Biexponential analysis of diffusion-related signal decay in normal human cortical and deep gray matter

Triexponential Diffusion Analysis of Diffusion-weighted Imaging for Breast Ductal Carcinoma in Situ and Invasive Ductal Carcinoma

Purpose

To obtain detailed information in breast ductal carcinoma in situ (DCIS) and invasive ductal carcinoma (IDC) using triexponential diffusion analysis.

Methods

Diffusion-weighted images (DWI) of the breast were obtained using single-shot diffusion echo-planar imaging with 15 b-values. Mean signal intensities at each b-value were measured in the DCIS and IDC lesions and fitted with the triexponential function based on a two-step approach: slow-restricted diffusion coefficient (D_s) was initially determined using a monoexponential function with b-values > 800 s/mm². The diffusion coefficient of free water at 37°C was assigned to the fast-free diffusion coefficient (D_f). Finally, the perfusion-related diffusion coefficient (D_p) was derived using all the b-values. Furthermore, biexponential analysis was performed to obtain the perfusion-related diffusion coefficient (D^*) and the perfusion-independent diffusion coefficient (D). Monoexponential analysis was performed to obtain the apparent diffusion coefficient (ADC). The sensitivity and specificity of the aforementioned diffusion coefficients for distinguishing between DCIS and IDC were evaluated using the pathological results.

Results

The D_s, D, and ADC of DCIS were significantly higher than those of IDC (P < 0.01 for all). There was no significant correlation between D_p and D_s, but there was a weak correlation between D^* and D. The combination of D_p and D_s showed higher sensitivity and specificity (85.9% and 71.4%, respectively), compared to the combination of D^* and D (81.5% and 33.3%, respectively).

Conclusion

Triexponential analysis can provide detailed diffusion information for breast tumors that can be used to differentiate between DCIS and IDC.

A Fast Protocol for Multiparametric Characterisation of Diffusion in the Brain and Brain Tumours

Multi-parametric tissue characterisation is demonstrated using a 4-minute protocol based on diffusion trace acquisitions. Three diffusion regimes are covered simultaneously: pseudo-perfusion, Gaussian, and non-Gaussian diffusion. The clinical utility of this method for fast multi-parametric mapping for brain tumours is explored. A cohort of 17 brain tumour patients was measured on a 3T hybrid MR-PET scanner with a standard clinical MRI protocol, to which the proposed multi-parametric diffusion protocol was subsequently added. For comparison purposes, standard perfusion and a full diffusion kurtosis protocol were acquired. Simultaneous amino-acid (¹⁸F-FET) PET enabled the identification of active tumour tissue. The metrics derived from the proposed protocol included perfusion fraction, pseudo-diffusivity, apparent diffusivity, and apparent kurtosis. These metrics were compared to the corresponding metrics from the dedicated acquisitions: cerebral blood volume and flow, mean diffusivity and mean kurtosis. Simulations were carried out to assess the influence of fitting methods and noise levels on the estimation of the parameters. The diffusion and kurtosis metrics obtained from the proposed protocol show strong to very strong correlations with those derived from the conventional protocol. However, a bias towards lower values was observed. The pseudo-perfusion parameters showed very weak to weak correlations compared to their perfusion counterparts. In conclusion, we introduce a clinically applicable protocol for measuring multiple parameters and demonstrate its relevance to pathological tissue characterisation.

Diffusion MR Imaging with T2-based Water Suppression (T2wsup-dMRI)

Purpose: This study proposes and assesses a new diffusion MRI (dMRI) technique to solve problems related to the quantification of parameter maps (apparent diffusion coefficient [ADC] or mean diffusivity [MD], fractional anisotropy [FA]) and misdrawing of fiber tractography (FT) due to cerebrospinal fluid (CSF)-partial volume effects (PVEs) for brain tissues by combining with the T2-based water suppression (T2wsup) technique.

Methods: T2wsup–diffusion-weighted imaging (DWI) images were obtained by subtracting those images from the acquired multi-b value (b) DWI images after correcting the signal intensities of multiecho time (TE) images using long TE water signal-dominant images. Quantitative parameter maps and FT were obtained from minimum data points and were compared with those using the standard (without wsup) DWI method, and partly compared with those obtained using other alternative DWI methods of applying fluid attenuation inversion recovery (FLAIR), non-b-zero (NBZ) by theoretical or noise-added simulation and MR images.

Results: In the T2wsup-dMRI method, the hyperintense artifacts due to CSF-PVEs in MRI data were dramatically suppressed even at lower b (≲ 500 s/mm²) while keeping the tissue SNR. The quantitative parameter map values became precisely close to the pure tissue values precisely even in water (CSF) PVE voxels in healthy brain tissues (T2 ≲ 100 ms). Furthermore, the fiber tracts were correctly connected, particularly at the fornix in closest contact to the CSF.

