Pulsatility analysis of the circle of Willis

Abstract

Purpose

To evaluate the phenomenological significance of cerebral blood pulsatility imaging in aging research.

Methods

N = 38 subjects from 20 to 72 years of age (24 females) were imaged with ultrafast MRI with a sampling rate of 100 ms and simultaneous acquisition of pulse oximetry data. Of these, 28 subjects had acceptable MRI and pulse data, with 16 subjects between 20 and 28 years of age, and 12 subjects between 61 and 72 years of age. Pulse amplitude in the circle of Willis was assessed with the recently developed method of analytic phase projection to extract blood volume waveforms.

Results

Arteries in the circle of Willis showed pulsatility in the MRI for both the young and old age groups. Pulse amplitude in the circle of Willis significantly increased with age (p = 0.01) but was independent of gender, heart rate, and head motion during MRI.

Discussion and conclusion

Increased pulse wave amplitude in the circle of Willis in the elderly suggests a phenomenological significance of cerebral blood pulsatility imaging in aging research. The physiologic origin of increased pulse amplitude (increased pulse pressure vs. change in arterial morphology vs. re-shaping of pulse waveforms caused by the heart, and possible interaction with cerebrospinal fluid pulsatility) requires further investigation.

Introduction

Cerebrovascular pulsatility has gained significant importance as a research topic, primarily due to its potential impact on aging-related brain health. With advancing age, and in certain conditions such as chronic hypertension, the physical properties of the brain vasculature, and subsequently the vascular network, including its viscoelasticity, undergo changes [1], [2], [3], [4], [5]. These changes can lead to a reduction of the absorption of blood pressure pulsations, an increased impedance, and the potential for damage, including hemorrhagic stroke and microbleeds. Notably, small-scale changes that may not be evident in conventional imaging have attracted attention as potential contributors to conditions like dementia [6], [7], [8]. Furthermore, there is a growing body of evidence linking cerebrovascular health to various aspects of cognitive function and neurodegenerative diseases. For instance, aortic stiffness has been associated with cerebral small-vessel disease in hypertensive patients [9], cognitive decline correlates with the pulse wave velocity [10], and neurodegenerative diseases such as Alzheimer's disease are believed to be connected to cerebrovascular dysregulation [11], [12], [13], [14], [15]. Additionally, central artery stiffness has been reported to impact the perfusion of deep subcortical matter [16], central arterial aging appears to be linked to an increased volume of white matter hyperintensities [17], and arterial stiffness is associated with beta-amyloid deposition in the elderly [18]. In a more indirect manner, the pressure gradient induced by arterial pulsatility could potentially serve as a driving force in the brain's paravascular waste clearance system [19], [20], which plays a crucial role in brain health by facilitating the removal of metabolic waste products.

Therefore, it would be advantageous to directly image vascular changes in the brain. However, there are only limited in vivo options for imaging vascular dynamics in the human brain. Arterial spin labelling is probably the most advanced current method with the highest spatial resolution [21], [22]. It provides quantitative blood flow values in the capillary bed, assuming steady flow [23]. In contrast, the important parameter of arterial compliance depends on the pulsatile component of the flow. It can be imaged for larger vessels locally with transcranial Doppler ultrasound [24], [25]. Pulsatile flow components can also be imaged over the whole brain with 4D phase contrast angiography [26]. However, there has been recent progress in imaging pulsatility [27], [28], [29], [30], [31], [32], [33], [34], [35], [36] in the brain with fast echo-planar imaging (EPI). It is important to note that in the main cerebral arteries, pulse wave velocity is typically higher in magnitude (up to about 12 m/s) [37] than blood flow velocity (about 30 to 100 cm/s; varies widely with age, cardiac phase, blood pressure, type of artery, and other factors [38], [39].

In this contribution, we utilize the method of MRI hypersampling by analytic phase projection [40], which has been proven to reveal pulse waveforms in the main cerebral arteries. Importantly, this method can be seamlessly integrated into clinical MRI scans without the requirement for non-standard equipment or pulse sequences.

