Comparison of computational fluid dynamics with transcranial Doppler ultrasound in response to physiological stimuli

Abstract

Cerebrovascular haemodynamics are sensitive to multiple physiological stimuli that require synergistic response to maintain adequate perfusion. Understanding haemodynamic changes within cerebral arteries is important to inform how the brain regulates perfusion; however, methods for direct measurement of cerebral haemodynamics in these environments are challenging. The aim of this study was to assess velocity waveform metrics obtained using transcranial Doppler (TCD) with flow-conserving subject-specific three-dimensional (3D) simulations using computational fluid dynamics (CFD). Twelve healthy participants underwent head and neck imaging with 3 T magnetic resonance angiography. Velocity waveforms in the middle cerebral artery were measured with TCD ultrasound, while diameter and velocity were measured using duplex ultrasound in the internal carotid and vertebral arteries to calculate incoming cerebral flow at rest, during hypercapnia and exercise. CFD simulations were developed for each condition, with velocity waveform metrics extracted in the same insonation region as TCD. Exposure to stimuli induced significant changes in cardiorespiratory measures across all participants. Measured absolute TCD velocities were significantly higher than those calculated from CFD (P range < 0.001-0.004), and these data were not correlated across conditions (r range 0.030-0.377, P range 0.227-0.925). However, relative changes in systolic and time-averaged velocity from resting levels exhibited significant positive correlations when the distinct techniques were compared (r range 0.577-0.770, P range 0.003-0.049). Our data indicate that while absolute measures of cerebral velocity differ between TCD and 3D CFD simulation, physiological changes from resting levels in systolic and time-averaged velocity are significantly correlated between techniques.

Keywords: Cerebral vasculature; Computational fluid dynamics; Stimuli; Transcranial Doppler ultrasound.

Fig. 1

Example TCD probe as well as consecutively spaced CFD constrained planes A demonstrating sampling of data within the right M1 segment. Within the CFD simulations, maximal velocity was calculated and extracted at each of these planes and averaged into a mean value representative of the peak velocity envelope from TCD insonation of the right M1 segment in each participant. Example velocity waveforms from TCD and CFD sources from an individual are provided. Velocity waveform metrics were then extracted and compared between sources across a range of different exposure conditions (rest, hypercapnia and exercise)

Fig. 2

MRA-derived 3D cerebrovascular reconstructions of each participant

Fig. 3

Correlation plots of inlet blood flow (tCBF) with the velocity waveform characteristics of systolic (A, D, G), average (B, E, F) and end-diastolic (C, F, I) maximal velocity extracted from CFD (white) and TCD (black) data in the right M1 segment of the MCA for the conditions of rest (A–C), hypercapnia (D–F) and exercise (G–I). Pearsonʼs correlation coefficient (r) and P-value (P) are displayed for each data source per correlation plot

Fig. 4

Correlation plots of the relative change (Δ%) in inlet blood flow (tCBF) with the relative change in systolic (A, D), average (B, E) and end-diastolic (C, F) maximal velocity extracted from CFD (white) and TCD (black) data in the right M1 segment of the MCA for responses from rest to hypercapnia (A–C) and rest to exercise (D–F). Pearsonʼs correlation coefficient (r) and P-value (P) are displayed for each data source per correlation plot

Fig. 5

Distributions of systolic (A, D, G), average (B, E, H) and end-diastolic (C, F, I) velocity extracted from CFD (white) and TCD (grey) data in the right M1 segment. Individual differences between CFD and TCD data are presented as black markers with grey connecting lines. The solid black lines connecting the cross (X) in each box indicate the means of the respective distributions. These data were collected for each of the stimuli conditions of rest (A–C), hypercapnia (D–F) and exercise (G–I). Stars (*; inter-source between CFD and TCD data) and crosses (^†; intra-source hypercapnia or exercise data compared to rest data) indicate the level of significance (* or ^†P < 0.05; ** or ^††P < 0.001) using paired t-tests

Fig. 6

Correlation plots for absolute systolic (A, D, G), average (B, E, H) and end-diastolic (C, F, I) maximal velocity extracted from CFD and TCD data in the right M1 segment of the MCA. These data are collected from the rest (A–C), hypercapnia (D–F) and exercise (G–I) conditions. The linear regression equation (y), Pearson’s correlation coefficient (r) and P-value (P) are displayed for each correlation plot

Fig. 7

Distributions of the relative change (Δ%) in systolic, average and end-diastolic velocity extracted from CFD (white) and TCD (grey) data between responses from rest to hypercapnia (A–C) and to exercise (D–F) in the right M1 segment of the MCA. Individual differences between CFD and TCD relative change data are presented as black markers with grey connecting lines. The solid black line connecting the cross (X) in each box indicates the changing means of the distributions. A CFD data point of relative change in systolic velocity from rest to hypercapnia that is outside the higher quartile range limit is displayed as a hollow circle (o). Stars (*) indicate the level of significance (*P < 0.05; **P < 0.001; between CFD and TCD data) using paired t-tests

Fig. 8

Correlation plots of the relative change (Δ%) in systolic (A, D), average (B, E) and end-diastolic (C, F) maximal velocity extracted from CFD and TCD data in the right M1 segment of the MCA for responses from rest to hypercapnia (A–C) and from rest to exercise (D–F). The linear regression equation (y), Pearsonʼs correlation coefficient (r) and P-value (P) are displayed for each correlation plot