Characterizing Radial Undersampling Artifacts for Cardiac Applications Dana C. Peters, 1 * Pratik Rohatgi, 2 Rene ´ M. Botnar, 1 Susan B. Yeon, 1 Kraig V. Kissinger, 1 and Warren J. Manning 1,3 The undersampled radial acquisition has been widely employed for accelerated (by a factor R  N r /N p ) cardiac imaging, but the resulting reduction in image quality has not been well charac- terized. This investigation presents a method of measuring these artifacts through synthetic undersampling of high SNR images (SNR ≥ 30). After validating the method in phantoms, the method was applied to a study of short-axis, long-axis, and coronary MRI imaging in healthy subjects. For 60 projections (60 N p ), the total artifact is 10% for short and long-axis imag- ing (R  2.1) and 15% for coronary MRI (R  3.7). For 60 N p , the SD of artifact in the region of the heart is 2% for short- and long-axis imaging (R  2.1) and 3.5% for coronary MRI (R  3.7). The artifact content is less in the region of the heart than in the periphery. The artifact is very reproducible among subjects for standard views. A study of coronary MRI at progressively fewer projections (at constant scan time) showed that right coronary MRI images were acceptable if total artifact was <6.5% of image content (N p > 120, R  2.1). Magn Reson Med 55: 396 – 403, 2006. © 2006 Wiley-Liss, Inc. Key words: radial imaging; undersampling artifact; rapid imag- ing; projection reconstruction; cardiac imaging Many investigators have demonstrated the value of under- sampled radial acquisition for accelerated imaging (1– 6). There have been efforts to measure and assess the impact of radial undersampling on image quality (6 –10). Notably, Pipe et al. observed that by Parseval’s theorem for the Fourier transform, the artifact power for undersampled imaging is proportional to the signal power that resides in the misrep- resented Fourier coefficients (7). Nevertheless, the impact of radial undersampling on image quality is still not well un- derstood, compared to the understanding for other fast im- aging methods, e.g., parallel imaging (11,12), variable rate k-space sampling schemes (13) (14 –16), half Fourier (17), echo-planar imaging (18) or simply imaging with high re- ceiver bandwidth imaging (19,20). The important question is, at what undersampling level, for each application, does the image begin to deteriorate rapidly due to artifacts, beyond the typical SNR loss with square-root of acquisition time? It is not possible to provide a general rule for the permitted radial undersampling level for all applications, since artifacts de- pend on anatomy and spatial frequency content. Yet it is not currently known for each application what level of under- sampling is acceptable. Furthermore, because the radial un- dersampling artifact is so dispersed, artifacts are often judged visually to be acceptable (12), while producing unacceptable levels of noise-like diffuse spray (1,6,21), which effectively reduces the signal-to noise-ratio (SNR). And low SNR images (e.g., delayed enhancement imaging) will permit very little undersampling, but this is due to SNR limitations and not undersampling artifact. The purpose of this study is to validate a method for measuring artifacts and to determine the aliasing signal present for many levels of undersampling for typical car- diac applications. This allows determination of the artifact signal in percentages for each application. This level of artifact can be compared to the image noise present, i.e., is the aliasing signal above or below the noise? It allows realistic comparison of the artifact due to radial undersam- pling with artifacts or noise generated by other accelera- tion techniques. Furthermore, the assessment of artifact is important for designing 3D protocols that extend slice coverage through the use of undersampling, for example, for whole-heart coronary artery imaging (22). A method is validated and then employed for character- izing artifacts of functional SSFP images and coronary MRI. An estimate of the percentage content of an image that is artifact is obtained for the standard cardiac views. The crucial influence of image noise on artifact measure- ment is carefully explored. Finally, to interpret the results, coronary MRI was performed using progressively fewer projections, but maintained scan time (and therefore main- tained SNR) through acquiring increased partitions, and the images were subjectively and objectively assessed. THEORY Isolating the Artifact of an Undersampled Image Our working definition for full sampling is N p0 = f N r , with N r the number of readout points and f the fractional field-of-view (FOV) occupied, i.e., the ratio of the pre- scribed FOV to the filled FOV (90 to 70% for typical cardiac FOVs). Although this number of projections is less than that required by the Nyquist criteria (N pNyq = fN r  / 2), the undersampling artifact for N p0 = fN r is small (less than 2%). For undersampled radial imaging, N p = N p0 /R projections are acquired, where R is the acceleration fac- tor. The acceleration factor, R, is estimated in analogy to Cartesian undersampling as R = f N r N p . [1] 1 Beth Israel Deaconess Medical Center and Harvard Medical School, Depart- ment of Medicine, Cardiovascular Division, Boston, Massachusetts, USA. 2 Department of Biomedical Engineering, University of Michigan–Ann Arbor, Ann Arbor, Michigan, USA. 3 Beth Israel Deaconess Medical Center, Department of Radiology, Boston, Massachusetts, USA. Grant sponsor: American Heart Association. *Correspondence to: D. C. Peters, Beth Israel Deaconess Medical Center East, 330 Brookline Avenue, RW 453, Boston, MA 02215, USA. Email: dcpeters@bidmc.harvard.edu Received 15 March 2005; revised 28 September 2005; accepted 12 October 2005. DOI 10.1002/mrm.20782 Published online 11 January 2006 in Wiley InterScience (www.interscience. wiley.com). Magnetic Resonance in Medicine 55:396 – 403 (2006) © 2006 Wiley-Liss, Inc. 396