Conclusion: Solving the problem of CSF-PVE in the current dMRI technique using our proposed T2wsup-dMRI technique is easy, with higher SNR than those obtained with FLAIR or NBZ methods when applying to healthy brain tissues. The proposed T2wsup–dMRI could be useful in clinical settings, although further optimization of the pulse sequence and processing techniques and clinical assessments are required, particularly for long T2 lesions.

A Bayesian approach to diffusional kurtosis imaging

PURPOSE

Diffusional kurtosis metrics show high performance for detecting pathological changes and are therefore expected to be disease biomarkers. Kurtosis maps, however, tend to be noisy. The maps' visual quality is crucial for disease diagnosis, even when kurtosis is being used quantitatively. A Bayesian method was proposed to curtail the large statistical error inherent in kurtosis estimation while maintaining potential application to biomarkers.

THEORY

Gaussian priors are determined from first-step estimations implemented using the least-square method (LSM). The likelihood-function variance is determined from the residuals of the estimation. Although the proposed approach is similar to a regularized LSM, regularization parameters do not have to be artificially adjusted. An appropriate balance between denoising and preventing false shrinkages of metric dispersions is automatically achieved.

METHODS

Map qualities achieved using the conventional and proposed methods were compared. The receiver-operating characteristic analysis was performed for glioma-grade differentiation using simulated low- and high-grade glioma DWI datasets. Noninferiority of the proposed method was tested for areas under the curves (AUCs).

RESULTS

The noisier the conventional maps, the better the proposed Bayesian method improved them. Noninferiority of the proposed method was confirmed by AUC tests for all kurtosis-related metrics. Superiority of the proposed method was also established for several metrics.

CONCLUSIONS

The proposed approach improved noisy kurtosis maps while maintaining their performances as biomarkers without increasing data acquisition requirements or arbitrarily choosing LSM regularization parameters. This approach may enable the use of higher-order terms in diffusional kurtosis imaging (DKI) fitting functions by suppressing overfitting, thereby improving the DKI-estimation accuracy.

Probing in vivo cortical myeloarchitecture in humans via line-scan diffusion acquisitions at 7 T with 250-500 micron radial resolution

PURPOSE

The goal of this study was to measure diffusion signals within the cerebral cortex using the line-scan technique to achieve extremely high resolution in the radial direction (ie, perpendicular to the cortical surface) and to demonstrate the utility of these measurements for investigating laminar architecture in the living human brain.

METHODS

Line-scan diffusion data with 250-500 micron radial resolution were acquired at 7 T on 8 healthy volunteers, with each line prescribed perpendicularly to primary somatosensory cortex (S1) and primary motor cortex (M1). Apparent diffusion coefficients, fractional anisotropy values, and radiality indices were measured as a function of cortical depth.

RESULTS

In the deep layers of S1, we found evidence for high anisotropy and predominantly tangential diffusion, with low anisotropy observed in superficial S1. In M1, moderate anisotropy and predominantly radial diffusion was seen at almost all cortical depths. These patterns were consistent across subjects and were conspicuous without averaging data across different locations on the cortical sheet.

CONCLUSION

Our results are in accord with the myeloarchitecture of S1 and M1, known from prior histology studies: in S1, dense bands of tangential myelinated fibers run through the deep layers but not the superficial ones, and in M1, radial myelinated fibers are prominent at most cortical depths. This work therefore provides support for the idea that high-resolution diffusion signals, measured with the line-scan technique and receiving a boost in SNR at 7 T, may serve as a sensitive probe of in vivo laminar architecture.

Direction-averaged diffusion-weighted MRI signal using different axisymmetric B-tensor encoding schemes

Purpose

It has been shown, theoretically and in vivo, that using the Stejskal‐Tanner pulsed‐gradient, or linear tensor encoding (LTE), and in tissue exhibiting a “stick‐like” diffusion geometry, the direction‐averaged diffusion‐weighted MRI signal at high b‐values ( 7000<b<10000s/mm2) follows a power‐law, decaying as 1/b. It has also been shown, theoretically, that for planar tensor encoding (PTE), the direction‐averaged diffusion‐weighted MRI signal decays as 1/b. We aimed to confirm this theoretical prediction in vivo. We then considered the direction‐averaged signal for arbitrary b‐tensor shapes and different tissue substrates to look for other conditions under which a power‐law exists.

Methods

We considered the signal decay for high b‐values for encoding geometries ranging from 2‐dimensional PTE, through isotropic or spherical tensor encoding to LTE. When a power‐law behavior was suggested, this was tested using in silico simulations and, when appropriate, in vivo using ultra‐strong (300 mT/m) gradients.

