Biexponential diffusion attenuation in various states of brain tissue: implications for diffusion-weighted imaging

Characterization of cerebral white matter properties using quantitative magnetic resonance imaging stains

The image contrast in magnetic resonance imaging (MRI) is highly sensitive to several mechanisms that are modulated by the properties of the tissue environment. The degree and type of contrast weighting may be viewed as image filters that accentuate specific tissue properties. Maps of quantitative measures of these mechanisms, akin to microstructural/environmental-specific tissue stains, may be generated to characterize the MRI and physiological properties of biological tissues. In this article, three quantitative MRI (qMRI) methods for characterizing white matter (WM) microstructural properties are reviewed. All of these measures measure complementary aspects of how water interacts with the tissue environment. Diffusion MRI, including diffusion tensor imaging, characterizes the diffusion of water in the tissues and is sensitive to the microstructural density, spacing, and orientational organization of tissue membranes, including myelin. Magnetization transfer imaging characterizes the amount and degree of magnetization exchange between free water and macromolecules like proteins found in the myelin bilayers. Relaxometry measures the MRI relaxation constants T1 and T2, which in WM have a component associated with the water trapped in the myelin bilayers. The conduction of signals between distant brain regions occurs primarily through myelinated WM tracts; thus, these methods are potential indicators of pathology and structural connectivity in the brain. This article provides an overview of the qMRI stain mechanisms, acquisition and analysis strategies, and applications for these qMRI stains.

Magnetic resonance microscopy of human and porcine neurons and cellular processes

With its unparalleled ability to safely generate high-contrast images of soft tissues, magnetic resonance imaging (MRI) has remained at the forefront of diagnostic clinical medicine. Unfortunately due to resolution limitations, clinical scans are most useful for detecting macroscopic structural changes associated with a small number of pathologies. Moreover, due to a longstanding inability to directly observe magnetic resonance (MR) signal behavior at the cellular level, such information is poorly characterized and generally must be inferred. With the advent of the MR microscope in 1986 came the ability to measure MR signal properties of theretofore unobservable tissue structures. Recently, further improvements in hardware technology have made possible the ability to visualize mammalian cellular structure. In the current study, we expand upon previous work by imaging the neuronal cell bodies and processes of human and porcine α-motor neurons. Complimentary imaging studies are conducted in pig tissue in order to demonstrate qualitative similarities to human samples. Also, apparent diffusion coefficient (ADC) maps were generated inside porcine α-motor neuron cell bodies and portions of their largest processes (mean=1.7 ± 0.5 μm²/ms based on 53 pixels) as well as in areas containing a mixture of extracellular space, microvasculature, and neuropil (0.59 ± 0.37 μm²/ms based on 33 pixels). Three-dimensional reconstruction of MR images containing α-motor neurons shows the spatial arrangement of neuronal projections between adjacent cells. Such advancements in imaging portend the ability to construct accurate models of MR signal behavior based on direct observation and measurement of the components which comprise functional tissues. These tools would not only be useful for improving our interpretation of macroscopic MRI performed in the clinic, but they could potentially be used to develop new methods of differential diagnosis to aid in the early detection of a multitude of neuropathologies.

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.

Spatially variable Rician noise in magnetic resonance imaging

Magnetic resonance images tend to be influenced by various random factors usually referred to as "noise". The principal sources of noise and related artefacts can be divided into two types: arising from hardware (acquisition coil arrays, gradient coils, field inhomogeneity); and arising from the subject (physiological noise including body motion, cardiac pulsation or respiratory motion). These factors negatively affect the resolution and reproducibility of the images. Therefore, a proper noise treatment is important for improving the performance of clinical and research investigations. Noise reduction becomes especially critical for the images with a low signal-to-noise ratio, such as those typically acquired in diffusion tensor imaging at high diffusion weightings. The standard methods of signal correction usually assume a uniform distribution of the standard deviation of the noise across the image and evaluate a single correction parameter for the whole image. We pursue a more advanced approach based on the assumption of an inhomogeneous distribution of noise in space and evaluate correction factors for each voxel individually. The Rician nature of the underlying noise is considered for low and high signal-to-noise ratios. The approach developed here has been examined using numerical simulations and in vivo brain diffusion tensor imaging experiments. The efficacy and usefulness of this approach is demonstrated here and the resultant effective tool is described.

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.

Apparent diffusion coefficient with higher b-value correlates better with viable cell count quantified from the cavity of brain abscess

BACKGROUND AND PURPOSE

DWI by using higher b-values provides tissue diffusivity with less T2 shinethrough effect. VCD in the abscess cavity correlates with ADC values. The purpose of this study was to investigate which b-value-derived ADC correlates better with VCD.

