Increased diffusion sensitivity with hyperechos.

It is shown that the introduction of a 180 degrees refocusing pulse into a standard diffusion weighted stimulated echo sequence is equivalent to the simplest hyperecho sequence with identical diffusion weighting but equal or greater signal-to-noise (SNR) and thus equal or greater diffusion contrast. For high b-value imaging, the hyperecho sequence thus possesses the high diffusion contrast in the presence of small T(1)/T(2) ratios characteristic of stimulated echo sequences but with less than the 50% loss in SNR that is associated with the stimulated echo. For low b-value imaging, the hyperecho signal converges to that of the standard spin echo. The advantages of the two-pulse diffusion weighted hyperecho sequence are demonstrated theoretically. Experimental results are shown in the application to high angular resolution diffusion encoding (HARD) in normal human brain.     

Optimizing the functional diffusion map using Monte Carlo simulations

Purpose:

To optimize the diagnostic accuracy of the functional diffusion map for monitoring tumor treatment response in cancer patients.

Materials and Methods:

Using Monte Carlo simulations, measurement precision of the apparent diffusion coefficient (ADC), and particularly accuracy of threshold determination from healthy reference tissue, are evaluated by investigating the repeatability limit of the ADC as a function of different degrees of diffusion weighting of the sequence. Phantom and in‐vivo experiments are performed to verify and illustrate the results of the simulations.

Results:

While diagnostic accuracy of the functional diffusion map is hardly diminished by differing values of the T₂ relaxation time in tumor and reference tissue, it is shown to be impaired by differing ADCs, resulting in erroneously determined segmentation thresholds. This problem can be addressed by decreasing the maximum b‐factor and increasing the number of signal averages at the maximum b‐factor or, alternatively, the number of b‐factors while favoring schemes with higher b‐factors. Phantom experiments confirm the results of the simulations. In‐vivo data are presented to illustrate the effect of sequence optimization on the diagnostic accuracy of the functional diffusion map.

Conclusion:

The present work demonstrates that the diagnostic accuracy of the functional diffusion map can be impaired by inaccurate segmentation thresholds and derives means for its optimization that will increase the fidelity of future clinical studies. J. Magn. Reson. Imaging 2012;36:1002–1009. ©2012 Wiley Periodicals, Inc.     

Water diffusion and acute stroke

The occlusion of the middle cerebral artery was used as an experimental acute stroke model in 30 cats. The diffusion of water was followed by diffusion-sensitized MRI between 1 and 15 h after induction of stroke. It is demonstrated that images representing the trace of the diffusion tensor provide a much more accurate delineation of affected area than images representing the diffusion in one direction only. The reason is that the strong contrast caused by the anisotropy and orientation of myelin fibers is completely removed in the trace of the diffusion tensor. The trace images show a small contrast between white and gray matter. The diffusion coefficient of white matter is decreased in acute stroke to approximately the same extent as gray matter. It is further shown that the average lifetime of water in extra and intracellular space is shorter than 20 ms both for healthy and ischemic tissue indicating that myelin fibers are permeable to water. The anisotropy contrast did not change before or after induction of stroke, nor after sacrifice. Together, these observations are consistent with the view that the changes in water diffusion during acute stroke are directly related to cytotoxic oedema, i.e., to the change in relative volume of intra- and extracellular spaces. Changes in membrane permeability do not appear to contribute significantly to the changes in diffusion.     

Clinical applications of diffusion tensor imaging

Directionally-ordered cellular structures that impede water motion, such as cell membranes and myelin, result in water mobility that is also directionally-dependent. Diffusion tensor imaging characterizes this directional nature of water motion and thereby provides structural information that cannot be obtained by standard anatomic imaging. Quantitative apparent diffusion coefficients and fractional anisotropy have emerged from being primarily research tools to methods enabling valuable clinical applications. This review describes the clinical utility of diffusion tensor imaging, including the basic principles of the technique, acquisition, data analysis, and the major clinical applications.     

In vivo diffusion tensor imaging of the human prostate.

This study demonstrates the feasibility of in vivo prostate diffusion tensor imaging (DTI) in human subjects. We implemented an EPI-based diffusion-weighted (DW) sequence with seven-direction diffusion gradient sensitization, and acquired DT images from six subjects using cardiac gating with a phased-array prostate surface coil operating in a linear mode. We calculated two indices to quantify diffusion anisotropy. The direction of the eigenvector corresponding to the leading eigenvalue was displayed by means of a color-coding scheme. The average diffusion values of the prostate peripheral zone (PZ) and central gland (CG) were 1.95 +/- 0.08 x 10(-3) mm2 s and 1.53 +/- 0.34 x 10(-3) mm2 s, respectively. The average fractional anisotropy (FA) values for the PZ and CG were 0.46 +/- 0.04 and 0.40 +/- 0.08, respectively. The diffusion ellipsoid in prostate tissue was anisotropic and approximated a prolate model, as shown in the color maps of the anisotropy. Consistent with the tissue architecture, the prostate fiber orientations were predominantly in the superior-inferior (SI) direction for both the PZ and CG. This study shows the feasibility of in vivo DTI and establishes normative DT values for six subjects.     

