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Logo of nihpaAbout Author manuscriptsSubmit a manuscriptHHS Public Access; Author Manuscript; Accepted for publication in peer reviewed journal;
J Magn Reson Imaging. Author manuscript; available in PMC 2009 April 16.
Published in final edited form as:
PMCID: PMC2669671

Age-Related Non-Gaussian Diffusion Patterns in the Prefrontal Brain



To characterize age-related MR diffusion patterns of the prefrontal brain cortex microstructure using a new method for investigating the non-Gaussian behavior of water diffusion called diffusional kurtosis imaging (DKI).

Materials and Methods

Measures of mean diffusivity (MD), fractional anisotropy (FA) and mean kurtosis (MK) were compared in the prefrontal brain cortex of 24 healthy volunteers (adolescents, young adults, and elderly) ranging from age 13 to 85 years. A Mann-Whitney test was used to compare subject groups with respect to the diffusion measures, and linear regression was used to characterize the change in each diffusion measure as a function of age.


We found significant age-related changes in the elderly adult group, with increase of MD and decrease of FA.


The current study demonstrates distinct mean kurtosis patterns for different age-ranges, with significant age-related correlation for mean kurtosis (MK) and MK peak position, showing that diffusional kurtosis is able to characterize and measure age-related diffusion changes for both grey and white matter, in the developing and aging brain.

Keywords: diffusion, kurtosis, MRI, DKI, non-Gaussian, brain

The brain undergoes structural and morphological changes throughout the various stages of development and aging (1-3). The prefrontal brain shows significant volume changes (4) with increases in white matter and thinning of grey matter during adolescence and early adulthood, and white and grey matter loss with aging. All of these structural changes are reported to be associated with cognitive changes (2,5,6).

Diffusion tensor imaging (DTI) has been used to demonstrate age-related microstructural changes in the prefrontal brain. During brain development, water diffusivity decreases and anisotropy increases and, during aging, water diffusivity increases and anisotropy decreases (7-14). These prior studies have mainly focused on white matter changes because DTI is sensitive to tissue anisotropy. It has long been appreciated that diffusion-weighted magnetic resonance imaging is capable of yielding considerably more information than that contained in the diffusion metrics derived from DTI, namely the mean diffusivity (MD) and the fractional anisotropy (FA). In particular, the degree of diffusional non-Gaussianity is of interest because it is believed to arise from diffusion barriers, such as cell membranes and organelles, and water compartments (e.g., extracellular and intracellular). The mean kurtosis (MK), a principal metric of the diffusional non-Gaussianity obtained from a recently developed method called diffusional kurtosis imaging (DKI) (15-17), can be regarded as an index of tissue microstructural complexity. The MK differs from indices of diffusional anisotropy conventionally measured with DTI in that it does not require the microstructure of the tissue to be spatially oriented and hence is equally applicable to both grey and white matter. In the context of this work, the term microstructure refers to tissue structures with length scales comparable to or larger than the water molecule diffusion length for the experiment (typically 5 to 30 microns) but smaller than the voxel size. These structures could be, for example, cell membranes, axons sheaths, myelin layers, and so on, that act as barriers to the free diffusion of water within each voxel. The term complexity refers to the number, density, orientation, and degree of organization of these microstructures.

The goal of the present study is to characterize the age-related non-Gaussian diffusion patterns of brain tissue in the prefrontal brain region, including grey and white matter. A primary motivation is that the MK contributes additional information regarding water diffusion beyond that obtainable with conventional DTI. Such additional information can potentially provide a better characterization of age-related changes in the brain’s microstructural complexity, which in turn may be helpful in interpreting and differentiating alterations associated with neurodegenerative diseases. Here, we report distinct age-related MK patterns for normal subjects.



Twenty-four healthy volunteers were recruited from the New York University (NYU) Medical Center local community, NYU Alzheimer’s Disease Center, and the NYU Child Study Center and categorized into three groups (n = 8 for each group): adolescent (age range = 12–17 yr; mean = 15), young adult (age range = 26–47 yr; mean = 35), and elderly adult (age range = 63–85 yr; mean = 71). The subjects recruited from the NYU Alzheimer’s Disease Center and Child Center were screened for neurological or neuropsychological disorders. All subjects, including the young control group, had no neurological complaint, history of cerebrovascular disease, history of past head injury with loss of consciousness, epilepsy, migraine, hypertension, diabetes, and other types of disorders potentially affecting the central nervous system. The protocol was approved by the School of Medicine’s Institutional Review Board. Written informed consent for all subjects was obtained before study.