MATERIALS AND METHODS

Thirty patients with brain abscess underwent conventional MR imaging and DWI with b = 1000, 2000, and 3000 s/mm(2) on a 3T MR imaging scanner. ADC values were quantified by placing regions of interest inside the abscess cavity in all sections where the lesion was apparent on coregistered ADC maps derived from different b-values. VCD was measured on pus aspirated.

RESULTS

An increase in b-value was associated with a decrease in ADC values in normal parenchyma as well as in the abscess cavity. The most significant negative correlation of VCD was observed with b = 3000 s/mm(2) (r = -0.98, P = .01).

CONCLUSIONS

VCD in the abscess cavity can be best assessed at b = 3000 s/mm(2) secondary to the reduction in the T2 shinethrough effect. DWI with b = 3000 s/mm(2) is of promising value in the assessment of the therapeutic response of brain abscess.

Diffusion MRI at 25: exploring brain tissue structure and function

Diffusion MRI (or dMRI) came into existence in the mid-1980s. During the last 25 years, diffusion MRI has been extraordinarily successful (with more than 300,000 entries on Google Scholar for diffusion MRI). Its main clinical domain of application has been neurological disorders, especially for the management of patients with acute stroke. It is also rapidly becoming a standard for white matter disorders, as diffusion tensor imaging (DTI) can reveal abnormalities in white matter fiber structure and provide outstanding maps of brain connectivity. The ability to visualize anatomical connections between different parts of the brain, non-invasively and on an individual basis, has emerged as a major breakthrough for neurosciences. The driving force of dMRI is to monitor microscopic, natural displacements of water molecules that occur in brain tissues as part of the physical diffusion process. Water molecules are thus used as a probe that can reveal microscopic details about tissue architecture, either normal or in a diseased state.

Advantages of high b-value diffusion-weighted imaging to diagnose pseudo-responses in patients with recurrent glioma after bevacizumab treatment

BACKGROUND

The diagnosis of pseudo-responses after bevacizumab treatment is difficult. Because diffusion-weighted imaging (DWI) is associated with cell density, it may facilitate the differentiation between true- and pseudo-responses. Furthermore, as high b-value DWI is even more sensitive to diffusion, it has been reported to be diagnostically useful in various clinical settings.

MATERIALS AND METHODS

Between September 2008 and May 2011, 10 patients (5 males, 5 females; age range 6-65 years) with recurrent glioma were treated with bevacizumab. All underwent pre- and post-treatment MRI including T2- or FLAIR imaging, post-gadolinium contrast T1-weighted imaging, and DWI with b-1000 and b-4000. Response rates were evaluated by MacDonald- and by response assessment in neuro-oncology working group (RANO) criteria. We also assessed the response rate by calculating the size of high intensity areas using high b-value diffusion-weighted criteria. Prognostic factors were evaluated using Kaplan-Meier survival curves (log-rank test).

RESULTS

It was easier to identify pseudo-responses with RANO- than MacDonald criteria, however the reduction of edema by bevacizumab rendered the early diagnosis of tumor progression difficult by RANO criteria. In some patients with recurrent glioma treated with bevacizumab, high b-value diffusion-weighted criteria did, while MacDonald- and RANO criteria did not identify pseudo-responses at an early point after the start of therapy.

DISCUSSION AND CONCLUSION

High b-value DWI reflects cell density more accurately than regular b-value DWI. Our findings suggest that in patients with recurrent glioma, high b-value diffusion-weighted criteria are useful for the differentiation between pseudo- and true responses to treatment with bevacizumab.

Early (72-hour) detection of radiotherapy-induced changes in an experimental tumor model using diffusion-weighted imaging, diffusion tensor imaging, and Q-space imaging parameters: a comparative study

PURPOSE

To assess and compare the potential of various diffusion-related magnetic resonance imaging (MRI) parameters to detect early radiotherapy (RT)-induced changes in tumors.

MATERIALS AND METHODS

Nineteen tumors in a rat model were imaged on a clinical 3T system before and 72 hours after a single RT session. Diffusion imaging was performed using an echo planar sequence containing 16 b-factors and six gradient directions. This allowed us to perform a tensor analysis of mono- and biexponential decays and a q-space analysis. Parametric maps (both trace and fractional anisotropy) were reconstructed for: 2-point apparent diffusion coefficient (ADC), 16-point ADC, biexponential amplitudes and ADCs, and height, width, and kurtosis of the probability density function (PDF). A texture analysis yielded quantities such as average and contrast. The sensitivity of diffusion-related parameters was quantified in terms of the mean relative difference (when comparing pre- and post-RT status).

RESULTS

Traces and anisotropies display differences in response to RT. Average traces are most sensitive for ADCs and kurtosis. Average anisotropies are all very sensitive except the slow biexponential component. The best contrast (traces) was found for the ADCs and the width of the PDF.