Results

Our in vivo results confirmed the predicted 1/b power law for PTE. Moreover, our analysis showed that using an axisymmetric b‐tensor a power‐law only exists under very specific conditions: (a) “stick‐like” tissue geometry and purely LTE or purely PTE waveforms; and (b) "pancake‐like" tissue geometry and a purely LTE waveform.

Conclusions

A complete analysis of the power‐law dependencies of the diffusion‐weighted signal at high b‐values has been performed. Only three specific forms of encoding result in a power‐law dependency, pure linear and pure PTE when the tissue geometry is “stick‐like” and pure LTE when the tissue geometry is "pancake‐like". The different exponents of these encodings could be used to provide independent validation of the presence of different tissue geometries in vivo.

Brain lateralization probed by water diffusion at the atomic to micrometric scale

Combined neutron scattering and diffusion nuclear magnetic resonance experiments have been used to reveal significant interregional asymmetries (lateralization) in bovine brain hemispheres in terms of myelin arrangement and water dynamics at micron to atomic scales. Thicker myelin sheaths were found in the left hemisphere using neutron diffraction. 4.7 T dMRI and quasi-elastic neutron experiments highlighted significant differences in the properties of water dynamics in the two hemispheres. The results were interpreted in terms of hemisphere-dependent cellular composition (number of neurons, cell distribution, etc.) as well as specificity of neurological functions (such as preferential networking).

Anomalous water dynamics in brain: a combined diffusion magnetic resonance imaging and neutron scattering investigation

Water diffusion is an optimal tool for investigating the architecture of brain tissue on which modern medical diagnostic imaging techniques rely. However, intrinsic tissue heterogeneity causes systematic deviations from pure free-water diffusion behaviour. To date, numerous theoretical and empirical approaches have been proposed to explain the non-Gaussian profile of this process. The aim of this work is to shed light on the physics piloting water diffusion in brain tissue at the micrometre-to-atomic scale. Combined diffusion magnetic resonance imaging and first pioneering neutron scattering experiments on bovine brain tissue have been performed in order to probe diffusion distances up to macromolecular separation. The coexistence of free-like and confined water populations in brain tissue extracted from a bovine right hemisphere has been revealed at the micrometre and atomic scale. The results are relevant for improving the modelling of the physics driving intra- and extracellular water diffusion in brain, with evident benefit for the diffusion magnetic resonance imaging technique, nowadays widely used to diagnose, at the micrometre scale, brain diseases such as ischemia and tumours.

Dependence on b-value of the direction-averaged diffusion-weighted imaging signal in brain

PURPOSE

The dependence of the direction-averaged diffusion-weighted imaging (DWI) signal in brain was studied as a function of b-value in order to help elucidate the relationship between diffusion weighting and brain microstructure.

METHODS

High angular resolution diffusion imaging (HARDI) data were acquired from two human volunteers with 128 diffusion-encoding directions and six b-value shells ranging from 1000 to 6000s/mm² in increments of 1000s/mm². The direction-averaged signal was calculated for each shell by averaging over all diffusion-encoding directions, and the signal was plotted as a function of b-value for selected regions of interest. As a supplementary analysis, similar methods were also applied to retrospective DWI data obtained from the human connectome project (HCP), which includes b-values up to 10,000s/mm².

RESULTS

For all regions of interest, a simple power law relationship accurately described the observed dependence of the direction-averaged signal as a function of the diffusion weighting. In white matter, the characteristic exponent was 0.56±0.05, while in gray matter it was 0.88±0.11. Comparable results were found with the HCP data.

CONCLUSION

The direction-averaged DWI signal varies, to a good approximation, as a power of the b-value, for b-values between 1000 and 6000s/mm². The exponents characterizing this power law behavior were markedly different for white and gray matter, indicative of sharply contrasting microstructural environments. These results may inform the construction of microstructural models used to interpret the DWI signal.

REDUCING CSF PARTIAL VOLUME EFFECTS TO ENHANCE DIFFUSION TENSOR IMAGING METRICS OF BRAIN MICROSTRUCTURE

Technological advances over recent decades now allow for in vivo observation of human brain tissue through the use of neuroimaging methods. While this field originated with techniques capable of capturing macrostructural details of brain anatomy, modern methods such as diffusion tensor imaging (DTI) that are now regularly implemented in research protocols have the ability to characterize brain microstructure. DTI has been used to reveal subtle micro-anatomical abnormalities in the prodromal phase ofº various diseases and also to delineate "normal" age-related changes in brain tissue across the lifespan. Nevertheless, imaging artifact in DTI remains a significant limitation for identifying true neural signatures of disease and brain-behavior relationships. Cerebrospinal fluid (CSF) contamination of brain voxels is a main source of error on DTI scans that causes partial volume effects and reduces the accuracy of tissue characterization. Several methods have been proposed to correct for CSF artifact though many of these methods introduce new limitations that may preclude certain applications. The purpose of this review is to discuss the complexity of signal acquisition as it relates to CSF artifact on DTI scans and review methods of CSF suppression in DTI. We will then discuss a technique that has been recently shown to effectively suppress the CSF signal in DTI data, resulting in fewer errors and improved measurement of brain tissue. This approach and related techniques have the potential to significantly improve our understanding of "normal" brain aging and neuropsychiatric and neurodegenerative diseases. Considerations for next-level applications are discussed.