Utilizing the diffusion-to-noise ratio to optimize magnetic resonance diffusion tensor acquisition strategies for improving measurements of diffusion anisotropy.

It is well known that quantitative anisotropy measurements derived from the diffusion tensor are extremely sensitive to noise contamination. The level of noise in the diffusion tensor imaging (DTI) experiment is usually measured from some estimate of the signal-to-noise ratio (SNR) in the component diffusion-weighted (DW) images. This measure is, however, highly dependent on experimental parameters, such as the diffusion attenuation b-value and the diffusion coefficient of the subject. Conversely, the diffusion-to-noise ratio (DNR), defined as the SNR of the calculated diffusion tensor trace map, provides a reliable estimate of noise contamination, which is largely independent of such parameters. In this work it is demonstrated how reliable anisotropy measurements can be obtained using an image acquisition strategy that optimizes the DNR of the DTI experiment. This acquisition scheme is shown to provide noise-independent measurements of typical diffusion anisotropy values found in the human brain.     

Anisotropic anomalous diffusion assessed in the human brain by scalar invariant indices

A new method to investigate anomalous diffusion in human brain, inspired by the stretched‐exponential model proposed by Hall and Barrick, is proposed here, together with a discussion about its potential application to cerebral white matter characterization. Aim of the work was to show the ability of anomalous diffusion indices to characterize white matter structures, whose complexity is only partially accounted by diffusion tensor imaging indices. MR signal was expressed as a stretched‐exponential only along the principal axes of diffusion; whereas, in a generic direction, it was modeled as a combination of three stretched‐exponentials. Indices to quantify the tissue anomalous diffusion and its anisotropy, independently of the experiment reference frame, were derived. Experimental results, obtained on 10 healthy subjects at 3T, show that the new parameters are highly correlated to intrinsic local geometry when compared with Hall and Barrick indices. Moreover, they offer a different contrast in white matter regions when compared with diffusion tensor imaging. Specifically, the new indices show a higher capability to discriminate among areas of the corpus callosum associated to different distribution in axonal densities, thus offering a new potential tool to detect more specific patterns of brain abnormalities than diffusion tensor imaging in the presence of neurological and psychiatric disorders. Magn Reson Med, 2010. © 2010 Wiley‐Liss, Inc.     

Novel diffusion anisotropy indices: an evaluation

PURPOSE: To systematically evaluate diffusion anisotropy (DA) using newly defined indices based on the diffusion deviation and mean diffusivity approach. MATERIALS AND METHODS: Measures of amplitude, area, and volume of the DA index (DAI) were measured and compared with regard to their sensitivity to changes in DA, susceptibility to noise in the original diffusion-weighted (DW) images, and contrast-to-noise ratio (CNR) in homogenous regions. Simulations were performed under different levels of noise and DA. Human DTI data were acquired from eight normal volunteers. RESULTS: Indices of area and volume measures provided improved resolution for characterizing the DA compared to the eigenvalue ratio. The amplitude measure showed consistent performances with good CNR and less susceptibility to noise in the original data. CONCLUSION: These indices are rotationally invariant without the requirement of eigenvalue sorting. At low anisotropy, all indices have a similar CNR. For larger DA, the first index (the deviation tensor divided by the DT) shows improved sensitivity, contrast-to-noise ratio (CNR), and noise immunity compared to the other indices.     

Characterizing non-Gaussian diffusion by using generalized diffusion tensors.

Diffusion tensor imaging (DTI) is known to have a limited capability of resolving multiple fiber orientations within one voxel. This is mainly because the probability density function (PDF) for random spin displacement is non-Gaussian in the confining environment of biological tissues and, thus, the modeling of self-diffusion by a second-order tensor breaks down. The statistical property of a non-Gaussian diffusion process is characterized via the higher-order tensor (HOT) coefficients by reconstructing the PDF of the random spin displacement. Those HOT coefficients can be determined by combining a series of complex diffusion-weighted measurements. The signal equation for an MR diffusion experiment was investigated theoretically by generalizing Fick's law to a higher-order partial differential equation (PDE) obtained via Kramers-Moyal expansion. A relationship has been derived between the HOT coefficients of the PDE and the higher-order cumulants of the random spin displacement. Monte-Carlo simulations of diffusion in a restricted environment with different geometrical shapes were performed, and the strengths and weaknesses of both HOT and established diffusion analysis techniques were investigated. The generalized diffusion tensor formalism is capable of accurately resolving the underlying spin displacement for complex geometrical structures, of which neither conventional DTI nor diffusion-weighted imaging at high angular resolution (HARD) is capable. The HOT method helps illuminate some of the restrictions that are characteristic of these other methods. Furthermore, a direct relationship between HOT and q-space is also established.     

Biexponential diffusion tensor analysis of human brain diffusion data.

