Standardized Evaluation of Cerebral Arteriovenous Malformations using Flow Distribution Network Graphs and Dual-venc 4D Flow MRI

Abstract

Background

Cerebral arteriovenous malformations (AVMs) are pathological connections between arteries and veins. Dual-venc 4D flow MRI, an extended 4D flow MRI method with improved velocity dynamic range, provides time-resolved 3D cerebral hemodynamics.

Purpose

To optimize dual-venc 4D flow imaging parameters for AVM; to assess the relationship between spatial resolution, acceleration, and flow quantification accuracy; and to introduce and apply the Flow Distribution Network Graph (FDNG) paradigm for storing and analyzing complex neurovascular 4D flow data.

Study type

Retrospective cohort study.

Subects/ phantom

Scans were performed in a specialized flow phantom, 26 healthy subjects (age 41 ± 17 years) and five AVM patients (age 27-68 years).

Field strength/sequence

Dual-venc 4D flow with varying spatial resolution and acceleration factors were performed at 3T field strength.

Assessment

Quantification accuracy was assessed in vitro by direct comparison to measured flow. FDNGs were used to quantify and compare flow, peak velocity (PV), and pulsatility index (PI) between healthy controls with various Circle of Willis (CoW) anatomy and AVM patients.

Statistical tests

In vitro measurements were compared to ground truth with Student t-test. In vivo groups were compared with Wilcoxon rank-sum test and Kruskal-Wallis test.

Results

Flow was overestimated in all in vitro experiments, by an average 7.1±1.4% for all measurement conditions. Error in flow measurement was significantly correlated with number of voxels across the channel (P = 3.11×10⁻²⁸) but not with acceleration factor (P =0.74). For the venous-arterial PV and PI ratios, a significant difference was found between AVM nidal and extranidal circulation (P = 0.008 and 0.05 respectively), and between AVM nidal and healthy control circulation (P = 0.005 and 0.003 respectively).

Data Conclusions

Dual-venc 4D flow MRI and standardized FDNG analysis might be feasible in clinical applications. Venous-arterial ratios of PV and PI are proposed as network-based biomarkers characterizing AVM nidal hemodynamics.

INTRODUCTION

Cerebral arteriovenous malformation (AVM) is a pathological vascular connection between the arterial and venous cerebral vasculature. AVM affects not only the local region surrounding the nidus, but also the total amount of flow to the brain and the distribution of flow in extranidal vessels(1). Treatment options for AVM include staged endovascular embolization of individual feeding arteries to reduce AVM flow, which is associated with 5–15% overall risk of hemorrhage(2). Embolization treatment alters the distribution of cerebral blood flow(3). As specific treatment recommendations continue to evolve(4), there is a lack of quantitative data relating hemodynamic parameters to AVM hemorrhage risk. Digital subtraction angiography (DSA), the clinical standard for AVM evaluation and staged embolization guidance, provides excellent morphological and functional lesion characterization. However, DSA perturbs the native blood flow distribution(5), and typically does not provide quantitative information on cerebrovascular AVM hemodynamics.

Alternatively, 4D Flow MRI(6) is a non-invasive technique for assessment of time-resolved 3D blood flow velocities with full volumetric coverage of the brain. While accurate AVM diagnosis and Spetzler-Martin grading rely on other MR methods such as Time of Flight or contrast-enhanced MR angiography, only 4D Flow MRI can directly quantify cerebral hemodynamics on a voxelwise basis over the entire volume and is not redundant with structural imaging(3). Previous studies(7) (8) have shown the feasibility of 4D Flow MRI for characterizing complex 3D hemodynamics, identifying main feeding arteries and draining veins, and quantifying cerebral blood flow redistribution during staged embolization treatment in AVM. However, imaging AVMs requires large cerebral coverage and a large velocity dynamic range to assess both fast (arterial) and slow (venous) blood flow in vessels with diameters as small as 3mm, which is challenging (3) (9) (10). Using PEAK-GRAPPA acceleration (11) (a k-t method), dual-venc 4D Flow MRI enables simultaneous volumetric quantification of arterial and venous blood flow: two velocity encoding sensitivity (venc) settings are used within the same acquisition, resulting in a large velocity dynamic range and signal-to-noise ratio (SNR)(12). Limitations of this method include the trade-off between spatial resolution, temporal resolution, field of view (FOV) and scan time. As a benchmark, previous work at 1.5T field strength(13) and computational predictions(14) have established a minimum of 4–5 voxels across the diameter of a vessel for accurate flow quantification.

