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

Effect of diffusion-sensitizing gradient timings on the exponential, biexponential and diffusional kurtosis model parameters: in-vivo measurements in the rat thalamus

OBJECT

To investigate whether spacing (Delta) and duration (delta) of the diffusion-sensitizing gradient pulses differentially affect exponential (D'), biexponential (D (slow), D (fast) and f (slow)) and diffusional kurtosis (D and K) model parameters.

METHODS

Measurements were performed in the rat thalamus for b = 200-3,200 s mm(-2), sweeping Delta between 20 and 100 ms at delta = 15 ms, and delta between 15 and 50 ms at Delta = 60 ms. Linear regressions were performed for each model parameter vs. Delta or delta.

RESULTS

Increasing Delta from 20 to 100 ms increases D' (from 0.64 to 0.70 x 10(-3) mm(2)s(-1)) and D (slow) (from 0.26 to 0.33 x 10(-3) mm(2)s(-1)), reduces K (from 0.57 to 0.53), and has no effects on D (fast), f (slow) or D. Increasing delta from 15 to 50 ms increases D (from 0.80 to 0.88 x 10(-3) mm(2)s(-1)), and has no effects on the other parameters.

CONCLUSION

The parameters of the biexponential and diffusional kurtosis models are more sensitive than the exponential model to Delta and delta; however, observed effects are too small to account for the discrepancies found in literature.

High-b-value diffusion MR imaging and basal nuclei apparent diffusion coefficient measurements in variant and sporadic Creutzfeldt-Jakob disease

BACKGROUND AND PURPOSE

DWI using a standard b-value of 1000 s/mm(2) has emerged as the most sensitive sequence for the diagnosis of CJD. The purpose of this study was to investigate whether DWI at a high b-value (b = 3000 s/mm(2)) and ADC measurements in the basal nuclei improve the diagnosis of vCJD and sCJD compared with visual assessment of DWI at a standard b-value (b = 1000 s/mm(2)).

MATERIALS AND METHODS

Eight patients with vCJD, 9 patients with sCJD, and 5 healthy volunteers underwent DWI at b = 1000 s/mm(2), and 5 vCJD patients, 4 sCJD patients, and 1 growth hormone-related CJD patient underwent DWI at b = 3000 s/mm(2). Two consultant neuroradiologists performed a visual comparison of the b = 1000 and b = 3000 images. Mean MR SI and ADC values were determined for C, P, and DM thalamus ROIs bilaterally at each b-value. SI ratios for each ROI relative to white matter were calculated.

RESULTS

In 9 out of 10 patients, the higher b-value images were more sensitive to SI change, particularly in cortex and thalamus, with higher SI ratios at b = 3000 in the DM thalamus. For sCJD at b = 1000, we found significantly lower ADC values in the C and P compared with controls (mean C ADC = 587.3 +/- 84.7 mm(2)/s in sCJD patients versus 722.7 +/- 16.6 mm(2)/s in controls; P = .007), and at b = 3000, the differences were more pronounced. In comparison, in vCJD at b = 1000, ADC values were elevated in the Pu (mean Pu ADC = 837.6 +/- 33.0 mm/s(2) in vCJD patients versus 748.0 +/- 17.3 mm/s(2) in controls; P < .001) but failed to reach significance at b = 3000.

CONCLUSIONS

Our results demonstrate that b = 3000 DWI, being more sensitive to slowly diffusing tissue water, is more sensitive to pathology in sCJD than is conventional DWI. High-b-value DWI increases confidence in the radiologic diagnosis of human prion disease.

High-b-value diffusion-weighted imaging at 3 T to detect prostate cancer: comparisons between b values of 1,000 and 2,000 s/mm2

OBJECTIVE

The objective of our study was to investigate the diagnostic performance of 3-T MRI of the prostate using diffusion-weighted imaging (DWI) with high b values (1,000 and 2,000 s/mm2) and a phased-array coil in predicting localized prostate cancer.

MATERIALS AND METHODS

Forty-eight patients underwent single-shot echo-planar DWI at 3 T, followed by radical prostatectomy. DWI was performed at high b values of 1,000 and 2,000 s/mm2. Apparent diffusion coefficient (ADC) maps were analyzed by visual and quantitative assessment for tumor and benign tissue in the peripheral and transition zones. The visual and quantitative results of ADC maps obtained at b values of 1,000 and 2,000 s/mm2 were compared with the histopathologic findings.

RESULTS

To predict localized prostate cancer, the sensitivity of ADC maps obtained at a b value of 1,000 versus 2,000 s/mm2 was 88% and 71%, respectively, and the accuracy was 89% and 86% (p<0.01). The mean ADC values of tumors in both the peripheral and transition zones were significantly lower than those of benign tissues at both b values of 1,000 and 2,000 s/mm2 (p<0.001).

CONCLUSION

Prostate DWI performed at 3 T using high b values was able to improve differentiation of tumors from benign tissue. DWI performed using a b value of 1,000 s/mm2 was more sensitive and more accurate in predicting localized prostate cancer than DWI performed using a b value of 2,000 s/mm2.

Diffusion tensor magnetic resonance imaging of the normal breast

PURPOSE

The objective of this study was to evaluate diffusion anisotropy of the breast parenchyma and assess the range and repeatability of diffusion tensor imaging (DTI) parameters in normal breast tissue.

MATERIALS AND METHODS

The study was approved by our institutional review board and included 12 healthy females (median age, 36 years). Diffusion tensor imaging was performed at 1.5 T using a diffusion-weighted echo planar imaging sequence. Diffusion tensor imaging parameters including tensor eigenvalues (lambda(1), lambda(2), lambda(3)), fractional anisotropy (FA) and apparent diffusion coefficient (ADC) were measured for anterior, central and posterior breast regions.

