Self-diffusion in CNS tissue by volume-selective proton NMR

In vivo Correlation Tensor MRI reveals microscopic kurtosis in the human brain on a clinical 3T scanner

Diffusion MRI (dMRI) has become one of the most important imaging modalities for noninvasively probing tissue microstructure. Diffusional Kurtosis MRI (DKI) quantifies the degree of non-gaussian diffusion, which in turn has been shown to increase sensitivity towards, e.g., disease and orientation mapping in neural tissue. However, the specificity of DKI is limited as different sources can contribute to the total intravoxel diffusional kurtosis, including: variance in diffusion tensor magnitudes (K_iso), variance due to diffusion anisotropy (K_aniso), and microscopic kurtosis (μK) related to restricted diffusion, microstructural disorder, and/or exchange. Interestingly, μK is typically ignored in diffusion MRI signal modeling as it is assumed to be negligible in neural tissues. However, recently, Correlation Tensor MRI (CTI) based on Double-Diffusion-Encoding (DDE) was introduced for kurtosis source separation, revealing non negligible μK in preclinical imaging. Here, we implemented CTI for the first time on a clinical 3T scanner and investigated the sources of total kurtosis in healthy subjects. A robust framework for kurtosis source separation in humans is introduced, followed by estimation of μK (and the other kurtosis sources) in the healthy brain. Using this clinical CTI approach, we find that μK significantly contributes to total diffusional kurtosis both in gray and white matter tissue but, as expected, not in the ventricles. The first μK maps of the human brain are presented, revealing that the spatial distribution of μK provides a unique source of contrast, appearing different from isotropic and anisotropic kurtosis counterparts. Moreover, group average templates of these kurtosis sources have been generated for the first time, which corroborated our findings at the underlying individual-level maps. We further show that the common practice of ignoring μK and assuming the multiple gaussian component approximation for kurtosis source estimation introduces significant bias in the estimation of other kurtosis sources and, perhaps even worse, compromises their interpretation. Finally, a twofold acceleration of CTI is discussed in the context of potential future clinical applications. We conclude that CTI has much potential for future in vivo microstructural characterizations in healthy and pathological tissue.

Beyond the diffusion standard model in fixed rat spinal cord with combined linear and planar encoding

Information about tissue on the microscopic and mesoscopic scales can be accessed by modelling diffusion MRI signals, with the aim of extracting microstructure-specific biomarkers. The standard model (SM) of diffusion, currently the most broadly adopted microstructural model, describes diffusion in white matter (WM) tissues by two Gaussian components, one of which has zero radial diffusivity, to represent diffusion in intra- and extra-axonal water, respectively. Here, we reappraise these SM assumptions by collecting comprehensive double diffusion encoded (DDE) MRI data with both linear and planar encodings, which was recently shown to substantially enhance the ability to estimate SM parameters. We find however, that the SM is unable to account for data recorded in fixed rat spinal cord at an ultrahigh field of 16.4 T, suggesting that its underlying assumptions are violated in our experimental data. We offer three model extensions to mitigate this problem: first, we generalize the SM to accommodate finite radii (axons) by releasing the constraint of zero radial diffusivity in the intra-axonal compartment. Second, we include intracompartmental kurtosis to account for non-Gaussian behaviour. Third, we introduce an additional (third) compartment. The ability of these models to account for our experimental data are compared based on parameter feasibility and Bayesian information criterion. Our analysis identifies the three-compartment description as the optimal model. The third compartment exhibits slow diffusion with a minor but non-negligible signal fraction (∼12%). We demonstrate how failure to take the presence of such a compartment into account severely misguides inferences about WM microstructure. Our findings bear significance for microstructural modelling at large and can impact the interpretation of biomarkers extracted from the standard model of diffusion.

In vivo observation and biophysical interpretation of time-dependent diffusion in human cortical gray matter

The dependence of the diffusion MRI signal on the diffusion time t is a hallmark of tissue microstructure at the scale of the diffusion length. Here we measure the time-dependence of the mean diffusivity D(t) and mean kurtosis K(t) in cortical gray matter and in 25 ​gray matter sub-regions, in 10 healthy subjects. Significant diffusivity and kurtosis time-dependence is observed for t=21.2-100 ​ms, and is characterized by a power-law tail ∼t-ϑ with dynamical exponent ϑ. To interpret our measurements, we systematize the relevant scenarios and mechanisms for diffusion time-dependence in the brain. Using the effective medium theory formalism, we derive an exact relation between the power-law tails in D(t) and K(t). The estimated dynamical exponent ϑ≃1/2 in both D(t) and K(t) is consistent with one-dimensional diffusion in the presence of randomly positioned restrictions along neurites. We analyze the short-range disordered statistics of synapses on axon collaterals in the cortex, and perform one-dimensional Monte Carlo simulations of diffusion restricted by permeable barriers with a similar randomness in their placement, to confirm the ϑ=1/2 exponent. In contrast, the Kärger model of exchange is less consistent with the data since it does not capture the diffusivity time-dependence, and the estimated exchange time from K(t) falls below our measured t-range. Although we cannot exclude exchange as a contributing factor, we argue that structural disorder along neurites is mainly responsible for the observed time-dependence of diffusivity and kurtosis. Our observation and theoretical interpretation of the t-1/2 tail in D(t) and K(t) altogether establish the sensitivity of a macroscopic MRI signal to micrometer-scale structural heterogeneities along neurites in human gray matter in vivo.

