary signals. Using this method, we studied BP and BFV recordings collected from 39 patients with chronic ischemic infarctions and 40 age-matched non-stroke subjects during baseline resting conditions. The active CA function in non-stroke subjects was associated with an advanced phase in BFV oscillations compared to BP oscillations at frequencies from ∼0.02 to 0.38 Hz. The phase shift was reduced in stroke patients even at > = 6 months after stroke, and the reduction was consistent at all tested frequencies and in both stroke and non-stroke hemispheres. These results provide strong evidence that CA may be active in a much wider frequency region than previously believed and that the altered multiscale CA in different vascular territories following stroke may have important clinical implications for post-stroke recovery. Moreover, the stroke effects on multiscale cerebral blood flow regulation could not be detected by transfer function analysis, suggesting that nonlinear approaches without the assumption of stationarity are more sensitive for the assessment of the coupling of nonstationary physiological signals.

Cerebral autoregulation is an important mechanism that regulates blood supply to brain tissue to match metabolic demands during daily activities. Impaired cerebral autoregulation increases the dependence of cerebral blood flow on systemic blood pressure, and is associated with fatal outcomes in patients after brain injury and acute ischemic stroke. Reliable and noninvasive assessment of cerebral autoregulation is still a major challenge in medical diagnostics and clinic studies, mainly because blood pressure and flow are intrinsically nonstationary (possessing complex oscillations/fluctuations with varying amplitude and frequency) while traditional methods for assessment of the pressure-flow dependence assume stationary signals. We propose a new computational technique that is based on nonlinear theories without the assumption of stationary signals. This technique allows us to detect the degradation of cerebral autoregulation in patients with mild ischemic stroke even at >6 months after the insult. The degradation was present in both stroke and non-stroke sides and was accompanied by an altered pressure-flow interaction over a wide range of frequencies from 0.02–0.38 Hz. Our results challenges the traditionally accepted functional region of autoregulation (<∼0.1 Hz). The observed long-term influences of stroke highlight the importance of reliable monitoring of cerebral blood flow regulation for the management and daily care of stroke patients.

Microvascular brain damage with aging and hypertension: pathophysiological consideration and clinical implications

Loss of cognitive function and hypertension are two common conditions in the elderly and both significantly contribute to loss of personal independency. Microvascular brain damage - the result of age-associated alteration in large arteries and the progressive mismatch of their cross-talk with small cerebral arteries - represents a potent risk factor for cognitive decline and for the onset of dementia in older individuals. The present review discusses the complexity of factors linking large artery to microvascular brain disease and to cognitive decline and the evidence for possible clinical markers useful for prevention of this phenomenon. The possibility of dementia prevention by cardiovascular risk factors control has not been demonstrated. In the absence of research clinical trials specifically and primarily designed to demonstrate the antihypertensive treatment efficacy for reducing the risk of dementia, further evidence demonstrating that it is possible to limit the progression of microvascular brain damage is needed.

THE NONLINEAR AND NONSTATIONARY PROPERTIES IN EEG SIGNALS: PROBING THE COMPLEX FLUCTUATIONS BY HILBERT–HUANG TRANSFORM

The analysis of biological fluctuations provides an excellent route to probe the underlying mechanisms in maintaining internal homeostasis of the body, especially under the challenges of the ever-changing environment or disease processes. However, the features of nonlinearity and nonstationarity in physiological time series limit the reliability of the conventional analysis. Hilbert–Huang transform (HHT), based on nonlinear theory, is an innovative approach to extract the dynamic information at different time scales, in particular, from nonstationary signals. In this paper, HHT is introduced to analyze the alpha waves of human's electroencephalography (EEG), which seemly oscillate regularly between 8 and 12 Hz in healthy subject but getting irregular or disappeared in different demented status. Furthermore, conventional time–frequency analyses are adopted to collate the results from those methods and HHT. Finally, the potential usages of HHT are demonstrated in characterizing the biological signals qualitatively and quantitatively, including stationarity analysis, instantaneous frequency and amplitude modulation or correlation analysis. Such applications on EEG have successively disclosed the differences of alpha rhythms between normal and demented brains and the nonlinear characteristics of the underlying mechanisms. Hopefully, in addition to empower the studies of EEG varied in diseased, aging, and physiological processes, these methods might find other applications in EEG analysis.