RESULTS

Mean normal breast DTI measures were lambda(1)=2.51 x 10(-3) mm(2)/s, lambda(2)=1.89 x 10(-3) mm(2)/s, lambda(3)=1.39 x 10(-3) mm(2)/s, ADC=1.95+/-0.24 x 10(-3) mm(2)/s and FA=0.29+/-0.05 for b=600 s/mm(2). Significant regional differences were observed for both FA and ADC (P<.05), with higher ADC in the central breast and higher FA in the posterior breast. Comparison of DTI values calculated using b=0, 600 s/mm(2) vs. b=0, 1000 s/mm(2), showed significant differences in ADC (P<.001), but not FA. Repeatability assessment produced within-subject coefficient of variations of 4.5% for ADC and 11.4% for FA measures.

CONCLUSION

This study demonstrates anisotropy of water diffusion in normal breast tissue and establishes a normative range of breast FA values. Attention to the influence of breast region and b value on breast DTI measurements may be important for clinical interpretation and standardization of techniques.

Diffusion-weighted MR imaging of the liver

Magnetic resonance (MR) imaging plays an increasingly important role in the evaluation of patients with liver disease because of its high contrast resolution, lack of ionizing radiation, and the possibility of performing functional imaging sequences. With advances in hardware and coil systems, diffusion-weighted (DW) MR imaging can now be applied to liver imaging with improved image quality. DW MR imaging enables qualitative and quantitative assessment of tissue diffusivity (apparent diffusion coefficient) without the use of gadolinium chelates, which makes it a highly attractive technique, particularly in patients with severe renal dysfunction at risk for nephrogenic systemic fibrosis. In this review, acquisition parameters, postprocessing, and quantification methods applied to liver DW MR imaging will be discussed. The current clinical uses of DW MR imaging (liver lesion detection and characterization, compared and combined with conventional sequences) and the emerging applications of DW MR imaging (tumor treatment response and diagnosis of liver fibrosis and cirrhosis) will be reviewed. Also, limitations, mainly image quality and reproducibility of diffusion parameters, and future directions of liver DW MR imaging will be discussed.

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.

A new methodology for the estimation of fiber populations in the white matter of the brain with the Funk-Radon transform

The Funk-Radon Transform (FRT) is a powerful tool for the estimation of fiber populations with High Angular Resolution Diffusion Imaging (HARDI). It is used in Q-Ball imaging (QBI), and other HARDI techniques such as the recent Orientation Probability Density Transform (OPDT), to estimate fiber populations with very few restrictions on the diffusion model. The FRT consists in the integration of the attenuation signal, sampled by the MRI scanner on the unit sphere, along equators orthogonal to the directions of interest. It is easily proved that this calculation is equivalent to the integration of the diffusion propagator along such directions, although a characteristic blurring with a Bessel kernel is introduced. Under a different point of view, the FRT can be seen as an efficient way to compute the angular part of the integral of the attenuation signal in the plane orthogonal to each direction of the diffusion propagator. In this paper, Stoke's theorem is used to prove that the FRT can in fact be used to compute accurate estimates of the true integrals defining the functions of interest in HARDI, keeping the diffusion model as little restrictive as possible. Varying the assumptions on the attenuation signal, we derive new estimators of fiber orientations, generalizing both Q-Balls and the OPDT. Extensive experiments with both synthetic and real data have been intended to show that the new techniques improve existing ones in many situations.

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

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

Detection of apoptotic cell death in vitro in the presence of Gd-DTPA-BMA

Due to variability in patient response to cancer therapy, there is a growing interest in monitoring patient progress during treatment. Apoptotic cell death is one early marker of tumor response to treatment. Using known extracellular concentrations of gadolinium diethylenetriamine pentaacetic acid bismethylamide (Gd-DTPA-BMA) to vary the exchange regime, T(1) and T(2) relaxation data for acute myeloid leukemia (AML) cell samples were obtained and then analyzed using a two-pool model of relaxation with exchange. Leukemia cells treated with cisplatin to induce apoptosis exhibited a statistically significant (P < 0.05) decrease in intracellular longitudinal relaxation time, T(1I), from 1030 ms to 940 ms, a decrease (P < 0.001) in the intracellular water fraction, M(0I), from 0.86 to 0.68 and a statistically significant increase (P < 0.01) in transmembrane water exchange rate, k(IE), from 1.4 s(-1) to 6.8 s(-1). The changes in MR parameters correlated with quantitative histology, such as cellular cross-sectional area and average nuclear area measurements. The results of this study emphasize the importance of accounting for water exchange in dynamic contrast-enhanced MRI (DCE-MRI) studies, particularly those that examine tumor response to therapies in which apoptotic changes occur.

Enhanced detection of diffusion reductions in Creutzfeldt-Jakob disease at a higher B factor

BACKGROUND AND PURPOSE

Diffusion-weighted imaging (DWI) is sensitive to the cerebral manifestations of human prion diseases. The magnitude of diffusion weighting, termed "b factor," has only been evaluated at the standard b = 1000 s/mm(2). This is the first rigorous evaluation of b = 2000 s/mm(2) in Creutzfeldt-Jakob Disease (CJD).

MATERIALS AND METHODS

We compared DWI characteristics of 13 patients with CJD and 15 healthy controls at b = 1000 s/mm(2) and b = 2000 s/mm(2). Apparent diffusion coefficients (ADC) were computed and analyzed for the whole brain by voxel-wise analysis (by SPM5) as well as in anatomically defined volumes of interest (by FSL FIRST).

RESULTS

Measured ADC was significantly lower (by approximately 5%-15%) at b = 2000 s/mm(2) than at b = 1000 s/mm(2) and significantly lower in patients than in controls. The differences between patients and controls were greater and more extensive at b = 2000 s/mm(2) than at b = 1000 s/mm(2) in the expected regions (thalamus, putamen, and caudate nucleus).

CONCLUSIONS

Because higher b factors change the absolute value of observed ADC, as well as lesion detection, care should be taken when combining studies using different b factors. While the clinical application of high b factors is currently limited by a low signal intensity-to-noise ratio, it may offer more information in questionable cases, and our results confirm and extend the central role of diffusion imaging in human prion diseases.