MR Imaging

Experiments were conducted on a 3 Tesla (T) Trio system (Siemens Medical Solutions, Erlangen, Germany). The DKI pulse sequence and processing algorithm have been described previously (16,17). Briefly, this technique uses a diffusion-sensitizing pulse sequence and acquires three or more b-values (in contrast to two b-values in conventional DTI) to evaluate the nonlinearity of the logarithm of the signal intensity, ln(S), as a function of diffusion weighting, b (DTI, in contrast, assumes ln(S) to be a linear function of b). More precisely, the signal intensity data is fit to the functional form:

equation M1

where S0 is the signal intensity for b = 0, D is the apparent diffusion coefficient, and K is the apparent kurtosis coefficient. In the special case of free diffusion (such as in a water bottle), the apparent kurtosis coefficient will be zero and Eq. [1] reduces to the DTI model equation. Multiple gradient encoding directions can be used to obtain direction-dependent apparent diffusion coefficient and apparent kurtosis coefficient values, from which one can calculate the diffusion tensor and the diffusional kurtosis tensor (16,17). From the diffusion tensor, one may derive several standard diffusion metrics including the MD and the FA. From the diffusional kurtosis tensor, one may obtain additional diffusion metrics, including the mean kurtosis (MK), which corresponds to the apparent kurtosis coefficient averaged over all directions just as the mean diffusivity corresponds to the diffusion coefficient averaged over all directions. In this study, we will focus on the comparison of the three subject groups using two parameters, the MD and FA, associated with the diffusion tensor and one parameter, MK, associated with the diffusional kurtosis tensor. The DKI experiments were performed using a twice-refocused-spin-echo (TRSE) diffusion sequence (18) with 30 different diffusion encoding directions using an optimized sampling strategy (19,20). For each direction, six b-values (b = 0, 500, 1000, 1500, 2000, 2500 s/mm2) were used. Other imaging parameters were: TR = 2300 ms, TE = 108 ms, FOV = 256 × 256 mm2, matrix = 128 ×128, parallel imaging factor of 2 with 24 k-lines used as references, number of averages = two, 15 oblique axial slices to cover the frontal regions and temporal regions, slice thickness = 2 mm, voxel size 2 × 2 × 2 mm3. The total scan duration for the DKI sequence was 11 min and 57 s. For anatomical reference, a three-dimensional (3D) T1-weighted image was also acquired using a magnetization prepared rapid acquisition of gradient echoes (MPRAGE) sequence with the following parameters: TR = 2100 ms, TI = 1100 ms, shot spacing = 8.5 ms, TE = 3.9 ms, FOV = 256 × 256 mm2, matrix = 256 × 256, 75% rectangular FOV, parallel imaging factor of 2 with 24 k-lines used as references, 160 slices, slice thickness 1 mm, voxel size 1 × 1 × 1 mm3, scan duration 3 min and 47 s.

Data Processing

Three-dimensional motion correction was performed on the diffusion images using SPM (Statistical Parametric Mapping, University College London, UK) followed by spatial smoothing using a Gaussian filter with full-width-half-maximum of 2.5 mm. For each diffusion encoding direction, the signal intensities for the diffusion-weighted data were fitted to Eq. [1] to determine apparent diffusion coefficient and apparent kurtosis coefficient for that particular b direction. The apparent diffusion coefficient values from all directions were used to calculate the diffusion tensor, from which the MD and FA were obtained. The apparent kurtosis coefficient values from all 30 directions were averaged to determine the MK, as our previous study showed that this gives nearly identical results as the more rigorous approach of deriving the MK from the diffusional kurtosis tensor while being more computationally efficient (17). We emphasize that all 6 b-values and 30 directions were used in the calculation for all diffusion measures.