CONCLUSION

ADC performed well, but high b-values analysis added extra sensitive parameters for monitoring early RT-induced changes.

Diffusion, confusion and functional MRI

Diffusion MRI has been introduced in 1985 and has had a very successful life on its own. While it has become a standard for imaging stroke and white matter disorders, the borders between diffusion MRI and the general field of fMRI have always remained fuzzy. First, diffusion MRI has been used to obtain images of brain function, based on the idea that diffusion MRI could also be made sensitive to blood flow, through the intravoxel incoherent motion (IVIM) concept. Second, the IVIM concept helped better understand the contribution from different vasculature components to the BOLD fMRI signal. Third, it has been shown recently that a genuine fMRI signal can be obtained with diffusion MRI. This "DfMRI" signal is notably different from the BOLD fMRI signal, especially for its much faster response to brain activation both at onset and offset, which points out to structural changes in the neural tissues, perhaps such as cell swelling, occurring in activated neural tissue. This short article reviews the major steps which have paved the way for this exciting development, underlying how technical progress with MRI equipment has each time been instrumental to expand the horizon of diffusion MRI toward the field of fMRI.

White matter characterization with diffusional kurtosis imaging

Diffusional kurtosis imaging (DKI) is a clinically feasible extension of diffusion tensor imaging that probes restricted water diffusion in biological tissues using magnetic resonance imaging. Here we provide a physically meaningful interpretation of DKI metrics in white matter regions consisting of more or less parallel aligned fiber bundles by modeling the tissue as two non-exchanging compartments, the intra-axonal space and extra-axonal space. For the b-values typically used in DKI, the diffusion in each compartment is assumed to be anisotropic Gaussian and characterized by a diffusion tensor. The principal parameters of interest for the model include the intra- and extra-axonal diffusion tensors, the axonal water fraction and the tortuosity of the extra-axonal space. A key feature is that these can be determined directly from the diffusion metrics conventionally obtained with DKI. For three healthy young adults, the model parameters are estimated from the DKI metrics and shown to be consistent with literature values. In addition, as a partial validation of this DKI-based approach, we demonstrate good agreement between the DKI-derived axonal water fraction and the slow diffusion water fraction obtained from standard biexponential fitting to high b-value diffusion data. Combining the proposed WM model with DKI provides a convenient method for the clinical assessment of white matter in health and disease and could potentially provide important information on neurodegenerative disorders.

Diffusion imaging of whole, post-mortem human brains on a clinical MRI scanner

Diffusion imaging of post mortem brains has great potential both as a reference for brain specimens that undergo sectioning, and as a link between in vivo diffusion studies and "gold standard" histology/dissection. While there is a relatively mature literature on post mortem diffusion imaging of animals, human brains have proven more challenging due to their incompatibility with high-performance scanners. This study presents a method for post mortem diffusion imaging of whole, human brains using a clinical 3-Tesla scanner with a 3D segmented EPI spin-echo sequence. Results in eleven brains at 0.94 × 0.94 × 0.94 mm resolution are presented, and in a single brain at 0.73 × 0.73 × 0.73 mm resolution. Region-of-interest analysis of diffusion tensor parameters indicate that these properties are altered compared to in vivo (reduced diffusivity and anisotropy), with significant dependence on post mortem interval (time from death to fixation). Despite these alterations, diffusion tractography of several major tracts is successfully demonstrated at both resolutions. We also report novel findings of cortical anisotropy and partial volume effects.

Optimization of b-value sampling for diffusion-weighted imaging of the kidney

Diffusion-weighted imaging (DWI) involves data acquisitions at multiple b values. In this paper, we presented a method of selecting the b values that maximize estimation precision of the biexponential analysis of renal DWI data. We developed an error propagation factor for the biexponential model, and proposed to optimize the b-value samplings by minimizing the error propagation factor. A prospective study of four healthy human subjects (eight kidneys) was done to verify the feasibility of the proposed protocol and to assess the validity of predicted precision for DWI measures, followed by Monte Carlo simulations of DWI signals based on acquired data from renal lesions of 16 subjects. In healthy subjects, the proposed methods improved precision (P = 0.003) and accuracy (P < 0.001) significantly in region-of-interest based biexponential analysis. In Monte Carlo simulation of renal lesions, the b-sampling optimization lowered estimation error by at least 20-30% compared with uniformly distributed b values, and improved the differentiation between malignant and benign lesions significantly. In conclusion, the proposed method has the potential of maximizing the precision and accuracy of the biexponential analysis of renal DWI.