At increased field strength and with the introduction of dual-venc scans, resolution benchmarks from previous work should be re-evaluated. Additionally, current post-processing methods of 4D flow MRI typically include manually placed quantification planes, so complete quantification of neurovascular hemodynamics is cumbersome and operator-dependent, limiting the utilization of rich 4D Flow datasets. There is a lack of systematic, comprehensive characterization of neurovascular network variability in healthy variants and AVM patients.

The purpose of this study was to address the above limitations by establishing a protocol with optimized dual-venc 4D Flow MRI scan parameters and an efficient semi-automated post-processing workflow for assessment of AVM hemodynamics that accounts for vascular network variability.

MATERIALS AND METHODS

In Vitro Experiments

An in vitro flow phantom consisting of a cube with three flow channels (diameters 4, 6 and 8mm), each of which contains flow along all three spatial dimensions along edges of the cube, was constructed (Figure 1). The channels run parallel to one another through the central section. A steady flow gear pump (Micropump, Vancouver, WA, USA) was used to circulate water containing 2 mM gadobutrol (Gadavist, Bayer, Leverkusen, Germany). Total inlet flow was monitored with a flow meter (FLR1012, OMEGA Engineering, Stamford, CT, USA), and used to regulate the pump via proportional-integral-derivative (PID) feedback control programmed in LabView (National Instruments, Austin, TX, USA). Readout from the flowmeter was used as ground truth measurement for flow rate. Contrast-enhanced water was used to fill empty space in the phantom, providing a static reference for background phase correction.

Figure 1.

3D schematic of flow phantom consisting of a cube with 3 flow channels, each channel (4, 6, and 8mm) contains flow in 3 consecutive, orthogonal segments of identical length between inlet and outlet. To emulate branched flow networks, inlets to all channels are fed by branches of one flexible tube (pump source) outside imaged volume; channel outlets are similarly linked (pump return).

Three sets of experiments were performed: 1) One channel opened at a time, with flow such that the maximum velocity for each individual channel was between 40 – 80 cm/s. 2) All phantom flow channels open and operated in parallel, with flow such that the maximum velocity for each individual channel was between 50 – 100 cm/s. 3) The 6mm channel was scanned twice to provide data on the reproducibility of flow and PV.

For all three of these experiments, an identical image with the pump turned off was obtained for background phase correction.

Human Study Cohort

This Institutional Review Board (IRB) approved study included 26 healthy subjects (age 41 ± 17 years, 12 females) with appropriate informed consent. All AVM patients were scanned with dual-venc 4D flow MRI as part of the clinical MRI protocol for patients with unruptured AVM nidus > 5mm; data was obtained through IRB-approved retrospective chart review. Five AVM cases (age 27–68 years, 1 female: 2 frontal, 2 temporal, 1 parietal; Spetzler-Martin grade 3 – 5) were included.

4D Flow MRI Acquisitions

All flow phantom scans were performed on a 3T scanner (Siemens MAGNETOM Skyra, Erlangen, Germany) using the dual-venc 4D flow MRI sequence. The relaxivity of the solution (15) was 5.0/mM-s, so for a TR of 6.2 ms, Ernst angle $\alpha =acos\left(\text{exp}\left(-\frac{TR}{T1}\right)\right)=acos\left(exp\left(-\frac{6.2}{100}\right)\right)={20}^{{}^o}$ was chosen as flip angle for optimal phase contrast. Low and high vencs respectively were 40 and 80 cm/s for experiments with flow through only a single channel at a time, 50 and 100 cm/s for scans with simultaneous flow through all channels, allowing for optimal velocity aliasing correction(12). Each experimental setup was imaged at all combinations of isotropic spatial resolutions (0.8 mm)³, (1.0 mm)³, (1.2 mm)³, and (1.6 mm)³ and PEAK-GRAPPA(16) (11) acceleration factors of R=2, 3, and 5 as well as non-kt accelerated GRAPPA R=2 as a reference (Table 1). These parameter ranges allowed for systematic evaluation of flow quantification with 2–10 voxels across a given flow channel.

Table 1.