The region under study is the circle of Willis (COW), chosen for both pragmatic and scientific reasons. Pragmatically, the COW is easy to define in MRI, and for the sake of ultrafast imaging, it provides a suitable region with little inter-subject variability due to reproducible slice prescription. From a scientific standpoint, the COW holds a significant role in pulsatility, as it has been hypothesized to function as a pressure absorber mechanism that helps prevent damage to the cranial microvasculature and the blood–brain barrier [41]. However, it is worth noting that everything inside the skull pulsates in synchrony with the heartbeat [41], [42], [43], [44], [45], including cerebrospinal fluid, the cortical surface, and veins. The methods used in this study could potentially be useful for investigating pulsatility and pulse waves in other areas of the brain as well.

The research presented here is motivated by our enthusiasm for the exciting quest to better understand the aging human brain via biomedical imaging [46], [47], [48], [49], [50], [51], [52], [53], [54], [55], [56], [57], [58], [59], [60].

Materials and methods

Subjects

All participants were recruited using random market mailing within a 50-mile radius of Columbia University Irving Medical Center. Specifically, a marketing company provided a list of potential participants based on the requested demographics and geographical locations, and a questionnaire was sent to the identified individuals. All subjects gave their informed written consent prior to the scanning sessions and were compensated for their time spent taking part in this study. The experimental design of our study and the recruitment process were approved by Columbia University Institutional Review Board. Thirty-eight young and older but otherwise healthy participants (with cognitive scores within 2 standard deviations of the age-matched norm) between 20 and 72 years of age (24 female) were recruited. The MRI and pulse data were inspected for quality, and 28 subjects had acceptable MRI and pulse data. Specifically, the ten scans that could not be used for further analysis consisted of two scans that had an incorrect acquisition plane orientation, four scans that showed extreme head motion, and four scans that did not have usable pulse data. Of the remaining scans used for further analysis, 16 subjects were between 20 and 28 years of age (12 female) and 12 subjects between 61 and 72 years of age (5 female).

Imaging

Subjects were imaged using a 3 Tesla Siemens Magnetom Prisma scanner equipped with an 80 mT/m gradient system with a T₂*-weighted ultrafast echo-planar imaging (EPI) sequence (repetition time = 100 ms, echo time = 35 ms, flip angle = 62°, field-of-view of 22 cm, matrix size of 100 × 100, and slice thickness of 3 mm) with simultaneous and synchronized acquisition of pulse oximetry data from the index finger of the left hand. In addition, time-of-flight angiography images were acquired to allow for accurate slice positioning of the EPI sequence. Using sagittal, coronal, and axial views of the angiogram, the MRI operator was carefully placing a single EPI imaging slice through the center of the COW, attempting to cover it as much as possible. This slice was imaged with 3000 repetitions totaling 5 min scan time. This procedure was repeated for a mid-sagittal slice including parts of the fourth ventricle.

Pulse waveform analysis

Preprocessing of raw MRI data:

The first fMRI image of each subject was used as an anchor to which all subsequent 2999 images were aligned to by an intensity-based rigid image registration algorithm (MATLAB’s imregister function, which uses a regular step gradient descent optimizer. The minimum step size was set to 10^-3.). The EPI time series were detrended with a zero-lag high pass filter with a cutoff at 20 s, corresponding to 200 data points.

Preprocessing of pulse oximetry data

The pulse oximetry signals were filtered with a zero-lag lowpass filter with a cutoff at 1.5 Hz to enhance pseudo-periodicity [61], [62], [63] of the pulse signal, and to remove noise.