A prefrontal brain region of interest (ROI) (Fig. 1) was manually drawn on five consecutive slices, at the same anatomical level in all subjects, by the same reader, an experienced neuropathologist (MFF), blinded to subject demographics. All ROIs were defined on axial DKI images guided by the anatomical MPRAGE image, using ImageJ software ( (21). The prefrontal ROI in each axial slice extended from the most anterior point containing brain tissue to the dorsal border of the genu of the corpus callosum, and contained cerebral spinal fluid (CSF), grey matter, and white matter. The line at the level of the dorsal border of the genu of the corpus callosum was drawn perpendicular to the midline of the brain separating both hemispheres.

Figure 1
Prefrontal ROIs superimposed on each of the five DKI axial slices. Note that the ROI extended from the most anterior point containing brain tissue to the dorsal border of the genu of the corpus callosum (gCC), and included gray matter, white matter and ...

Statistical Analysis

Using ImageJ software, histograms were obtained for each subject using the ROI described above, normalized against the total number of voxels for each subject, so that the sum of all values within one histogram equals unity. The value intervals (bins) for MD, FA, and MK ranged from 0 to 3 μm2/ms, 0 to 1 (dimensionless) and 0 to 2 (dimensionless) with bin sizes of 0.047 μm2/ms, 0.016 and 0.031, respectively.

To compare subject groups, features of the histogram data were extracted in the form of one-dimensional variables (i.e., summary statistics). The group means and standard deviations for the diffusion metrics, MD, FA, and MK, were calculated over all voxels contained within the prefrontal ROI. A Mann-Whitney test was then applied to compare subject groups pairwise with respect to each of the three diffusion metric means (with Bonferroni correction). Additionally, the peak position for both MK ranges corresponding to grey (0.5–1) and white matter (1.031–2) tissue type were identified by using the weighted average position of the voxels contained on the upper 40% of the peak value. To assess the extent to which age-related changes in a given measure are different among adolescents, young adults and elderly subjects, the subjects were divided into three age domains depending on whether they were below 18 years of age, between 18 and 47 years of age, or over 47 years old at the time of image acquisition. The decision to partition patient ages at 18 and 47 years was mainly dictated by the ages of the subjects in the sample. Piecewise linear regression with knots (i.e., changes in slope) at ages 18 and 47 was used to characterize the change in each measure as a function of age. Specifically, the model for each measure assumed that age-related changes were linear within each of the three age domains with the lines in different domains allowed to have different slopes subject to the constraint that the lines intersect at the knots. The constraint is needed for continuity: without it the model would predict, for example, that a subject experiences an abrupt instantaneous change in the measure at the age of 18. The estimate of the slope parameter for the line characterizing age-related changes in a given measure within a specific age domain is an estimate of the mean rate of change in the measure per annum among subjects in that domain. Therefore, the estimated mean rate of change in each variable is reported as the estimate ± the standard error of the estimate of the relevant slope parameter in the piecewise linear regression model for that variable. All statistical computations were carried out using SAS version 9.0 (SAS Institute, Cary, NC). All reported P values (two-sided) are declared statistically significant when less than 0.05.


Because the MK is a comparatively new diffusion metric, its reproducibility as measured by DKI should be established. We therefore assessed the reproducibility of the MK measurement using data from three independently acquired data sets from three subjects. Minimum variance quadratic unbiased estimation of variance components was used to evaluate reproducibility in terms of the intraclass correlation coefficient, and the within-subject coefficient variation, that is, the within-subject standard deviation, expressed as a percentage of the mean. We observed a 5% within-subject coefficient of variation with an intraclass correlation coefficient of 0.88, which is more than adequate for this study. Shown in Figure 2 are the histograms from the prefrontal brain region for MD, FA, and MK for the three age groups studied. Because the DKI data fitting gives the FA and MD, as well as the MK, all the diffusion data were derived from a single dataset.

Figure 2
A–C: Histograms from the prefrontal brain for FA (A), MD (B), and MK (C) for the adolescent (dashed lines), Adult (dotted lines) and Elderly (solid lines) age groups. D–H: Scatter plot of mean FA (D), MD (E), MK (F), MK-Grey (G), and MK-White ...

The FA histograms (Fig. 2A) showed a significant mean FA reduction for the elderly adult group when compared with the young adult group (P < 0.002) and the adolescent group (P < 0.003), but no difference between the adolescent and young adult group (P = 0.703) was detected. Figure 2D shows that there was a significant shift in the mean FA rate of change between the adolescent and young adult groups (P < 0.05) and an additional significant shift between the young adult and elderly age groups (P < 0.05). The model showed that mean FA increased until age 18, decreased until age 47, and decreased at a greater rate after 47 (Table 1).