Scan parameters for in vitro imaging

In Vitro Data Subset	Isotropic voxel size [mm]	Channel Diameter [mm]	Voxels Across Channel	Flow [mL/s]	TR [ms]	TE [ms]	Temporal resolution [ms]	Low venc [cm/s]	High venc [cm/s]
Individual channel scans Standard GRAPPA R = 2 PEAK-GRAPPA R = 2, 3, 5 Phases/cycle: 7 FA = 20° PID-controlled flow 1 channel open per scan	0.8	8	10.0	18.3	6.8	3.87	95.2	40	80
		6	7.5	11.7
		4	5.0	4.2
	1.0	8	8.0	18.3	6.5	3.68	91.0
		6	6.0	11.7
		4	4.0	4.2
	1.2	8	6.7	18.3	6.3	3.58	88.2
		6	5.0	11.7
		4	3.3	4.2
	1.6	8	5.0	18.3	6.1	3.47	85.4
		6	3.8	11.7
		4	2.5	4.2
All-channel scans Standard GRAPPA R = 2 PEAK-GRAPPA R = 2, 3, 5 Phases/cycle: 7 FA = 20° PID-controlled flow All channels open simultaneously	0.8	8	10.0	33.0	6.7	3.72	93.8	50	100
		6	7.5
		4	5.0
	1.0	8	8.0	33.0	6.3	3.51	88.2
		6	6.0
		4	4.0
	1.2	8	6.7	33.0	6.1	3.39	85.4
		6	5.0
		4	3.3
	1.6	8	5.0	33.0	5.9	3.29	82.6
		6	3.8
		4	2.5

ECG for prospective gating was chosen to allow acquisition of 7 cardiac frames. After reconstruction, only the last cardiac time frame was analyzed, avoiding steady-state artifacts. To compare acquisition time for each set of in vitro conditions and assess clinical feasibility, acquisition times were normalized to a pulse of 80 bpm and a 140×200×40 mm³ FOV, a volume that typically covers the CoW (Supplemental Figure S1). All scans were acquired with 100% phase and slice resolution.

All in vivo dual-venc 4D Flow MRI data was collected using a 3 Tesla (Siemens MAGNETOM Skyra, Siemens Healthcare GmbH, Erlangen, Germany) scanner, with scan parameters as in Table 2.

Table 2.

Scan parameters for in vivo imaging: range and mean value for each cohort

	Resolution [mm]	TR [ms]	TE [ms]	FA [°]	Temporal resolution [ms]	Cardiac timeframes	Low VENC [cm/s]	High VENC [cm/s]
Control n = 26	0.8 – 1.6 (1.0)	4.2 – 7.4 (6.7)	2.6 – 4.4 (3.9)	15	29 – 104 (87)	6 – 25 (13)	44 – 90 (49)	100 – 200 (123)
AVM n = 5	1.2– 1.9 (1.4)	6.0– 6.2 (6.1)	3.3– 3.5 (3.4)	15	43– 87 (60)	7– 15 (12)	44–100 (60)	100– 200 (124)

MRI Post-Processing

All data were corrected for Maxwell terms(17) during reconstruction, and for eddy currents and velocity noise(18) using a specialized in-house tool(19) (Matlab, MathWorks, Natick, MA, USA). In vitro, background phase was corrected by subtracting the image collected under identical conditions but with flow turned off (20). As shown in Figure 2(A), a second tool(21) was used to segment vessels or channels, extract centerlines and automatically compute equidistant analysis planes positioned perpendicular to the centerline (every 1 mm in each flow segment). In vitro, 15 planes were positioned for each tube in regions far from bends and corners in channels. For control and patient data, the number of planes depended on the length of each vessel, as planes were placed automatically every 1 mm along the vessels’ centerline. At each plane, velocity and net flow were quantified. The lumen boundary was determined automatically at each analysis plane with additional manual adjustment of vessel contours if needed for delineation of the vessel wall from noise voxels and neighboring vessels. In vitro, the segmentation of the standard GRAPPA R=2 data set was used for analysis of PEAK-GRAPPA accelerated data sets with the same spatial resolution, to control for variation caused by segmentation differences. The number of voxels across the vessel (VAV) at each plane was estimated from the vessel area by:

$$VAV=\frac{2\times \sqrt{(Vesselarea∕pi)}}{acquiredresolutiondimension}$$ (1)

Figure 2.

Workflow for (A) in vitro flow phantom experiment and (B) in vivo healthy control and (C) in vivo AVM patient data: Preprocessing (noise and phase offset correction, generation of pseudo-complex difference PC-MRA), automated quantification (segmentation, centerpoint and centerline extraction, analysis plane placement (every 1 mm in each flow segment) with velocity profile, quantification). Only large arteries and veins, as well as those feeding or draining the AVM, were included in quantification and represented in a flow distribution network diagram (FDNG). The FDNG is a mechanism for internal representation of vessel connectivity that allows for straightforward computation of flow conservation across any vessel junction or the whole brain.

The flow, PV and PI values were calculated as the median value over the multiple planes along the centerline for each vessel. Finally, a flow distribution network graph (FDNG) was constructed for each 4D flow MRI data set, characterizing the relationship between vessel segments.

