Comparison of Computational Fluid Dynamics with Transcranial Doppler Ultrasound in Response to Physiological Stimuli

doi:10.21203/rs.3.rs-2975511/v1

Download PDF

Research Article

Comparison of Computational Fluid Dynamics with Transcranial Doppler Ultrasound in Response to Physiological Stimuli

https://doi.org/10.21203/rs.3.rs-2975511/v1

This work is licensed under a CC BY 4.0 License

Journal Publication

published 08 Oct, 2023

Read the published version in Biomechanics and Modeling in Mechanobiology →

You are reading this latest preprint version

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 is 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 relying on computational fluid dynamics (CFD). Twelve healthy participants underwent head and neck imaging with 3 Tesla magnetic resonance angiography. Velocity waveforms in the middle cerebral (MCA) artery were measured with transcranial Doppler ultrasound (TCD) while diameter and velocity was measured using duplex ultrasound in the internal carotid (ICA) and vertebral (VA) 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. Absolute measured TCD velocities were significantly higher than those calculated from CFD (all P < 0.05), and these data were not correlated across conditions (r range 0.030–0.377, all P > 0.05). However, relative changes in velocity from resting levels exhibited significant positive correlations when the distinct techniques were compared (r range 0.577–0.770, all P < 0.05). Our data indicate that whilst absolute measures of cerebral velocity differ between TCD and 3D CFD simulation, physiological changes from resting levels in time-averaged velocity are significantly correlated between these techniques.

Cerebral vasculature

computational fluid dynamics

transcranial Doppler ultrasound

stimuli

To maintain adequate oxygenation, nutrient supply and waste disposal, the cerebral vasculature is homeostatically regulated in response to physiological stressors such as hypercapnia and exercise (Ozturk and Tan 2018; Querido and Sheel 2007; Smith and Ainslie 2017). Assessment of cerebrovascular health is typically undertaken via measurement of changes in the function of intra-cranial arteries such as the middle cerebral artery (MCA) (Bae et al. 2014; Birch et al. 1995; Meng et al. 2019). Assessment of MCA velocity and localised haemodynamics are therefore important for diagnosis of cerebrovascular health, as well as physiological research.

One established method for directly measuring blood velocity, diameter, and flow within the brain is magnetic resonance imaging (MRI), where protocols such as magnetic resonance angiography (MRA) or 4D flow MRI are applied. MRI scans possess relatively high spatial resolution and are able to capture complex 3D structure and flows within cerebral arteries (Ainslie and Hoiland 2014). However, during conventional MRI scanning individuals are generally required to be in a supine or prone position for relatively long periods (10–20 minutes) (Markl et al. 2012; Stankovic et al. 2014; Zarrinkoob et al. 2021), which is challenging when external stimuli such as hypercapnia or exercise are of interest. An alternate method for determination of 3D haemodynamics in cerebral arteries involves computational fluid dynamics (CFD) simulation. Although not directly measuring flow, CFD simulations calculate momentum and pressure in a fluid domain and can be useful in situations where direct assessment is not possible. Consequently, CFD simulation represents an attractive approach for characterisation of rapid changes in cerebrovascular hemodynamics (e.g. in response to physiological stimuli), as it can leverage the high spatial resolution associated with 3D MRA imaging alongside the high temporal resolution associated with duplex ultrasound that can be measured in the internal carotid (ICA) and vertebral (VA) arteries to provide inlet flow conditions (Thomas et al. 2020). In addition to estimating cerebral artery velocities, CFD simulations can also provide useful velocity-derived haemodynamic information, such as the localised 3D wall shear stress distribution and indications of oscillatory shear, enabling further understanding of the interactions of blood flow with the surrounding vessel endothelium.

Transcranial Doppler (TCD) is an ultrasound technique which is commonly used for measuring intra-cranial blood flow velocity (BFv). TCD is non-invasive, reproducible and can be used in real-time with high temporal resolution (Willie et al. 2011). Due to its portability and low cost, is it used extensively to better characterise cerebrovascular responses to physiological stimuli including hypercapnia, hypocapnia, exercise, vessel occlusion, shear-mediated endothelial responses and neurovascular coupling (Bishop et al. 1986; Coverdale et al. 2014; Hoiland et al. 2017; Phillips et al. 2016; Thomas et al. 2020). Despite these benefits, TCD can only measure blood velocity due to resolution constraints which prevent B-mode imaging of arterial diameter (Willie et al. 2011). Additionally, TCD measures are angle dependent, however may devices use standard angle correction factors independent of individual vessel geometries which could influence the angle of insonation. Determination of blood flow and localised 3D haemodynamics is therefore limited using TCD. Whilst velocity in the MCA can be measured directly via TCD, and indirectly via flow-conserving 3D CFD simulations, and comparisons between these approaches have been undertaken under static conditions (Groen et al. 2018; Panerai et al. 2016; Rivera et al. 2016; Shen et al. 2020), few studies have compared CFD and TCD methods in response to physiological stimuli (Coverdale et al. 2014).

In this study we compared velocity waveform responses to the stimuli of hypercapnia and submaximal exercise between simulated cerebrovascular velocities calculated using CFD methods and independently measured TCD ultrasound. Our CFD approach combined ICA and VA duplex ultrasound measurements to prescribe volumetric flow inlet boundary conditions, and used 3D geometry based on individual MRA cerebrovascular reconstructions. We hypothesised that flow-conserving CFD and TCD-derived waveform velocity metrics would be similar in absolute terms, and correlated at rest and in response to physiological stimuli.

3.1 Participant Cohort and Medical Imaging

The experimental procedures used in this study were approved by The University of Western Australia Human Research Ethics Committee. A total of twelve healthy participants (6 female, 6 male) were recruited for this study with ages ranging between 19 and 28 years old. Participants were made aware of the experimental procedure and associated risk. Written consent was obtained for each participant prior to commencement of the experimental study. Prior to cerebrovascular stimuli, each participant underwent a 3 Tesla time-of-flight (3T TOF) MRA (Siemens MAGNETOM Skyra) neck and head scan. This scan had a pixel size of 0.31 mm and a slice thickness of 0.75 mm.

