Variability and fractal analysis of middle cerebral artery blood flow velocity and arterial blood pressure in subarachnoid hemorrhage

Association between blood pressure control during aneurysm clipping and functional outcomes in patients with aneurysmal subarachnoid hemorrhage

Objectives

We explored the relationship between blood pressure variability (BPV) during craniotomy aneurysm clipping and short-term prognosis in patients with aneurysmal subarachnoid hemorrhage to provide a new method to improve prognosis of these patients.

Methods

We retrospectively analyzed the differences between patient groups with favorable modified Rankin Scale (mRS ≤ 2) and unfavorable (mRS > 2) prognosis, and examined the association between intraoperative BPV and short-term prognosis.

Results

The intraoperative maximum systolic blood pressure (SBPmax, p = 0.005) and the coefficient of variation of diastolic blood pressure (DBPCV, p = 0.029) were significantly higher in the favorable prognosis group. SBPmax (OR 0.88, 95%CI 0.80-0.98) and Neu% (OR 1.22, 95%CI 1.03-1.46) were independent influence factors on prognosis. Patients with higher standard deviations of SBP (82.7% vs. 56.7%; p = 0.030), DBP (82.7% vs. 56.7%; p = 0.030), and DBPCV (82.7% vs. 56.7%; p = 0.030) had more favorable prognosis.

Conclusion

Higher SBPmax (≤180 mmHg) during the clipping is an independent protective factor for a 90-day prognosis. These results highlight the importance of blood pressure (BP) control for improved prognosis; higher short-term BPV during clipping may be a precondition for a favorable prognosis.

Fractal Analysis of the Cerebrovascular System Pathophysiology

The cerebrovascular system is characterized by parameters such as arterial blood pressure (ABP), cerebral perfusion pressure (CPP), and cerebral blood flow velocity (CBFV). These are regulated by interconnected feedback loops resulting in a fluctuating and complex time course. They exhibit fractal characteristics such as (statistical) self-similarity and scale invariance which could be quantified by fractal measures. These include the coefficient of variation, the Hurst coefficient H, or the spectral exponent α in the time domain, as well as the spectral index ß in the frequency domain. Prior to quantification, the time series has to be classified as either stationary or nonstationary, which determines the appropriate fractal analysis and measure for a given signal class. CBFV was characterized as a nonstationary (fractal Brownian motion) signal with spectral index ß between 2.0 and 2.3. In the high-frequency range (>0.15 Hz), CBFV variability is mainly determined by the periodic ABP variability induced by heartbeat and respiration. However, most of the spectral power of CBFV is contained in the low-frequency range (<0.15 Hz), where cerebral autoregulation acts as a low-pass filter and where the fractal properties are found. Cerebral vasospasm, which is a complication of subarachnoid hemorrhage (SAH), is associated with an increase in ß denoting a less complex time course. A reduced fractal dimension of the retinal microvasculature has been observed in neurodegenerative disease and in stroke. According to the decomplexification theory of illness, such a diminished complexity could be explained by a restriction or even dropout of feedback loops caused by disease.

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.

Association of transcranial Doppler blood flow velocity slow waves with delayed cerebral ischemia in patients suffering from subarachnoid hemorrhage: a retrospective study

Background

Cerebral vasospasm (VS) and delayed cerebral ischemia (DCI) constitute major complications following subarachnoid hemorrhage (SAH). A few studies have examined the relationship between different indices of cerebrovascular dynamics with the occurrence of VS. However, their potential association with the development of DCI remains elusive. In this study, we investigated the pattern of changes of different transcranial Doppler (TCD)-derived indices of cerebrovascular dynamics during vasospasm in patients suffering from subarachnoid hemorrhage, dichotomized by the presence of delayed cerebral ischemia.

Methods

A retrospective analysis was performed using recordings from 32 SAH patients, diagnosed with VS. Patients were divided in two groups, depending on development of DCI. Magnitude of slow waves (SWs) of cerebral blood flow velocity (CBFV) was measured. Cerebral autoregulation was estimated using the moving correlation coefficient Mxa. Cerebral arterial time constant (tau) was expressed as the product of resistance and compliance. Complexity of CBFV was estimated through measurement of sample entropy (SampEn).

Results

In the whole population (N = 32), magnitude of SWs of ipsilateral to VS side CBFV was higher during vasospasm (4.15 ± 1.55 vs before: 2.86 ± 1.21 cm/s, p < 0.001). Ipsilateral SWs of CBFV before VS had higher magnitude in DCI group (N = 19, p < 0.001) and were strongly predictive of DCI, with area under the curve (AUC) = 0.745 (p = 0.02). Vasospasm caused a non-significant shortening of ipsilateral values of tau and increase in SampEn in all patients related to pre-VS measurements, as well as an insignificant increase of Mxa in DCI related to non-DCI group (N = 13).

Conclusions

In patients suffering from subarachnoid hemorrhage, TCD-detected VS was associated with higher ipsilateral CBFV SWs, related to pre-VS measurements. Higher CBFV SWs before VS were significantly predictive of delayed cerebral ischemia.