Mathematical description of q-space in spherical coordinates: exact q-ball imaging

Novel methodologies have been recently developed to characterize the microgeometry of neural tissues and porous structures via diffusion MRI data. In line with these previous works, this article provides a detailed mathematical description of q-space in spherical coordinates that helps to highlight the differences and similarities between various related q-space methodologies proposed to date such as q-ball imaging (QBI), diffusion spectrum imaging (DSI), and diffusion orientation transform imaging (DOT). This formulation provides a direct relationship between the orientation distribution function (ODF) and the diffusion data without using any approximation. Under this relationship, the exact ODF can be computed by means of the Radon transform of the radial projection (in q-space) of the diffusion MRI signal. This new methodology, termed exact q-ball imaging (EQBI), was put into practice using an analytical ODF estimation in terms of spherical harmonics that allows obtaining model-free and model-based reconstructions. This work provides a new framework for combining information coming from diffusion data recorded on multiple spherical shells in q-space (hybrid diffusion imaging encoding scheme), which is capable of mapping ODF to a high accuracy. This represents a step toward a more efficient development of diffusion MRI experiments for obtaining better ODF estimates.

A multi-compartmental SE-BOLD interpretation for stimulus-related signal changes in diffusion-weighted functional MRI

A new interpretation is proposed for stimulus-induced signal changes in diffusion-weighted functional MRI. T(2)-weighted spin-echo echo-planar images were acquired at different diffusion-weightings while visual stimulation was presented to human volunteers. The amplitudes of the positive stimulus-correlated response and post-stimulus undershoot (PSU) in the functional time-courses were found to follow different trends as a function of b-value. Data were analysed using a three-compartment signal model, with one compartment being purely vascular and the other two dominated by fast- and slow-diffusing molecules in the brain tissue. The diffusion coefficients of the tissue were assumed to be constant throughout the experiments. It is shown that the stimulus-induced signal changes can be decomposed into independent contributions originating from each of the three compartments. After decomposition, the fast-diffusion phase displays a substantial PSU, while the slow-diffusion phase demonstrates a highly reproducible and stimulus-correlated time-course with minimal undershoot. The decomposed responses are interpreted in terms of the spin-echo blood oxygenation level dependent (SE-BOLD) effect, and it is proposed that the signal produced by fast- and slow-diffusing molecules reflect a sensitivity to susceptibility changes in arteriole/venule- and capillary-sized vessels, respectively. This interpretation suggests that diffusion-weighted SE-BOLD imaging may provide subtle information about the haemodynamic and neuronal responses.

Diffusion-weighted MRI measurements on stroke patients reveal water-exchange mechanisms in sub-acute ischaemic lesions

The aim of this study was to investigate the diffusion time dependence of signal-versus-b curves obtained from diffusion-weighted magnetic resonance imaging (DW-MRI) of sub-acute ischaemic lesions in stroke patients. In this case series study, 16 patients with sub-acute ischaemic stroke were examined with DW-MRI using two different diffusion times (60 and 260 ms). Nine of these patients showed sufficiently large lesions without artefacts to merit further analysis. The signal-versus-b curves from the lesions were plotted and analysed using a two-compartment model including compartmental exchange. To validate the model and to aid the interpretation of the estimated model parameters, Monte Carlo simulations were performed. In eight cases, the plotted signal-versus-b curves, obtained from the lesions, showed a signal-curve split-up when data for the two diffusion times were compared, revealing effects of compartmental water exchange. For one of the patients, parametric maps were generated based on the extracted model parameters. These novel observations suggest that water exchange between different water pools is measurable and thus potentially useful for clinical assessment. The information can improve the understanding of the relationship between the DW-MRI signal intensity and the microstructural properties of the lesions.

Effects of echo time on diffusion quantification of brain white matter at 1.5 T and 3.0 T

The aim was to investigate the effects of echo time (TE) on diffusion quantification of brain white matter. Seven rhesus monkeys (all males; age, 4-6 years; weight, 5-7 kg) underwent diffusion tensor imaging (DTI) with a series of TEs in 1.5 T and 3.0 T MR scanners. The mean diffusivity (MD), fractional anisotropy (FA), primary (lambda(1)), and transverse eigenvalues (lambda(23)) were measured in a region of interest at the bilateral internal capsule. Pearson correlation showed that the FA and lambda(1) increased and lambda(23) decreased with TE both at 1.5 T and 3.0 T except for the MD. Repeated measurement analysis of variance (ANOVA) also showed significantly higher FA and lower MD and lambda(23) at 3.0 T than those at 1.5 T (P<0.01), but no statistical differences were found in lambda(1) between these two field strengths (P=0.709). These findings implied that TE and field strength might influence diffusion quantification in brain white matter.

Diffusion-weighted magnetic resonance imaging as a cancer biomarker: consensus and recommendations

On May 3, 2008, a National Cancer Institute (NCI)-sponsored open consensus conference was held in Toronto, Ontario, Canada, during the 2008 International Society for Magnetic Resonance in Medicine Meeting. Approximately 100 experts and stakeholders summarized the current understanding of diffusion-weighted magnetic resonance imaging (DW-MRI) and reached consensus on the use of DW-MRI as a cancer imaging biomarker. DW-MRI should be tested as an imaging biomarker in the context of well-defined clinical trials, by adding DW-MRI to existing NCI-sponsored trials, particularly those with tissue sampling or survival indicators. Where possible, DW-MRI measurements should be compared with histologic indices including cellularity and tissue response. There is a need for tissue equivalent diffusivity phantoms; meanwhile, simple fluid-filled phantoms should be used. Monoexponential assessments of apparent diffusion coefficient values should use two b values (>100 and between 500 and 1000 mm2/sec depending on the application). Free breathing with multiple acquisitions is superior to complex gating techniques. Baseline patient reproducibility studies should be part of study designs. Both region of interest and histogram analysis of apparent diffusion coefficient measurements should be obtained. Standards for measurement, analysis, and display are needed. Annotated data from validation studies (along with outcome measures) should be made publicly available. Magnetic resonance imaging vendors should be engaged in this process. The NCI should establish a task force of experts (physicists, radiologists, and oncologists) to plan, organize technical aspects, and conduct pilot trials. The American College of Radiology Imaging Network infrastructure may be suitable for these purposes. There is an extraordinary opportunity for DW-MRI to evolve into a clinically valuable imaging tool, potentially important for drug development.

