Phase dynamics of cerebral blood flow in subarachnoid haemorrhage in response to sodium nitrite infusion

Aneurysmal subarachnoid haemorrhage (SAH) is a devastating subset of stroke. One of the major determinates of morbidity is the development of delayed cerebral ischemia (DCI). Disruption of the nitric oxide (NO) pathway and consequently the control of cerebral blood flow (CBF), known as cerebral autoregulation, is believed to play a role in its pathophysiology. Through the pharmacological manipulation of in vivo NO levels using an exogenous NO donor we sought to explore this relationship. Phase synchronisation index (PSI), an expression of the interdependence between CBF and arterial blood pressure (ABP) and thus cerebral autoregulation, was calculated before and during sodium nitrite administration in 10 high-grade SAH patients acutely postrupture. In patients that did not develop DCI, there was a significant increase in PSI around 0.1 Hz during the administration of sodium nitrite (33%; p-value 0.006). In patients that developed DCI, PSI did not change significantly. Synchronisation between ABP and CBF at 0.1 Hz has been proposed as a mechanism by which organ perfusion is maintained, during periods of physiological stress. These findings suggest that functional NO depletion plays a role in impaired cerebral autoregulation following SAH, but the development of DCI may have a distinct pathophysiological aetiology.


Introduction
Aneurysmal subarachnoid haemorrhage (SAH) is a devastating subset of stroke, characterised by high patient mortality and long-term disability. [1] As a result, SAH is estimated to cost the UK economy £510 million/year [2], with the loss of productive years equal to that of ischaemic stroke. One of the major causes of morbidity and mortality is the development of secondary neurological injuries, 3-14 days after the initial bleed, previously termed "vasospasm" but now known as delayed cerebral ischemia (DCI). [3] The underlying aetiology of DCI is poorly understood, despite it affecting 30% of SAH patients who survive to hospital admission. [4] The phenomenon of early brain injury (EBI) has recently attracted attention as an important mechanism in the development of DCI. The term refers to a multifactorial global cerebral injury that develops in the first 72 hours following SAH. [5] A growing body of clinical studies suggest that disruption to cerebral blood flow (CBF) control may play a critical role in the pathophysiology of EBI, and that its severity directly correlates with the development of DCI. [6 14] As a consequence, the role of the nitric oxide (NO) signalling pathway EBI has garnered considerable interest. [15] Animal models suggest that NO levels demonstrate a biphasic response following SAH.
Haemoglobin and its breakdown products, buffer free NO and inhibit endothelial NO synthase (eNOS) function resulting in profound early nitric oxide depletion. This followed at 6-72 hours by an increase in inducible NO synthase (iNOS) activity and an elevation of NO above baseline levels. [16,17] Whilst studies in humans almost universally demonstrate elevated NO products in the EBI period, evidence corelating changes in NO and the develop of DCI is far from conclusive. Both relatively decreased [18,19] and increased [20,21] levels have been shown to demonstrate an association with the development of DCI.
One of the primary obstacles in determining the role of NO is the inability to measure NO levels directly due to its exceptional short biological half-life. NO levels are extrapolated from the measurement of NO breakdown products within the cerebrospinal fluid (CSF), and therefore, neither account for regional distribution or biological availability of NO. Alternatively, it may be possible to probe the NO pathway by determining the cerebral response to in vivo manipulation of the NO levels using an exogenous nitric oxide donor.
During the last decade, a series of pre-clinical and clinical studies have demonstrated that the inorganic anion nitrite represents an important endogenous storage pool of NO. [22] In ischemic or hypoxic tissue environments, where enzymatic production of NO is limited by the requirement for molecular oxygen, nitrite is reduced to form NO. Critically the magnitude of this storage pool is modifiable by loading with exogenously administered nitrite. [23] Following the administration of sodium nitrite, Garry et al., demonstrated significant increase in the electroencephalographic (EEG) spectral alpha/delta power ratio (ADR) in high grade SAH patients. [24] ADR has been shown to correlate with regional CBF after ischemic stroke. [25] Furthermore, primate autologous blood clot injection models of SAH suggest that sodium nitrite may prevent or reverse the cerebrovascular manifestations of DCI. [26,27] These findings support the hypothesis that disruption to the NO pathway plays an important role in the disruption of CBF control during EBI.
However, direct examination of the relationship between the NO pathway, CBF control and EBI has not previously been investigated.
The control of CBF with respect to arterial blood pressure (ABP) is classical referred to as cerebral autoregulation. [28] Utilising induced changes or naturally occurring spontaneous oscillations in ABP it is possible to characterise the dynamic relationship between ABP and CBF mathematically and, therefore, to derive metrics to quantify dynamic cerebral autoregulation (dCA). [29] Normal dCA is often described in terms of a high pass filter, where low frequency changes in ABP are dampened. [29] Efforts to demonstrate that disruption to the NO signalling pathway has a discernible effect on dCA utilising healthy volunteer models have been so far inconclusive. [30 32] This may be in part due to the methods chosen to determine dCA, which assume that dCA can be described as a linear time-invariant system. However, both these assumptions are likely to be untrue, especially at low frequencies where non-linearity and non-stationarity have a pronounced effect. [33 35] To address non-stationarity, Latka et al. utilised the continuous wavelet transform [36], an integral transform that uses wavelets, which are essentially wave-like functions with compact support i.e. they are zero outside some finite time interval (Figure 1a). [37] Wavelets are localised in both time and frequency; thus, they can be used to extract the time-varying spectral features of a signal. By determining the instantaneous phase of the ABP and CBF signals, Latka et al. derived a statistic, the phase synchronisation index (PSI) ( ), to describe the interdependence of the two signals in relation to the variance of their phase difference over time. [36] Repeated studies have shown that the PSI of healthy volunteers demonstrates a highly consistent morphology (Figure 1b). [38 41] We propose that examination of changes to the characteristic morphology of the PSI may represent a more sensitive method of determining the effects of NO on dCA. As a result, the aim of the study was to examine the role of the NO pathway on dCA during EBI in high grade SAH using pharmacological manipulation of in vivo NO levels and utilising a novel non-stationary analysis technique. We hypothesised that SAH would be associated with impaired CBF phase dynamics, and that manipulating the NO pathway with intravenous sodium nitrite would result in normalisation of this relationship.