Biexponential analysis of diffusion-tensor imaging of the brain in patients with cirrhosis before and after liver transplantation

BACKGROUND AND PURPOSE

DTI has shown increased MD of water molecules in the brain of patients with cirrhosis, consistent with low-grade edema. This study further characterizes this edema by using biexponential analysis of DTI data, a technique that may differentiate cytotoxic and vasogenic edema.

MATERIALS AND METHODS

A total of 41 patients with cirrhosis awaiting liver transplantation and 16 healthy controls were studied by DTI by using a single-shot echo-planar technique with 11 b-values (range, 0-7500 s/mm(2)) and 6 noncollinear directions. Measurements were fitted to biexponential function to determine MD and FA for the fast and slow diffusion components. Regions of interest were selected in the parietal white matter and corticospinal tract. The assessment was repeated 1 year after liver transplantation in 24 of these patients.

RESULTS

In parietal white matter, patients with cirrhosis showed an increase in fast MD and a decrease in fast FA that normalized after liver transplantation. In the corticospinal tract, there was an increase in fast and slow MD that normalized after transplantation, and a decrease in FA that persisted posttransplantation. There was no association of DTI parameters with minimal HE (n =12).

CONCLUSIONS

Biexponential analysis of DTI supports the presence of edema in the brain of patients with cirrhosis that reverts after transplantation. In parietal white matter, the increase in brain water was mainly located in the interstitial compartment, while the corticospinal tract showed a mixed pattern (intra- and extracellular). In addition, the findings on posttransplantation were consistent with microstructural damage along the corticospinal tract.

Correlation of 18F-FDG uptake with apparent diffusion coefficient ratio measured on standard and high b value diffusion MRI in head and neck cancer

Although the clinical applications of (18)F-FDG PET/CT and diffusion-weighted MRI (DWI) are similar to each other in head and neck cancer, the image acquisition methods in the 2 modalities are significantly different. (18)F-FDG PET/CT traces glucose metabolism, a nonspecific process essential for tumor growth. On the other hand, DWI provides information on Brownian motion of water molecules in tissues, which represents cellularity. The aim of our study was to investigate whether apparent diffusion coefficient (ADC) values at b = 1,000 (ADC(1,000)) and 2,000 (ADC(2,000)) s/mm(2) or whether the change (ADC(ratio)) of ADC values from b = 1,000 to 2,000 s/mm(2) has any significant correlation with the standardized uptake value (SUV) in patients with head and neck squamous cell carcinoma (HNSCC).

METHODS

Our hospital's institutional review board approved this retrospective study. We included 47 patients (32 men and 15 women) with histopathologically proven HNSCC, who underwent both DWI (at both b = 1,000 s/mm(2) and b = 2,000 s/mm(2)) and (18)F-FDG PET/CT in the 2 wk before treatment. ADC(ratio) maps were generated using a pixel-by-pixel computation for which ADC(ratio) is (ADC(2,000)/ADC(1,000)) × 100. The mean ADC(1,000), ADC(2,000), and ADC(ratio) values were evaluated within a manually placed polygonal region of interest within the main tumor on every slice of the ADC(1,000), ADC(2,000), and ADC(ratio) maps, respectively. In addition, the maximal SUV (SUV(max)) and mean SUV (SUV(mean)) were measured for the entire tumor region of interest. Comparisons were made using Pearson correlation analysis, and partial correlation coefficients were derived.

RESULTS

No significant correlation was found between the mean ADC(1,000) and SUV(mean) (r = -0.222, P = 0.1325) or the mean ADC(2,000) and SUV(mean) (r = -0.1214, P = 0.4163). However, the ADC(ratio) was significantly and positively correlated to both the SUV(mean) (r = 0.667, P < 0.001) and SUV(max) (r = 0.5855, P < 0.001).

CONCLUSION

The ADC(ratio) and SUV were significantly correlated with each other in primary HNSCC patients, possibly because of a higher-cellularity region as a result of relatively increased tumor proliferation. Further studies are warranted to investigate the possible complementary role of DWI and PET/CT in various clinical settings, including staging and treatment response.

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.

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).

More accurate estimation of diffusion tensor parameters using diffusion Kurtosis imaging

With diffusion tensor imaging, the diffusion of water molecules through brain structures is quantified by parameters, which are estimated assuming monoexponential diffusion-weighted signal attenuation. The estimated diffusion parameters, however, depend on the diffusion weighting strength, the b-value, which hampers the interpretation and comparison of various diffusion tensor imaging studies. In this study, a likelihood ratio test is used to show that the diffusion kurtosis imaging model provides a more accurate parameterization of both the Gaussian and non-Gaussian diffusion component compared with diffusion tensor imaging. As a result, the diffusion kurtosis imaging model provides a b-value-independent estimation of the widely used diffusion tensor parameters as demonstrated with diffusion-weighted rat data, which was acquired with eight different b-values, uniformly distributed in a range of [0,2800 sec/mm(2)]. In addition, the diffusion parameter values are significantly increased in comparison to the values estimated with the diffusion tensor imaging model in all major rat brain structures. As incorrectly assuming additive Gaussian noise on the diffusion-weighted data will result in an overestimated degree of non-Gaussian diffusion and a b-value-dependent underestimation of diffusivity measures, a Rician noise model was used in this study.