[Brain apparent diffusion coefficient: differences caused by age, sex, laterality, and distinct b value]

OBJECTIVE

To analyze the effects of age, sex, and b value on the apparent diffusion coefficient (ADC) in brain areas affected by neurodegenerative diseases.

MATERIAL AND METHODS

We studied the ADC of the genu and splenium of the corpus callosum and of the hippocampus in normal patients using diffusion magnetic resonance imaging (dMRI) with b1,000 s/mm2 and b3,000 s/mm2. We calculated the differences between the ADC (diffusion differential [DD]) with b1,000 and with b3,000 for each region. Patients were classified into the following age groups (<or=30 years old, 31-60 years old, >60 years old). We used a Kruskal-Wallis one-way ANOVA and the Bonferroni correction to analyze the differences in ADC and DD between age groups and between sexes. Pearson's chi-square test was used to correlate the ADC and DD with age.

RESULTS

In the right hippocampus, we observed differences in ADC (b1,000, p=0.011; b3,000, p=0.024) and DD (p=0.006) with age. Differences in ADC were observed between the 31-60 year-old age group and the >60 year-old age group (p=0.009) for b1,000, and between the<30 year-old age group and the 31-60 year-old age group (p=0.036) for b3,000. The DD in the >60 year-old age group was different from the rest. In the corpus callosum, there were significant differences between sexes in the DD of the genu (p=0.016). The DD was correlated with age in the right hippocampus (r=0.321, p=0.023).

CONCLUSIONS

Our data indicate greater stability in mean ADC values with b3000 during aging. It might be useful to analyze the ADC with a higher b in patients with neurodegenerative diseases.

Measuring small compartmental dimensions with low-q angular double-PGSE NMR: The effect of experimental parameters on signal decay

In confined geometries, the MR signal attenuation obtained from single pulsed gradient spin echo (s-PGSE) experiments reflects the dimension of the compartment, and in some cases, its geometry. However, to measure compartment size, high q-values must be applied, requiring high gradient strengths and/or long pulse durations and diffusion times. The angular double PGSE (d-PGSE) experiment has been proposed as a means to extract dimensions of confined geometries using low q-values. In one realization of the d-PGSE experiment, the first gradient pair is fixed along the x-axis, and the orientation of the second gradient pair is varied in the X-Y plane. Such a measurement is sensitive to microscopic anisotropy induced by the boundaries of the restricting compartment, and allows extraction of the compartment dimension. In this study, we have juxtaposed angular d-PGSE experiments and simulations to extract sizes from well-characterized NMR phantoms consisting of water filled microcapillaries. We are able to accurately extract sizes of small compartments (5mum) using the angular d-PGSE experiment even when the short gradient pulse (SGP) approximation is violated and over a range of mixing and diffusion times. We conclude that the angular d-PGSE experiment may fill an important niche in characterizing compartment sizes in which restricted diffusion occurs.

Estimation of cell membrane permeability and intracellular diffusion coefficient of human gray matter

The signal intensity of diffusion-weighted imaging (DWI) is sensitive to the intra- and extracellular diffusion coefficient of water and cell membrane permeability. We applied a method we proposed in previous papers to estimate noninvasively the membrane permeability and intracellular diffusion coefficient of normal human brain (gray matter) in 3 normal volunteers. We theoretically compared predicted signals and experiment results using a 1.5-tesla magnetic resonance (MR) imaging system. We acquired images using an echo planar imaging (EPI) sequence, applying motion-probing gradient (MPG) pulses in 3 directions. We periodically performed numerical simulations for various combinations of membrane permeability and intracellular diffusion coefficients using the finite-difference method. By minimizing the difference between signals obtained experimentally and those from numerical simulation, we could estimate membrane permeability (76+/-9 mm2/s mum) and intracellular diffusion coefficient (1.0+/-0.0 mm2/s) for the human brain. The estimated membrane permeability was the criterion value for diagnosing disease in gray matter.

The tensor distribution function

Diffusion weighted magnetic resonance imaging is a powerful tool that can be employed to study white matter microstructure by examining the 3D displacement profile of water molecules in brain tissue. By applying diffusion-sensitized gradients along a minimum of six directions, second-order tensors (represented by three-by-three positive definite matrices) can be computed to model dominant diffusion processes. However, conventional DTI is not sufficient to resolve more complicated white matter configurations, e.g., crossing fiber tracts. Recently, a number of high-angular resolution schemes with more than six gradient directions have been employed to address this issue. In this article, we introduce the tensor distribution function (TDF), a probability function defined on the space of symmetric positive definite matrices. Using the calculus of variations, we solve the TDF that optimally describes the observed data. Here, fiber crossing is modeled as an ensemble of Gaussian diffusion processes with weights specified by the TDF. Once this optimal TDF is determined, the orientation distribution function (ODF) can easily be computed by analytic integration of the resulting displacement probability function. Moreover, a tensor orientation distribution function (TOD) may also be derived from the TDF, allowing for the estimation of principal fiber directions and their corresponding eigenvalues.