Several studies have shown that in tissues over an extended range of b-factors, the signal decay deviates significantly from the basic monoexponential model. The true nature of this departure has to date not been identified. For the current study, line scan diffusion images of brain suitable for biexponential diffusion tensor analysis were acquired in normal subjects on a clinical MR system. For each of six noncollinear directions, 32 images with b-factors ranging from 5 to 5000 s/mm2 were collected. Biexponential fits yielded parameter maps for a fast and a slow diffusion component. A subset of the diffusion data, consisting of the images obtained at the conventional range of b-factors between 5 and 972 s/mm2, was used for monoexponential diffusion tensor analysis. Fractional anisotropy (FA) of the fast-diffusion component and the monoexponential fit exhibited no significant difference. FA of the slow-diffusion biexponential component was significantly higher, particularly in areas of lower fiber density. The principal diffusion directions for the two biexponential components and the monoexponential solution were largely the same and in agreement with known fiber tracts. The second and third diffusion eigenvector directions also appeared to be aligned, but they exhibited significant deviations in localized areas.     

Construction of a temperature‐controlled diffusion phantom for quality control of diffusion measurements

Purpose

To construct a temperature‐controlled diffusion phantom with known diffusion properties and geometry in order to facilitate the comparison and optimization of diffusion sequences with the objective of increasing the precision of experimentally derived diffusion parameters.

Materials and Methods

A temperature‐stabilized diffusion phantom made up of two crossing strands of hydrophobic polyethylene fibers was constructed. Reproducibility and temperature dependence of several diffusion parameters was investigated and compared with computer simulations. Furthermore, in order to stimulate actual use, the precision of measurement of different diffusion‐encoding schemes was compared using bootstrap analysis.

Results

The measured values of the diffusion parameters are highly reproducible and feature strong temperature dependence which is reproduced in simulations, underlining the necessity of a temperature‐stabilized environment for quality control. The exemplary application presented here demonstrates that the phantom allows comparing and optimizing different diffusion sequences with regard to their measurement precision.

Conclusion

The present work demonstrates that the diffusion phantom facilitates and improves the comparison and quality control of diffusion sequences and the ensuing parameters. The results show that an accurate temperature control is a vital prerequisite for highly reproducible calibration measurements. As such, the phantom might provide a valuable calibration tool for clinical studies. J. Magn. Reson. Imaging 2009;29:692–698. © 2009 Wiley‐Liss, Inc.     

Dependence on diffusion time of apparent diffusion tensor of ex vivo calf tongue and heart.

The time dependence of the apparent diffusion tensor of ex vivo calf heart and tongue was measured for diffusion times (tau(d)) between 32 and 810 ms. The results showed evidence of restricted diffusion in the muscle tissues of both organs. In regions where the myofibers are parallel, the largest eigenvalue (lambda(1)) of the diffusion tensor remained the same for all diffusion times measured, while the other eigenvalues (lambda(2), lambda(3)) decreased by 29-36% between tau(d) = 32 ms and tau(d) = 400 ms. In regions where the fibers cross, the lambda(1) also changed, decreasing by 17% between tau(d) = 32 ms and tau(d) = 400 ms. The restricting compartment size and volume fraction were effectively estimated by fitting the time courses of the eigenvalues to a model consisting of a nonrestricted compartment and a cylindrically restricted compartment. To our knowledge, this study is the first demonstrating diffusion time dependence of measured water diffusion tensor in muscular tissue. With improvement in scanning technology, future studies may permit noninvasive, in vivo detection of changes in muscle myoarchitecture due to disease, treatment, and exercise.     

Comparison of apparent diffusion coefficients and distributed diffusion coefficients in high‐grade gliomas

Purpose:

To compare apparent diffusion coefficients (ADCs) with distributed diffusion coefficients (DDCs) in high‐grade gliomas.

Materials and Methods:

Twenty patients with high‐grade gliomas prospectively underwent diffusion‐weighted MRI. Traditional ADC maps were created using b‐values of 0 and 1000 s/mm². In addition, DDC maps were created by applying the stretched‐exponential model using b‐values of 0, 1000, 2000, and 4000 s/mm². Whole‐tumor ADCs and DDCs (in 10^?3 mm²/s) were measured and analyzed with a paired t‐test, Pearson's correlation coefficient, and the Bland‐Altman method.

Results:

Tumor ADCs (1.14 ± 0.26) were significantly lower (P = 0.0001) than DDCs (1.64 ± 0.71). Tumor ADCs and DDCs were strongly correlated (R = 0.9716; P < 0.0001), but mean bias ± limits of agreement between tumor ADCs and DDCs was ?0.50 ± 0.90. There was a clear trend toward greater discordance between ADC and DDC at high ADC values.

Conclusion:

Under the assumption that the stretched‐exponential model provides a more accurate estimate of the average diffusion rate than the mono‐exponential model, our results suggest that for a little diffusion attenuation the mono‐exponential fit works rather well for quantifying diffusion in high‐grade gliomas, whereas it works less well for a greater degree of diffusion attenuation. J. Magn. Reson. Imaging 2010;31:531–537. © 2010 Wiley‐Liss, Inc.