Constrained maximum likelihood estimation of the diffusion kurtosis tensor using a Rician noise model

A computational framework to obtain an accurate quantification of the Gaussian and non-Gaussian component of water molecules' diffusion through brain tissues with diffusion kurtosis imaging, is presented. The diffusion kurtosis imaging model quantifies the kurtosis, the degree of non-Gaussianity, on a direction dependent basis, constituting a higher order diffusion kurtosis tensor, which is estimated in addition to the well-known diffusion tensor. To reconcile with the physical phenomenon of molecular diffusion, both tensor estimates should lie within a physically acceptable range. Otherwise, clinically and artificially significant changes in diffusion (kurtosis) parameters might be confounded. To guarantee physical relevance, we here suggest to estimate both diffusional tensors by maximizing the joint likelihood function of all Rician distributed diffusion weighted images given the diffusion kurtosis imaging model while imposing a set of nonlinear constraints. As shown in this study, correctly accounting for the Rician noise structure is necessary to avoid significant overestimation of the kurtosis values. The performance of the constrained estimator was evaluated and compared to more commonly used strategies during simulations. Human brain data were used to emphasize the need for constrained estimators as not imposing the constraints give rise to constraint violations in about 70% of the brain voxels.

Recent advances in diffusion MRI modeling: Angular and radial reconstruction

Recent advances in diffusion magnetic resonance image (dMRI) modeling have led to the development of several state of the art methods for reconstructing the diffusion signal. These methods allow for distinct features to be computed, which in turn reflect properties of fibrous tissue in the brain and in other organs. A practical consideration is that to choose among these approaches requires very specialized knowledge. In order to bridge the gap between theory and practice in dMRI reconstruction and analysis we present a detailed review of the dMRI modeling literature. We place an emphasis on the mathematical and algorithmic underpinnings of the subject, categorizing existing methods according to how they treat the angular and radial sampling of the diffusion signal. We describe the features that can be computed with each method and discuss its advantages and limitations. We also provide a detailed bibliography to guide the reader.

Reconstruction of the orientation distribution function in single- and multiple-shell q-ball imaging within constant solid angle

q-Ball imaging is a high-angular-resolution diffusion imaging technique that has been proven very successful in resolving multiple intravoxel fiber orientations in MR images. The standard computation of the orientation distribution function (the probability of diffusion in a given direction) from q-ball data uses linear radial projection, neglecting the change in the volume element along each direction. This results in spherical distributions that are different from the true orientation distribution functions. For instance, they are neither normalized nor as sharp as expected and generally require postprocessing, such as artificial sharpening. In this paper, a new technique is proposed that, by considering the solid angle factor, uses the mathematically correct definition of the orientation distribution function and results in a dimensionless and normalized orientation distribution function expression. Our model is flexible enough so that orientation distribution functions can be estimated either from single q-shell datasets or by exploiting the greater information available from multiple q-shell acquisitions. We show that the latter can be achieved by using a more accurate multiexponential model for the diffusion signal. The improved performance of the proposed method is demonstrated on artificial examples and high-angular-resolution diffusion imaging data acquired on a 7-T magnet.

A simple method for rectified noise floor suppression: Phase-corrected real data reconstruction with application to diffusion-weighted imaging

Diffusion-weighted MRI is an intrinsically low signal-to-noise ratio application due to the application of diffusion-weighting gradients and the consequent longer echo times. The signal-to-noise ratio worsens with increasing image resolution and diffusion imaging methods that use multiple and higher b-values. At low signal-to-noise ratios, standard magnitude reconstructed diffusion-weighted images are confounded by the existence of a rectified noise floor, producing poor estimates of diffusion metrics. Herein, we present a simple method of rectified noise floor suppression that involves phase correction of the real data. This approach was evaluated for diffusion-weighted imaging data, obtained from ethanol and water phantoms and the brain of a healthy volunteer. The parameter fits from monoexponential, biexponential, and stretched-exponential diffusion models were computed using phase-corrected real data and magnitude data. The results demonstrate that this newly developed simple approach of using phase-corrected real images acts to reduce or even suppress the confounding effects of a rectified noise floor, thereby producing more accurate estimates of diffusion parameters.