Flow Distribution Network Graphs

FDNGs were implemented within the post-processing tool using the directed graph data type in Matlab. Within this data type, flow channels or vessels were represented by graph edges and the junctions between them were represented as nodes. For each vessel, the start and end nodes were differentiated according to the flow direction. Connections between channels were automatically detected based on coinciding coordinates of centerline endpoints, shown as red points in Figure 2(B-C), and refined manually.

CoW architecture classification was based on high spatial resolution (0.25×0.25×0.5 mm) time-of-flight (TOF) read by two experienced radiologists (Authors 3 and 4). The CoW architecture was then represented in the connectivity pattern of each individual’s FDNG. When a vessel was angiographically present on TOF, but not visible on the magnitude image of the 4D Flow MRI data, a zero value was entered for that vessel in the FDNG of that individual for all hemodynamic parameters. The median value of each derived hemodynamic parameter (net flow, PV and PI) for each vessel was stored as an edge weight in the FDNG. The final FDNG for an individual thus contains connectivity, flow direction, and hemodynamic parameters computed from 4D Flow.

To simplify visualization and identify subject groups with identical CoW architecture, a standardized set of coordinates for each junction point was used to visualize FDNGs of healthy controls (Figure 2B). Healthy subject datasets were assigned to groups based on CoW variants (i.e. network connectivity) by directly comparing FDNGs based on graph homology. Group FDNGs contain the shared connectivity and flow direction of the group, and group mean values of hemodynamic parameters for each vessel.

Derived Quantities from FDNG

To assess the error in flow measurement from MRI in vitro, total flow to the phantom was compared with the controlled pump flow rate measured by the flow meter. For single-channel measurements accuracy was determined by direct comparison to ground truth flow. For parallel-channel measurements the sum of the median flow within all three channels was calculated as total flow to the phantom during the experiments with all channels open. Then, the flow conservation error was evaluated as

$$Flowconservationerror=\Vert 1-\frac{totalflowmeasuredbyMRI}{totalflowsetatpumpcontroller}\Vert$$ (2)

Reproducibility for flow and PV was quantified by the repeatability coefficient RPC(22):

$$RPC=1.96\sqrt{2{\sigma }^2}$$ (3)

In vivo, the following parameters were derived from the FDNG. Pulsatility index (PI) was estimated plane-wise by:

$$Pulsatilityindex=\frac{PV-meanvelocityoflasttimepoint}{meanvelocityovercardiaccycle}$$ (4)

For quantities representing multiple vessels, flow values were added while PV or PI were averaged.

For in vivo data, no ground truth values are available, but internal consistency of flow rate was assessed via flow conservation error across the arterial side of the vascular network. Flow conservation error was calculated as:

$$Flowconservationerror=\Vert 1-\frac{totalflowinACAs,MCAsandPCAs(ifsuppliedbyICA)}{totalflowinICAs}\Vert$$ (5)

To account for the distribution of healthy subjects by age, sex, and body habitus, flow values (Q) in all branches were normalized by total cerebral blood flow (TCBF), as in Figure 3A:

$$TCBF=\sum inflows=Q_{LICA}+Q_{LICA}+Q_{BA}$$ (6)

Figure 3.

Standardized FDNG with full COW, illustrating metrics including A. Total cerebral Blood flow or Mean Incoming Blood Velocity (equations 6-7), B. Arterial flow or PV (equations 8-9) and C. Venous-Arterial Flow, PV or PI ratio (equations 10-11). The general COW network is represented with vessels in light grey and vessels involved in equations 6-11 were colored either dark grey (if they are in the numerator of the equation) or black (if they are in the denominator). Arrowheads show direction of flow.

Similarly, average arterial PV values were normalized by mean incoming blood velocity (MIBV), the mean PV of the supplying arteries (left and right ICAs and BA):

$$MIBV=Mean(P{V}_{LICA}+P{V}_{LICA}+P{V}_{BA})$$ (7)

To describe arterial hemodynamics, the following normalized arterial flow and PV were calculated (Figure 3B):

$$Arterialflow=\sum (Q_{MCA},Q_{ACA},Q_{PCA})∕TCBF$$ (8)

With Q_MCA, Q_ACA and Q_PCA being the sum of left and right MCA, ACA and PCA flow, respectively.

$$Arterialpeakvelocity=Mean(P{V}_{MCA},P{V}_{ACA},)∕MIBV$$ (9)

With PV_MCA, PV_ACA and PV_PCA being the mean of left and right MCA, ACA and PCA PV, respectively.

