The diffusion of water through a biologic tissue can be regarded as a random process. Hence, the chance of a particular water molecule diffusing from one location to another in a given period of time is governed by a probability distribution. In the simplest models, this distribution has a Gaussian form with its width (i.e., standard deviation) proportional to the diffusion coefficient. However, for time intervals on the order of tens of milliseconds, the complex structure of most tissues, consisting of various types of cells and their membranes, can cause the diffusion displacement probability distribution to deviate substantially from a Gaussian form (1). This deviation from Gaussian behavior can be quantified using a convenient dimensionless metric called the excess kurtosis. Since the deviation from Gaussian behavior is governed by the complexity of the tissue within which the water is diffusing, this excess diffusional kurtosis can be regarded as a measure of a tissue's degree of structure.

In this article, we describe a method, which has previously been presented in an abbreviated form (2), for estimating the excess kurtosis of water diffusion in vivo by means of pulsed-field-gradient MRI. We term this method diffusional kurtosis imaging (DKI). The method is based on the same type of pulse sequences employed for conventional diffusion-weighted imaging (DWI), but the required *b* values are somewhat larger than those usually used to measure diffusion coefficients. In the brain, *b* values of about 2000 s/mm^{2} are sufficient, which can now be readily obtained on modern clinical MRI systems. Thus, DKI provides a practical clinical technique for quantifying non-Gaussian water diffusion and thereby for probing the microscopic structure of biologic tissues.

DKI has a close relationship to *q*-space imaging techniques (3), and *q*-space imaging methods have indeed recently been employed to estimate diffusional kurtosis (4, 5). The principal difference between *q*-space imaging and the approach presented here is that *q*-space imaging seeks to estimate the full diffusion displacement probability distribution rather than just the kurtosis. As a consequence, *q*-space imaging is more demanding in terms of imaging time and gradient strengths. A key idea of the work presented here is that the excess diffusional kurtosis may be approximately determined from just the first three terms of an expansion of the logarithm of the NMR signal intensity in powers of *b*. It is for this reason that measuring the diffusional kurtosis requires only modest increases in *b* values beyond those typically employed for DWI.

In addition to presenting the underlying theory of DKI, we also show parametric maps of excess diffusional kurtosis in the human brain and in a phantom. In particular, we find sharp differences between the diffusional kurtosis in white and gray matter, confirming the preliminary results reported by Jensen and Helpern (2). We believe that DKI is potentially of value for the assessment of neurologic diseases, such as multiple sclerosis and epilepsy, with associated white matter abnormalities. Additionally, DKI may be useful for investigating abnormalities in tissues with isotropic structure, such as gray matter, where techniques like diffusion tensor imaging (DTI) are less applicable.