High-pass Filter Model Research Articles

The frequency response of cerebral autoregulation

The frequency-response of pressure autoregulation is not well delineated; therefore, the optimal frequency of arterial blood pressure (ABP) modulation for measuring autoregulation is unknown. We hypothesized that cerebrovascular autoregulation is band-limited and delineated by a cutoff frequency for which ABP variations induce cerebrovascular reactivity. Neonatal swine (n = 8) were anesthetized using constant minute ventilation while positive end-expiratory pressure (PEEP) was modulated between 6 and 0.75 cycles/min (min(-1)). The animals were hemorrhaged until ABP was below the lower limit of autoregulation (LLA), and PEEP modulations were repeated. Vascular reactivity was quantified at each frequency according to the phase lag between ABP and intracranial pressure (ICP) above and below the LLA. Phase differences between ABP and ICP were small for frequencies of >2 min(-1), with no ability to differentiate cerebrovascular reactivity between ABPs above or below the LLA. For frequencies of <2 min(-1), ABP and intracranial pressure (ICP) showed phase shift when measured above LLA and no phase shift when measured below LLA [above vs. below LLA at 1 min(-1): 156° (139-174°) vs. 30° (22-50°); P < 0.001 by two-way ANOVA for both frequency and state of autoregulation]. Data taken above LLA fit a Butterworth high-pass filter model with a cutoff frequency at 1.8 min(-1) (95% confidence interval: 1.5-2.2). Cerebrovascular reactivity occurs for sustained ABP changes lasting 30 s or longer. The ability to distinguish intact and impaired autoregulation was maximized by a 60-s wave (1 min(-1)), which was 100% sensitive and 100% specific in this model.

Recovery of the blood pressure – cerebral flow relation after carotid stenting in elderly patients

As a sensitive and convenient means for the cerebral hemodynamic monitoring, dynamic cerebral autoregulation testing could be especially useful in medical conditions where less invasive diagnostics and therapies are preferred. This study analysed the effect of carotid stenting on dynamic autoregulation in elderly patients focussing on the relation between blood pressure and cerebral blood flow velocity. We examined 20 patients age 69 +/- 8 years with coexisting cerebrovascular and medical risk factors before and at least six month after stenting of severe carotid stenoses. Data were compared to 24 age-matched healthy controls. Slow spontaneous oscillations were studied in continuous recordings of Transcranial Doppler and beat-to-beat blood pressure. Analysis was based on the "high-pass filter model", which predicts a positive phase relationship between these oscillations. Whereas phase shift angles were diminished (20.4 +/- 14.1 degrees ) before stenting, after stenting these values were significantly increased to normal (48.1 +/- 16.6 degrees ), to the level of controls (46.7 +/- 15.9 degrees ). Medical conditions such as coronary artery disease, arterial hypertension, and dyslipidemia did not diminish this recovery. The level of increase was inversely correlated with the initial autoregulatory deficit (r = -0.68) which was largest with insufficient collateral blood supply and symptomatic carotid stenoses. The study showed that an impaired cerebral autoregulation may recover after stent-guided carotid angioplasty even in the elderly with co-existing medical conditions. In this respect to regain vasomotor capability, patients with cerebrovascular risk factors seemed to benefit particularly.

Impact of vertebral artery disease on dynamic cerebral autoregulation

This study applied dynamic cerebral autoregulation (DCA) testing distally to severe bilateral vertebral artery disease (BVAD). Using continuous monitoring of beat-to-beat blood pressure and transcranial Doppler of the posterior cerebral arteries (PCA) were examined in 20 patients with BVAD and 22 controls. DCA testing was based on the 'high-pass filter model', which predicts a positive phase relationship between spontaneous oscillations (M-waves 3-9 cpm and R-waves 9-20 cpm) in blood pressure and cerebral blood flow velocity. In patients with BVAD, DCA testing detected autoregulatory deficits of different degrees. The lowest M-wave phase shift angles were found in the PCA territory distally to intracranial BVAD. This study suggests that DCA testing of the PCA could help to quantify the hemodynamic impact of BVAD. It highlights the relevance of functional TCD sonography as a useful diagnostic tool for the hemodynamic evaluation of vertebrobasilar disease.