Modified triexponential analysis of intravoxel incoherent motion for brain perfusion and diffusion

BACKGROUND

To noninvasively obtain more detailed information on brain perfusion and diffusion using modified triexponential analysis.

METHODS

On a 3.0 Tesla MRI, diffusion-weighted imaging of the brain with multiple b-values was performed in healthy volunteers (n = 12). We derived perfusion-related, fast-free, and slow-restricted diffusion coefficients (Dp , Df , and Ds , respectively) and fractions (Fp , Ff , and Fs , respectively) in the frontal and occipital white matter, caudate nucleus, and putamen calculated from triexponential function by a two-step approach. Ds was initially determined using monoexponential function in b-values over 1000 s/mm(2) and was applied to triexponential function. Additionally, the literature value of the diffusion coefficient of free water at 37 °C was assigned to Df . Finally, Dp and fractions were derived using all b-values. Moreover, biexponential analysis was performed and compared with triexponential analysis. We also determined regional cerebral blood flow (rCBF) using arterial spin labeling and assessed its relation with each diffusion parameter.

RESULTS

Significant positive correlations between Dp and rCBF were found in the caudate nucleus (R = 0.84; P = 0.01) and putamen (R = 0.86; P = 0.01), whereas no diffusion parameters were significantly correlated with rCBF on biexponential analysis (P > 0.05 for all).

CONCLUSION

Diffusion analysis with triexponential function enables noninvasive gathering of more detailed information on brain perfusion and diffusion.

Accuracies and Contrasts of Models of the Diffusion-Weighted-Dependent Attenuation of the MRI Signal at Intermediate b-values

The diffusion-weighted-dependent attenuation of the MRI signal E(b) is extremely sensitive to microstructural features. The aim of this study was to determine which mathematical model of the E(b) signal most accurately describes it in the brain. The models compared were the monoexponential model, the stretched exponential model, the truncated cumulant expansion (TCE) model, the biexponential model, and the triexponential model. Acquisition was performed with nine b-values up to 2500 s/mm² in 12 healthy volunteers. The goodness-of-fit was studied with F-tests and with the Akaike information criterion. Tissue contrasts were differentiated with a multiple comparison corrected nonparametric analysis of variance. F-test showed that the TCE model was better than the biexponential model in gray and white matter. Corrected Akaike information criterion showed that the TCE model has the best accuracy and produced the most reliable contrasts in white matter among all models studied. In conclusion, the TCE model was found to be the best model to infer the microstructural properties of brain tissue.

Avian egg latebra as brain tissue water diffusion model

PURPOSE

Simplified models of non-monoexponential diffusion signal decay are of great interest to study the basic constituents of complex diffusion behavior in tissues. The latebra, a unique structure uniformly present in the yolk of avian eggs, exhibits a non-monoexponential diffusion signal decay. This model is more complex than simple phantoms based on differences between water and lipid diffusion, but is also devoid of microscopic structures with preferential orientation or perfusion effects.

METHODS

Diffusion scans with multiple b-values were performed on a clinical 3 Tesla system in raw and boiled chicken eggs equilibrated to room temperature. Diffusion encoding was applied over the ranges 5-5,000 and 5-50,000 s/mm(2). A low read-out bandwidth and chemical shift was used for reliable lipid/water separation. Signal decays were fitted with exponential functions.

RESULTS

The latebra, when measured over the 5-5,000 s/mm(2) range, exhibited independent of preparation clearly biexponential diffusion, with diffusion parameters similar to those typically observed in in vivo human brain. For the range 5-50,000 s/mm(2), there was evidence of a small third, very slow diffusing water component.

CONCLUSION

The latebra of the avian egg contains membrane structures, which may explain a deviation from a simple monoexponential diffusion signal decay, which is remarkably similar to the deviation observed in brain tissue.