Table 1
Annual Rate of Change (×10−3) of Diffusion Measures by Aging Range

The MD histograms (Fig. 2B) were qualitatively similar for all three groups. The elderly adult group demonstrated a wider distribution of values, with increased MD when compared with young adult (P < 0.002) and adolescent (P < 0.001) groups. There was a significant shift in the mean MD rate of change between the young and elderly adult group (P < 0.002) but no significant shift between the adolescent and young adult group (P = 0.917). The model showed that mean MD increased at a relatively slow rate until age 47, after which it increased more rapidly (Table 1; Fig. 2E).

The MK histograms (Fig. 2C) had a more complex profile showing distinct ranges/peaks for CSF (~0.45), grey matter (~0.75), and white matter (~1.25). The elderly adult group was the only group to show a CSF peak, representing an increase of the number of voxels with CSF values, which reflect the degree of brain atrophy in this group. Additionally, the MK data demonstrated several interesting features: (i) the transition from the adolescent group to the young adult group showed a shift to a higher kurtosis value for both grey and white matter peaks, consistent with an overall increase of the degree of microstructural complexity in both tissue types; (ii) the transition from the young adult group to the elderly adult group showed a shift to lower kurtosis values for the white matter peak, suggestive of the white matter degradation known to occur with aging. The white matter kurtosis value range for the elderly adult group and the adolescent group were similar, indicating comparable microstructural complexity.

MK was significantly higher for the young adult group compared with both the adolescent group (P < 0.009) and the elderly adult group (P < 0.02). There was a significant shift in the mean MK rate of change between the adolescent and young adult groups (P < 0.012), and an additional significant shift between the young adult and elderly age groups (P < 0.016). The model showed that mean MK increased rapidly each year of age until 18, then increased slowly until age 47, followed by a decrease (Table 1; Fig. 2F).

MK grey matter peak location showed a significant shift in the rate of change between the young adult and elderly age group (P < 0.001), but no significant evidence of an additional shift between the adolescent and young adult groups (P = 0.134). The model showed that MK grey matter peak location increased rapidly until age 18, then increased slowly between the ages of 18 and 47, and even more slowly after that (Table 1; Fig. 2G).

MK white matter peak location showed a significant shift in the rate of age-related change between the adolescent and young adult groups (P < 0.003), but no significant shift between the young adult and elderly age groups (P = 0.831). The model showed that MK white matter peak location increased rapidly until age 18, and then decreased steadily (Table 1; Fig. 2H).


Diffusion-weighted MRI provides a powerful tool for probing tissue microstructure on the micrometer scale and is, therefore, a potential candidate for developing a noninvasive neuroimaging measure of tissue complexity. Although DTI and its associated indices of FA and MD are the most common diffusion measures used to date, it is well known that diffusion-weighted imaging is capable, in principle, of yielding considerably more information than that contained in DTI. However, because DTI is incapable of measuring non-Gaussian diffusion, DKI is potentially a more sensitive and specific indicator of the diffusional heterogeneity and, hence, tissue microstructure.

The data presented herein support significant age-associated micro-structural changes within the prefrontal cortex and reveal, for the first time, age-related changes in MK. During the period of adolescence the FA tended to increase rapidly, possibly reflecting the ongoing process of myelination and white matter organization still present during this age range, which is in agreement with postmortem studies (22). Additionally, our data showed a significant age-related FA decrease and MD increase with aging. For the elderly adult group, the FA histogram (Fig. 2A) clearly showed an increase of the fraction of voxels for the FA range of 0–0.2, reflective of increased cerebrospinal fluid consequent to increased brain atrophy. Moreover, the mean FA for the range of 0.2 and above showed a shift to lower FA in the elderly group and an associated increase in MD, which likely reflects the white matter degeneration demonstrated by postmortem studies (23) of subjects in this age group. Our FA and MD results are in general agreement with several previous DTI studies (7,9,12-14). However, a direct comparison to the present study would be difficult due to methodological differences regarding population sample, brain regions of interest and the analytical approach used that varied from voxel-based analysis, region of interest-based or histogram analysis.