A systematic study of linear dynamic modeling of intracranial pressure dynamics

Our group has proposed a generic time series data mining framework and demonstrated its potential as a noninvasive intracranial pressure (ICP) assessment approach. The linear dynamic model (LDM) was used in our previous work without rigorous justification. In the current study, we performed a systematic study of the practical performance of the LDM for ICP dynamics by investigating three important aspects to consider in using the LDM to model ICP dynamics. Those three aspects include the fitness of the LDM to data, the generalizability of the models, and the choice of input signals to the models. Our study results show that the fitness of the LDM to data is excellent and the LDM for ICP dynamics is well generalizable, which is of particular interest to adopting our time series data mining framework for noninvasive ICP assessment.

Spontaneous fluctuations in cerebral blood flow regulation: contribution of PaCO2

To investigate the temporal variability of dynamic cerebral autoregulation (CA), the transient response of cerebral blood flow to rapid changes in arterial blood pressure, a new approach was introduced to improve the temporal resolution of dynamic CA assessment. Continuous bilateral recordings of cerebral blood flow velocity (transcranial Doppler, middle cerebral artery), end-tidal Pco2 (PetCO2, infrared capnograph), and blood pressure (Finapres) were obtained at rest and during breath hold in 30 young subjects (25 ± 6 yr old) and 30 older subjects (64 ± 4 yr old). Time-varying estimates of the autoregulation index [ARI( t)] were obtained with an autoregressive-moving average model with coefficients expanded by orthogonal decomposition. The temporal pattern of ARI( t) varied inversely with PetCO2, decreasing with hypercapnia. At rest, ARI( t) showed spontaneous fluctuations that were significantly different from noise and significantly correlated with spontaneous fluctuations in PetCO2 in the majority of recordings (young: 72% and old: 65%). No significant differences were found in ARI( t) due to aging. This new approach to improve the temporal resolution of dynamic CA parameters allows the identification of physiologically meaningful fluctuations in dynamic CA efficiency at rest and in response to changes in arterial CO2.

The relationship between blood pressure and cognitive function

The relationship between blood pressure (BP) and cognitive outcomes in elderly adults has implications for global health care. Both hypertension and hypotension affect brain perfusion and worsen cognitive outcomes. The presence of hypertension and other vascular risk factors has been associated with decreased performance in executive function and attention tests. Cerebrovascular reserve has emerged as a potential biomarker for monitoring pressure-perfusion-cognition relationships. A decline in vascular reserve capacity can lead to impaired neurovascular coupling and decreased cognitive ability. Endothelial dysfunction, microvascular disease, and mascrovascular disease in midlife could also have an important role in the manifestations and severity of multiple medical conditions underlying cognitive decline late in life. However, questions remain about the role of antihypertensive therapies for long-term prevention of cognitive decline. In this Review, we address the underlying pathophysiology and the existing evidence supporting the role of vascular factors in late-life cognitive decline.

Nonlinear pressure-flow relationship is able to detect asymmetry of brain blood circulation associated with midline shift

Reliable and noninvasive assessment of cerebral blood flow regulation is a major challenge in acute care monitoring. This study assessed dynamics of flow regulation and its relationship to asymmetry of initial computed tomography (CT) scan using multimodal pressure flow (MMPF) analysis. Data of 27 patients (38 +/- 15 years old) with traumatic brain injury (TBI) were analyzed. Patients were selected from bigger cohort according to criteria of having midline shift on initial CT scan and intact skull (no craniotomy or bone flap). The MMPF analysis was used to extract the oscillations in cerebral perfusion pressure (CPP) and blood flow velocity (BFV) signals at frequency of artificial ventilation, and to calculate the instantaneous phase difference between CPP and BFV oscillations. Mean CPP-BFV phase difference was used to quantify pressure and flow relationship. The TBI subjects had smaller mean BP-BFV phase shifts (left, 8.7 +/- 9.6; right 10.2 +/- 8.3 MCAs, mean +/- SD) than values previously obtained in healthy subjects (left, 37.3 +/- 7.6 degrees; right, 38.0 +/- 8.9 degrees; p < 0.0001), suggesting impaired blood flow regulation after TBI. The difference in phase shift between CPP and BFV in the left and right side was strongly correlated to the midline shift (R = 0.78; p < 0.0001). These findings indicate that the MMPF method allows reliable assessment of alterations in pressure and flow relationship after TBI. Moreover, mean pressure-flow phase shift is sensitive to the displacement of midline of the brain, and may potentially serve as a marker of asymmetry of cerebral autoregulation.