White matter organization in relation to upper limb motor control in healthy subjects: exploring the added value of diffusion kurtosis imaging

Diffusion tensor imaging (DTI) characterizes white matter (WM) microstructure. In many brain regions, however, the assumption that the diffusion probability distribution is Gaussian may be invalid, even at low b values. Recently, diffusion kurtosis imaging (DKI) was suggested to more accurately estimate this distribution. We explored the added value of DKI in studying the relation between WM microstructure and upper limb coordination in healthy controls (N = 24). Performance on a complex bimanual tracking task was studied with respect to the conventional DTI measures (DKI or DTI derived) and kurtosis metrics of WM tracts/regions carrying efferent (motor) output from the brain, corpus callosum (CC) substructures and whole brain WM. For both estimation models, motor performance was associated with fractional anisotropy (FA) of the CC-genu, CC-body, the anterior limb of the internal capsule, and whole brain WM (r s range 0.42-0.63). Although DKI revealed higher mean, radial and axial diffusivity and lower FA than DTI (p < 0.001), the correlation coefficients were comparable. Finally, better motor performance was associated with increased mean and radial kurtosis and kurtosis anisotropy (r s range 0.43-0.55). In conclusion, DKI provided additional information, but did not show increased sensitivity to detect relations between WM microstructure and bimanual performance in healthy controls.

Analysis of multiple B-value diffusion-weighted imaging in pediatric acute encephalopathy

Acute encephalopathy is a disease group more commonly seen in children. It is often severe and has neurological sequelae. Imaging is important for early diagnosis and prompt treatment to ameliorate an unfavorable outcome, but insufficient sensitivity/specificity is a problem. To overcome this, a new value (fraction of high b-pair (F_H)) that could be processed from clinically acceptable MR diffusion-weighted imaging (DWI) with three different b-values was designed on the basis of a two-compartment model of water diffusion signal attenuation. The purpose of this study is to compare F_H with the apparent diffusion coefficient (ADC) regarding the detectability of pediatric acute encephalopathy. We retrospectively compared the clinical DWI of 15 children (1–10 years old, mean 2.34, 8 boys, 7 girls) of acute encephalopathy with another 16 children (1–11 years old, mean 4.89, 9 boys, 7 girls) as control. A comparison was first made visually by mapping F_H on the brain images, and then a second comparison was made on the basis of 10 regions of interest (ROIs) set on cortical and subcortical areas of each child. F_H map visually revealed diffusely elevated F_H in cortical and subcortical areas of the patients with acute encephalopathy; the changes seemed more diffuse in F_H compared to DWI. The comparison based on ROI revealed elevated mean F_H in the cortical and subcortical areas of the acute encephalopathy patients compared to control with significant difference (P<0.05). Similar findings were observed even in regions where the findings of DWI were slight. The reduction of mean ADC was significant in regions with severe findings in DWI, but it was not constant in the areas with slighter DWI findings. The detectability of slight changes of cortical and subcortical lesions in acute encephalopathy may be superior in F_H compared to ADC.

Probing tissue microstructure with restriction spectrum imaging: Histological and theoretical validation

Water diffusion magnetic resonance imaging (dMRI) is a powerful tool for studying biological tissue microarchitectures in vivo. Recently, there has been increased effort to develop quantitative dMRI methods to probe both length scale and orientation information in diffusion media. Diffusion spectrum imaging (DSI) is one such approach that aims to resolve such information based on the three-dimensional diffusion propagator at each voxel. However, in practice, only the orientation component of the propagator function is preserved when deriving the orientation distribution function. Here, we demonstrate how a straightforward extension of the linear spherical deconvolution (SD) model can be used to probe tissue orientation structures over a range (or "spectrum") of length scales with minimal assumptions on the underlying microarchitecture. Using high b-value Cartesian q-space data on a rat brain tissue sample, we demonstrate how this "restriction spectrum imaging" (RSI) model allows for separating the volume fraction and orientation distribution of hindered and restricted diffusion, which we argue stems primarily from diffusion in the extraneurite and intraneurite water compartment, respectively. Moreover, we demonstrate how empirical RSI estimates of the neurite orientation distribution and volume fraction capture important additional structure not afforded by traditional DSI or fixed-scale SD-like reconstructions, particularly in gray matter. We conclude that incorporating length scale information in geometric models of diffusion offers promise for advancing state-of-the-art dMRI methods beyond white matter into gray matter structures while allowing more detailed quantitative characterization of water compartmentalization and histoarchitecture of healthy and diseased tissue.

Effect of cerebral spinal fluid suppression for diffusional kurtosis imaging

PURPOSE

To evaluate the cerebral spinal fluid (CSF) partial volume effect on diffusional kurtosis imaging (DKI) metrics in white matter and cortical gray matter.

MATERIALS AND METHODS

Four healthy volunteers participated in this study. Standard DKI and fluid-attenuated inversion recovery (FLAIR) DKI experiments were performed using a twice-refocused-spin-echo diffusion sequence. The conventional diffusion tensor imaging (DTI) metrics of fractional anisotropy (FA), mean, axial, and radial diffusivity (MD, D[symbol in text], D[symbol in text] together with DKI metrics of mean, axial, and radial kurtosis (MK, K[symbol in text], K[symbol in text], were measured and compared. Single image slices located above the lateral ventricles, with similar anatomical features for each subject, were selected to minimize the effect of CSF from the ventricles.