Quantifying brain microstructure with diffusion MRI: Theory and parameter estimation

We review, systematize and discuss models of diffusion in neuronal tissue, by putting them into an overarching physical context of coarse-graining over an increasing diffusion length scale. From this perspective, we view research on quantifying brain microstructure as occurring along three major avenues. The first avenue focusses on transient, or time-dependent, effects in diffusion. These effects signify the gradual coarse-graining of tissue structure, which occurs qualitatively differently in different brain tissue compartments. We show that transient effects contain information about the relevant length scales for neuronal tissue, such as the packing correlation length for neuronal fibers, as well as the degree of structural disorder along the neurites. The second avenue corresponds to the long-time limit, when the observed signal can be approximated as a sum of multiple nonexchanging anisotropic Gaussian components. Here, the challenge lies in parameter estimation and in resolving its hidden degeneracies. The third avenue employs multiple diffusion encoding techniques, able to access information not contained in the conventional diffusion propagator. We conclude with our outlook on future directions that could open exciting possibilities for designing quantitative markers of tissue physiology and pathology, based on methods of studying mesoscopic transport in disordered systems.

Improved stimulated echo in diffusion magnetic resonance imaging: introducing a π pulse for SNR enhancement

PURPOSE

Anomalous diffusion in biological tissues can be examined by diffusion MRI for various applications, including tumor diagnosis and measurement of brain fiber pathways. However, the measurement of anomalous diffusion requires high b-values for the diffusion gradient in MRI, and current MRI methods cannot provide a high SNR. This study aimed to improve on the standard stimulated echo (STE) to enhance the SNR in diffusion MRI with high b-values.

METHODS

Because of hardware limitations and human safety considerations, prolonging the diffusion time (Δ) is 1 of the few methods available to realize high b-values. Here, we propose a new echo mechanism for diffusion MRI to enhance SNRs under long Δ. By introducing a π pulse at the midpoint between 2nd and 3rd π/2 pulses of STE, we refocus the magnetic moment vectors in the longitudinal plane before the third π/2 pulse is applied, which preserves the full echo signals. This sequence was compared with STE and spin echo (SE). Nine Δs were tested in a phantom. Multi b-values with 2 Δs were tested in a mouse liver, brain, and tumor.

RESULTS

Compared with STE and SE, the proposed improved STE (ISTE) exhibited an improved SNR in the phantom experiment and improved performance in the in vivo experiments.

CONCLUSION

By using the proposed echo mechanism in diffusion MRI, we enhanced the SNR of the images, which enables us to investigate diffusion behavior at higher b-values and further facilitates the development of quantitative diffusion MRI and radiomics.

Diffusion time dependence of microstructural parameters in fixed spinal cord

Biophysical modelling of diffusion MRI is necessary to provide specific microstructural tissue properties. However, estimating model parameters from data with limited diffusion gradient strength, such as clinical scanners, has proven unreliable due to a shallow optimization landscape. On the other hand, estimation of diffusion kurtosis (DKI) parameters is more robust, and its parameters may be connected to microstructural parameters, given an appropriate biophysical model. However, it was previously shown that this procedure still does not provide sufficient information to uniquely determine all model parameters. In particular, a parameter degeneracy related to the relative magnitude of intra-axonal and extra-axonal diffusivities remains. Here we develop a model of diffusion in white matter including axonal dispersion and demonstrate stable estimation of all model parameters from DKI in fixed pig spinal cord. By employing the recently developed fast axisymmetric DKI, we use stimulated echo acquisition mode to collect data over a two orders of magnitude diffusion time range with very narrow diffusion gradient pulses, enabling finely resolved measurements of diffusion time dependence of both net diffusion and kurtosis metrics, as well as model intra- and extra-axonal diffusivities, and axonal dispersion. Our results demonstrate substantial time dependence of all parameters except volume fractions, and the additional time dimension provides support for intra-axonal diffusivity to be larger than extra-axonal diffusivity in spinal cord white matter, although not unambiguously. We compare our findings for the time-dependent compartmental diffusivities to predictions from effective medium theory with reasonable agreement.

What dominates the time dependence of diffusion transverse to axons: Intra- or extra-axonal water?

