Optimised diffusion-weighting for measurement of apparent diffusion coefficient (ADC) in human brain

Selection of the optimum b factor for diffusion-weighted magnetic resonance imaging assessment of ischemic stroke

The purpose of this study was to determine the diffusion sensitivity factor b that optimizes the contrast-to-noise ratio (CNR) for both diffusion-weighted signal intensity and the apparent diffusion coefficient (ADCNR) when evaluating ischemic stroke by diffusion-weighted MRI. The relative contrast, noise levels, CNR, and ADCNR were calculated for typical ADC values in human brain, 780 microm(2)/s in adults and 1200 microm(2)/s in neonates in normal tissue, 20-40% less in acute and subacute stroke, and 50% more in chronic stroke. The optimum b factor depends strongly on the ADC, whether TE is fixed or varies with the b factor, whether CNR or ADCNR is measured, and anisotropy. The optimum b factor in adults is 1000 s/mm(2) in acute and chronic stroke, and 1200 s/mm(2) in subacute stroke. The optimum values are about 200 s/mm(2) lower in neonates than in adults. The CNR and ADCNR are within 10% of the optimum over at least a 2-fold range of b factors, from 68-136% of the optimum b factor. If a single b factor is to be used for all situations, a diffusion b factor of 1000 s/mm(2) is recommended.

Optimization of diffusion measurements using Cramer-Rao lower bound theory and its application to articular cartilage

A novel approach to optimized diffusion measurements by minimizing the Cramer-Rao lower bound (CRLB) with respect to the b-values used for diffusion measurement was investigated. The applicability of the CRLB to these measurements is shown by the close agreement between the CRLB prediction and the actual precision obtained from experimental results. Where studies using a propagation-of-errors approach have restricted the optimization of the diffusion measurement to two b-values and to specific diffusion coefficient values, the CRLB approach sets no bounds on the number of b-values and is applicable to any system. The optimal number of b-values depends on the ratio of the maximum and minimum diffusion coefficients in the sample (the D(ratio)) and on the number of acquisitions. For a D(ratio) above 6.8 the optimal number of b-values increases to three; at a D(ratio) of 21.8 it increases to four. The optimized sampling schemes for ADC measurements in a variety of representative tissues found in the human body are given. For cartilage the optimal five-point acquisition scheme requires one measurement at a b-value of 0 and four at 1036 sec mm(-2), whereas brain requires one at 0, three at 660, and one at 1987 sec mm(-2).

Analytical error propagation in diffusion anisotropy calculations

PURPOSE

To develop an analytical formalism describing how noise and selection of diffusion-weighting scheme propagate through the diffusion tensor imaging (DTI) computational chain into variances of the diffusion tensor elements, and errors in the relative anisotropy (RA) and fractional anisotropy (FA) indices.

MATERIALS AND METHODS

Singular-value decomposition (SVD) was used to determine the tensor variances, with diffusion-weighting scheme and measurement noise incorporated into the design matrix. Anisotropy errors were then derived using propagation of error. To illustrate the applications of the model, 12 data sets were acquired from each human subject, over a range of b-values (500-2500 seconds/mm2) and diffusion-weighting gradient directions (N = 6-55). The mean RA and FA values and their respective errors were calculated within a region of interest (ROI) in the splenium. The RA and FA errors as a function of b-value and N were evaluated, and a number of diffusion-weighting schemes were assessed based on a new metric, sum of diffusion tensor variances.

RESULTS

When the acquisition time was held constant, the sum of the diffusion tensor variances decreased as N increased. The same trend was also observed for several diffusion-weighting schemes with constant condition number when noise in the diffusion-weighted (DW) images was assumed unity. Errors in both FA and RA increased with b-value and decreased with N. The FA error in the splenium was approximately threefold smaller than RA error, irrespective of b-value or N.

CONCLUSION

The condition number may not adequately characterize the noise sensitivity for a given diffusion-weighting scheme. Signal averaging may not be as effective as increasing N, especially when N is small (e.g., N < 13). Due to its smaller error, FA is preferred over RA for quantitative DTI applications.

Computation of the fractional anisotropy and mean diffusivity maps without tensor decoding and diagonalization: Theoretical analysis and validation

Diffusion tensor MRI (DT-MRI) is a promising modality for in vivo mapping of the organization of deep tissues. The most commonly used DT-MRI invariant maps are the mean diffusivity, mu(D), relative anisotropy (RA), and fractional anisotropy (FA). Because of the computational burden, anisotropy maps are generally computed offline. The availability of a simple procedure to compute RA, FA, and mu(D) online would make DT-MRI more useful in clinical applications that require immediate feedback. In this study, analytical expressions that relate the commonly used tensor anisotropy measures obtained from the decoded and diagonalized DT with those obtained from the first and second moments of the measured diffusion-weighted (DW) data are derived. Specifically, it is shown that for the principal icosahedron encoding scheme, RA is related to the mean and standard deviation (SD) of the DW measurements that can be computed online. Since FA is commonly used as an anisotropy measure, an analytical expression relating RA and FA was derived from the tensor invariants. These results were validated using both Monte Carlo simulations and high-resolution, normal whole-brain DT-MRI measurements acquired with different b-factors, encoding schemes, and signal-to-noise ratio (SNR) levels. The bias introduced by the rotationally variant encoding schemes into the diffusion measures is also investigated.

Eddy current correction in diffusion-weighted imaging using pairs of images acquired with opposite diffusion gradient polarity

In echo-planar-based diffusion-weighted imaging (DWI) and diffusion tensor imaging (DTI), the evaluation of diffusion parameters such as apparent diffusion coefficients and anisotropy indices is affected by image distortions that arise from residual eddy currents produced by the diffusion-sensitizing gradients. Correction methods that coregister diffusion-weighted and non-diffusion-weighted images suffer from the different contrast properties inherent in these image types. Here, a postprocessing correction scheme is introduced that makes use of the inverse characteristics of distortions generated by gradients with reversed polarity. In this approach, only diffusion-weighted images with identical contrast are included for correction. That is, non-diffusion-weighted images are not needed as a reference for registration. Furthermore, the acquisition of an additional dataset with moderate diffusion-weighting as suggested by Haselgrove and Moore (Magn Reson Med 1996;36:960-964) is not required. With phantom data it is shown that the theoretically expected symmetry of distortions is preserved in the images to a very high degree, demonstrating the practicality of the new method. Results from human brain images are also presented.

In vivo monitoring of age-related changes in rat brain using quantitative diffusion magnetic resonance imaging and magnetic resonance relaxometry

Diffusion-weighted magnetic resonance imaging (MRI) has been proven to be a sensitive diagnostic tool to examine age associated acute and chronic changes in brain tissue. The aim of our study was to examine whether there are differences in brain diffusion and transverse relaxation time between young and adult rats. In an experimental MR scanner, 24 young (age: 3 months) and 26 adult rats (age: 12 months) were examined using diffusion-weighted and transverse relaxation time (T2)-weighted MRI sequences. There were no differences in the T2 relaxation time between the two animal groups, either local or global. However, the mean apparent diffusion coefficient (ADC) within the whole brain was significantly lower (P<0.0005) in the adult animals (765+/-35 x 10(-6) mm(2)/s) than in the young animals (829+/-45 x 10(-6) mm(2)/s). ADC decrease was mainly found in the cerebral cortex. These results can be attributed to an activity-related or central nervous system damage-related internal water shift from the extracellular to the intracellular space without a net increase in water content in brain tissue. Our study also shows that age-related changes in diffusion should be considered when performing longitudinal studies in rats.

Cortical spreading depression in the feline brain following sustained and transient stimuli studied using diffusion-weighted imaging

Cortical spreading depression (CSD) was induced by transient (10 min) applications of KCl in agar upon the cortical surface of alpha-chloralose anaesthetised cats. Its features were compared with CSD resulting from sustained applications of crystalline KCl through a mapping of the apparent diffusion coefficient (ADC) using diffusion-weighted echo planar imaging (DWI) over a poststimulus period of 60-100 min. Individual CSD events were computationally detected with the aid of Savitzky-Golay smoothing applied to critically sampled data derived from regions of interest (ROIs) made up of 2 x 2 pixel matrices. The latter were consistently placed at three selected sites on the suprasylvian gyrus (SG) and six sites on the marginal gyrus (MG). The CSD events thus detected were then quantitatively characterised for each ROI using the original time series. Both stimuli consistently elicited similar spreading patterns of initial, primary CSD events that propagated over the SG and marginal MG and were restricted to the hemispheres on which the stimuli were applied. There followed secondary events over smaller extents of cortical surface. Sustained stimuli elicited primary and secondary CSD events with similar amplitudes of ADC deflection that were distributed around a single mean. The ADC deflections were also conserved in peak amplitude throughout the course of their propagation. The initial primary event showed a poststimulus latency of 1.1 +/- 0.1 min. Successive secondary events followed at longer, but uniform, time intervals of around 10 min. Primary and secondary CSDs showed significantly different velocities of conduction (3.32 +/- 0.43 mm min(-1) vs. 2.11 +/- 0.21 mm min(-1), respectively; n = 5) across the cerebral hemisphere. In contrast, transient stimuli produced significantly fewer numbers of CSD events (3.8 +/- 0.5 events per animal, n = 5) than did sustained stimuli (7.4 +/- 0.5 events per animal, mean +/- S.E.M., n = 5, P = 0.002). The peak ADC deflection of their primary CSD events declined by approximately 30 % as they propagated from their initiation site to the interhemispheric boundary. The primary CSD event following a transient stimulus showed a latency of 1.4 +/- 0.1 min. It was followed by successive and smaller secondary ADC deflections that were separated by progressively longer time intervals. Conduction velocities of secondary events were similar to those of primary events. Conduction velocities of both primary and secondary events were slower than their counterparts following a sustained stimulus. ADC changes associated with CSD thus persist at times well after stimulus withdrawal and vary markedly with the nature of the initiating stimulus even in brain regions remote from the stimulus site.

Effect of intravenous gadolinium-DTPA on diffusion-weighted images: evaluation of normal brain and infarcts

BACKGROUND AND PURPOSE

Diffusion-weighted imaging (DWI) is usually done before administration of intravenous contrast agents. Repetition of DWI is occasionally necessary after administration, but the effects of contrast material on DWI and apparent diffusion coefficient (ADC) values have not yet been fully examined. The present study assesses whether administration of gadolinium-based contrast material significantly affects DWI and ADC values.

METHODS

We examined DWI data from 39 patients (mean age, 67.9 years; range, 34 to 87 years) who were evaluated with a stroke protocol at our institute. All patients were scanned at the acute or subacute stages of infarct from 3 hours to 5 days after symptom onset. We obtained DWI images using single-shot echo-planar imaging with a b value of 1000 s/mm2. Patients were injected with 0.1 mmol gadopentetate dimeglumine per 1 kg body weight. We examined the signal-to-noise ratio of the normal brain and the infarct and evaluated the contrast-to-noise ratio of each lesion. In addition, we compared the ADC values calculated from the DWI images before and after administration of contrast. The statistical significance of differences between precontrast and postcontrast administration was determined by use of a paired t test.

RESULTS

The signal-to-noise and contrast-to-noise ratios of the DW images were not significantly different before and after administration of contrast agent. The ADC values were slightly lower after administration of contrast agent for both normal brain (P=0.0011) and infarcts (P=0.038). The estimated differences in the ADC values were approximately 1.3% and 3.5% for normal brain and infarcts, respectively.

CONCLUSIONS

The lack of a significant difference between the signal-to-noise and contrast-to-noise ratios of DW images before and after administration of contrast agent indicates the feasibility of postcontrast DWI.

Diffusion-weighted imaging of cerebral infarctions: are higher B values better?

PURPOSE

The purpose of this work is to determine whether high -value ( = 3,000 s/mm ) diffusion-weighted (DW) imaging is superior to low -value ( = 1,000 s/mm ) DW imaging for the detection of cerebral infarctions older than 6 h.