Estimation of pulse wave form and amplitude

For each subject, MRI pulse waveforms were extracted from the EPI-MRI data by analytic phase projection (APP) [40], [64], [65]. APP is a generalized form of retrospective gating. It overcomes the arbitrary limitation that the phase within an inter-beat interval is assumed to increase linearly: In APP, the phase of the pulse oximetry signal is estimated from the analytic phase of the pulse oximetry signal via a Hilbert transform. Thus, it can be nonlinear, leading to a more accurate gating for variable inter-beat intervals [66]. Then, each MRI data point is mapped to its corresponding phase, leading to a reordering of MRI data points in time, analogously to retrospective gating. Both retrospective gating and APP increase the number of data points during one cardiac cycle; it is equal to the total number of sampled MRI images, N (here, N = 3000). This provides a highly oversampled cardiac phase. This oversampling improves waveform estimation by partially averaging out factors that limit the temporal sampling accuracy. These factors include temporal blurring of the signal by the EPI readout time and estimation errors of the Hilbert phase. The pulse oximetry signals were then shifted in time to match the MRI acquisition sample times. The amount of shift was estimated by searching for the maximum average pulse signal amplitude in the hypersampled MRI data. The average pulse signal amplitude was averaged from the amplitudes in each voxel in the brain, by using a hand-drawn mask that excluded ventricles and skull areas. Finally, pulse waveforms were estimated by smoothing the hypersampled MRI signal with a zero-lag filter, retaining six cycles per cardiac cycle. For the display of waveforms in Fig. 1, waveforms were foot-to-foot normalized, after the sign of the waveform was determined by computation of the Q-value, a measure to assess the skewness of temporal correlations in a time series [67]. For negative Q, the sign of the waveform was inverted. This procedure was used to solve the problem that the sign of the MRI signal is not pre-determined, and this way the systolic upstroke appeared to have positive slope.

Fig. 1.

MRI pulse waves. A) The square root of MRI pulse wave amplitudes over the brain slice acquired with ultrafast MRI, for a single subject. The region of interest for the analysis of the circle of Willis and the baseline region without dominant pulsatility are highlighted. B) The maximum-amplitude MRI pulse wave in the circle of Willis shows the characteristic systolic upstroke starting at around phase value −2.5 rad. In addition, the maximum-amplitude baseline signal is shown in gray. C) Maximum-amplitude waveforms for all subjects, baseline-normalized.

Motion assessment

For each subject, head motion was quantified by the standard deviation of the rotation angle of the rigid transformation used for motion correction, using MATLAB’s imregtform function. In order to exclude the possibility that the amount of head motion during MRI scanning biased pulsatility measures, this parameter was included as a covariate in the statistical analysis.

Statistics

Two circular regions of interest (ROIs) were defined for each fMRI data set (Fig. 1): 1. An ROI centered at the COW, and 2. an ROI centered in a brain area nearby without noticeable pulsatility, used as baseline. The MRI pulse amplitude was computed for these ROIs as the average of the differences between the maximum and minimum waveform value. In the COW, this amplitude was then divided by the median amplitude from the baseline ROI. To evaluate the age dependence of pulsatility, a multiple regression analysis was performed with MRI pulse amplitudes in the COW as dependent variable and age, heart rate, motion, and gender as independent variables. Gender was used as a categorical variable. In addition, another multiple regression analysis was used to test for the possibility that the baseline ROI depends on any of the three independent variables. The same analysis was performed on the maximum amplitude voxel in the fourth ventricle, and normalized to a baseline ROI of 13 voxels in the center of the pons, which generally showed very low pulsatility amplitude.

Results

Pulse amplitude maps could reliably be obtained from all 28 subjects and showed pulsatility in the circle of Willis, parts of the middle cerebral arteries, arteries in the scalp, and other regions, including spaces filled with cerebrospinal fluid (CSF). An example pulse amplitude map is shown in Fig. 1 for a single subject. Estimates of pulse waveforms often showed characteristic features such as the systolic upstroke and dicrotic notch (Fig. 1C), but overall show significant inter-subject variability.

A multiple regression analysis revealed that pulse amplitude in the COW increased with age (p = 0.01) but was not significantly dependent on heart rate, gender, or head motion during MRI. In the baseline region, pulse amplitude did not depend on age, heart rate, motion, or gender. The statistics is summarized in Table 1, and the increase of pulse amplitude with age in the COW is shown in Fig. 2.

Table 1.

Multiple linear regression analysis. Number of observations: 28, Error degrees of freedom: 23. COW: Root Mean Squared Error: 3.33, R-squared: 0.261, Adjusted R-Squared: 0.132, F-statistic vs. constant model: 2.03, p-value = 0.124. Baseline: Root Mean Squared Error: 0.11, R-squared: 0.113,  Adjusted R-Squared: -0.0418, F-statistic vs. constant model: 0.729, p-value = 0.581

	Circle of Willis			Baseline
Variable	Estimate	t-value	p-value	Estimate	t-value	p-value
Intercept	7.7	1.5	0.1	0.3	1.8	0.09
Age	0.1	2.8	0.01	−0.0007	−0.6	0.6
Heart rate	−0.04	−0.5	0.6	0.0005	0.2	0.9
Gender	−1.5	−1.0	0.3	−0.05	−1.1	0.3
Motion	−1286	−1.3	0.2	11	0.3	0.7

Fig. 2.