3.2 Cerebrovascular Stimuli Procedure

Participants were exposed to conditions previously described by Thomas et al. (2020), consisting of rest (5 minutes recumbent), hypercapnia (5 min of 6% CO₂ via Douglas bag recumbent) and submaximal exercise (5 min recumbent cycling at 90 Watts) conditions respectively. Each session was conducted in the morning for all participants, who were instructed to fast (no food, tea or coffee) and abstain from consumption of alcohol or performing exercise in the 24 hours prior to the session. After each of the exposure condition durations, we simultaneously measured velocity (Doppler ultrasound) and intraluminal diameter (B-mode ultrasound) in the left and right ICAs and VAs using two identical 10-MHz linear array probes and high-resolution ultrasound machines (Terason 3200, Teratech, Burlington, MA) using standardised search techniques (Willie et al. 2011). Continuously during each condition, we measured the velocity envelope in the right M1 segment of the MCA via the middle transtemporal window using a 2-MHz TCD probe (TCD, Spencer Technologies, Seattle, WA) which was held in place with a headpiece (M600 bilateral head frame, Spencer Technologies) as per methods described previously (Hoiland et al. 2017). Throughout all exposure conditions, we continuously measured end-tidal partial pressure of CO₂ (PETCO₂) and O₂ using a gas analyser (Gas Analyzer, ADInstruments, New South Wales, Australia). For analysis and calculation of ICA and VA flow and TCD MCA velocities, we considered steady state data sampled within the final 30 second period of each 5-minute exposure condition. To mitigate cerebral priming, participants underwent a 10-minute washout period, remaining in a recumbent position, between each exposure condition, which was sufficient to return metrics (mean arterial pressure, heart rate, PETCO₂, time-average MCA velocity from TCD) to baseline levels across all participants.

3.3 MRA Reconstruction and Ultrasound Analysis

3.3.1 MRA 3D Reconstruction

To create the 3D fluid domain for the CFD simulations, we imported the DICOM images from the MRA scans into in-house image reconstruction software. We used region-growing techniques to select similar intensity labeled pixels greater than an intensity value of 200 to outline the fluid contained within the cerebrovascular geometry. The software uses an inbuilt marching cubes algorithm to create a 3D isosurface. This isosurface was globally smoothed to within 5% of the starting volume, which was then imported into STAR-CCM+ (v12, Siemens, Munich, Germany) to perform surface repair, remove reconstruction artifacts and perform local smoothing. Outlets were truncated perpendicular to the vessel centerline at least two bifurcations downstream from the Circle of Willis (CoW).

3.3.2 Duplex and TCD Ultrasound

The duplex ultrasound measurements of diameter and velocity at the ICAs and VAs over three cardiac cycles (Kurmanavichius et al. 1989) were converted to time varying volume flow rates assuming Poiseuille flow and waveform averaged and processed as described previously (Tallon et al. 2022; Thomas et al. 2020). This resulted in spline fitted and peak aligned data. Total cerebral blood flow (tCBF) was calculated as the sum of time-averaged flows in the ICAs and VAs. Similarly, envelope TCD velocity waveform data from three cardiac cycles within the right M1 segment were combined into an average waveform using the same process for each participant.

3.4 Computational Fluid Dynamics

3.4.1 Computational Mesh

The simulations were developed in the commercial CFD package STAR-CCM+ (V12, Siemens, Germany) and followed recommendations for development of cerebrovascular simulations (Berg et al. 2019). We used a combination of a polyhedral element mesh for the core of the fluid domain and 20 prism layer elements in the near wall boundary to sufficiently capture the velocity gradients and ensure accurate calculation of wall shear stress. In addition, we prescribed extrusions at the fluid boundaries equal to 11 times the boundary diameter to ensure adequate development of flow upstream and downstream of the fluid domain (Bluestein et al. 1997). Mesh core density was set proportional to local vessel diameter and the mesh settings were prescribed as per our previously published work (Thomas et al. 2020). These settings had been optimised to ensure mesh independence using the grid convergence index (Roache 1994) and used the subject with the greatest inlet velocity measurements for this optimization. Optimal mesh size was deemed sufficient when the grid convergence index for wall shear stress within the CoW was found to fall below 3% (Thomas et al. 2020). Final mesh sizes ranged from 9.1 to 16.7 million cells per geometry.

3.4.2 Boundary Conditions

Boundary conditions followed methods as described previously (Thomas et al. 2020). Briefly, the volumetric flow waveforms derived from duplex ultrasound at the ICAs and VAs were converted to mass flow waveforms assuming a fluid density of 1050 kg m^− 3 (Levitt et al. 2017). The measured mass flow waveforms for the rest, hypercapnia and submaximal exercise conditions were all prescribed at the corresponding extruded inlet using a plug flow condition, which allowed for natural development of flow throughout the extrusions before entering the subject specific cerebrovascular 3D geometry. Outlet boundary conditions were implemented using the same WALNUT code described previously (Thomas et al. 2020), which initially splits blood flow exiting the fluid domain into seven regions (left and right posterior, left and right middle, anterior, cerebellum and ophthalmic arteries), with different flow distributions to these regions based on the average volumetric flow measured at the ICAs and VAs. Within these seven regions within the brain, flow was then split using an adaptation of the Murray’s law formulation (Chnafa et al. 2018) as defined in Eq. 1, using an exponent of n = 2.33 (Thomas et al. 2020).

$${Q}_{out,i}={Q}_{in,region}\times \frac{{d}_{i}^{n}}{\sum _{j=1}^{N}{d}_{j}^{n}}$$

Where Q_out,i is the flow out of outlet i, Q_in,region is the WALNUT calculated flow into the region of the cerebral vasculature which is shared by outlet i as described previously (Thomas et al. 2020), d is outlet diameter and n is the flow split exponent.

3.4.3 Physical Assumptions

Blood was assumed incompressible with a density of 1050 kg m^− 3 (Levitt et al. 2017). The non-Newtonian nature of blood viscosity was modelled using the Carreau-Yasuda viscosity model using parameters appropriate for blood flow leading to and within the CoW (η_∞ = 0.0022 Pa s; η₀ = 0.022 Pa s; λ = 0.11 s; a = 0.644; n = 0.392) (Kim et al. 2006). We assumed the arterial walls were rigid, with a no-slip boundary condition and a laminar flow regime in line with previous cerebrovascular simulations (Alnæs et al. 2007; Kim et al. 2006; Shojima et al. 2004; Thomas et al. 2020).

