Synopsis

The pulse pressure wave is an indicator for vascular health. Given the importance of vascular health to the central nervous system, we developed a method to extract intracranial pulse waveforms along the main cerebral arteries from dynamic MRI data. The resulting “pulse wave profiles” track the pulse shape along the main arteries of the brain. The simultaneous acquisition of pulse waveforms within the whole brain at once allows for a system analysis of the vasculature. A Matlab toolbox to compute pulse wave profiles is provided.

Introduction

The pulse pressure wave in the carotid and femoral arteries is an indicator for vascular health, as arterial compliance and the associated pulse wave velocity^1,2 are reliable prognostic markers for cardiovascular morbidity and mortality³. Given the importance of vascular health to the central nervous system, there is a need for diagnostic methods to extend the evaluation of pressure waves to the brain. Cerebrovascular compliance absorbs the impact of the pulse pressure wave on the brain and enables steady perfusion throughout the cardiac cycle^4,5. In addition, the pressure gradient caused by arterial pulsatility could be a driving force in the brain’s paravascular waste clearance system^6,7.

The arterial pulse leaves a clear signal in dynamic MRI data of brain vasculature^8-15, originating from pulsations of the vascular wall, vessel movement, blood flow effects, and other factors. Here we propose a method to extract the pulse waveforms along the main cerebral arteries from dynamic 7T MRI data, and present pulse wave profiles, diagrams of stacked pulse waveforms obtained from points along the artery. Pulse wave profiles afford a compact, visual, easily interpreted means for displaying information contained in pulse pressure waves. A link to software used to generate the profiles is provided.

Methods

Data: Dynamic EPI scans acquired on healthy subjects on a 7 Tesla MRI scanner¹⁶, covering regions between frontal and occipital cortex.

Analysis: For each subject, pulse waveforms were extracted from EPI data by hypersampling, a generalized form of retrospective gating¹⁷. Waveforms were estimated by smoothing the hypersampled signal with a zero-lag filter, retaining six cycles per cardiac cycle, and subsequent amplitude normalization. Waveforms were shifted to offset their relative slice acquisition time and then shifted by a constant amount to position the wave foot at the beginning of the cardiac cycle. From the resulting waveform amplitude volumes, maximum intensity projections (MIPs) were created (Fig. 1B). From those, start and end points on the middle cerebral artery (MCA; Fig. 1A) were selected. A reinforcement learning algorithm based on the Bellman equation^18,19 was used to define all the intermediate points on the MCA (overlay in Fig. 1B).

Pulse wave profiles: The pulse wave profiles were created by stacking all waveforms (Fig. 1C) vertically and color coding their values (Fig. 1D). Wave peaks and troughs were detected automatically and labelled with black and white markers, respectively, to guide the eye.

Wave transfer functions: Wave transfer functions relating input to output waveforms in a linear I/O model in frequency space were computed from averaged proximal (towards the heart) and distal (towards the venous system) waveforms (Fig. 1E).

Results

Pulse amplitude maps with an automatically tracked MCA, a pulse wave profile, averaged pulse waveforms, and the corresponding wave transfer function are shown in Fig. 1 for a single subject. Estimates of pulse waveforms show characteristic features such as a systolic upstroke and dicrotic notch (Fig. 1C). Pulse waveforms change with position on the MCA (Fig. 1D), also measured by the transfer function’s gain and phase (Fig. 1E).

Figure 2 shows an animation of the pulse wave traversing the brain.

Figure 3 shows MRI pulse wave profiles for 12 subjects. There is variability between subjects. For example, the slope of the line connecting the wave feet, related to pulse wave velocity, varies considerably between subjects.

Discussion

The simultaneous acquisition of pulse waveforms within the whole brain at once allows for a system analysis that is usually possible only with invasive methods²⁰. For example, timing information in the pulse wave profiles will facilitate estimation of properties such as pulse wave velocity. Transfer functions, which are independent of the incoming pulse shape, can be estimated from the pulse wave profiles to assess downstream wave reflection. The origins of the signals observed with these methods are currently under investigation^9,14.

Conclusion

MRI pulse wave profiles consist of estimates of pulse waveforms as the pulse travels down an artery or vein of a human brain. The peaks and troughs of these profiles contain information about local and non-local (via reflection) physical properties of the cerebrovascular system. We have observed a noteworthy variability in a sample of healthy subjects. Because of the significance of pulse pressure wave physiology in vascular health, our findings invite further studies of the origin of this variability, and a Matlab toolbox has been provided for this purpose.

Acknowledgements

We would like to thank the authors of the “Forrest Gump” study¹⁶ for providing their MRI data base. Disclosure: This work uses algorithms that are part of patent applications by Cornell University.

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