FULL PAPER A Simple and Robust Test Object for the Assessment of Isotropic Diffusion Kurtosis Jonathan Phillips 1,2,3 * and Geoffrey D Charles-Edwards 3,4 Purpose: To create a robust test object for the assessment of isotropic diffusion kurtosis and to investigate the relationships between barrier concentration and kurtosis and diffusion coefficients. Theory and Methods: Diffusion kurtosis imaging is an exten- sion of conventional diffusion-weighted magnetic resonance imaging which provides a means of assessing the degree to which diffusion processes of spin-bearing particles are non- Gaussian, a property that is quantified by the kurtosis. We present a set of test objects, each possessing a different con- centration of colloidal dispersion, allowing barrier concentra- tion of the dispersed colloidal particles to be related to the kurtosis of the water diffusion. Diffusion coefficients from the kurtosis model and the monoexponential model are compared. Results: A relationship between barrier concentration and kur- tosis is found, demonstrating that the diffusion process becomes less Gaussian as the barrier concentration is increased. Differences in the two estimates for the diffusion coefficients are examined. The test object is robust, displaying long-term reproducibility of results. Conclusions: Colloidal dispersions provide a suitable and sta- ble test object for the assessment and reproducibility measure- ments of kurtosis. Magn Reson Med 73:1844–1851, 2015. V C 2014 Wiley Periodicals, Inc. Key words: kurtosis; diffusion; magnetic resonance imaging INTRODUCTION Diffusion-weighted magnetic resonance imaging (MRI) is a technique for sensitizing the MRI signal to the local diffusion properties of water. It is widely used in clinical imaging, particularly in the areas of neurology and oncology, to generate quantitative information such as the apparent diffusion coefficient (ADC) or information about diffusion anisotropy through calculation of the diffusion tensor. Typically, such techniques assume the diffusion process to be Gaussian. However, due to the barriers present, such as cell membranes and organelles, the diffusion propagator will deviate from a Gaussian form since the presence of obstacles creates strong corre- lations in the diffusive motion. Typically the ADC from the Gaussian model is an underestimate of the true value of the diffusion coefficient (1–4). However, in studies investigating the non-Gaussianity, the ADC is not com- monly calculated via the non-Gaussian model, e.g., (5); rather the ADC is calculated assuming Gaussian diffu- sion. The non-Gaussianity, quantified by the kurtosis, may be probed by acquiring at least three diffusion- weightings (quantified by the b-value) typically with a maximum b-value of at least about 1500 s mm 22 . This forms the basis of the rapidly growing field of diffusion kurtosis imaging (DKI). Although non-Gaussian diffusion has been observed in nonimaging nuclear magnetic reso- nance (NMR) investigations at least since the work of Tanner and Stejskal in 1968 (6), the suggestion of extracting the kurtosis from the characteristic signal attenuation in diffusion-weighted MRI was first sug- gested by Jensen et al. in 2005 (7) and the first applica- tion of DKI to human tissue, specifically neural imaging, soon followed (8). Since then, DKI has been applied in the brain: see, e.g., the review (9), used to characterize age-related MR diffusion patterns of the prefrontal brain cortex microstrucure (10), head and neck squamous cell carcinoma (4), grading the cerebral gliomas (11–13), diag- nosis of Parkinson’s disease (14), multiple sclerosis (15,16), mild cognetive impairment and Alzheimer’s dis- ease (17,18), traumatic brain injury (19), cerebral infarc- tion (20) as well as neural tissue characterization in rodents (21–25). Typical kurtosis values include: 0.57 in the healthy prostate (26), 0.41 in gray matter and 0.70 in white matter (3). DKI has also been shown to provide additional information in white matter microstructure and upper limb motor control (27). DKI is not restricted to the assessment of water diffusion: for 3 He diffusion in the lung, the kurtosis was found to be 0.34 in healthy bronchioles and 0.21 in unhealthy bronchioles (28). In Ref. 29 white matter fascicles were modeled as an array of thick-walled tubes, arranged periodically in a lattice and immersed in an outer medium. ADCs of water paral- lel and perpendicular to a pack of mylelinated axons were predicted. The low ADC in the myelin acts as a barrier for the axonal fluid and mainly the extra-axonal fluid determined the measured ADC which was found to decrease as the myelin sheath radius increases. In Ref. 30, the authors use diffusion-weighted MRI to assess the anisotropy of water diffusion in aqueous suspensions of colloidal platelets. Even though the authors do not com- ment on it, the kurtosis is clearly different when the gra- dient field is applied in different directions in the 1 Institute of Life Science, College of Medicine, Swansea University, Singleton Park, Swansea, UK. 2 Medical Engineering and Physics, King’s College London, Faraday Building, 124–126 Denmark Hill, London, UK. 3 Medical Physics, St. Thomas’ Hospital, Westminster Bridge Road, London, UK. 4 Division of Imaging Sciences and Biomedical Engineering, King’s College London, London, UK. Grant sponsor: Department of Health (via the National Institute for Health Research [NIHR] comprehensive Biomedical Research Centre award to Guy’s & St Thomas’ NHS Foundation Trust in partnership with King’s Col- lege London and King’s College Hospital NHS Foundation Trust). *Correspondence to: Jonathan Phillips, Ph.D., Institute of Life Science (Building 2), College of Medicine, Swansea University, Swansea, Singleton Park, United Kingdom. E-mail: J.W.Phillips@swansea.ac.uk Correction added after online publication 25 June 2014. The Abstract style format was updated due to a publisher’s error. Correction added after online publication 28 July 2014. A duplicate “Theory and Methods” head- ing was removed from the Abstract due to a publisher’s error. Received 28 January 2014; revised 28 April 2014; accepted 15 May 2014 DOI 10.1002/mrm.25311 Published online 10 June 2014 in Wiley Online Library (wileyonlinelibrary. com). Magnetic Resonance in Medicine 73:1844–1851 (2015) V C 2014 Wiley Periodicals, Inc. 1844