3.4.4 Simulation Execution

Simulations ran for three consecutive cardiac cycles to ensure flow stabilization, with results extracted from the fourth cardiac cycle. We used an implicit unsteady segregated flow solver and second-order temporal discretization with an automated time-step control which permitted the time-step to vary between 0.001 and 0.005 s depending on the Courant number. New time-steps were triggered if absolute continuity and momentum residuals fell below a value of 10^− 9, or if the number of inner iterations reached 50. Our simulations were executed using the STAR-CCM + finite-volume method on Magnus, a Cray XC40 supercomputer (Pawsey Supercomputing Centre, Perth, Australia) housing a total of 1488 compute nodes each containing 24 cores per node. We ran each simulation utilizing 25 nodes over a collective of 500 cores. The rest, hypercapnia and exercise simulations required an average of 3000, 2800 and 2000 core hours respectively to run, which equated to total simulation run times ranging from approximately 3 to 7 h.

3.5 Data Collection, Analysis and Statistics

Simulations were allowed to stabilise over three cardiac cycles, after which we extracted maximal BFv waveforms from each simulation over the fourth cardiac cycle using the average of the maximum value from three consecutively spaced constrained planes located within the right M1 segment (Fig. 1) to represent the region insonated using TCD. The velocity waveforms extracted from the simulation and from the TCD ultrasound envelope for each participant and exposure condition were analysed for their characteristics using a custom MATLAB script (R2016, Mathworks, Natick, MA). We extracted the systolic, cardiac cycle time-average and end-diastolic velocities from the envelope of these waveforms. We used paired t-tests for comparison of distributions and Pearson’s correlation and Bland-Altman plots to investigate the correlations between absolute and relative change in CFD and TCD data for each participant in response to different stimuli. Normality was tested using the Shapiro-Wilk test. Where applicable, data is presented as group mean ± standard deviation. Statistical significance was assumed for p-values where P < 0.05.

4.1 MRA Reconstructions and Participant Cardiorespiratory Responses

Participants had an average age, BMI and VO₂max score of 22.9 ± 3.4 years, 21.6 ± 2.9 kg m^− 2 and 44.7 ± 9.4 mL kg^− 1 min^− 1 respectively. Reconstructed 3D models from MRA data of each of the twelve cases all exhibited a complete Circle of Willis and are presented in Fig. 2. Participant cardiorespiratory responses including PETCO₂, mean arterial blood pressure (MAP), heart rate (HR) as well as ultrasound derived time-averaged volumetric blood flow at the ICAs and VAs as summed tCBF under resting, hypercapnia and exercise conditions are displayed in Table 1. Compared to rest, hypercapnia significantly increased all cardiorespiratory measures and blood flows (all P < 0.05). Although exercise also significantly increased all cardiorespiratory measures (PETCO₂, MAP and HR all P < 0.05), blood flow to the brain did not significantly increase from rest (all P > 0.05). Individual CFD and TCD velocity waveform data for resting, hypercapnic and exercise conditions for each case can be found in Online Resource 1.

Table 1

Participant cardiorespiratory responses under different conditions.
	Rest (Average ± SD)	Hypercapnia (Average ± SD)	Exercise (Average ± SD)
PETCO₂ (mmHg)	42.2 ± 2.5	50.7 ± 1.9††	43.8 ± 4.2†
MAP (mmHg)	100.0 ± 8.1	106.0 ± 11.8†	124.8 ± 15.2††
HR (bpm)	68.7 ± 9.5	74.1 ± 8.1†	120.4 ± 21.3††
Blood flow (mL min^− 1)
LICA	268.9 ± 63.3	374.6 ± 79.3††	272.8 ± 67.2
RICA	218.8 ± 74.2	308.6 ± 79.3†	262.9 ± 50.3
LVA	74.2 ± 26.4	119.4 ± 30.9††	79.7 ± 27.1
RVA	56.2 ± 18.3	97.0 ± 32.3††	68.4 ± 34.0
tCBF (ml min^− 1)	618.1 ± 129.7	899.7 ± 128.4††	683.7 ± 124.3

Data are mean ± standard deviation. LICA = left internal carotid artery; RICA = right internal carotid artery; LVA = left vertebral artery; RVA = right vertebral artery. Crosses (†) indicate the level of significance (†P < 0.05; ††P < 0.001) compared to rest.

4.2 Absolute and Relative Changes in Total Cerebral Flow and MCA Velocity

Correlations between absolute velocity characteristics from CFD and TCD sources with tCBF from the ICAs and VAs across all stimuli were compared (Fig. 3). Correlations of tCBF to velocity from the CFD data were all significantly and positively correlated (all P ≤ 0.05, r range 0.576–0.835), while TCD data yielded very mild positive correlations that were not significant (all P > 0.05, r range 0.010–0.443), irrespective of exposure conditions or velocity metric.

We also investigated correlations between relative changes in velocity characteristics from CFD and TCD sources with relative change in tCBF in response to stimuli (Fig. 4). We again observed strong positive and significant correlations between the relative change in tCBF and MCA velocity calculated from CFD simulations across both responses to hypercapnia and exercise (all P < 0.05, r range 0.635–0.955). Despite correlations of relative changes in TCD velocity metrics with tCBF remaining positive and generally becoming stronger, outside of average velocity from rest to exercise (r = 0.588, P = 0.044), these correlations still remained mild and were not significant (remaining P > 0.05, r range 0.158–0.535).

4.3 Absolute MCA Velocity Data Distributions and Correlations at Rest and During Physiological Stimuli

Distributions of CFD and TCD derived velocity waveform metrics across the different exposure conditions is presented in Fig. 5. In response to hypercapnia and relative to rest, both CFD and TCD data exhibited significant increases (all P < 0.05) in velocity metrics relative to their respective resting measures. In response to exercise, all TCD velocity metrics increased significantly compared to rest (all P < 0.05), whereas only CFD average velocity increased significantly compared to rest (40.4 ± 9.4 vs 48.1 ± 11.3, P = 0.039). Measurements of maximal systolic, average and end diastolic velocity were all significantly higher (all P < 0.05) in the TCD data compared to the CFD simulations. The distribution means of the systolic velocity ranged from 33–73% higher in the TCD data compared to CFD across the exposure conditions. Distribution means were also higher for average velocity, with increases between 62–85% when comparing TCD to CFD data across all exposure conditions. The highest differences were present in end diastolic velocity, with increases ranging from 85–106% between TCD and CFD data across all conditions.