Increase of mean pulse amplitudes with age in the circle of Willis. The two age groups have different mean value with a p-value of 0.013 (post-hoc non-parametric Wilcoxon test). The amplitudes used here were normalized by the median baseline amplitude for each subject. The subject of Fig. 1 is marked with an arrow. The inset shows the distribution of the residuals of a linear regression fit and the p-value for the hypothesis that the residuals are not normally distributed.

Discussion

Our interpretation of age-related increase of fMRI derived pulse wave amplitude in the circle of Willis is as follows. In general, arterial blood flow consists of two components: The steady and the pulsatile flow [68], [69], [70]. Outside the capillary bed [71], the former is mainly affected by peripheral vascular resistance, while the latter is mainly affected by arterial stiffness. After the age of 60, increases in blood pressure are primarily attributable to an increase of systolic pressure, leading to a rapid increase of pulse pressure, the difference between systolic and diastolic pressure [72]. We suggest that increased pulse pressure in cerebral arteries causes increased pulse amplitude in the COW, because the pulsatile blood flow experiences a relatively greater increase than the steady flow. An alternative explanation for larger pulse wave amplitudes could be that the arterial compliance, the ratio of blood volume and blood pressure, increases with age in the circle of Willis. However, due to the lack of information about intracranial blood pressure, and the fact that this explanation would contradict the general trend of an increase of arterial stiffness with age, this seems to be less likely.

The observed variability of waveform shapes across subjects is likely partially related to the known interindividual variation of COW structure and function in the general population, including hypoplastic posterior communicating arteries and duplicated/missing communicating arteries. For an overview of COW variance studies see Vrselja et al. [41] and the later meta-analysis by Jones et al. [73]. In one study, a complete COW was identified in less than half of the population [74]. The variability in pulse waveforms is accompanied by interindividual variability of pulsatility amplitude and anatomy in the present sample: Supplementary Fig. 1 shows pulse amplitude maps for the scanned slice through the COW, and Supplementary Fig. 2 MRA maximum-intensity projections of all subjects.

The COW is embedded into the subarachnoid space, which is also filled with CSF. We cannot exclude that the CSF in this space might pulsate itself. For another CSF filled space, the aqueduct, it is known that CSF pulsatility increases with age in healthy subjects [75] (but also see references [76], [77], [78], [79], [80], [81] for missing or opposite age effects on cerebral CSF pulsatility). In our study, it was difficult to separate possible CSF contributions to pulsatility with the present resolution of the pulsatility scan. Therefore, to assess the age dependence of CSF pulsatility in this subject sample, an analysis of the fourth ventricle, scanned in mid-sagittal orientation but otherwise with identical parameters as the COW MRIs, was performed. It is plausible that pulsatility of the CSF in small CSF filled spaces can be picked up with the same method of analytic phase projection. A highly significant age dependence of CSF pulsatility was observed (Supplementary Fig. S3A), and the CSF pulse waveforms showed a pronounced separation between the two age groups, too (Supplementary Fig. S3B). Therefore, this result, obtained with our specific protocol and in this specific group of subjects, needs to be considered in the interpretation of pulsatility of the COW. The question whether CSF pulsation is partially responsible for the here observed age increase of pulsatility could be better assessed with blood-flow sensitive imaging such as phase-contrast MRI [82]. This would allow for a separation of pulsatility into fast (blood) and slow (CSF) motion components, and is planned in our future research.

It is an open question whether the increase in waveform amplitude is due to a change of the wave form before it enters the brain, due to a change inside the cerebral arteries, or due to an altered wave reflection at the arteriole/capillary level. A more thorough investigation would have to involve the measurement of wave forms at the aortic or carotid level [83], [84], and MRI of larger brain regions. It is neither clear from the present data if an actual re-shaping of the waves or an amplification, or a combined effect thereof, takes place [85], [86], [87], [88], [89], [90]. For a detailed analysis of wave forms, one would have to acquire data with higher spatial resolution that would allow for probing specific vessels rather than the average pulse amplitude in the circle of Willis. With faster imaging methods and higher field MRI [91], [92], [93], [94], [95], studies like these are now within reach and subject of further research.

