In vivo assessment of SNR and v/VENC contributions to velocity uncertainty in PC-MRI

Background: In phase-contrast (PC) MRI, precision of velocity measurements is described by velocity-to-noise ratio (VNR)¹. VNR is defined as π·SNR·(v/VENC), where SNR is the signal-to-noise ratio of the magnitude image, v is measured velocity, and VENC is the velocity encoding parameter. Current practice assumes that high SNR is sufficient to ensure reliable velocity quantification^2,3, since VNR increases with SNR. However, VNR also depends on v/VENC ratio. Therefore, we sought to quantify the relative contributions of SNR and v/VENC to velocity precision in vivo.

Methods: Twenty healthy volunteers (8M, 12F; age 41.4±17.0 years) underwent aortic 2D PC-MRI on a 1.5T scanner (GE Healthcare). Each subject was imaged with VENC=150, 200, and 300 cm/s, and flip angles=5°, 15°, and 20° (to vary the SNR).

Aorta, background, and static tissue masks were automatically segmented using in-house software. All measurements were performed at peak flow. SNR was computed as mean aortic signal divided by background noise standard deviation, with Rayleigh correction. VNR was also quantified.

Phase noise (σ_ϕ) measured in static tissue was converted to velocity noise via σ_v = (VENC/π)·σ_ϕ. Percent uncertainty was calculated as the ratio of velocity noise to the measured velocity amplitude (100·σ_v/|v|). Independent contributions of SNR and v/VENC were assessed using partial R².

Results: VNR scaled linearly with magnitude-derived SNR across all VENC settings (Fig. 1). Regression slopes decreased systematically with increasing VENC, indicating that for a given SNR, higher VENC values yield proportionally lower VNR.

Percent uncertainty decreased with both SNR and v/VENC, following hyperbolic relationships (Fig. 2). Partial R² analysis showed that SNR explained 64% of the variance in percent uncertainty, while v/VENC contributed 36%, confirming that both factors independently reduced velocity uncertainty. In practice, aortic velocity uncertainty falls below 10% if VNR ≥14.1, and below 5% if VNR ≥28.3 (Fig. 3).

Conclusion: High SNR alone does not guarantee reliable velocity precision in PC-MRI. For typical aortic peak velocities, an SNR of ~15-25 with VENC ≤200 cm/s is sufficient to achieve < 10% velocity uncertainty. Higher VENC values require higher SNR ( >30) to reach the same level of precision. At lower SNR (~10-15), maintaining v/VENC ≥0.5 is necessary to remain within 10-15% uncertainty. Diastolic frames would be especially vulnerable to noise propagation because both v/VENC and magnitude SNR are reduced, leading to a markedly lower VNR and higher uncertainty compared with systole, even when acquisition parameters are unchanged.

Funding: NIH NHLBI R56HL159710 and R01HL162671

Figure 1. The relationship between SNR and VNR at peak systole. Regression slopes decreased with increasing VENC, indicating that for a given SNR, higher VENC values yield proportionally lower VNR.
Figure 2. Percent uncertainty as a function of SNR and v/VENC. Percent uncertainty decreased hyperbolically with increasing SNR (left) and with increasing normalized velocity (v/VENC, right).
Figure 3. Relationship between VNR and the percent uncertainty of peak velocity measurements. Data follow a hyperbolic inverse relation. Dashed black reference lines indicate the thresholds for 10% and 5% uncertainty.