Participants
In this study we performed an extended analysis of the haemodynamic data collected by Garry et al. [24] Of the 14 patients included in the original study, 10 patients had continuous transcranial Doppler ultrasonography (TCD) and ABP waveforms recorded of sufficient quality required for the present analysis.
All patients aged 18-80 years admitted to the John Radcliffe Hospital, Oxford after having suffered severe aneurysmal SAH (World Federation of Neurosurgeons (WFNS) grade 3-5) and successful treatment with endovascular coiling were eligible for inclusion.
Exclusion criteria included contraindications to sodium nitrite, specifically, severe cardiovascular compromise and pre-existing methaemoglobinaemia. Written informed consent was obtained from the next of kin, and from participants themselves, if they regained capacity to consent. The study was approved by the South Central Oxford C NHS Health Research Authority Ethics Committee 12/SC/0366. All patients were managed in line with local clinical guidelines on the intensive care unit.
Sedation was maintained with a combination of propofol, fentanyl, and midazolam with neuromuscular blockade using atracurium as required. Mean arterial blood pressure (MAP) was maintained between 60-90 mmHg using an infusion of noradrenaline. All patients received oral nimodipine 60mg 4 hourly and had plasma magnesium levels maintained at 1-1.2 mmol/L. Patients with hydrocephalus were treated with external ventricular drainage.

Study Design and Data Collection
All participants received an infusion of sodium nitrite at 10 mcg/kg/min for one hour via a peripherally sited intravenous canula. Sodium nitrite has been established as safe for long term use in human SAH. [42] In this instance, the dosing schedule was developed as a compromise between ensuring adequate plasma nitrite levels and minimisation of cardiovascular effects.
Continuous measurements of middle cerebral artery (MCA) blood flow velocity, arterial blood pressure (ABP), intracranial pressure (ICP) and end tidal CO2 (PETCO2) and O2 (PETO2) were made prior to and during the infusion of sodium nitrite. CBF velocity (CBFV; cm/s) in the MCA was monitored using TCD (EZ-Dop, DWL, Germany; 2 MHz). Insonation of the MCA M1 segment was performed using a probe fixed at a constant angle and position relative to the head with a custom-made headset.
This was initially performed bilaterally to assess for the best temporal window and then continuously recorded unilaterally from the best side. ABP (mmHg) was monitored via an intraarterial catheter sited in the radial artery (Baxter Healthcare, UK). ICP (mmHg) was monitored with an intraparenchymal microsensor inserted into the frontal lobe (Codman, UK). 3 patients did not have ICP monitoring. End tPETCO2 and PETO2 (kPa) were monitored using side stream infrared and optical sensors, respectively (AD Instruments, New Zealand). All data was sampled at 100 Hz on a Power-1401 data acquisition interface (Cambridge Electronic Design, UK) and recorded for off-line analysis.
All drug infusions were documented and changes in rate were minimised for the duration of the recording. The diagnosis of delayed cerebral ischemia/infarction was made by the attending clinicians, independent to the study, in line with consensus multi-disciplinary guidelines. [43] We ha e e lici l a ided he e f he e m a a m a id confusion between angiographic vasospasm and the clinical manifestations of cerebral ischemia which historically has also been termed vasospasm. Each surviving patient was followed up at 3-6 months post-rupture using the modified Rankin scale (mRS). [44]

Data Pre-processing
Data pre-processing was carried out using custom written MATLAB [45] scripts. Baseline data consisted of 30 minutes of recordings made prior to the infusion. Infusion data consisted of 45 minutes of recordings made 5 minutes after the start of the infusion, to account for dead space in the peripheral canula and connectors.
Data was divided into 15 minute segments, in line with Latka et al. [36] and visually screened to exclude those containing excessive artefacts lasting longer than three cardiac cycles. Short periods of artefact, less than three cardiac cycles, were removed and replaced by linear interpolation. [46] This resulted in the exclusion of 4 out of 50 data segments (8% of data).
Beat-to-beat average values of CBFV, ABP and ICP were obtained via waveform integration using the time of the BP diastolic value to indicate each cardiac cycle. The non-uniformly spaced timeseries were resampled uniformly at 5 Hz using spline (thirdorder polynomials) interpolation. No detrending, normalization, or filtering was performed, in line with the CARNET (Cerebral Autoregulation Network) transfer function analysis white paper. [47] PETCO2 values were calculated via waveform peak identification.

Wavelet Phase Synchronisation
A continuous wavelet transform was performed on all ABP and CBFV waveform segments using the MATLAB CWT function. [45] Continuous wavelet analysis is performed by starting with a prototype wavelet, known as the mother wavelet ( ), that is scaled (i.e dilated or shrunk) in such a way that the wavelet shape remains constant, but the duration is altered. This results in the formation of a daughter wavelet at each scale A relationship between the scale of the daughter wavelet and frequency can then be approximated using: Where is the pseudofrequency of scale and is the central frequency of the mother wavelet. For comparability with the majority of studies investigating CBF control, we will primarily refer to frequency rather than scale.
Input signals are finite in length, however, the wavelet function extends beyond the borders of these timeseries. As a consequence, the resulting convolution will exhibit edge effects. It is therefore necessary to define a cone of influence (COI), for which edge effects cannot be ignored and are therefore excluded from the analysis. We consider the COI as the area that the wavelet power has dropped to − of the value at the edge. [48] The COI for larger scales (where the daughter wavelet is dilated to a greater degree) will occupy a larger proportion of the timeseries. The larger the scale, the longer the daughter wavelet and, therefore, extension beyond the border of the timeseries.
It possible to resolve the amplitude of a signal by time and scale and also by the phase.
By utilising a complex mother wavelet, i.e. one that contains both real and imaginary components, the instantaneous phase of the signal ( ) at a given scale a is given by: where | , 0 | is the compex modulus of the complex wavelet coefficients.
In this analysis, we employed the complex Morlet wavelet with bandwidth and centre frequency , both equal to 1, as per Latka et al. [36] The equation defining the complex mother Morlet wavelet is given by: The real and imaginary parts of the complex Morlet are plotted in Figure 1a. As can be seen, the Morlet wavelet is a sinusoidal wave modulated by a Gaussian function.
From the instantaneous phase representations of the ABP and CBFV timeseries, , 0 and , 0 , respectively, the instantaneous phase difference Δ , 0 can be defined as:

Statistical Analysis
Statistical analysis of the PSI was carried out using R (R Foundation for Statistical Computing) [49] and the analysis package nlme (R package version 3.

Physiological data
There was a significant decrease in mean arterial blood pressure (MAP) following administration of sodium nitrite (mean baseline MAP 77.5 mmHg to mean infusion MAP 71.1 mmHg; p = 0.005, paired two tailed S de e ). The e e e ig ifica changes in CBFV, ICP, or PETCO2 values (Table 2).

Phase Synchronisation Analysis
Inspection  Within condition comparisons identified that there was no significant difference in mean baseline PSI between patients that developed DCI and those that did not (p value = 0.175).
However, there was a significant difference in mean PSI during the infusion (p value =

Main findings
The aim of this study was to investigate the role of the NO pathway on the phase dynamics of CBF after SAH using an exogenous NO donor. By utilising the continuous wavelet transform and phase synchronisation analysis, we have been able to identify changes in the dynamic phase relationship between CBFV and ABP following the administration of exogenous nitric oxide donor.
Most importantly, we have identified that SAH patients that did not go on to develop DCI demonstrate a significant increase in mean phase synchronisation index in the 0.1 Hz range following the administration of sodium nitrite. Whereas, in patients that did develop DCI, there was no change in mean phase synchronisation index within the same frequency range. Importantly, the examined SAH patients were indistinguishable at baseline with respect to PSI.

Low frequency pulsatile flow
Latka et al. suggested that the peak in phase synchronisation between ABP and CBF at around 0.1 Hz is the result of the synchronisation of low frequency oscillations in arterial blood pressure, known as Mayer waves, and CBF. [36] Mayer waves are thought to result from baroreflex-mediated changes in sympathetic outflow to systemic vasculature [52] and were considered represent an epiphenomenon of normal baroreflex operation with no specific function. [53] Yet a growing body of evidence suggests that they play an essential role in maintaining organ perfusion, especially during periods of physiological stress.
In a study performed by Rickards  It has been proposed that rhythmic fluctuations in ABP provide a pump-like effect improving tissue perfusion during physiological stress via increases in the pressure gradient within the vasculature. [59] Alternatively, there is evidence from computational models to suggest that oscillatory flow is beneficial to radial oxygen diffusivity. [60] Although a direct comparison with the PSI in healthy volunteers produced by Latka et al. [36] is subject to several caveats (see limitations), the apparent absence of the peak in PSI around 0.1 Hz in the baseline data is suggestive of impaired baseline cerebral perfusion. Unfortunately, comparison with previous studies investigating CBF control in SAH is difficult. The majority of studies utilised linear correlation at frequencies < 0.05 Hz as a metric of CBF control [6 9,14], and did not report results on the coupling between ABP at CBF around 0.1 Hz. In the single study that performed a frequency domain analysis [11], the reported frequency band (0.03 Hz 0.15 Hz) encompasses much of the very low frequency domain (0.02-0.07 Hz). [29] As will be expanded upon later, an increased coherence in the very low frequency band is associated with impaired dynamic cerebral autoregulation, as would be likely after SAH, and would therefore mask any reduction in coherence we may expect to observe around 0.1 Hz.
Despite this, a comparable study using continuous wavelet transforms and PSI in traumatic brain injury patients also identified the absence of the 0.1 Hz centred peak in PSI when compared to matched controls. [40] This suggests that disruption to low frequency pulsatile flow may represent a common pathophysiological process in acute brain injuries.

Role of Nitric Oxide
The increase of 0.1 Hz-centred phase synchronisation following administration of sodium nitrite suggests that NO plays a critical role in the synchronisation between low frequency oscillations in ABP and CBF. Furthermore, the absence of the 0.1 Hz centred peak in the baseline synchronisation index supports evidence suggesting functional disruption to the NO signalling pathways during EBI. [15] There is a strong biological plausibility to the above assertion. Pulsatile flow is known to induce endothelial sheer stress and the liberation of NO [61], which in turn induces vascular smooth muscle relaxation via cyclic guanosine monophosphate (cGMP) dependent processes. [62] Vasodilatation of peripheral resistance vessels downstream of the insonated middle cerebral artery segment would promote flow and therefore increase CBFV in the insonated segment. [63] Furthermore, inhibition of NO synthase in isolated cerebral blood vessels has been shown to induce chaotic vasomotion at 0.