Brownian motion of water molecules provides an essential length scale, the diffusion length, commensurate with cell dimensions in biological tissues. Measuring the diffusion coefficient as a function of diffusion time makes in vivo diffusion MRI uniquely sensitive to the cellular features about three orders of magnitude below imaging resolution. However, there is a longstanding debate, regarding which contribution - intra- or extra-cellular - is more relevant in the overall time-dependence of the MRI-derived diffusion metrics. Here we resolve this debate in the human brain white matter. By varying not just the diffusion time, but also the gradient pulse duration of a standard diffusion MRI sequence, we identify a functional form of the measured time-dependent diffusion coefficient transverse to white matter tracts in 10 healthy volunteers. This specific functional form is shown to originate from the extra-axonal space, and provides estimates of the fiber packing correlation length for axons in a bundle. Our results offer a metric for the outer axonal diameter, a promising candidate marker for demyelination in neurodegenerative diseases. From the methodological perspective, our analysis demonstrates how competing models, which describe different physics yet interpolate standard measurements equally well, can be distinguished based on their prediction for an independent "orthogonal" measurement.

Comparison of T2, T1rho, and diffusion metrics in assessment of liver fibrosis in rats

PURPOSE

To evaluate the value of T₂ , T₁ rho, and diffusion metrics in assessment of liver fibrosis in rats.

MATERIALS AND METHODS

Liver fibrosis in a rat model (n = 72) was induced by injection of carbon tetrachloride (CCl₄ ) at 3T. T₂ , T₁ rho, and diffusion parameters (apparent diffusion coefficient (ADC), D_true ) via spin echo (SE) diffusion-weighted imaging (DWI) and stimulated echo acquisition mode (STEAM) DWI with three diffusion times (DT: 80, 106, 186 msec) were obtained in surviving rats with hepatic fibrosis (n = 52) and controls (n = 8). Liver fibrosis stage (F0-F6) was identified based on pathological results using the traditional liver fibrosis staging method for rodents. Nonparametric statistical methods and receiver operating characteristic (ROC) curve analysis were employed to determine the diagnostic accuracy.

RESULTS

Mean T₂ , T₁ rho, ADC, and D_true with DT = 186 msec correlated with the severity of fibrosis with r = 0.73, 0.83, -0.83, and -0.85 (all P < 0.001), respectively. The average areas under the ROC curve at different stages for T₁ rho and diffusion parameters (DT = 186 msec) were larger than those of T₂ and SE DWI (0.92, 0.92, and 0.92 vs. 0.86, 0.82, and 0.83). The corresponding average sensitivity and specificity for T₁ rho and diffusion parameters with a long DT were larger (89.35 and 88.90, 88.36 and 89.97, 90.16 and 87.13) than T₂ and SE DWI (90.28 and 79.93, 85.30 and 77.64, 78.21 and 82.41). The performances of T₁ rho and D_true (DT = 186 msec) were comparable (average AUC: 0.92 and 0.92).

CONCLUSION

Among the evaluated sequences, T₁ rho and STEAM DWI with a long DT may serve as superior imaging biomarkers for assessing liver fibrosis and monitoring disease severity.

LEVEL OF EVIDENCE

1 J. Magn. Reson. Imaging 2017;45:741-750.

In vivo observation and biophysical interpretation of time-dependent diffusion in human white matter

The presence of micrometer-level restrictions leads to a decrease of diffusion coefficient with diffusion time. Here we investigate this effect in human white matter in vivo. We focus on a broad range of diffusion times, up to 600 ms, covering diffusion length scales up to about 30 μm. We perform stimulated echo diffusion tensor imaging on 5 healthy volunteers and observe a relatively weak time-dependence in diffusion transverse to major fiber tracts. Remarkably, we also find notable time-dependence in the longitudinal direction. Comparing models of diffusion in ordered, confined and disordered media, we argue that the time-dependence in both directions can arise due to structural disorder, such as axonal beads in the longitudinal direction, and the random packing geometry of fibers within a bundle in the transverse direction. These time-dependent effects extend beyond a simple picture of Gaussian compartments, and may lead to novel markers that are specific to neuronal fiber geometry at the micrometer scale.

Mesoscopic structure of neuronal tracts from time-dependent diffusion

Interpreting brain diffusion MRI measurements in terms of neuronal structure at a micrometer level is an exciting unresolved problem. Here we consider diffusion transverse to a bundle of fibers, and show theoretically, as well as using Monte Carlo simulations and measurements in a phantom made of parallel fibers mimicking axons, that the time dependent diffusion coefficient approaches its macroscopic limit slowly, in a (ln t)/t fashion. The logarithmic singularity arises due to short range disorder in the fiber packing. We identify short range disorder in axonal fibers based on histological data from the splenium, and argue that the time dependent contribution to the overall diffusion coefficient from the extra-axonal water dominates that of the intra-axonal water. This dominance may explain the bias in measuring axon diameters in clinical settings. The short range disorder is also reflected in the asymptotically linear frequency dependence of the diffusion coefficient measured with oscillating gradients, in agreement with recent experiments. Our results relate the measured diffusion to the mesoscopic structure of neuronal tissue, uncovering the sensitivity of diffusion metrics to axonal arrangement within a fiber tract, and providing an alternative interpretation of axonal diameter mapping techniques.

