IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 26, NO. 11, NOVEMBER 2007 1437 Accuracy of -Space Related Parameters in MRI: Simulations and Phantom Measurements Jimmy Lätt*, Markus Nilsson, Carin Malmborg, Hannah Rosquist, Ronnie Wirestam, Freddy Ståhlberg, Daniel Topgaard, and Sara Brockstedt Abstract—The accuracy of -space measurements was evaluated at a 3.0-T clinical magnetic resonance imaging (MRI) scanner, as compared with a 4.7-T nuclear magnetic resonance (NMR) spectrometer. Measurements were performed using a stimu- lated-echo pulse-sequence on -decane as well as on polyethylene glycol (PEG) mixed with different concentrations of water, in order to obtain bi-exponential signal decay curves. The diffusion coefficients as well as the modelled diffusional kurtosis were obtained from the signal decay curve, while the full-width at half-maximum (FWHM) and the diffusional kurtosis were obtained from the displacement distribution. Simulations of restricted diffusion, under conditions similar to those obtainable with a clinical MRI scanner, were carried out assuming various degrees of violation of the short gradient pulse (SGP) condition and of the long diffusion time limit. The results indicated that an MRI system can not be used for quantification of structural sizes less than about 10 m by means of FWHM since the parameter underestimates the confinements due to violation of the SGP condition. However, FWHM can still be used as an important contrast parameter. The obtained kurtosis values were lower than expected from theory and the results showed that care must be taken when interpreting a kurtosis estimate deviating from zero. Index Terms—Diffusion, displacement distribution, kurtosis, magnetic resonance imaging (MRI), -space. I. INTRODUCTION B Y THE use of a pulsed gradient spin-echo (PGSE) pulse sequence [1] it is possible to use the -space methodology for assessment of the dynamic displacement of molecules that occurs due to their self-diffusion [2]. This approach has been employed in several in vitro and ex vivo studies performed with nuclear magnetic resonance (NMR) spectrometers to gain Manuscript received June 1, 2007; revised August 15, 2007. This work was supported in part by the Swedish Research Council under Grant 13514, in part by the Swedish Cancer Society under Grant CAN 2006/1272, in part by the Swedish Society of Medicine, in part by the Lund University Hospital Donation Funds, and in part by the Knut and Alice Wallenberg Foundation (KAW 1998. 0182). Asterisk indicates corresponding author. *J. Lätt is with the Department of Medical Radiation Physics, Clinical Sci- ences, Lund University, SE-221 85 Lund, Sweden (e-mail: jimmy.latt@med.lu. se). M. Nilsson, H. Rosquist and R. Wirestam are with the Department of Med- ical Radiation Physics, Clinical Sciences, Lund University, SE-221 85 Lund, Sweden. C. Malmborg and D. Topgaard are with the division of Physical Chemistry 1, Centre for Chemistry and Chemical Engineering, Lund University, SE-22100 Lund, Sweden. F. Ståhlberg and S. Brockstedt are with the Department of Medical Radiation Physics, Clinical Sciences, Lund University, SE-221 85 Lund, Sweden and with the Department of Diagnostic Radiology, Clinical Sciences, Lund University, SE-221 85 Lund, Sweden. Digital Object Identifier 10.1109/TMI.2007.907278 knowledge about the origin of the diffusion signal in biological materials and to improve the differentiation between healthy and pathologic tissue [3]–[7]. During the last decade, the -space concept has been adopted from the NMR environment and implemented in the clinical setting of magnetic resonance imaging (MRI) [8]–[11]. Attempts have been made to visualize and determine cell sizes in vivo [12], although the possibility to correctly quantify confinement sizes with an MRI system has not been sufficiently clarified. In NMR spectrometry, the -space methodology is well established, but the fundamental differences between an NMR spectrometer and a clinical MRI scanner, such as the gradient system performance, the magnetic field strength and the SNR, are likely to hamper the accuracy of -space analyses in the MRI environment. In order to resolve small structures which restrict the self-diffusion a large time integral of the diffusion encoding gradients is required, but the duration of the diffusion encoding gradients must at the same time be kept short compared with the time required for the molecules to diffuse across the whole confinement, i.e., , where is the size of the confinement and is the diffusion coefficient. This requirement is known as the short gradient pulse (SGP) condition, and a violation will lead to an underestimation of the confinement [13]–[16]. In MRI, this requirement is commonly violated in order to achieve a sufficiently high -space resolution, since the gradient system amplitudes are typically two orders of magnitude lower on MRI scanners than on NMR spectrometers (about 50 mT/m compared to about 10 T/m). Furthermore, the use of a long in MRI requires a long echo time (TE), resulting in a lowered SNR due to T2 relaxation. Extensive displacement distribution measurements and sim- ulations have been carried out under conditions achievable with NMR spectrometers [16]–[20], but few studies have evaluated the effects of the limitations associated with clinical scanners. A related approach for obtaining structural information from the displacement distribution is to analyse the corresponding diffraction pattern in the signal domain [21], and studies have been performed with the primary aim of evaluating this possi- bility with an NMR system [22], [23]. Recently, a phantom ex- periment and an ex vivo study of fixated rat brain, designed to resolve confinements from diffraction patterns, were conducted by Weng et al. on a clinical scanner equipped with an insert gra- dient coil [24]. However, to the best of our knowledge a diffrac- tion pattern has not yet been measured in vivo and it has been speculated that the complexity of the tissue, as well as an ex- pected distribution of confinement sizes, would cancel out the characteristics of such a pattern [23], [25]. In the clinical set- ting, Assaf et al. used -space imaging in an in vivo study of 0278-0062/$25.00 © 2007 IEEE