Phase dynamics in cerebral autoregulation

Complex continuous wavelet transforms are used to study the dynamics of instantaneous phase difference delta phi between the fluctuations of arterial blood pressure (ABP) and cerebral blood flow velocity (CBFV) in a middle cerebral artery. For healthy individuals, this phase difference changes slowly over time and has an almost uniform distribution for the very low-frequency (0.02-0.07 Hz) part of the spectrum. We quantify phase dynamics with the help of the synchronization index gamma = (sin delta phi)2 + (cos delta phi)2 that may vary between 0 (uniform distribution of phase differences, so the time series are statistically independent of one another) and 1 (phase locking of ABP and CBFV, so the former drives the latter). For healthy individuals, the group-averaged index gamma has two distinct peaks, one at 0.11 Hz [gamma = 0.59 +/- 0.09] and another at 0.33 Hz (gamma = 0.55 +/- 0.17). In the very low-frequency range (0.02-0.07 Hz), phase difference variability is an inherent property of an intact autoregulation system. Consequently, the average value of the synchronization parameter in this part of the spectrum is equal to 0.13 +/- 0.03. The phase difference variability sheds new light on the nature of cerebral hemodynamics, which so far has been predominantly characterized with the help of the high-pass filter model. In this intrinsically stationary approach, based on the transfer function formalism, the efficient autoregulation is associated with the positive phase shift between oscillations of CBFV and ABP. However, the method is applicable only in the part of the spectrum (0.1-0.3 Hz) where the coherence of these signals is high. We point out that synchrony analysis through the use of wavelet transforms is more general and allows us to study nonstationary aspects of cerebral hemodynamics in the very low-frequency range where the physiological significance of autoregulation is most strongly pronounced.

Univariate modeling and forecasting of energy consumption: the case of electricity in Lebanon

In Lebanon, electric power is becoming the main energy form relied upon in all economic sectors of the country. Also, the time series of electrical energy consumption in Lebanon is unique due to intermittent power outages and increasing demand. Given these facts, it is critical to model and forecast electrical energy consumption. The aim of this study is to investigate different univariate-modeling methodologies and try, at least, a one-step ahead forecast for monthly electric energy consumption in Lebanon. Three univariate models are used, namely, the autoregressive, the autoregressive integrated moving average (ARIMA) and a novel configuration combining an AR(1) with a highpass filter. The forecasting performance of each model is assessed using different measures. The AR(1)/highpass filter model yields the best forecast for this peculiar energy data.

Analysis and modeling of frequency-specific habituation of the goldfish vestibulo-ocular reflex.

Modification of the vestibulo-ocular reflex (VOR) by vestibular habituation is an important paradigm in the study of neural plasticity. The VOR is responsible for rotating the eyes to maintain the direction of gaze during head rotation. The response of the VOR to sinusoidal rotation is quantified by its gain (eye rotational velocity/head rotational velocity) and phase difference (eye velocity phase--inverted head velocity phase). The frequency response of the VOR in naïve animals has been previously modeled as a high-pass filter (HPF). A HPF passes signals above its corner frequency with gain 1 and phase 0 but decreases gain and increases phase lead (positive phase difference) as signal frequency decreases below its corner frequency. Modification of the VOR by habituation occurs after prolonged low-frequency rotation in the dark. Habituation causes a reduction in low-frequency VOR gain and has been simulated by increasing the corner frequency of the HPF model. This decreases gain not only at the habituating frequency but further decreases gain at all frequencies below the new corner frequency. It also causes phase lead to increase at all frequencies below the new corner frequency (up to some asymptotic value). We show that habituation of the goldfish VOR is not a broad frequency phenomena but is frequency specific. A decrease in VOR gain is produced primarily at the habituating frequency, and there is an increase in phase lead at nearby higher frequencies and a decrease in phase lead at nearby lower frequencies (phase crossover). Both the phase crossover and the frequency specific gain decrease make it impossible to simulate habituation of the VOR simply by increasing the corner frequency of the HPF model. The simplest way to simulate our data is to subtract the output of a band-pass filter (BPF) from the output of the HPF model of the naïve VOR. A BPF passes signals over a limited frequency range only. A BPF decreases gain and imparts a phase lag and lead, respectively, as frequency increases and decreases outside this range. Our model produces both the specific decrease in gain at the habituating frequency, and the phase crossover centered on the frequency of habituation. Our results suggest that VOR habituation may be similar to VOR adaptation (in which VOR modification is produced by visual-vestibular mismatch) in that both are frequency-specific phenomena.

Spontaneous blood pressure oscillations and cerebral autoregulation.