A distinction is made in AVM patient data between nidal (feeding or draining the AVM nidus) and extranidal hemodynamics (vessels supplying or draining the brain excluding the nidus). (Supplement 2).

For flow, PV and PI, a venous-arterial ratio was computed to characterize differences between venous and arterial flow, caused by blood passing through either the small vessels of the brain or through an AVM. In controls, the venous-arterial flow ratio is as in Figure 3C:

$$Venous-arterialflowratio=\sum Q_{SSS},Q_{STR}∕\sum Q_{MCA},Q_{ACA},Q_{PCA}$$ (10)

With Q_MCA, Q_ACA and Q_PCA being the sum of left and right MCA, ACA and PCA flow, respectively.

The venous-arterial ratio for PV or PI (labeled X) was calculated by:

$$Venous-arterialPVorPIratio=Mean(X_{SSS}+X_{STR})∕Mean(X_{MCA},X_{ACA},X_{PCA})$$ (11)

Statistics

All continuous values are reported as mean ± standard deviation unless otherwise specified. P-values < 0.05 were considered significant. In vitro, values from multiple measurements along a single channel with steady flow were compared to ground truth with one-sided Student t-test. The dependence of accuracy and flow conservation error on voxels across vessel and acceleration were assessed with a mixed-effect linear model as well as one-way ANOVA with acceleration as factor. To investigate the relationship between in vitro optimization of spatial resolution and in vivo results, flow conservation error was compared between controls with high and low numbers of voxels across the vessel and between controls with high and low resolution, with the thresholds for both defined using the in vitro results. Group FDNGs for controls were used to compare flow and PV for individual vessels, and to compare metrics derived from the FDNG between subject groups. In vivo, nonparametric tests of significance were used because the normality assumption is not applicable to the small population analyzed. Thus pairwise group comparisons of flow conservation and FDNG metrics used the Wilcoxon rank-sum test; comparisons among multiple anatomical control subgroups were assessed using the Kruskal-Wallis test.

RESULTS

In Vitro Experiments

A FOV of 140mm × 200mm × 40mm, corresponding to the principal intracranial vessels, could be acquired in less than 20 minutes for spatial resolutions larger or equal to (1 mm)³ independent of acceleration factor (Supplemental Figure S1). With the highest isotropic resolution tested (0.8 mm isotropic), this volume can be acquired in less than 20 minutes only with R = 5.

Only Individual Flow Channels Open

Flow was overestimated in all experiments, by an average of 7.1±1.4% for all sets of measurement conditions (Figure 4A). Error in this measurement was found to decrease by 5.0% for every additional voxel across the vessel (P = 3.11×10⁻²⁸). Overall, there was no significant relationship between acceleration factor and flow measurement error (P = 0.74). For R=5, flow conservation error was consistently within 10% for 6 or more voxels across vessel.

Figure 4.

In vitro phantom experiment. (A) Flow measurements for each channel plotted relative to number of voxels across it. For each channel, expected flow varies with pump flow rate. Dashed lines show ground truth (blue) and 10% error (orange). Red squares indicate mean flow measurement error significantly higher than 10%. (B) Sum of parallel flows in phantom, relative to number of imaged voxels across smallest (4 mm) channel. (C) Repeatability coefficient for net flow, expressed as percent of the mean flow rate. (D) Repeatability coefficient for peak velocity, expressed as percent of the mean value.

All Flow Channels Open

For experiments with all channels open (Figure 4B), flow conservation error ranged from 1.0±0.6% (GRAPPA R=2, 0.8mm isotropic resolution) to 18.8±4.5% (R=5, 1.2mm resolution). Flow conservation error decreased 2.5% with unit increase in VAV (P = 0.0002) and increased (relative to GRAPPA R=2) with PEAK-GRAPPA R=2 (8.4%, P = 0.02), R=3 (6.5%, P = 0.07), and R=2 (14.7%, P = 4.24×10⁻⁵). At R=5, flow conservation error was within 15% for 4 or 5 voxels across vessel.