RESULTS

In white matter, differences of less than 10% were observed between diffusion metrics measured with standard DKI and FLAIR-DKI sequences, suggesting minimal CSF contamination. For gray matter, conventional DTI metrics differed by 19% to 52%, reflecting significant CSF partial volume effects. Kurtosis metrics, however, changed by 11% or less, indicating greater robustness with respect to CSF contamination.

CONCLUSION

Kurtosis metrics are less sensitive to CSF partial voluming in cortical gray matter than conventional diffusion metrics. The kurtosis metrics may then be more specific indicators of changes in tissue microstructure, provided the effect sizes for the changes are comparable.

White matter integrity, fiber count, and other fallacies: the do's and don'ts of diffusion MRI

Diffusion-weighted MRI (DW-MRI) has been increasingly used in imaging neuroscience over the last decade. An early form of this technique, diffusion tensor imaging (DTI) was rapidly implemented by major MRI scanner companies as a scanner selling point. Due to the ease of use of such implementations, and the plausibility of some of their results, DTI was leapt on by imaging neuroscientists who saw it as a powerful and unique new tool for exploring the structural connectivity of human brain. However, DTI is a rather approximate technique, and its results have frequently been given implausible interpretations that have escaped proper critique and have appeared misleadingly in journals of high reputation. In order to encourage the use of improved DW-MRI methods, which have a better chance of characterizing the actual fiber structure of white matter, and to warn against the misuse and misinterpretation of DTI, we review the physics of DW-MRI, indicate currently preferred methodology, and explain the limits of interpretation of its results. We conclude with a list of 'Do's and Don'ts' which define good practice in this expanding area of imaging neuroscience.

Two-step anomalous diffusion tensor imaging

We extend the formalism of anomalous diffusion imaging to include directional anisotropy of fitted parameters. The resulting technique is termed anomalous diffusion tensor imaging (aDTI), and allows the directional properties of the distributed diffusion coefficient (α) and the anomalous diffusion exponent, (γ) to be analysed using the same analytical techniques as regular diffusion tensor imaging (DTI). Together, these parameters quantify the rate of diffusion (α) and the complexity of the diffusion environment (γ). We generated tensor images for the anomalous exponent tensor (Γ) and distributed diffusivity tensor (A) from in vivo human brain data and present images of eigenvalues, eigenvectors, Trace/3 (Tr), fractional anisotropy (FA) and tensor shape measures. In white matter, A is found to have a median Tr = 0.56 × 10(- 3) mm(2) s(- 1), FA = 0.58 and Γ Tr = 0.69, FA = 0.13. We observed that white matter shows a similar anisotropic geometry for the distributed diffusion tensor as for the regular diffusion tensor, whereas the anomalous exponent tensor exhibits a different shape characteristic which may be informative of tissue microstructure.

Diffusion kurtosis as an in vivo imaging marker for reactive astrogliosis in traumatic brain injury

Diffusion Kurtosis Imaging (DKI) provides quantifiable information on the non-Gaussian behavior of water diffusion in biological tissue. Changes in water diffusion tensor imaging (DTI) parameters and DKI parameters in several white and gray matter regions were investigated in a mild controlled cortical impact (CCI) injury rat model at both the acute (2 h) and the sub-acute (7 days) stages following injury. Mixed model ANOVA analysis revealed significant changes in temporal patterns of both DTI and DKI parameters in the cortex, hippocampus, external capsule and corpus callosum. Post-hoc tests indicated acute changes in mean diffusivity (MD) in the bilateral cortex and hippocampus (p<0.0005) and fractional anisotropy (FA) in ipsilateral cortex (p<0.0005), hippocampus (p=0.014), corpus callosum (p=0.031) and contralateral external capsule (p=0.011). These changes returned to baseline by the sub-acute stage. However, mean kurtosis (MK) was significantly elevated at the sub-acute stages in all ipsilateral regions and scaled inversely with the distance from the impacted site (cortex and corpus callosum: p<0.0005; external capsule: p=0.003; hippocampus: p=0.011). Further, at the sub-acute stage increased MK was also observed in the contralateral regions compared to baseline (cortex: p=0.032; hippocampus: p=0.039) while no change was observed with MD and FA. An increase in mean kurtosis was associated with increased reactive astrogliosis from immunohistochemistry analysis. Our results suggest that DKI is sensitive to microstructural changes associated with reactive astrogliosis which may be missed by standard DTI parameters alone. Monitoring changes in MK allows the investigation of molecular and morphological changes in vivo due to reactive astrogliosis and may complement information available from standard DTI parameters. To date the use of diffusion tensor imaging has been limited to study changes in white matter integrity following traumatic insults. Given the sensitivity of DKI to detect microstructural changes even in the gray matter in vivo, allows the extension of the technique to understand patho-morphological changes in the whole brain following a traumatic insult.