[Analyses of restricted diffusion of water molecules using trabecular bone phantom]

We have reported that the apparent diffusion coefficient (ADC) was correlated with bone mineral density, but the relation between the restricted diffusion of the water molecules and the trabecular bone structure was unclear. The purpose of our study is to clarify this relationship using two component analyses with an original phantom. With an increase in the interspace area of the simulated trabecular bone, the ADC of the fast component was increased, and the fraction of the fast component was also increased. On the other hand, with an increase in the interspace area of the simulated trabecular bone, the ADC of the slow component was decreased, and the fraction of the slow component was increased. Moreover, the ADC and fraction of the dry vertebral bone agreed with those of the simulated trabecular bone. This result means that our phantoms can reproduce the actual trabecular bone structure, which induces the restricted diffusion. The diffusion of the water molecules was separated into fast and slow components because of the restricted diffusion of the trabecular bone structure. Our original phantom enables analyzing restricted diffusion, and this analytical method obtains more detailed information on trabecular bone structure.

Magnetic resonance imaging: a potential tool in assessing the addition of hyperthermia to neoadjuvant therapy in patients with locally advanced breast cancer

The poor overall survival for patients with locally advanced breast cancers has led over the past decade to the introduction of numerous neoadjuvant combined therapy regimens to down-stage the disease before surgery. At the same time, more evidence suggests the need for treatment individualisation with a wide variety of new targets for cancer therapeutics and also multi modality therapies. In this context, early determination of whether the patient will fail to respond can enable the use of alternative therapies that can be more beneficial. The purpose of this review is to examine the potential role of magnetic resonance imaging (MRI) in early prediction of treatment response and prognosis of overall survival in locally advanced breast cancer patients enrolled on multi modality therapy trials that include hyperthermia. The material is organised with a review of dynamic contrast (DCE)-MRI and diffusion weighted (DW)-MRI for characterisation of phenomenological parameters of tumour physiology and their potential role in estimating therapy response. Most of the work published in this field has focused on responses to neoadjuvant chemotherapy regimens alone, so the emphasis will be there, however the available data that involves the addition of hyperthermia to the regimen will be discussed The review will also include future directions that include the potential use of MRI imaging techniques in establishing the role of hyperthermia alone in modifying breast tumour microenvironment, together with specific challenges related to performing such studies.

Effects of intracellular organelles on the apparent diffusion coefficient of water molecules in cultured human embryonic kidney cells

The apparent diffusion coefficient (ADC) of water in tissues is dependent on the size and spacing of structures in the cellular environment and has been used to characterize pathological changes in stroke and cancer. However, the factors that affect ADC values remain incompletely understood. Measurements of ADC are usually made using relatively long diffusion times; so they reflect the integrated effects of cellular structures over a broad range of spatial scales. We used temporal diffusion spectroscopy to study diffusion in packed cultured human embryonic kidney cells over a range of effective diffusion times following microtubule and actin/cytoskeleton depolymerization and disassembly of the Golgi complex. While Golgi disruption did not change ADC, depolymerization of the microtubule and the actin filament networks caused small decreases in ADC at short diffusion times only. Temporal diffusion spectroscopy provided a novel way to assess intracellular influences on the diffusion properties of tissue water.

Assessment of multiexponential diffusion features as MRI cancer therapy response metrics

The aim of this study was to empirically test the effect of chemotherapy-induced tissue changes in a glioma model as measured by several diffusion indices calculated from nonmonoexponential formalisms over a wide range of b-values. We also compared these results to the conventional two-point apparent diffusion coefficient calculation using nominal b-values. Diffusion-weighted imaging was performed over an extended range of b-values (120-4000 sec/mm(2) ) on intracerebral rat 9L gliomas before and after a single dose of 1,3-bis(2-chloroethyl)-1-nitrosourea. Diffusion indices from three formalisms of diffusion-weighted signal decay [(a) two-point analytical calculation using either low or high b-values, (b) a stretched exponential formalism, and (c) a biexponential fit] were tested for responsiveness to therapy-induced differences between control and treated groups. Diffusion indices sensitive to "fast diffusion" produced the largest response to treatment, which resulted in significant differences between groups. These trends were not observed for "slow diffusion" indices. Although the highest rate of response was observed from the biexponential formalism, this was not found to be significantly different from the conventional monoexponential apparent diffusion coefficient method. In conclusion, parameters from the more complicated nonmonoexponential formalisms did not provide additional sensitivity to treatment response in this glioma model beyond that observed from the two-point conventional monoexponential apparent diffusion coefficient method.

Evaluating the accuracy and precision of a two-compartment Kärger model using Monte Carlo simulations

Specific parameters of the neuronal tissue microstructure, such as axonal diameters, membrane permeability and intracellular water fractions are assessable using diffusion MRI. These parameters are commonly estimated using analytical models, which may introduce bias in the estimated parameters due to the approximations made when deriving the models. As an alternative to using analytical models, a database of signal curves generated by fast Monte Carlo simulations can be employed. Simulated diffusion MRI measurements were generated and evaluated using the two-compartment Kärger model as well as the simulation model based on a database containing signal curves from approximately 60000 simulations performed with different combinations of microstructural parameters. A protocol based on a pulsed gradient spin echo sequence with diffusion times of 30 and 60 ms and with gradient amplitudes obtainable with a clinical MRI scanner was employed for the investigations. When using the analytical model, a major negative bias (up to approximately 25%) in the estimated intracellular volume fraction was observed for short exchange times, while almost no bias was seen for the simulation model. In general, the simulation model improved the accuracy of the estimated parameters as compared to the analytical model, except for the exchange time parameter.

From single-pulsed field gradient to double-pulsed field gradient MR: gleaning new microstructural information and developing new forms of contrast in MRI

One of the hallmarks of diffusion NMR and MRI is its ability to utilize restricted diffusion to probe compartments much smaller than the excited volume or the MRI voxel, respectively, and to extract microstructural information from them. Single-pulsed field gradient (s-PFG) MR methodologies have been employed with great success to probe microstructures in various disciplines, ranging from chemistry to neuroscience. However, s-PFG MR also suffers from inherent shortcomings, especially when specimens are characterized by orientation or size distributions: in such cases, the microstructural information available from s-PFG experiments is limited or lost. Double-pulsed field gradient (d-PFG) MR methodology, an extension of s-PFG MR, has attracted attention owing to recent theoretical studies predicting that it can overcome certain inherent limitations of s-PFG MR. In this review, we survey the microstructural features that can be obtained from conventional s-PFG methods in the different q regimes, and highlight its limitations. The experimental aspects of d-PFG methodology are then presented, together with an overview of its theoretical underpinnings and a general framework for relating the MR signal decay and material microstructure, affording new microstructural parameters. We then discuss recent studies that have validated the theory using phantoms in which the ground truth is well known a priori, a crucial step prior to the application of d-PFG methodology in neuronal tissue. The experimental findings are in excellent agreement with the theoretical predictions and reveal, inter alia, zero-crossings of the signal decay, robustness towards size distributions and angular dependences of the signal decay from which accurate microstructural parameters, such as compartment size and even shape, can be extracted. Finally, we show some initial findings in d-PFG MR imaging. This review lays the foundation for future studies, in which accurate and novel microstructural information could be extracted from complex biological specimens, eventually leading to new forms of contrast in MRI.

MR diffusion kurtosis imaging for neural tissue characterization

In conventional diffusion tensor imaging (DTI), water diffusion distribution is described as a 2nd-order three-dimensional (3D) diffusivity tensor. It assumes that diffusion occurs in a free and unrestricted environment with a Gaussian distribution of diffusion displacement, and consequently that diffusion weighted (DW) signal decays with diffusion factor (b-value) monoexponentially. In biological tissue, complex cellular microstructures make water diffusion a highly hindered or restricted process. Non-monoexponential decays are experimentally observed in both white matter and gray matter. As a result, DTI quantitation is b-value dependent and DTI fails to fully utilize the diffusion measurements that are inherent to tissue microstructure. Diffusion kurtosis imaging (DKI) characterizes restricted diffusion and can be readily implemented on most clinical scanners. It provides a higher-order description of water diffusion process by a 2nd-order 3D diffusivity tensor as in conventional DTI together with a 4th-order 3D kurtosis tensor. Because kurtosis is a measure of the deviation of the diffusion displacement profile from a Gaussian distribution, DKI analyses quantify the degree of diffusion restriction or tissue complexity without any biophysical assumption. In this work, the theory of diffusion kurtosis and DKI including the directional kurtosis analysis is revisited. Several recent rodent DKI studies from our group are summarized, and DKI and DTI compared for their efficacy in detecting neural tissue alterations. They demonstrate that DKI offers a more comprehensive approach than DTI in describing the complex water diffusion process in vivo. By estimating both diffusivity and kurtosis, it may provide improved sensitivity and specificity in MR diffusion characterization of neural tissues.

Voxel-based analysis of the diffusion tensor

INTRODUCTION

Diffusion tensor imaging (DTI) has provided important insights into the neurobiological basis for normal development and aging and various disease processes in the central nervous system. The aim of this article is to review the current protocols for DTI acquisition and preprocessing and statistical testing for a voxelwise analysis of DTI, focused on statistical parametric mapping (SPM) and tract-based spatial statistics (TBSS).

METHODS

We tested the effects of distortion correction induced by gradient nonlinearity on fractional anisotropy (FA) maps or FA skeletons processed via two SPM-based methods (coregistration and FA template methods), or TBSS-based method, respectively.