In vivo investigation of restricted diffusion in the human brain with optimized oscillating diffusion gradient encoding

PURPOSE

Previous studies in phantoms and animals using animal MR systems have shown promising results in using oscillating gradient spin echo (OGSE) diffusion acquisition to depict microstructure information. The OGSE approach has also been shown to be a sensitive biomarker of tumor treatment response and white matter-related diseases. Translating these studies to a human MR scanner faces multiple challenges due to the much weaker gradient system. The goals of this study are to optimize the OGSE acquisition for a human MR system and investigate its applicability in the in vivo human brain.

METHODS

An analytical analysis of the OGSE modulation spectrum was provided. Based on this analysis and thorough simulation experiments, the OGSE acquisition was optimized in terms of diffusion waveform shape, waveform timing, and sequence timing-to achieve higher diffusion sensitivity and better sampling of the diffusion spectrum.

RESULTS

The trapezoid-cosine waveform was found to be the optimal OGSE waveform. At the three employed peak encoding frequencies of 18 Hz, 44 Hz, and 63 Hz, the waveform polarity for the least blurry sampling of the diffusion spectrum was 90+/180-, 90+/180+, and 90+/180+, respectively. For the highest diffusion-to-noise ratio at 63 Hz, the b-value was 200 s/mm(2) and the echo time was 116 ms. Using the optimized sequence, a frequency dependence of the measured apparent diffusion coefficients was observed in white matter-dominant regions such as the corpus callosum.

CONCLUSION

The obtained results demonstrate, for the first time, the potential of using an OGSE acquisition for investigating microstructure information on a human MR system.

Diffusion Tensor Metric Measurements as a Function of Diffusion Time in the Rat Central Nervous System

MRI and Monte Carlo simulated data of pulsed gradient spin echo experiments were used to study the effects of diffusion time, gradient strength and b-value on diffusion tensor (DT) metrics using real and simulated fixed rat spines. Radial (λ⊥) in grey matter and simulation data, axial (λ||) in both grey and white matter in fixed rat spinal cords and mean diffusivity in all tissues showed a significant decrease with diffusion time at b = 1 μm2/ms. All diffusivities significantly decreased with b-value at g = 116 mT/m and at Δeff = 23 ms. The fractional anisotropy (FA) significantly increased with diffusion time at b = 1 μm2/ms in the simulation data and grey matter. FA significantly increased in white matter and simulation data and significantly decreased in grey matter with b-value at g = 116 mT/m and at Δeff = 23 ms. These data suggest that DTI metrics are highly dependent on pulse sequence parameters.

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.

DTI at long diffusion time improves fiber tracking

While diffusion-tensor-imaging tractography provides remarkable in vivo anatomical connectivity of the central nervous system, the majority of DTI studies to date are predominantly limited to tracking large white-matter fibers. This study investigated DTI tractography using long diffusion time (t(diff)) to improve tracking of thinner fibers in fixed rhesus monkey brains. Stimulated Echo Acquisition Mode (STEAM) sequence on a 3T Siemens TRIO was modified to include a diffusion module. DTI was acquired using STEAM with t(diff) of 48 and 192 ms with matched signal-to-noise ratios (SNR). Comparisons were also made with the conventional double-spin echo (DSE) at a short t(diff) of 45 ms. Not only did the fractional anisotropy increase significantly with the use of long diffusion time, but directional entropy measures indicated that there was an increased coherence amongst neighboring tensors. Further, the magnitude of the major eigenvector was larger at the t(diff) = 192 ms as compared to the short t(diff). Probabilistic connectivity maps at long t(diff) showed larger areas of connectivity with the use of long diffusion time, which traversed deeper into areas of low anisotropy. With tractography, it was found that the length of the fibers, increased by almost 10% in the callosal fibers that branch into the paracentral gyrus, the precentral gyrus and the post central gyrus. A similar increase of about 20% was observed in the fibers of the internal capsule. These findings offer encouraging data that DTI at long diffusion time could improve tract tracing of small fibers in areas of low fractional anisotropy (FA), such as at the interfaces of white matter and grey matter.