Reproducibility Analysis

Average flow repeatability coefficient was 5.6% of ensemble mean for all combinations of resolution and acceleration (at most 9.2%). Average repeatability coefficient of PV was 1.5% of the mean PV (at most 2.2%). For both flow and PV, there was no significant association with acceleration factor (P = 0.89 and 0.59 respectively) and the negative trend with VAV was not significant (P = 0.48 and 0.75 respectively). Bland-Altman analysis of flow rate (Supplemental Figure S2) showed significant offset in 3 of 16 combinations of resolution and acceleration (highest significant offset was 1.7% per mL/s, at PEAK-GRAPPA R=2, (1.2mm)³, P = 0.002). Bias was significant in 9 of 16 combinations (highest 1.06% of ground truth flow, at PEAK-GRAPPA R=5, (1.2mm)³, P = 2.14×10⁻¹²). Bland-Altman analysis of PV (Supplemental Figure S3) showed significant offset in 2 of 16 combinations (highest 2.1 m/s, at standard GRAPPA R=2, (1.2mm)³, P = 0.0006). A significant bias was observed in 7 of 16 combinations (highest 0.006 m/s of ground truth flow, at PEAK-GRAPPA R=3, (0.8 mm)³, P = 0.001).

Healthy Control Study

Average flow conservation error (Equation 2) over the control cohort (n = 26) was 20±14%. The difference in flow conservation error between controls with a median 4 or more voxels across the vessel was 12%, vs 25% in those with less than 4 (P = 0.027). Number of voxels across vessel is negatively correlated to voxel size with R²=0.83, P = 1.31×10⁻¹⁰ (Supplemental Figure S4). The mean number of voxels across the vessels for 0.8mm isotropic scans was 4.17 vs 2.98 for all others combined (P = 1.75×10⁻⁵). Flow conservation error at 0.8mm isotropic resolution was 11% vs 28% for lower resolution scans (P = 0.004).

The control cohort yielded 7 CoW network variants, distinguished by presence or absence of posterior communicating arteries (PCOM), the supplying artery of the posterior cerebral artery (carotid, basilar, or both), and in two subjects an aplastic right anterior cerebral artery (ACA). The cohort included three controls with unique variants, one group of two subjects, and another three groups with at least four subjects with similar variants. The largest group had both PCOMs present (n=13), the second group had only the left PCOM (n=4), and the third group showed no PCOMs (n=4). The group with only two subjects had no PCOMs and a left fetal PCA. The three individual variants were: right PCOM only, right PCOM with left fetal PCA, and left PCOM only with no right ACA. Only the groups with four or more subjects were used for group comparison.

In generating the FDNGs on average 1.3 vessels were visible on TOF but not 4D flow; in most cases these were posterior communicating arteries (PCOM). Figure 5 shows one representative individual FDNG for each of the three unique variant groups with at least 4 subjects, as well as standardized group FDNGs.

Figure 5.

(A) For each of the most common COW architectures in the sample, velocity pathlines at systole are shown for a representative subject. For each of these subjects a network graph (blue) is superimposed on the PCMRA (yellow). Within-group standardized FDNG colors show group mean vessel flow as percentage of total inflow over group. (B) For each AVM case, the FDNG shows median flow [mL/cycle] in each vessel.

Based on group FDNGs, increased left transverse sinus (LTS) flow (P = 0.045) and significantly decreased right transverse sinus (RTS) flow (P = 0.027) were observed in the left-PCOM group compared to both-PCOM, with right sinus predominance unlike both-PCOM and no-PCOM groups. No significant difference between control groups was observed by Kruskal-Wallis test for TCBF (P = 0.27), MIBV (P = 0.19), normalized arterial blood flow (P = 0.88), normalized arterial PV (P = 0.12), nor in venous-arterial ratios of flow (0.51), PV (0.43) or PI (0.86).

Patient Study

Flow pathlines and individual-level FDNGs for AVM cases highlight their heterogeneous network connectivity (Figure 6). There is no significant difference between controls and AVM patients (Figure 7A) in TCBF (P = 0.09) or MIBV (P = 0.12). There is also no significant difference in normalized arterial flow (Figure 7B) between controls and either nidal or extranidal circulation in AVM patients (P = 0.89 and 0.94 respectively), nor between the relative amount of arterial flow going to the nidal versus extranidal circulation (P = 0.54). There are no significant differences between any groups (P = 0.77) in the venous-arterial flow ratio (Figure 7C).

Figure 6.

(A) Velocity pathlines at approximate systole (determined on an individual basis, at typically approx. 240 ms after recorded R wave) for 5 AVM cases; (B) For each AVM case, the FDNG shows median flow [mL/cycle] in each vessel.

Figure 7.

In-vivo blood flow derived parameter comparison between controls and AVM patients: (A) TCBF [mL/cycle] (B) Arterial flow [% TCBF] (C) Venous-arterial flow ratio (D) Arterial PV [m/s] (E) Venous-arterial PV ratio (F) Venous-arterial PV ratio. Dashed lines denote a ratio of 1 for cerebral arterial flow relative to TCBF or venous relative to arterial flow. Significant differences are denoted by asterisks between measurements connected by brackets.

