Effect of gradient pulse duration on MRI estimation of the diffusional kurtosis for a two-compartment exchange model

Diffusional kurtosis time dependence and the water exchange rate for the multi-compartment Kärger model

PURPOSE

To demonstrate an analytic formula giving the time dependence of the diffusional kurtosis for the Kärger model (KM) with an arbitrary number of exchanging compartments and its application in estimating the mean KM water exchange rate.

THEORY AND METHODS

The general formula for the kurtosis is derived from a power series solution for the multi-compartment KM. A lower bound on the exchange rate is established from the observation that the kurtosis is always a logarithmically convex function of time. Both the kurtosis time dependence and the lower bound are illustrated with numerical calculations. The lower bound is also applied to previously published data for the time dependence of the kurtosis in both brain and tumors.

RESULTS

The kurtosis for the multi-compartment KM is given by a sum in which each term is associated with an eigenvector of the exchange rate matrix. The lower bound is determined from the most negative value for the logarithmic derivative of the kurtosis with respect to time. In the cerebral cortex, the lower bound is found to vary from 15 to 76 s-1 , depending on the experimental details, while for the tumors considered, it varies from 2 to 4 s-1 .

CONCLUSION

The time dependence of the kurtosis for the multi-compartment KM has a simple analytic solution that allows a lower bound for the mean KM water exchange rate to be determined directly from experiment. This may be useful in tissues with complex microstructure that is difficult to model explicitly.

Evaluation of cellular water exchange in a mouse glioma model using dynamic contrast-enhanced MRI with two flip angles

This manuscript aims to evaluate the robustness and significance of the water efflux rate constant (k_io) parameter estimated using the two flip-angle Dynamic Contrast-Enhanced (DCE) MRI approach with a murine glioblastoma model at 7 T. The repeatability of contrast kinetic parameters and k_io measurement was assessed by a test-retest experiment (n = 7). The association of k_io with cellular metabolism was investigated through DCE-MRI and FDG-PET experiments (n = 7). Tumor response to a combination therapy of bevacizumab and fluorouracil (5FU) monitored by contrast kinetic parameters and k_io (n = 10). Test-retest experiments demonstrated compartmental volume fractions (v_e and v_p) remained consistent between scans while the vascular functional measures (F_p and PS) and k_io showed noticeable changes, most likely due to physiological changes of the tumor. The standardized uptake value (SUV) of tumors has a linear correlation with k_io (R² = 0.547), a positive correlation with F_p (R² = 0.504), and weak correlations with v_e (R² = 0.150), v_p (R² = 0.077), PS (R² = 0.117), K^trans (R² = 0.088) and whole tumor volume (R² = 0.174). In the treatment study, the k_io of the treated group was significantly lower than the control group one day after bevacizumab treatment and decreased significantly after 5FU treatment compared to the baseline. This study results support the feasibility of measuring k_io using the two flip-angle DCE-MRI approach in cancer imaging.

Time dependence in diffusion MRI predicts tissue outcome in ischemic stroke patients

Purpose:

Reperfusion therapy enables effective treatment of ischemic stroke presenting within 4–6 hours. However, tissue progression from ischemia to infarction is variable, and some patients benefit from treatment up until 24 hours. Improved imaging techniques are needed to identify these patients. Here, it was hypothesized that time dependence in diffusion MRI may predict tissue outcome in ischemic stroke.

Methods:

Diffusion MRI data were acquired with multiple diffusion times in five non-reperfused patients at 2, 9, and 100 days after stroke onset. Maps of “rate of kurtosis change” (k), mean kurtosis, ADC, and fractional anisotropy were derived. The ADC maps defined lesions, normal-appearing tissue, and the lesion tissue that would either be infarcted or remain viable by day 100. Diffusion parameters were compared (1) between lesions and normal-appearing tissue, and (2) between lesion tissue that would be infarcted or remain viable.

Results:

Positive values of k were observed within stroke lesions on day 2 (P = .001) and on day 9 (P = .023), indicating diffusional exchange. On day 100, high ADC values indicated infarction of 50 ± 20% of the lesion volumes. Tissue infarction was predicted by high k values both on day 2 (P = .026) and on day 9 (P = .046), by low mean kurtosis values on day 2 (P = .043), and by low fractional anisotropy values on day 9 (P = .029), but not by low ADC values.

Conclusions:

Diffusion time dependence predicted tissue outcome in ischemic stroke more accurately than the ADC, and may be useful for predicting reperfusion benefit.

Comparison of cumulant expansion and q-space imaging estimates for diffusional kurtosis in brain

PURPOSE

To compare estimates for the diffusional kurtosis in brain as obtained from a cumulant expansion (CE) of the diffusion MRI (dMRI) signal and from q-space (QS) imaging.