Comparisons of multi b-value DWI signal analysis with pathological specimen of breast cancer

Previous studies have reported that the signal attenuation of diffusion weighted magnetic resonance imaging for tumor tissues displays a non-monoexponential biexponential decay, and the apparent diffusion coefficients (ADCs) can be divided into a fast and slow diffusion component by using a simple biexponential decay model. The purpose of this study is to examine the non-monoexponential character of the diffusion weighted magnetic resonance imaging signal attenuations of breast cancers, estimate the fast and slow diffusion components, and compare them with the extra- and intracellular component information obtained from the pathological specimens. Twenty-two subjects having breast cancers underwent diffusion weighted magnetic resonance imaging using six b-values up to 3500 s/mm(2) and the signal attenuations were analyzed using the biexponential function. The derived slow component fraction correlated with the cellular fraction and the ADCs converged to 0.2-0.3 × 10(-3) mm(2) /s for the higher cellular fractions. The ADCs of the fast component ranged from 1.3 to 3.9 × 10(-3) mm(2) /s and showed no correlation with the extracellular components. This result suggests that the main reason for the decreasing ADC of a breast tumor is the decreasing fraction of the fast component and the increasing fraction of the slow component having a low ADC rather than the decreasing ADC of the fast component by the restricted water diffusion in the reduced extracellular spaces.

Non-Gaussian diffusion imaging: a brief practical review

The departure from purely mono-exponential decay of the signal, as observed from brain tissue following a diffusion-sensitized sequence, has prompted the search for alternative models to characterize these unconventional water diffusion dynamics. Several approaches have been proposed in the last few years. While multi-exponential models have been applied to characterize brain tissue, several unresolved controversies about the interpretations of the results have motivated the search for alternative models that do not rely on the Gaussian diffusion hypothesis. In this brief review, diffusional kurtosis imaging (DKI) and anomalous diffusion imaging (ADI) techniques are addressed and compared with diffusion tensor imaging. Theoretical and experimental issues are briefly described to allow readers to understand similarities, differences and limitations of these two non-Gaussian models. However, since the ultimate goal is to improve specificity, sensitivity and spatial localization of diffusion MRI for the detection of brain diseases, special attention will be paid on the clinical feasibility of the proposed techniques as well as on the context of brain pathology investigations.

Non-Gaussian diffusion in human brain tissue at high b-factors as examined by a combined diffusion kurtosis and biexponential diffusion tensor analysis

Diffusion tensor imaging (DTI) permits non-invasive probing of tissue microstructure and provides invaluable information in brain diagnostics. Our aim was to examine approaches capable of capturing more detailed information on the propagation mechanisms and underlying tissue microstructure in comparison to the conventional methods. In this work, we report a detailed in vivo diffusion study of the human brain in an extended range of the b-factors (up to 7000 s mm(-2)) performed on a group of 14 healthy volunteers at 3T. Combined diffusion kurtosis imaging (DKI) and biexponential diffusion tensor analysis (BEDTA) were applied to quantify the attenuation curves. New quantitative indices are suggested as map parameters and are shown to improve the underlying structure contrast in comparison to conventional DTI. In particular, fractional anisotropy maps related to the slow diffusion tensor are shown to attain significantly higher values and to substantially improve white matter mapping. This is demonstrated for the specified regions of the frontal and occipital lobes and for the anterior cingulate. The findings of this work are substantiated by the statistical analysis of the whole slice histograms averaged over 14 subjects. Colour-coded directional maps related to the fast and slow diffusion tensors in human brain tissue are constructed for the first time and these demonstrate a high degree of axial co-alignment of the two tensors in the white matter regions. It is concluded that a combined DKI and BEDTA offers a promising framework for monitoring tissue alteration during development and degeneration or as a consequence of the neurological disease.

A biexponential DWI study in rat brain intracellular oedema

PURPOSE

To examine the changes in MR parameters derived from diffusion weighted imaging (DWI) biexponential analysis in an in vivo intracellular brain oedema model, and to apply electron microscopy (EM) to shed more light on the morphological background of MR-related observations.

MATERIALS AND METHODS

Intracellular oedema was induced in ten male Wistar rats (380-450g) by way of water load, using a 20% body weight intraperitoneal injection of 140mmol/L dextrose solution. A 3T MRI instrument was used to perform serial DWI, and MR specroscopy (water signal) measurements. Following the MR examination the brains of the animals were analyzed for EM.