A tensor model and measures of microscopic anisotropy for double-wave-vector diffusion-weighting experiments with long mixing times

Experiments with two diffusion-weighting periods applied successively in a single experiment, so-called double-wave-vector (DWV) diffusion-weighting experiments, are a promising tool for the investigation of material or tissue structure on a microscopic level, e.g. to determine cell or compartment sizes or to detect pore or cell anisotropy. However, the theoretical descriptions presented so far for experiments that aim to investigate the microscopic anisotropy with a long mixing time between the two diffusion weightings, are limited to certain wave vector orientations, specific pore shapes, and macroscopically isotropic samples. Here, the signal equations for fully restricted diffusion are re-investigated in more detail. A general description of the signal behavior for arbitrary wave vector directions, pore or cell shapes, and orientation distributions of the pores or cells is obtained that involves a fourth-order tensor approach. From these equations, a rotationally invariant measure of the microscopic anisotropy, termed MA, is derived that yields information complementary to that of the (macroscopic) anisotropy measures of standard diffusion-tensor acquisitions. Furthermore, the detailed angular modulation for arbitrary cell shapes with an isotropic orientation distribution is derived. Numerical simulations of the MR signal with a Monte-Carlo algorithms confirm the theoretical considerations. The extended theoretical description and the introduction of a reliable measure of the microscopic anisotropy may help to improve the applicability and reliability of corresponding experiments.

Modeling dendrite density from magnetic resonance diffusion measurements

Diffusion-weighted imaging (DWI) provides a noninvasive tool to probe tissue microstructure. We propose a simplified model of neural cytoarchitecture intended to capture the essential features important for water diffusion as measured by NMR. Two components contribute to the NMR signal in this model: (i) the dendrites and axons, which are modeled as long cylinders with two diffusion coefficients, parallel (D(L)) and perpendicular (D(T)) to the cylindrical axis, and (ii) an isotropic monoexponential diffusion component describing water diffusion within and across all other structures, i.e., in extracellular space and glia cells. The model parameters are estimated from 153 diffusion-weighted images acquired from a formalin-fixed baboon brain. A close correspondence between the data and the signal model is found, with the model parameters consistent with literature values. The model provides an estimate of dendrite density from noninvasive MR diffusion measurements, a parameter likely to be of value for understanding normal as well as abnormal brain development and function.

Myelination and long diffusion times alter diffusion-tensor-imaging contrast in myelin-deficient shiverer mice

Diffusion tensor imaging (DTI) using variable diffusion times (t(diff)) was performed to investigate wild-type (wt) mice, myelin-deficient shiverer (shi) mutant mice and shi mice transplanted with wt neural precursor cells that differentiate and function as oligodendrocytes. At t(diff) = 30 ms, the diffusion anisotropy "volume ratio" (VR), diffusion perpendicular to the fibers (lambda( perpendicular)), and mean apparent diffusion coefficient (<D>) of the corpus callosum of shi mice were significantly higher than those of wt mice by 12 +/- 2%, 13 +/- 2%, and 10 +/- 1%, respectively; fractional anisotropy (FA) and relative anisotropy (RA) were lower by 10 +/- 1% and 11 +/- 3%, respectively. Diffusion parallel to the fibers (lambda(//)) was not statistically different between shi and wt mice. Normalized T(2)-weighted signal intensities showed obvious differences (27 +/- 4%) between wt and shi mice in the corpus callosum but surprisingly did not detect transplant-derived myelination. In contrast, diffusion anisotropy maps detected transplant-derived myelination in the corpus callosum and its spatial distribution was consistent with the donor-derived myelination determined by immunohistochemical staining. Anisotropy indices (except lambda(//)) in the corpus callosum showed strong t(diff) dependence (30-280 ms), and the differences in lambda( perpendicular) and VR between wt and shi mice became significantly larger at longer t(diff), indicative of improved DTI sensitivity at long t(diff). In contrast, anisotropy indices in the hippocampus showed very weak t(diff) dependence and were not significantly different between wt and shi mice across different t(diff). This study provides insights into the biological signal sources and measurement parameters influencing DTI contrast, which could lead to developing more sensitive techniques for detection of demyelinating diseases.

Apparent diffusion coefficient of intervertebral discs related to matrix composition and integrity