Systolic, average and end diastolic velocity extracted from CFD and TCD waveforms, under the conditions of rest (Fig. 6), hypercapnia (Fig. 7) and exercise (Fig. 8), were generally uncorrelated and exhibited weak positive relationships that were not significant (all P > 0.05, r range 0.030–0.377).

4.4 Relative Change in MCA Velocity Data Distributions and Correlations in Response to Physiological Stimuli

We investigated the distributions of the relative changes in velocity waveform metrics from rest to hypercapnia and rest to exercise between the CFD and TCD datasets (Fig. 9). We found that the relative change in velocity metrics from rest to hypercapnia were similar and not significantly different between CFD and TCD (all P > 0.05), with the means of CFD relative velocity changes found to be slightly higher than the changes from TCD data for systolic (34 ± 30% vs 28 ± 12%, P = 0.579), average (44 ± 26% vs 39 ± 15%, P = 0.532) and end diastolic velocity (58 ± 33% vs 49 ± 22%, P = 0.477). One case exhibited a relative change in systolic velocity from CFD data in response to hypercapnia greater than the higher quartile range limit. While small differences between CFD and TCD distributions were observed for average (22 ± 27% vs 32 ± 20%, P = 0.323) and end diastolic (19 ± 29% vs 26 ± 24%, P = 0.566) velocities in response to exercise, the change in systolic velocity was significantly higher in the TCD data compared to CFD (40 ± 18% vs 14 ± 22%, P = 0.006).

In comparison to absolute data, correlations of CFD to TCD data for the relative change in the velocity waveform metrics of systolic, average and end diastolic velocity from rest to hypercapnia (Fig. 10) and rest to exercise (Fig. 11) yielded moderate positive correlations. Changes in systolic (r = 0.588, P = 0.04) and average (r = 0.577, P = 0.05) velocity from rest to hypercapnia were significantly correlated, while end diastolic velocity (r = 0.448, P = 0.14) was not significantly correlated. Similarly, for the change from rest to exercise, relative changes in systolic (r = 0.604, P = 0.04) and average (r = 0.770, P < 0.01) velocity were found to be significantly correlated between CFD and TCD data, while end diastolic (r = 0.508, P = 0.09) velocity was not significantly correlated. Excluding relative systolic velocity change bias from rest to exercise (-27%), biases fell within ± 10% for all other velocity metrics and exposure conditions. A mild positive proportional bias was observed across most relative velocity change metrics.

Although CFD has previously been compared with TCD methods under static conditions (Groen et al. 2018; Panerai et al. 2016; Rivera et al. 2016; Shen et al. 2020), few studies have compared these approaches in response to ecologically valid physiological stimuli (Coverdale et al. 2014). This study aimed to investigate waveform velocities at rest and during hypercapnia and exercise. We compared measurements derived from TCD to velocities calculated via CFD simulations (derived from 3D MRA combined with ICA and VA duplex ultrasound). In contrast to our hypothesis, we observed that CFD and TCD-derived waveform velocity metrics were different and did not correlate at rest, but that changes in response to physiological stimuli were similar and significantly related.

5.1 Differences between TCD and CFD Data

The higher velocity data we observed using TCD compared to CFD at rest could potentially be explained by overestimation from TCD methods, underestimation from CFD simulations, or a combination. Although TCD velocity is a well-established method for measuring MCA BFv, higher TCD velocities have been observed previously due to phenomenon such as spectral broadening, which can exaggerate peak BFv by up to 35% when lower MHz probes are used (Eicke et al. 1995; Hoskins 1996). When comparing BFv between TCD and MRI based methods, Seitz et al. (2001) found that TCD velocities exceeded MRA velocities by around 30%, and they also reported low correlations between these approaches. Chang et al. (2011) also reported 30% greater velocities via TCD, but found that phase contrast MRA techniques correlated strongly with TCD. Conversely, a study by Meckel et al. (2013) compared 4D phase contrast MRI and transcranial color-coded duplex sonography and also observed that TCD derived data were higher, with weak to mild correlations between these approaches. Leung et al. (2013) also reported higher peak velocities using TCD than phase contrast MRA, but reported strong correlations when data were compared between approaches. Taken together, these studies indicate that, at rest and in response to some physiological stimuli, TCD approaches generate higher velocities compared to MRI based methods, and the degree to which they correlate is variable. In our study we also found higher TCD values, although our differences in comparison to CFD were larger than those previously reported for TCD versus MRI methods, suggesting that additional factors (discussed below) may explain the discrepancies we observed.

We also observed that TCD derived velocities were not significantly correlated with duplex ultrasound tCBF (measured in the ICA and VA), either at rest or during exposure to stimuli. This is despite both approaches being based on Doppler ultrasound. This suggests that cerebral autoregulation may affect MCA BFv in a manner distinct from any impact on extracranial ICA and VA blood flows. Hypercapnia is generally considered to induce MCA dilation (Coverdale et al. 2014; Coverdale et al. 2015; Verbree et al. 2014; Willie et al. 2012), and changes in MCA diameter could increase the variability of measured TCD velocities, compared to the corresponding ICA and VA duplex ultrasound derived flows. It is important to note, however, that MCA diameter change due to ventilatory effects is debated in the literature (Ainslie and Hoiland 2014; Brothers and Zhang 2016; Hoiland and Ainslie 2016; Willie et al. 2012), with some studies reporting that MCA diameter does not change in response to hypercapnia (Serrador et al. 2000). Hence, hypercapnic responses may vary between individuals and study populations. Furthermore, whilst hypercapnia may dilate the ICA and VA, the mechanisms responsible may relate to increased shear stress secondary to downstream intracranial dilation, rather than direct effects of CO₂ which are more apparent in the MCA. Distinct time courses of dilation may contribute to the lack of correlation in responses we observed between these arteries and techniques. Interestingly, in response to exercise, cerebral vessels can undergo vasoconstriction, associated with hyperventilatory effects (Ogoh and Ainslie 2009), with the magnitude of diameter change being smaller than that associated with hypercapnia (Verbree et al. 2017). This may explain our observation that, in contrast to our hypercapnic findings, changes in TCD-derived MCA time-averaged BFv in response to exercise were significantly correlated with tCBF based on ICA/VA duplex ultrasound (r = 0.588, P = 0.044).