This MRI experiment was not specifically designed to investigate pulsatility in the circle of Willis, and follows up on the incidental finding of pulsatility using fast fMRI [96], [97], [98], [99]. As such, it was not optimized for detecting pulsatility, and the study design and MRI parameters chosen here might not all be optimal for MRI studies of cerebral pulsatility. Therefore, we are concluding the discussion by reviewing some specific considerations for MRI studies of pulsatility in the circle of Willis.

The pulse wave from the heart to the finger experiences a different distance and vasculature than the pulse wave from the heart to the circle of Willis. The temporal shift between signals measured on the finger with pulse oximetry and the signal measured with MRI [98] in the circle of Willis should therefore show interindividual variability, which might contain useful information. For example, increased pulse wave velocities caused by increased arterial stiffness would affect this shift. However, our technical setup with a lack of absolute reference times precluded such an analysis.

The flip angle of 62° was not optimized to be maximally flow sensitive. A flip angle of 90° would be more suitable to emphasize inflowing blood and would possibly result in an increase of pulse wave amplitudes [100]. In order to develop pulsatility imaging of the circle of Willis, with its combination of blood vessels of different diameters, as a diagnostic tool, a thorough study of the effects of MRI parameters could be worthwhile to undertake. Imaging parameters such as resolution, flip angle, and echo times will have to be optimized to maximize sensitivity of such a tool.

Impressive progress in vascular pulsatility imaging has been made with phase-contrast angiography and related fast MRI methods [83], [101], [102], [103], [104], [105], [106], [107], [108], [109]. We believe that high-resolution 4D phase contrast, combined with high-resolution angiographic imaging, and peripheral blood pressure and pulse wave velocity measurements, will provide a powerful approach to investigate further the cause and effects of age- and disease-related changes of pulsatility in this region.

The observed pulsatility in the circle of Willis was not strong enough to accurately estimate the cardiac phase from the signal itself, which was overcome by estimating the phase with analytic phase projection [40]. However, for sufficiently strong signals, it is possible to estimate the phase from the MRI data itself [98], [110], [111], [112], which could increase accuracy of waveform estimates. Such an approach could pave the way to a more detailed analysis of pulse waveform shapes and their potential interpretation.

This study was designed to compare young and old subjects with each other [84]. However, it is known from sonography studies that in men, carotid artery distensibility and compliance begin to decrease around 30 years of age [113]. Our study does not catch potential changes in cerebrovascular physiology in this age group. In order to investigate potential precursors of increased risk of future cerebrovascular disease [114], it would be worthwhile to include the cohort of the 30 to 60 years old, too.

Conclusion

We have evaluated the significance of cerebral blood pulsatility imaging in the circle of Willis and investigated its changes with age. We showed that the arteries of the circle of Willis exhibit MRI-pulsatility for both the young and old age groups, and that pulse amplitude significantly increases with age. This suggests a phenomenological significance of cerebral blood pulsatility imaging in aging research. However, the physiologic origin of increased pulse amplitude requires further investigation.

Data sharing

The MRI data is available upon request for scientific researchers. The APP algorithm has been published before [40] and is also available here:

www.mathworks.com/matlabcentral/fileexchange/68807-pwp.

Author contributions

H. U. Voss: Data curation; Formal analysis; Investigation; Methodology; Software; Writing – original draft. O. R. Razlighi Conceptualization; Data curation; Investigation; Project administration; Resources; Supervision; Writing – review & editing.

CRediT authorship contribution statement

Henning U. Voss: Writing – review & editing, Writing – original draft, Validation, Software, Methodology, Investigation, Formal analysis. Qolamreza R. Razlighi: Writing – review & editing, Writing – original draft, Supervision, Resources, Project administration, Investigation, Funding acquisition, Data curation, Conceptualization.

Declaration of competing interest

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: The corresponding author is the inventor of patent WO 2019/199960A1, awarded to Cornell University, that describes the method of hypersampling used in this work.

Appendix A. Supplementary data

The following are the Supplementary data to this article: