Non-Gaussian water diffusion kurtosis imaging of prostate cancer

Purpose

To evaluate the non-Gaussian water diffusion properties of prostate cancer (PCa) and determine the diagnostic performance of diffusion kurtosis (DK) imaging for distinguishing PCa from benign tissues within the peripheral zone (PZ), and assessing tumor lesions with different Gleason scores.

Materials and Methods

Nineteen patients who underwent diffusion weighted (DW) magnetic resonance imaging using multiple b-values and were pathologically confirmed with PCa were enrolled in this study. Apparent diffusion coefficient (ADC) was derived using a monoexponential model, while diffusion coefficient (D) and kurtosis (K) were determined using a DK model. Differences between the ADC, D and K values of benign PZ and PCa, as well as those of tumor lesions with Gleason scores of 6, 7 and ≥ 8 were assessed. Correlations between parameters D and K in PCa were analyzed using Pearson’s correlation coefficient. ADC, D and K values were correlated with Gleason scores of 6, 7 and ≥ 8, respectively.

Results

ADC and D values were significantly (p < 0.001) lower in PCa (0.79 ± 0.14 μm²/ms and 1.56 ± 0.23 μm²/ms, respectively) compared to benign PZ (1.23 ± 0.19 μm²/ms and 2.54 ± 0.24 μm²/ms, respectively). K values were significantly (p < 0.001) greater in PCa (0.96 ± 0.20) compared to benign PZ (0.59 ± 0.08). D and K showed fewer overlapping values between benign PZ and PCa compared to ADC. There was a strong negative correlation between D and K values in PCa (Pearson correlation coefficient r = − 0.729; p < 0.001). ADC and K values differed significantly in tumor lesions with Gleason scores of 6, 7 and ≥ 8 (p < 0.001 and p = 0.001, respectively), although no significant difference was detected for D values (p = 0.325). Significant correlations were found between the ADC value and Gleason score (r = − 0.828; p < 0.001), as well as the K value and Gleason score (r = 0.729; p < 0.001).

Conclusion

DK model may add value in PCa detection and diagnosis. K potentially offers a new metric for assessment of PCa.     

Intermolecular double quantum coherences (iDQc) and diffusion-weighted imaging (DWI) imaging of the human brain at 1.5 T

To study the sensitivity of intermolecular double quantum coherences (iDQc) imaging contrast to brain microstructure and brain anisotropy, we investigated the iDQC contrast between differently structured areas of the brain according to the strength and the direction of the applied correlation gradient. Thus diffusion-weighted imaging (DWI) and diffusion tensor imaging (DTI) maps have been obtained. This procedure, which consists of analyzing both iDQc and DWI images at different gradient strength and gradient direction, could be a promising tool for clinical brain investigations performed with higher than 1.5 T magnetic fields.     

Diffusion kurtosis imaging for the assessment of renal fibrosis of chronic kidney disease: A preliminary study

Purpose: To investigate the potential of diffusion kurtosis imaging (DKI) for the assessment of renal fibrosis in chronic kidney disease (CKD), using histopathology as the reference standard.Methods: Eighty-nine CKD patients and twenty healthy volunteers were recruited in this study. DKI was performed in all participants and all CKD patients received renal biopsy. The values of mean diffusivity (MD) and mean kurtosis (MK) in the renal cortex and medulla were compared between CKD patients and healthy volunteers. The Spearman correlation coefficient was calculated to assess the relationship between MD, MK values and the estimated glomerular filtration rate (eGFR), serum creatinine (SCr), 24 h urinary protein (24 h-UPRO), histopathological fibrosis score.Results: The medullary MD values were significantly lower than cortex, while the cortical MK values were significantly lower than medulla for all participants. Renal parenchymal MD values were significantly lower in the CKD patients than healthy controls, whereas MK values were significantly higher in the CKD patients than healthy controls. In the CKD patients, the significantly negative correlation was observed between the renal parenchymal MD values and the 24 h-UPRO, SCr, histopathological fibrosis score, as well as between the renal parenchymal MK values and the eGFR, while the significantly positive correlation was found between the renal parenchymal MD values and the eGFR, as well as between the renal parenchymal MK values and the 24 h-UPRO, SCr, histopathological fibrosis score.Conclusion: DKI shows great potential in the noninvasive assessment of renal fibrosis in CKD.     

Diffusion tensor imaging to study anisotropy in a particular porous system: the trabecular bone network

During the last decade, considerable effort has been invested into the development of diffusion tensor imaging (DTI) mainly used to investigate cerebral morphology. The aim of this paper is to review and to discuss our recent results about high magnetic field DTI application to study spongy bone tissue. Due to its peculiar properties, spongy bone represents a particular porous system sample. Strategies to perform DTI on porous systems and issues linked to DTI outcome interpretation are presented on the basis of our results concerning trabecular bone network characterization.     

Elevations of diffusion anisotropy are associated with hyper-acute stroke: a serial imaging study

Diffusion tensor imaging (DTI) studies of human ischemic stroke within 24 h of symptom onset have reported variable findings of changes in diffusion anisotropy. Serial DTI within 24 h may clarify these heterogeneous results. We characterized longitudinal changes of diffusion anisotropy by analyzing discrete ischemic white matter (WM) and gray matter (GM) regions during the hyperacute (2.5-7 h) and acute (21.5-29 h) scanning phases of ischemic stroke onset in 13 patients. Mean diffusivity (MD), fractional anisotropy (FA) and T2-weighted signal intensity were measured for deep and subcortical WM and deep and cortical GM areas in lesions outlined by a > or =30% decrease in MD. Average reductions of approximately 40% in relative (r) MD were observed in all four brain regions during both the hyperacute and acute phases post stroke. Overall, 9 of 13 patients within 7 h post symptom onset showed elevated FA in at least one of the four tissues, and within the same cohort, 11 of 13 patients showed reduced FA in at least one of the ischemic WM and GM regions at 21.5-29 h after stroke. The fractional anisotropy in the lesion relative to the contralateral side (rFA, mean+/-S.D.) was significantly elevated in some patients in the deep WM (1.10+/-0.11, n=4), subcortical WM (1.13+/-0.14, n=4), deep GM (1.07+/-0.06, n=1) and cortical GM (1.22+/-0.13, n=5) hyperacutely (< or =7 h); however, reductions of rFA at approximately 24 h post stroke were more consistent (rFA= 0.85+/-0.12).     

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 (λ₁, λ₂, λ₃), fractional anisotropy (FA) and apparent diffusion coefficient (ADC) were measured for anterior, central and posterior breast regions.

Results

Mean normal breast DTI measures were λ₁=2.51×10⁻³ mm²/s, λ₂=1.89×10⁻³ mm²/s, λ₃=1.39×10⁻³ mm²/s, ADC=1.95±0.24×10⁻³ mm²/s and FA=0.29±0.05 for b=600 s/mm². 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/mm² vs. b=0, 1000 s/mm², 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.     

Non-Gaussian diffusion imaging: a brief practical review

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

Feasibility of diffusional kurtosis tensor imaging in prostate MRI for the assessment of prostate cancer: Preliminary results

Purpose

To assess the feasibility of full diffusional kurtosis tensor imaging (DKI) in prostate MRI in clinical routine. Histopathological correlation was achieved by targeted biopsy.

Materials and Methods

Thirty-one men were prospectively included in the study. Twenty-one were referred to our hospital with increased prostate specific antigen (PSA) values (> 4 ng/ml) and suspicion of prostate cancer. The other 10 men were volunteers without any history of prostate disease. DKI applying diffusion gradients in 20 different spatial directions with four b-values (0, 300, 600, 1000 s/mm²) was performed additionally to standard functional prostate MRI. Region of interest (ROI)-based measurements were performed in all histopathologically verified lesions of every patient, as well as in the peripheral zone, and the central gland of each volunteer.

Results

DKI showed a substantially better fit to the diffusion-weighted signal than the monoexponential apparent diffusion coefficient (ADC). Altogether, 29 lesions were biopsied in 14 different patients with the following results: Gleason score 3 + 3 = 6 (n = 1), 3 + 4 = 7 (n = 7), 4 + 3 = 7 (n = 6), 4 + 4 = 8 (n = 1), and 4 + 5 = 9 (n = 2), and prostatitis (n = 12). Values of axial (K_ax) and mean kurtosis (K_mean) were significantly different in the tumor (K_ax 1.78 ± 0.39, K_mean 1.84 ± 0.43) compared with the normal peripheral zone (K_ax 1.09 ± 0.12, K_mean 1.16 ± 0.13; p < 0.001) or the central gland (K_ax 1.40 ± 0.12, K_mean 1.44 ± 0.17; p = 0.01 respectively). There was a minor correlation between axial kurtosis (r = 0.19) and the Gleason score.

Conclusion

Full DKI is feasible to utilize in a routine clinical setting. Although there is some overlap some DKI parameters can significantly distinguish prostate cancer from the central gland or the normal peripheral zone. Nevertheless, the additional value of DKI compared with conventional monoexponential ADC calculation remains questionable and requires further research.     