Another potential factor affecting differences between CFD and TCD derived data may relate to differences in posture. MRA scans and subsequent 3D geometries used in the CFD simulations are collected with subjects supine. This contrasts with the semi-recumbent position during physiological testing (trunk angle ~ 60°). An increase in MCA diameter due to this difference in posture could contribute to lower calculated CFD MCA BFv, although data regarding postural impacts on MCA diameter remain limited and variable. Sato et al. (2012a) measured neck artery flows and MCA BFv using TCD in supine and 60° head-up tilt, finding that both MCA BFv and ICA volumetric blood flows were significantly higher supine. Garrett et al. (2017) also found that MCA BFv was significantly higher supine compared to upright. Serrador et al. (2000) used a combination of TCD and MRI to measure MCA BFv and diameter in supine participants who underwent simulated orthostatic stress via lower body negative pressure, finding that although MCA BFv was significantly higher supine compared to during lower body pressure, no significant changes in MCA diameter were observed. Despite documented changes in velocity in the MCA between postures, the limited evidence reviewed above suggests that MCA diameter may not change in distinct postures. Therefore, differences in calculated CFD BFv may be more attributable to the incoming blood flow, rather than postural variations in MCA lumen diameter.

The differences we observed between TCD and CFD calculated MCA BFv data cannot be ascribed to differences between the CFD data and duplex ICA and VA derived blood flow, as the latter were highly correlated. This is not surprising, given that duplex ICA and VA derived blood flows were inputs for the CFD simulations from which MCA BFv data were derived. Indeed, ICA and VA flows derived from duplex ultrasound have been found to correlate with MRI based estimates (Khan et al. 2017; Oktar et al. 2006). The average ICA and VA ultrasound flows collected in our study were similar to previous studies at rest and during exposure to stimuli (Oktar et al. 2006; Sato et al. 2012b; Skytioti et al. 2016; Steventon et al. 2018; Tallon et al. 2022; Willie et al. 2012).

In summary, we found that MCA BFv derived from TCD was higher than that calculated from CFD, potentially due to TCD-related phenomena such as spectral broadening. In addition, we observed that TCD BFv metrics were not correlated with extracranial duplex ultrasound derived flows in the ICAs and VAs. In contrast, CFD calculated BFv was significantly correlated with ICA and VA flows at rest and in response to stimuli. Nonetheless, future studies interested in using CFD to aid in calculating velocity, shear stress, oscillatory shear and other important cerebrovascular haemodynamics in response to physiological stimuli may require further model refinement.

5.2 Relative Change Responses between TCD and CFD Data

Despite the differences between TCD and CFD measured in absolute terms that we describe above, an arguably more important question is whether changes in velocity responses to physiological stimuli derived using each technique are correlated. We observed that relative changes from baseline data in response to hypercapnia and exercise were similar and highly correlated in our study when TCD and CFD approaches were compared. Comparison of relative changes in velocity may minimise the impact of systematic sources of variability in either method, since relative changes could serve to reduce consistent within-subject error through normalisation. In concert with this, it is plausible that inherent physiological variability between individuals may be reduced when a standardised stimulus (hypercapnia, exercise) is applied. Hypercapnia induced similar changes in velocity metrics between TCD and CFD sources. In response to exercise, average velocity was also similar, but systolic velocity was higher by TCD assessment (in keeping with findings above). These data suggest that hypercapnia may induce a more consistent response among individuals compared to exercise, which is a compound and complex stimulus. Nonetheless, relative changes in average MCA BFv derived from TCD and CFD approaches, in response to both hypercapnia and exercise, were significantly correlated. Our findings therefore indicate that TCD or CFD methods result in similar changes in physiological responses in MCA BFv in humans. CFD simulations therefore provide relative change data, which is consistent with that derived from TCD, with the added benefit of being able to derive further haemodynamic metrics such as time averaged wall shear stress or oscillatory shear in response to ecologically relevant stimuli such as hypercapnia and exercise.

5.3 Limitations

Due to fundamental limitations in MRI scanning, the axial slice thickness direction is likely aligned with the cross-section of the MCA in most cases. This may lead to reduced resolution in the MRA scans about the MCA cross-section, which may then influence the flow in the CFD simulations and hence the CFD derived MCA velocities. Given the nature of the imaging modality used and orientation required for collecting images, this variation in slice thickness is difficult to account for, but could be rectified by manually adjusting the MCA cross-sectional region of the 3D models using surface meshing tools to reflect a diameter from an axial plane selected closest to the centerline of the MCA. Additionally, and as discussed above, MRA scanning was performed in resting supine participants. Ideally, provided availability of specialised equipment, MRA scans should be captured during or in response to stimuli, allowing any individual changes in vessel diameters to be embedded into each of the CFD simulations. Similarly, true validation of CFD methods was unable to be performed in this study. Independently captured time varying image datasets using 4D flow MRI methods may provide additional validation for future cerebrovascular CFD simulations.

While we used previously established methods (Kurmanavichius et al. 1989; Thomas et al. 2020) for ultrasound waveform averaging, additional averaging of cardiac cycles may also serve to reduce the variability in results. Similarly, the flow in the ICAs and VAs was calculated using previously established methods assuming Poiseuille flow (Tallon et al. 2022; Thomas et al. 2020). Although flow calculation using this method has been found to be relatively consistent with Womersley-derived flow in larger arteries such as the common carotid (Mynard and Steinman 2013), it may nonetheless have contributed to flow variation. Future CFD simulations should consider calculating Womersley-derived flow from duplex ultrasound data.