Improved noninvasive intracranial pressure assessment with nonlinear kernel regression

The only established technique for intracranial pressure (ICP) measurement is an invasive procedure requiring surgically penetrating the skull for placing pressure sensors. However, there are many clinical scenarios where a noninvasive assessment of ICP is highly desirable. With an assumption of a linear relationship among arterial blood pressure (ABP), ICP, and flow velocity (FV) of major cerebral arteries, an approach has been previously developed to estimate ICP noninvasively, the core of which is the linear estimation of the coefficients f between ABP and ICP from the coefficients w calculated between ABP and FV. In this paper, motivated by the fact that the relationships among these three signals are so complex that simple linear models may be not adequate to depict the relationship between these two coefficients, i.e., f and w , we investigate the adoption of several nonlinear kernel regression approaches, including kernel spectral regression (KSR) and support vector machine (SVM) to improve the original linear ICP estimation approach. The ICP estimation results on a dataset consisting of 446 entries from 23 patients show that the mean ICP error by the nonlinear approaches can be reduced to below 6.0 mmHg compared to 6.7 mmHg of the original approach. The statistical test also demonstrates that the ICP error by the proposed nonlinear kernel approaches is statistically smaller than that estimated with the original linear model (p < 0.05). The current result confirms the potential of using nonlinear regression to achieve more accurate noninvasive ICP assessment.

Nonlinear phase interaction between nonstationary signals: a comparison study of methods based on Hilbert-Huang and Fourier transforms

Phase interactions among signals of physical and physiological systems can provide useful information about the underlying control mechanisms of the systems. Physical and biological recordings are often noisy and exhibit nonstationarities that can affect the estimation of phase interactions. We systematically studied effects of nonstationarities on two phase analyses including (i) the widely used transfer function analysis (TFA) that is based on Fourier decomposition and (ii) the recently proposed multimodal pressure flow (MMPF) analysis that is based on Hilbert-Huang transform (HHT)-an advanced nonlinear decomposition algorithm. We considered three types of nonstationarities that are often presented in physical and physiological signals: (i) missing segments of data, (ii) linear and step-function trends embedded in data, and (iii) multiple chaotic oscillatory components at different frequencies in data. By generating two coupled oscillatory signals with an assigned phase shift, we quantify the change in the estimated phase shift after imposing artificial nonstationarities into the oscillatory signals. We found that all three types of nonstationarities affect the performances of the Fourier-based and the HHT-based phase analyses, introducing bias and random errors in the estimation of the phase shift between two oscillatory signals. We also provided examples of nonstationarities in real physiological data (cerebral blood flow and blood pressure) and showed how nonstationarities can complicate result interpretation. Furthermore, we propose certain strategies that can be implemented in the TFA and the MMPF methods to reduce the effects of nonstationarities, thus improving the performances of the two methods.

Transcranial Doppler for evaluation of cerebral autoregulation

Transcranial Doppler ultrasound (TCD) can measure cerebral blood flow velocity in the main intracranial vessels non-invasively and with high accuracy. Combined with the availability of non-invasive devices for continuous measurement of arterial blood pressure, the relatively low cost, ease-of-use, and excellent temporal resolution of TCD have stimulated the development of new techniques to assess cerebral autoregulation in the laboratory or bedside using a dynamic approach, instead of the more classical 'static' method. Clinical applications have shown consistent results in certain conditions such as severe head injury and carotid artery disease. Studies in syncopal patients revealed a more complex pattern due to aetiological non-homogeneity and methodological limitations mainly due to inadequate sample-size. Different analytical models to quantify autoregulatory performance have also contributed to the diversity of results in the literature. The review concludes with specific recommendations for areas where further validation and research are needed to improve the reliability and usefulness of TCD in clinical practice.