The normalized arterial PV was significantly lower in extranidal cerebral arteries of the AVM patients (P = 0.0005) and nidal arteries (P = 0.0005) than healthy controls (Figure 7D). For the venous-arterial PV and PI ratios (Figure 7E-F), a significant difference was found between AVM nidal and extranidal circulation (P = 0.008 and 0.05 respectively), and between AVM nidal and healthy control circulation (P = 0.005 and 0.003 respectively), but not between controls and the extranidal circulation of AVM patients (P = 0.32 and 0.65 respectively).

DISCUSSION

To identify parameter sets for evaluating the hemodynamics of AVM patients with sufficient spatial resolution and coverage, dual-venc 4D flow MRI data was systematically evaluated with varied imaging parameter settings in an in vitro flow phantom experiment. The primary findings from this study were that flow measurement accuracy strongly depends on the number of voxels across vessels independently of acceleration factor, and no significant effect of acceleration factor was observed in the single-channel accuracy study. Flow measurement accuracy within 10–15% was achieved with 5 voxels across the vessel for all acceleration factors. Flow conservation error across multiple channels was significantly correlated with increasing acceleration and decreasing voxels across the vessel. For 4 or more voxels across, conservation error was <15%. Repeatability of both flow and PV was high. There was no relationship between Bland-Altman bias or offset with resolution or acceleration, and where statistically significant bias or offset values were observed, the magnitude of these effects was small; bias in flow was less than the flow measurement error even at the best-performing conditions (1.36%). Scan times under 20 minutes are achievable using high acceleration factors, and given that the current study used 100% phase and slice resolution, acquisition time could be reduced further in practice.

For efficient and standardized evaluation of the brain vessels, a flow distribution network graph (FDNG) was successfully developed as a new paradigm for relating hemodynamic information to the pattern of connectivity between flow channels. A feasibility study including 26 healthy controls and five AVM patients was performed using dual-venc 4D flow MRI and novel FDNG analysis. Flow conservation error was significantly lower in scans with a median of at least 4 voxels across the vessel (consistent with the in vitro findings) and this result translates to in vivo imaging parameters using an isotropic spatial resolution of at least 0.8mm.

Additionally, FDNG analysis enabled streamlined comparison of different CoW architectures in healthy controls. Most metrics did not vary significantly between control groups, though a difference in transverse sinus predominance was identified between the both-PCOM and left PCOM groups.

AVM cases demonstrated the application of the FDNG concept to uniformly adapt quantitative metrics to complex architectures, including arterial flow ratio and venous-arterial ratios of PV and PI. Arterial flow, PV and PI trended higher relative to TCBF in all control groups than in nidal or extranidal arteries of AVMs, and though arterial flow is variable between patients, generally the amount of flow diverted to the nidus is comparable to flow supplying the rest of the brain. Venous-arterial ratios of PV and PI were significantly higher in AVM nidal flow than either normal vasculature in AVM patients or healthy controls. Clinical interpretation of this result requires further study. However, by using the FDNG paradigm all metrics identified here can be computed for any brain AVM regardless of complexity level, thus accommodating many possible anatomical variations.

In the absence of reliable biomarkers for treatment-related risk stratification of AVMs, endovascular treatment strategies remain controversial(23) (24). Because the neurovasculature consists of many vessels connected in complex and often patient-dependent patterns, the connectivity of flow channels is key to understanding the significance of hemodynamic measurements and obtaining such biomarkers. FDNGs provide a standardized format to visualize and quantitatively compare variants in CoW architecture. The flow conservation at connections between channels, a metric of internal validation in the absence (as in many clinical applications) of ground truth, can be quantified easily with FDNG and was consistent with in vitro results in this study.

With the parameters evaluated here, clinically feasible scan times are achievable. Based on in vitro results, at least 5 voxels across a vessel should be used for flow quantification within 10–15%. However, 4 voxels across a typical vessel (achievable in vivo with 0.8mm isotropic resolution) will yield flow conservation < 15% and high reproducibility of flow and PV.

FDNGs allowed hemodynamic quantification of both normal controls and AVM patients with complex vessel architecture. Overall, the few observed significant differences between control groups could be related to symmetry characteristics of the neurovascular networks. The two symmetric groups had right transverse sinus predominance, which is most common on a population level(25) and consistent with previously published 4D flow results that did not distinguish between CoW morphologies, while the asymmetric left-PCOM group had reversed, left transverse sinus predominance(26).