Differential Outcome Response
Our findings clearly demonstrate that the increase in 0.1 Hz centred phase synchronisation following administration of sodium nitrite occurs in patients that did not go on to develop DCI but was not present in those patients that did develop DCI. These findings replicate the differential EEG response also observed by Garry et al. [24] A possible explanation for the differential response is that the patients who developed DCI sustained a more severe injury in the acute period following aneurysmal rupture with a resulting greater functional NO depletion. Furthermore, there is evidence to suggest a correlation between subarachnoid haemorrhage blood volume and the development of DCI. [70,71] Elevated free haemoglobin and its breakdown products would result in increased buffering of both endogenous NO and NO liberated from the infused sodium nitrite.
If the result of decreased NO bioavailability in those who develop DCI, we may expect to observe an increase in phase synchronisation with longer or larger infusions. However, it is likely that changes in downstream signalling factors also contribute significantly.
Animal models have shown both reduced expression of vascular smooth muscle soluble guanylate cyclase [72] and increased rates of cGMP hydrolysis [73] during DCI.
Additionally, higher levels of 20-HETE in the CSF of patients has been associated with the development of DCI. [68] Modelling work by Catherall showed that cGMP only has influence over vascular smooth muscle phosphorylation, and, therefore, contractility, over a limited range of intracellular calcium concentrations. [74] Excitotoxicity, resulting in elevated intracellular calcium concentration, is a known pathophysiological component of SAH. [75] It is plausible that in patients that develop DCI, modulating cGMP concentrations via NO will have no effect due to significantly elevated intracellular calcium concentrations. This correlates with evidence that the calcium channel antagonist, nimodipine, improves outcomes following SAH. [76] Alternatively, functional NO depletion maybe a characteristic of EBI only in patients that do not develop DCI. Whereas, in patients that develop DCI cerebral NO concentration, via iNOS dependent production, have exceeded the functional operating range, potentially reaching cytotoxic levels, rending additional increases ineffectual. This would be consistent with evidence demonstrating higher NO breakdown products in patients that develop DCI [20,21], and the hypothesis that NO mediated toxicity results in DCI. [15]

Dynamic Cerebral Autoregulation
When considered in the frequency domain, normal dCA is characterised by low coherence, low gain and high phase lead in the very low frequency range, and increasing coherence and gain, and decreasing phase lead as frequencies increase. [29] Applying this interpretation, the high coherence observed at 0.1 Hz during central hypovolemia should be considered to reflect impaired dCA. However, as previously described, the increase in coherence appears to protect cerebral perfusion, suggesting a relationship more complex than that of a simple high pass filter. Given that the majority of studies investigating dCA in SAH have only considered the very low frequency band (0.02 0.07 Hz) and the apparent complex relationship at higher frequencies, we will regard frequencies below 0.07 Hz to reflect dCA. proposed to recouple endothelial NO synthase function, resulting in increased NO levels. [78] One explanation for the failure to observe a significant difference may be the reduced length of data available at low frequencies. As frequencies decrease the COI increases, reducing the available data for analysis.

Limitations
The small sample size and absence of a control group represent the major limitations of the present study. Furthermore, we have used morphological differences in the PSI between our patient population and healthy volunteers, derived from Latka et al., [36] to guide subsequent analysis. However, caution must be applied in drawing conclusions regarding the aetiology of these differences. Our patient population was sedated and mechanically ventilated, with many of them receiving vasopressor drugs. These factors alone may result in significantly different phase synchronisation characteristics and, although attempts have been made to account for within patient differences, they limit the ability to draw firm comparisons. Future studies should include a control population drawn from sedated and ventilated patients without acute neurological injury.
Unmeasured variability, in the form of natural oscillations of PETCO2, may account for a proportion of the low phase synchronisation at certain frequencies. [33,41] However, these studies was performed in spontaneously breathing healthy volunteers. Given that in our study all the patients were mechanically ventilated with pressure controlled intermittent positive pressure ventilation, the variability of PETCO2 is very low. As such, there appeared no advantage to adding additional complexity by incorporating PETCO2 into the analysis approach. Furthermore, inclusion of PETCO2 had no effect on PSI estimates at 0.1 Hz and therefore would be unlikely to influence our primary finding.
Average PETCO2 levels were, however, considered in the mixed effects linear model.

Conclusion
We have demonstrated that pharmacological manipulation of in vivo NO levels in patients with high grade SAH results in increased synchronisation between ABP and CBF around 0.1 Hz in patients that do not develop DCI. Such synchronisation has been proposed as a mechanism by which cerebral perfusion is maintained during periods of physiological stress. These findings suggest that functional NO depletion plays a role in impaired CBF control during EBI, but that the development of DCI may have a distinct pathophysiological aetiology.  for frequencies below 0.07 Hz, for the different conditions. Bars represent 95% confidence intervals.
a) A significant increase of PSI in patients that did not develop DCI following sodium nitrite is visible. PSI is also significantly larger in patients that did not develop DCI, than those that did during the infusion of sodium nitrite. b) No significant differences are visible.