Variability Predictors of Vasospasm in Subarachnoid Hemorrhage: A Feasibility Study

BACKGROUND

Mean cerebral blood flow velocity (mean-CBFV) obtained from Transcranial Doppler (TCD) poorly predicts cerebral vasospasm in patients with aneurysmal subarachnoid hemorrhage (aSAH). Variability descriptors of mean-CBFV obtained during extended TCD recordings may improve this prediction. We assessed the feasibility of generating reliable linear and non-linear descriptors of mean-CBFV variability using extended recordings in aSAH patients and in healthy controls. We also explored which of those metrics might have the ability to discriminate between aSAH patients and healthy controls, and among patients who would go on to develop vasospasm and those who would not.

METHODS

Bilateral mean-CBFV, blood pressure, and heart rate were continuously recorded for 40 minutes in aSAH patients (n = 8) within the first 5 days after ictus, in age-matched healthy controls (n = 8) and in additional young controls (n = 8). We obtained linear [standard deviation, coefficient of variations, and the very-low (0.003-0.040 Hz), low (0.040-0.150 Hz), and high-frequency (0.15-0.4 Hz) power spectra] and non-linear (Fractality, deterministic Chaos analyses) variability metrics.

RESULTS

We successfully obtained TCD recordings from patients and healthy controls and calculated the desired metrics of mean-CBFV variability. Differences were appreciable between aSAH patients and healthy controls, as well as between aSAH patients who later developed vasospasm and those who did not.

CONCLUSIONS

A 40-minute TCD recording provides reliable variability metrics in aSAH patients and healthy controls. Future studies are required to determine if mean-CBFV variability metrics remain stable over time, and whether they may serve to identify patients who are at greatest risk of developing cerebral vasospasm after aSAH.

Complexity of cerebral blood flow velocity and arterial blood pressure in subarachnoid hemorrhage using time-frequency analysis

We investigated changes of time-frequency (TF) complexity, in terms of Rényi entropy and a measure of concentration, of middle cerebral blood flow velocity (CBFV) and arterial blood pressure in relation to the development of cerebral vasospasm in 15 patients after aneurysmal subarachnoid hemorrhage. Interhemispheric differences in the period of no vasospasm and vasospasm were also compared. Results show reduced complexity of TF representations of CBFV on the side of aneurysm before vasospasm was identified. This potentially can serve as an early-warning indicator of future derangement of cerebral circulation.

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

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

The effect of ventricular assist devices on cerebral blood flow and blood pressure fractality

Biological signals often exhibit self-similar or fractal scaling characteristics which may reflect intrinsic adaptability to their underlying physiological system. This study analysed fractal dynamics of cerebral blood flow in patients supported with ventricular assist devices (VAD) to ascertain if sustained modifications of blood pressure waveform affect cerebral blood flow fractality. Simultaneous recordings of arterial blood pressure and cerebral blood flow velocity using transcranial Doppler were obtained from five cardiogenic shock patients supported by VAD, five matched control patients and five healthy subjects. Computation of a fractal scaling exponent (α) at the low-frequency time scale by detrended fluctuation analysis showed that cerebral blood flow velocity exhibited 1/f fractal scaling in both patient groups (α = 0.95 ± 0.09 and 0.97 ± 0.12, respectively) as well as in the healthy subjects (α = 0.86 ± 0.07). In contrast, fluctuation in blood pressure was similar to non-fractal white noise in both patient groups (α = 0.53 ± 0.11 and 0.52 ± 0.09, respectively) but exhibited 1/f scaling in the healthy subjects (α = 0.87 ± 0.04, P < 0.05 compared with the patient groups). The preservation of fractality in cerebral blood flow of VAD patients suggests that normal cardiac pulsation and central perfusion pressure changes are not the integral sources of cerebral blood flow fractality and that intrinsic vascular properties such as cerebral autoregulation may be involved. However, there is a clear difference in the fractal scaling properties of arterial blood pressure between the cardiogenic shock patients and the healthy subjects.

Common multifractality in the heart rate variability and brain activity of healthy humans

The influence from the central nervous system on the human multifractal heart rate variability (HRV) is examined under the autonomic nervous system perturbation induced by the head-up-tilt body maneuver. We conducted the multifractal factorization analysis to factor out the common multifractal factor in the joint fluctuation of the beat-to-beat heart rate and electroencephalography data. Evidence of a central link in the multifractal HRV was found, where the transition towards increased (decreased) HRV multifractal complexity is associated with a stronger (weaker) multifractal correlation between the central and autonomic nervous systems.

Complexity of the human cerebral circulation

The cerebral circulation shows both structural and functional complexity. For time scales of a few minutes or more, cerebral blood flow (CBF) and other cerebrovascular parameters can be shown to follow a random fractal point process. Some studies, but not all, have also concluded that CBF is non-stationary. System identification techniques have been able to explain a substantial fraction of the CBF variability by applying linear and nonlinear multivariate models with classical determinants of flow (arterial blood pressure, arterial CO(2) and cerebrovascular resistance, CVR) as inputs. These findings raise the hypothesis that fractal behaviour is not inherent to CBF but might be simply transmitted from its determinants. If this is the case, future investigations could focus on the complexity of the residuals or the unexplained variance of CBF. In the low-frequency range (below 0.15 Hz), changes in CVR due to pressure and metabolic autoregulation represent an important contribution to CBF variability. A small body of work suggests that parameters describing cerebral autoregulation can also display complexity, presenting significant variability that might also be non-stationary. Fractal analysis, entropy and other nonlinear techniques have a role to play to shed light on the complexity of cerebral autoregulation.