RESULTS

Following the water load induction, apparent diffusion coefficient (ADC) values started declining from 724±43μm(2)/s to 682±26μm(2)/s (p<0.0001). ADC-fast values dropped from 948±122 to 840±66μm(2)/s (p<0.001). ADC-slow showed a decrease from 226±66 to 191±74μm(2)/s (p<0.05). There was a shift from the slow to the fast component at 110min time point. The percentage of the fast component demonstrated moderate, yet significant increase from 76.56±7.79% to 81.2±7.47% (p<0.05). The water signal was increasing by 4.98±3.52% compared to the base line (p<0.01). The results of the E.M. revealed that water was detected intracellularly, within astrocytic preivascular end-feet and cell bodies.

CONCLUSION

The unexpected volume fraction changes (i.e. increase in fast component) detected in hypotonic oedema appear to be substantially different from those observed in stroke. It may suggest that ADC decrease in stroke, in contrast to general presumptions, cannot be explained only by water shift from extra to intracellular space (i.e. intracellular oedema).

MRI quantification of non-Gaussian water diffusion by kurtosis analysis

Quantification of non-Gaussianity for water diffusion in brain by means of diffusional kurtosis imaging (DKI) is reviewed. Diffusional non-Gaussianity is a consequence of tissue structure that creates diffusion barriers and compartments. The degree of non-Gaussianity is conveniently quantified by the diffusional kurtosis and derivative metrics, such as the mean, axial, and radial kurtoses. DKI is a diffusion-weighted MRI technique that allows the diffusional kurtosis to be estimated with clinical scanners using standard diffusion-weighted pulse sequences and relatively modest acquisition times. DKI is an extension of the widely used diffusion tensor imaging method, but requires the use of at least 3 b-values and 15 diffusion directions. This review discusses the underlying theory of DKI as well as practical considerations related to data acquisition and post-processing. It is argued that the diffusional kurtosis is sensitive to diffusional heterogeneity and suggested that DKI may be useful for investigating ischemic stroke and neuropathologies, such as Alzheimer's disease and schizophrenia.

Diffusion imaging of brain tumors

MRI offers a tremendous armamentarium of different methods that can be employed in brain tumor characterization. MR diffusion imaging has become a widely accepted method to probe for the presence of fluid pools and molecular tissue water mobility. For most clinical applications of diffusion imaging, it is assumed that the diffusion signal vs diffusion weighting factor b decays monoexponentially. Within this framework, the measurement of a single diffusion coefficient in brain tumors permits an approximate categorization of tumor type and, for some tumors, definitive diagnosis. In most brain tumors, when compared with normal brain tissue, the diffusion coefficient is elevated. The presence of peritumoral edema, which also exhibits an elevated diffusion coefficient, often precludes the delineation of the tumor on the basis of diffusion information alone. Serially obtained diffusion data are useful to document and even predict the cellular response to drug or radiation therapy. Diffusion measurements in tissues over an extended range of b factors have clearly shown that the monoparametric description of the MR diffusion signal decay is incomplete. Very high diffusion weighting on clinical systems requires substantial compromise in spatial resolution. However, after suitable analysis, superior separation of malignant brain tumors, peritumoral edema and normal brain tissue can be achieved. These findings are also discussed in the light of tissue-specific differences in membrane structure and the restrictions exerted by membranes on diffusion. Finally, measurement of the directional dependence of diffusion permits the assessment of white matter integrity and dislocation. Such information, particularly in conjunction with advanced post-processing, is considered to be immensely useful for therapy planning. Diffusion imaging, which permits monoexponential analysis and provides directional diffusion information, is performed routinely in brain tumor patients. More advanced methods require improvement in acquisition speed and spatial resolution to gain clinical acceptance.

On high b diffusion imaging in the human brain: ruminations and experimental insights

Interest in the manner in which brain tissue signal decays with b factor in diffusion imaging schemes has grown in recent years following the observation that the decay curves depart from purely monoexponential decay behavior. Regardless of the model or fitting function proposed for characterizing sufficiently sampled decay curves (vide infra), the departure from monoexponentiality spells increased tissue characterization potential. The degree to which this potential can be harnessed to improve specificity, sensitivity and spatial localization of diseases in brain, and other tissues, largely remains to be explored. Furthermore, the degree to which currently popular diffusion tensor imaging methods, including visually impressive white matter fiber "tractography" results, have almost completely ignored the nonmonoexponential nature of the basic signal decay with b factor is worthy of communal introspection. Here we limit our attention to a review of the basic experimental features associated with brain water signal diffusion decay curves as measured over extended b-factor ranges, the simple few parameter fitting functions that have been proposed to characterize these decays and the more involved models, e.g.,"ruminations," which have been proposed to account for the nonmonoexponentiality to date.