Does diffusion kurtosis imaging lead to better neural tissue characterization? A rodent brain maturation study

Diffusion kurtosis imaging (DKI) can be used to estimate excess kurtosis, which is a dimensionless measure for the deviation of water diffusion profile from Gaussian distribution. Several recent studies have applied DKI to probe the restricted water diffusion in biological tissues. The directional analysis has also been developed to obtain the directionally specific kurtosis. However, these studies could not directly evaluate the sensitivity of DKI in detecting subtle neural tissue alterations. Brain maturation is known to involve various biological events that can affect water diffusion properties, thus providing a sensitive platform to evaluate the efficacy of DKI. In this study, in vivo DKI experiments were performed in normal Sprague-Dawley rats of 3 different ages: postnatal days 13, 31 and 120 (N=6 for each group). Regional analysis was then performed for 4 white matter (WM) and 3 gray matter (GM) structures. Diffusivity and kurtosis estimates derived from DKI were shown to be highly sensitive to the developmental changes in these chosen structures. Conventional diffusion tensor imaging (DTI) parameters were also computed using monoexponential model, yielding reduced sensitivity and directional specificity in monitoring the brain maturation changes. These results demonstrated that, by measuring directionally specific diffusivity and kurtosis, DKI offers a more comprehensive and sensitive detection of tissue microstructural changes. Such imaging advance can provide a better MR diffusion characterization of neural tissues, both WM and GM, in normal, developmental and pathological states.

High b-value diffusion-weighted imaging in normal and malignant peripheral zone tissue of the prostate: effect of signal-to-noise ratio

PURPOSE

To determine whether the apparent diffusion coefficient (ADC) obtained using a high b-value (2,000 s/mm2) is superior to that using a standard b-value (1,000 s/mm2) for discriminating malignant from normal peripheral tissue in the prostate.

METHODS

Twenty-six patients with biopsy-proven prostate cancer underwent 1.5T magnetic resonance (MR) imaging including single-shot, echo-planar diffusion-weighted imaging (DWI) with repetition time/echo time, 3500/88 ms; 4-mm slice thickness; 1-mm interslice gap; 144x128 matrix; field of view, 250x250 mm; number of excitations, 10; and b-values, 0, 1,000, and 2,000 s/mm2. For each patient, ADC values were obtained for malignant and normal tissue using b=1,000 and 2,000 in a monoexponential model. Signal-to-noise (SNR) and contrast-to-noise (CNR) ratios in DWI were also evaluated.

RESULTS

At b=1,000, the mean ADC (x10(-3) mm2/s) for malignant tissue was 0.82+/-0.27 (range 0.43-1.29) and for normal tissue, 1.69+/-0.23 (1.31-2.18). At b=2000, the mean ADC for malignant tissue was 0.61+/-0.19 (0.30-0.94) and for normal tissue, 1.01+/-0.14 (0.73-1.35). Significant ADC overlap between the malignant and normal tissue was recognized at b=2000. As b-value increased, the mean SNR within malignant tissue decreased by 21.6%, and mean CNR decreased 17.3%.

CONCLUSIONS

Under the same imaging conditions, measuring ADC using a high b-value (2,000 s/mm2) in a monoexponential model has little diagnostic advantage over using the standard b-value (1,000 s/mm2) in discriminating malignant from normal prostate tissue.

High b-value diffusion tensor imaging of the neonatal brain at 3T

BACKGROUND AND PURPOSE

Diffusion-weighted MR imaging studies of the adult brain have shown that contrast between lesions and normal tissue is increased at high b-values. We designed a prospective study to test the hypothesis that diffusion tensor imaging (DTI) obtained at high b-values increases image contrast and lesion conspicuity in the neonatal brain.

MATERIALS AND METHODS

We studied 17 neonates, median (range) age of 10 (2-96) days, who were undergoing MR imaging for clinical indications. DTI was performed on a Philips 3T Intera system with b-values of 350, 700, 1500, and 3000 s/mm(2). Image contrast and lesion conspicuity at each b-value were visually assessed. In addition, regions of interest were positioned in the central white matter at the level of the centrum semiovale, frontal and occipital white matter, splenium of the corpus callosum, posterior limb of the internal capsule, and the thalamus. Apparent diffusion coefficient (ADC) and fractional anisotropy (FA) values for these regions were calculated.

RESULTS

Isotropic diffusion image contrast and lesion-to-normal-tissue contrast increased with increasing b-value. ADC values decreased with increasing b-value in all regions studied; however, there was no change in FA with increasing b-value.

CONCLUSIONS

Diffusion image contrast increased at high b-values may be useful in identifying lesions in the neonatal brain.

A highly sensitive radial diffusion measurement method for white matter tract investigation

This article describes a novel approach for local estimation of the radial diffusion coefficient (D(perpendicular)) in white matter (WM) regions containing well-oriented nervous fibers. The method is based on the assumption that the diffusion process in well-organized WM regions responds to a cylindrical symmetry. The increased precision in the estimation of D(perpendicular) provided by this local approach compared to standard techniques based on diffusion tensor imaging is demonstrated using numerical simulations. An in vivo validation of the technique is also provided, showing its application to the corpus callosum of six healthy volunteers, highlighting the sensitivity of the method. Assuming that D(perpendicular) is sensitive to myelin integrity, our technique has the potential to investigate pathophysiological aspects of several neurological and psychiatric disorders with improved precision in targeted WM tracts.

Reduced encoding diffusion spectrum imaging implemented with a bi-Gaussian model

Diffusion spectrum imaging (DSI) can map complex fiber microstructures in tissues by characterizing their 3-D water diffusion spectra. However, a long acquisition time is required for adequate q-space sampling to completely reconstruct the 3-D diffusion probability density function. Furthermore, to achieve a high q-value encoding for sufficient spatial resolution, the diffusion gradient duration and the diffusion time are usually lengthened on a clinical scanner, resulting in a long echo time and low signal-to-noise ratio of diffusion-weighted images. To bypass long acquisition times and strict gradient requirements, the reduced-encoding DSI (RE-DSI) with a bi-Gaussian diffusion model is presented in this study. The bi-Gaussian extrapolation kernel, based on the assumption of the bi-Gaussian diffusion signal curve across biological tissue, is applied to the reduced q-space sampling data in order to fulfill the high q-value requirement. The crossing phantom model and the manganese-enhanced rat model served as standards for accuracy assessment in RE-DSI. The errors of RE-DSI in estimating fiber orientations were close to the noise limit. Meanwhile, evidence from a human study demonstrated that RE-DSI significantly decreased the acquisition time required to resolve complex fiber orientations. The presented method facilitates the application of DSI analysis on a clinical magnetic resonance imaging system.