While tremendous work has been performed to characterize degenerative disc disease through gross morphologic, biochemical, and histologic grading schemes, the development of an accurate and noninvasive diagnostic tool is required to objectively detect changes in the matrix with aging and disc degeneration. In the present study, quantitative magnetic resonance was used to determine if the quality of the nutritional supply to the intervertebral disc at various ages and levels of degeneration could be assessed through measurement of the apparent diffusion coefficients (ADCs). Modifications of the nucleus pulposus matrix content, specifically of water and glycosaminoglycan contents, with age and disc degeneration, were reflected in correlating changes in the ADCs. From unforced stepwise linear regression analyses, relations were established showing that decreases in glycosaminoglycan or water contents in the nucleus pulposus resulted in direct decreases in the ADCs. Relations obtained for the ADCs of the nucleus pulposus were direction dependent, in conformity with the anisotropic diffusion in the intervertebral discs. Changes in matrix integrity, as evidenced by the percentage of denatured collagen, were also detected in the nucleus pulposus with a low positive correlation to the ADC along the height of the disc and an inverse statistically significant regression to the ADC along the anterior to posterior axis of the disc. Correlations between the matrix content and integrity of the annulus fibrosus and its ADCs were not as evident, with only the ADC in the lateral direction of the disc of the anterior annulus fibrosus able to reflect changes in matrix content. The information obtained by the ADCs, particularly of the nucleus pulposus, can potentially be used in combination with quantitative T1, T2, and MT parameters to noninvasively obtain a quantitative assessment of the disc matrix composition and structural integrity.

Oscillating gradient measurements of water diffusion in normal and globally ischemic rat brain

Oscillating gradients were used to probe the diffusion-time/frequency dependence of water diffusion in the gray matter of normal and globally ischemic rat brain. In terms of a conventional definition of diffusion time, the oscillating gradient measurements provided the apparent diffusion coefficient (ADC) of water with diffusion times between 9.75 ms and 375 micros, an order of magnitude shorter than previously studied in vivo. Over this range, ADCs increased as much as 24% in vivo and 50% postmortem, depending on the nature of the oscillating gradient waveform used. Novel waveforms were employed to sample narrow frequency bands of the so-called diffusion spectrum. This spectral description of ADC includes the effects of restriction and/or flow, and is independent of experimental parameters, such as diffusion time. The results in rat brain were found to be consistent with restricted diffusion and the known micro-anatomy of gray matter. Differences between normal and postmortem data were consistent with an increase in water restriction and/or a decrease in flow, and tentatively suggest that physical changes following the onset of ischemia occur on a scale of about 2 microm, similar to a typical cellular dimension in gray matter.

The basis of anisotropic water diffusion in the nervous system - a technical review

Anisotropic water diffusion in neural fibres such as nerve, white matter in spinal cord, or white matter in brain forms the basis for the utilization of diffusion tensor imaging (DTI) to track fibre pathways. The fact that water diffusion is sensitive to the underlying tissue microstructure provides a unique method of assessing the orientation and integrity of these neural fibres, which may be useful in assessing a number of neurological disorders. The purpose of this review is to characterize the relationship of nuclear magnetic resonance measurements of water diffusion and its anisotropy (i.e. directional dependence) with the underlying microstructure of neural fibres. The emphasis of the review will be on model neurological systems both in vitro and in vivo. A systematic discussion of the possible sources of anisotropy and their evaluation will be presented followed by an overview of various studies of restricted diffusion and compartmentation as they relate to anisotropy. Pertinent pathological models, developmental studies and theoretical analyses provide further insight into the basis of anisotropic diffusion and its potential utility in the nervous system.

Diffusion time dependence of the apparent diffusion tensor in healthy human brain and white matter disease

The diffusion time dependence of the brain water diffusion tensor provides information regarding diffusion restriction and hindrance but has received little attention, primarily due to limitations in gradient amplitude available on clinical MRI systems, required to achieve short diffusion times. Using new, more powerful gradient hardware, the diffusion time dependence of tensor-derived metrics were studied in human brain in the range 8-80 ms, which encompasses the shortest diffusion times studied to date. There was no evidence for a change in mean diffusivity, fractional anisotropy, or in the eigenvalues with diffusion time in healthy human brain. The findings are consistent with a model of unrestricted, but hindered water diffusion with semipermeable membranes, likely originating from the extracellular space in which the average extracellular separation is less than 7 microns. Similar findings in two multiple sclerosis plaques indicated that the size of the water diffusion space in the lesion did not exceed this dimension.

Acute and chronic changes of the apparent diffusion coefficient in neurological disorders--biophysical mechanisms and possible underlying histopathology

Diffusion-weighted imaging (DWI) of the brain has become a valuable tool for the reliable detection and diagnosis of several neurological disorders. Although DWI is in wide use in daily practice, the underlying biophysical mechanisms that contribute to changes in the apparent diffusion coefficient (ADC) are still under discussion. Alterations in the apparent water diffusion rate reflect pathological changes in the brain tissue state, via changes in the diffusion characteristics of the intra- and extra-cellular water compartments including restricted diffusion, water exchange across permeable boundaries, the concept of the extra-cellular tortuosity and the intra- and extra-cellular volume fraction. A reduction of the ADC has been detected in acute neurological diseases, while disease states associated with dominant acute vasogenic edema formation or chronic tissue destruction usually show elevations of the ADC. Compromise of energy metabolism is likely to contribute to a reduction of the ADC while already minor structural disintegration may contribute to elevations of the ADC.