In the CFD simulations, outlet boundary conditions were distributed using resting regional flow measurements derived from literature and diameter-based flow splitting exponents which were constant across all outlets. In the absence of regional brain blood flow data, particularly in response to stimuli, an exponent value appropriate for cerebrovascular vessels was used (Thomas et al. 2020). However, research has suggested that this exponent may vary for each individual outlet (Chnafa et al. 2017; Chnafa et al. 2018). A localised outlet splitting method as described by Chnafa et al. (2018), provided access to measured flow data in the brain, may be more appropriate in future CFD based cerebrovascular research.

Finally, with only 12 participants, the number of cases investigated in this study is relatively small and was limited to young, healthy individuals with no pre-existing cardiovascular diseases. However, despite the low number of cases, we nonetheless observed statistically significant results which may have important implications for future physiological research.

5.4 Conclusion

In this study we aimed to compare data in the cerebral vasculature under resting conditions, and in response to physiological stimuli (hypercapnia, exercise), using TCD ultrasound and independently constructed flow-conserving CFD simulations. Although we found differences between absolute velocity data obtained between CFD and TCD, measurements of change in velocity in response to stimuli showed good agreement, particularly for relative changes in time-averaged velocity. Therefore, in addition to absolute measurements, investigation of relative-changes in velocity in response to physiological stimuli may be an important tool for future research using TCD ultrasound or for haemodynamic analysis using CFD cerebral vasculature simulations.

Acknowledgements

We acknowledge the resources provided by the Pawsey Supercomputing Centre with funding from the Australian Government and the Government of Western Australia. H.T.C is supported by a Forrest Research Foundation Scholarship. D.J.G. is supported by a National Health and Medical Research Council Principal Research Fellowship (APP1080914).

Author Contributions

H.T.C., H.J.T., D.J.G., and B.J.D. conceived and designed research; H.J.T., K.J.S. and D.J.G. performed experiments; H.T.C., L.J.K. and B.J.D. developed simulations; H.T.C., L.J.K., and B.J.D. analysed data; H.T.C., L.J.K., B.J.D. and D.J.G. prepared figures; H.T.C, B.J.D. and D.J.G. drafted manuscript; all authors edited, revised and approved the final version of manuscript.

Statements and Declarations

There are no competing interests.