The non-Gaussian diffusion patterns of brain tissue microstructure in the prefrontal brain region, as measured by DKI, showed several interesting features that are consistent with what is known from previous histopathological studies (1-3,22). First, MK increased during the transition from adolescence to adulthood, consistent with continuing myelination and an overall increase of the microstructural complexity in this brain region. Second, MK decreased with aging, which is probably associated with the degenerative changes and neuronal shrinkage. Furthermore, the analysis of the peak position for both MK grey and white matter tissue types (Fig. 2G,H) illustrated patterns consistent with known histological patterns of brain maturation (6). The grey matter MK peak position showed a shift to higher values with increasing age, which is consistent with the known increase of the cortical cell-packing density (6). The MK white matter peak location showed a rapid shift to higher values up until age 18, likely reflecting the intense and continuous myelination and fiber organization that occurs at this time, with a shift to lower values with aging, probably related to the decrease of myelin density and myelinated fibers (23). Visual differences in grey-to-white matter voxel fraction ratio were also evident in the MK histograms. The adolescent group had the highest ratio followed by the younger adult group followed by the elderly adult group. This order is in agreement with postmortem studies (1,3,23).

Although structural MRI studies have shown age-related volume changes in grey matter, only few reports have shown age-related MD grey matter patterns, with these reporting mostly global changes or changes in subcortical grey matter (24,25) and some reporting no significant changes with aging (26). However, to our knowledge, no diffusion patterns representing age-related changes in the prefrontal cortical grey matter structural integrity have been previously reported. The non-Gaussian diffusion patterns of brain tissue microstructure in the prefrontal brain reported in this study demonstrate specific changes in cortical grey matter consistent with known age-related morphological changes for specific age ranges. Because age-related changes in prefrontal cortex are associated with cognitive changes (4) and changes in patterns of brain activation (27), our ability to characterize and measure age-related grey matter diffusion changes is potentially of clinical interest.

Since age-related DTI changes have been reported to be more pronounced in the frontal lobe, particularly in the prefrontal region, we decided to initially focus on this region. We chose to use an ROI encompassing a large amount of the frontal lobe instead of smaller, more regionally specific ROIs to demonstrate that MK can segment, measure, and assess both grey and white matter from a large ROI containing both tissue types without the need to draw individual tissue-type (grey and white matter) specific ROIs, which highlights a particular strength of this technique. Another advantage of this technique is that unlike other diffusion parameters (e.g., FA and MD), MK is relatively insensitive to partial volume effects (28). A direct advantage of this is that the measurement is less sensitive to the subjectivity (size and location) of the definition of the ROI. Hence, with MK it is possible to obtain the same sensitivity to diffusional changes in the brain using large ROIs.

There are some limitations to this study, mainly the modest number of subjects studied and the lack of full brain coverage. However, even though the number of subjects was small, it still allowed the demonstration of statistically significant age-related diffusion changes. Additionally, in future longitudinal studies with whole brain coverage, we will seek to investigate additional brain regions. Nevertheless, we believe it is important to report these preliminary results because this is the first study demonstrating the application of diffusional kurtosis measurements in assessing age-related changes and highlighting one advantage using this technique, namely the quantification of microstructural complexity in both grey and white matter.

The current study demonstrates distinct MK patterns for different age ranges, with significant age-related correlation for MK and MK peak position, indicating that diffusion kurtosis is able to characterize and measure age-related diffusion changes for both grey and white matter, in the developing and aging brain. In summary, our results suggest that microstructural complexity in the prefrontal cortex, as measured by MK, increases sharply during adolescence, continues to increase throughout adulthood, albeit more slowly, while eventually decreasing with aging.


The authors acknowledge the helpful discussions with Dr. Ramani and the technical support of Kamila Szulc and Vitria Adisetiyo. J.A.H. was funded by Werner Dannheisser Trust, Litwin Fund for Alzheimer’s Research, Institute for the Study of Aging, and the NIH. S.H.F. also received funding from the NIH.

Contract grant sponsor: Werner Dannheisser Trust; Contract grant sponsor: Litwin Fund for Alzheimer’s Research; Contract grant sponsor: Institute for the Study of Aging; Contract grant sponsor: NIH; Contract grant number: 1R01AG027852; Contract grant number: P30 AG08051.


Published online in Wiley InterScience (


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