METHOD

Echo planar DW imaging was performed at 1.5 T in 26 consecutive patients (mean age 66 years) referred for clinical diagnosis of definite acute/subacute cerebral infarction (6 h to 14 days old). The DW imaging sequences were performed using matched parameters (TR = 10,000 ms, TE (eff)= 97 ms, FOV = 24 cm, 128 x 192 matrix, slice = 5 mm, NEX = 2) with values of 1,000 and 3,000 s/mm. Areas of infarction were compared visually by two experienced neuroradiologists. Quantitative measures of MR signal and noise levels in the infarcted areas compared with contralateral normal brain were also obtained.

RESULTS

The median time after infarction was 2.5 days (range 10 h to 14 days). By visual inspection, all infarctions were reliably identified on both the = 1,000 and the = 3,000 images. The gross signal ratio (infarct/normal brain) was approximately 33% higher in the = 3,000 images, but the = 3,000 images were rated as noticeably "noisier" by both observers in every case. This visual observation was confirmed quantitatively: The signal-to-noise (SNR) and contrast-to-noise (CNR) ratios were 70% and 51% higher in the = 1,000 than the = 3,000 images (p < 0.0005 for both).

CONCLUSION

For the evaluation of late acute/subacute cerebral infarctions, high -value ( = 3,000 s/mm(2) ) DW imaging offers no apparent diagnostic advantages compared with = 1,000 images and is significantly inferior in terms of SNR and CNR.

Increased anisotropy in acute stroke: a possible explanation

BACKGROUND AND PURPOSE

The increase in fractional anisotropy (FA) in acute stroke has yet to be explained. Using an engineering methodology known as pq diagrams, we sought to explain the increase in FA by describing changes in the total magnitude of the diffusion tensor (L) as well as the isotropic (p) and anisotropic (q) components.

METHODS

Diffusion tensor imaging was performed in 10 patients with stroke <27 hours old. The diffusion tensor was decomposed into the p and q components and plotted to describe the diffusion trajectories. FA was also calculated and compared.

RESULTS

There was significant and consistent reduction in p, q, and L (p: mean, -50.0%; range, -36.6% to -64.5%; q: mean, -50.8%; range, -30.8% to -72.8%; L: mean, -50.3%; range, -37.0% to -65.1%). There were inconsistent changes in FA (mean, -0.5%; range, -44.9% to +45.0%). Five patients had elevated FA due to proportionately higher loss of L than q.

CONCLUSIONS

Changes in FA only occur when there is a change in the ratio of q/L. Acute elevation of FA occurred in the context of a larger reduction in L than q. The elevation in FA occurs in the context of a reduction in the anisotropic tensor and therefore is a consequence of ratio-metric measurement. This appears to clarify the reported increase in FA in terms of alterations in the shape of the apparent diffusion tensor. pq diagrams appear to offer improved resolution of acute diffusion changes in ischemia.

Isotropic resolution diffusion tensor imaging with whole brain acquisition in a clinically acceptable time

Our objective was to develop a diffusion tensor MR imaging pulse sequence that allows whole brain coverage with isotropic resolution within a clinically acceptable time. A single-shot, cardiac-gated MR pulse sequence, optimized for measuring the diffusion tensor in human brain, was developed to provide whole-brain coverage with isotropic (2.5 x 2.5 x 2.5 mm) spatial resolution, within a total imaging time of approximately 15 min. The diffusion tensor was computed for each voxel in the whole volume and the data processed for visualization in three orthogonal planes. Anisotropy data were further visualized using a maximum-intensity projection algorithm. Finally, reconstruction of fiber-tract trajectories i.e., "tractography" was performed. Images obtained with this pulse sequence provide clear delineation of individual white matter tracts, from the most superior cortical regions down to the cerebellum and brain stem. Because the data are acquired with isotropic resolution, they can be reformatted in any plane and the sequence can therefore be used, in general, for macroscopic neurological or psychiatric neuroimaging investigations. The 3D visualization afforded by maximum intensity projection imaging and tractography provided easy visualization of individual white matter fasciculi, which may be important sites of neuropathological degeneration or abnormal brain development. This study has shown that it is possible to obtain robust, high quality diffusion tensor MR data at 1.5 Tesla with isotropic resolution (2.5 x 2.5 x 2.5 mm) from the whole brain within a sufficiently short imaging time that it may be incorporated into clinical imaging protocols.

Diffusion-weighted MR imaging in the brain in children: findings in the normal brain and in the brain with white matter diseases

PURPOSE

To establish quantitative standards for age-related changes in diffusion restriction of cerebral white matter in healthy children and to compare data with results in children with white matter diseases.

MATERIALS AND METHODS

Diffusion-weighted magnetic resonance (MR) imaging was performed in 44 children (age range, 7 days to 7.5 years) without brain abnormalities and in 13 children with proved leukodystrophy. Apparent diffusion coefficient (ADC) and apparent anisotropy (AA) were measured in 11 regions of interest within white matter. Age-related changes were analyzed with regression analysis.

RESULTS

During normal brain myelination, ADCs in different anatomic regions were high at birth (range, 1.04 x 10(-9) m(2)/sec +/- 0.05 [SD] to 1.64 x 10(-9) m(2)/sec +/- 0.09) and low after brain maturation (range, 0.75 x 10(-9) m(2)/sec +/- 0.02 to 0.92 x 10(-9) m(2)/sec +/- 0.02). AA was low at birth (range, 0.05 +/- 0.01 to 0.52 +/- 0.04) and high after brain maturation (range, 0.25 +/- 0.02 to 0.85 +/- 0.03). Age relationship could be expressed with monoexponential functions for all anatomic regions. Anisotropy preceded the myelination-related changes at MR imaging. ADC and AA in four children with Pelizaeus-Merzbacher disease were identical with results in healthy newborn children and showed no age dependency. In peroxisomal disorders, Krabbe disease, and mitochondriopathy, demyelination on T1- and T2-weighted MR images led to expected findings at diffusion-weighted MR imaging, with high ADC and low AA, whereas in Canavan disease and metachromatic leukodystrophy, the opposite findings were revealed, with low ADC within the demyelinated white matter.

CONCLUSION

During early brain myelination, diffusion restriction in normal white matter increases. Anisotropy precedes myelination changes that are visible at MR imaging. Compared with T1- and T2-weighted MR imaging, diffusion-weighted MR imaging in white matter diseases reveals additional information.