The effect of the diffusion time and pulse gradient duration ratio on the diffraction pattern and the structural information estimated from q-space diffusion MR: experiments and simulations

q-Space diffusion MRI (QSI) provides a means of obtaining microstructural information about porous materials and neuronal tissues from diffusion data. However, the accuracy of this structural information depends on experimental parameters used to collect the MR data. q-Space diffusion MR performed on clinical scanners is generally collected with relatively long diffusion gradient pulses, in which the gradient pulse duration, delta, is comparable to the diffusion time, Delta. In this study, we used phantoms, consisting of ensembles of microtubes, and mathematical models to assess the effect of the ratio of the diffusion time and the duration of the diffusion pulse gradient, i.e., Delta/delta, on the MR signal attenuation vs. q, and on the measured structural information extracted therefrom. We found that for Delta/delta approximately 1, the diffraction pattern obtained from q-space MR data are shallower than when the short gradient pulse (SGP) approximation is satisfied. For long delta the estimated compartment size is, as expected, smaller than the real size. Interestingly, for Delta/delta approximately 1 the diffraction peaks are shifted to even higher q-values, even when delta is kept constant, giving the impression that the restricted compartments are even smaller than they are. When phantoms composed of microtubes of different diameters are used, it is more difficult to estimate the diameter distribution in this regime. Excellent agreement is found between the experimental results and simulations that explicitly account for the use of long duration gradient pulses. Using such experimental data and this mathematical framework, one can estimate the true compartment dimensions when long and finite gradient pulses are used even when Delta/delta approximately 1.

High b-value q-space diffusion-weighted MRI of the human cervical spinal cord in vivo: feasibility and application to multiple sclerosis

Q-space analysis is an alternative analysis technique for diffusion-weighted imaging (DWI) data in which the probability density function (PDF) for molecular diffusion is estimated without the need to assume a Gaussian shape. Although used in the human brain, q-space DWI has not yet been applied to study the human spinal cord in vivo. Here we demonstrate the feasibility of performing q-space imaging in the cervical spinal cord of eight healthy volunteers and four patients with multiple sclerosis. The PDF was computed and water displacement and zero-displacement probability maps were calculated from the width and height of the PDF, respectively. In the dorsal column white matter, q-space contrasts showed a significant (P < 0.01) increase in the width and a decrease in the height of the PDF in lesions, the result of increased diffusion. These q-space contrasts, which are sensitive to the slow diffusion component, exhibited improved detection of abnormal diffusion compared to perpendicular apparent diffusion constant measurements. The conspicuity of lesions compared favorably with magnetization transfer (MT)-weighted images and quantitative CSF-normalized MT measurements. Thus, q-space DWI can be used to study water diffusion in the human spinal cord in vivo and is well suited to assess white matter damage.

Ischemia-induced changes of intracellular water diffusion in rat glioma cell cultures

Diffusion-weighted MRI is commonly used in the diagnosis and evaluation of ischemic stroke because of the rapid decrease observed in the apparent diffusion coefficient (ADC) of tissue water following ischemia. Although this observation has been clinically useful for many years, the biophysical mechanisms underlying the reduction of tissue ADC are still unknown. To help elucidate these mechanisms, we have employed a novel three-dimensional (3D) hollow-fiber bioreactor (HFBR) perfused cell culture system that enables cells to be grown to high density and studied via MRI and MRS. By infusing contrast media into the HFBR, signals from intracellular water and extracellular water are spectroscopically resolved and can be investigated individually. Diffusion measurements carried out on C6 glioma HFBR cell cultures indicate that ischemia-induced cellular swelling results in an increase in the ADC of intracellular water from 0.35 microm(2)/ms to approximately 0.5 microm(2)/ms (diffusion time = 25 ms).

Rapid generation of biexponential and diffusional kurtosis maps using multi-layer perceptrons: a preliminary experience

OBJECT

To investigate whether multi-layer perceptrons (MLPs) could be used to determine biexponential and diffusional kurtosis model parameters directly from diffusion-weighted images.

MATERIALS AND METHODS

Model parameters were determined with least-squares fitting and with MLPs. The corresponding estimates were compared with linear regressions, t tests and Levene's tests. Residuals were also compared.

RESULTS

Strong linear correlation was found for all parameters. MLP estimates were unbiased for the biexponential but not for the kurtosis model, and generally had smaller variance. Residuals were smaller for MLP estimates. The maps generated by the two methods were visually very similar.

CONCLUSION

Multi-layer perceptrons are potentially useful as a curve fitting method for these models.

Compartmental relaxation and diffusion tensor imaging measurements in vivo in lambda-carrageenan-induced edema in rat skeletal muscle

Integrated diffusion tensor T(2) measurements were made on normal and edematous rat muscle, and the data were fitted with one- and two-compartment models, respectively. Edematous muscle exhibited a short-lived component (T(2) = 28 +/- 6 ms), with diffusion characteristics similar to that of normal muscle, and a long-lived component (T(2) = 96 +/- 27 ms), with greater mean apparent diffusion coefficient (ADC) and lower fractional anisotropy (FA). With this two-component description of diffusion and relaxation, values of ADC and FA estimated with a conventional pulsed-gradient spin-echo sequence will depend on the echo time, relative fraction of short-lived and long-lived water signals, and the intrinsic ADC and FA values within the tissue. On the basis of the relative differences in water diffusion properties between long-lived and short-lived water signals, as well as the similarities between the short-lived component and normal tissue, it is postulated that these two signal components largely reflect intracellular and extracellular water.