Ainslie PN, Hoiland RL (2014) Transcranial Doppler ultrasound: Valid, invalid, or both? Journal of Applied Physiology 117:1081-1083. https://doi.org/10.1152/japplphysiol.00854.2014
Alnæs MS, Isaksen J, Mardal K-A, Romner B, Morgan MK, Ingebrigtsen T (2007) Computation of Hemodynamics in the Circle of Willis. Stroke 38:2500-2505. https://doi.org/10.1161/STROKEAHA.107.482471
Bae DH, Choi KS, Yi HJ, Chun HJ, Ko Y, Bak KH (2014) Cerebral Infarction after Traumatic Brain Injury: Incidence and Risk Factors. Korean journal of neurotrauma 10:35-40. https://doi.org/10.13004/kjnt.2014.10.2.35
Berg P, Saalfeld S, Voß S, Beuing O, Janiga G (2019) A review on the reliability of hemodynamic modeling in intracranial aneurysms: why computational fluid dynamics alone cannot solve the equation. Neurosurgical focus 47:E15. https://doi.org/10.3171/2019.4.focus19181
Birch AA, Dirnhuber MJ, Hartley-Davies R, Iannotti F, Neil-Dwyer G (1995) Assessment of autoregindependention by means of periodic changes in blood pressure. Stroke 26:834-837. https://doi.org/10.1161/01.str.26.5.834
Bishop CC, Powell S, Rutt D, Browse NL (1986) Transcranial Doppler measurement of middle cerebral artery blood flow velocity: a validation study. Stroke 17:913-915. https://doi.org/10.1161/01.STR.17.5.913
Bluestein D, Niu L, Schoephoerster RT, Dewanjee MK (1997) Fluid mechanics of arterial stenosis: Relationship to the development of mural thrombus. Annals of Biomedical Engineering 25:344. https://doi.org/10.1007/BF02648048
Brothers RM, Zhang R (2016) CrossTalk opposing view: The middle cerebral artery diameter does not change during alterations in arterial blood gases and blood pressure. J Physiol 594:4077-4079. https://doi.org/10.1113/JP271884
Chang W et al. (2011) Velocity Measurements in the Middle Cerebral Arteries of Healthy Volunteers Using 3D Radial Phase-Contrast HYPRFlow: Comparison with Transcranial Doppler Sonography and 2D Phase-Contrast MR Imaging. American Journal of Neuroradiology 32:54-59. https://doi.org/10.3174/ajnr.A2240
Chnafa C et al. (2017) Vessel calibre and flow splitting relationships at the internal carotid artery terminal bifurcation. Physiol Meas 38:2044-2057. https://doi.org/10.1088/1361-6579/aa92bf
Chnafa C, Brina O, Pereira VM, Steinman DA (2018) Better Than Nothing: A Rational Approach for Minimizing the Impact of Outflow Strategy on Cerebrovascular Simulations. AJNR Am J Neuroradiol 39:337-343. https://doi.org/10.3174/ajnr.A5484
Coverdale NS, Gati JS, Opalevych O, Perrotta A, Shoemaker JK (2014) Cerebral blood flow velocity underestimates cerebral blood flow during modest hypercapnia and hypocapnia. Journal of Applied Physiology 117:1090-1096. https://doi.org/10.1152/japplphysiol.00285.2014
Coverdale NS, Lalande S, Perrotta A, Shoemaker JK (2015) Heterogeneous patterns of vasoreactivity in the middle cerebral and internal carotid arteries. American journal of physiology Heart and circulatory physiology 308:H1030-1038. https://doi.org/10.1152/ajpheart.00761.2014
Eicke BM, Kremkau FW, Hinson H, Tegeler CH (1995) Peak velocity overestimation and linear-array spectral Doppler. Journal of neuroimaging: official journal of the American Society of Neuroimaging 5:115-121. https://doi.org/10.1111/jon199552115
Garrett ZK, Pearson J, Subudhi AW (2017) Postural effects on cerebral blood flow and autoregulation. Physiol Rep 5. https://doi.org/10.14814/phy2.13150
Groen D, Richardson RA, Coy R, Schiller UD, Chandrashekar H, Robertson F, Coveney PV (2018) Validation of Patient-Specific Cerebral Blood Flow Simulation Using Transcranial Doppler Measurements. Front Physiol 9:721. https://doi.org/10.3389/fphys.2018.00721
Hoiland RL, Ainslie PN (2016) CrossTalk proposal: The middle cerebral artery diameter does change during alterations in arterial blood gases and blood pressure. J Physiol 594:4073-4075. https://doi.org/10.1113/jp271981
Hoiland RL et al. (2017) Shear-mediated dilation of the internal carotid artery occurs independent of hypercapnia. American Journal of Physiology-Heart and Circulatory Physiology 313:H24-H31. https://doi.org/10.1152/ajpheart.00119.2017
Hoskins PR (1996) Accuracy of maximum velocity estimates made using Doppler ultrasound systems. Br J Radiol 69:172-177. https://doi.org/10.1259/0007-1285-69-818-172
Khan MA et al. (2017) Measurement of cerebral blood flow using phase contrast magnetic resonance imaging and duplex ultrasonography. Journal of cerebral blood flow and metabolism: official journal of the International Society of Cerebral Blood Flow and Metabolism 37:541-549. https://doi.org/10.1177/0271678x16631149
Kim CS, Kiris C, Kwak D, David T (2006) Numerical simulation of local blood flow in the carotid and cerebral arteries under altered gravity. J Biomech Eng 128:194-202. https://doi.org/10.1115/1.2165691
Kurmanavichius J, Baumann H, Huch R, Huch A (1989) Determination of the minimum number of cardiac cycles necessary to ensure representative blood flow velocity measurements. Journal of perinatal medicine 17:33-39. https://doi.org/10.1515/jpme.1989.17.1.33
Leung J, Behpour A, Sokol N, Mohanta A, Kassner A (2013) Assessment of intracranial blood flow velocities using a computer controlled vasoactive stimulus: A comparison between phase contrast magnetic resonance angiography and transcranial doppler ultrasonography. Journal of Magnetic Resonance Imaging 38:733-738. https://doi.org/https://doi.org/10.1002/jmri.23911
Levitt MR et al. (2017) Computational fluid dynamics of cerebral aneurysm coiling using high-resolution and high-energy synchrotron X-ray microtomography: comparison with the homogeneous porous medium approach. Journal of neurointerventional surgery 9:0-0. https://doi.org/10.1136/neurintsurg-2016-012479
Markl M, Frydrychowicz A, Kozerke S, Hope M, Wieben O (2012) 4D flow MRI. Journal of Magnetic Resonance Imaging 36:1015-1036. https://doi.org/https://doi.org/10.1002/jmri.23632
Meckel S et al. (2013) Intracranial artery velocity measurement using 4D PC MRI at 3 T: comparison with transcranial ultrasound techniques and 2D PC MRI Neuroradiology 55:389-398. https://doi.org/10.1007/s00234-012-1103-z
Meng Y, Yu K, Zhang L, Liu Y (2019) Cognitive Decline in Asymptomatic Middle Cerebral Artery Stenosis Patients with Moderate and Poor Collaterals: A 2-Year Follow-Up Study. Medical science monitor: international medical journal of experimental and clinical research 25:4051-4058. https://doi.org/10.12659/msm.913797
Mynard JP, Steinman DA (2013) Effect of velocity profile skewing on blood velocity and volume flow waveforms derived from maximum Doppler spectral velocity. Ultrasound in medicine & biology 39:870-881. https://doi.org/10.1016/j.ultrasmedbio.2012.11.006
Ogoh S, Ainslie PN (2009) Cerebral blood flow during exercise: mechanisms of regulation. J Appl Physiol (1985) 107:1370-1380. https://doi.org/10.1152/japplphysiol.00573.2009
Oktar SO, Yücel C, Karaosmanoglu D, Akkan K, Ozdemir H, Tokgoz N, Tali T (2006) Blood-Flow Volume Quantification in Internal Carotid and Vertebral Arteries: Comparison of 3 Different Ultrasound Techniques with Phase-Contrast MR Imaging. American Journal of Neuroradiology 27:363-369
Ozturk ED, Tan CO (2018) Human cerebrovascular function in health and disease: insights from integrative approaches. Journal of physiological anthropology 37:4. https://doi.org/10.1186/s40101-018-0164-z
Panerai RB, Jara JL, Saeed NP, Horsfield MA, Robinson TG (2016) Dynamic cerebral autoregulation following acute ischaemic stroke: Comparison of transcranial Doppler and magnetic resonance imaging techniques. Journal of Cerebral Blood Flow & Metabolism 36:2194-2202. https://doi.org/10.1177/0271678x15615874
Phillips AA, Chan FH, Zheng MM, Krassioukov AV, Ainslie PN (2016) Neurovascular coupling in humans: Physiology, methodological advances and clinical implications. Journal of cerebral blood flow and metabolism: official journal of the International Society of Cerebral Blood Flow and Metabolism 36:647-664. https://doi.org/10.1177/0271678x15617954
Querido JS, Sheel AW (2007) Regulation of cerebral blood flow during exercise. Sports medicine 37:765-782. https://doi.org/10.2165/00007256-200737090-00002
Rivera CP, Veneziani A, Ware RE, Platt MO (2016) Original Research: Sickle cell anemia and pediatric strokes: Computational fluid dynamics analysis in the middle cerebral artery. Experimental Biology and Medicine 241:755-765. https://doi.org/10.1177/1535370216636722
Roache PJ (1994) Perspective: A Method for Uniform Reporting of Grid Refinement Studies. Journal of Fluids Engineering 116:405-413. https://doi.org/10.1115/1.2910291
Sato K, Fisher JP, Seifert T, Overgaard M, Secher NH, Ogoh S (2012a) Blood flow in internal carotid and vertebral arteries during orthostatic stress. Exp Physiol 97:1272-1280. https://doi.org/10.1113/expphysiol.2012.064774
Sato K, Sadamoto T, Hirasawa A, Oue A, Subudhi AW, Miyazawa T, Ogoh S (2012b) Differential blood flow responses to CO₂ in human internal and external carotid and vertebral arteries. J Physiol 590:3277-3290. https://doi.org/10.1113/jphysiol.2012.230425
Seitz J, Strotzer M, Schlaier J, Nitz WR, Völk M, Feuerbach S (2001) Comparison between magnetic resonance phase contrast imaging and transcranial Doppler ultrasound with regard to blood flow velocity in intracranial arteries: work in progress. Journal of neuroimaging : official journal of the American Society of Neuroimaging 11:121-128. https://doi.org/10.1111/j.1552-6569.2001.tb00021.x
Serrador JM, Picot PA, Rutt BK, Shoemaker JK, Bondar RL (2000) MRI Measures of Middle Cerebral Artery Diameter in Conscious Humans During Simulated Orthostasis. Stroke 31:1672-1678. https://doi.org/10.1161/01.STR.31.7.1672
Shen Y, Wei Y, Bokkers RPH, Uyttenboogaart M, van Dijk JMC (2020) Study protocol of validating a numerical model to assess the blood flow in the circle of Willis. BMJ Open 10:e036404. https://doi.org/10.1136/bmjopen-2019-036404
Shojima M et al. (2004) Magnitude and role of wall shear stress on cerebral aneurysm: computational fluid dynamic study of 20 middle cerebral artery aneurysms. Stroke 35:2500-2505. https://doi.org/10.1161/01.STR.0000144648.89172.0f
Skytioti M, Søvik S, Elstad M (2016) Internal carotid artery blood flow in healthy awake subjects is reduced by simulated hypovolemia and noninvasive mechanical ventilation. Physiological reports 4:e12969. https://doi.org/10.14814/phy2.12969
Smith KJ, Ainslie PN (2017) Regulation of cerebral blood flow and metabolism during exercise. Exp Physiol 102:1356-1371. https://doi.org/10.1113/EP086249
Stankovic Z, Allen BD, Garcia J, Jarvis KB, Markl M (2014) 4D flow imaging with MRI. Cardiovasc Diagn Ther 4:173-192. https://doi.org/10.3978/j.issn.2223-3652.2014.01.02
Steventon JJ et al. (2018) Cerebrovascular Function in the Large Arteries Is Maintained Following Moderate Intensity Exercise. Front Physiol 9:1657. https://doi.org/10.3389/fphys.2018.01657
Tallon CM et al. (2022) Dynamic onset response of the internal carotid artery to hypercapnia is blunted in children compared with adults. Physiological Reports 10:e15406. https://doi.org/10.14814/phy2.15406
Thomas HJ et al. (2020) Assessment of cerebrovascular responses to physiological stimuli in identical twins using multimodal imaging and computational fluid dynamics. Journal of Applied Physiology 129:1024-1032. https://doi.org/10.1152/japplphysiol.00348.2020
Verbree J, Bronzwaer A, van Buchem MA, Daemen M, van Lieshout JJ, van Osch M (2017) Middle cerebral artery diameter changes during rhythmic handgrip exercise in humans. Journal of cerebral blood flow and metabolism: official journal of the International Society of Cerebral Blood Flow and Metabolism 37:2921-2927. https://doi.org/10.1177/0271678X16679419
Verbree J et al. (2014) Assessment of middle cerebral artery diameter during hypocapnia and hypercapnia in humans using ultra-high-field MRI. J Appl Physiol (1985) 117:1084-1089. https://doi.org/10.1152/japplphysiol.00651.2014
Willie CK et al. (2011) Utility of transcranial Doppler ultrasound for the integrative assessment of cerebrovascular function. Journal of neuroscience methods 196:221-237. https://doi.org/10.1016/j.jneumeth.2011.01.011
Willie CK et al. (2012) Regional brain blood flow in man during acute changes in arterial blood gases. J Physiol 590:3261-3275. https://doi.org/10.1113/jphysiol.2012.228551
Zarrinkoob L, Wåhlin A, Ambarki K, Eklund A, Malm J (2021) Quantification and mapping of cerebral hemodynamics before and after carotid endarterectomy, using four-dimensional flow magnetic resonance imaging. Journal of vascular surgery 74:910-920.e911. https://doi.org/10.1016/j.jvs.2021.01.074

