Caval to pulmonary 3D flow distribution in patients with Fontan circulation and impact of potential 4D flow MRI error sources

Abstract

Purpose: Uneven flow distribution in patients with Fontan circulation is suspected to lead to complications. 4D flow MRI offers evaluation using time-resolved pathlines; however, the potential error is not well understood. The aim of this study was to systematically assess variability in flow distribution caused by well-known sources of error.

Methods: 4D flow MRI was acquired in 14 patients with Fontan circulation. Flow distribution was quantified by the % of caval venous flow pathlines reaching the left and right pulmonary arteries. Impact of data acquisition and data processing uncertainties were investigated by (1) probabilistic 4D blood flow tracking at varying noise levels, (2) down-sampling to mimic acquisition at different spatial resolutions, (3) pathline calculation with and without eddy current correction, and (4) varied segmentation of the Fontan geometry to mimic analysis errors.

Results: Averaged among the cohort, uncertainties accounted for flow distribution errors from noise ≤3.2%, low spatial resolution ≤2.3% to 3.8%, eddy currents ≤6.4%, and inaccurate segmentation ≤3.9% to 9.1% (dilation and erosion, respectively). In a worst-case scenario (maximum additive errors for all 4 sources), flow distribution errors were as high as 22.5%.

Conclusion: Inaccuracies related to postprocessing (segmentation, eddy currents) resulted in the largest potential error (≤15.5% combined) whereas errors related to data acquisition (noise, low spatial resolution) had a lower impact (≤5.5%-7.0% combined). Whereas it is unlikely that these errors will be additive or affect the identification of severe asymmetry, these results illustrate the importance of eddy current correction and accurate segmentation to minimize Fontan flow distribution errors.

Keywords: 4D flow MRI; Fontan circulation; background phase errors; congenital heart disease; flow distribution; probabilistic tracking; segmentation; uncertainty; velocity noise.

Figure 1

Particle trace pathlines. a) Idealized pathline calculation. Top: Simplified 2D velocity field (u_x, u_y) with constant velocity magnitude V and changing velocity direction for 3 successive time-frames, t₀-t₁, t₁-t₂ and t₂-t₃, in a region containing 4 voxels. Bottom: A time-resolved pathline is emitted from location (X(t₀), Y(t₀)) = (0, 0) where u_x (X(t₀) = 0, Y(t₀)=0, t₀-t₁) = 0 and u_y (X(t₀) = 0, Y(t₀)=0, t₀-t₁) = V. This results in particle motion to (0, VΔt) where Δt is the time between frames. Thus at t₁ the particle has traversed to location (X(t₁), Y(t₁)) = (0, VΔt) where u_x (X(t₁) = 0,Y(t₁) = VΔt, t₁-t₂) = V and u_y (X(t₁) = 0,Y(t₁) = VΔt, t₁-t₂)= 0. Stepping through each time-frame, the resulting pathline trajectory (X(t), Y(t)) is shown by the dashed line. Note the voxels of the velocity field used to determine the pathline trajectory for each time-frame are shaded gray. b) Noise added to the velocity field generates a probabilistic pathline from the same emitter location. c) Schematic illustration of probabilistic flow tracking approach in Fontan circulation for one emitter point (X(t₀), Y(t₀), Z(t₀)). Left: The dashed lines represent the pathline trajectory for 3 successive time-frames. When velocity noise is not considered, there is only one possible flow pathway from this emitter point. Right: To see the effects of varying local measurement uncertainty, random time-varying velocity noise is added to the velocity data field for three repeat trajectory calculations (experiments), i=1 to N_exp = 3, using a Monte Carlo simulation approach. For the same emitter point, multiple probabilistic pathlines are thus generated (i.e. the red, orange and green dashed lines are the pathlines generated from experiments 1, 2 and 3, respectively). The resulting locations are labeled as (X(t), Y(t), Z(t))_i corresponding to the location at time t during experiment number i.

Figure 2

Fontan flow visualization and distribution analysis. a–c) To visualize the distribution of blood flow originating in the caval veins (i.e. IVC and SVC) into the pulmonary arteries (i.e. LPA and RPA), time-resolved particle trace pathlines are emitted from locations in the IVC and SVC. The time-averaged PC-MRA (gray) depicts the cardiovascular anatomy. d) Fontan flow distribution analysis volumes and planes. The Fontan volume is shown in gray. The IVC and SVC volumes were separated from the Fontan volume to be used as emitter volumes. Analysis planes in the LPA and RPA were placed close to the Fontan connection to capture flow pathlines reaching either vessel.

Figure 3

Probabilistic flow distribution quantification. For an example patient, the simulation is shown with σ = 0.06 m/s as input. After completing steps 1–3, the first experiment is shown (top right). Steps 1–3 are repeated multiple times (N_exp=100) to give the final probabilistic flow distribution result (bottom right) where uncertainty values (in % flow distribution) are underlined.

Figure 4

Top: Pathlines without and with noise added. Traditional pathlines are shown on the left (σ = 0 m/s). For comparisons, probabilistic simulations are shown with different noise levels, i.e. σ = 0.06 m/s (middle) and σ = 0.10 m/s (right). Bottom: The mean flow distribution is shown as the experiments were completed from 1 to N_exp=100 at two different noise levels (i.e. σ = 0.06 m/s and σ = 0.10 m/s) for the IVC (left) and SVC (right) simulations.

Figure 5

Traditional pathlines results (i.e. σ = 0 m/s). Boxplots and scatterplots (i.e. showing each data point) are shown. The data points showing preferential flow, i.e. absolute difference between flow distribution to the LPA and RPA is ≥20%, are shaded (dark gray = to the LPA, light gray = to the RPA).

Figure 6

Flow distribution results. Traditional pathlines (left) and probabilistic simulation results at two noise levels (σ = 0.04 m/s: middle, σ = 0.10 m/s: right) are shown for three patients: A, B and C = 3, 4 and 12, respectively). For each noise level, the flow distribution results (in %) for all 100 experiments are reported and the probabilistic pathlines from 5 experiments are visualized.

Figure 7

Probabilistic flow distribution results with increasing levels of added velocity noise (i.e. none to 10% of typical venc). For each patient, the mean of the % flow distributions (i.e. among experiments during simulation at each noise level) is reported (top) and the uncertainty, or standard deviation (bottom). For simplicity, only the flow distribution to the LPA is shown because flow distribution is normalized and so the % flow to the RPA is equal to 100% minus this value. Patient-specific results (noted by black circles) were interpolated among these data at the level of patient-specific velocity noise.

Figure 8

Bland-Altman plots for simulated error sources. The potential effects of low spatial resolution (a–b), phase background errors (c) and Fontan segmentation (d–e) are shown. These errors were simulated and the flow distribution was evaluated independent of added measurement noise (i.e. at σ=0 m/s) and compared to the original results (i.e. also at σ=0 m/s but evaluated at the acquired resolution, with eddy current correction and the manually segmented Fontan). The results both for SVC and IVC flow are included. Again for simplicity (and as in Figure 7), only % flow to the LPA is shown.