Computation of diffusion function measures in q-space using magnetic resonance hybrid diffusion imaging

The distribution of water diffusion in biological tissues may be estimated by a 3-D Fourier transform (FT) of diffusion-weighted measurements in q-space. In this study, methods for estimating diffusion spectrum measures (the zero-displacement probability, the mean-squared displacement, and the orientation distribution function) directly from the q-space signals are described. These methods were evaluated using both computer simulations and hybrid diffusion imaging (HYDI) measurements on a human brain. The HYDI method obtains diffusion-weighted measurements on concentric spheres in q-space. Monte Carlo computer simulations were performed to investigate effects of noise, q-space truncation, and sampling interval on the measures. This new direct computation approach reduces HYDI data processing time and image artifacts arising from 3-D FT and regridding interpolation. In addition, it is less sensitive to the noise and q-space truncation effects than conventional approach. Although this study focused on data using the HYDI scheme, this computation approach may be applied to other diffusion sampling schemes including Cartesian diffusion spectrum imaging.

ROBUST MAXIMUM LIKELIHOOD ESTIMATION IN Q-SPACE MRI

Q-space imaging is an emerging diffusion weighted MR imaging technique to estimate molecular diffusion probability density functions (PDF's) without the need to assume a Gaussian distribution. We present a robust M-estimator, Q-space Estimation by Maximizing Rician Likelihood (QEMRL), for diffusion PDF's based on maximum likelihood. PDF's are modeled by constrained Gaussian mixtures. In QEMRL, robust likelihood measures mitigate the impacts of imaging artifacts. In simulation and in vivo human spinal cord, the method improves reliability of estimated PDF's and increases tissue contrast. QEMRL enables more detailed exploration of the PDF properties than prior approaches and may allow acquisitions at higher spatial resolution.

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

Diffusion imaging with high-b factors, high spatial resolution and cerebrospinal fluid signal suppression was performed in order to characterize the biexponential nature of the diffusion-related signal decay with b-factor in normal cortical gray and deep gray matter (GM). Integration of inversion pulses with a line scan diffusion imaging sequence resulted in 91% cerebrospinal fluid signal suppression, permitting accurate measurement of the fast diffusion coefficient in cortical GM (1.142+/-0.106 microm2/ms) and revealing a marked similarity with that found in frontal white matter (WM) (1.155+/-0.046 microm2/ms). The reversal of contrast between GM and WM at low vs high b-factors is shown to be due to a significantly faster slow diffusion coefficient in cortical GM (0.338+/-0.027 microm2/ms) than in frontal WM (0.125+/-0.014 microm2/ms). The same characteristic diffusion differences between GM and WM are observed in other brain tissue structures. The relative component size showed nonsignificant differences among all tissues investigated. Cellular architecture in GM and WM are fundamentally different and may explain the two- to threefold higher slow diffusion coefficient in GM.

Towards better MR characterization of neural tissues using directional diffusion kurtosis analysis

MR diffusion kurtosis imaging (DKI) was proposed recently to study the deviation of water diffusion from Gaussian distribution. Mean kurtosis, the directionally averaged kurtosis, has been shown to be useful in assessing pathophysiological changes, thus yielding another dimension of information to characterize water diffusion in biological tissues. In this study, orthogonal transformation of the 4th order diffusion kurtosis tensor was introduced to compute the diffusion kurtoses along the three eigenvector directions of the 2nd order diffusion tensor. Such axial (K(//)) and radial (K( upper left and right quadrants)) kurtoses measured the kurtoses along the directions parallel and perpendicular, respectively, to the principal diffusion direction. DKI experiments were performed in normal adult (N=7) and formalin-fixed rat brains (N=5). DKI estimates were documented for various white matter (WM) and gray matter (GM) tissues, and compared with the conventional diffusion tensor estimates. The results showed that kurtosis estimates revealed different information for tissue characterization. For example, K(//) and K( upper left and right quadrants) under formalin fixation condition exhibited large and moderate increases in WM while they showed little change in GM despite the overall dramatic decrease of axial and radial diffusivities in both WM and GM. These findings indicate that directional kurtosis analysis can provide additional microstructural information in characterizing neural tissues.

Characterization of anomalous diffusion from mr signal may be a new probe to tissue microstructure

Observation of translational self-diffusion of water molecules using magnetic resonance (MR) techniques has proven to be a powerful means to probe tissue microstructure. The collected MR signal depends on experimentally controllable parameters as well as the descriptors of tissue geometry. In order to obtain the latter, one needs to employ accurate models to characterize the dependence of the signal on the varied experimental parameters. In this work, a simple model describing diffusion in disordered media and fractal spaces is shown to describe the diffusion-time dependence of the diffusion attenuated MR signal obtained from biological specimens successfully. The model enables one to quantify the evolution of the average water displacement probabilities in terms of two exponents--dw and ds. The experiments performed on excised human neural tissue samples and human red blood cell ghosts indicate that these two parameters are sensitive to tissue microstructure. Therefore, it may be possible to use the proposed scheme to generate novel contrast mechanism for classifying and segmenting tissue.

Line scan diffusion spectrum of the denervated rat skeletal muscle

PURPOSE

To detect the earlier changes of the skeletal muscle of rats after peripheral nerve injury by measuring the apparent diffusion coefficient (ADC) on diffusion MR spectroscopy.

MATERIALS AND METHODS

The posterior tibial nerve was transected in six rats (nerve transection group) and was only dissected in six rats (control group). At one, three, five, seven, 14, and 28 days after the surgery, both the T2 value and the ADC of gastrocnemius muscle were measured using a line-scan diffusion spectrum on a 1.5T clinical MR imager on both groups.