Diffusion tensor brain imaging and tractography

Diffusion-tensor MR imaging is a promising tool to evaluate white-matter integrity by quantitative and graphic maps including neural fiber tractogram. Current challenges afoot are to obtain higher quality diffusion-weighted MR images (high SNR, isotropic voxel, and high spatial resolution), to create a robust mathematical framework to process the data, to construct a user-friendly computer-based algorithm, to reveal determinants of diffusion process, and to establish analytical methodology.

Diffusion-weighted MRI used to detect in vivo modulation of cortical spreading depression: comparison of sumatriptan and tonabersat

Spreading cortical depolarization and depression of electroencephalographic activity (SD) may underlie the aura and spreading neurovascular events of migraine. Cortical depolarization may also precipitate the progressive development of cerebral pathology following ischemia. However, data on SD in the human brain are sparse, most likely reflecting the technical difficulties involved in performing such clinical studies. We have previously shown that the transient cerebral water disturbances during SD can be quantitatively investigated in the gyrencephalic brain using repetitive diffusion-weighted magnetic resonance imaging (DWI). To investigate whether DWI could detect modulation of the spatiotemporal properties of SD in vivo, the effects of the antimigraine drug sumatriptan (0.3 mg/kg iv) and the novel anticonvulsant tonabersat (10 mg/kg ip) were evaluated in the cat brain. Supporting previous findings, sumatriptan did not affect the numbers of events (range, 4-8), the duration of SD activity (39.8 +/- 4.4 min, mean +/- SEM), and event velocity (2.2 +/- 0.4 mm min(-1)); tonabersat significantly reduced SD event initiation (range, 0-3) and duration (13.2 +/- 5.0 min) and increased primary event velocity (5.4 +/- 0.7 mm min(-1)). However, both drugs significantly decreased, by >50%, the spatial extent of the first KCl-evoked SD event, and sumatriptan significantly increased event propagation across the suprasylvian sulcus (5.5 +/- 0.6 vs 2.4 +/- 0.4 events in controls). These results demonstrate (1) the feasibility of using DWI to evaluate therapeutic effects on SD, and (2) that sumatriptan may directly modulate the spatial distribution of SD activity in the gyrencephalic brain.

Echo planar magnetic resonance imaging of anisotropic diffusion in asparagus stems

MR diffusion-weighted imaging (DWI) uses the signal loss associated with the random thermal motion of water molecules in the presence of magnetic field gradients to derive a number of parameters that reflect the translational mobility of the water molecules in tissues. In highly organized but asymmetric structures, this mobility may be affected by the obstacles present and this in a direction-dependent way. Important examples of this are white brain matter and the stem of certain plants, both containing fibrous components where diffusion of water molecules across fibers is much more restricted than along the fibers. Diffusion that exhibits such directional dependence is said to be anisotropic, and diffusion tensor magnetic resonance imaging allows localized characterization of this behavior. Interpretation of the information obtained in terms of the underlying tissue structure is often hampered by the complexity of factors that can produce the observed behavior. A phantom that exhibits well-defined anisotropic diffusion and yields sufficient signal can help the experimental testing of the relevant methods and models. In this paper, we have used a phantom consisting of asparagus stems as a test object for assessing the value of the acquisition and postprocessing techniques commonly used in the clinic for this kind of investigation. Because of its strongly fibrous and cylindrically symmetric morphology, exhibiting a well-defined sub-classification of cells on the basis of size and shape, asparagus allows a relatively simple interpretation of the results obtained in the diffusion experiments. Our experiments show that the known structural information about the main cell types encountered correlates well with the behavior patterns of the diffusion parameters.

High b-value diffusion-weighted MRI of normal brain

PURPOSE

As MR scanner hardware has improved, allowing for increased gradient strengths, we are able to generate higher b values for diffusion-weighted (DW) imaging. Our purpose was to evaluate the appearance of the normal brain on DW MR images as the diffusion gradient strength ("b value") is increased from 1,000 to 3,000 s/mm2.

METHOD

Three sets of echo planar images were acquired at 1.5 T in 25 normal subjects (mean age 61 years) using progressively increasing strengths of a diffusion-sensitizing gradient (corresponding to b values of 0, 1,000, and 3,000 s/mm2). All other imaging parameters remained constant. Qualitative assessments of trace images were performed by two neuroradiologists, supplemented by quantitative measures of MR signal and noise in eight different anatomic regions.

RESULTS

As gradient strength increased from b = 1,000 to 3,000, both gray and white matter structures diminished in signal as expected based on their relative diffusion coefficients [calculated average apparent diffusion coefficient (ADC) values: gray matter = 8.5 x 10(-4) mm2/s, white matter = 7.5 x 10(-4) mm2/s]. The signal-to-noise ratios for the b = 1,000 images were approximately 2.2 times higher than for the b = 3,000 images (p < 0.0001). As the strength of the diffusion-sensitizing gradient increased, white matter became progressively hyperintense to gray matter. Relative to the thalamus, for example, the average MR signal intensity of white matter structures increased by an average of 27.5%, with the densely packed white matter tracts (e.g., middle cerebellar peduncle, tegmentum, and internal capsule) increasing the most.

CONCLUSION

Brain DW images obtained at b = 3,000 appear significantly different from those obtained at b = 1,000, reflecting expected loss of signal from all areas of brain in proportion to their ADC values. Consequently, when all other imaging parameters are held constant, b = 3,000 DW images appear significantly noisier than b = 1,000 images, and white matter tracts are significantly more hyperintense than gray matter structures.

MR diffusion tensor imaging of white matter tract disruption in stroke at 3 T

Recent advances in MR diffusion weighted imaging (DWI) enable the identification of anisotropic white matter tracts with diffusion tensor imaging (DTI). We aimed to use a novel DTI technique to safely study patients with recent stroke in a high field (3 T) MR machine with its intrinsically higher spatial resolution and signal-to-noise ratio. Of ten patients studied, six had disruption of white matter tracts as determined by DTI. A further patient had distortion of white matter tracts around an infarct rather than actual disruption of the tracts themselves. The lack of tract destruction may imply a beneficial prognosis, information that is not available with conventional DWI.