The relationship between spontaneous oscillations in cerebral blood flow velocity (CBFV) and arterial blood pressure (ABP) was analysed in normal subjects in order to evaluate whether these relationships provide information about cerebral autoregulation. CBFV was measured using transcranial Doppler sonography and continuous ABP and heart rate using Finapres in 50 volunteers. Measurements were made over 5 min in a supine position and 6 min in a tilted position. Coefficients of variation were calculated using power- and cross-spectral analysis in order to quantify amplitudes within two frequency ranges: 3-9 cycles per min (cpm) (M-waves); and 9-20 cpm (R-waves). Correlations, coherence values, phase angle shifts and gains were also computed between corresponding waves in CBFV and in ABP. A clear correlation was seen for M-waves and R-waves between CBFV and ABP and coherence values were large enough to calculate phase angle shifts and gains. Phase angles for M-waves were larger and gains lower than was the case for R-waves, either tilted or supine. These data are consistent with a highpass filter model of cerebral autoregulation. Relatively high CBFV/ABP gain values (between 1.4 and 2.0) suggest that the principle of frequency-dependent vascular input impedances has to be considered in addition to autoregulatory feedback mechanisms. Spontaneous ABP oscillations in the M-wave and R-wave ranges may serve as a basis for continuous autoregulation monitoring.

Cross-spectral analysis of cerebral autoregulation dynamics in high risk preterm infants during the perinatal period.

In preterm infants intraventricular hemorrhage occurs predominantly within the perinatal period, which may be due to a "lost autoregulation" of cerebral blood flow (CBF). In this study, perinatal autoregulation dynamics were investigated in high risk preterm infants by cross-spectral analysis (CSA), which is a statistical tool in the analysis of time series. In 15 ventilated preterm infants of 25-32 gestational weeks, a total number of 30 records were made between 24 and 96 h of life. Doppler-derived CBF velocity (CBFv), used as a quantitative measure for CBF, and direct mean arterial blood pressure (MABP) were measured continuously for 10 min. The spectral power of low frequency (LF, 0.02-0.2 Hz) oscillations in CBFv and MABP was quantified by spectral analysis. From the results of CSA, a LF phase-shift between the CBFv and MABP LF oscillations was calculated in each record. Within the study group, the LF spectral power of CBFv and MABP was initially low and increased significantly until 96 h of life. The LF phase-shift was about 0 degrees at 24 h and increased significantly to 55 degrees at 96 h of life. The initially low LF spectral power of CBFv and MABP may indicate a perinatal depression of autonomic nervous centers, which are thought to control LF oscillations of vital parameters. In the light of a high pass filter model for autoregulation, the initially low LF phase-shift may indicate an initially impaired autoregulation, which supports the "lost autoregulation" hypothesis.

Phase relationship between cerebral blood flow velocity and blood pressure. A clinical test of autoregulation.

This study investigates the usefulness, as a test of dynamic autoregulation, of phase shift angle analysis between oscillations in cerebral blood flow velocity (CBFV) and in arterial blood pressure (ABP) during deep breathing. Fifty healthy volunteers, 20 patients with occlusive cerebrovascular diseases (OCD), and 10 patients with arteriovenous malformations (AVM) took part in the study. All subjects received transcranial Doppler monitoring of both middle cerebral arteries (MCAs). In addition, continuous blood pressure monitoring was performed with the use of noninvasive servo-controlled infrared finger plethysmography during deep breathing at a rate of 6/min. With the use of a high-pass filter model of autoregulation, autoregulation was quantified as phase shift angle between oscillations in CBFV and ABP at a frequency of 6/min. A phase shift angle of 0 degrees indicates total absence of autoregulation, while 90 degrees can be gauged as optimal autoregulation. In addition, vasomotor reactivity of both MCAs to CO2 stimulation was assessed among patients and calculated as percent increase in CBFV per millimeter of mercury of increase in CO2. All normal subjects showed positive phase shift angles between CBFV and ABP (mean +/- SD, 70.5 +/- 29.8 degrees). OCD patients presented with significantly decreased phase shift angles for the MCA only on the pathological side (51.7 +/- 35.1 degrees; P < .05). Patients with AVM showed significantly reduced phase shift angles on both the affected side (26.8 +/- 13.5 degrees; P < .001) and the unaffected side (40.6 +/- 26.6 degrees; P < .01). In patients' groups, phase shift angle and vasomotor reactivity correlated significantly (r = .66; P < .001) after results from all MCAs were pooled. Results confirm the high-pass filter model of cerebral autoregulation: Normal subjects showed predicted positive phase shift angles between CBFV and ABP oscillations. Patients with expected autoregulatory disturbances showed significant decreases in phase shift angles. Close correlations existed between autoregulation and CO2-induced vasomotor reactivity.