RESULTS

In the nerve transection group, the T2 ratio compared to the contralateral side increased gradually over four weeks after the transection, while the ADC ratio increased right after the surgery and began to decrease at five days. Four weeks after the transection, the ADC ratio returned to normal while the T2 ratio stayed at a high value. The control group indicated an almost constant T2 and ADC ratio during the experimental periods.

CONCLUSION

The ADC of the skeletal muscle increased quickly after the transection of the dominant peripheral nerve and was detectable one day after the surgery. Diffusion MRI can be a useful tool for early detection of peripheral nerve injury instead of T2-weighted MRI or electromyography (EMG).

Technology insight: water diffusion MRI--a potential new biomarker of response to cancer therapy

Diffusion-weighted MRI (DW-MRI) is a functional imaging technique that displays information about the extent and direction of random water motion in tissues. Water movement in tissues is modified by interactions with hydrophobic cellular membranes, intracellular organelles and macromolecules. DW-MRI provides information on extracellular-space tortuosity, tissue cellularity and the integrity of cellular membranes. Images can be sensitive to large or small displacements of water, therefore, macroscopic water flows and microscopic water displacements in the extracellular space can be depicted. Preclinical and clinical data indicate a number of potential roles of DW-MRI in the characterization of malignancy, including determination of lesion aggressiveness and monitoring response to therapy. This Review outlines the biological basis of observations made on DW-MRI and describes how measurements are acquired and quantified, and discusses the interpretation of images and limitations of the technique. The strength of evidence for adoption of DW-MRI as a biomarker for the assessment of tumor response is presented.

q-Space diffusion of myelin-deficient spinal cords

The apparent water diffusion anisotropy in white matter (WM) of excised spinal cords of myelin-deficient (md) rats and their age-matched controls was studied by high-b-value q-space diffusion MRS and MRI at different diffusion times. Non-monoexponential signal decay was observed at long diffusion times. The mean displacements in the md spinal cords were found to be higher than those of the controls. The apparent anisotropy (AA) of the fast-diffusing component was found to decrease more dramatically with the increase in diffusion time for the md spinal cords as compared with controls, whereas the AA of the slow-diffusing component in the controls was found to increase with the increase in diffusion time while that of the md cords decreased with the increase in diffusion time. When diffusion MRI was performed, similar diffusion anisotropy was extracted for the md and control spinal cords at diffusion times of 22 and 50 ms. Only at a diffusion time of about 200 ms was a significant difference obtained in the AA of the two groups. This originates from the much smaller increase in the mean displacement perpendicular to the fiber direction in the control group vs. the md group when the diffusion time was increased.

High b-value q-space diffusion MRS of nerves: structural information and comparison with histological evidence

High b-value q-space diffusion MRS was used to study the diffusion characteristics of formalin-fixed swine optic and sciatic nerves over a large range of diffusion times (3.7-99.3 ms). The very short diffusion time range was studied with a 1 ms resolution. The displacement distribution profiles obtained were fitted to a bi-Gaussian function, and structural parameters were extracted from the q-space diffusion MRS data. This structural information was correlated with axon sizes obtained by histological examination. It was found that high b-value q-space diffusion MRS can easily distinguish between the two nerve types. The root mean square displacements (rmsds) of both the slow and fast diffusing components of the optic nerves were found to be smaller than those of the sciatic nerves. When the rmsd was plotted against the square root of the diffusion time (t(d)(1/2)), it was found that all four components showed an increase in rmsd; this increase was significantly smaller than expected from the Einstein equation. However, the most restricted component is the slow diffusing component of the optic nerve. This is also the only diffusing component that shows a large change in the slope (i.e. a 'breaking point') of the plot of rmsd as a function of t(d)(1/2). This rmsd is very similar to the mean axon size of these optic nerves determined histologically. Such a change in slope was less apparent for the slow diffusing component of sciatic nerves, which showed a wider distribution of axon size in histological images. The fast diffusing components of both nerve types showed only a small gradual change in the slope of rmsd plotted against t(d)(1/2). These findings are discussed in the context of component assignment, origin of restriction, and relationships between the structural information extracted from q-space diffusion MRS and histological examination.

In vivo visualization of displacement-distribution-derived parameters in q-space imaging

OBJECTIVE

This study aimed to explore the potential of in vivo q-space imaging in the differentiation between different cerebral water components.

MATERIALS AND METHODS

Diffusion-weighted imaging was performed in six directions with 32 equally spaced q values and a maximum b value of 6600 s/mm(2). The shape of the signal-attenuation curve and the displacement propagator were examined and compared with a normal distribution using the kurtosis parameter. Maps displaying kurtosis, fast and slow components of the apparent diffusion coefficients, fractional anisotropy and directional diffusion were calculated. The displacement propagator was further described by the full width at half and at tenth maximum and by the probability density of zero displacement P(0). Three healthy volunteers and three patients with previously diagnosed multiple sclerosis (MS) were examined.

RESULTS

Simulations indicated that the kurtosis of a signal-attenuation curve can determine if more than one water component is present and that care must be taken to select an appropriate threshold. It was possible to distinguish MS plaques in both signal and diffusional kurtosis maps, and in one patient, plaques of different degree of demyelinization showed different behavior.

DISCUSSION

Our results indicate that in vivo q-space analysis is a potential tool for the assessment of different cerebral water components, and it might extend the diagnostic interpretation of data from diffusion magnetic resonance imaging.

Efficient computation of PDF-based characteristics from diffusion MR signal

We present a general method for the computation of PDF-based characteristics of the tissue micro-architecture in MR imaging. The approach relies on the approximation of the MR signal by a series expansion based on Spherical Harmonics and Laguerre-Gaussian functions, followed by a simple projection step that is efficiently done in a finite dimensional space. The resulting algorithm is generic, flexible and is able to compute a large set of useful characteristics of the local tissues structure. We illustrate the effectiveness of this approach by showing results on synthetic and real MR datasets acquired in a clinical time-frame.