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

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

Investigation of feline brain anatomy for the detection of cortical spreading depression with magnetic resonance imaging

Cortical spreading depression (CSD) and peri-infarct depolarisation (PID) are related phenomena that have been associated with the human clinical syndromes of migraine (CSD), head injury and stroke (PID). Nevertheless the existence of CSD in man remains controversial, despite the detection of this phenomenon in the brains of most, if not all, other animal species investigated. This failure to unambiguously detect CSD clinically may be at least partly due to the anatomically complex, gyrencephalic structure of the human brain. This study was designed to establish conditions for the study of CSD in the brain of a gyrencephalic species using the noninvasive technique of magnetic resonance imaging (MRI). The 3-dimensional (3D) gyrencephalic anatomy of the cat brain was examined to determine the imaging conditions necessary to detect CSD events. Orthogonal transverse, sagittal and horizontal T1-weighted image slices showed that the marginal and suprasylvian gyri were the most appropriate cortical structures to study CSD. This was in view of (1) their simple geometry: (2) their lengthy extent of grey matter orientated rostrocaudally in the cortex: (3) their separation by a sulcus across which CSD spread could be studied and (4) the discontinuity in the grey matter in these regions between the right and left hemispheres dorsal to the corpus callosum. The structure suggested by the T1-weighted images was corroborated by systematic diffusion tensor imaging to map the fractional anisotropy and diffusion trace. Thus a single horizontal image plane could visualise the neighbouring suprasylvian and marginal gyri of both cerebral hemispheres, whereas its complex shape and position ruled out the ectosylvian gyrus for CSD studies. With the horizontal imaging plane, CSD events were reproducibly detected by animating successive diffusion-weighted MR images following local KCl stimulation of the cortical surface. In single image frames, CSD detection and characterisation required image subtraction or statistical mapping methods that, nevertheless, yielded concordant results. In repeat experiments, CSD events were qualitatively similar in appearance whether elicited by sustained or transient KCl applications. Our experimental approach thus successfully describes cat brain anatomy in vivo, and elucidates the necessary conditions for the application of MRI methods to detect CSD propagation.

Comparison of gradient encoding schemes for diffusion-tensor MRI

The accuracy of single diffusion tensor MRI (DT-MRI) measurements depends upon the encoding scheme used. In this study, the diffusion tensor accuracy of several strategies for DT-MRI encoding are compared. The encoding strategies are based upon heuristic, numerically optimized, and regular polyhedra schemes. The criteria for numerical optimization include the minimum tensor variance (MV), minimum force (MF), minimum potential energy (ME), and minimum condition number. The regular polyhedra scheme includes variations of the icosahedron. Analytical comparisons and Monte Carlo simulations show that the icosahedron scheme is optimum for six encoding directions. The MV, MF, and ME solutions for six directions are functionally equivalent to the icosahedron scheme. Two commonly used heuristic DT-MRI encoding schemes with six directions, which are based upon the geometric landmarks of a cube (vertices, edge centers, and face centers), are found to be suboptimal. For more than six encoding directions, many methods are able to generate a set of equivalent optimum encoding directions including the regular polyhedra, and the ME, MF and MV numerical optimization solutions. For seven directions, a previously described heuristic encoding scheme (tetrahedral plus x, y, z) was also found to be optimum. This study indicates that there is no significant advantage to using more than six encoding directions as long as an optimum encoding is used for six directions. Future DT-MRI studies are necessary to validate these observations. J. Magn. Reson. Imaging 2001;13:769-780.

Analysis of partial volume effects in diffusion-tensor MRI

The diffusion tensor is currently the accepted model of diffusion in biological tissues. The measured diffusion behavior may be more complex when two or more distinct tissues with different diffusion tensors occupy the same voxel. In this study, a partial volume model of MRI signal behavior for two diffusion-tensor compartments is presented. Simulations using this model demonstrate that the conventional single diffusion tensor model could lead to highly variable and inaccurate measurements of diffusion behavior. The differences between the single and two-tensor models depend on the orientations, fractions, and exchange between the two diffusion tensor compartments, as well as the diffusion-tensor encoding technique and diffusion-weighting that is used in the measurements. The current single compartment model's inaccuracies could cause diffusion-based characterization of cerebral ischemia and white matter connectivity to be incorrect. A diffusion-tensor MRI imaging experiment on a normal human brain revealed significant partial volume effects between oblique white matter regions when using very large voxels and large diffusion-weighting (b approximately 2.69 x 10(3) sec/mm(2)). However, the apparent partial volume effects in white matter decreased significantly when smaller voxel dimensions were used. For diffusion tensor studies obtained using typical diffusion-weighting values (b approximately 1 x 10(3) sec/mm(2)) partial volume effects are much more difficult to detect and resolve. More accurate measurements of multiple diffusion compartments may lead to improved confidence in diffusion measurements for clinical applications.

Diffusion tensor imaging: concepts and applications

The success of diffusion magnetic resonance imaging (MRI) is deeply rooted in the powerful concept that during their random, diffusion-driven displacements molecules probe tissue structure at a microscopic scale well beyond the usual image resolution. As diffusion is truly a three-dimensional process, molecular mobility in tissues may be anisotropic, as in brain white matter. With diffusion tensor imaging (DTI), diffusion anisotropy effects can be fully extracted, characterized, and exploited, providing even more exquisite details on tissue microstructure. The most advanced application is certainly that of fiber tracking in the brain, which, in combination with functional MRI, might open a window on the important issue of connectivity. DTI has also been used to demonstrate subtle abnormalities in a variety of diseases (including stroke, multiple sclerosis, dyslexia, and schizophrenia) and is currently becoming part of many routine clinical protocols. The aim of this article is to review the concepts behind DTI and to present potential applications.

Noise correction for the exact determination of apparent diffusion coefficients at low SNR

Noise in MR image data increases the mean signal intensity of image regions due to the usually performed magnitude reconstruction. Diffusion-weighted imaging (DWI) is especially affected by high noise levels for several reasons, and a decreasing SNR at increasing diffusion weighting causes systematic errors when calculating apparent diffusion coefficients (ADCs). Two different methods are presented to correct biased signal intensities due to the presence of complex noise: 1) with Gaussian intensity distribution, and 2) with arbitrary intensity distribution. The performance of the correction schemes is demonstrated by numerical simulations and DWI measurements on two different MR systems with different noise characteristics. These experiments show that noise significantly influences the determination of ADCs. Applying the proposed correction schemes reduced the bias of the determined ADC to less than 10% of the bias without correction. Magn Reson Med 45:448-453, 2001.