Nonlinear assessment of cerebral autoregulation from spontaneous blood pressure and cerebral blood flow fluctuations

Cerebral autoregulation (CA) is an most important mechanism responsible for the relatively constant blood flow supply to brain when cerebral perfusion pressure varies. Its assessment in nonacute cases has been relied on the quantification of the relationship between noninvasive beat-to-beat blood pressure (BP) and blood flow velocity (BFV). To overcome the nonstationary nature of physiological signals such as BP and BFV, a computational method called multimodal pressure-flow (MMPF) analysis was recently developed to study the nonlinear BP-BFV relationship during the Valsalva maneuver (VM). The present study aimed to determine (i) whether this method can estimate autoregulation from spontaneous BP and BFV fluctuations during baseline rest conditions; (ii) whether there is any difference between the MMPF measures of autoregulation based on intra-arterial BP (ABP) and based on cerebral perfusion pressure (CPP); and (iii) whether the MMPF method provides reproducible and reliable measure for noninvasive assessment of autoregulation. To achieve these aims, we analyzed data from existing databases including: (i) ABP and BFV of 12 healthy control, 10 hypertensive, and 10 stroke subjects during baseline resting conditions and during the Valsalva maneuver, and (ii) ABP, CPP, and BFV of 30 patients with traumatic brain injury (TBI) who were being paralyzed, sedated, and ventilated. We showed that autoregulation in healthy control subjects can be characterized by specific phase shifts between BP and BFV oscillations during the Valsalva maneuver, and the BP-BFV phase shifts were reduced in hypertensive and stroke subjects (P < 0.01), indicating impaired autoregulation. Similar results were found during baseline condition from spontaneous BP and BFV oscillations. The BP-BFV phase shifts obtained during baseline and during VM were highly correlated (R > 0.8, P < 0.0001), showing no statistical difference (paired-t test P > 0.47). In TBI patients there were strong correlations between phases of ABP and CPP oscillations (R = 0.99, P < 0.0001) and, thus, between ABP-BFV and CPP-BFV phase shifts (P < 0.0001, R = 0.76). By repeating the MMPF 4 times on data of TBI subjects, each time on a selected cycle of spontaneous BP and BFV oscillations, we showed that MMPF had better reproducibility than traditional autoregulation index. These results indicate that the MMPF method, based on instantaneous phase relationships between cerebral blood flow velocity and peripheral blood pressure, has better performance than the traditional standard method, and can reliably assess cerebral autoregulation dynamics from ambulatory blood pressure and cerebral blood flow during supine rest conditions.

ADAPTIVE DATA ANALYSIS OF COMPLEX FLUCTUATIONS IN PHYSIOLOGIC TIME SERIES

We introduce a generic framework of dynamical complexity to understand and quantify fluctuations of physiologic time series. In particular, we discuss the importance of applying adaptive data analysis techniques, such as the empirical mode decomposition algorithm, to address the challenges of nonlinearity and nonstationarity that are typically exhibited in biological fluctuations.

Multimodal Pressure Flow Analysis: Application of Hilbert Huang Transform in Cerebral Blood Flow Regulation

Quantification of nonlinear interactions between two nonstationary signals presents a computational challenge in different research fields, especially for assessments of physiological systems. Traditional approaches that are based on theories of stationary signals cannot resolve nonstationarity-related issues and, thus, cannot reliably assess nonlinear interactions in physiological systems. In this review we discuss a new technique "Multi-Modal Pressure Flow method (MMPF)" that utilizes Hilbert-Huang transformation to quantify dynamic cerebral autoregulation (CA) by studying interaction between nonstationary cerebral blood flow velocity (BFV) and blood pressure (BP). CA is an important mechanism responsible for controlling cerebral blood flow in responses to fluctuations in systemic BP within a few heart-beats. The influence of CA is traditionally assessed from the relationship between the well-pronounced systemic BP and BFV oscillations induced by clinical tests. Reliable noninvasive assessment of dynamic CA, however, remains a challenge in clinical and diagnostic medicine.In this brief review we: 1) present an overview of transfer function analysis (TFA) that is traditionally used to quantify CA; 2) describe the a MMPF method and its modifications; 3) introduce a newly developed automatic algorithm and engineering aspects of the improved MMPF method; and 4) review clinical applications of MMPF and its sensitivity for detection of CA abnormalities in clinical studies. The MMPF analysis decomposes complex nonstationary BP and BFV signals into multiple empirical modes adaptively so that the fluctuations caused by a specific physiologic process can be represented in a corresponding empirical mode. Using this technique, we recently showed that dynamic CA can be characterized by specific phase delays between the decomposed BP and BFV oscillations, and that the phase shifts are significantly reduced in hypertensive, diabetics and stroke subjects with impaired CA. In addition, the new technique enables reliable assessment of CA using both data collected during clinical test and spontaneous BP/BFV fluctuations during baseline resting conditions.