THEORY AND METHODS

For the CE estimates of the kurtosis, the CE was truncated to quadratic order in the b-value and fit to the dMRI signal for b-values from 0 up to 2000s/mm². For the QS estimates, b-values ranging from 0 up to 10,000s/mm² were used to determine the diffusion displacement probability density function (dPDF) via Stejskal's formula. The kurtosis was then calculated directly from the second and fourth order moments of the dPDF. These two approximations were studied for in vivo human data obtained on a 3T MRI scanner using three orthogonal diffusion encoding directions.

RESULTS

The whole brain mean values for the CE and QS kurtosis estimates differed by 16% or less in each of the considered diffusion encoding directions, and the Pearson correlation coefficients all exceeded 0.85. Nonetheless, there were large discrepancies in many voxels, particularly those with either very high or very low kurtoses relative to the mean values.

CONCLUSION

Estimates of the diffusional kurtosis in brain obtained using CE and QS approximations are strongly correlated, suggesting that they encode similar information. However, for the choice of b-values employed here, there may be substantial differences, depending on the properties of the diffusion microenvironment in each voxel.

Abnormal structural and functional hypothalamic connectivity in mild traumatic brain injury

PURPOSE

To investigate whether there is imaging evidence of hypothalamic injury in patients with mild traumatic brain injury (MTBI), which is a major public health problem due to the high prevalence and difficulty in diagnosis and treatment.

MATERIALS AND METHODS

Twenty-four patients (mean age 34.2, range, 18-56 years) with symptomatic MTBI and 22 age-matched healthy controls (mean age 37.0, range 20-61 years) participated in the study. Diffusion kurtosis imaging was performed with diffusion-weighted images acquired along 30 gradient directions and three b-values (b = 0, 1000, 2000 s/mm² ) based on a twice-refocused spin-echo sequence with a 3T magnetic resonance imaging (MRI) scanner. Resting-state functional (f)MRI with standard echo planar imaging (EPI) were performed to localize the resting-state networks (RSN) and hypothalamic functional connectivity.

RESULTS

There were significantly reduced mean kurtosis (P = 0.0092) and radial kurtosis (P = 0.0078) in patients as compared to controls in the hypothalamus. Furthermore, there was a significant negative correlation (r = -0.675, P = 0.0007) between radial kurtosis in the hypothalamus and fatigue severity scale in patients. The MTBI group also showed disrupted hypothalamic RSNs, with significantly decreased positive connectivity in medial prefrontal cortex, inferior posterior parietal, and cingulate regions but increased connectivity in the peri-hypothalamic regions and cerebellum, together with significantly decreased negative RSNs in visual and bilateral premotor areas (cluster corrected P < 0.05).

CONCLUSION

Our results show disruption of functional and structural hypothalamic connectivity in patients with MTBI, and might further the understanding of an array of clinical symptoms in MTBI such as sleep disturbance and fatigue.

LEVEL OF EVIDENCE

2 J. Magn. Reson. Imaging 2017;45:1105-1112.

Double-pulsed diffusional kurtosis imaging

Diffusional kurtosis imaging (DKI) is extended to double-pulsed-field-gradient (d-PFG) diffusion MRI sequences. This gives a practical approach for acquiring and analyzing d-PFG data. In particular, the leading d-PFG effects, beyond what conventional single-pulsed field gradient (s-PFG) provides, are interpreted in terms of the kurtosis for a diffusion displacement probability density function (dPDF) in a six-dimensional (6D) space. The 6D diffusional kurtosis encodes the unique information provided by d-PFG sequences up to second order in the b-value. This observation leads to a compact expression for the signal magnitude, and it suggests novel data acquisition and analysis methods. Double-pulsed DKI (DP-DKI) is demonstrated for in vivo mouse brain with d-PFG data obtained at 7 T. Copyright © 2014 John Wiley & Sons, Ltd.

Leading non-Gaussian corrections for diffusion orientation distribution function

An analytical representation of the leading non-Gaussian corrections for a class of diffusion orientation distribution functions (dODFs) is presented. This formula is constructed from the diffusion and diffusional kurtosis tensors, both of which may be estimated with diffusional kurtosis imaging (DKI). By incorporating model-independent non-Gaussian diffusion effects, it improves on the Gaussian approximation used in diffusion tensor imaging (DTI). This analytical representation therefore provides a natural foundation for DKI-based white matter fiber tractography, which has potential advantages over conventional DTI-based fiber tractography in generating more accurate predictions for the orientations of fiber bundles and in being able to directly resolve intra-voxel fiber crossings. The formula is illustrated with numerical simulations for a two-compartment model of fiber crossings and for human brain data. These results indicate that the inclusion of the leading non-Gaussian corrections can significantly affect fiber tractography in white matter regions, such as the centrum semiovale, where fiber crossings are common.