Diffusion-weighted imaging of the spine using radial k-space trajectories

INTRODUCTION

Diffusion-weighted MR imaging (DWI) of the spine requires robust imaging methods, that are insensitive to susceptibility effects caused by the transition from bone to soft tissue and motion artifacts due to breathing, swallowing, and cardiac motion. The purpose of this study was to develop a robust imaging method suitable for DWI of the spine.

METHODS AND SUBJECTS

A radial k-space spin echo sequence has been implemented, which is self-navigating because each acquisition line passes through the origin of k-space. Influence of cardiac motion and associated flow of cerebrospinal fluid is minimized by cardiac gating with a finger photoplethysmograph. The sequence has been tested on a 1.5T system. Diffusion-weighted images of six normal volunteers were acquired in the sagittal plane with 4 b values between 50 and 500 s mm(-2). Because of the symmetries of the cord, diffusion measurements in the head-foot (HF) or left-right (LR) directions were sufficient to measure the dominant effects of anisotropy.

RESULTS

The apparent diffusion coefficients (ADCs) measured, respectively, in the LR and HF directions were (0.699+/-0.050)x10(-3) and (1.805+/-0.086)x10(-3) mm(2) s(-1) in the spinal cord, (1.588+/-0.082)x10(-3) and (1.528+/-0.052)x10(-3) mm(2) s(-1) in the intervertebral disks, and (0.346+/-0.047)x10(-3) and (0.306+/-0.035)x10(-3) mm(2) s(-1) in the vertebrae of the cervicothoracic spine.

CONCLUSION

Diffusion-weighted spin echo sequences with radial trajectories in k-space provide a means of achieving robust, high quality diffusion-weighted imaging and measuring ADCs in the spine. The application of the diffusion-weighting gradients in different directions allows diffusion anisotropy to be measured.

Condition number as a measure of noise performance of diffusion tensor data acquisition schemes with MRI

Diffusion tensor mapping with MRI can noninvasively track neural connectivity and has great potential for neural scientific research and clinical applications. For each diffusion tensor imaging (DTI) data acquisition scheme, the diffusion tensor is related to the measured apparent diffusion coefficients (ADC) by a transformation matrix. With theoretical analysis we demonstrate that the noise performance of a DTI scheme is dependent on the condition number of the transformation matrix. To test the theoretical framework, we compared the noise performances of different DTI schemes using Monte-Carlo computer simulations and experimental DTI measurements. Both the simulation and the experimental results confirmed that the noise performances of different DTI schemes are significantly correlated with the condition number of the associated transformation matrices. We therefore applied numerical algorithms to optimize a DTI scheme by minimizing the condition number, hence improving the robustness to experimental noise. In the determination of anisotropic diffusion tensors with different orientations, MRI data acquisitions using a single optimum b value based on the mean diffusivity can produce ADC maps with regional differences in noise level. This will give rise to rotational variances of eigenvalues and anisotropy when diffusion tensor mapping is performed using a DTI scheme with a limited number of diffusion-weighting gradient directions. To reduce this type of artifact, a DTI scheme with not only a small condition number but also a large number of evenly distributed diffusion-weighting gradients in 3D is preferable.

A quantitative analysis of cortical spreading depression events in the feline brain characterized with diffusion-weighted MRI

Cortical spreading depression (CSD) in the gyrencephalic cat brain was detected with diffusion-weighted echoplanar (DWEP) magnetic resonance imaging (4-8/min for 1-2 hours) using a horizontal imaging plane through the suprasylvian (SG) and marginal gyri. A t-statistic mapping technique allowed a quantitative characterization of the passage of events through single-image pixels (0.15 mm(2)), thus providing a resolution unavailable to previous studies in which time-dependent changes instead were derived from averaging data over relatively large ROIs. Using the enhanced analysis, CSD events initiated by KCl could be quantified for the first time as primary or secondary according to their spatial and temporal features. Primary events covered 26.2 +/- 9.9 mm(2)of cortical surface (mean +/- SD, n = 7 experiments) and propagated rapidly (3.5 +/- 0.65 mm * min(-1)) with a hemispherical geometry. In contrast, the subsequent secondary events were multiple, spatially restricted (covering 7.6 +/- 4.6 mm(2), P < 0.005), slower in propagation (2.6 +/- 0.41 mm * min(-1), P < 0.012), and often confined to the originating gyrus (26 out of 59 events). However, both event types were associated with significantly reduced apparent diffusion coefficients (ADCs; from 800 to approximately 660 x 10(-6) mm(2)* s(-1), P < 0.05) that were similar for both primary (21 +/- 5.1%) and secondary waves (18 +/- 7. 7%) and that had similar durations (full width at half-maximal height: 86 +/- 17 vs. 79 +/- 20 seconds, respectively). These findings associate CSD for the first time with two categories of ADC disturbance that are similar in amplitude and duration but that differ in spatial extent, velocity, and extensiveness of spread.

Gradient preemphasis calibration in diffusion-weighted echo-planar imaging

This article describes a method which enables fast and objective pulse-sequence-specific preemphasis calibration, using standard pulse sequences and system hardware. The method is based on a k-space measurement technique, and has been applied to single-shot, diffusion-weighted, spin-echo, echo-planar imaging (DW-SE-EPI), which is particularly sensitive to eddy-current-induced image distortions. The efficiency of the technique was demonstrated not only by the reduction of eddy-current fields to a negligible level using full preemphasis compensation, but also by the fact that adjustment of the slow time-base alone sufficed for the practical elimination of image distortions in the DW-SE-EPI images and the subsequent diffusion tensor maps (in a phantom and a human brain). By seeking to eliminate directly the effect of eddy-current-induced phase shifts during the EPI data collection, the method is free of the complications and restrictions associated with other eddy-current correction techniques for DW-SE-EPI (such as acquisition of additional calibration scans, intense postprocessing, extensive pulse-sequence modifications), making their use redundant.