No competing interests reported.

ESM1.tif

Download PDF

Journal Publication

published 08 Oct, 2023

Read the published version in Biomechanics and Modeling in Mechanobiology →

Editorial decision: Major revision
26 Jun, 2023
Reviews received at journal
11 Jun, 2023
Reviewers agreed at journal
04 Jun, 2023
Reviewers invited by journal
04 Jun, 2023
Editor assigned by journal
25 May, 2023
Submission checks completed at journal
24 May, 2023
First submitted to journal
24 May, 2023

You are reading this latest preprint version

Comparison of Computational Fluid Dynamics with Transcranial Doppler Ultrasound in Response to Physiological Stimuli

Status:

Journal Publication

Version 1

Abstract

Figures

Introduction

Materials and Methods

3.1 Participant Cohort and Medical Imaging

3.2 Cerebrovascular Stimuli Procedure

3.3 MRA Reconstruction and Ultrasound Analysis

3.3.1 MRA 3D Reconstruction

3.3.2 Duplex and TCD Ultrasound

3.4 Computational Fluid Dynamics

3.4.1 Computational Mesh

3.4.2 Boundary Conditions

3.4.3 Physical Assumptions

3.4.4 Simulation Execution

3.5 Data Collection, Analysis and Statistics

Results

4.1 MRA Reconstructions and Participant Cardiorespiratory Responses

4.2 Absolute and Relative Changes in Total Cerebral Flow and MCA Velocity

4.3 Absolute MCA Velocity Data Distributions and Correlations at Rest and During Physiological Stimuli

4.4 Relative Change in MCA Velocity Data Distributions and Correlations in Response to Physiological Stimuli

Discussion

5.1 Differences between TCD and CFD Data

5.2 Relative Change Responses between TCD and CFD Data

5.3 Limitations

5.4 Conclusion

Declarations

Acknowledgements

Author Contributions

Statements and Declarations

References

Additional Declarations

Supplementary Files

Status:

Journal Publication

Version 1