Comparison of different mathematical models of diffusion-weighted prostate MR imaging

Purpose

To evaluate which mathematical model (monoexponential, biexponential, statistical, kurtosis) fits best to the diffusion-weighted signal in prostate magnetic resonance imaging (MRI).

Materials and Methods

24 prostate 3-T MRI examinations of young volunteers (YV, n= 8), patients with biopsy proven prostate cancer (PC, n= 8) and an aged matched control group (AC, n= 8) were included. Diffusion-weighted imaging was performed using 11 b-values ranging from 0 to 800 s/mm².

Results

Monoexponential apparent diffusion coefficient (ADC) values were significantly (P<.001) lower in the peripheral (PZ) zone (1.18±0.16 mm²/s) and the central (CZ) zone (0.73±0.13 mm²/s) of YV compared to AC (PZ 1.92±0.17 mm²/s; CZ 1.35±0.21 mm²/s). In PC ADC_mono values (0.61±0.06 mm²/s) were significantly (P<.001) lower than in the peripheral of central zone of AC. Using the statistical analysis (Akaike information criteria) in YV most pixels were best described by the biexponential model (82%), the statistical model, respectively kurtosis (93%) each compared to the monoexponential model. In PC the majority of pixels was best described by the monoexponential model (57%) compared to the biexponential model.

Conclusion

Although a more complex model might provide a better fitting when multiple b-values are used, the monoexponential analyses for ADC calculation in prostate MRI is sufficient to discriminate prostate cancer from normal tissue using b-values ranging from 0 to 800 s/mm².     

On the effects of dephasing due to local gradients in diffusion tensor imaging experiments: relevance for diffusion tensor imaging fiber phantoms

The effect of susceptibility differences between fluid and fibers on the properties of DTI fiber phantoms was investigated. Thereto, machine-made, easily producible and inexpensive DTI fiber phantoms were constructed by winding polyamide fibers of 15 microm diameter around a circular acrylic glass spindle. The achieved fractional anisotropy was 0.78+/-0.02. It is shown by phantom measurements and Monte Carlo simulations that the transversal relaxation time T(2) strongly depends on the angle between the fibers and the B(0) field if the susceptibilities of the fibers and fluid are not identical. In the phantoms, the measured T(2) time at 3 T decreased by 60% for fibers running perpendicular to B(0). Monte Carlo simulations confirmed this result and revealed that the exact relaxation time depends strongly on the exact packing of the fibers. In the phantoms, the measured diffusion was independent of fiber orientation. Monte Carlo simulations revealed that the measured diffusion strongly depends on the exact fiber packing and that field strength and -orientation dependencies of measured diffusion may be minimal for hexagonal packing while the diffusion can be underestimated by more than 50% for cubic packing at 3 T. To overcome these effects, the susceptibilities of fibers and fluid were matched using an aqueous sodium chloride solution (83 g NaCl per kilogram of water). This enables an orientation independent and reliable use of DTI phantoms for evaluation purposes.     

Propagation of the kurtosis parameter of Hermite-cosh-Gaussian beams

Starting from the propagation equation of Hermite-cosh-Gaussian (HChG) beams and the intensity moments definition, an analytical expression for the propagation of the kurtosis parameter of unapertured HChG beams passing through paraxial optical ABCD systems is derived and illustrated numerically. Special interesting cases are discussed, in particular, the kurtosis parameter of HChG beams at the waist plane is obtained readily from our general propagation expression.     

Intravoxel incoherent motion imaging of the kidney: alterations in diffusion and perfusion in patients with renal dysfunction

Purpose

To investigate the relationship between estimated glomerular filtration rate (eGFR) and parameters calculated using intravoxel incoherent motion (IVIM) imaging of the kidneys.

Materials and Methods

We studied 365 patients, divided into 4 groups based on eGFR levels (mL/min/1.73 m²): group 1, eGFR ≥ 80(n = 80); group 2, eGFR 60–80 (n = 156); group 3, eGFR 30–60 (n = 114); and group 4 ,eGFR < 30 (n = 15). IVIM imaging was used to acquire diffusion-weighted images at 12 b values. The diffusion coefficient of pure molecular diffusion (D), the diffusion coefficient of microcirculation or perfusion (D*), and perfusion fraction (f) were compared among the groups using group 1 as control.

Results

In the renal cortex, D* values were significantly lower in groups 2, 3, and 4 than in group 1. The D value of renal cortex was significantly low in only group 3. In the renal medulla, the D* and D values were significantly lower only in groups 2 and 3, respectively.