The distribution of CoW variants is consistent with population studies showing about 0.6% prevalence of unilaterally absent PCOM, but 34% prevalence of unilaterally hypoplastic PCOM(27) which may contribute little hemodynamically. Notably, a previous 4D flow study found a 24–29% prevalence of variant anatomies in healthy controls (middle-aged and older) versus 38% in Alzheimer’s disease patients in addition to significant differences in arterial PI between the groups(28). This suggests that flow distribution differences between these variants may have clinical significance, which may be clarified by larger cohort studies with FDNG.

A study using 2D phase-contrast MRI found higher flow in ipsilateral vs. contralateral arteries relative to the AVM(29). The present study extends these findings using the connectivity relationship of feeding vs. non-feeding arteries, to identify nidal flow values comparable to extranidal flow. Though Shakur et al found higher mean velocities in ipsilateral versus contralateral arteries, the present study identifies extranidal arterial peak velocities to be lower than that of controls, and nidal arterial peak velocities to be lower than both, when normalized to the MIBV, a result that suggests a complex deregulation of hemodynamics extending beyond the AVM nidus. Normalized PV values reported here are the median value across many individual planes, rather than the single fastest flow measured within the vessel, which may also contribute to divergent results. In this study, arterial PV and PI was also found to distinguish the supposedly normal extranidal circulation in AVM cases from the circulation of healthy controls. This suggests that the entire cerebrovascular network is impacted hemodynamically by an AVM, though the clinical importance of this metric requires further study to evaluate. The FDNG paradigm extends previously described parameters to the venous system. Venous-arterial PI ratio, which is the inverse of the damping factor proposed by Gosling(30), intuitively characterizes a lack of damping by the AVM nidus relative to normal vasculature, so a higher venous-arterial PI ratio across the nidus than in the normal vessels of controls is consistent with previous findings. Though lower PI in feeding arteries compared to contralateral vessels, identified in a study of 72 AVMs, was independent of morphological predictors of hemorrhage risk(29), other studies of AVM show outflow resistance (31) (32) and lower ratio of time-to-peak in draining veins vs. feeding arteries(33) are correlated to a higher rupture risk. This suggests that biomarkers characterizing the hemodynamics of the venous side of the AVM may be relevant for risk stratification.

The study had several important limitations. There is evident overestimation of flow in vitro, which is expected due to partial volume effects (given that flow channels are at most 2–10 times the width of an imaged voxel). The results do not indicate a statistically significant relationship between flow quantification accuracy and acceleration: this may be partially due to using the same vessel segmentation from the standard GRAPPA R=2 data set for all data with the same spatial resolution but different acceleration factors. In practice, increased acceleration may also contribute to increased difficulty of segmentation of a single data set, resulting in a decrease in accuracy not accounted for here.

For this preliminary assessment of the FDNG paradigm, CoW architecture was characterized by the presence or absence of a vessel on TOF MRA. However, the hemodynamic impact and clinical significance of vessels such as the PCOMs may vary depending on their size, which is not accounted for by this method. This is a potential source of variability within control groups.

The cohort size limited the total number of healthy variants observed, as well as the number of individuals with each variant. This restricted the current work to comparisons between only the 3 most common variants of the 7 observed. Due to the small sample size, the effect of age or sex was also not examined, though previous studies suggest that both flow and PV vary significantly with age(34). Also, the field of view used in this study precluded examination of variants in the branches of the basilar artery proximal to the posterior cerebral artery, which are common and likely to be present in this cohort. However, as a result of normalizing by TCBF, neither cohort age or sex nor field of view limitations are likely to impact results related to flow measurements.

Increased hemorrhage risk is associated with untreated AVMs containing single draining veins, venous stenosis, and diffuse morphology (31) (35). The AVM cohort in this study was too small to investigate whether the hemodynamic parameters identified here are related to risk or to these risk-associated features. Further investigation is needed to determine whether these findings are related to specific AVM features.

In conclusion, a Flow Distribution Network Graph framework is presented for investigating intracranial neurovascular networks using dual-venc 4D Flow MRI. The accuracy of dual-venc 4D flow MRI was characterized at physiologically relevant scan conditions in vitro and in vivo using the FDNG paradigm. Dual-venc 4D flow MRI, due to its large dynamic velocity range, presents an opportunity to quantitatively and comprehensively assess the hemodynamics of major arteries and veins in the neurovascular network. Venous-arterial ratios of PI and PV were proposed as biomarkers to differentiate AVM nidal flow from normal, brain-supplying flow in both patients and controls. These network-based biomarkers provide a basis for future studies to standardize data presentation and analysis in an expanded AVM cohort, and for future correlation with treatment outcomes.