Minimal gradient encoding for robust estimation of diffusion anisotropy

This study has investigated the relationship between the noise sensitivity of measurement by magnetic resonance imaging (MRI) of the diffusion tensor (D) of water and the number N of diffusion-weighting (DW) gradient directions, using computer simulations of strongly anisotropic fibers with variable orientation. The DW directions uniformly sampled the diffusion ellipsoid surface. It is shown that the variation of the signal-to-noise ratio (SNR) of three ideally rotationally invariant scalars of D due to variable fiber orientation provides an objective quantitative measure for the diffusion ellipsoid sampling efficiency, which is independent of the SNR value of the baseline signal obtained without DW; the SNR variation decreased asymptotically with increasing N. The minimum number N(0) of DW directions, which minimized the SNR variation of the three scalars of D was determined, thereby achieving the most efficient ellipsoid sampling. The resulting time efficient diffusion tensor imaging (DTI) protocols provide robust estimation of diffusion anisotropy in the presence of noise and can improve the repeatability/reliability of DTI experiments when there is high variability in the orientation of similar anisotropic structures, as for example, in studies which require repeated measurement of one individual, intersubject comparisons or multicenter studies.

Correction of eddy current-induced artefacts in diffusion tensor imaging using iterative cross-correlation

Geometric distortions of echo-planar images produced by the strong eddy currents present in the diffusion tensor imaging experiment are a major confound to the accurate quantification of diffusion coefficients, and measures of diffusion anisotropy based upon them. Here we investigate how the method of iterative cross-correlation (ICC) of baseline and diffusion-weighted images (DWIs) originally proposed by Haselgrove and Moore (Magn. Reson. Med. 36:960-964; 1996) can be extended to correct high b-value DWIs, without the need for extrapolation of distortion parameters determined from low b-value images. Monte Carlo simulations of synthetic brain images show that the maximum value of the trace of the b-matrix, Tr(b), at which distorted DWIs can be accurately corrected by direct comparison with the undistorted baseline image is approximately 300 s mm(-2). Removal of the cerebrospinal fluid signal greatly extends this value of Tr(b) (up to approximately 2000 s mm(-2)), thereby allowing direct comparison of baseline and distorted images. The use of ICC distortion parameters determined from separate calibrations of water phantom images is also investigated, and found to be effective in correcting geometric distortions observed in the DWIs collected as part of a human volunteer diffusion tensor imaging study. This work suggests that distorted DWIs acquired at high values of b may be corrected using the ICC algorithm without collecting additional low b-value images, thus allowing simplified methods of measuring the apparent diffusion tensor D, based on collecting a small number of DWIs, to be implemented in quantitative patient examinations.

Cortical spreading depression in the gyrencephalic feline brain studied by magnetic resonance imaging

1.Time-lapse diffusion-weighted magnetic resonance imaging (DWI) was used to detect and characterize complex waves of cortical spreading depression (CSD) evoked with KCL placed upon the suprasylvian gyrus of anaesthetized cats. 2. The time-lapse representations successfully demonstrated primary CSD waves that propagated with elliptical wavefronts selectively over the ipsilateral cerebral hemispheres with a velocity of 3.8 +/- 0.70 mm min(-1) (mean +/- S.E.M. of 5 experiments). 3. In contrast, the succeeding secondary waves often remained within the originating gyrus, were slower (velocity 2.0 +/- 0.18 mm min(-1), more fragmented and varied in number. 4. Computed traces of the apparent diffusion coefficients (ADCs) showed negative deflections followed by monotonic decays (amplitudes: primary wave, -19.9 +/- 2.8%; subsequent waves, -13.6 +/- 1.9% duration at half-maximal decay, 150-200 s) when determined from regions of interest (ROIs) through which both primary and succeeding CSD waves propagated. 5. The passage of both the primary and the succeeding waves often correlated with transient DC potential deflections recorded from the suprasylvian gyrus. 6. The detailed waveforms of the ADC and the T2*-weighted (blood oxygenation level-dependent: BOLD) traces showed a clear reciprocal correlation. These imaging features that reflect disturbances in cellular water balance agree closely with BOLD measurements that followed the propagation velocities of the first and subsequent CSD events. They also provide a close physiological correlate for clinical observations of cortical blood flow disturbances associated with human migraine.

Acute cerebral infarction: quantification of spin-density and T2 shine-through phenomena on diffusion-weighted MR images

PURPOSE

To quantify the relative contributions of spin density and T2 effects ("shine through") on diffusion-weighted (DW) magnetic resonance (MR) images of acute and subacute cerebral infarction.

MATERIALS AND METHODS

In 30 patients, 1.5-T imaging was performed within the first 7 days after onset of cerebral infarction. Estimates of T2, spin density, and apparent diffusion coefficient (ADC) in the region of stroke and contralateral normal brain were computed by means of standard regression techniques after quadruple-echo conventional MR imaging and single-shot echo-planar DW imaging with a maximum b value of 1,000 sec/mm2. Expected signal intensity (S) enhancement ratios resulting from independent changes in T2, spin density, and ADC were then calculated for the DW sequence.

RESULTS

The overall SI of cerebral infarction on DW images was significantly higher than that of normal brain throughout the 1st week after stroke (mean relative SI enhancement ratio, 2.29; P < .001). During the first 2 days after stroke, decreased ADC within the stroke region made the dominant contribution to increased SI on DW images. By day 3, increased T2 values in the stroke region became equally important, and, from days 3-7, the contribution to SI from T2 effects became dominant. A slight increase of spin density in the stroke region made a relatively small and constant contribution to DW SI over the 1st week.

CONCLUSION

The increased SI of subacute cerebral infarction on DW images reflects not only a shortening of ADC but a prolongation of T2 and spin-density values.