RESULTS

With two SPM-based methods, we found similar results in some points (e.g., significant FA elevation for uncorrected images in anterior-dominant white matter and for corrected images in bilateral middle cerebellar peduncles) and different results in other points (e.g., significantly larger FA for corrected images with coregistration method, but significantly smaller with FA template method in bilateral internal capsules, extending to corona radiata, and semioval centers). In contrast, there was no area with significant difference between uncorrected and corrected FA skeletons with TBSS-based method.

CONCLUSION

The discrepancy among these results was not explained in full, but possible explanations were misregistration and smoothing for the SPM-based methods and insensitivity to FA changes outside the local centers of white matter bundles for TBSS-based method.

Pulsed-gradient spin-echo monitoring of restricted diffusion in multilayered structures

A general mathematical basis is developed for computation of the pulsed-gradient spin-echo signal attenuated due to restricted diffusion in multilayered structures (e.g., multiple slabs, cylindrical or spherical shells). Individual layers are characterized by (different) diffusion coefficients and relaxation times, while boundaries between adjacent layers are characterized by (different) permeabilities. Arbitrary temporal profile of the applied magnetic field can be incorporated. The signal is represented in a compact matrix form and the explicit analytical formulas for the elements of the underlying matrices are derived. The implemented algorithm is faster and much more accurate than classical techniques such as Monte Carlo simulations or numerical resolutions of the Bloch-Torrey equation. The algorithm can be applied for studying restricted diffusion in biological systems which exhibit a multilayered structure such as composite tissues, axons and living cells.

Theoretical models of the diffusion weighted MR signal

Diffusion MRI plays a very important role in studying biological tissue structure and functioning both in health and disease. Proper interpretation of experimental data requires development of theoretical models that connect the diffusion MRI signal to salient features of tissue microstructure at the cellular level. In this review, we present some models (mostly, relevant to the brain) for describing diffusion attenuated MR signals. These range from the simplest approach, where the signal is described in terms of an apparent diffusion coefficient, to rather complicated models, where consideration is given to signals originating from extra- and intracellular spaces and where account is taken of the specific geometry and orientation distribution of cells. To better understand the characteristics of the diffusion attenuated MR signal arising from the complex structure of whole tissue, it is instructive to appreciate first the characteristics of the signal arising from simple single-cell-like structures. For this purpose, we also present here a theoretical analysis of models allowing exact analytical calculation of the MR signal, specifically, a single-compartment model with impermeable boundaries and a periodic structure of identical cells separated by permeable membranes. Such pure theoretical models give important insights into mechanisms contributing to the MR signal formation in the presence of diffusion. In this review we targeted both scientists just entering the MR field and more experienced MR researchers interested in applying diffusion methods to study biological tissues.

BOLD background gradient contributions in diffusion-weighted fMRI--comparison of spin-echo and twice-refocused spin-echo sequences

The interaction ('cross terms') between diffusion-weighting gradients and susceptibility-induced background gradient fields around vessels has an impact on apparent diffusion coefficient (ADC) measurements and diffusion-weighted functional magnetic resonance imaging (DFMRI) experiments. Monte-Carlo (MC) simulations numerically integrating the Bloch equations for a large number of random walks in a vascular model were used to investigate to what extent such interactions would influence the extravascular signal change as well as the ADC change observed in DFMRI experiments. The vascular model consists of a set of independent, randomly oriented, infinite cylinders whose internal magnetic susceptibility varies as the state changes between rest and activation. In such a network, the cross terms result in the observation of a functional increase in ADC accompanied by a descending percent signal change with increasing diffusion weighting. It is shown that the twice-refocused spin-echo sequence permits sufficient yet not total suppression of such effects compared to the standard Stejskal-Tanner spin-echo diffusion weighting under experimentally relevant conditions.

Diffusion-weighted (DW) and dynamic contrast-enhanced (DCE) magnetic resonance imaging (MRI) for monitoring anticancer therapy

There is an increasing awareness that anatomical approaches based on measurements of tumor size have significant limitations for assessing therapy response. Functional imaging techniques are increasing being used to monitor response to therapies with novel mechanisms of action, often predicting the success of therapy before conventional measurements have changed. Dynamic contrast-enhanced and diffusion magnetic resonance imaging (MRI) are the most advanced in their evidence base, and in this manuscript we focus on them as response parameters. Technology, data gathering methods, and current limitations for these techniques are addressed. With few exceptions, most studies shows that successful treatment is reflected by increases in tumor water diffusion values visible as increased apparent diffusion coefficient values. Most response assessment studies also show that successful treatment results in decreases in tumor vascularization and microvessel permeability.