Michael Schär^{1}, Sahar Soleimanifard^{1}, Gabriele Bonanno^{1,2}, Jérôme Yerly^{3,4}, Allison G Hays^{2}, and Robert G Weiss^{1,2}

Coronary endothelial function (CEF) can be measured noninvasively with MRI by quantifying changes in

**In-vivo SNR:**
To have an estimate of the SNR for the subsequent in vitro work, right and left
coronary arteries were imaged with the current CEF protocol^{4} in 10 subjects at 3T. The SNR was determined by averaging
and subtracting 2 cardiac phases with minimal motion^{13}.

**Simulations:**
Area
measurements of circular vessels were simulated by varying partial volume (528
steps, Figure 1A), vessel diameter (2.5-5mm), imaging voxel size Δx (0.4-1mm), SNR (10-150), and Fourier interpolation (factors
1, 2, 4, 8). Areas were measured with full-width at half-maximum
(FWHM) and used to determine precision (standard deviation) and accuracy (mean
of the difference from the true value).

**Phantom:** A phantom with precision-drilled holes (diameters 3-3.42mm
in steps of 0.02mm, each 5 times^{10}) was placed in a container filled with
gadolinium-doped water (T1~200ms). Spiral cine MRI was acquired 10 times orthogonal
to the drilled holes with the current standard CEF protocol (Δx=0.89mm, 20
interleaves, 18s breath-hold) and a high-resolution protocol (Δx=0.6mm, 26
interleaves, 23s). Images were deblurred locally^{14}. CSA was measured
with FWHM, and CSA precision and accuracy were determined as above. To
determine the limit of CSA change that is detectable, a statistical test based
on the area under the curve (AUC) of the receiver operating characteristic
curve (ROC) was used as proposed by Yerly et al.^{10} A nonparametric ROC
curve was computed from the measured areas of two different diameters for each
combination of diameters. The CSA change between two diameters was considered
statistically detectable if the AUC ≥ 0.95, and the smallest area
difference that consistently passed this test was determined for every
diameter.

**In-vivo SNR:
**Mean in vivo coronary SNR with the standard CEF protocol was 53±19
(mean±standard deviation); and 70±6 (n=5, ranging from 62-76) and 35±8 (30-50) at
the level of the RCA and LAD, respectively.

**Simulations
and Phantom: **Figure 1 shows
example simulated vessel images with different zero-filling factors and added
noise. Example phantom images with zero filling factors 1 and 8 are shown in
Figure 2. Figure 3 shows that 8-fold Fourier interpolation improves area
measurement precision by a factor of 6.5 and 4.9 in the simulations and
phantoms scans, respectively, while slightly reducing accuracy (increased
underestimation). The simulations show that both precision and accuracy can be
improved with increased spatial resolution as long as the SNR stays above 20
(Figure 4). Phantom measurements (Figure 5A-B) confirm those simulations and
show that both precision and accuracy can be improved with smaller voxel sizes
as long as SNR ≥ 30. The limit of area-change detection is <4% for SNR > 60,
and <5% for SNR > 30 with the current protocol, and <3.5% for SNR >
40 with the high-resolution protocol (Figure 5C).

1. Suwaidi JA, Hamasaki S, Higano ST, Nishimura RA, Holmes DR, Lerman A. Long-term follow-up of patients with mild coronary artery disease and endothelial dysfunction. Circulation. 2000;101:948–954.

2. Schächinger V, Britten MB, Zeiher AM. Prognostic impact of coronary vasodilator dysfunction on adverse long-term outcome of coronary heart disease. Circulation. 2000;101:1899–1906.

3. Halcox JPJ, Schenke WH, Zalos G, Mincemoyer R, Prasad A, Waclawiw MA, Nour KRA, Quyyumi AA. Prognostic Value of Coronary Vascular Endothelial Dysfunction. Circulation. 2002;106:653–658.

4. Hays AG, Hirsch GA, Kelle S, Gerstenblith G, Weiss RG, Stuber M. Noninvasive visualization of coronary artery endothelial function in healthy subjects and in patients with coronary artery disease. J Am Coll Cardiol. 2010;56:1657–1665.

5. Hays AG, Kelle S, Hirsch GA, Soleimanifard S, Yu J, Agarwal HK, Gerstenblith G, Schar M, Stuber M, Weiss RG. Regional Coronary Endothelial Function Is Closely Related to Local Early Coronary Atherosclerosis in Patients With Mild Coronary Artery Disease: Pilot Study. Circ Cardiovasc Imaging. 2012;5:341–348.

6. Hays AG, Stuber M, Hirsch GA, Yu J, Schär M, Weiss RG, Gerstenblith G, Kelle S. Non-Invasive Detection of Coronary Endothelial Response to Sequential Handgrip Exercise in Coronary Artery Disease Patients and Healthy Adults. PLoS ONE. 2013;8:e58047.

7. Iantorno M, Schär M, Soleimanifard S, Brown TT, Moore R, Barditch-Crovo P, Stuber M, Lai S, Gerstenblith G, Weiss RG, Hays AG. Coronary artery endothelial dysfunction is present in HIV-positive individuals without significant coronary artery disease: AIDS. 2017;31:1281–1289.

8. Hays AG, Iantorno M, Soleimanifard S, Steinberg A, Schär M, Gerstenblith G, Stuber M, Weiss RG. Coronary vasomotor responses to isometric handgrip exercise are primarily mediated by nitric oxide: a noninvasive MRI test of coronary endothelial function. Am J Physiol Heart Circ Physiol. 2015;308:H1343-1350.

9. Zhu X, Tomanek B, Sharp J. A pixel is an artifact: On the necessity of zero-filling in fourier imaging. Concepts Magn Reson Part A. 2013;42A:32–44.

10. Yerly J, Gubian D, Knebel J-F, Schenk A, Chaptinel J, Ginami G, Stuber M. A phantom study to determine the theoretical accuracy and precision of radial MRI to measure cross-sectional area differences for the application of coronary endothelial function assessment: Precision of in vitro Coronary Area Measurements. Magn Reson Med [Internet]. 2017 [cited 2017 Aug 23];Available from: http://doi.wiley.com/10.1002/mrm.26646

11. Iantorno M, Hays AG, Schär M, Krishnaswamy R, Soleimanifard S, Steinberg A, Stuber M, Gerstenblith G, Weiss RG. Simultaneous Noninvasive Assessment of Systemic and Coronary Endothelial FunctionCLINICAL PERSPECTIVE. Circ Cardiovasc Imaging. 2016;9:e003954.

12. Hays AG, Iantorno M, Schär M, Mukherjee M, Stuber M, Gerstenblith G, Weiss RG. Local coronary wall eccentricity and endothelial function are closely related in patients with atherosclerotic coronary artery disease. J Cardiovasc Magn Reson. 2017;19:51.

13. National Electrical Manufacturers Association. Determination of signal-to-noise ratio (SNR) in diagnostic magnetic resonance imaging. Rosslyn: National Electrical Manufacturers Association; 2008.

14. Noll DC, Pauly JM, Meyer CH, Nishimura DG, Macovski A. Deblurring for non-2D Fourier transform magnetic resonance imaging. Magn Reson Med. 1992;25:319–333.