The effects of microscopic tissue parameters on the diffusion weighted magnetic resonance imaging experiment

This review examines the way in which microscopic tissue parameters can affect MR experiments which are sensitive to diffusion. The interaction between the intra- and extravascular as well as that between the intra- and extracellular spaces is examined. Susceptibility gradients due to the presence of deoxyhemoglobin can cause diffusion-induced signal losses which are significant in functional magnetic resonance experiments, particularly at higher main magnetic field strengths. This is also true of the fast response that manifests itself as an early negative signal change in functional magnetic resonance experiments. The fields surrounding paramagnetic vessels are described and the way in which diffusion in these fields contributes to functional signal changes is examined. Flow in the capillary bed can be a confounding factor in experiments which aim to examine the diffusion characteristics of extravascular water. It is potentially also a method for assessing capillary perfusion. The intravoxel incoherent motion experiment is described in terms of how significantly this effect can influence diffusion attenuation curves from water. The major models for describing water diffusion in tissue are presented, as are the main experimental results that have contributed to an understanding of the mechanisms of diffusion contrast. The widely accepted view that changes in the diffusion characteristics are caused by a shift of water to the intracellular space and a concomitant change in extracellular tortuosity is examined critically. More recent experiments that indicate that a reduction in the intracellular diffusion may occur simultaneously with the cell swelling are described and their compatibility with existing models discussed.

Water diffusion in rat brain in vivo as detected at very large b values is multicompartmental

The diffusion-weighted signal attenuation of water in rat brain was measured with pulsed-field gradient nuclear magnetic resonance methods in a single voxel under in vivo and global ischemic conditions. The diffusion-attenuated water signal was observed in vivo at b values of 300 ms/microm2 (strength of diffusion weighting) and diffusion times up to 400 ms. A series of constant diffusion time (CT) experiments with varied gradient directions and diffusion times revealed a multiexponential decay with apparent diffusion coefficients (ADC) covering two orders of magnitude from 1 to 0.01 microm2/ms. In a four-exponential fit, the observed changes during global ischemia could be fully explained by changes in the relative volume fractions only with unchanged ADCs. An anisotropy of the ADC, detected at small b values, was not observed for the ADC at large b values, but for the concomitant volume fractions. An inverse Laplace Transform of the CT curves, performed with CONTIN, resulted in continuously distributed diffusion coefficients, for which the term 'diffusogram' is proposed. This approach was more appropriate than a discrete exponential model with four to six components, being related to the morphology of brain tissue and its cell size distribution. On the basis of an analytical, quantitative model, it is suggested that the measured ADC at small b values reflects mainly properties of the restricting boundaries, i.e. the relative volume fractions and the extracellular tortuosity, while the intrinsic intracellular diffusion constant and the exchange time are predicted to have minor influence.

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

Diffusion-weighted single voxel experiments conducted at b-values up to 1 x 10(4) smm-2 yielded biexponential signal attenuation curves for both normal and ischemic brain. The relative fractions of the rapidly and slowly decaying components (f1, f2) are f1 = 0.80 +/- 0.02, f2 = 0.17 +/- 0.02 in healthy adult rat brain and f1 = 0.90 +/- 0.02, f2 = 0.11 +/- 0.01 in normal neonatal rat brain, whereas the corresponding values for the postmortem situation are f1 = 0.69 +/- 0.02, f2 = 0.33 +/- 0.02. It is demonstrated that the changes in f1 and f2 occur simultaneously to those in the extracellular and intracellular space fractions (fex, f(in)) during: (i) cell swelling after total circulatory arrest, and (ii) the recovery from N-methyl-D-aspartate induced excitotoxic brain edema evoked by MK-801, as measured by changes in the electrical impedance. Possible reasons for the discrepancy between the estimated magnitude components and the physiological values are presented and evaluated. Implications of the biexponential signal attenuation curves for diffusion-weighted imaging experiments are discussed.

Line scan diffusion imaging

A novel line scan diffusion imaging sequence (LSDI) is introduced. LSDI is inherently insensitive to motion artifacts and high quality diffusion maps of the brain can be obtained rapidly without the use of head restraints or cardiac gating. Results from a stroke study and abdominal diffusion images are presented. The results indicate that it is feasible to use the LSDI technique for clinical evaluation of acute ischemic stroke. In contrast to echo-planar diffusion imaging, LSDI does not require modified gradient hardware and can be implemented on conventional scanners. Thus, LSDI should dramatically increase the general availability of robust clinical diffusion imaging.