Conclusion

As renal dysfunction progresses, renal perfusion might be reduced earlier and affected more than molecular diffusion in the renal cortex. These changes are effectively detected by IVIM MR imaging.     

Non-Gaussian diffusion MRI assessment of brain microstructure in mild cognitive impairment and Alzheimer’s disease

We report the first application of a novel diffusion-based MRI method, called diffusional kurtosis imaging (DKI), to investigate changes in brain tissue microstructure in patients with mild cognitive impairment (MCI) and AD and in cognitively intact controls. The subject groups were characterized and compared in terms of DKI-derived metrics for selected brain regions using analysis of covariance with a Tukey multiple comparison correction. Receiver operating characteristic (ROC) and binary logistic regression analyses were used to assess the utility of regional diffusion measures, alone and in combination, to discriminate each pair of subject groups. ROC analyses identified mean and radial kurtoses in the anterior corona radiata as the best individual discriminators of MCI from controls, with the measures having an area under the ROC curve (AUC) of 0.80 and 0.82, respectively. The next best discriminators of MCI from controls were diffusivity and kurtosis (both mean and radial) in the prefrontal white matter (WM), with each measure having an AUC between 0.77 and 0.79. Finally, the axial diffusivity in the hippocampus was the best overall discriminator of MCI from AD, having an AUC of 0.90. These preliminary results suggest that non-Gaussian diffusion MRI may be beneficial in the assessment of microstructural tissue damage at the early stage of MCI and may be useful in developing biomarkers for the clinical staging of AD.     

Simultaneous magnetic resonance imaging of diffusion anisotropy and diffusion gradient

The theory of diffusion gradient-weighted MRI (DGWI) is presented in this paper. The Bloch-Torrey equation was modified to include the effect of intravoxel spatial-location variation of water diffusion (diffusion gradient) on MRI signal, in addition to the effect of intravoxel spatial-direction variation of water diffusion (diffusion anisotropy). An analytical solution for a diffusion-encoding spin-echo pulse sequence was derived. Unlike water diffusion which attenuates the image signal intensity, this newly derived solution relates the spatial gradient of the water diffusion with the phase of the image signal. This novel MRI technique directly measures both the water diffusion and its spatial gradient, and thus offers a noninvasive imaging tool to simultaneously investigate the intravoxel inhomogeneity and anisotropy of tissue structures. In addition, as demonstrated with our preliminary data, this new method may be utilized to delineate the interfaces of tissues with different diffusion. This method is an extension of the successful diffusion tensor MRI (DTI), but requires no additional data acquisition. In addition to the measured diffusion tensor, this new method provides measurements of the spatial derivatives of the three principal diffusivities of the tensor, thereby providing additional information for improving white matter fiber tractography.     

An empirical characterization of the quality of DTI data and the efficacy of dyadic sorting

Metrics calculated from images acquired using the diffusion tensor imaging (DTI) technique possess a systematic bias that depends on signal-to-noise ratio (SNR). Dyadic sorting provides a simple method for remediating some of this bias within a region(s) of interest (ROI). Although this bias and its removal using dyadic sorting have been studied previously within a theoretical framework, one can employ precise geometric knowledge of microstructures to perform an empirical comparison between expected DTI results and those measured with a scanner. In this project, the biasing effect of low SNR (approximately 1-10) on DTI eigenvalues was measured directly using water-filled capillary structures of two different sizes, and the magnitude of the corrective effect of dyadically sorting eigenvector-eigenvalue pairs was characterized. Multiple DTI series were acquired for determining DTI metrics at eight unique SNR values, using T(R) to vary signal intensity via T(1) contrast. Differences between the second and third eigenvalues, which should be equal for prolate geometry, ranged from approximately 23% to 45% and from 19% to 41% for large and small inner diameter capillaries after sorting eigenvalues by magnitude, and ranged from approximately 1% to 18% and from 1% to 4% after dyadic sorting. A high-resolution DTI series was used to observe the effect of ROI size on dyadic sorting. For restriction of diffusion on the scale of the small capillary at SNR approximately 18, an ROI with > or =50 pixels is adequate to determine fractional anisotropy to 99% accuracy, while larger ROI are required to resolve the two smaller eigenvalues to the same accuracy ( approximately 330-390 pixels). At low values of SNR, the iteration of dyadic sorting is suggested to achieve good accuracy. A method for the incorporation of empirical measurements into a bias-correction map, which would be useful for characterizing uncertainty and for reducing systematic bias in DTI data, is introduced.     