A study of rotationally invariant and symmetric indices of diffusion anisotropy

This study investigated the properties of a class of rotationally invariant and symmetric (relative to the principal diffusivities) indices of the anisotropy of water self-diffusion, namely fractional anisotropy (FA), relative anisotropy (RA), and volume ratio (VR), with particular emphasis to their measurement in brain tissues. A simplified theoretical analysis predicted significant differences in the sensitivities of the anisotropy indices (AI) over the distribution of the principal diffusivities. Computer simulations were used to investigate the effects on AI image quality of three magnetic resonance (MR) diffusion tensor imaging (DTI) acquisition schemes, one being novel: the schemes were simulated on cerebral model fibres varying in shape and spatial orientation. The theoretical predictions and the results of the simulations were corroborated by experimentally determined spatial maps of the AI in a normal feline brain in vivo. We found that FA mapped diffusion anisotropy with the greatest detail and SNR whereas VR provided the strongest contrast between low- and high-anisotropy areas at the expense of increased noise contamination and decreased resolution in anisotropic regions. RA proved intermediate in quality. By sampling the space of the effective diffusion ellipsoid more densely and uniformly and requiring the same total imaging time as the published schemes, the novel DTI scheme achieved greater rotational invariance than the published schemes, with improved noise characteristics, resulting in improved image quality of the AI examined. Our findings suggest that significant improvements in diffusion anisotropy mapping are possible and provide criteria for the selection of the most appropriate AI for a particular application.

The reduction of the sorting bias in the eigenvalues of the diffusion tensor

One of the most intrinsic quantities when measuring the diffusion properties of a system is the set of principal diffusivities, which represents diffusion along the fibre axes. System noise is a well-known cause of systematic sorting bias when closely spaced diffusivities are ordered according to their magnitude and leads to their inaccurate estimation. This paper describes a new method for the ordering of the principal diffusivities in which local fibre directional coherence was used as a basis for sorting. The method was applied and tested in computer simulations and experimental data acquired in an isotropic water phantom and healthy human brain. Our results demonstrate that this method leads to significant reduction in the sorting bias in comparison to other techniques and thus a more accurate estimation of the eigenvalues. The method is advantageous over other proposed alternatives to the conventional magnitude sorting method because it is not reliant on a large region-of-interest averaging scheme.

Diffusion-weighted magnetic resonance imaging: theory and potential applications to child neurology

Magnetic resonance imaging (MRI) is an excellent tool for the investigation of neurological disorders in children. Diffusion-weighted MRI (DWI) is sensitive to the diffusion (or molecular displacement) of water in tissue. The purpose of this article is to describe briefly the basic theory behind DWI and to discuss its potential applications to neurological disorders in children. We demonstrate that DWI is a sensitive technique for the detection of acute brain injury, and that it is well suited for monitoring brain development, particularly myelination and white matter changes.

In vivo diffusion characteristics of rat spinal cord

Complete apparent diffusion tensor (ADTs) of spinal cord was measured in vivo in nine rats at 2.0 T. Two rotationally invariant parameters, the trace, which is a measure of the mean diffusivity, and the lattice index (LI), which reflects the degree of orientation coherence of tissue, have been estimated from the ADT. The mean white matter (WM) trace value (3.05 +/- 0.26 mm2/sec) was found to be substantially higher than the gray matter (GM) trace (2.36 +/- 0.39 mm2/sec), in contrast with the published results on fixed, excised cord. Statistically significant anisotropic diffusion was observed in both WM and GM, with greater anisotropy in the WM (LI = 0.67 +/- 0.06) than in the GM (LI = 0.51 +/- 0.05).

A comparative study of acquisition schemes for diffusion tensor imaging using MRI

This study has investigated the effects of the selection of the diffusion-weighted (DW) gradient directions on the precision of a diffusion tensor imaging (DTI) experiment. The theoretical analysis provided a quantitative framework in which the noise performance of DTI schemes could be assessed objectively and for the development of novel DTI schemes, which employ multiple DW gradient directions. This generic framework was first applied to the examination of two commonly used DTI schemes, which employed 6 DW gradient directions and hitherto were used indiscriminately under the sole condition of noncollinearity. It was then used to design and assess a novel 12-DW-gradient-direction DTI protocol, which employed the same total number of DW acquisitions as the two conventional schemes (12). This theoretical investigation was then corroborated using rigorous simulation and DTI experiments on both an isotropic phantom and a healthy human brain. Both the theoretical and the experimental analysis demonstrated that the two conventional schemes showed a significantly different noise performance and that use of the new multiple-DW-gradient-direction scheme clearly improved the precision of the DTI measurements.

Calculation of apparent diffusion coefficients (ADCs) in brain using two-point and six-point methods

We evaluated the relative accuracy of calculating apparent diffusion coefficients (ADCs) of intracranial tissues using a two-point versus a six-point regression technique. Echo planar diffusion-weighted MRI was performed at 1.5 T in three standard locations and in pathologic regions in 10 subjects using gradient strengths corresponding to b values of 1, 100, 200, 500, 800, and 1,000 s/mm2. Estimation of ADCs was made using two methods: a nonlinear regression model using measurements from the full set of b values (six-point technique) and linear estimation using b values of 1 and 1,000 only (two-point technique). A high correlation between the two methods was noted (R2 = 0.999), and the mean percentage difference was 0.84%. These results suggest there is little error in estimating brain ADCs using a two-point technique.

A theoretical study of the effect of experimental noise on the measurement of anisotropy in diffusion imaging

Diffusion tensor imaging (DTI) is a modality known to be highly sensitive to the detrimental effects of experimental noise. Here, using Monte Carlo simulations, we compare and contrast how noise complicates the measurement of diffusion anisotropy in diffusion tensor and conventional diffusion-weighted imaging (DWI). As the signal-to-noise ratio (SNR) decreases below a value of approximately 20, the eigenvalues (lambda(i)) of the diffusion tensor D are found to diverge rapidly from their true values, with the result that the measured anisotropy can be significantly in error and isotropic structures falsely assigned a high level of anisotropy. The effect of noise on the rotationally variant indices, calculated from a conventional diffusion-weighted imaging experiment, is found to be much less insidious, because the apparent diffusion coefficients (ADCs) diverge only slowly as the signal-to-noise decreases. Thus, although rotationally variant indices almost always underestimate the true diffusion anisotropy, they show only a small susceptibility to experimental noise and hence, are preferred to their rotationally invariant counterparts when the signal-to-noise ratio is small.