Apparent diffusion coefficients in benign and secondary progressive multiple sclerosis by nuclear magnetic resonance

The diffusion characteristics of water in brain white matter were studied in patients with benign and secondary progressive multiple sclerosis (MS), and also in normal controls. In the MS patients, both lesions and normal-appearing white matter (NAWM) were examined to assess whether pathological differences might be evident from the diffusion behavior. A volume-selective technique was used to reduce data acquisition time and improve the reliability and precision of the measurements. This also allowed the time-dependence of apparent diffusion coefficients to be assessed. While lesions from both patient groups showed an elevated diffusion coefficient, no differences between the two groups were found. In addition, NAWM was elevated for both patient groups compared with the control group, although this was only statistically significant for patients with a benign disease course. The degree of elevation of the diffusion coefficient within the individual lesions measured was not related to the disability of the patient. Pathological differences between lesions in patients with different disease courses, if they exist, have not been detected in this study of brain water diffusion.

Diffusion MRI: precision, accuracy and flow effects

After a decade of evolution and application of diffusion imaging, a large body of literature has been accumulated. It is in this context that the accuracy and precision of diffusion-weighted and quantitative diffusion MRI are reviewed. The emphasis of the review is on practical methods for clinical human imaging, particularly in the brain. The requirements for accuracy and precision are reviewed for various clinical and basic science applications. The methods of measuring and calculating diffusion effects with MRI are reviewed. The pulse gradient spin echo (PGSE) methods are emphasized as these methods are used most commonly in the clinical setting. Processing of PGSE data is reviewed. Various PGSE encoding schemes are also reviewed in terms of the accuracy and precision of isotropic and anisotropic diffusion measurements. The broad range of factors impacting the accuracy of the PGSE methods and other encoding schemes is then considered. Firstly, system inaccuracies such as background imaging gradients, gradient linearity, refocusing RF pulses, eddy currents, image misregistration, noise and dynamic range are considered. A second class of inaccuracies is contributed by the bulk effects of the imaged object, and include sample background gradients, subject motion of cerebrospinal fluid and organs, and aperiodic organ motion. A final category of potential inaccuracies is classified as being contributed by microscopic, biophysical tissue properties and include partial volume effects, anisotropy, restriction, diffusion distance, compartmentation, exchange, multiexponential diffusion decay, T2 weighting and microvascular perfusion. Finally, the application of diffusion methods to studies of blood flow in the microvasculature (i.e. the arterioles, capillaries and venules) are reviewed in detail, particularly in terms of feasibility and the stringent accuracy and precision requirements. Recent provocative studies examining the use of PGSE approaches to suppress microvascular signals in brain functional MRI (fMRI) are also reviewed.

Interpretation of DW-NMR data: dependence on experimental conditions

This review examines the effect of experimental conditions on the data obtainable from diffusion weighted NMR experiments. The origin and forms of the Stejskal-Tanner experiment are presented, and the relative merits of bipolar to monopolar diffusion weighting gradient pulses are discussed, as are those of spin-echo and stimulated-echo weighting schemes. The short pulse Stejskal-Tanner experiment as required for q-space imaging is described. Criteria for successful diffusion weighted imaging are given, and current strategies for diffusion weighted imaging are evaluated against these. The range of biological objects accessible to diffusion weighted NMR is summarized, together with the associated experimental limitations. In the final section the dependence of diffusion weighted NMR data on diffusion time and b-value range is examined, and the relationship between apparent restricted diffusion and the size of the extracellular space is demonstrated.

The application of porous-media theory to the investigation of time-dependent diffusion in in vivo systems

Recent developments in solid-boundary porous-media theory have shown that useful structural information can be extracted from the time-dependent diffusion coefficient, D(t), of the fluid filling the interstitial space. This theoretical framework provides a basis from which to understand the results from diffusion experiments performed in other types of systems (e.g. biological). Structural information about porous media can be obtained from the short-time behavior of D(t) in the form of the ratio of the surface area to pore volume, S/V. The long-time behavior of D(t) in porous media provides an indirect measure of the macroscopic structure. In this case, the long-time diffusion coefficient, D(eff), reflects the tortuosity, T, of the medium; a property of both the connectivity of the diffusion paths and the volume fraction of the sample. Measurements of D(t) were performed in RIF-1 tumors, using both spectroscopy and imaging, and the data were used to calculate S/V and T. The results were compared with histological sections in order to correlate S/V and T with differences in tissue structure (i.e. necrotic vs non-necrotic tumor tissue). Based on spectroscopic measurements, there is a trend towards decreasing S/V and T with increasing tumor volume, consistent with the interpretation that water in necrotic tissue is experiencing relatively fewer restricting barriers (as compared to non-necrotic tumor tissue). Based on D(t) maps generated from RIF-1 tumors, D(eff), and hence T appears to be much more sensitive than S/V in differentiating between necrotic and non-necrotic tissue. In addition to characterizing diseased tissue, S/V and particularly T appear to be sensitive to structural changes that would accompany tumor treatment and should therefore provide a useful tool for monitoring the progress of therapeutic interventions.