Diffusion tensor imaging of native and degenerated human articular cartilage

Diffusion tensor imaging (DTI) is potentially sensitive to collagen degeneration in cartilage. In this study, DTI was measured on human cartilage samples with interventions of trypsin and collagenase. The measured preferred diffusion direction was consistent with the zonal structure of collagen network. The glycosaminoglycan concentration decreased and apparent diffusion coefficient increased with both interventions. The fractional anisotropy (FA) was not affected by trypsin and showed a slight increase with combined trypsin and collagenase intervention. DTI in cartilage is technically challenging due to the low FA and the almost undetectable change with collagen disruption seen here.     

Use of capillaries in the construction of an MRI phantom for the assessment of diffusion tensor imaging: demonstration of performance

Although diffusion tensor imaging (DTI) shows great potential for the diagnosis of a variety of pathologies, no consensus for an appropriate assessment standard of DTI exists. This study examined the feasibility of using water-filled arrays of glass capillaries to construct a DTI phantom suitable for making repeated and reproducible measurements required in a quality assessment program. Three phantoms were constructed using arrays of capillaries with three inner diameters (23, 48, and 82 μm). Data were acquired using DTI protocols; the fractional anisotropy (FA), mean apparent diffusion coefficient (ADC) and principal eigenvectors of the diffusion tensors were calculated. This study demonstrated four results: (1) echo-planar images show that susceptibility within the capillary arrays does not lead to substantial differences in precessional frequency in regions containing the arrays and neither do the regions show noticeable image distortion; (2) principal eigenvectors of the diffusion tensors agree to within <10.3° of the array orientations; (3) mean FA values (0.18–0.50) and ADC values (1.40–1.93×10−³ mm²/s) within specified regions of interest are in general agreement with simulations after a simple noise correction; and (4) these array performance characteristics are observable using a typical clinical DTI protocol.     

Diffusion tensor imaging fiber tracking with local tissue property sensitivity: phantom and in vivo validation

Diffusion tensor imaging (DTI) provides directional information that can be used to delineate brain white matter connections noninvasively via fiber tracking. The most commonly used methods for tractography are based on the streamline tracking algorithm for track propagation and a set of empirically and globally defined criteria for track termination. In this study, we propose a streamline tracking algorithm with high-order propagation accuracy and a single termination criterion based on tissue property to minimize user intervention and biases introduced during tracking process. These advantages and the agreement with histological reports are demonstrated in our tracking results in phantoms and in humans.     

Diffusional kurtosis imaging of cingulate fibers in Parkinson disease: Comparison with conventional diffusion tensor imaging

Objective

The pathological changes in Parkinson disease begin in the brainstem; reach the limbic system and ultimately spread to the cerebral cortex. In Parkinson disease (PD) patients, we evaluated the alteration of cingulate fibers, which comprise part of the limbic system, by using diffusional kurtosis imaging (DKI).

Methods

Seventeen patients with PD and 15 age-matched healthy controls underwent DKI with a 3-T MR imager. Diffusion tensor tractography images of the anterior and posterior cingulum were generated. The mean kurtosis (MK) and conventional diffusion tensor parameters measured along the images in the anterior and posterior cingulum were compared between the groups. Receiver operating characteristic (ROC) analysis was also performed to compare the diagnostic abilities of the MK and conventional diffusion tensor parameters.

Results

The MK and fractional anisotropy (FA) in the anterior cingulum were significantly lower in PD patients than in healthy controls. The area under the ROC curve was 0.912 for MK and 0.747 for FA in the anterior cingulum. MK in the anterior cingulum had the best diagnostic performance (mean cutoff, 0.967; sensitivity, 0.87; specificity, 0.94).

Conclusions

DKI can detect alterations of the anterior cingulum in PD patients more sensitively than can conventional diffusion tensor imaging. Use of DKI can be expected to improve the ability to diagnose PD.     

A closed form of a kurtosis parameter of a hypergeometric-Gaussian type-Ⅱ beam

Based on the irradiance moment definition and the analytical expression of waveform propagation for hypergeometricGaussian type-Ⅱ beams passing through an ABCD system, the kurtosis parameter is derived analytically and illustrated numerically. The kurtosis parameters of the Gaussian beam, modified Bessel modulated Gaussian beam with quadrature radial and elegant Laguerre–Gaussian beams are obtained by treating them as special cases of the present treatment. The obtained results show that the kurtosis parameter depends on the change of the beam order m and the hollowness parameter p, such as its decrease with increasing m and increase with increasing p.